Flowmeter accuracy: CFD analyses, experimental and field tests for two case studies of EPAL André Manuel Lopes da Cruz Morais Thesis to obtain the Master of Science Degree in Hydraulics and Water Resources Civil Engineering Supervisor: Professor Helena Margarida Machado da Silva Ramos Supervisor: Engineer Miguel Vasco Quintas Fernandes Examination Committee Chairperson: Professor António Alexandre Trigo Teixeira Supervisor: Professor Helena Margarida Machado da Silva Ramos Member of the Committee: Professor António Bento Franco October 2014
Transcript
Flowmeter accuracy: CFD analyses, experimental and field
tests for two case studies of EPAL
André Manuel Lopes da Cruz Morais
Thesis to obtain the Master of Science Degree in Hydraulics and Water Resources
Civil Engineering
Supervisor: Professor Helena Margarida Machado da Silva Ramos
Supervisor: Engineer Miguel Vasco Quintas Fernandes
Examination Committee
Chairperson: Professor António Alexandre Trigo Teixeira
Supervisor: Professor Helena Margarida Machado da Silva Ramos
Member of the Committee: Professor António Bento Franco
October 2014
i
Resumo
Em 2009, uma equipa de engenheiros da EPAL identificou algumas incongruências
resultantes da medição de caudal em dois importantes circuitos hidráulicos: entre a estação
elevatória de Castelo do Bode e a estação de tratamento de águas da Asseiceira e, entre a
estação elevatória de Vila Franca de Xira e o reservatório de A-dos-Bispos. O estudo
desenvolvido concluiu que o erro da medição estaria, provavelmente, associado aos medidores
de caudal dentro das estações elevatórias e que a baixa exatidão deveria estar relacionado com
perturbações induzidas pela geometria das instalações.
Este trabalho surge no seguimento desse estudo. Com o objetivo de avaliar a hipótese
admitida procedeu-se à utilização de um modelo CFD (Dinâmica Computacional de Fluidos) de
modo a simular as condições existentes para os dois circuitos. Para tal analisaram-se as
condições de funcionamento dos dois circuitos hidráulicos da EPAL a estudar, considerando
como condições de fronteira os valores de caudal e pressão medidos in situ.
Com vista a validar os resultados obtidos com o modelo, uma intensa campanha de
ensaios experimentais foi desenvolvida no laboratório da EPAL, sendo obtidos dois tipos de
resultados:
- com recurso a um doppler efetuou-se a medição de perfis de velocidade que puderam ser
comparados com os provenientes do modelo;
- recorrendo ao método volumétrico, utilizado no laboratório da EPAL, calculou-se o erro
associado a cada medidor de caudal para vários pontos de ensaio.
Por fim, após a validação e calibração do modelo, novas geometrias foram propostas
por forma a minorar os efeitos que se verificaram.
Palavras chave: medição de caudal, medidores de caudal (caudalímetros), CFD, turbulência,
geometria da instalação, perturbações do escoamento.
ii
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Abstract
In 2009, a team of engineers of EPAL identified some incongruenceses regarding flow
measurement in two major hydraulic circuits: between the pumping station of Castelo do Bode
and Asseiceira treatment plant and between Vila Franca de Xira pumping station and A-dos-
Bispos tank. From the study developed a conclusion was reached which stated that the error of
the measurement would be associated to the flowmeters in the pumping stations and the low
accuracy would be connected to the perturbations induced by the geometry.
In order to verify the source of the problem, and assess the hypotheses drawn, a CFD
(Computational Fluid Dynamics) model, COMSOL Multiphysics, was used to simulate the real
conditions for the two circuits. The two hydraulic circuits were simulated using as boundary
conditions the values measured in situ.
To validate the results provided by the model, an intense campaign of experiments was
developed in EPAL laboratory. In this campaign two types of results were obtained:
- using an ultrasonic doppler velocimeter (UDV) the velocity distribution profiles were
measured which allowed the comparison of these profiles with the ones provided by the CFD;
- using the volumetric method and taking advantage of the flowmeters capability, an error
evaluation was estimated.
Lastly, having the model validated and calibrated, a new layout/geometry was proposed
in order to mitigate the perturbations induced by the current geometry.
Figure 2.1 - Velocity profile distribution: a) turbulent flow; b) laminar flow (adapted from
Frenzel et al., 2011). ................................................................................................................. 8 Figure 2.2 - Typical velocity measurement for a turbulent flow - U represents the average
velocity while u'(t) represents the fluctuating velocity component (adapted from Versteeg and
Malalasekra, 2007). ................................................................................................................... 9 Figure 2.3 - Schematic image of the turbulent flow vortexes. ..................................................... 9
Figure 2.4 - Total shear stress variation for a circular pipe turbulent flow (adapted from Çengel
and Cimbala, 2006). ................................................................................................................ 10 Figure 2.5 - Sub-layers relative position though a pipe in the turbulent flow (adapted from
Çengel and Cimbala, 2006). .................................................................................................... 11
Figure 3.1 - Examples of the electromagnetic flowmeters components - a) primary element; b)
convertor (adapted from Frenzel et al., 2011). ......................................................................... 14 Figure 3.2 - Electromagnetic flowmeter accuracy curve. .......................................................... 14
Figure 3.3 - Operating principle of an electromagnetic flow meter (adapted from Frenzel et al.,
2011). ..................................................................................................................................... 15 Figure 3.4 - Weighting factor distribution W in the electrode plane (adapted from Frenzel et al.,
Figure 3.5 - Examples of two electromagnetic flowmeters - a) big diameter flowmeter (DN 1400); b) small diameter flowmeter (DN100) - photographs provided by Eng. Miguel
Figure 4.2 - Mesh examples: a) mesh cross section - the mesh cells closer to the wall (boundary layer) have a higher density and are much smaller than the other ones; b) mesh refinements near
Figure 5.2 - Probe and probe holder. In this image the probe is in the 20º slope angle. ............. 32
Figure 5.3 - Laboratory layout - a) inlet - manometer (left) and thermometer (right); b) three
reference flowmeters (blue arrows) ......................................................................................... 32 Figure 5.4 - High accuracy tank - a) 1000 L b) 5000 and 10000 L
Figure 5.5 - Geometry 1, type 1 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow,
DN100 identified by the green arrow. The UDV probe measured in the pipe sections identified
by the red arrow. ..................................................................................................................... 35 Figure 5.6 - UDV profiles for 100 m
3/h for Geometry 1, type 1 - a) profiles measured in the
location identified as A in Figure 5.5; b) profiles measured in the location identified as B in
Figure 5.8 - Geometry 1, type 2 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow,
DN100 identified by the green arrow. The UDV probe measured in the pipe section identified
by the red arrow. ..................................................................................................................... 37 Figure 5.9 - UDV profiles for Geometry 1, type 2, measured at the location identified as A in
Figure 5.8 for 100 m3/h. .......................................................................................................... 38
Figure 5.10 - Geometry 1, type 3 experiment - flow direction identified by the blue arrow;
DN80 flowmeter identified by the yellow arrow, DN100 identified by the green arrow. The UDV probe measured in the pipe section identified by the red arrow. ...................................... 38
Figure 5.11 - UDV profiles for Geometry 1, type 3, measured at the location identified as A in
Figure 5.12 - Geometry 1, type 4 experiment - experiment layout detail - flow direction
identified by the blue arrow. DN80 flowmeter identified by the yellow arrow, DN100 identified
by the green one. The UDV probe measured in the pipe section identified by the red arrow. .... 39 Figure 5.13 - UDV profiles for Geometry 1, type 4 measured at the location identified as A in
Figure 5.12 for 100 m3/h. ........................................................................................................ 40
Figure 5.14 - Geometry 2, type 1 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow,
DN100 flowmeter identified by the green arrow. ..................................................................... 40
Figure 5.15 - Geometry 2, type 2 experiment - flow direction identified by the blue arrow;
DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow. ..................................................................................................................................... 41
Figure 5.16 - Geometry 3, type 1 experiment - a) experiment layout (flow direction identified by
the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow. ..................................................................... 42
Figure 5.17 - Geometry 3, type 2 experiment - a) experiment layout (flow direction identified by
the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow. ..................................................................... 43
Figure 5.18 - Geometry 4, type 1 - a) photograph taken from upstream to downstream (flow
direction identified by the blue arrow); b) photograph taken from downstream to upstream -
DN100 flowmeter previously used identified by the green arrow, DN100 flowmeter used only in these tests identified by the red arrow. ................................................................................. 44
Figure 5.19 - a) simulation geometry for Geometry 1, type 1 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter by the green arrow). ................................................................................... 45
Figure 5.20 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.19); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.19). ..................... 46 Figure 5.21 - Geometry 1, type 1 velocity distribution profiles provided by the program -
profiles a) and b) section A and B of Figure 5.5, respectively for 100 m3/h; profiles c) and d)
same then profiles a) and b) for 12 m3/h. ................................................................................. 47
Figure 5.22 - a) simulation geometry for Geometry 1, type 2 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow,
DN100 flowmeter identified by the green arrow). .................................................................... 47 Figure 5.23 - Geometry 1, type 2 velocity distribution profile provided by the program - section
A of Figure 5.8 for 100 m3/h. .................................................................................................. 48
Figure 5.24 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.22); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.22). ..................... 48
Figure 5.25 - a) simulation geometry for Geometry 1, type 3 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow). .................................................................... 49
Figure 5.26 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.25); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.25). ..................... 49
Figure 5.27 - Geometry 1, type 3 velocity distribution profiles provided by the program - section
Figure 5.28 - a) simulation geometry for Geometry 1, type 4 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow,
DN100 flowmeter identified by the green arrow). .................................................................... 50
Figure 5.29 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m
3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.28); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.28). ..................... 50
Figure 5.30 - Geometry 1, type 4 velocity distribution profile provided by the program - section
A of Figure 5.12 for 100 m3/h. ................................................................................................ 51
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Figure 5.31 - a) simulation geometry for Geometry 2, type 1 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow,
DN100 flowmeter identified by the green arrow). .................................................................... 51 Figure 5.32 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.31); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.31). ..................... 52 Figure 5.33 - a) simulation geometry for Geometry 2, type 2 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow,
DN100 flowmeter identified by the green arrow). .................................................................... 52
Figure 5.34 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m
3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.33); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.33). ..................... 53
Figure 5.35 - a) simulation geometry for Geometry 3, type 1 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by yellow arrow, DN100
flowmeter identified by the green arrow). ................................................................................ 53
Figure 5.36 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m
3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.35); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.35). ..................... 54
Figure 5.37 - a) simulation geometry for Geometry 3, type 2 (blue arrow identifies the flow
direction); b) modelling geometry detail (DN80 flowmeter identified by yellow arrow, DN100 flowmeter identified by green arrow). ..................................................................................... 54
Figure 5.38 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter (green arrow of
Figure 5.37); profiles b) and d) DN80 flowmeter (yellow arrow of Figure 5.37). ..................... 55
Figure 5.39 - a) simulation geometry for Geometry 4, type 1 (blue arrows identifies the flow
direction); b) modelling geometry detail - DN100 flowmeters identified by the green and purple
arrows (previous flowmeter identified by the green arrow; new arrow identified by the red arrow, according to Figure 5.18). ............................................................................................ 55
Figure 5.40 - Velocity distribution profiles in the pipe cross section defined by the electrodes -
a) and b) 100 m3/h; c) and d) 12 m
3/h. Profiles a) and c) DN100 flowmeter identified by the
green arrow, Figure 5.39; profiles b) and d) DN100 flowmeter identified by the purple arrow,
Figure 5.41 - UDV profiles for 100 m3/h for Geometry 1, type 1 (blue triangles - experimental
results; red rectangles - simulated results) - a) profiles measured in the location identified as A
in Figure 5.5; b) profiles measured in the location identified as B in Figure 5.5. ...................... 57
Figure 5.42 - UDV profiles for 12 m3/h for Geometry 1, type 1 (blue triangles - experimental
results; red rectangles - simulated results) - a) profiles measured in the location identified as A in Figure 5.5; b) profiles measured in the location identified as B in Figure 5.5. ...................... 57
Figure 5.43 - UDV profiles for Geometry 1, type 2 measured at the location identified as A in
Figure 5.8 for 100 m3/h (blue triangles - experimental results; red rectangles - simulated results).
Figure 5.45 - UDV profiles for Geometry 1, type 4 measured at the location identified as A in
Figure 5.12 for 100 m3/h (blue triangles - experimental results; red rectangles - simulated
results). ................................................................................................................................... 59 Figure 6.1 - EPAL production and transport system (adapted from the theoretical slides of
Figure 6.2 - Existing geometry - the orange circle represents the pump location (adapted from EPAL design draws). .............................................................................................................. 65
Figure 6.3 - Schematic representation of the existing geometry in Castelo do Bode pumping
station (pump location identified by the green pipe section; flowmeter identified by the red line;
flow direction identified by the blue arrow) - a) Plan; b) 3D view. ........................................... 65
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Figure 6.4 - Castelo do Bode pumping station - photographs of the different parts of the
hydraulic circuit from upstream to downstream (flow direction identified by blue arrows). ...... 66
Figure 6.5 - Castelo do Bode modelling geometry - the flowmeter section represented by the red arrow; flow direction identified by the blue arrow. .................................................................. 66
Figure 6.6 - Streamlines simulation along the hydraulic circuit for the CBC current situation
(flowmeter section identified by the red arrow), in m/s. ........................................................... 68 Figure 6.7 - Velocity distribution simulation in the electrodes cross section for CBC current
Figure 6.8 - Castelo do Bode proposed modelling geometry - the flowmeter section represented
by the red arrow; flow direction identified by the blue arrow (added pipe in red). .................... 69 Figure 6.9 - Streamlines simulation along the hydraulic circuit for the CBC proposed situation
(flowmeter section identified by the red arrow), in m/s. ........................................................... 69
Figure 6.10 - Velocity distribution simulation in the electrodes cross section for CBC proposed situation. ................................................................................................................................. 70
Figure 6.11 - Vila Franca de Xira side view from pumping station 2 (adapted from EPAL design
draws). .................................................................................................................................... 70 Figure 6.12 - Vila Franca de Xira modelling geometry. ........................................................... 71
Figure 6.13 - Streamline simulation along the hydraulic circuit for the VFXC current situation,
in m/s. ..................................................................................................................................... 72
Figure 6.14 - Velocity distribution simulation in the electrodes cross section for VFXC current situation. ................................................................................................................................. 73
Figure 6.15 - Vila Franca de Xira proposed modelling geometry - the flowmeter section
represented by the red arrow; flow direction identified by the blue arrow (added pipe in red). .. 73 Figure 6.16 - Streamlines simulation along the hydraulic circuit for the VFXC proposed
situation (flowmeter section identified by the red arrow), in m/s. ............................................. 74
Figure 6.17 - Velocity distribution simulation in the electrodes cross section for VFXC
Table 5.1 - Schematic test notation matrix. .............................................................................. 34 Table 5.2 - Tests results of the Geometry 1, type 1 experiments and the relative errors for both
flowmeters and volume flow rates. .......................................................................................... 35
Table 5.3 - Tests results of the Geometry 1, type 2 experiment and the relative errors for both flowmeters and volume flow rates. .......................................................................................... 38
Table 5.4 - Tests results of the Geometry 1, type 3 experiments and the relative errors for both
flowmeters and volume flow rates. .......................................................................................... 39
Table 5.5 - Tests results of the Geometry 1, type 4 experiments and the relative errors for both flowmeters and volume flow rates. .......................................................................................... 40
Table 5.6 - Tests results of the Geometry 2, type 1 experiments and the relative errors for both
flowmeters and volume flow rates. .......................................................................................... 41 Table 5.7 - Tests results of the Geometry 2, type 2 experiments and the relative errors for both
flowmeters and volume flow rates. .......................................................................................... 41
Table 5.8 - Tests results of the Geometry 3, type 1 experiments and the relative errors for both flowmeters and volume flow rates. .......................................................................................... 42
Table 5.9 - Tests results of the Geometry 3, type 2 experiments and the relative errors for both
flowmeters and volume flow rates. .......................................................................................... 43
Table 5.10 - Tests results of the Geometry 4, type 1 experiments and the relative errors for DN100 flowmeter used in the previous experiments for different volume flow rates. ............... 44
Table 5.11 - Tests results of the Geometry 4, type 1 experiments and the relative errors for
DN100 flowmeter used in this experiments for different volume flow rates. ............................ 44 Table 5.12 - Boundary, mesh and study conditions for Geometry 1, type 1, test 3 simulation for
the 100 and 12 m3/h volume flow rate. .................................................................................... 45
Table 5.13 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates tested, for Geometry 1, type 1. ....................................... 46 Table 5.14 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates tested, for Geometry 1, type 2. ....................................... 47
Table 5.15 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 1, type 3. ....................................... 49
Table 5.16 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates, for Geometry 1, type 4. ................................................. 51 Table 5.17 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates tested, for Geometry 2, type 1. ....................................... 52
Table 5.18 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates tested, for Geometry 2, type 2. ....................................... 53 Table 5.19 - Errors associated to CFD simulations according to the procedure developed for the
two diameters and volume flow rates tested, for Geometry 3, type 1. ....................................... 54
Table 5.20 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 3, type 2. ....................................... 55
Table 5.21 - Errors associated to CFD simulations according to the procedure developed for the
two flowmeters and volume flow rates tested, for Geometry 4, type 1...................................... 56 Table 5.22 - Values of the errors calculated with the volumetric method and the spreadsheet
one, for Geometry 1 and respective flowmeters. ...................................................................... 59
Table 5.23 - Values of the errors calculated with the volumetric method and the spreadsheet
one, for Geometry 2 and respective flowmeters. ...................................................................... 61 Table 5.24 - Values of the errors calculated with the volumetric method and the spreadsheet
one, for Geometry 3 and respective flowmeters. ...................................................................... 61
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Table 5.25 - Values of the errors calculated with the volumetric method and the spreadsheet
one, for Geometry 4. Test 1. - new DN100 flowmeter (red arrow of Figure 5.39). Test 2 -
DN100 flowmeter used in the previous tests (green arrow of Figure 5.39). .............................. 62 Table 6.1 - Physical characteristic of the main pipes and flowmeter for CBC. .......................... 67
Table 6.2 - CBC current situation: simulation input values and characteristics. ........................ 67
Table 6.3 - Physical characteristic of the main pipes and flowmeter for VFXC. ....................... 71 Table 6.4 - VFXC current situation simulation values and characteristics. ............................... 72
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List of Symbols
Symbol Description Unities
A area; cross-section m2
B magnetic induction field T
C1ε, C2ε, Cμ experimentally defined constants (-)
D diameter m; mm
average gravity's acceleration components m/s2
k kinetic turbulent energy m2/s
2
i internal (thermal) energy J
p pressure Pa; bar
average pressure's field component Pa
Pk viscous stress and buoyancy's effect turbulence's production (-)
Q volume flow rate m3/s; m
3/h
t time s
T temperature ºC
u velocity vector
ui,j flow's velocity components m/s
uτ friction velocity m/s
average flow's velocity components m/s
u'i,j flow's velocity fluctuating component m/s
average flow's velocity fluctuating components m/s
U average flow's velocity m/s
UE electrical voltage V
V flow's velocity m/s
volume m3; L
y distance from the wall m
δZ Newton step (-)
δi,j Kronecker symbol (-)
δw distance of computational domain start for wall functions m
ε turbulent energy's dissipation rate m2/s
3
λ second viscosity N.s/m2
λ' Newton damping factor (-)
μ dynamic viscosity, first viscosity Kg/(m.s)
μT eddy/turbulent viscosity Kg/(m.s)
ν kinetic viscosity m2/s
xviii
ρ density Kg/m3
σk, σε Prandtl turbulent variables (-)
τlam laminar shear stress N/m2
τturb turbulent shear stress/Reynolds stress N/m2
τw wall shear stress N/m2
φ random function (-)
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Acronyms
CAD Computer assisted design
CBC Castelo do Bode's (hydraulic) circuit
CFD Computational fluid dynamics
EPAL Empresa Portuguesa de Águas Livres
HDPE High density poly-ethylene
MUMPS Multifrontal massively parallel sparse direct solver
NRW Non Revenue Water
PDE Partial differential equations
RANS Reynolds-averaged Navier-Stokes equations
UDV Ultrasonic doppler velocimeter
VFXC Vila Franca de Xira's (hydraulic) circuit
xx
1
1. Introduction
1.1. Framework
Fluid flow in circular pipes are one of the most common problems in practical hydraulic
engineer. Since in this flows the water is primarily driven by a pressure difference, the pipe can
easily withstand large pressure differences. For that reason, the pipes have a circular cross
section, which allows the pipe not to be significantly distorted due to that differential. There are
several examples of this flows. Both hot and cold water used at home. Water distribution
systems in our cities are extensive pipe networks, as well as other important pipe systems such
as hydropower and pumping systems.
EPAL is the company which provides, maintains and manages the pipe network and the
water, downstream from the inlet reservoirs and all the system until the consumers in the city of
Lisbon, as well as several municipalities around it.
Throughout the years, EPAL has installed flowmeters in many of its hydraulics circuits.
As a result, management teams responsible for the system exploitation can now control the in
and outflow in those systems. The flowmeters correct measurement is an extremely important
factor in terms of the company management. Amongst other domains of interest, the measured
flow values are one of the key issues to detect leaks in the system.
During the management of EPAL systems, some incongruencies were notice regarding
the flowmeters records. This incongruencies would indicate the occurrence of leaks in pipes.
Nevertheless, it was verify that pipes were tight. This conclusion implies that a new problem is
not yet identified.
For the company, the problem of an accurate flow measurement has relevant impacts
regarding both the planning and the investment decisions. Therefore, in May of 2009, the EPAL
Direção de Gestão de Ativos - Departamento de Manutenção (Braga and Fernandes, 2009) lead
a study with the intention to obtain answers to this problem. An EPAL team was formed,
composed by experts on flow measurement, with the objective to study two hydraulic circuits:
between Vila Franca de Xira pumping station and the A-dos-Bispos tank, and between Castelo
do Bode pumping station and the Asseiceira water treatment plant. The study undertaken did not
reach any specific conclusions concerning this problem except that the problem would,
probably, be associated to the flowmeters in the pumping stations.
This work appears to fulfil the need for answers to this problem: taking into account the
studies already made, the collected information and the obtained results, an analysis to the
variables which can disturb the flow is carried out, namely the pipes geometry and the way it
can disturbs the flow and the flowmeters register and for which levels of pressure and volume
flow rate they occur.
2
1.2. Objectives and general methodology
The main objective of this work is to identify how different geometrical layouts would
influence the flowmeters accuracy. The purpose is to assess how vertical or horizontal curves,
expansions and reductions, among other different geometries would influence the flow and,
consequently the flow measurement. Since EPAL is a company whose main purpose is to sell
water, the accuracy of the measurement is quite important, not only for the efficiency of the
system but also for the company management and decisions.
To fulfil such goal, a CFD (Computational Fluid Dynamics) model, COMSOL
Multiphysics, was used to simulate the flow in two different hydraulics circuits. This model
allows analysis of specific optimized modules for several areas, with specialized solvers,
element types, materials, which allows the analysis of several problems. Regarding the CFD
model, this module allows the analysis of several types of fluid flow problems, as for laminar
and turbulent regimes, as well as fluid-structure interaction, among others. Of all the available
options, the study developed used the turbulent flow, an option from the fluid flow module.
To assess the accuracy of the computed result several experiments were developed.
Their purpose was not only to identify the influence of several perturbations in the flow
measurement, using two flowmeters in series, but also to compare the computed velocity
profiles to those obtained from the experiments with an ultrasonic doppler velocimeter. This
action would allow the model validation since the computed results and the experimental ones
ought to be similar.
Two hydraulic circuits are under analyses: the Castelo do Bode and the Vila Franca de
Xira hydraulic circuits. The method behind the analyses made for these circuits is to verify the
current conditions and then simulate them in order to identify for which the existing
perturbations could be disregarded.
1.3. Work structure
This work is divided in seven chapters. This first chapter is an introductory one. In
Chapter 2 a background review is made. Several concepts regarding hydro kinematics, flow
characteristic parameters and turbulence phenomena will be addressed and discussed, since
these concepts are important factors in order to assure measurement accuracy.
In Chapter 3 several characteristics of electromagnetic flowmeters are attended to. The
electromagnetic flowmeter operating principles and the suppliers installation requirements to
guarantee accurate measurements are explained in Chapter 3.
The mathematical modelling is explained in Chapter 4. The governing equations of the
turbulent flow are addressed as well as the constitutive equations and the advantages and
disadvantages of the turbulent k-ε model. The simulation characteristics, namely the boundary
3
conditions and the in and outlet conditions, the mesh definition and the solution convergence are
also attended in Chapter 4.
Since this work uses a CFD model in order to achieve analyses goals, it is necessary to
validate the results obtained. To do so, some experiments were developed to validate the
simulation results. Both the computational and experimental results, and the conclusions
reached are presented in Chapter 5.
Chapter 6 contains the several analysis made for two important hydraulic systems: the
Castelo do Bode and Vila Franca de Xira. The importance of the case studies is explained in this
chapter and the main conclusions are presented.
Lastly, in Chapter 7 the principal results and conclusions are presented, as well as some
recommendations for subsequent studies are also drawn.
4
5
2. Background review
2.1. Brief introduction
This chapter summarizes several concepts learned throughout the years in the multiple
Hydraulic subjects. Throughout this work, references are made to some simple but fundamental
concepts that need to be explained. Concepts regarding hydro kinematics, flow characteristic
parameters and the turbulent phenomena are briefly explained in this chapter.
In fluid mechanic, materials are characterized as fluids or non-fluids, whereas in classic
mechanics matter is regarded as solids, fluids or gases. Kinematics is the branch of mechanics
which studies the motion variables without taking into account the forces which maintain or
induce the movement. Variables as velocity, acceleration and displacement are examples of
kinematic variables. Hence, hydro kinematics is the subject that studies the variables which
describe the motion in water flows.
According to the literature, there are many flow characteristic parameters: viscosity,
velocity, gravity, cross section geometrical characteristics and roughness are the most common
and important. For circular pipe flows, these parameters may be reduced to only three
fundamental parameters: diameter of the pipe, viscosity and the average velocity.
Regarding the mentioned parameters the first is a mechanical characteristic of the cross
section. Therefore, it is associated to each individual pipe. If the pipe characteristics are known,
this parameter is defined. The remaining two parameters are not so simple to obtain. They
depend on the flow characteristics, and will be briefly discussed in the following sections.
The turbulence is one of the most important phenomena regarding fluid flows, as well
as one of the most complex flow problems. Since the most significant engineering problems
evolve turbulence, i.e. turbulent flows, in the last section of this chapter the turbulence problem
will be addressed.
2.2. Hydro kinematics
2.2.1. Streamlines
The flow path of a particle may be defined as the geometrical position of all the spots
occupied by a particle throughout the time. For each orthogonal axis, flow path need to verify
equation [2.1], since each particle is moving within the fluid and at its velocity (Cardoso, 2009).
[2.1]
Streamlines are lines in which all points have its tangent coincident to the direction of
the velocity. This concept is related to the velocity vector, and depends on the point position as
well as the considered time instant. Since for variable flows the direction and intensity of the
velocity vector change in time and in space, the streamlines are defined for a certain time
6
instant. They can be thought as an instantaneous flow photograph: for a certain time, t,
streamlines are the imaginary lines which connect all points with the tangent coincident to the
velocity direction (Quintela, 2002).
Considering the velocity can be decomposed in the three orthogonal axis as presented in
equation [2.2],
[2.2]
is possible to represent streamline equations, [2.3], for a tri-dimensional flow:
[2.3]
To obtain a certain streamline the procedure is to integrate equations [2.3], for a certain
time instant, t.
If a flow is characterized as steady, streamlines do not change with time. In this case,
streamlines and flow path coincide. However, it is possible for streamlines to coincide with the
flow path in an unsteady flow (e.g. when a valve is closed in a system which connects two tanks
by a pipe: the flow will be variable, nonetheless trajectories and streamlines remain coincident).
2.2.2. Steady flow
A flow is called permanent or steady if the velocity changes from point to point, but
remains constant throughout the time, i.e.
[2.4]
In steady flows the fluid properties only depend on the coordinates. All time change
variations are nil. Therefore, and as presented in 2.2.1, for a steady flow, flow paths coincide
with the streamlines.
Uniform flow can be defined as a flow in which the velocity has the same magnitude
and direction at every point of the fluid. Combining these two concepts, it yields in a steady
uniform flow. For this conditions the flow variables do not change nor with position or with
time. Pipe water flow with constant diameter is a typical example of uniform steady flow.
Hence, in a pipe, when the section remains constant, the flow is uniform (Manzanares, 1980).
Nevertheless, when the section is not always the same along a pipe, the steady flow is not
always uniform; it is classified as gradually or rapidly varied. Gradually varied flows occur
when streamlines curvature is gentle. That is the case of expansions/reductions in pipe pressure
flows. In the other hand, when streamlines curvatures are accentuated the flow is rapidly varied
and it occurs often nearby singularities (Manzanares, 1980).
7
2.3. Characteristic parameters
2.3.1. Reynolds number
The Reynolds number corresponds to the ratio between the inertial and the viscous
forces. For circular pipes, the Reynolds number can be calculated according to equation [2.5]:
[2.5]
According to Reynolds experience in 1883, for Reynolds numbers bellow a critical
value (i.e. Re<2000) the flow regime is laminar. For laminar flows, the flow is smooth and
adjacent fluid layers slide past each other in an almost orderly manner. These flows require
small velocity values or a large viscosity value. For oil the laminar flow occurs quite often;
since it has high viscosity, the internal friction originates the behaviour described.
When Reynolds numbers are bigger than the critical value, the flow corresponds to a
turbulent one. For turbulent flows, the fluid motion is random and chaotic as described both in
section 2.4.1 and in Chapter 4. Physically, for large Reynolds numbers the inertial forces are
much higher than the viscous ones (Lamb, 1932). Therefore, the viscous stress cannot prevent
the random fluctuations. For lower Reynolds numbers the viscous stress is enough to eliminate
those fluctuations (Streeter and Wylie, 1982). Water flow in pressurized circular pipes, which is
the matter of this research, are most often non laminar flows.
There is a transition between laminar and turbulent regimes where the critical value for
Reynolds number is not a common accepted value. The literature is not clear because some
authors believe the critical value is around 2000 while other think that 2300 is a more accurate
value. Nonetheless, an assumption is required. Therefore, throughout this work the Reynolds
critical value will be considered equal to 2000, what means that flows with Reynolds number
smaller than 2000 will be characterized as laminar. Flows with Reynolds numbers higher than
2000 but smaller than 4000 will be characterized as transition flows meanwhile flows with
Reynolds numbers higher than 4000 will be classified as turbulent.
In spite of what was mentioned in this section, the transition between laminar and
turbulent flow depends on the geometry, the surface roughness and temperature, the flow
velocity, the type of fluid, not only on the ratio between inertial and viscous forces (Yih, 1969).
Nevertheless this simplification is more than sufficient to access, quite accurately, the flow
regime.
2.3.2. Average velocity
In a turbulent flow, the velocity at a given point and time instant is equal to the sum of
two components: the average velocity (in time), that is responsible for the particles downstream
motion, and the fluctuation velocity, of random nature. In these flows, the flow paths are very
irregular. This irregularity causes a certain velocity homogenization in the cross section. As a
8
result, the velocity profile presents a more regular distribution in the turbulent flow than in the
laminar flow, Figure 2.1. Thus, the relation between the maximum velocity (in the pipe centre)
and the average velocity in turbulent flows are often between 0.8 and 0.9, much higher than the
one that is verified in laminar flow (i.e. 0.5).
a) b)
Figure 2.1 - Velocity profile distribution: a) turbulent flow; b) laminar flow (adapted from Frenzel et al., 2011).
Near the pipe wall the velocity tends to be zero. When the distance to the wall increases
the velocity increases until it reaches its biggest value is the middle of the pipe cross section.
Afterwards, and since the velocity flow profile is, often, symmetric, the velocity decreases until
zero close to the wall. The velocity is not constant throughout. Since it is not feasible to describe
the flow velocity as it really is, a new concept is necessary in order to provide a velocity that can
be easily used.
The average flow velocity is defined as the integral of the velocity profile divided by the
cross section, as expressed in equation [2.6]. This concept is quite important since it
corresponds to a simplification of the real velocity profile (with all its random components), to a
constant one. The components considered are the mean while the fluctuating ones are
disregarded. The average flow velocity, is defined as the velocity of a theoretical flow, with
constant velocity in all points, U, that corresponds to the same volume flow rate through the
same cross section.
[2.6]
2.4. Turbulence and turbulent flow
2.4.1. Turbulence and turbulent flow
Has explained in section 2.3.1, below a critical value of Reynolds number, 2000, the
flow behaves in a orderly manner, called the laminar flow. For Reynolds number higher than
2000, the flow characteristics change: the flow motion becomes more and more unsteady and
the flow tends to a random and chaotic behaviour, called the turbulent flow (Hinze, 1959). For
turbulent flows, the flow paths behave in a quite irregular and odd way; different particles flow
paths cross each other paths.
9
According to Novais-Barbosa, 1985, the flow variables change both in intensity and
direction, throughout the time, in a large flow region. Due to this factor, the characteristic
variables of the flow (i.e. velocity and pressure) are written as the sum between the mean value
of a certain variable, with the corresponding fluctuating part (Versteeg and Malalasekra, 2007).
Figure 2.2 represents an example of the described property for a velocity measurement in a
turbulent flow. The decomposition of the flow variables in its mean and fluctuating components
is called Reynolds decomposition.
Figure 2.2 - Typical velocity measurement for a turbulent flow - U represents the average velocity while u'(t) represents the fluctuating velocity component (adapted from Versteeg and Malalasekra, 2007).
Other characteristic of the turbulent flow is its well marked tri-dimensional behaviour.
This is due to the turbulent fluctuating components (Lumley, 1992). In addition, vortexes, also
called turbulent eddies, with a wide range of length scales are moving inside the flow (Figure
2.3), which originate tri-dimensional fluctuations in all properties of the flow (Tenneks and
Lumley, 1972). This is the reason for the odd flow paths behaviour: the eddies motion and the
fluctuating components bring together or send away particles that were far from or close to each
other, respectively. This yields that mass, heat and momentum are exchanged in a very rapid
and effective way (Çengel and Cimbala, 2006).
Figure 2.3 - Schematic image of the turbulent flow vortexes.
Large turbulent eddies interact with the flow mean energy by a process called vortex
stretching (Tritton, 1988). Once velocities gradients exist within the flow, the eddies are then
10
distorted and stretched, since one end is moving faster than the other. Large scale turbulent
eddies are influenced by the inertial forces while the viscous effects can be neglected
(Bradshaw, 1973). This large eddies will then create smaller ones providing, in this process,
energy to maintain the turbulence (Batchelor, 1967). For the smaller scale eddies, both the
viscous and the inertial effect are equally relevant. For this smaller eddies the system produces
work against the viscous stress. Thus, energy is dissipated, leading to the increase of energy
losses, characteristics of turbulent flows (Pope, 2000).
In other words, once turbulence begins, the turbulent flow is able to maintain itself since
it can produce new eddies to replace those disappeared due to viscous dissipation. Turbulence
is, therefore, self-sustaining (White, 1991). Nevertheless, in a turbulent flow the dissipation of
energy is very significant. When a continuous input of energy to the flow does not exist, the
turbulence is progressively deadened, creating a more homogeneous and isotropic flow.
Further considerations regarding the turbulent regime flow are presented in Chapter 4.
2.4.2. Shear stress in the turbulent regime
According to Çengel and Cimbala, 2006, the total shear stress in the turbulent regime
can be considered as the sum of two components: the laminar and the turbulent components, as
expressed by equation [2.7].
[2.7]
The laminar shear component attends to the friction between layers of fluid in the flow
direction, equation [2.8], whereas the turbulent component accounts for friction between the
fluctuating particles and the mean fluid equation [2.9]. The turbulent stress is also called
Reynolds stress.
[2.8]
[2.9]
Along the pipe, the relative distribution of total shear stress as long as of its both
components is represented in Figure 2.4.
Figure 2.4 - Total shear stress variation for a circular pipe turbulent flow (adapted from Çengel and Cimbala, 2006).
11
Reynolds stress is quite difficult to quantify, since it is defined by the components of the
fluctuating velocity (White, 1991). In order to achieve mathematical closure to this problem,
many semi-empirical models have been developed in order to provide an estimation of the
Reynolds stress. In Chapter 4 one of the many available models will be addressed, as well as a
more detailed explanation about the turbulent stress.
2.4.3. Turbulent velocity profile in pipes
Since most considerations along this work are due to the analysis of the velocity profile
it is important to make some comments about it. Has presented in Figure 2.1 the laminar and the
turbulent flow velocity profiles are quite different.
Laminar velocity profile presents a parabolic shape, meanwhile, the turbulent velocity
profile is much fuller with a very steep drop near the wall. In the later phenomena, it is possible
to identify four different layers: the viscous, the buffer, the transition or inertial and the overlap
or turbulent sub-layers.
Regarding the viscous sub-layer, it corresponds to a thin layer, near the pipe wall, in
which the viscous effects are the dominant ones (White, 1991; Bakewell and Lumley, 1967). As
presented in Figure 2.1 a), the profile is almost linear and the flow is, therefore, smooth. For this
reason, this sub-layer is also called as linear sub-layer.
Adjacent to the viscous sub-layer is the buffer one. This is a transition layer were
turbulence is gaining importance, nonetheless, the dominant effects are, still, the viscous ones.
Next to the buffer sub-layer is the overlap, transition or inertial sub-layer. In this sub-layer the
turbulent effects gain more and more importance, however they are not the dominant ones.
Lastly, the turbulent or outer layer occupies the remain part of the flow, in which
turbulent effects are the dominants effects. The viscous effects lose their importance in this sub-
From the system of equations [3.1], for higher velocities the measure accuracy is,
according to the suppliers of flowmeters, the highest, 0.2 %. Since the velocity values within the
purpose of this work, as well as the most common velocity values in the system of the company,
15
are often between 0.5 and 1 m/s, the third condition is the most important. For it, and has it is
quite obvious, the measurement accuracy range varies from 0.2 to 0.4 % - a very high accuracy.
3.2. Operating principle
In order to measure the volume flow rate, electromagnetic flowmeters make use of
Faraday principle. In 1831, Michael Faraday succeeded in producing an electric current from a
magnetic field. He discovered that if an electric conductor is moving in a magnetic field
perpendicular to the motion direction, an electrical current is induced, and that current is
proportional to the magnetic field force as well as the motion velocity. Considering the
conductor as water, the flow passing through a magnetic field induces an electrical current
proportional to the flow velocity. The electromagnetic flowmeter operating principle is
represented in Figure 3.3 as well as by equation [3.2].
[3.2]
Equation [3.2] states that the electrical voltage is proportional to the magnetic field
multiplied by the flow velocity and the pipe diameter. For an incompressible steady flow, the
flow rate passing through a circular cross section is given by the mass conservation equation
[3.3].
[3.3]
Combining equation [3.2] and [3.3], it yields that the electrical current induced by the
flow passing through is directly proportional to the value of the volume flow rate:
The principle described above and represented by Figure 3.3 requires a magnetic field
within the pipe section as well as a free interferences voltage measure. Therefore, the flowmeter
has built in two coils which creates the magnetic field. The electrical voltage produced is, then,
measured using two metallic electrodes. All this happen in the primary element. The measured
voltage is displayed by the convertor and sent to the company data centre.
Figure 3.3 - Operating principle of an electromagnetic flow meter (adapted from Frenzel et al., 2011).
16
According to Frenzel et al., 2011, the electrical current induced by the flow is only
taken in account in the cross section defined by the electrodes, which is perpendicular to the
flow. This fact implies the non consideration of the tri-dimensional flow nature, which means
that only the parallel component of the velocity is relevant for the volume flow rate
measurement.
A question arise: since the flow velocity profile is not the same throughout the entire
cross section, what is the weight that the flowmeter assigns for each point within the cross
section? To solve this problem, the suppliers of these equipments use a weighting factor, W.
Figure 3.4 represents the weighting factor distribution in the cross section, which assumes the
value of 1 at the cross section centre, as expected; nearby the electrodes, the voltage induced is
greater than the one induced in the poles.
Figure 3.4 - Weighting factor distribution W in the electrode plane (adapted from Frenzel et al., 2011).
In the cross section, to each point corresponds a different weighting factor W.
Therefore, the induced electric current has different weights. The sum of the product between
the velocity and the respective weighting factor corresponds to the electrical current, which is
proportional to the volume flow rate. Despite being a good method to determine the volume
flow rate in an homogenous magnetic field constant throughout with symmetric velocity
profiles, this formulation does not provide good results for non symmetric velocity profiles. In
those cases it would overevaluate some values and underevaluate others. This would lead to a
volume flow rate that would not correspond to the real one.
To avoid this problem, the suppliers of the equipment considerate a magnetic induction
field inversely proportional to the weighting factor W, as shown in equation [3.4].
[3.4]
17
According to equation [3.4], for a cross section region in which the weighting factor is
small, the magnetic induction field is increased, and vice versa. This action ensures good results
even for none symmetrical velocity profiles.
3.3. Installation requirements
According to several authors the electromagnetic flowmeters (Figure 3.5) are only
disturbed by the existence of particles that might change the magnetic properties of the fluid.
Properties like temperature, viscosity and the fluid density do not affect the measurements.
However, as it is said in Quintela (2002), is necessary to guarantee the existence of linear and
rectilinear flow paths, to insure the measurement accuracy.
To take into account such condition, the suppliers stipulate minimum installation
requirements for each kind of geometry, to insure the measurement accuracy. In Annex A are
presented the installation requirements imposed by the suppliers for the most common
geometries.
a) b)
Figure 3.5 - Examples of two electromagnetic flowmeters - a) big diameter flowmeter (DN 1400); b) small diameter flowmeter (DN100) - photographs provided by Eng. Miguel Fernandes, EPAL.
The case studies analysed in this work fulfilled the installation requirements specified
by the suppliers of the equipments. Nevertheless, and as addressed in Chapter 6, these
requirements are not sufficient to guarantee an accurate measure.
18
19
4. Mathematical modelling
4.1. Governing equations
The motion of a fluid in three dimensions is well described by five partial differential
equations (PDE): the mass conservation (one equation), the momentum equations (three
equations) and the energy equation (one equation) (Versteeg and Malalasekra, 2007). These are
mathematical statements of physic conservation laws. The first equation states that the mass of
the fluid is conserved. The momentum equations represent that the change in the momentum
rate is equal to the sum of forces applied on a fluid particle, which is Newton second law. The
energy equation represents the first law of thermodynamics which states the increment in the
internal energy is equal to the difference between the heat accumulated by the system and the
work done.
According to the same authors, these five equations have four thermodynamic unknown
variables: ρ, p, i and T. If a thermodynamic equilibrium is considered, the thermodynamic
variables can be written by means of two state variables. Thermodynamic equilibrium is the
assumption that, despite the rapidly change of the properties of the fluid particles from place to
place, the fluid is able to, thermodynamically, adjust itself towards the new conditions almost
instantaneously. The assumption of thermodynamic equilibrium provides two more equations,
thus eliminating all but two variables: the state variables.
At this stage there are seven equations. The introduction of a Newtonian model that
relates the viscous stress with gradients of velocity components yields in a closed mathematical
system with seven equations (the mass, the energy and three momentum equations as well as the
two equations due to the assumption of thermodynamic equilibrium) and seven unknowns (the
velocity, the four thermodynamic variables and the first and second viscosities). For an
incompressible fluid the density is constant throughout. Therefore, and according with the
mentioned authors, there is no linkage between the three kinds of equations (mass, energy and
momentum). So, for an incompressible flow, the governing equations are the mass conservation
and the three momentum equations (or Navier-Stokes equations). For an incompressible flow, a
heat transfer problem is the only one that requires the energy equation solving alongside the
others (Versteeg and Malalasekra, 2007).
Hence, it is time to address the main equations for an incompressible fluid, through the
mass and the momentum equations. The mass conservation equation can be written according to
equation [4.1]
[4.1]
or in a equivalent form by equation [4.2].
20
[4.2]
Equation [4.2] corresponds to the unsteady, three-dimensional mass conservation or continuity
equation (in another way to the one presented in equation [3.3]), for a compressible fluid. The
first term of the left hand side of the equation represents the density change throughout the time.
For steady flows this term is equal to zero. The second term is the convective term. When
working with an incompressible fluid, the value of the density is always the same throughout.
Therefore, and considering a steady flow, equation [4.2] becomes equal to:
[4.3]
or in an equivalent notation,
[4.4]
As mentioned, the momentum equilibrium equations contain the viscous stress
components. To deal with these variables, a suitable model (Newtonian one) needs to be taken
into account. For a Newtonian fluid, the viscous stress is proportional to the deformations rate
(Versteeg and Malalasekra, 2007). It is possible to relate the viscous stress to linear and
volumetric deformations. Through mathematical manipulation of the equilibrium equations,
new equations are reached. Named by the two nineteenth-century scientists who, separately,
derived them, the Navier-Stokes equations can be written according to equation [4.5]:
[4.5]
For an incompressible fluid, the viscosity value is constant. The second term of the right
hand side equation is nil, and the third term (which represents the shear stress due to the
dynamic viscosity) can be written as shown in equation [4.6].
[4.6]
Thus, for a Newtonian incompressible fluid, the Navier-Stokes equations can be written
as presented in equation [4.7].
[4.7]
The RANS equations correspond to a simplification of Navier-Stokes equations. In
1889, Reynolds proposed a mathematical tool, kwon as Reynolds decomposition, in which the
flow variables could be decomposed in its mean value and its fluctuating component, as
represented in equation [4.8]:
21
[4.8]
on which φ(t) represents the flow variable, represents the time average (or mean) flow
variable and φ' corresponds to its fluctuating component. This simplification originated the
RANS equations (Reynolds averaged Navier-Stokes equations), which are used, manly, to
describe turbulent flows and which are the main support of the nowadays CFDs. For the large
majority of engineering problems is not necessary to attend to the turbulent fluctuations details.
For this reason, the CFD users are often satisfied with the averaged flow properties. This is why
the RANS equations are so important and accepted in turbulent problems solving (Versteeg and
Malalasekra, 2007).
Due to the turbulent flow main characteristics, it is possible to approximate the Navier-
Stokes equations to average solutions in time. For a steady Newtonian incompressible fluid flow
the Navier-Stokes equations may be rewrote in the RANS form (equation [4.9]).
[4.9]
The left hand side of the equation represents the change in the mean momentum of fluid
element due to both the unsteadiness and the convection in/by the mean flow. This change is
balanced by the mean body force, the isotropic stress due to the mean pressure field, the viscous
stress and the Reynolds stress. This last component, highly nonlinear, corresponds to the
apparent stress due to the velocity field fluctuation. This stress causes the velocity decrease of
faster moving fluid layers and the velocity increase in slower moving fluid layers.
The Reynolds stress appearance turns the turbulence in a highly complex problem.
Unlike the viscous stress which can be directly related with the flow properties trough the
constitutive equations, Reynolds stress is due to the flow itself. This term corresponds to a
nonlinear element, which requires numerical models to be able to reach a solution for RANS
equations. For this reason, several turbulent models were developed to attend to the Reynolds
stress problem; in this work the turbulent model used was the k-ε model. This model is often
used and presents good results regarding the turbulence problem.
4.2. k-ε turbulence models
For high Reynolds numbers, the flow is characterized as turbulent. This kind of flow,
due to the turbulence characteristics, needs specific models that allow them to make a
correlation between the velocity and pressure fields.
As presented in section 2.4, one of the main characteristics of the turbulent flow is the
occurrence of vortexes with a wide range of length scales both in time as in space (White,
1991). This vortexes lead to the overlap between the flow random and average movements
throughout the time. When turbulence happens, whether it is local or throughout the flow, there
22
is a transference of energy between the energy of the flow to the bigger vortexes kinetic energy
due to tangential forces, in a phenomena called vortex stretching (Quintela, 2002). Thus, areas
that present bigger vorticity take part of the flow kinetic energy. Big vortexes collapse in
smaller ones, while the viscosity effect dissipates energy, which results in an increase of energy
losses (Versteeg and Malalasekra, 2007). Therefore, the vortexes effects are felt all through the
flow until the viscosity forces are able to dissipate its effects. The energy responsible for the
turbulent movement is the only energy available to create vortexes, corresponding to the only
energy that can be dissipated.
Boussinesq, 1877, postulated that Reynolds stress was proportional to mean
deformation rates. Equation [4.10] represents Boussinesq assumption for incompressible fluids,
[4.10]
where k corresponds to the turbulent kinetic energy. In an equivalent way, Boussinesq defined
the concept of turbulent (eddy) viscosity, in which he assumed that the turbulent tangential
stress (Reynolds stress) would be proportional to the average velocity rate.
In the turbulent flow, the equilibrium equation tensor considers not only the viscose
stress but also the turbulence associated stress, the Reynolds stress. Thus, the eddy stress does
not correspond to a flow property, however eddy stress depends on turbulence, which means
that it changes within the fluid.
The k-ε turbulence models correspond to the most common and most used models. This
are semi-empirical models with two extra transport equations which allows the turbulent flow
properties representation. The first equation takes into account the turbulent kinetic energy, and
corresponds to the k variable, and the second equation corresponds to the turbulent dissipation
rate, variable ε. These equations take into account the convection and diffusion effects due to
the turbulence intensity (Pope, 2000). Assuming both a turbulent flow and a non-significant
molecular viscosity, the kinetic turbulent energy and the turbulent dissipation rate can be
calculated by equations [4.11] and [4.12] respectively.
[4.11]
ε
[4.12]
where Cε1, Cε2 are constants experimentally determined for homogeneous flows with isotropic
turbulence. The production of turbulence due to viscous and buoyancy forces, Pk, can be
estimated according to equation [4.13], while the turbulent (or eddy) viscosity can be defined as
shown in equation [4.14].
[4.13]
23
[4.14]
Considering a black box tool model, the software assumes the values presented in Table
4.1. Those values have been determined using data concerning several turbulent flows data, and
present, for the most turbulent flow problems, results with a high accuracy. In spite of what has
been said, it is possible to change this values, if that is considered relevant. Since these models
are very robust, with accurate results concerning turbulence, its major utilization worldwide is
According to COMSOL tutorials, the distance δw is automatically computed, according
to equation [4.18], in such a way that δw+, which corresponds to the distance from the wall
where the logarithmic layer meets the viscous sub layer, is equal to 11.06. Because δw is limited
form below, so that it never becomes smaller than half of the height of the boundary mesh cell,
δw+
can become higher than 11.06, when the mesh is relatively coarse.
[4.18]
27
The friction velocity, uτ, is calculated according to equation [4.19].
[4.19]
Regardless, for the all simulations the fluid was always considered as water, with
constant density and viscosity equal to 999.62 Kg/m3 and m
2/s, respectively.
4.3.3. Mesh definition
One of the most important steps in CFD simulations corresponds to the mesh definition.
The mesh allows the discretisation of the geometry into smaller units, called mesh elements. Its
resolution and element quality are extremely important aspects to take into consideration when
validating a model. Decreased resolution can originate low accurate results (Gresho, 1991),
meanwhile, low mesh element quality can led to convergence issues (Lumley, 1978). Seldom, a
mesh consisted by finer elements is easier to built than a larger elements mesh. Nonetheless, a
finer mesh requires more computational effort. Therefore, the most efficient meshes are often
those defined with fine elements in an area and coarser elements in others.
COMSOL mesh generator discretizes the domains as tetrahedral, hexahedral, prism or
pyramid mesh elements. Regarding the boundaries, they are discretized as triangular or
quadrilateral boundary elements while geometry edges are discretized into edge elements.
The model default uses a physic controlled mesh. This means that for each physical
model chosen, COMSOL as associated a certain mesh, according to the physical characteristics
of the model. As an alternative, it is possible to define a user-controlled mesh. The user,
manually, builds and edits the mesh in order to adapt it to the current problem.
The physics-controlled mesh defines automatically the size attributes and operations
sequences necessary to create a problem adapted mesh. These physics-controlled sequences are
based on heuristics, as well as the knowledge of experts gathered in several investigations. For
the CFD model, it is necessary to define a boundary layer. A boundary layer mesh is a high
density mesh along walls, Figure 4.2 a). This boundary layer is used in fluid flow problems in
order to solve the thin layer near the solid walls where the gradients of the flow variables are
high, viscous sub-layer (Bakewell et al., 1967; Wosnik, Castillo and George, 2000).
a) b)
Figure 4.2 - Mesh examples: a) mesh cross section - the mesh cells closer to the wall (boundary layer) have a higher density and are much smaller than the other ones; b) mesh refinements near singularities.
28
4.3.4. Solver and solution convergence
COMSOL has built in several types of solvers as well as studies. In order to achieve
these objectives, the chosen study was the stationary one and the linear system solver was one
called MUMPS. Since only these were used, only these will be explained.
In order to provide a solution, the user must define the type of study, the linear solver as
well as the nonlinear method. Despite being quite odd to state the software requires a linear
solver, as well as a nonlinear method, the statement is accurate. There are always nonlinear
components in fluid flows that need to be taken into account. Since nonlinear problem are quite
difficult to solve, COMSOL uses an iterative method to solve the nonlinear partial differential
equations. Each nonlinear iteration requires the solution of a linear system of equations. In other
words, the software divides the nonlinear problem in smaller linear problems and solve them.
The linear system solver chosen was the MUMPS which work as a sparse linear system,
in the form expressed in equation [4.20].
[4.20]
Using the lower and upper, LU, factorization of matrix A the software computes the solution x.
In order to achieve a solution MUMPS use several algorithms that permute the columns of the
matrix A with the intention to minimize the number of non-zeros in the L and U factors.
It is possible to run the solver in a segregated or coupled form. The differences are not
very important since the algorithm is, basically, the same. The only relevant difference between
them is how they solve the equations: either in a segregated or in a coupled way.
From the several nonlinear methods available the chosen one was the Newton.
COMSOL uses an invariant form of the damped Newton method. Starting with the initial guess,
Z0, the software forms the linear model. It then solves the linear model for the Newton step (δZ)
considered, using the linear system solver (MUMPS). The following step made by the model is
to compute a new iteration. The new iteration is calculated according to equation where λ' is the
damping factor, smaller than one but always positive.
[4.21]
The software estimates the error of the new iteration and, if the error of the current
iteration is bigger than the one of the previous iteration, the code decreases the damping factor
and recomputed the iteration. This procedure will occur until either the error is smaller than the
error calculated for the previous iteration or the damping factor reaches its minimum value
. When a successful step is reached, the algorithm computes the next iteration.
The nonlinear iteration finish when the relative tolerance exceeds the relative computed
error. Figure 4.3 is an example of a solution convergence. The software stops the iteration when
29
the relative error is smaller than and the dumping factor is equal to 1. Otherwise the
solution would not converge and the iteration would continue.
Figure 4.3 - Convergence solution example.
30
31
5. Experiments
5.1. Introduction
In order to assess the computational results provided by the CFD model, to ensure their
quality, an intense campaign of experiments were developed to validate them.
Since the case studies are based on two major EPAL hydraulic circuits, the experiments
were limited to the real conditions. Therefore, to complement the analyses, some experiments
were developed in EPAL laboratory in order to compare and validate the computed simulations
with the experimental results. In the adopted methodology, the boundary conditions of the real
system were implemented. The velocity profiles calculated by the CFD model were compared to
the ones measured with an ultrasonic doppler velocimeter (UDV).
In order to use the UDV, the pipes could not be of steel, because the available UDV was
not able to measure correctly in this material. Therefore, new pipes had to be made in HDPE in
order to account for this factor. In order to guarantee a higher perturbations assessment two
different pipe diameters were available for several experiments: DN100 and DN80.
The UDV operating principle is the following (MET-FLOW, 2014): an ultrasonic probe
is placed near the wall of the pipe with a certain slope. An ultrasound is emitted and travels
across the pipe cross section. When the ultrasound hits a fluid particle some energy of the
ultrasound disperses and produces an echo. After a certain time the echo reaches the probe.
Then, by mathematical manipulation, the equipment delivers a velocity value. Figure 5.1
The UDV uses an ultrasonic wave in order to provide the velocity profile. In the
presence of air the equipment signal is not able to read the signal. For that reason the probe
needs to be well installed. In order to accomplish such, the probe is put in a specific probe
holder, Figure 5.2, which is a plastic rectangle on which several holes are made and to each hole
a certain angle is associated. This probe holder as two functions: to guarantee stability to the
probe, since it makes possible to attach it to the pipe; and also to make sure that there is no air
between the pipe and the probe. This is accomplished by inserting a gel in the hole where the
probe will be put, guarantying, thus, that the probe is always in contact with it.
32
Figure 5.2 - Probe and probe holder. In this image the probe is in the 20º slope angle.
Several experiments were developed with the intention to mimic a large number of
geometries that could induce perturbations and be relevant for the flow measurement:
perturbations caused by vertical and horizontal curves, reductions and expansions, and its
cumulative effects.
To assess if the results provided were accurate, several measurements were made with
the UDV which provided a velocity distribution profile. The position of the UDV was changed
in order to have more than one section where the results comparison could be made. The same
happened with the flowmeters: their position was changed to assess how different straight
distances would influence the reading. The flowmeters error was calculated according to the
description made in Annex B. Therefore, several results were available to assess the accuracy of
the results.
The experiments took place in the laboratory of EPAL, Laboratório de Contadores de
Água, at Olivais, Lisbon. Regarding the in and outlet conditions, those were imposed by the
facility constrains and the equipment characteristics. The inlet condition corresponded to the
pressure measured upstream by a manometer, meanwhile the outlet condition was the volume
flow rate verified downstream by referenced flowmeters, Figure 5.3.
a) b)
Figure 5.3 - Laboratory layout - a) inlet - manometer (left) and thermometer (right); b) three reference flowmeters (blue arrows)
33
Downstream the flowmeters, there are two high accuracy tanks, Figure 5.4. These tanks
are certificated and calibrated by a traceable laboratory using the International System of Units.
The volume of water read in those tanks, after the experiment, is used for the calculus of the
errors of flowmeters, by the volumetric method application. In Annex B several more
considerations were drown regarding this subject.
a) b)
Figure 5.4 - High accuracy tank - a) 1000 L b) 5000 and 10000 L (tank identified by the yellow arrow).
The procedure followed in the several experiments consisted in the following steps: the
water was pumped from the drinkable water tanks to the laboratory, at a pressure of,
approximately, 6 bar. After a couple of minutes, in order to guarantee that the flow is under
steady state conditions, the experiment started. The velocity profile was measured with the
UVD. The initial and the final volumes were registered as well as the pressure and the duration
of the experiment. After the measurements and the data registered, the first experiment was
concluded. For the same geometry, the position of the flowmeter was changed and the
procedure repeated. When the measurement was concluded in all the required points, and when
all the flowmeter results in all sections were registered, the geometry was changed and the
procedure repeated until all geometries and tests were developed.
The tests developed are schematically represented in Table 5.1. The UVD
measurements were made in the middle section of the identified pipes and only for the vertical
plan, due to constraints related to the use of the UVD and the use of the EPAL facilities. In
Annex B are presented in a more detail the geometries studied, the intents behind the
alternatives and the explanation for the procedure and respective justification.
34
Table 5.1 - Schematic test notation matrix.
Notation Scheme Observations
Geom
etr
y 1
Type
1
Vertical plan perturbation.
DN80 flowmeter - colour blue;
DN100 flowmeter - colour green.
UDV measurements in the
red pipes identified by A and B.
Type
2
UDV measurements in the red pipes identified by A.
Perturbation due to vertical
curves with a small distance to dissipate before
the DN80 flowmeter.
Type
3
UDV measurements in the
red pipes identified by A. Perturbation due to vertical
curves without any straight distance from the DN80
flowmeter.
Type
4
UDV measurements in the
red pipes identified by A. Perturbation due to vertical
curves with a long straight distance from the DN80
flowmeter.
Geom
etr
y 2
Type
1
Vertical plan perturbation
DN80 flowmeter - colour blue;
DN100 flowmeter - colour green.
Perturbation due to vertical
curve and counter curve with a small straight
distance from the DN80 flowmeter.
Type
2
Perturbation due to vertical curve and counter curve
with a large straight
distance from the DN80 flowmeter.
Geom
etr
y 3
Type
1
Horizontal plan
perturbation. DN80 flowmeter -
colour blue; DN100 flowmeter -
colour green.
Perturbation due to vertical
curve and counter curve with a small straight
distance from the DN80 flowmeter.
Type
2
Perturbation due to vertical curve and counter curve
with a large straight distance from the DN80
flowmeter.
Geom
etr
y 4
Type
1
Three plans
perturbations. DN100 flowmeter -
colour green.
Perturbation due to vertical
curves and rotation of the vertical orthogonal axis.
35
5.2. Experimental results
5.2.1. Geometry 1
5.2.1.1. Type 1
As a result of the methodology developed there were available two kinds of results: the
velocity profiles and the relative errors. The first type of data was provided by the UDV
measurements, while the relative error was calculated with the volumetric volume (Annex B).
For Geometry 1, four tests were developed in order to obtain the maximum data
possible for the model validation. The types of tests of Geometry 1 can be consulted in Annex B
1. Four tests were made for two different volume flow rates, corresponding to 17 UDV
measurements. In each UDV measurement, the velocity in more than 100 different points was
captured in a total of 100 profiles.
In Figure 5.5 is presented the layout of Type 1experience. The locations that guarantee
the placement of the probe holder were the ones identified by the red arrows in Figure 5.5 b).
a) b)
Figure 5.5 - Geometry 1, type 1 experiment - a) experiment layout (flow direction identified by the blue arrow); b)
experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 identified by the green arrow. The UDV probe measured in the pipe sections identified by the red arrow.
In this experiment, two different volume flows rate were tested: 100 and 12 m3/h. The
results achieved are presented in Table 5.2. The negative value of the error represents an
underevaluation on the volume that passed through the flowmeter meanwhile a positive error
represents an overevaluation on the volume.
Table 5.2 - Tests results of the Geometry 1, type 1 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 4980 5032 5000 180 173 104 -0.40% 0.64%
12 1006 1016 1018 305 285 13 -1.18% -0.20%
A
B
36
As mentioned in Chapter 3 the flowmeter error decreases with the velocity increase, as
it happens for the DN100 flowmeter. Nevertheless, for the DN80 flowmeter the error increases
for the volume flow rate increase. The reason for this factor is that the geometry induced
perturbations increase with the increase of the volume flow rate. And this increase is higher than
the gain in accuracy of the flowmeter.
The profiles measured using the UDV are presented in Figure 5.6 and Figure 5.7 for 100
and 12 m3/h, respectively.
a)
b)
Figure 5.6 - UDV profiles for 100 m3/h for Geometry 1, type 1 - a) profiles measured in the location identified as A in Figure 5.5; b) profiles measured in the location identified as B in Figure 5.5.
UDV is a very sensitive equipment, specially to electromagnetic noise. Due to layout
constrains, the points where the profiles measurement was made, were near the flowmeters. The
flowmeters induce an electromagnetic field in order to measure which has influence on the
probe reading and some problems that can arise. Another important factor was the absence of
seeding. The seeding phenomena is the introduction of small particles, usually of a liquid or a
fine powder, with the purpose to facilitate the detection of particles by the ultrasound wave.
Since the water for these tests was pumped directly from the treated water tanks it was not
possible to introduce any substance. The problem of this action is that some particles are
disregarded and the profile, sometimes, is not the one it should be. Lastly, the UDV is not able
to measure near the walls. Therefore, some initial and final points were disregarded.
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1 U
, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
37
a)
b)
Figure 5.7 - UDV profiles for 12 m3/h for Geometry 1, type 1 - a) profiles measured in the location identified as A in Figure 5.5; b) profiles measured in the location identified as B in Figure 5.5.
5.2.1.2. Type 2
In Figure 5.8 is presented the layout of Type 2 experience.
a) b)
Figure 5.8 - Geometry 1, type 2 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 identified by the green arrow. The
UDV probe measured in the pipe section identified by the red arrow.
In order to have a correct and accurate measurement, the UDV probe cannot be in
contact with air. The only location where the UDV probe could be located was the one
identified by the red arrow (Figure 5.8 b)).
Based on the same considerations made in section 5.2.1.1, the results achieved are
presented in Table 5.3.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
A
38
Table 5.3 - Tests results of the Geometry 1, type 2 experiment and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 5094 5024 5000 180 175 103 1.88% 0.48%
12 1047 1004 1020 306 277 13 2.65% -1.57%
The profiles for the volume flow rate of 12 m3/h were not carried out. Despite being the
second experiment presented, following the design order, these experiments were the last to be
made. The measured for 100 m3/h are presented in Figure 5.9.
Figure 5.9 - UDV profiles for Geometry 1, type 2, measured at the location identified as A in Figure 5.8 for 100 m3/h.
5.2.1.3. Type 3
The layout of experience Type 3 differs from the Type 2 layout in the position of the
DN80 flowmeter. In Figure 5.8 the DN80 flowmeter is upstream of a long pipe and downstream
of a very small one. The adopted layout for these tests was achieved by changing the small pipe
in such a way that the flowmeter is downstream of a vertical curve (Figure 5.10).
Figure 5.10 - Geometry 1, type 3 experiment - flow direction identified by the blue arrow; DN80 flowmeter identified
by the yellow arrow, DN100 identified by the green arrow. The UDV probe measured in the pipe section identified by the red arrow.
The previous considerations remain valid for these tests and the results achieved are
those presented in Table 5.4. The profiles measured using the UDV are presented in Figure 5.11
for the different volume flow rates.
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
A
39
Table 5.4 - Tests results of the Geometry 1, type 3 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 5026 4916 5000 180 172 105 0.52% -1.68%
12 1035 998 1020 306 295 12 1.47% -2.16%
a)
b)
Figure 5.11 - UDV profiles for Geometry 1, type 3, measured at the location identified as A in Figure 5.10- a) 100 m3/h; b) 12 m3/h.
5.2.1.4. Type 4
The layout of experience Type 4 is presented in Figure 5.12. Taking into consideration
all the previous assumptions, the results obtained for these tests are presented in Table 5.5.
Figure 5.12 - Geometry 1, type 4 experiment - experiment layout detail - flow direction identified by the blue arrow. DN80 flowmeter identified by the yellow arrow, DN100 identified by the green one. The UDV probe measured in the
pipe section identified by the red arrow.
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1 U
, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
A
40
Table 5.5 - Tests results of the Geometry 1, type 4 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 5047 5004 5000 180 174 103 0.94% 0.08%
12 1026 1033 1019 306 283 13 0.69% 1.37%
Figure 5.13 - UDV profiles for Geometry 1, type 4 measured at the location identified as A in Figure 5.12 for 100 m3/h.
The profiles measured using the UDV are presented in Figure 5.13, only for 100 m3/h
volume flow rate. The profiles measured for the 12 m3/h are not presented since they exhibits an
odd behaviour.
5.2.2. Geometry 2
5.2.2.1. Type 1
Geometry 2, Annex B 2, is analogous to Geometry 1, but there is the absence of a
straight pipe between curves. Despite being a small difference, these tests are important in order
to simulate the hydraulic circuit of Vila Franca de Xira (Chapter 6).
The UVD from CEHIDRO (hydraulic Lab) had time limitations to be used. Hence, the
results obtained in these tests were the relative error for the two flowmeters at two different
volume flow rates.
In Figure 5.14 is presented the layout of Type 1 experience.
a) b)
Figure 5.14 - Geometry 2, type 1 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow.
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1 U
, m
/s
Relative to the pipe diameter
41
As mentioned in section 5.2.1.1, the experiments were developed for two different
volume flow rates. Table 5.6 summarizes the results obtained for this test.
Table 5.6 - Tests results of the Geometry 2, type 1 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 4936 4939 5000 180 172 105 -1.28% -1.22%
12 1016 1007 1020 367 278 13 -0.39% -1.27%
The relative errors in these tests were all negative. For the different volume flow rate the
flowmeters underevaluated the volume passed through. While in section 5.2.1.1 the DN100
flowmeter behaved according to equation [3.1], in these tests the DN80 flowmeter was the one
that behaved according to equation [3.1]. The justification is the same presented in section
5.2.1.1.
5.2.2.2. Type 2
In Figure 5.15 is presented the layout of Type 2 experience.
Figure 5.15 - Geometry 2, type 2 experiment - flow direction identified by the blue arrow; DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow.
Table 5.7 - Tests results of the Geometry 2, type 2 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 4823 5049 5000 180 167 108 -3.54% 0.98%
12 989 1027 1020 367 279 13 -3.04% 0.69%
Table 5.7 summarizes the results obtained for these experiments. The relative errors in
these tests are negative for the DN100 flowmeter and positive for the DN80. By analysis of
Table 5.7, is clear that the increase of accuracy resulting on the velocity increasing is not
42
enough to minimize the effect caused by the geometrical perturbations. The error in this test,
regarding the DN100 flowmeter, is a very high one. The justification for these errors can only
be associated to the position of the flowmeter.
5.2.3. Geometry 3
5.2.3.1. Type 1
The layout of Geometry 3, Annex B 3, is the same as the one presented for Geometry 2.
The difference is the Geometry 3 had the purpose to analyse the horizontal perturbations. This
means that Geometry 3 tests took place in the horizontal plan, whereas Geometry 2 tests were
developed in the vertical one.
The results obtained in these tests were the relative errors for the two flowmeters at two
different volume flow rates, due to constraints on the UDV availability.
In Figure 5.16 is presented the layout of Type 1 experience.
a) b)
Figure 5.16 - Geometry 3, type 1 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow.
The conditions of the tests remained the same that were presented previously. The
results of each test are presented in Table 5.8.
Table 5.8 - Tests results of the Geometry 3, type 1 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 4940 4955 5000 180 163 110 -1.20% -0.90%
12 1029 998 1020 367 258 14 0.88% -2.16%
Since the DN80 flowmeter presents the theoretical behaviour expressed by equation
[3.1], it is valid to state that the geometry induced perturbations are not very significant for that
flowmeter. Nevertheless, for the DN100 flowmeter the statement is, most probably, not valid,
since the error increases with the volume flow rate increasing.
43
5.2.3.2. Type 2
In Figure 5.17 is presented the layout of Type 2 experience.
a) b)
Figure 5.17 - Geometry 3, type 2 experiment - a) experiment layout (flow direction identified by the blue arrow); b) experiment layout detail - DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow.
Table 5.9 - Tests results of the Geometry 3, type 2 experiments and the relative errors for both flowmeters and volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
DN80
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
DN80
[%]
100 4946 4904 5000 180 166 108 -1.08% -1.92%
12 998 1014 1020 367 290 13 -2.16% -0.59%
Table 5.9 summarizes the results obtained for the these tests. DN100 flowmeter presents
the theoretical behaviour described in Chapter 3. In the other hand, the DN80 flowmeter
presents an error evolution different from the theoretical behaviour. The perturbation induced by
the geometry are higher than the gain in accuracy, since the error increases with the volume
flow rate increasing.
5.2.4. Geometry 4
5.2.4.1. Type 1
The layout of Geometry 4, Annex B 4, was developed in order to simulate the layout of
Castelo do Bode pumping station (Chapter 6). This geometry has the purpose to assess the
perturbations caused by vertical curves associated with a rotation along the vertical orthogonal
axis.
For this geometry only one diameter was used, the DN100. In order to maximize the
information available two DN100 flowmeters were used in series. Therefore there are two
different results, for 100 and 12 m3/h volume flow rate in two different sections.
The layout of the tests for Geometry 4 is presented in Figure 5.18.
44
a) b)
Figure 5.18 - Geometry 4, type 1 - a) photograph taken from upstream to downstream (flow direction identified by
the blue arrow); b) photograph taken from downstream to upstream - DN100 flowmeter previously used identified by the green arrow, DN100 flowmeter used only in these tests identified by the red arrow.
The results obtained for the DN100 flowmeter used in previous experiments are
presented in Table 5.10. The error calculated for the 100 m3/h is an extremely high value
probably by the malfunction of the equipment due to a large turbulent phenomena.
Table 5.10 - Tests results of the Geometry 4, type 1 experiments and the relative errors for DN100 flowmeter used in the previous experiments for different volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
100 3565 5000 180 170 106 -28.70%
12 1006 1021 306 258 14 -1.47%
The values achieved from the experiments considering the new DN100 flowmeter are
presented in Table 5.11.
Table 5.11 - Tests results of the Geometry 4, type 1 experiments and the relative errors for DN100 flowmeter used in this experiments for different volume flow rates.
Tests results Error
Qtheoretical
[m³/h]
DN100
[L]
reference
[L]
ttheoretical
[s]
treal
[s]
Qref.
[m3/h]
DN100
[%]
100 4896 5000 180 170 106 -2.08%
12 1010 1021 306 258 14 -1.08%
The results show that the error for the 100 m3/h volume flow rate is much similar to the
errors presented for the previous geometries, corroborating the possible equipment malfunction.
45
5.3. Computational simulation
5.3.1. Geometry 1
5.3.1.1. Type 1
Once the experimental results were obtained, several computational simulations were
made in order to compare the results with the experiments. The results available were of two
kinds: the velocity distribution profile, in the same pipe section where the UDV was installed,
and the velocity distribution profile across the electrodes of flowmeters cross section, which
allowed the estimation of the volume flow rate and the subsequent flowmeter error.
For the several tests, the boundary conditions for the simulations were the same that the
ones verified/measured at the laboratory.
Figure 5.19 represents the geometry used for the simulation of the layout presented in
Figure 5.5.
a) b)
Figure 5.19 - a) simulation geometry for Geometry 1, type 1 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter by the green arrow).
Input data are presented in Table 5.12.
Table 5.12 - Boundary, mesh and study conditions for Geometry 1, type 1, test 3 simulation for the 100 and 12 m3/h volume flow rate.
100 m3/h 12 m
3/h
Inlet 5.6 bar 5.8 bar
Outlet 0.59 m/s 0.07 m/s
Wall No-slip No-slip
Mesh Physics-controlled Physics-controlled
Flow
Conditions Steady state Steady state
In order to estimate the error associated to the flowmeter position a procedure was
created using the information of Figure 3.4. A spreadsheet was developed in such a way that
through points exported from the model a volume flow rate estimation could be calculated.
46
Subsequently the error was calculated, subtracting to the calculated value the input volume flow
rate value, dividing the result by the input value. This procedure is explained in Annex C.
In Figure 5.20 is represented the velocity distribution in the electrodes cross section for
the two different volume flow rates and flowmeters studied.
a) b)
c) d)
Figure 5.20 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.19); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.19).
The errors calculated with the spreadsheet developed are presented in Table 5.13.
Table 5.13 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 1, type 1.
DN80 DN100
100 m3/h 0.45 % -0.48 %
12 m3/h -0.55 % -1.27 %
In Figure 5.21 are presented the profiles provided by the model for the section of the
UDV position.
47
a) b)
c) d)
Figure 5.21 - Geometry 1, type 1 velocity distribution profiles provided by the program - profiles a) and b) section A and B of Figure 5.5, respectively for 100 m3/h; profiles c) and d) same then profiles a) and b) for 12 m3/h.
5.3.1.2. Type 2
Figure 5.22 represents the geometry used for the simulation of the layout presented in
Figure 5.8.
a) b)
Figure 5.22 - a) simulation geometry for Geometry 1, type 2 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow).
The relevant features for these simulations are the same presented in Table 5.12. The
errors calculated with the spreadsheet developed are presented in Table 5.14.
Table 5.14 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 1, type 2.
DN80 DN100
100 m3/h 0.61 % 1.11 %
12 m3/h -1.48 % 1.61 %
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
48
The profile provided by the model correspondent to the UDV measurement position, is
presented in Figure 5.23, for the 100 m3/h volume flow rate.
Figure 5.23 - Geometry 1, type 2 velocity distribution profile provided by the program - section A of Figure 5.8 for 100 m3/h.
The velocity distribution profiles are presented for two flowmeters and for two different
volume flow rates in Figure 5.24.
a) b)
c) d)
Figure 5.24 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.22); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.22).
5.3.1.3. Type 3
Figure 5.25 represents the geometry used for the simulation of the layout presented in
Figure 5.10.
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
49
a) b)
Figure 5.25 - a) simulation geometry for Geometry 1, type 3 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow).
The relevant features for these simulations are the same presented in Table 5.12. The
velocity distribution profiles are presented for the two flowmeters and for the two different
volume flow rates in Figure 5.26.
a) b)
c) d)
Figure 5.26 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.25); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.25).
The errors calculated with the spreadsheet developed are presented in Table 5.15.
Table 5.15 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 1, type 3.
DN80 DN100
100 m3/h -1.76 % 1.11 %
12 m3/h -2.08 % 1.61 %
The profiles presented by the model correspondent to the UDV measurement are in
Figure 5.27.
50
a) b)
Figure 5.27 - Geometry 1, type 3 velocity distribution profiles provided by the program - section A of Figure 5.10: a) 100 m3/h; b) 12 m3/h.
5.3.1.4. Type 4
Figure 5.28 represents the geometry used for the simulation of the layout presented in
Figure 5.12.
a) b)
Figure 5.28 - a) simulation geometry for Geometry 1, type 4 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow).
The relevant features for these simulations are presented in Table 5.12. The velocity
distribution profiles for the two flowmeters and different volume flow rates are in Figure 5.29.
a) b)
c) d)
Figure 5.29 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.28); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.28).
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
51
The errors calculated with the spreadsheet developed are presented in Table 5.16.
Table 5.16 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates, for Geometry 1, type 4.
DN80 DN100
100 m3/h 0.16 % 1.11 %
12 m3/h 0.75% 1.61%
The profile presented by the model correspondent to the UDV measurement is presented
in Figure 5.30.
Figure 5.30 - Geometry 1, type 4 velocity distribution profile provided by the program - section A of Figure 5.12 for 100 m3/h.
5.3.2. Geometry 2
5.3.2.1. Type 1
Figure 5.31 represents the geometry used for the simulation of the layout presented in
Figure 5.14.
a) b)
Figure 5.31 - a) simulation geometry for Geometry 2, type 1 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow).
The boundary conditions and other important modelling features are the same as the
presented in Table 5.12. The velocity distribution profiles for both flowmeters and volume flow
rates are presented in Figure 5.32.
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
52
a) b)
c) d)
Figure 5.32 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.31); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.31).
The errors calculated with the spreadsheet developed are presented in Table 5.17.
Table 5.17 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 2, type 1.
DN80 DN100
100 m3/h -0.94 % -1.19 %
12 m3/h -1.38 % -0.48 %
5.3.2.2. Type 2
Figure 5.33 represents the geometry used for the simulation of the layout presented in
Figure 5.15.
a) b)
Figure 5.33 - a) simulation geometry for Geometry 2, type 2 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by the yellow arrow, DN100 flowmeter identified by the green arrow).
Using the same features presented in Table 5.12, the velocity distribution profiles
achieved for both flowmeters and volume flow rates are the ones presented in Figure 5.34.
53
a) b)
c) d)
Figure 5.34 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.33); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.33).
The errors calculated with the spreadsheet developed are presented in Table 5.18.
Table 5.18 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 2, type 2.
DN80 DN100
100 m3/h 1.04 % -3.45 %
12 m3/h 0.75 % -3.15 %
5.3.3. Geometry 3
5.3.3.1. Type 1
Figure 5.35 represents the geometry used for the simulation of the layout presented in
Figure 5.16.
a) b)
Figure 5.35 - a) simulation geometry for Geometry 3, type 1 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by yellow arrow, DN100 flowmeter identified by the green arrow).
54
a) b)
c) d)
Figure 5.36 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.35); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.35).
Using the same features presented in Table 5.12, the velocity distribution profiles
achieved for both flowmeters and volume flow rates are the ones presented in Figure 5.36. The
errors calculated with the spreadsheet developed are presented in Table 5.19.
Table 5.19 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 3, type 1.
DN80 DN100
100 m3/h -1.86 % -1.09 %
12 m3/h -2.22 % 0.95 %
5.3.3.2. Type 2
Figure 5.37 represents the geometry used for the simulation of the layout presented in
Figure 5.17.
a) b)
Figure 5.37 - a) simulation geometry for Geometry 3, type 2 (blue arrow identifies the flow direction); b) modelling geometry detail (DN80 flowmeter identified by yellow arrow, DN100 flowmeter identified by green arrow).
55
a) b)
c) d)
Figure 5.38 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c) and d) 12 m3/h. Profiles a) and c) DN100 flowmeter (green arrow of Figure 5.37); profiles b) and d) DN80 flowmeter
(yellow arrow of Figure 5.37).
Using the same features presented in Table 5.12, the velocity distribution profiles
achieved for both flowmeters and volume flow rates are the ones presented in Figure 5.38. The
errors calculated with the spreadsheet developed are presented in Table 5.20.
Table 5.20 - Errors associated to CFD simulations according to the procedure developed for the two diameters and volume flow rates tested, for Geometry 3, type 2.
DN80 DN100
100 m3/h -1.01 % -1.23 %
12 m3/h -0.67 % -2.08 %
5.3.4. Geometry 4
5.3.4.1. Type 1
Figure 5.39 represents the geometry used for the simulation of the layout presented in
Figure 5.18.
a) b)
Figure 5.39 - a) simulation geometry for Geometry 4, type 1 (blue arrows identifies the flow direction); b) modelling geometry detail - DN100 flowmeters identified by the green and purple arrows (previous flowmeter identified by the
green arrow; new arrow identified by the red arrow, according to Figure 5.18).
56
a) b)
c) d)
Figure 5.40 - Velocity distribution profiles in the pipe cross section defined by the electrodes - a) and b) 100 m3/h; c)
and d) 12 m3/h. Profiles a) and c) DN100 flowmeter identified by the green arrow, Figure 5.39; profiles b) and d) DN100 flowmeter identified by the purple arrow, Figure 5.39.
The velocity distribution profiles in both sections and volume flow rates are presented
in Figure 5.40. The errors calculated with the spreadsheet developed are presented in Table
5.21.
Table 5.21 - Errors associated to CFD simulations according to the procedure developed for the two flowmeters and volume flow rates tested, for Geometry 4, type 1.
DN100 Green arrow Purple arrow
100 m3/h -1.55 % -2.15 %
12 m3/h -1.51 % -1.01 %
5.4. Results discussion
The profile measurement with the UDV was most of the times quite toilsome. The
reason for it was the good water quality of EPAL. In tests like the ones made, it is advisable to
introduce some particles (this phenomenon is called seeding) in order to have a better reflexion
of the ultrasonic wave. As mentioned in section 5.1 the water used in the tests was treated water,
directly from the tanks that make the distribution. For that reason, seeding was out of question.
Since the water was very clean, the UDV measurements were very difficult. Several trials
needed to be made in order to UDV be able to provide reasonable profiles.
For Geometry 1, type 1 experiment, the results present a good approximation between
the experimental and simulated results, Figure 5.41 and Figure 5.42.
57
a)
b)
Figure 5.41 - UDV profiles for 100 m3/h for Geometry 1, type 1 (blue triangles - experimental results; red rectangles - simulated results) - a) profiles measured in the location identified as A in Figure 5.5; b) profiles measured in the
location identified as B in Figure 5.5.
a)
b)
Figure 5.42 - UDV profiles for 12 m3/h for Geometry 1, type 1 (blue triangles - experimental results; red rectangles - simulated results) - a) profiles measured in the location identified as A in Figure 5.5; b) profiles measured in the
location identified as B in Figure 5.5.
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
58
Regarding the simulation described in section 5.2.1.2 the profiles for the volume flow
rate of 12 m3/h were not carried out. Despite being the second experiment presented, following
the design order, these experiments were the last to be made. The profiles measured for the 100
m3/h are presented in Figure 5.43. It is clear that, through a comparison between the calculated
and the measured profiles, the calculated is a good approximation of the real conditions.
Figure 5.43 - UDV profiles for Geometry 1, type 2 measured at the location identified as A in Figure 5.8 for 100 m3/h (blue triangles - experimental results; red rectangles - simulated results).
For Geometry 1 types 6, Figure 5.44, the results achieved reveal a good approximation
between the experimental and computed results.
a)
b)
Figure 5.44 - UDV profiles for Geometry 1, type 3 measured at the location identified as A in Figure 5.10 (blue triangles - experimental results; red rectangles - simulated results) - a) 100 m3/h; b) 12 m3/h.
For the Geometry 1, type 4, the 12 m3/h profiles were not presented since the results
were not adequate. The profiles obtained were very chaotic and nil in almost every point. The
justification for this was, very likely, due to the existence of air between the ultrasonic probe
and the pipe wall. The probe cannot be in contact with air, otherwise it could not measure. To
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
59
avoid it a gel was introduced in order to prevent this situation. Nevertheless, when the
experiment was taking place the gel might have been insufficient and the problem was not
detected. Only when the results analyses were made the problem arose. Since the UDV was no
longer available at EPAL laboratory, there were no profiles to present for the 12 m3/h for the
Geometry 1, type 4 simulations. The 100 m3/h computed results are similar to the experiments
(Figure 5.43).
Figure 5.45 - UDV profiles for Geometry 1, type 4 measured at the location identified as A in Figure 5.12 for 100 m3/h (blue triangles - experimental results; red rectangles - simulated results).
The profiles presented above have some peeks. The justification for this behaviour is
due to the fluctuations in velocity and the existence of vortexes, both characteristic phenomena
of turbulent flows. Hence, the occurrence for such values is a common phenomenon for
turbulent flows studies.
Through the comparison between the profiles obtained with the UDV and those
computed by the model, Figure 5.41 to Figure 5.45, it is clear that the profiles are very similar.
These results allow to conclude that the CFD model is validated and makes possible the
assumption that for other simulations, if mesh features, types of boundary conditions and
materials properties remain the same, the model would also provide good results. Thus,
according to these remarks, the results achieved are validated.
Table 5.22 - Values of the errors calculated with the volumetric method and the spreadsheet one, for Geometry 1 and respective flowmeters.
Q = 100 m
3/h Q = 12 m
3/h
Error Error
Experimental Model Experimental Model
Test DN100
[%] DN80 [%]
DN100 [%]
DN80 [%]
DN100 [%]
DN80 [%]
DN100 [%]
DN80 [%]
Type 1 -0.40% 0.64% -0.48% 0.71% -1.18% -0.20% -1.27% -0.55%
Type 2 1.88% 0.48% 1.11% 0.41% 2.65% -1.57% 1.61% -1.48%
Type 3 0.52% -1.68% 1.11% -1.76% 1.47% -2.16% 1.61% -2.08%
Type 4 0.94% 0.08% 1.11% 0.16% 0.69% 1.37% 1.61% 0.75%
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
U, m
/s
Relative to the pipe diameter
60
The discussion of results would not be concluded without error analyses. The following
tables present the errors calculated by the volumetric method (experimental error) and the ones
calculated with the spreadsheet developed (model error).
For the errors of DN100, for the volume flow rate of 100 m3/h (Table 5.22) it is verified
that the error associated to type 1 is the smallest one. Changing the position of the flowmeter,
maintaining the volume flow rate, the errors vary. The position of the flowmeter in experiments
type 2, 3 and 4 remained constant. Only the upstream layout was slightly changed as is clear in
Annex B1. If the geometry remained completely the same, and since the errors changed, the
conclusion was that the DN100 flowmeter has not repeatable measurements. The repeatability
phenomena is an important one for every industry which requires accurate measurements.
Measurement repeatability is the property of an equipment that for the same test conditions, it
presents very similar errors. Since the geometry changes slightly, the conclusion is not entirely
valid.
The difference of errors verified in type 2, 3 and 4 for the experimental results may be
due to some minor installation problems (such as the position of the gasket inserted in between
flanges which can obstruct a very small part of the pipe) that, since the model was not
developed with such detail level were not assessed by the computed results but were assessed by
the flowmeter. For this reason the errors calculated with the computed results remain the same
for the three tests. The commentaries of the results concerning the same flowmeter, for a
volume flow rate of 12 m3/h, are completely analogous to the presented ones.
The type 3 experiment is the one where the value of the error is the highest for the
DN80 with a volume flow rate of 100 m3/h. Of all the experiments made the type 3 experiment
corresponded to the worst layout since the flow has not enough pipe length in order to dissipate
the perturbation caused by the vertical curves. The type 1 and type 2 present very similar errors.
The fact that the experimental error verified in type 1 is higher than the one verified in type 2 is
surprising because the existence of 8º reduction/expansion cones (as occurs for this situation) is
considered as good procedure for the flowmeters manufactures. The probable reason for this
discrepancy can be installation problems. The experimental result for type 4 present the
minimum error, as would be expected, since the perturbations due to the upstream perturbations
can be dissipated throughout the straight pipes.
Lastly, the results for the DN80 with a volume flow rate of 12 m3/h behave as expected.
The only out of ordinary situation is the one associated to type 4. As mentioned in the previous
paragraph the error ought to be low. Nevertheless, the error has the same magnitude as the error
of type 2. The justification for this must be, again, some problems in the installation, which may
induce perturbations not simulated by the CFD model.
61
Table 5.23 - Values of the errors calculated with the volumetric method and the spreadsheet one, for Geometry 2 and respective flowmeters.
Q = 100 m
3/h Q = 12 m
3/h
Error Error
Experimental Model Experimental Model
Test DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
Type 1 -1.28% -1.22% -1.19% -0.94% -0.39% -1.27% -0.48% -1.38%
Type 2 -3.54% 0.98% -3.45% 1.04% -3.04% 0.69% -3.15% 0.75%
Regarding Geometry 2, the type 2 is the worst theoretical layout for the DN100 while
the type 1 is the worst layout for the DN80. And the experimental results corroborate the
expected ones. The DN100 flowmeter results, Table 5.23, show that the errors associated to a
layout where the flowmeter is immediately downstream vertical perturbations are quite
important. The same flowmeter, far from the vertical curves present a much smaller error. For
DN80 flowmeter results, the errors associated to the flowmeter closer to the vertical curves
(type 1) present a higher error, for both volume flow rates, than the flowmeter of type 2, as
expected.
Table 5.24 - Values of the errors calculated with the volumetric method and the spreadsheet one, for Geometry 3 and respective flowmeters.
Q = 100 m
3/h Q = 12 m
3/h
Error Error
Experimental Model Experimental Model
Test DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
DN100
[%]
DN80
[%]
Type 1 -1.20% -0.90% -1.23% -1.01% 0.88% -2.16% 0.95% -2.22%
Type 2 -1.08% -1.92% -1.09% -1.86% -2.16% -0.59% -2.08% -0.67%
Since Geometry 3 differs from Geometry 2 by the plan where it occurs, the errors
verified in both geometries ought to be similar. Nevertheless only the results for the 12 m3/h
volume flow rate are consistent to the previous ones. The theoretical behaviour of the
flowmeters is well described by the 12 m3/h flow: when the meter is close to a curve its error is
higher than when the same flowmeter is far from the vertical curves. Regarding the 100 m3/h
flow errors, Table 5.24, the results provided by the model present the behaviour expected,
meanwhile the experimental results do not. There is no clear justification for the behaviour
presented by flowmeters. If the errors of the 12 m3/h were consistent with the ones verified for
the 100 m3/h volume flow rate, it would indicate that an horizontal curve did not influence the
meter in a significant way. Nevertheless, that behaviour does not occur. The only plausible
justification is that some perturbations due to some installations problems were significant,
which caused the flowmeters miss reading.
62
Table 5.25 - Values of the errors calculated with the volumetric method and the spreadsheet one, for Geometry 4. Test 1. - new DN100 flowmeter (red arrow of Figure 5.39). Test 2 - DN100 flowmeter used in the previous tests
(green arrow of Figure 5.39).
Q = 100 m
3/h Q = 12 m
3/h
Error Error
Test Experimental Model Experimental Model
Type 1, test 1 -2.08% -2.15% -1.08% -1.01%
Type 1, test 2 -28.70% -1.55% -1.47% -1.51%
The theoretical error of the flowmeters ought to increase with the decrease in the
volume flow rate. Nevertheless, through the analyses of Table 5.25, it is clear that the error
associated to the 100 m3/h are bigger than the 12 m
3/h (type 1, test 1). The subsequent
conclusion is that the errors associated to the geometry are much higher than the increase on
accuracy. Regarding the errors of Type 1, test 2, which assess the perturbations induced by
vertical curves and a vertical rotation in the vertical orthogonal axis, the errors are very
different. While for 12 m3/h the perturbations induce a small error, for the 100 m
3/h the error is
very significant, around -28 %. This value is very odd since this flowmeter had never presented
such an error. The justification for this value is most probably due to an extremely intense
turbulence, which might have induced flow contractions which could have influenced, largely,
the flowmeter measurement.
As mentioned throughout this section, the pipes and flowmeter installation, are an
important factor in flow measurement accuracy. The error associated to the position of the
gasket, which may obstruct the pipes, are important and, in several situations, avoidable errors.
In these experiments, due to the large number of gaskets, it is mathematically improbable to
assume the errors could be preventable. However, in practice, since the number of gaskets is
much smaller these errors can be disregarded if the engineering good practices are followed.
The flowmeter have a gain in accuracy for the increase of volume flow rate. The
behaviour described was developed for flowmeters which fulfilled the manufactures installation
requirements. The analyses made did not take into account the requirements defined.
Nevertheless, through this analyses a conclusion is possible to be drawn: the gain in accuracy
resulted from a higher velocity is not enough to guarantee, in all situations, an accurate
measurement.
From what has been said, a relevant conclusion can be reached: the error in the flow
measurement is achieved through the sum of the errors associated to the flow measurement
equipment (flowmeter) with the one associated to the layout or geometry of the upstream and
downstream pipes, but also to the installation errors, associated to several hydraulic
elements/components such as valves, disassembly joints, suction cups, as well as the already
mentioned gaskets.
63
6. Case studies
6.1. Brief description
EPAL is the largest Portuguese water company, not only in customers but also in
volume and network length. The company has five important systems: Alviela, Tejo, Vila
Franca de Xira-Telheiras, Castelo do Bode and Circunvalação systems, which are represented in
Figure 6.1. All the EPAL network length is over 2000 km, nonetheless, considering only the
Alviela, Tejo and Castelo do Bode systems, the driving pipes have more than 700 km of length
and have a nominal production capacity of more than 1 000 000 m3/day of volume flow rate.
Along these three systems, there are two water treatment plants, 31 pumping stations, 28 tanks
and 20 chlorine injection spots.
As the largest water company in Portugal, EPAL provides water to 34 municipalities in
the right Tagus river bank as well as to the entire city of Lisbon. In the Portuguese capital EPAL
is responsible not only for the provision of water but also for the maintenance of all the pipe
network within the city.
Figure 6.1 - EPAL production and transport system (adapted from the theoretical slides of Saneamento, 2012/2013)
Throughout EPAL system there are several flowmeters to assess the in and out flows of
water, providing key, and almost instantaneous, information about the water passing through the
all system. Several problems were detected when the water balances were made. To assess the
importance and causes of these problems, an expert study was undertaken.
The study developed by an expert team of EPAL considered two different main
hydraulic circuits: Castelo do Bode and Vila Franca de Xira circuits (the study was not
developed for the all system but only to a part of it, referred as circuit). These circuits have a
significant importance in the company management: about 90% of the total water volume
comes from the dam of Castelo do Bode, which is pumped in Castelo do Bode pumping stations
64
1 and 2 and about 60% of the water volume is pumped in Vila Franca de Xira pumping stations.
As a result, it is very important to EPAL to estimate, accurately enough, the volume flow rate
passing through for an efficient system management.
Castelo do Bode hydraulic circuit (CBC) connects the Castelo do Bode dam to a
downstream pumping station which pumps water to the Asseiceira water treatment plant. Since
the study developed by an expert engineer team of EPAL concluded that the most likely
unknown phenomena was happening in the flowmeters in the pumping station.
Vila Franca de Xira hydraulic circuit (VFXC) connects the Vila Franca de Xira
pumping station to the A-dos-Bispos tank. Just like in CBC, the problems verified had a large
probability to be associated with the flowmeters in the pumping station.
The physical characteristics of the pipes and the flowmeters were the same of the study
developed in 2009. Regarding the relevant variables of the flow: velocity, pressure and volume
flow rate, several data were available - values used in the 2009 study and recent values,
provided by the management teams.
The procedure developed consisted in several simulations of current conditions. After
that, the obtained results were analyzed to assess the magnitude and origin of the problem. If the
problem magnitude and importance could be dissipated throughout the geometry, the
flowmeters location may be changed. Otherwise a new geometry would be developed in order
to mitigate the detected problems.
The model was considered validated by the intense campaign of experiments presented
and discussed in Chapter 5. Maintaining the features of the experimental tests is valid to assume
that the results provided by the model regarding these two hydraulic circuits will also
correspond to good approximations. Taking into account these hypotheses the results achieved
are presented in the following sections.
6.2. Castelo do Bode hydraulic system
6.2.1. Adopted geometry
The first step developed consisted in the definition of the studied geometry. CFD -
COMSOL has incorporated a tool which allows the user to import a geometry from a CAD
software. Nonetheless, EPAL did not have Castelo do Bode pumping station design draws in a
CAD format, so, it was necessary to draw the geometry in CAD based on the available design
draws. Figure 6.2 represents a small part of Castelo do Bode pumping station.
65
Figure 6.2 - Existing geometry - the orange circle represents the pump location (adapted from EPAL design draws).
Using Auto-CAD, a schematic representation of the facility was developed. Figure 6.3
represents that scheme in two views: a) plan; b) 3D view. Represented by the colour green is the
pump location and the red line represents, in a schematic way, the location of the flowmeter.
a) b)
Figure 6.3 - Schematic representation of the existing geometry in Castelo do Bode pumping station (pump location
identified by the green pipe section; flowmeter identified by the red line; flow direction identified by the blue arrow) - a) Plan; b) 3D view.
The flow arrives by the drive pipe (right/left side of Figure 6.3 a)/b) respectively), and
follows through the pump (represented by the green section) by a vertical pipe in the top of the
drive pipe, Figure 6.4 a). Afterwards, the flow reaches the delivery pipe with a 30º angle,
sidewise, Figure 6.4 d), having passed by two 90º curves, Figure 6.4 b) and c).
66
a) b)
c) d)
Figure 6.4 - Castelo do Bode pumping station - photographs of the different parts of the hydraulic circuit from upstream to downstream (flow direction identified by blue arrows).
The problems detected by the expert team of EPAL were thought to be correlated to the
flowmeters in the pumping station. The problem to be studied corresponded to the flow
disturbances and the way they can influence the flow measurement. Since the flow passes
though a pump, the disturbances from upstream can be disregarded; this is the same to state that
the perturbations caused by the pump are the most significant for this analysis.
The pressure is measured immediately downstream the pump, therefore it was
considered the problem to be well described if the geometry took into account only pipes
downstream of the pump. Hence, the geometry used for simulating the disturbances
corresponded to the one represented in Figure 6.5.
Figure 6.5 - Castelo do Bode modelling geometry - the flowmeter section represented by the red arrow; flow direction identified by the blue arrow.
67
The characteristics of the pipe are presented in Table 6.1 as well as the flowmeters, and
are constant for the majority of the simulations made.
Table 6.1 - Physical characteristic of the main pipes and flowmeter for CBC.
Material Steel
Expansion DN700 to DN800
Remaining pipes DN800
Flowmeter DN800
6.2.2. Simulations
6.2.2.1. Current situation
In order to develop the simulations it is necessary to attend the following procedure: the
first step corresponds to the definition of the geometry, after which is necessary to identify the
characteristics of the fluid (i.e. water); next step consists in the definition of the in and outlet
boundaries; finally it is necessary to specify the mesh and choose if the problem is or not time
dependent.
The geometry used for this simulation was the same presented in Figure 6.5 where the
water flows from the right to the left, as explained in section 6.2.1. The inlet boundary condition
is the pressure measured downstream the pump, that is 9.5 bar, in average. The outlet boundary
condition is the average velocity measured by the flowmeter, i.e. 1.5 m/s. The walls have a no-
slip condition, which states that the fluid does not pass through them, i.e., the walls are
impermeable. The mesh chosen was the normal physics-controlled one and the simulation did
not considered the influence of time, it means a stationary regime. Table 6.2 summarizes the
conditions defined for this simulation.
Table 6.2 - CBC current situation: simulation input values and characteristics.
Inlet 9.5 bar
Outlet 1.5 m/s
Wall No-slip
Mesh Physics-controlled
Flow
Conditions Steady state
In Figure 6.6 are represented the streamlines velocity filed.
68
Figure 6.6 - Streamlines simulation along the hydraulic circuit for the CBC current situation (flowmeter section identified by the red arrow), in m/s.
According to the literature, to guarantee the measurement accuracy the electromagnetic
flowmeters require parallel streamlines. In the flowmeter section, the streamlines appear to be
parallel to each other. This fact would indicate that the flowmeter would present an accurate
measure. However, that is not what was verified.
The velocity distribution across the electrodes cross section of the flowmeter is
represented in Figure 6.7. The velocity distribution across the electrodes section is not
symmetric, as should be expected. The velocity changes largely within the cross section: from
zero near the wall to over 1.7 m/s in the right lower side, where the velocity attains the biggest
value. This behaviour was not expected because the flow passes through two ninety degree
curves after the pump, therefore, it would be reasonable to anticipate that the perturbations
induced by them would be, in practice, nil, according to manufactures experience. Nonetheless
it is important not to forget the second curve has a rotation in the z axis. Therefore, the non-
symmetric cross section seems to be due to the existing geometry.
Figure 6.7 - Velocity distribution simulation in the electrodes cross section for CBC current situation.
69
Using the spreadsheet mentioned in Chapter 5 and presented in Annex C, the error
associated to the flow measure was calculated equal to - 0.71 %. The error verified by EPAL
team of experts was around -1 %. Since the errors are alike the model is considered to give good
results. The differences are due to the simplifications that are characteristics of basic assumption
of the CFD model and to some effects that are not being taken into consideration related to
geometrical simplifications.
6.2.2.2. Proposed situation
In order to get a solution that presents a very low error three different procedures were
possible: changing the geometry and maintaining the values of volume flow rate and pressure,
changing the in and outlet values and maintaining the geometry or change the both aspects. The
chosen procedure was the first one, since the volume flow rate and pressure demanded
downstream would remain the same.
Trough analyses of the results the existing layout would not be enough to guarantee the
dissipation of the perturbations. For that reason, a new pipe, with 20 m of length, was added in
order to make possible the complete dissipation of the disturbances. Considering the flowmeter
in the same location than the previous simulation (i.e. the flowmeter has 24 m of straight pipe
upstream and 4 m downstream), the modelling geometry used is presented in Figure 6.8.
Figure 6.8 - Castelo do Bode proposed modelling geometry - the flowmeter section represented by the red arrow; flow direction identified by the blue arrow (added pipe in red).
The boundary conditions and mesh features are the same presented in Table 6.2. In
Figure 6.9 are represented the streamlines velocity filed.
Figure 6.9 - Streamlines simulation along the hydraulic circuit for the CBC proposed situation (flowmeter section identified by the red arrow), in m/s.
70
In this simulation, the streamlines in the flowmeter cross section appear to be parallel,
hence, the flowmeter should measure without a significant error. The velocity distribution
across the electrodes plan is represented in Figure 6.10.
Figure 6.10 - Velocity distribution simulation in the electrodes cross section for CBC proposed situation.
As it is noticeable the profile presents minor perturbations than the one represented in
Figure 6.7. However, the velocity distribution is still not exactly symmetric. The perturbation, is
still noticeable several meters ahead of the last singularity. For this amount of volume flow rate
and pressure the error associated to this simulation, according to the procedure developed, is
0.37 %.
6.3. Vila Franca de Xira hydraulic system
6.3.1. Adopted geometry
Even though VFXC is not as important as CBC, volume wise, it is one of the most
important facilities for EPAL, in a strategic point of view: all the water which arrives to Lisbon,
and the surrounding municipalities, is pumped in the Vila Franca de Xira pumping stations.
Therefore a careful analysis of this circuit is quite important for the company efficiency.
As mentioned in section 6.2.1, COMSOL has an option which allows the geometry
import form a CAD software. Since Vila de Franca de Xira pumping station is a recent facility,
the design draws were available in a CAD format. The adopted geometry for these simulations
was defined according to the EPAL existing design draws. Figure 6.11 represents the existing
facilities.
Figure 6.11 - Vila Franca de Xira side view from pumping station 2 (adapted from EPAL design draws).
71
The driving pipe is in the image right side. The flow is pumped from the driving pipe,
passes through an S (called horse neck), continues straight ahead, where there is a diameter
reduction followed by the flowmeter. After the flowmeter, there is an expansion, and,
afterwards, the pipe reaches the delivery pipe.
Given that the detected problems were consider to be correlated with the flowmeter
inside the pumping station the same simplifications, and reasons for them, made for the CBC
were regarded valid and, therefore, made for this simulations. This means that the geometry
considered disregards the pump as well as the upstream pipes. Figure 6.12 represents the
modelling geometry for the several simulations made.
Figure 6.12 - Vila Franca de Xira modelling geometry.
The characteristics of the pipes and flowmeters are presented in Table 6.3.
Table 6.3 - Physical characteristic of the main pipes and flowmeter for VFXC.
Material Steel
Expansion/Reduction DN800 to DN500
Remaining pipes DN800
Flowmeter DN500
6.3.2. Simulations
6.3.2.1. Current situation
The procedure described in section 6.2.2 was the same followed for these
simulations. For the several simulations made, while their values may vary, the boundary
conditions remain constant. The same happens with the geometry: regardless the base geometry
(Figure 6.12), some alterations to the geometry can occur from one simulation to another
The existing geometry is the one presented in Figure 6.12. The inlet boundary condition
considered was the pressure measured downstream the pump, right side of Figure 6.12, which
was considered equal to 14.1 bar. The outlet condition was considered as the average velocity,
considering the volume flow rate measured by the flowmeter. The walls were considered
impermeable and the mesh used was the coarse physics-controlled one, while the simulation
was run for the steady state regime. The conditions defined for this simulation are summarized
in Table 6.4.
72
Table 6.4 - VFXC current situation simulation values and characteristics.
Inlet 14.1 bar
Outlet 1.96 m/s
Wall No-slip
Mesh Physics-controlled
Flow
conditions Steady state
In Figure 6.13 are represented the streamlines velocity field. In Figure 6.13, the so
called horse neck (the S shaped pipe, in the right side of the figure) induces a significant
perturbation on the flow: the streamlines cross each other paths in a disorganized behaviour.
When they achieve the reduction cone the streamlines tend to stabilize and became more and
more parallel. In the flowmeter section the streamlines are parallel which, as mentioned before,
is the necessary condition to guarantee the measurement accuracy.
Figure 6.13 - Streamline simulation along the hydraulic circuit for the VFXC current situation, in m/s.
In Figure 6.14 is presented the distribution of the velocity across the flowmeter
electrodes cross section. Comparing it to the one for CBC, Figure 6.7, it is apparent that for
CBC the profile is much more distorted than for VFXC. While in Castelo do Bode there are
several curves and rotations in Vila Franca de Xira the major perturbation to the flow is the
horse neck. Since for the VFXC the flow passes through a reduction cone the flows tends to
stabilize the velocity distribution. For that reason the cross section is an almost constant one.
73
Figure 6.14 - Velocity distribution simulation in the electrodes cross section for VFXC current situation.
To estimate the error associated to this simulation the developed spreadsheet was used,
which resulted in an error of 2.53 %. The error verified by EPAL team of experts was between 2
and 3 %, which means the results of the model are valid. Once again, small differences can be
due to simplifications associated to the CFD model application, to the geometry used and
respective effects, that were disregarded.
6.3.2.2. Proposed situation
As mentioned in section 6.2.2.2, three ways to propose a new solution were available:
either to maintain the geometry/in and outlet values and change the in and outlet
values/geometry, respectively, or change the both. As happened for the CBC situation, the
proposed solution concerned only with the change in geometry. Trough the analyses of the
results the existing layout would not be enough to guarantee the dissipation of the perturbations.
For that reason, a new pipe, with 5 m of length, was added before the reduction cone in order to
make possible the complete dissipation of the disturbances. Considering the flowmeter in the
same location than the previous simulation (i.e. the flowmeter has 8 m of straight pipe upstream
the reduction cone and 4 m downstream the expansion cone), the modelling geometry used is
presented Figure 6.15.
Figure 6.15 - Vila Franca de Xira proposed modelling geometry - the flowmeter section represented by the red arrow; flow direction identified by the blue arrow (added pipe in red).
74
The boundary conditions and mesh features are the same presented in Table 6.2. In
Figure 6.16 are represented the streamlines velocity filed.
Figure 6.16 - Streamlines simulation along the hydraulic circuit for the VFXC proposed situation (flowmeter section identified by the red arrow), in m/s.
In this simulation, the streamlines in the flowmeter cross section appear to be parallel,
hence, the flowmeter should measure without a significant error. The velocity distribution
across the electrodes plan is represented in Figure 6.17.
Figure 6.17 - Velocity distribution simulation in the electrodes cross section for VFXC proposed situation.
As it is noticeable the profile represented in Figure 6.17 is very similar to the one
represented in Figure 6.14. As it happened in section 6.3.2.1 the perturbations are not very
noticeable since the flow passes through the reduction cone. For this amount of volume flow
rate and pressure the error associated to this simulation, according to the procedure developed,
is around 0.22 %.
75
7. Conclusions
7.1. Main conclusions
This work concerns an important and relevant field of knowledge in water supply
companies, the flow measurement. Worldwide, water companies have several instruments in
order to measure the amount of water distributed or just transported. These equipments are quite
vital for the management of those companies since important improvements are made according
to the data provided by the available meters. The data provided by these meters also influences
several tools regarding the management of the system, as the Non Revenue Water (NRW) and
water balances. The NRW is the volume of treated water that is not purchased, despite being
treated water. Therefore the value of this parameter ought to be close to zero, in order to achieve
a higher efficient system. The water balances are important tools to detect leaks throughout the
supply and distribution processes. Both the mentioned tools require accurate measurements,
otherwise these tools loss their importance.
The flow measurement can be also correlated to the system efficiency, both energetic
and related to the treatment plants. Usually, the systems are in part driven by gravity and by
pressure differences which require a pumping station. If the measurement accuracy is
guaranteed it is possible to achieve a higher energy efficiency level in the pumping stations,
which makes possible the working period plan in the lower energy tariffs, depending on the
regularization ability, taking into account the water needs downstream. Regarding the water
treatment plants, and since the process to treat raw water into drinking water requires various
products, and since that procedure is expensive, the accurate information about the in and
outflow to these plants can be carefully monitored in order to minimize the costs without
neglecting the downstream needs.
The main goal of this work was to assess the possible perturbations due to the flow
measurement accuracy. Often, problems involving pressure pipes can be considered as a 2D
problem. However, in this case the turbulence associated to the several perturbations originated
by the geometry, induces problems that need to be deled as a 3D problem. The occurrence of
perturbations in the three orthogonal plans, and its cumulative effects, do not allow the use of a
2D model. This fact yielded in a more complex and toilsome model which had the advantage of
presenting a better and more accurate solution.
Before discussing the results achieved, it is both relevant and important to draw some
assessments regarding the CFD model. The CFD model as a mathematical tool provides good
approximation to the reality. Any physical phenomena is always too complex to be model, even
more when the phenomena is associated to turbulence. Turbulence is a relative poorly studied
phenomena. For that reason the results achieved and the alterations proposed must be
considered accordingly.
76
The spreadsheet developed (Annex C) was a verified procedure that was consistent with
the work developed. In other words, it was found this procedure worked for both the case
studies and experiments. The conclusion that this procedure is plenty valid for other situations
cannot be assumed. To assess about the universal validity of this procedure more tests need still
to be made. Nevertheless, it was found that for the case studies, the results achieved previously
in the 2009 EPAL analyses and now specifically through the experiments and CFD results are
consistent.
Regarding the CBC current simulation, the most relevant conclusion regards the error
calculated by the spreadsheet developed. The results of the model presented an error very
similar to the one verified by the real tests developed in 2009 by the EPAL team of engineers. It
may seem odd that for error of only -1 % causes such problems. This conclusion entails a much
important, since one of the three hypotheses is happening:
- the Asseiceira facility where the outflow flowmeters are in, introduce perturbations, which
leads to a large uncertainty;
- the Asseiceira performance of the outflow flowmeters may have lost accuracy;
- Asseiceira treatment plant loses around 4 % of the raw water that arrives form Castelo do
Bode dam.
Through intensive interaction and discussion with the engineers responsible for the
2009 developed study, it was found that this fact had already been noticed without experiments
and CFD analyses.
Regarding the proposed situation, the geometry advised is not feasible, because the
addition of a 20 m straight pipe is not possible since the layout is built and the space is limited.
However this result intends to assess the installation requirements proposed by the suppliers
(current situation) are not sufficient to dissipate such perturbations.
For the VFXC current simulation the error calculated was of 2.53 %. This value is
accordingly to the error estimated in 2009. Since in 2009, the engineers of EPAL made an
intense test campaign regarding the tight of the pipe, and since it was proved the pipe had no
leaks, the conclusion is that the error is, in fact, associated to the flowmeters and the facilities
where they are inserted.
As already happened for CBC, the proposed geometry for VFXC to minimize the
installation errors is not possible to be implemented since the facility is already built. And the
conclusion reached is the same drawn for CBC: the installation requirements proposed by the
suppliers, in this case the 8º cones, are not sufficient to dissipate the perturbations induced by
the flow passing through the called horse neck.
According to the literature, the accuracy of the flowmeter is guarantee if the streamlines
in the electrodes section are parallel which means a linear flow. According to the results
achieved, the streamlines appear to be parallel. Nevertheless the errors calculated, which proved
77
the errors calculated in 2009, are very significant errors for an equipment with such a high
accuracy. The errors associated to the installation and the geometry are, therefore, a very
important and relevant issue that is not always taken into account by engineers responsible for
the design nor by the teams responsible for the installation of the equipments. If these factors
are not addressed properly the flow measurement is not accurate and the several tools associated
to it lose their importance.
From all remarks made throughout this document, it is reasonable to state that this work
emphasizes the enormous importance of flow measurement for water companies all over the
world, regarding a more efficient and rational management.
7.2. Further developments
The feedback obtained through the large interaction with EPAL engineers, evidenced
that this work is certainly a trigger to new ones, because, and as it happens in all times in
science, a new fact is always the first step to new discoveries. Therefore, in order to provide a
guide of the most relevant studied that need to be undertaken, the following points consist on
relevant further works:
- Considering that all over the world there are several companies which have many problems
with facilities and flowmeters, and since it is obvious that each change has high costs, three
different works are proposed to investigation:
- Develop a model for each type of flowmeters technology (electromagnetic, ultasonic,
ventury) according to each flow measuring range;
- Develop analyses for several types of facilities including different types of singularities,
as curves, valves, bends, among others.
- Develop a well-defined procedure in order to provide an automatic tool which could be
able to present an accurate estimative of the uncertainty flow measurement. Building on
the CFD model and the spreadsheet developed obtain a faster error approximation from a
certain type of geometry, volume flow rate and pressure.
- Since one of the most relevant conclusions was Asseiceira treatment plant could have an
important problem (high uncertainty measurement or leakage), which represents a serious and
problematic finding, it is proposed to develop further experimental tests in order to verify how
the system efficiency can be improved.
- Develop the model of Asseiceira three output flowmeters and study how the different
facilities could affect uncertainty;
- Develop real tests and fine tuning the model;
- Develop a smaller facility to do deep tests in laboratory with significant flow range
conditions;
78
- Develop an intense leak campaign detections with pipes and tanks improvements if
necessary.
79
References
[1]. Abbott, M. B. and Basco, D. R., 1989. Computational Fluid Dynamics - An
Introduction of Engineers. Longman Scientific & Technical, Harlow.
[2]. Associação Portuguesa de Distribuição e Drenagem de Águas. Guia de Contadores
Parte I - Características gerais dos contadores de água.
[3]. Associação Portuguesa de Distribuição e Drenagem de Águas, 2000. Guia de
Contadores Parte II - Condições de Instalação e Critérios de Selecção.
[4]. Bakewell, H. P. and Lumley, J. L., 1967. Viscous sublayer and adjacent wall region in
the turbulent pipe flow. Phys. Fluids 10, 1880-1889.
[5]. Batchelor, G. K., 1967. An Introduction to Fluid Dynamics. Cambridge University
Press, Cambridge, United Kingdom.
[6]. Boussinesq, M. J., 1872.Compl. Rend. Acad. Sci. Paris 72, 256
[7]. Bradshaw, P., 1973. Effects of streamline curvature on turbulent. AGAR-Dograph 169,
AGARD, Paris.
[8]. Braga, F. and Fernandes, M., 2009. Analise de eventuais perdas na rede de adução de
EPAL: casos de estudo. EPAL, Lisboa.
[9]. Cardoso, A. H., 2009. Hidráulica Geral I - Apontamentos complementares das aulas
teóricas. IST, Lisboa.
[10]. Çengel, Y. A. and Cimbala, J. M., 2006. Fluid Mechanics - Fundamentals and
Applications. McGraw-Hill; USA.
[11]. COMSOL 4.3, 2012. COMSOL Multiphysics Reference Guide. USA.
[12]. COMSOL 4.3, 2012. COMSOL Multiphysics User's Guide. USA.
[13]. Drenthen, J. G., Kurth. M., Klooster, J. and Vermeulen, M., 2009. Reducing installation
effects on ultrasonic flow meter. 27th North Sea Measurement Conference, Tonsberg.
[14]. EN 14154-2. Water meters - Part 2: Installation and conditions of use.
[15]. EN 14154-3. Water meters - Part 3: Test methods and equipment.
[16]. Fletcher, C. A. J., 1991. Computational Techniques for Fluid Dynamics. Springer-
Verlag, Berlin.
[17]. Frenzel, F., Grothey, H., Habersetzer, C., Hiatt, M., Hogrefe, W., Kirchner, M.,
Lütkepohl, G., Marchewka, W., Mecke, U., Ohm, M., Otto, F., Rackebrandt, K.-H., Sievert, D.,
Thöne, A., Wegener, H.-J., Buhl, F., Koch, C., Deppe, L., Horlebein, E., Schüssler, A., Pohl, U.,
Jung, B., Lawrence, H., Lohrengel, F., Rasche, G., Pagano, S., Kaiser, A. and Mutongo, T.,
counter curve with a small straight distance from the DN80 flowmeter. Theoretically, this
layout would provide good results for the DN100 flowmeter and bad for the DN80.
Type 2
Perturbation due to vertical curve and counter curve with a large straight distance
from the DN80 flowmeter. Theoretically, this layout would provide good results for the
DN80 flowmeter and bad for the DN100.
Geo
metr
y 4
Type 1 Three plans perturbations.
DN100 flowmeter - colour green.
Perturbation due to vertical curves and
rotation of the vertical orthogonal axis.
B4
To compare the results provided by the model to the ones achieved in the experimental
campaign, an UDV was used in order to measure several velocity profiles that would be
compared to the results provided by the model. If the results were similar the model was
validated. Otherwise it was not.
Annexes B1 to B4 the pipes are represented with four different colours: red, green, blue
and black. These colours represent the existing pipes, the DN100 flowmeter location, the DN80
flowmeter location and the especially made pipes for these test, respectively. Despite the fact
that all the pipes were all made of HDPE, the UDV position was restricted to a few points due
to the length of the probe holder. Otherwise the ultrasonic probe was not able to measure, since
the prove would be always in contact with air. For that reason, the sections identified by the
colour red and marked as A or B were chosen. The flow direction is from the left to the right in
Annexes B1 to B4.
Annex B1 - Geometry 1 (1/2)
Type 1 (mm)
Type 2 (mm)
Annex B1 - Geometry 1 (2/2)
Type 3 (mm)
Type 4 (mm)
Annex B2 - Geometry 2
Type 1 (mm)
Type 2 (mm)
Annex B3 - Geometry 3 layout
Type 1 (mm)
Type 2 (mm)
Annex B4 - Geometry 4 layout
Type 1 (mm)
C1
Annex C - Spreadsheet developed for the calculus of the error of the
cross section correspondent to the flowmeter, provided by the model
As mentioned in Chapter 3, the flowmeter calculates the flow passed through it
according to Figure 3.4. In order to assess what would the volume flow rate measured by the
flowmeter be if the velocity distribution was equal to the one computed by the model, in an
Excel spreadsheet several automatic procedures were implemented.
The first step involved the definition of the limits presented in Figure 3.4. To do so,
Figure 3.4 was placed in a CAD software with an appropriate scale in order to provide several
points which were then used to define equations that corresponded to the limits presented in
Figure 3.4.
The relevant data for this analyses was the data associated to the electrodes cross section
of the flowmeter. The data redrawn from the model was a plan that had the three coordinates, x,
y and z (one of this coordinates was usually the same throughout), and the average velocity, U.
Since the coordinates were associated to the position of each flowmeter, and since the position
would change, as well as the diameter, the procedure need to take into account such factor in
order to provide a rapid and universal method. To do so, the procedure developed consisted in
mathematical manipulation of the axis of the circle in such a way that the diameter was equal to
1. Then, the points of the circle suffered a translation to the point 0,0 as presented in Annex C 1.
Annex C 1 - Figure representing the calculated limits (black continuous lines) analogous to Figure 3.4. Data provided by the model represented by the blue ticks.
Annex C 1 represents only the geometric location of the points provided by the model.
To each two coordinates is associated a velocity. To each limit is associated a certain weight,
therefore, the velocity of the points located near the limits (with a maximum error of 0.5%) was
multiplied by the correspondent weighting factor. Since only a few points satisfied the
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.55 -0.35 -0.15 0.05 0.25 0.45
C2
conditions required this procedure was not enough to provide a good result. Hence, the
subsequent step was the interpolation of the points in between the limits which were then
multiplied by the correspondent weighting factor. This procedure was made for all the limits
except the ones that are closer to the electrodes.
The limits near the electrodes were very difficult to assess. Closely to the electrodes the
weight was not entirely known. For that reason another assumption was made: the factor was
calculated according to the equation presented in Annex C 2. The function represented in Annex
C 2 was defined through experimental data available and it was verified that the results provided
by this method were valid for the case studies. The x variable is the value resulted from the
subtraction of the number of the total data point to the ones that were in the region near to the
electrodes section.
Annex C 2 - Function for the calculus of the factor for the region near the electrodes (blue marks represent the experimental data used in the definition of the function).
Known the remaining factor the calculus of the velocity was made through the sum of
the velocity of each point multiplied by the corresponding weighting factor and dividing the
result for sum of the several weighting factor. The error was then calculated subtracting to the
velocity calculated the velocity used as boundary condition and dividing the result by the value
of the latter ones, as is expressed by equation [C.1].
[C.1]
As mentioned the procedure developed presented good results for the case studies.
Nevertheless, the assumption that the procedure is valid for every other condition is not valid.
To assess if the procedure presents good results for every case, more situations need to be tested
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