Dynamic weighing calibration method for liquid flowmeters - A new approach

Dissertation zur Erlangung des akademischen Grades

Doktoringenieur (Dr.-Ing.)

vorgelegt der

Fakultät für Maschinenbau der

Technischen Universität Ilmenau

von Herrn

Dipl.-Ing. Jesus Jaime Aguilera Mena geboren am 16.09.1979 in Durango/Mexiko

Tag der Einreichung: 13.12.2011

Tag der Verteidigung: 14.06.2012

Doktorvater: Univ.-Prof. Dr.-Ing. habil. Thomas Fröhlich / TU Ilmenau

2. Gutachter: Dir. u. Prof. Dr. Roman Schwartz / PTB Braunschweig

3. Gutachter: Univ.-Prof. Dr.-Ing. habil. Tino Hausotte / FAU Erlangen-Nürnberg

urn:nbn:de:gbv:ilm 1-2012000461

Contents

CONTENTS

1. INTRODUCTION l

1.1 The importance of fluid flow measurements 1

1.2 Motivation of the research work 2

1.3 Structure of the research work 2

2. CURRENT SITUATION AND GOAL OF THE RESEARCH WORK 4

2.1 Definition of mass and volumetric flow 4

2.2 Definition of a flowmeter 5

2.3 Traceability chain of fluid flow measurements 7

2.4 Working principle of a liquid flow primary standard 8

2.5 Current situation 11

2.5.1 Gravimetric and volumetric flying start-and-stop

liquid flow primary standard 11

2.5.2 Gravimetric and volumetric standing start-and-stop

liquid flow primary standard 12

2.5.3 Dynamic level gauging volumetric

liquid flow primary standard 14

2.5.4 ISO dynamic gravimetric liquid flow primary standard 15

2.5.5 Dynamic weighing liquid flow primary standard

with immersed pipe 17

2.5.6 Dynamic weighing liquid flow primary standard

assisted by an in-line flowmeter 18

2.6 The proposed dynamic weighing

liquid flow primary standard 20

3. INPUT SIGNAL, MODELING OF THE DYNAMIC WEIGHING

LIQUID FLOW STANDARD AND THE

CONNECTING VOLUME EFFECT 2 2

3.1 Input signal 24 3.1.1 Collected water mass force 24

3.1.2 Hydrodynamic force 25

3.1.3 Buoyancy force 27

3.1.4 Total fluid force and its block diagram representation 27

3.2 The weighing system and its numerical representation 28

3.2.1 Spring force 30

3.2.2 Inertial force and system total mass 31

3.2.3 Damping force 32

3.2.4 1-Degree-of-Freedom motion equation of the weighing system 33

3.2.5 Technical considerations in regards to the modeling

of the weighing system 37

3.2.6 General representation of the weighing system internal filter

and the discrete time representation of its output signal 38

3.3 The connecting volume effect in liquid flow measurements 42

3.3.1 Accuracy considerations in relation to

the connecting volume effect in dynamic liquid flow measurements 46

FILTERING TECHNIQUES FOR THE DETERMINATION

AND ACCURACY OF MASS FLOW RATE (PROCESS MODEL) 49

4.1 Derivation of a process noise filter for the attenuation of

the hydrodynamic force effect upon the balance output response

and the determination of mass flow rate 51

4.2 Proposed filter algorithms for an improved mass flow rate

calculation based on the identification and

reduction of measurement noise 57

4.2.1 Central moving average filter 58

4.2.2 Least-Mean-Square adaptive filter 60

4.2.3 Linear Kaiman filter 65

4.3 Summary 73

NUMERICAL DETERMINATION OF MASS FLOW RATE

AND THE RESPONSE OF THE DYNAMIC WEIGHING

LIQUID FLOW STANDARD 74

5.1 Fluid forces acting upon the weighing system (input signal) 75

5.2 Frequency response of the weighing system 77

5.3 Continuous time and discrete time response of the balance 81

5.4 Hydrodynamic force filter 85

5.5 Proposed measurement noise filters 87

5.5.1 Central moving average filter 87

5.5.2 Least-Mean-Square adaptive filter 89

5.5.3 Linear Kaiman filter 91

5.5.4 Summary 95

5.6 The influence of the data sampling frequency

Contents

and the low pass filter cutoff frequency upon the mass flow rate

estimate values and its measurement accuracy enhancement 96

6. EXPERIMENTAL RESULTS 102

6.1 Transfer standard used for the liquid flow comparison 102

6.2 Data acquisition system 104

6.3 Implementation of an accelerometer to detect

the initial time of the measurement process 105

6.4 Usage of a non-contact laser displacement sensor to

characterize the water jet impact height 107

6.5 Characterization of the weighing system's stiffness

and damping coefficients 109

6.6 Results I l l

6.6.1 Hydrodynamic force filter 112

6.6.2 Analytical and experimental estimation of the hydrodynamic force 114

6.6.3 Estimation of the collected mass force 115

6.6.4 Time offset correction 117

6.6.5 Summary 122

7. CONCLUSIONS AND OUTLOOK 126

NOMENCLATURE 130

REFERENCES 135