Multi-regime Shape Optimization of Fan Vanes

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 3, pp. 407421 (2014)

407

MULTI-REGIME SHAPE OPTIMIZATION OF FAN VANES FOR

ENERGY CONVERSION EFFICIENCY USING CFD, 3D OPTICAL

SCANNING AND PARAMETERIZATION

Zoran Milas, Damir Vuina* and Ivo Marini-Kragi

FESB-Department of Electrical Engineering, Mechanical Engineering and Naval Architecture, University

of Split, R. Boskovica 32, Split, Croatia

* E-Mail: [email protected] (Corresponding Author)

ABSTRACT: An enhanced reverse engineering procedure was developed for roof fan re-design. An original numerical workflow for robust shape optimization based on maximum energy conversion efficiency was developed.

It operates using a sample of multiple operating regimes coupled with CFD simulations. The initial shape solution

was originally obtained in point cloud form by optical 3D scanning and subsequent B-spline based parameterization

of shape. The CFD simulation of the scanned shape using 3D RANS based software was shown to agree very well

with the measured features, experimentally obtained in our lab with the actual initial-shape fan. By manipulating the

control points of parametric curves, the developed evolutionary optimization workflow was subsequently able to

create shape-optimized vanes. This original procedure was applied to cases of constant-thickness and profiled single

curvature vanes, both for single-regime and robust multi-point operating conditions. The corresponding increase in

efficiency gained by our computational procedure was correlated with respective velocity and pressure distributions

and suppression of flow separation. The novel numerical procedure developed here therefore provides a numerical

framework for generic object geometry to re-shape itself autonomously. The change in shape ensures maximum

energy conversion efficiency for a given composition of operating regimes. The gain in efficiency with optimized

vane shapes proves to be significant in the wide range of flow rates around the best efficiency point.

Keywords: CFD, centrifugal fan, shape optimization, performance, efficiency

1. INTRODUCTION

Fans make a significant class of machines

consuming energy if their usage of electric energy

is considered on the large scale. Despite the fact

of usually being small in size or unit power, the

respective energy consumption of these machines

is of growing interest because of their multitude.

The efficiency of these lightweight turbomachines

is getting into the focus since there is a large

margin for respective improvements and

consequently potential for energy consumption

reductions.

In the last three decades, CFD modeling of

turbomachinery flows has evolved from quasi 3D

potential flow models to fully 3D viscous models

(Keck and Sick, 2008; Menter et al., 2004).

The development of computer resources and

efficient numerical codes allowed for the

integration of stationary and rotating

turbomachine components into a common

computational domain. This has eliminated the

need for imposing boundary conditions at the

interfaces between turbomachine components.

The respective influence of the flow in each of the

components can freely propagate upstream and

downstream during the course of calculation,

which requires a proper exchange of flow

variables at the interfaces.

The flow in turbomachines is unsteady due to the

interaction between the rotating and stationary

parts, e.g. between the impeller and the diffuser or

the scrolled housing of centrifugal turbomachines.

Transient modeling at the interface between the

impeller zone and stationary zones (upstream-

downstream) accounts for physical sliding

between these zones. This results in unsteady

flow models in which the velocity and pressure

oscillations are resolved during one impeller

revolution in very short time steps.

Circumferential periodicity can usually not be

assumed and hence the entire impeller must be

modeled. Due to excessive computational time,

this is inappropriate in the design phase (Brost et

al., 2002). The frozen rotor approach is a

compromise whereby the impeller is fixed in a

certain angular position with respect to the

stationary part. The resulting steady flow model is

much simpler for calculation. The prediction of

turbomachine performance using the frozen rotor

simulation is typically fairly good when compared

with transient simulations (Gugau, 2002).

Received: 19 Jan. 2014; Revised: 2 Apr. 2014; Accepted: 2 May. 2014

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 3 (2014)

408

However, the quality of the prediction

deteriorates at flow rates far away from the design

or best efficiency flow rates. The fixed position of

the impeller allows that any non-uniformity at the

impeller outlet is carried away too deep inside the

stationary zone in comparison with experimental

evidence.

Preliminary design or sizing of the turbomachines

is traditionally based on 1D flow analysis and

statistical correlations between dimensionless

parameters that are derived from previous

experimental evidence on high efficient designs

(Bois, 2005; Braembussche, 2005). CFD

calculations have largely replaced elaborate

experiments because they can model details of

very complex geometries.

Numerical optimization using non-gradient,

gradient and especially evolutionary algorithms

has opened entirely new horizons for the

engineering designers, (Arora, 1989; Rao, 1996;

Deb, 2000; Goldberg, 1989; Papadrakakis et al.,

2004; Derakhshan et al., 2013). Adapting

methods and algorithms known from

computational geometry and employing them to

parametrically represent geometric shapes of

objects has provided the missing link between

CFD and numerical optimization, (Hardee et al.,

1999; Dai et al., 2005; Rogers and Adams, 1976;

Bohm et al., 1984; Farin, 1993). These three

basic ingredients, numerical optimization

algorithms, parametric geometry representation

and CFD simulation have been coupled in this

paper to provide full-scale shape optimization of

roof fan vanes.

In complex flow simulations, soft computing

approaches including surrogate models for the

evaluation of excellence and constraints based on

simulation models are applied frequently along

with heuristic optimizers (Taormina et al., 2012;

Zhang et al., 2009; Cheng et al., 2005). These

methods can sometimes replace deterministic

evaluation based on simulations with

corresponding response provided by advanced

numerical approximation methods. Once trained

using corresponding data, methods such as neural

networks can deliver adequate approximation

results very fast. On the other hand, soft

optimizers such as genetic algorithms or particle

swarm methods operate consistently without

gradient information and without getting trapped

in local optima, however demanding more

computational resources. There are numerous

examples of such approaches in different

engineering disciplines.

Traditionally, vanes have been designed for a

predefined nominal operating point. Nevertheless,

the approach developed here has provided for

multi-regime shape optimization as the optimizer

engages the CFD simulator over a range of

regimes. These were generated as a random

sample corresponding to the predicted distribution

of operating regimes of the roof fan. This

approach results in the optimum design for the

overall operation of the fan rather than peak

optimum performance at the nominal point, which

is usually accompanied by a sharp decrease of

performance beyond the nominal point.

The objective was to provide a complete generic

re-engineering procedure. CAD models typically

consist of many interconnected partitioned

geometric entities with corresponding parameters,

relationships and constraints, which are not

appropriate for shape optimization. We have

therefore based our approach on the integral

parametric geometric model to provide a compact

and scalable overall geometric set for the shape

optimization model.

There are several novel aspects of the developed

procedure. The first novel aspect is the shape of

the vane which is modeled using B-spline

surfaces allowing the vane to assume virtually

any shape in 2D or 3D space by manipulating the

corresponding parametric form. The second novel

aspect is the fact that by virtue of the developed

workflow, the vane has the capacity to re-shape

itself autonomously for maximum energy

conversion efficiency. Re-shaping is achieved by

means of an evolutionary optimizer, numerically

coupled with a CFD simulator. The latter is set-up

as a numerical service provided to our

computational workflow by an external node

delivered by independent software. The automatic

re-shaping of generic vanes for maximum energy

conversion efficiency is based on multi-point

operating regimes sampled to represent the

overall life-cycle operation of the fan. Another

novel aspect is the fact that the vane is modeled as

a completely generic shape and its initial

geometry is provided for by optical 3D scanning

of an existing vane for increased numerical

efficiency due to an adequate starting solution.

The response of the CFD simulator and the CFD

model used in the workflow were validated by

carrying out extensive laboratory tests.

Numerical shape optimization of vanes is a rather

complex undertaking as it involves many

challenges. Computational modeling of the

respective geometry is one of the difficulties as it

needs to be capable of modeling global and local

variations of shape by using only a modest-size

data-set of shape parameters, since otherwise the

dimensionality of the subsequent optimization


409

space is very high. CFD models are another major

concern, as appropriate turbulence models and

domain discretization exhibit a major influence on

the simulation results. Numerical integration in

the form of a workflow is another important asset

as it needs to encapsulate both process flows with

synchronization of processes and the necessary

data-mining. The data transfers within the

workflow include results for all candidate

designs, in particular pressure distributions and

velocities in selected regions of the domain. On

the input side of the CFD, the current shapes of

the candidate designs need to be communicated to

the simulators (data-burying). The definition of the excellence criteria is also crucial. As the fan

operates across a range of operating regimes,

single-point shape optimization is of limited

value. More realistic optimization is

accomplished by robust optimization for a given

distribution of the operating regimes. Moreover,

the design variables may include additional

parameters beyond those which control the shape

of the vanes. For example, the rotational velocity

of the fan may be a controllable parameter for all

regimes under the conditions of prescribed flow

rates and output pressure.

The roadmap of the paper includes the following

elements:

- basics of the background physics and CFD models

- basics of numerical modeling of generic shape - key elements of the optimization procedures developed in the paper

- presentation of optimization/simulation cases and discussion of results

2. ROOF FAN DESIGN AND

PERFORMANCE

Roof fans make a significant part of the fan

market, approximately 30% of fans for non-

residential ventilation are roof fans (Radgen et al.,

2008). By unit power they belong to the group of

low power fans, 2 kW of installed power is an

upper limit for most roof fan types. Their overall

efficiency (accounting for the electric motor

losses) rapidly increases with fan size-power. For

most below- kilowatt- range power fans, the peak

overall efficiency ranges between 0.3-0.5.

A specific feature of roof fan design is that the

scroll housing is no longer required. Roof fans

can expel the waste air into the ambient directly

from the impeller, as shown in Fig 1. No volute-

like housing is necessary which is reduced to

being merely a weather shield. It can be a simple

axisymmetrical cap (cowl) above the electric

motor and impeller, such that it doesn't obstruct

the outflow from the impeller. This allows the fan

outflow to be dispersed horizontally above the

roof. Vertical outflow from the roof fan is another

viable solution. A more complex housing is

required in order to divert the radial outflow from

the impeller into the upward swirl-like flow. In

both cases the far field flow conditions are

axisymmetrical.

Fig. 1 Roof fan.

The most indicative fan parameters are the

increase of the total pressure in fan tp and the

fan efficiency . Roof fans belong to the class of exhaust fans without pressure duct. The outlet

dynamic pressure 2/v2oodp for this class of

fans is ignored according to the rules of AMCA,

Eurovent. Correspondingly the expression for

tp reduces to:

VAdpVAdpp iiiAi

ioo

Ao

ot /)v)(v

2

1(/)v( 2

(1)

where op and ip are the static pressures, ov

and

iv

the absolute velocities at the fan outlet oA

and fan inlet section iA respectively, the air

density, and V the volume flow rate. The fan overall efficiency is PpV t /

, where

P is the fan power equal to the electric motor net output. For the purpose of CFD-based prediction

of efficiency , the fan power P is calculated as:

P = mvfdi PPMM (2)

iM is the torque of the aerodynamic (hydraulic)

forces acting on the impeller interior surfaces.

fdM is the torque of the shear stress (friction)

forces on the impeller hub and shroud outer

surface. The last two terms, vP and mP , account

for the volumetric and mechanical losses of

power respectively. Due to modifications to the

roof fan that was investigated in the experimental


410

part of this work, both terms only exhibit minor

impact on the overall efficiency.

The torque of the aerodynamic forces is

calculated by integrating pressure and shear stress

along the walls of the fan impeller according to:

dArpdAnrMM ywyA

fdi )()(

(3)

where n

is the normal vector of the impeller wall

surface A , r

is the corresponding radius vector

and w

is the wall shear stress. Subscript y

indicates the components in the direction of y

coordinate axis coinciding with the axis of

rotation.

CFD prediction of the fan performance has to be

validated by comparing CFD results with

experimental ones. This requires that the fan

geometry and boundary conditions in CFD

analysis are the same as in the experiment. The

elements of geometry required for the simulation

of the centrifugal roof fan impeller with a

horizontal outlet are axisymmetrical hub, shroud

and electric motor with external rotor casing.

Together with the vane, the geometry of impeller

is fully defined as shown in Fig. 2. The fan

geometry data are given in Table 1, and they refer

to the impeller design of the standard roof fan

with backward inclined flat vanes of constant

thickness

For the purpose of more comprehensive

laboratory testing, the standard roof fan was

slightly modified. The supporting structure of the

fan was removed in order to provide an un-

obstructed outflow from the impeller and easy

access for the velocity probe to the impeller outlet

(Fig. 3).

The electric motor of the impeller with an

external rotor was attached to the suspension plate

as in the original design. The suspension plate

affects the flow around the impeller.

Consequently, the flow in the clearance between

the impeller hub and suspension plate had to be

modeled in CFD simulation.

The sealing of the gap between the impeller and

the intake pipe was significantly improved by

using the comb type labyrinth seal. As a result,

the sealing gap flow only had minor impact on the

fan performance, and hence the gap flow was not

modeled in CFD analysis. The intake pipe has the

same diameter as the impeller eye.

The measurements of the velocity close to the

impeller inlet allowed for the control of proper

inlet boundary conditions to be applied in

impeller inlet allowed for the control of proper

inlet boundary conditions to be applied in CFD

Fig. 2 Roof fan impeller.

Table 1 Impeller geometry data.

Impeller diameter (outlet) D (mm) 325

Impeller eye Do (mm) 235

External rotor

(el. motor) der (mm) 138

Impeller width b (mm) 75

Nr. of vanes z 14

Vane outlet angle (O) 45

Vane thickness t (mm) 1,5

Fig. 3 Roof fan laboratory test stand, 1-impeller, 2-

suspension plate, 3-labyrinth seal, 4-intake

pipe, 5-bellmouth with inlet screen.

analysis. A rather uniform inlet velocity

distribution was measured during experiments.

Fig. 3 illustrates the fan characteristics

determined by the measurements in the University

laboratory of fluid mechanics. Angular velocity of


411

the fan impeller was constant throughout the

measurements =103 s-1. The impeller Reynolds number ( /2D ) was about 7E+5, where is the viscosity of air.

The pressure at the fan inlet and from the

(pressure) velocity probes was measured using the

Digitron 2080P differential pressure transducers

with the measuring range of 2500 Pa. The pressure differences were mostly below 100 Pa.

Accounting for the factory calibration of the

transducers, the maximum uncertainty of the

measured pressure was about 1 Pa with 95%

confidence.

The fan flow rate was determined and calculated

by means of the velocity profiles that were

measured in the intake pipe cross section. The air

velocity was measured using the two point Pitot

tube and cross flow probe from Airflow

Instruments and Turboinstitute respectively. The

uncertainty of the calculated flow rates was less

than 25 m3/h. The fan efficiency was determined

based on the net output of the fan electric motor.

The net input electric power was measured by two

meter method using OEL 0120 Watt-meters from Iskra Inc. It was corrected for motor losses using

the motor characteristic as specified by the motor

supplier Marvent-Systemair. The uncertainty of

the calculated fan efficiency was 1%.

The measured pressure and flow rate at the best

efficiency point (BEP) of the experimental fan

were 80 Pa and 1000 m3/h respectively. These

values are assumed to be the design ones for the

optimization procedure in Section 4.

3. CFD MODELING OF FAN FLOW AND

VALIDATION

Numerical modeling of the impeller flow

generally requires a 3D non-stationary viscous

model in order to correctly capture the physics of

the flow for a wide range of flow rates.

The development of boundary layer along the

impeller vanes can be accompanied by the

separation of the leading edge and followed by

reattachment. The rotation and curved vane

passages contribute to the secondary flows

associated with secondary losses.

At off-design conditions the recirculation zones

are large and they affect the impeller flow.

The fan flow is highly turbulent, and the

modeling of turbulence significantly affects the

numerical prediction of separation and swirl flow

as well. In principle, this requires more advanced

turbulence models, e.g. the (direct) Reynolds

stress model. Its numerical complexity usually

restrains the selection to the class of two equation

models of turbulent viscosity: k and k models or their hybrid SST model. In numerical terms, robust 2-eq. turbulence models moderately

contribute to the expansion of the system of

equations governing the flow.

The continuity and momentum equations, as well

as those for the transport of turbulence kinetic

energy k and its dissipation , can be cast into the general transport equation. For the stationary

flow of incompressible fluid the general transport

equation is:

S

xx jj

j

)v( (4)

where is the Reynolds averaged transport

variable, the diffusion coefficient, S the

source-sink term and jv the Cartesian velocity

components ( j =1, 2, 3). For the k turbulence

model , , S are specified as follows:

1,v , ,j k

/,/, ,0 tktE

)( , ,)

v( ,0 21

CPC

kPf

xxx

pS kki

i

j

E

ji

E

in which Ep is the effective pressure

(Ep = 2 / 3 )p k , kP the production of k , E

the effective viscosity consisting of molecular

and turbulent viscosity t . k , , 1C and

2C are the model constants. if stands for

the centrifugal and Coriolis force:

ijjjji xx kjijke v2 in the rotating

reference frame. kv is the relative velocity, i

the angular velocity components and ijke the

permutation symbol.

The second order accurate scheme is used for the

spatial discretisation of convective fluxes in the

finite volume formulation of Eq. (4).

The computational domain required for the CFD

analysis consists of the intake channel, impeller,

and outflow zone as shown in Fig. 4. The

suspension plate which is part of the outflow zone

geometry also has to be modeled since it

influences fluid flow.

The frozen rotor approach is applied to the fan

impeller analysis. Flow inside any of the vane

channels is the same regardless of the impeller

angular position due to the axisymmetric far-field

conditions. The impeller flow can be analyzed in

a single vane channel or impeller segment


412

Fig. 4 Computational domain: a) 3D view, b)

impeller segment.

embedding a single vane, Fig.4.

The stationary flow model can thus be applied to

the segment of the computational domain.

The treatment of boundary conditions for the fan

flow, i.e. along the outlet of the computational

domain is of particular interest. Boundary

conditions must provide for free development of

flow downstream of the impeller outlet (Zhang et

al., 1996; Moradnia et al., 2014) and upstream of

the impeller as well. The computational domain is

therefore extended downstream of the impeller

exit by an additional outflow zone. The constant

pressure boundary conditions are most

appropriate for the flow at the exit from the

outflow zone. The periodical boundary conditions

are imposed in the circumferential direction. An

additional inflow zone upstream of the fan

impeller represents a part of the laboratory intake

pipe. The fan flow rate is prescribed at the inlet

cross section located eight pipe diameters away

from the impeller. The turbulence kinetic energy

and dissipation at the inlet are based on the

turbulence intensity (estimated 5%) and eddy

length scale (equal to the intake pipe diameter)

respectively.

Simulations of the flow were executed using

commercial CFD software (ANSYS). Initially,

SST and k - model were used for modeling

turbulence. The results with standard k - model

agreed better with the experimental ones. In all

simulations further on the standard k - model

with a scalable wall function for smooth walls

was used. Scalable wall functions overcome the

problem associated with lowy values of the

near-wall grid. This occurs either with

excessively fine grids or with moderately refined

grids in the area close to the separation point.

They value of the grid points closest to the wall

can no longer be in the log law region as

presumed by wall functions. Scalable wall

functions limit the y values above the lower

edge of the log layer ( 11y ). The y is

defined by means of the velocity scale *u based

on turbulence kinetic energy2/14/1* kCu .

The grid characteristics are presented in Table 2

and Fig. 5. The optimization described in section

4 is accompanied by many variations in the fan

geometry. In order to keep the meshing

computational effort relatively low, the impeller

is meshed using tetrahedral cells.

Close to the vanes, the impeller grid is refined by

applying prism layers. The structure of the grid

along the periodic boundaries was identical.

Therefore no interpolation was required for

matching the values between the periodic

boundaries.

Fig. 5 Grid characteristics.

Table 2 Grid characteristics.

Sub-domain Grid type Cell

number

Reference

frame

Intake pipe structured,

hexahedral cells 1944 stationary

Impeller unstructured,

tetrahedral cells 51 908 rotating

Outflow zone unstructured,

tetrahedral cells 23449 stationary

The dependence of the solution with regard to the

grid resolution is tested. Fig. 6 shows that grid-

independent solution for the fan efficiency and

pressure is achieved using a grid with N 75000 cells.

The convergence criteria for the solution of the

discretized equations were defined as maximum

residual of 10-4

.

Numerical results for the fan pressure capacity performance follow the slope of the experimental

characteristic as shown in Fig. 7. At the design

flow rate of V = 1000 m3/h fan pressure as predicted by CFD

agrees well with the experimental value. There is

a minor under-prediction of the fan pressure (less


413

than 5%) for partial flows. The standard deviation

of CFD results relative to the experimental

pressure curve is 10%. This is mainly due to

overshooting of the CFD prediction at overflow

rates.

The CFD prediction of fan efficiency deviates

from the experiment almost in the same way as

for the fan pressure. The standard deviation of the

CFD predicted values with respect to

experimental curve is about 10%.

Fig. 6 Impact of grid resolution on CFD prediction of

fan pressure pt and efficiency at V =1000 m

3/h.

Fig. 7 Comparison of experimental fan performance

and CFD prediction for initial design with flat

vanes.

4. PARAMETERIZATION OF FAN VANE

AND OPTIMIZATION

The objective of this paper is enhanced reverse

engineering, whereby the term enhanced refers to

shape optimization of the vanes. Optimum design

refers to changing the shape of some object such

that certain excellence criteria are maximized

within given constraints (Arora, 1989; Rao,

1996). The idea is to use the vanes of the existing

fan as the initial geometric solution for the

process of evolutionary shape optimization, where

different shape representation can be applied

(Hardee et al., 1999; Dai et al., 2005; Rogers and

Adams, 1976; Bohm et al., 1984; Farin, 1993).

The authors of this paper have also studied a

number of parameterizations (Vucina et al.,

2012). The approach applied in this paper is to

use 2D parametric entities to represent shape, in

particular B-spline curves.

A B-spline curve of degree d using (n+1) 2D

control points Q is defined as

,0

( ) ( ) , 0,1n

i d i

i

t N t t

x Q

1

,0

1

, , 1 1, 1

1 1

1 ,( ) , 0

0 ,

( ) ( ) ( ) , 1 , 0

i i

i

i jii j i j i j

i j i i j i

t t tN t i n d

otherwise

t tt tN t N t N t j d i n d j

t t t t

where N are the basis functions defined

recursively using a non-decreasing sequence of

scalars- knots ti:

0 , 0

, 11

1 , 1 1

i

i d

i dt d i n

n d

n i n d

(7)

The B-spline curve possesses the property of local

control since Ni,j(t) have non-zero values only in

the interval [ti, ti+j+1], hence the curve is formed

locally by a few adjacent control points in Q only.

The numerical procedure in this paper starts by

generating B-spline curves that represent the

given existing shape of the blades accordingly,

which provides the initial solution for the

optimizer. The implementation of this step was

carried out numerically by fitting B-spline curves

according to the following procedure. A straight-

forward method of fitting a B-spline curve to a

point cloud which was originally obtained by

optical scanning was used in this paper. The

(m+1) data points P are assumed to be ordered

with increasing sample times sequence sk according to the parameter values according to

0 0( ) / ( )k k mt s s s s .

The curve fitting procedure results in determining

the control points Q such that the least square

error 2

,

0 0

1( ) ( )

2

m n

j d k j k

k j

E N t

Q Q P (8)

is minimized. The minimum of this quadratic

error function is obtained from the corresponding

necessary conditions which results in a linear

system of equations,

,0 0 0

0 , 0, ( )m n m

ki kj j ki k rc c d r

k j k

a a a i n a N t

Q P

Two different approaches were applied to

represent the geometry of the blade. The first

approach is using a B-spline curve to define the

corresponding shape of a constant-thickness

blade. The second approach is engaging yet

(5)

(6)

(9)


414

another B-spline function to represent the

thickness distribution (profile) of a more general

blade with arbitrary shape.

This paper considers 2D shape optimization of the

vanes. Generally, the vane surfaces are double

curvature surfaces (two radii of curvature).

However, due to technological limitations, such

types of vanes are more difficult to fabricate than

single curvature vanes. This paper therefore

initially considers single curvature vanes. The

vane geometry is represented by the single B-

spline curve for the case of constant vane

thickness, although it is later also parameterized

to allow variable vane thickness profiles.

The paper considers both flat (fixed-thickness)

and profiled vanes as these are interesting from

the industrial application point of view. As of the

optimization point of view in this paper, the

model and the algorithms are the same, with the

only difference being that profiled vanes

introduce more shape variables and require non-

penetration constraints for the vane faces

implemented via move limits of the respective

variables.

Genetic algorithms (Deb, 2000; Goldberg, 1989;

Papadrakakis et al., 2004) were applied as multi-

objective numerical optimizers (MOGA) with

SOBOL initialization. Using a multi-objective

optimization algorithm (we have used MOGA-II

algorithm) changes the way in which the

respective fitness value is assigned to an

individual within the population. Instead of

directly using the objective and constraints values

for calculating the fitness, MOGA applies the

formulation based on Pareto optimality.

The optimization variables are the positions of

respective B-spline control points, and the

corresponding outputs are the pressure difference,

efficiency and residuals. The optimization

objective is maximum efficiency. The ranges of

optimization variables were constrained such that

for any current shape of vanes, they physically

remain inside the modeled segment of impeller, i.e. do not penetrate adjacent periodic segments.

The total fan pressure pt has also been constrained such that it must amount to be greater

than 70 Pa and lower than 90 Pa at the flow rate

of 1000 m3/h. Since the total fan pressure for

some geometry changes with the flow rate, this

constraint must be applied only at the nominal

rate and ignored for other flow rates. In addition,

it has been noticed that for some highly curved

and wavy vanes, CFD computation didnt achieve convergence, so those results had to be discarded.

With that in mind, another constraint is the

residual which was restricted to stay below

0.0001.

The shape optimization variables are denoted as

Li as shown in Fig. 8. The variables were hence

the distances of the control points from the x-z

plane. The point L4 (central point of spline closest

to the axis) was fixed such that it is not present in

workflow. This was necessary in order to improve

the numerical efficiency of shape optimization.

Otherwise, equal (in shape) but translated (as

rigid bodies) vanes would be considered different

candidate solutions by the optimizer, thus

deteriorating the convergence properties of shape

optimization. Only the deformation modes

(degrees of freedom) should be allowed for the vanes and the rigid-body motion modes must be prevented from taking place during shape

optimization.

Fig. 8 Parameterization of vane.

Beside the already mentioned input variables,

another one designated as C was added. This

input variable enabled the cutting of the leading

edge of the vane as shown in Fig. 8. Changing

that variable changed the length of vane.

Shape optimization is applied only to the vanes of

fan. The rest of geometry stays unchanged, i.e. the

hub and the shroud remain the same as in the

initial design. While the shape of the vane was

changed, the shape of computational domain also

remained the same. This naturally restricted the

range of change of candidate vane shapes such

that stayed within the computational domain.

Changing the vane shape without changing the

computational domain can be a severe restriction,


415

since it limits the vane between two periodic

boundaries. Numerical tests on the same problem

with the modification as stated next were

conducted to investigate this possible restriction.

The respective modification was that the

computational domain was forced to change in

such a way that the vane is always located at the

center between two periodic boundaries. In order

to do that, the periodic boundaries where

geometrically modeled as B-spline surfaces that

change together with the vane. These test

optimizations yielded the same results as the one

with fixed periodic boundaries. This result

empirically confirms that changing the vane shape

without changing the computational domain

shape is not a severe restriction in the case

presented in this paper.

In order to terminate the optimization procedure,

several convergence criteria in shape optimization

were applied. The optimization process converged

when there was no improvement in the efficiency

during a few generations. Typically for case 1, the

procedure converged after 1000 iterations, as

shown on Fig. 9. If the procedure was continued

only negligible improvements of the energy

efficiency where obtained.

Fig. 9 Fan efficiency () convergence during optimization, Nd- generation.

Several authors have approached the problem of

optimum design of pumps and fans (Derakhshan

et al., 2013) using different sets of design

variables and procedures. Nevertheless, the

method proposed here is highly generic as it

encompasses very flexible modeling of shape,

initial shapes obtained by scanning existing fans,

and robust multi-regime optimization.

The following is the overall procedure developed

in this paper:

1. 3D optical scanning of the existing rotor to provide the point cloud representing the initial

shape solution.

2. Parameterization of the 3D scanned point cloud into computational geometry entities, in

particular B-splines, the control points of which

represent the variables for the optimizer, the

vector x. Optionally, deriving 2D shape

representation for 2D cases.

3. Definition and generation of the numerical sample of operating regimes for the fan,

representative of the future actual distribution.

4. Definition of the excellence criteria and objective functions for the optimizer such that the

fitness functions for the candidate designs can be

evaluated, in particular the efficiency of energy

conversion, base on (1)-(2). This leads towards

the ultimate objective of this paper, re-engineered

fan vanes for maximized energy conversion

efficiency under the circumstances of multi-

regime operation.

5. Definition of the optimization constraints, for example bounds for control points mobility.

6. Launching the genetic algorithms- based optimizer with corresponding operators and

parameter values, including selection operators,

cross-over operators and probabilities, mutation,

elitism, fitness scaling, etc.

7. Linking an array of CFD simulators to provide values of excellence and constraints for all

candidate designs represented by corresponding

B-splines curves, across the numerical sample of

flow regimes.

8. Iteratively shape-optimizing the vanes within the numerical cycle embedding the optimizer,

shape modeler and CFD simulators.

Fig. 10 Shape optimization variables, vanes with

constant thickness, (MODEFRONTIER).


416

Since the paper considers 2D shape optimization,

there is a vector of shape variables (L_i and C) as

shown in Fig. 10 and the following is the list of

entities in the figure:

Q flow rate O_residual - output variable from ANSYS,

residual

O_DP - output variable from ANSYS, fan

pressure pt O_ef - output variable from ANSYS, fan

efficiency

C_residual - constraint of residual

C_DP - constraint of pressure

B_ef - optimization goal, maximum efficiency

DOE- generator of initial population designs

MOGA-II- multi-objective genetic- algorithm

based optimizer

ANSYSWB74- CFD simulator

The paper goes beyond applying optimization and

CFD codes, as particular codes are not of any

significance here. The actual contributions of the

paper are in fully generic modeling of vane shape

by using parametric surfaces, in particular B-

splines to model vanes rather than some physical

parameters of vanes as it is usually done.

In the basic vane shape optimization approaches

that have been used in other papers only a few

physical features of the vane were varied as shape

optimization variables. Many authors use for

example inlet and outlet vane angles, curvatures

and locations of vane edges as shape variables.

Such variables, while physically sound and

intuitively reasonable, provide very limited shape

modeling capacity, hence the generic geometric

modeling developed here is superior in terms of

modeling freedom.

Use of fully generic modeling of vane shape

enables the optimizer to generate almost arbitrary

geometric shapes and evaluate those using

instances of CFD simulation software operating

on submitted candidate shapes. The developed

generic geometry modeling is adjustable to

particular local requirements. It can range from

basic global shape to high fidelity in local shape

phenomena with corresponding sizes of

parametric sets and resulting dimensionalities of

optimization space.

In order to accomplish this procedure, middle-

ware software was needed for data mining and

coordination of the applications in the numerical

workflow. In a generic numerical workflow, any

optimizers and CFD codes can operate jointly.

Beyond commercial off-the-shelf software,

proprietary and in-house codes have also been

used as well. In-house simulators implementing

the described turbulent model and physical model

equations can be plugged in as the simulation

node in the workflow in Fig. 10.

With more advanced models, the multi-objective

model generally also includes further terms as

objective functions such as the pressure difference

(which may simultaneously be both a constraint

and an excellence criterion), generated noise (both

in absolute terms and respective distribution),

physical dimensions, etc. It is obvious that these

individual excellence criteria are not concurrent.

They can generally be modeled (i) based on the

weighted sum approach with the a-priori

compromise formulation, (ii) using the Pareto

approach and a-posteriori decision-making.

Both the cases of flat (fixed-thickness) and

profiled vanes were considered. In terms of

operating conditions, single-point (nominal)

operation and multi-point (robust) optimization

scenarios were implemented.

In the real world, fans are used not only for one

flow rate, but within some range close to its best-

efficiency flow rate. Multi-point optimization is

developed here to provide the best vane shapes

that will be more energy efficient during the

course of real life application of the fan. In order

to specify such operational flow rate range, one

can use statistical distributions defined by mean

flow rate and corresponding standard deviations.

The particular distribution used in the paper is the

normal distribution with mean flow value of 1000

m3/h and with standard deviation of 150 m

3/h.

During the optimization process, each candidate

design was evaluated in 10 simulations using

different flow rates. Each design was evaluated

using flow rate values which were elements of a

numerical sample generated randomly based on

the defined normal distribution. In some of the

optimization cases considered the vanes thickness

distribution was another design degree of

freedom. The workflow in that case needs to

accommodate additional shape variables.

Table 3 Optimization cases and specifics.

Index Vane shape Optimized Constraints

Case 1 flat, const.

thickness N

design

flowV =1000 m3/h

Case 2 curved, const.

thickness Y

optimized for

V =1000 m3/h

Case 3 curved, const

thickness Y

optimized for range

of flows

Case 4 curved, variable

thickness Y

optimized for

V =1000 m3/h


417

5. RESULTS OF OPTIMIZATION

In order to distinguish among the results of

optimization the following indexing is applied in

Table 3 and related to the individual shape

optimization scenarios for maximum energy

conversion efficiency:

The case 1 is not interesting in itself, but it

provides the nominal reference values for

benchmarking with optimized vanes. It also

serves the purpose of validation of the CFD

model based on actual experimental results from

our lab.

Pressure and efficiency characteristics of the fan

with vanes optimized for single flow rate (case 2)

are compared with the initial design (case 1) in

Fig. 11. The fan pressure performance curve is

much steeper and the respective efficiency

decreases rapidly at overflow. The flow rate at

best efficiency point (BEP) is slightly lower than

the design flow rate (1000 m3/h).

Fan efficiency close to BEP flow rate is higher.

An increase in peak efficiency (almost 10%) is

much larger than case 1 CFD overshooting. This

implies that the optimization has actually

provided a better design of the impeller vanes.

Fig. 11 Comparison of fan performance for initial flat

vane design (case 1) and optimized vanes (case

2, case 3), design/mean flow rate V =1000 m

3/h.

Fig. 12 Flat vane (case 1) and optimized vane (case 2).

The vane of the optimized fan (case 2) shown in

Fig. 12 is almost flat close to the leading edge and

gradually changes into being curved towards the

impeller outlet. The vane outlet angle is smaller

(380) compared with the flat vane design (45

0).

The effect of vane shape optimization on the flow

pattern is of interest. Particularly those aspects of

the flow related to the losses in vane passages.

Fig. 13 presents the wall shear stress distribution

on both sides of the impeller vane for the initial

case 1 and optimized shape, case 2. The analysis

reveals the areas of low shear stresses that may

potentially be accompanied by the separation of

flow.

Fig. 13 Wall shear stress contours along vane surface:

a) case 1- flat vane, b) case 2-, press.- vane

pressure side, suct.- vane suction side, LE-

vane leading edge, TE vane trailing edge.

Therefore a detailed analysis of the velocity field

in various cross sections of the vane passage was

carried out at the design flow rate. The cross

sections were arranged as planes normal to the

axis of rotation and located at distance y from the impeller hub. Fig. 14a shows that separation

occurs at the vane suction side close to the shroud

outlet (y =0,75 b2) for the initial flat vane (case 1). There is a large recirculation zone near the

vane passage outlet. For the optimized vane shape

(case 2), the separation is almost completely

suppressed in this area as shown in Fig. 14b.

Fig. 14 Velocity vector plot around flat vane (case 1)

and optimized vane (case 2) in x-z plane

normal to axis of rotation, located at distance

y =0,75 b2 from impeller hub.


418

The suppression of separation contributes to the

higher efficiency obtained by the optimized vane

shape (case 2). No separation close to the vane

leading edge can be identified for both vane

shapes.

The pressure distribution along the vane suction

side in Fig. 15 has changed locally, but the

streamwise pressure gradients in the area of

suppressed separation is the same. There is no

area of the minimum pressure stretching along the

vane leading edge as in case 1 and this indicates

that better inflow to the optimized vane is

achieved.

Fig. 15 Pressure distribution on vane suction side: a)

case 1, b) case 2.

The optimization of the vane shape for the range

of flow rates centered at the mean value of 1000

m3/h (case 3) results in negligibly lower peak

efficiency compared to case 2 in Fig. 11. The top

of the efficiencycapacity curve is more rounded and the BEP flow rate is the same as for the flat

vane impeller.

The curvature of the vane (case 3) changes

gradually from the leading to the trailing edge as

shown in Fig. 16. The vane outlet angle is

somewhat smaller than for the vane optimized for

single value of flow rate (case 2). The velocity

pattern in the cross section close to the shroud

(Fig. 17) is almost the same as in Fig. 14b and

there is no indication of separation.

Fig. 16 Flat vane (case 1) and vane optimized for multi

values of flow rates (case 3).

Fig. 17 Velocity vector plot around optimized vane

(case 3),y =0,75 b2.

By allowing the variable thickness distribution of

vane, the highest efficiency was obtained for the

vane shape (case 4) in Fig. 18. The thickness of

the vane has been increased in the mid-section but

has remained almost the same at the leading-

trailing edge. The inner part of the vane profile is

wedge-like with respect to the inflow, while the

outer part is tapered. The vane outlet angle is 330

being the smallest one among those for the

optimized vane shapes.

Fig. 18 Constant thickness vane (case 2) and profiled

vane (case 4, variable thickness vane)

optimized for design flow rate of V =1000 m

3/h.

The profiled vane (case 4) provides the highest

fan efficiency not only at the BEP (=55%) but almost in the entire range of flow rates as shown

in Fig. 19. The BEP flow rate is the same as for

case 2 and the corresponding fan pressure of 95

Pa is higher than any of BEP pressure values of

the optimized designs.

The overall structure of the novel numerical

procedure developed in this paper is presented

integrally in Fig. 20. The blade is modeled as a

general geometric entity by applying B-spline


419

surfaces and can assume any shape. The genesis

of new physical designs of blade shapes is

accomplished by the evolutionary optimizer,

taking into account the given geometric feasibility

conditions (e.g. no self-intersecting curves or

surfaces). The corresponding genotypes are

decoded into phenotypes representing 3D shapes

via parametric surfaces and fed into the overall

physical model of the blade and rotor geometry.

Subsequently, the respective geometry is

submitted for CFD simulation for a given sample

of flow regimes. Such a workflow provides for

robust shape optimization. Numerical efficiency

is achieved by starting from an existing shape

design acquired by optical 3D scanning,

partitioning and parameterization into

mathematical surfaces.

Fig. 19 Effect of profiled vane (case 4) on fan

performance (case 2: fan optimized with

constant vane thickness).

Fig. 20 Shape re-engineering workflow for optimized

energy conversion.

The excellence criterion thereby is the maximum

efficiency of energy conversion at the blade for

multiple randomly sampled flow regimes. Hence

the workflow in Fig. 20 will let the blade re-shape

itself towards optimal geometry for the given

composition of regimes, leading to the

respectively optimal shape for the overall

lifecycle-based energy conversion efficiency.

6. CONCLUSIONS

The proposed approach develops a numerical

system which successfully implements shape

optimization of fan vanes combined with CFD

simulation and parameterization of 3D scanned

vanes as the initial shape solution. The procedure

developed in the paper proves that it is indeed

possible to have a numerical procedure that

autonomously re-engineers the shape of the

vanes. It does this for maximum energy

conversion efficiency, and for the assumed multi-

regime operation distribution.

The procedure develops a path towards

customization and individualization of energy

conversion devices based on optimization for the

particular operating environment.

The numerical optimization code and CFD code

have been coupled for the purpose of modifying

the roof fan impeller shape according to the given

excellence criteria. The CFD code used for the fan

flow analysis has been validated by experiment.

Fan characteristics predicted by the CFD code

were compared with those obtained by laboratory

experiments in the test facility set up for that

purpose. Very good agreement between the CFD

prediction and experiment is demonstrated.

The SST turbulence model with automatic wall

functions has not provided better agreement with

experimental results compared to the k model with scalable wall functions. Both turbulence

models over-predict the fan pressure and fan

efficiency at overflow.

The optimized fans have a higher peak efficiency

( = 5-10%) compared to the initial design with flat vanes. The increase in efficiency is achieved

with optimized vanes of curved 2D shape. This

increase is consistent with the suppression of

separation of flow in vane passages that was

noticed in the velocity field analysis.

The outlet angle of the optimized vanes is smaller

in comparison with the initial flat vane design.

However, the vane inlet angle remained almost

unchanged. Trimming of the vane leading edge

was allowed but only minor displacement of the

leading edge was noticed as the result of

optimization. The meridional section of the

impeller was kept unchanged during optimization

as well as the number of impeller vanes.

The most promising optimized vane shape is the

one obtained for the given range of flow rates. It

displays almost constant curvature and this


420

modification of the flat vane design can be easily

implemented in fan fabrication.

The peak efficiency of the optimized fans still

leaves room for further improvements. Based on

the promising results of the current study, the

planed future work will include full 3D stationary

regime simulations. It will include additional

degrees of freedom including a variable number

of vanes and controllable fan rotational speed.

This will be implemented using the concept of

robust optimization for a selected distribution of

operating regimes.

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FiguresFig. 1 Roof fan.Fig. 2 Roof fan impeller.Fig. 3 Roof fan laboratory test stand, 1-impeller, 2-suspension plate, 3-labyrinth seal, 4-intakepipe, 5-bellmouth with inlet screen.Fig. 4 Computational domain: a) 3D view, b)impeller segment.Fig. 5 Grid characteristics.Fig. 6 Impact of grid resolution on CFD prediction offan pressure Dpt and efficiency h at V& =1000m3/h.Fig. 7 Comparison of experimental fan performanceand CFD prediction for initial design with flatvanes.Fig. 8 Parameterization of vane.Fig. 9 Fan efficiency () convergence during optimization, Nd- generation.Fig. 10 Shape optimization variables, vanes with constant thickness, (MODEFRONTIER).Fig. 11 Comparison of fan performance for initial flatvane design (case 1) and optimized vanes (case2, case 3), design/mean flow rate V& =1000m3/h.Fig. 12 Flat vane (case 1) and optimized vane (case 2).Fig. 13 Wall shear stress contours along vane surface:a) case 1- flat vane, b) case 2-, press.- vanepressure side, suct.- vane suction side, LEvaneleading edge, TE vane trailing edge.Fig. 14 Velocity vector plot around flat vane (case 1)and optimized vane (case 2) in x-z planenormal to axis of rotation, located at distanceDy =0,75 b2 from impeller hub.Fig. 15 Pressure distribution on vane suction side: a)case 1, b) case 2.Fig. 16 Flat vane (case 1) and vane optimized for multivalues of flow rates (case 3).Fig. 17 Velocity vector plot around optimized vane(case 3), Dy =0,75 b2.Fig. 18 Constant thickness vane (case 2) and profiledvane (case 4, variable thickness vane)optimized for design flow rate of V& =1000m3/h.Fig. 19 Effect of profiled vane (case 4) on fan performance (case 2: fan optimized with constant vane thickness).Fig. 20 Shape re-engineering workflow for optimized energy conversion.

TablesTable 1 Impeller geometry data.Table 2 Grid characteristics.Table 3 Optimization cases and specifics.

1. INTRODUCTION2. ROOF FAN DESIGN ANDPERFORMANCE3. CFD MODELING OF FAN FLOW ANDVALIDATION4. PARAMETERIZATION OF FAN VANEAND OPTIMIZATION5. RESULTS OF OPTIMIZATION6. CONCLUSIONSREFERENCES

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Multi-regime Shape Optimization of Fan Vanes

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