CHARACTERIZATION of TURBOCHARGER PERFORMANCE and SURGE in a NEW EXPERIMENTAL FACILITY
Thesis
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By Gregory David Uhlenhake, B.S. Graduate Program in Mechanical Engineering
The Ohio State University 2010
Master‟s Examination Committee: Dr. Ahmet Selamet, Advisor Dr. Rajendra Singh Dr. Philip Keller
Copyright by Gregory David Uhlenhake 2010
ABSTRACT
The primary goal of the present study was to design, develop, and construct a cold turbocharger test facility at The Ohio State University in order to measure performance characteristics under steady state operating conditions and to investigate surge for a variety of automotive turbocharger compression systems. A specific turbocharger is used for a thermodynamic analysis to determine facility capabilities and limitations as well as for the design and construction of the screw compressor, flow control, oil, and compression systems. Two different compression system geometries were incorporated.
One system allowed performance measurements left of the compressor surge line, while the second system allowed for a variable plenum volume to change surge frequencies.
Temporal behavior, consisting of compressor inlet, outlet, and plenum pressures as well as the turbocharger speed, is analyzed with a full plenum volume and three impeller tip speeds to identify stable operating limits and surge phenomenon. A frequency domain analysis is performed for this temporal behavior as well as for multiple plenum volumes with a constant impeller tip speed. This analysis allows mild and deep surge frequencies to be compared with calculated Helmholtz frequencies as a function of impeller tip speed and plenum volume.
ii The steady state performance data was used as an input to a lumped parameter model which was implemented to predict the overall system dynamics during surge with simplified geometry consisting of a compressor, duct, and plenum. In addition to the comparison between the lumped parameter model and experimental results, a parametric study of the time lag constant is performed to examine its effect on the system predictions.
Experimental mild surge frequencies were found to be similar to the calculated
Helmholtz frequency, while deep surge frequencies were 63-82% of the Helmholtz frequency depending upon the load control valve setting. The model matched the measured plenum pressure amplitudes well; however, the predicted plenum pressure frequencies were slightly higher than the experimental results. Some of the reasons for the deviation from experimental results include map extrapolations, system inputs, and the simplifications in the model geometry relative to the experimental setup. Overall, the primary goal of developing a bench-top capability to measure steady state performance characteristics and unsteady surge was achieved, while also providing a comparison with a lumped parameter model using simplified geometries.
iii
Dedicated to my family
iv
ACKNOWLEDGEMENTS
I would like to thank my advisor, Prof. Ahmet Selamet, for his assistance and guidance throughout my Master‟s studies. I am in debt to Prof. Selamet for his patience, enthusiasm, and dedication throughout my research and correcting this thesis. I would also like to express thanks to Prof. Rajendra Singh for his time to serve as a member of the examination committee. I am grateful to Rick Renwick, Tom McCarthy, and
Dr. Kevin Tallio of the Ford Motor Company along with the College of Engineering for providing support to build the turbocharger test facility at The Ohio State University.
Additionally, I would like to thank Dr. Philip Keller at BorgWarner Inc. for providing the turbochargers and technical information used in this study, reviewing this thesis, and serving as a member of the examination committee.
For the past two years, I have had the opportunity and privilege of working with an extraordinary group of people at the Center for Automotive Research. I would like to thank Don Williams for his support throughout the project in component design and manufacturing. Additionally, special thanks go to Cam Giang, Ricky Dehner, Asim
Iqbal, Hyunsu Lee, Dr. Emel Selamet, and Kevin Fogarty for their help through various stages of the study. I am also grateful to Frank Ohlemacher for his assistance and time interacting with various contractors and the facilities department of the university while
v building the turbocharger test facility. Finally, I would like to thank Dr. Shawn Midlam-
Mohler for his assistance with LabView and Prof. Michael Dunn and his associates for taking time to discuss certain data acquisition principles.
Last, but certainly not least, I would like to thank my family for their constant support and encouragement throughout my entire academic career.
vi
VITA
November 12, 1985……………………….Born - St. Henry, Ohio
2008……………………………………….B.S. Mechanical Engineering, The Ohio State University
2009 – Present…………………………….Graduate Research Associate, The Ohio State University
PUBLICATIONS
Heydinger, G., Uhlenhake, G. D., Guenther, D., and Dunn, A.L., 2008, “Comparison of Collision and Noncollision Marks on Vehicle Restraint Systems.” SAE Paper 2008-01- 0160.
Uhlenhake, G. D., Dunn, A. L., Guenther, D. A., Heydinger, Gary, and Heydinger, Grant, 2009, “Vehicle Coast Analysis: Typical SUV Characteristics,” SAE International Journal of Passenger Cars - Mechanical Systems 1, 526-535.
FIELDS OF STUDY
Major Field: Mechanical Engineering
vii
TABLE of CONTENTS
ABSTRACT ...... ii
ACKNOWLEDGEMENTS ...... v
VITA ...... vii
LIST of FIGURES ...... x
LIST of TABLES ...... xxiii
NOMENCLATURE ...... xxiv
1. INTRODUCTION ...... 1
1.1 Background ...... 1 1.2 Literature Review ...... 3 1.3 Objective ...... 15 2. DESIGN of EXPERIMENTAL SETUP ...... 16
2.1 Turbocharger Operating Ranges and Thermodynamic Analysis ...... 16 2.2 Compressor Selection ...... 28 2.3 Control Valve Design ...... 31 2.4 Flow Meter Design ...... 36 2.5 Oil System Design ...... 46 2.6 Data Acquisition and Control System and Instrumentation Selection ...... 48 2.7 Turbine and Compressor System Geometry ...... 52 3. LUMPED PARAMETER MODEL ...... 58
3.1 Literature Review ...... 59 3.2 Selected Model, Assumptions, and Method of Calculation ...... 69 3.3 Model Results without a Time Lag ...... 71
viii 3.3.1 Time Step Validation ...... 72 3.3.2 Comparison of Model Results without a Time Lag with Fink (1988) ...... 76 3.4 Model Results with a Time Lag ...... 85 3.4.1 Time Step Validation ...... 85 3.4.2 Time Lag Constant Study and Comparison with Experimental Results ...... 88 4. EXPERIMENTAL RESULTS...... 94
4.1 Small and Large “B” Compression System Geometries ...... 94 4.2 Small and Large “B” Performance Characteristics ...... 96 4.3 Mild and Deep Surge Temporal Behavior ...... 101 4.3.1 Temporal Behavior - U 230 m/s, Full Plenum Volume ...... 107 4.3.2 Temporal Behavior - 310 m/s, Full Plenum Volume ...... 127 4.3.3 Temporal Behavior - 370 m/s, Full Plenum Volume ...... 139 4.3.4 Temporal Behavior – Full Volume Summary ...... 155 4.3.5 Temporal Behavior – Variable Volume and Speed Study ...... 156 5. COMPARISON BETWEEN MODEL and EXPERIMENTAL RESULTS ...... 161
5.1 Performance Characteristic Input into the Model ...... 161 5.2 Model Inputs ...... 167 5.3 Comparison between Model and Experiments ...... 169 5.3.1 Stable - Point (1) ...... 170 5.3.2 Mild Surge – Point (2) ...... 173 5.3.3 Deep Surge – Point (3) ...... 177 6. CONCLUDING REMARKS ...... 182
APPENDIX A: EXPERIMENTAL RESULTS WITH VARIABLE VOLUME and U 310 m/s ...... 187
APPENDIX B: NON-DIMENSIONAL CHARACTERISTIC FIT COEFFICIENTS for SECTION 5.1 ...... 200
REFERENCES ...... 201
ix
LIST of FIGURES
Figure 1.1: Turbocharger-Engine System Schematic (Rammal and Abom, 2007) ...... 2
Figure 1.2: Typical Compressor Map (Baines, 2005)...... 5
Figure 1.3: Typical Turbine Efficiency Map (Baines, 2005)...... 6
Figure 1.4: Typical Turbine Mass Flow Map (Baines, 2005) ...... 6
Figure 1.5: Stall and Surge Characteristics (Cumpsty, 1989) ...... 9
Figure 1.6: Typical Centrifugal Compression System ...... 10
Figure 2.1: Typical Turbocharger Compressor Operating Ranges (Baines, 2005) ...... 17
Figure 2.2: BorgWarner K03 Turbine Efficiency Map ...... 19
Figure 2.3: BorgWarner K03 Turbine Mass Flow Map ...... 20
Figure 2.4: BorgWarner 1880 DCF Compressor Map and 10.92 kW Line ...... 24
Figure 2.5: Facility Schematic ...... 27
Figure 2.6: Quincy QSI-750 Screw Compressor ...... 30
Figure 2.7: QSI-750 Screw Compressor Performance Characteristic (0.42 kg/s at 8.48 bar – 298 K and 1 bar inlet) ...... 31
Figure 2.8: Segmented Ball Valve with Actuator and Controller ...... 33
Figure 2.9: Turbine Flow Control Valve Capability with Accumulator at 110 psig ...... 33
Figure 2.10: Turbine Flow Control Valve Capability with Accumulator at 75 psig ...... 34
Figure 2.11: Compressor Load Control Valve Capability ...... 35
Figure 2.12: Orifice Flow Meter Installation (Miller, 1996) ...... 36
Figure 2.13: ANSI 2530 Straight Length Req. for Maximum Accuracy (Miller, 1996) ...41
Figure 2.14: Orifice #1 (57.15 mm) Comparison ...... 42 x Figure 2.15: Orifice #2 (50.80 mm) Comparison ...... 42
Figure 2.16: Orifice #3 (41.91 mm) Comparison ...... 43
Figure 2.17: Orifice #4 (31.75 mm) Comparison ...... 43
Figure 2.18: Orifice #5 (22.86 mm) Comparison ...... 44
Figure 2.19: Orifice #6 (17.27 mm) Comparison ...... 44
Figure 2.20: Orifice #7 (15.49 mm) Comparison ...... 45
Figure 2.21: Oil System Schematic ...... 48
Figure 2.22: Small “B” System ...... 54
Figure 2.23: Large “B” System ...... 54
Figure 2.24: Large “B” Compressor Outlet Schematic ...... 56
Figure 2.25: Compressor Inlet Schematic ...... 56
Figure 2.26: Small “B” Compressor Outlet Schematic ...... 57
Figure 3.1: Experimental and Theoretical Results for B = 1.29 (Greitzer, 1976) ...... 62
Figure 3.2: Experimental and Theoretical Results (Hansen et al., 1981) ...... 63
Figure 3.3: Compression System Model Results for T =0.235, (a) Fixed Speed, (b) Variable Speed (Fink, 1992) ...... 64
Figure 3.4: Non-Dimensional Pressure Rise and Torque Characteristics (Fink, 1992) .....65
Figure 3.5: Characteristic Extrapolation Values (Theotokatos and Kyrtatos, 2001) ...... 69
Figure 3.6: Flow Coefficient Amplitude Time Step Study – Without a Time Lag ...... 74
Figure 3.7: Flow Coefficient Frequency Time Step Study – Without a Time Lag ...... 74
Figure 3.8: Head Coefficient Amplitude Time Step Study – Without a Time Lag ...... 75
Figure 3.9: Head Coefficient Frequency Time Step Study – Without a Time Lag ...... 75
Figure 3.10: Predictions without Time Lag for T =0.2400; (a) Present Model, (b) Fink‟s Model (1988)...... 78
xi Figure 3.11: Predictions without Time Lag for T =0.2398; (a) Present Model, (b) Fink‟s Model (1988)...... 79
Figure 3.12: Predictions without Time Lag for =0.2397; (a) Present Model, (b) Fink‟s Model (1988)...... 80
Figure 3.13: Predictions without Time Lag for =0.2350; (a) Present Model, (b) Fink‟s Model (1988)...... 81
Figure 3.14: Predictions without Time Lag for =0.2300; (a) Present Model, (b) Fink‟s Model (1988)...... 82
Figure 3.15: Predictions without Time Lag for =0.2000; (a) Present Model, (b) Fink‟s Model (1988)...... 83
Figure 3.16: Predictions without Time Lag for =0.1000; (a) Present Model, (b) Fink‟s Model (1988)...... 84
Figure 3.17: Flow Coefficient Amplitude Time Step Study – Time Lag ...... 86
Figure 3.18: Flow Coefficient Frequency Time Step Study – Time Lag ...... 87
Figure 3.19: Head Coefficient Amplitude Time Step Study – Time Lag ...... 87
Figure 3.20: Head Coefficient Frequency Time Step Study – Time Lag ...... 88
Figure 3.21: Experimental Results; (a) =0.236, (b) =0.235 (Fink, 1988) ...... 89
Figure 3.22: Time Lag Model Results, =0.2360, τ = Fink (1988) ...... 90
Figure 3.23: Time Lag Model Results, =0.2350, τ = Fink (1988) ...... 91
Figure 3.24: Time Lag Model Results, =0.2360, τ = Greitzer (1976) ...... 92
Figure 3.25: Time Lag Model Results, =0.2350, τ = Greitzer (1976) ...... 93
Figure 4.1: Measured Pressure Ratio Characteristics; Magnified view in * will be discussed in Section 4.3.3...... 99
Figure 4.2: Measured Efficiency Characteristics ...... 100
Figure 4.3: Measured Torque Characteristics ...... 100
xii Figure 4.4: Typical Mild Surge Frequency Analysis – Compressor Inlet SPL ...... 106
Figure 4.5: Typical Mild Surge Temporal Behavior - Static Pressure at the
Compressor Inlet, p1 ...... 107
Figure 4.6: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 111
Figure 4.7: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 112
Figure 4.8: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 112
Figure 4.9: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 113
Figure 4.10: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 114
Figure 4.11: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 114
Figure 4.12: U = 230 m/s, Full Volume, mc, cor0.0194 kg/s, c 0.0826, B 0.67 ; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 115
Figure 4.13: U = 230 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 116
xiii Figure 4.14: U = 230 m/s, Full Volume, mc, cor0.0194 kg/s, c 0.0826, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 116
Figure 4.15: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 117
Figure 4.16: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 118
Figure 4.17: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 118
Figure 4.18: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 119
Figure 4.19: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 120
Figure 4.20: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 120
Figure 4.21: U = 230 m/s, Full Volume, mc, cor0.0169 kg/s, c 0.0720, B 0.67 ; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 121
Figure 4.22: U = 230 m/s, Full Volume, mc, cor0.0169 kg/s, c 0.0720, B 0.67 ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 122
xiv Figure 4.23: U = 230 m/s, Full Volume, mc, cor0.0169 kg/s, c 0.0720, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 122
Figure 4.24: U = 230 m/s, Full Volume, mc, cor0.0138 kg/s, c 0.0588, B 0.68;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 123
Figure 4.25: U = 230 m/s, Full Volume, ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 124
Figure 4.26: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 124
Figure 4.27: U = 230 m/s, Full Volume, mc, cor0.0096 kg/s, c 0.0409, B 0.68; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 125
Figure 4.28: U = 230 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 126
Figure 4.29: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 126
Figure 4.30: U = 310 m/s, Full Volume, mc, cor0.0283 kg/s, c 0.0894, B 0.87; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 129
Figure 4.31: U = 310 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 130
xv Figure 4.32: U = 310 m/s, Full Volume, mc, cor0.0283 kg/s, c 0.0894, B 0.87; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 130
Figure 4.33: U = 310 m/s, Full Volume, mc, cor0.0267 kg/s, c 0.0843, B 0.87;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 131
Figure 4.34: U = 310 m/s, Full Volume, ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 132
Figure 4.35: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 132
Figure 4.36: U = 310 m/s, Full Volume, mc, cor0.0258 kg/s, c 0.0815, B 0.86; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 133
Figure 4.37: U = 310 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 134
Figure 4.38: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 134
Figure 4.39: U = 310 m/s, Full Volume, mc, cor0.0209 kg/s, c 0.0660, B 0.88; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 135
Figure 4.40: U = 310 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 136
xvi Figure 4.41: U = 310 m/s, Full Volume, mc, cor0.0209 kg/s, c 0.0660, B 0.88; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 136
Figure 4.42: U = 310 m/s, Full Volume, mc, cor0.0158 kg/s, c 0.0499, B 0.89;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 137
Figure 4.43: U = 310 m/s, Full Volume, ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 138
Figure 4.44: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 138
Figure 4.45: U = 370 m/s, Full Volume, mc, cor0.0518 kg/s, c 0.1371, B 1.01; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 141
Figure 4.46: U = 370 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 142
Figure 4.47: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 142
Figure 4.48: U = 370 m/s, Full Volume, mc, cor0.0493 kg/s, c 0.1305, B 1.01; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 143
Figure 4.49: U = 370 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 144
xvii Figure 4.50: U = 370 m/s, Full Volume, mc, cor0.0493 kg/s, c 0.1305, B 1.01; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 144
Figure 4.51: U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 145
Figure 4.52: U = 370 m/s, Full Volume, ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 146
Figure 4.53: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 146
Figure 4.54: U = 370 m/s, Full Volume, mc, cor0.0359 kg/s, c 0.0950, B 1.00; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 147
Figure 4.55: U = 370 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 148
Figure 4.56: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 148
Figure 4.57: U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 149
Figure 4.58: U = 370 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 150
xviii Figure 4.59: U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 150
Figure 4.60: U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 151
Figure 4.61: U = 370 m/s, Full Volume, ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 152
Figure 4.62: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 152
Figure 4.63: U = 370 m/s, Full Volume, mc, cor0.0170 kg/s, c 0.0450, B 1.02; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 153
Figure 4.64: U = 370 m/s, Full Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 154
Figure 4.65: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 154
Figure 4.66: Dominant Surge Frequencies as a Function of Tip Speed ...... 160
Figure 4.67: Dominant Surge Frequencies as a Function of Plenum Volume...... 160
Figure 5.1: Non-Dimensional Pressure Ratio Characteristic ...... 163
Figure 5.2: Non-Dimensional Torque Characteristic ...... 163
Figure 5.3: Detailed View of Non-Dimensional Pressure Ratio Characteristic ...... 166
Figure 5.4: Comparison to Experiments for U 370 m/s ...... 170
xix Figure 5.5: Plenum Pressure, pP , Comparison, Stable;
U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.01 ...... 171
Figure 5.6: Speed, N , Comparison, Stable;
U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.01 ...... 172
Figure 5.7: Predicted Mass Flow Rate for Compressor vs. Throttle, Stable ...... 172
Figure 5.8: Plenum Pressure, , Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00 ...... 174
Figure 5.9: Plenum Pressure, pP , FFT Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00 ...... 174
Figure 5.10: Speed, N , Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00 ...... 175
Figure 5.11: Predicted Mass Flow Rate for Compressor vs. Throttle, Mild Surge ...... 176
Figure 5.12: Predicted Pressure vs. Mass Flow Rate, Mild Surge ...... 176
Figure 5.13: Plenum Pressure, , Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01 ...... 178
Figure 5.14: Plenum Pressure, , FFT Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01 ...... 178
Figure 5.15: Speed, N , Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01 ...... 180
Figure 5.16: Predicted Mass Flow Rate for Compressor vs. Throttle, Deep Surge ...... 180
Figure 5.17: Predicted Pressure vs. Mass Flow Rate, Deep Surge ...... 181
Figure A.1: U = 310 m/s, Half Volume, mc, cor0.0248 kg/s, c 0.0783, B 0.64 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 188
xx Figure A.2: U = 310 m/s, Half Volume, mc, cor0.0248 kg/s, c 0.0783, B 0.64 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 189
Figure A.3: U = 310 m/s, Half Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 189
Figure A.4: U = 310 m/s, Half Volume, mc, cor0.0217 kg/s, c 0.0685, B 0.64;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 190
Figure A.5: U = 310 m/s, Half Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 191
Figure A.6: U = 310 m/s, Half Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 191
Figure A.7: U = 310 m/s, Quarter Volume, mc, cor0.0241 kg/s, c 0.0761, B 0.48; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 192
Figure A.8: U = 310 m/s, Quarter Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 193
Figure A.9: U = 310 m/s, Quarter Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 193
Figure A.10: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 194
xxi Figure A.11: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49; (a) Static Pressure at the Compressor
Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 195
Figure A.12: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N ...... 195
Figure A.13: U = 310 m/s, Eighth Volume, mc, cor0.0234 kg/s, c 0.0739, B 0.38; (a) Static Pressure at the Compressor
Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 196
Figure A.14: U = 310 m/s, Eighth Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 197
Figure A.15: U = 310 m/s, Eighth Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 197
Figure A.16: U = 310 m/s, Eighth Volume, mc, cor0.0204 kg/s, c 0.0644, B 0.38; (a) Static Pressure at the Compressor Outlet, , and Plenum, , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure, ...... 198
Figure A.17: U = 310 m/s, Eighth Volume, ; (a) Static Pressure at the Compressor Inlet, , (b) Frequency Domain Analysis of Compressor Inlet Pressure, ...... 199
Figure A.18: U = 310 m/s, Eighth Volume, ; (a) Turbocharger Rotational Speed, , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, ...... 199
xxii
LIST of TABLES
Table 2.1: Turbine Power Calculation Results ...... 23
Table 2.2: Orifice Sizes...... 40
Table 2.3: Orifice Calibration Coefficients ...... 46
Table 2.4: Predicted Input and Output Channels for DAQ/Control System ...... 51
Table 4.1: Plenum Volume Settings ...... 95
L Table 4.2: Calculated c Ratios ...... 103 Ac
Table 4.3: Experimental Matrix (with Calculated c , , U , a p , fH , and B ) ...... 105
Table 4.4: Variable Volume Mild and Deep Surge Frequency Summary – Experimental Results ...... 157
Table B.1: Curve Fit Coefficients ...... 200
xxiii
NOMENCLATURE
a Speed of Sound
A Area
B Non-Dimensional Stability Parameter
C Non-Dimensional Compressor Characteristic cp Specific Heat at Constant Pressure
Cd Discharge Coefficient dD, Diameter
E Modulus of Elasticity
F Non-Dimensional Throttle Characteristic
Fad Thermal Correction f Friction Factor, Frequency g Gravitational Constant
I Turbocharger Spool Moment of Inertia k Stall Cell Development Number
L Length m Mass Flow Rate
M Mach Number
MFP Mass Flow Parameter (vertical scale in Fig. (2.3)) N Turbocharger Shaft Speed in rev/min
xxiv n Number of Time Steps p Pressure
P Power r2 Impeller Tip Radius
R Ideal Gas Constant Re Reynolds Number s Distance
T Temperature, Torque t Time, Thickness
t Time Step
U Impeller Tip Speed u Velocity
V Volume
Y1 Compressibility Coefficient z Elevation
Greek Thermal Correction Coefficient
Diameter Ratio
Specific Heat Ratio
Non-dimensional Torque
Efficiency
Dynamic Viscosity
Poisson‟s Ratio
Density
xxv Time Lag Constant
C Flow Coefficient, x U
Non-dimensional Pressure Rise Angular speed
Subscripts 0 Total 1 Compressor Inlet 2 Compressor Outlet 3 Turbine Inlet 4 Turbine Outlet
Ambient b Reverse c Compressor cor Corrected d Orifice
D Pipe, Drive f Corrected, Forward, Final
H Helmholtz i Initial
M Measured m Mechanical mer Meridonial
P Plenum red Reduced
xxvi ref Reference t Turbine
T Throttle ts Total to Static tt Total to Total ss Steady State v Volute
Miscellaneous Designates Time Average When Placed Over a Quantity
xxvii
CHAPTER 1
INTRODUCTION
1.1 Background
With growing focus on climate change and energy conservation, automakers are looking to improve the efficiency of internal combustion engines. One source of inefficiency is the significant amount of fuel energy wasted through the exhaust process.
Turbochargers recover some of that energy to elevate intake pressure, improving power density and internal combustion engine efficiency. This allows for downsized, smaller volume engines to have similar power outputs as larger, non-turbocharged engines.
Turbochargers, however, are complex systems with additional ducting and their physics are not as well understood as some of the more developed technology within an internal combustion engine system. Therefore, many benefits exist in the development of a facility and model to quantify the system performance.
Figure 1.1 is a schematic of a typical turbocharged engine system. The turbocharger consists of a turbine and compressor connected via a shaft and bearing system. The high temperature and pressure exhaust gas is expanded through the turbine generating power. This power is transferred by the common shaft to the centrifugal compressor which elevates the pressure of the air entering the engine. The elevated 1 pressure increases the density, hence the mass flow rate, allowing for a downsized engine to create a similar amount of torque as the larger engine. This technique improves the overall system efficiency as the same power is generated with less friction, due to reduced bearing and cylinder wall surface areas, and a portion of the otherwise wasted energy is recovered by the turbine. Baines (2005), for example, estimates the wasted combustion energy in a non-turbocharged engine as 30-40% of the total energy released by the combustion of fuel. Additionally, the downsized engine allows for compact vehicle packaging. Nearly all modern diesel engines and an increasing number of spark ignition engines are now turbocharged to take advantage of the higher efficiency, reduced exhaust pollutants, and more compact packaging.
Figure 1.1: Turbocharger-Engine System Schematic (Rammal and Abom, 2007)
2 1.2 Literature Review
Turbocharging and supercharging are the two most basic methods of forced induction with Fig. 1.1 representing a simple installation of the former. Turbocharged systems typically have better power and efficiency from mid to high engine operating speeds while superchargers have good performance at low engine speeds. Supercharging differs from turbocharging as the screws that increase the air pressure are mechanically driven by the engine, therefore, there is not an efficiency increase by recovering wasted combustion energy. Therefore, turbocharging is the most common forced induction method in today‟s automotive world. In engines with more than one bank of cylinders, twin or parallel turbocharging is often employed with one turbocharger per bank of cylinders. Also, sequential systems with multiple turbochargers are used to maximize the range of operation of the forced induction system. Finally, super-turbocharged systems use a supercharger and a turbocharger to take advantage of the supercharger‟s quick response and the turbocharger‟s high mass flow rate performance. The broad application of turbochargers makes it very important to understand the multiple variations of the turbomachinery components that make up the turbocharger and its performance characteristics.
While most compressors in turbochargers may be of the centrifugal design, both axial and centrifugal compressors turn the flow to elevate pressure. In axial compressors the flow is turned at a fixed radius from the hub to the tip of the compressor blades.
However, in centrifugal compressors, the flow enters the compressor at the inducer, is turned in the radial direction, and exits the impeller at the tip which has a larger radius
3 than the hub. This larger radius allows the centrifugal compressor to elevate the pressure higher than that of the axial compressor (Korpela, 2009). To achieve pressure ratios above modest levels in axial compressors, multiple stages are required (Baines, 2005).
However, multiple stage axial compressors, which are typically the choice for high pressure equipment such as gas turbine engines and aircraft propulsion, are smaller than multiple stage centrifugal compressors (Peng, 2008). Just like axial compressors elevate pressure less than centrifugal compressors, axial turbines reduce the pressure less than radial turbines as all the flow turning happens at a constant radius on the turbine blade, whereas in a radial turbine, the flow is turned from the outer radius to the inner radius of the turbine blade. This allows axial turbines to have a higher efficiency than radial turbines but with a smaller range of operation, therefore they are typically used for installations that tend to operate at one operating point for significant amounts of time.
Centrifugal compressors and radial turbines are often the choice for most automotive turbochargers as multiple stages are not required alleviating the cost, complexity, and manufacturing requirements while also improving range of operation.
Figures 1.2-1.4 show typical centrifugal compressor and radial turbine maps for automotive turbochargers. Figure 1.2 shows the static outlet to total inlet pressure ratio against the mass flow rate corrected with respect to a reference temperature and pressure.
Constant speed lines, which are normalized against inlet temperature, and total-to-static efficiency contours may also be noted.
4
Figure 1.2: Typical Compressor Map (Baines, 2005)
Figure 1.3 depicts, for a typical radial turbine, the mechanical efficiency (the turbine total-to-static efficiency multiplied by the turbocharger shaft, bearing, and seal efficiencies) vs. the total inlet to static outlet pressure ratio. Within the efficiency map, turbine rotational speeds are noted next to their respective curves. The mass flow map for a typical radial turbine is shown in Fig. 1.4. The turbine mass flow parameter, mT , is plotted against the total inlet to static outlet pressure ratio where m , T , and p p are the mass flow rate, temperature, and pressure at the turbine inlet. The same turbine rotational speeds from Figure 1.4 are noted next to their respective curves.
5
Figure 1.3: Typical Turbine Efficiency Map (Baines, 2005)
Figure 1.4: Typical Turbine Mass Flow Map (Baines, 2005)
When trying to match a turbocharger to an engine, the compressor and turbine are selected such that the mass flow rates, pressure ratios, and efficiencies are a good fit with the engine and its application. Engine designers strive to maximize efficiency at a variety
6 of engine mass flow rate and torque values which dictate the compressor and turbine mass flow rates and pressure ratios. Therefore, high efficiencies and wide ranges of operation are desired for both the turbine and the compressor.
The three boundaries that define the range of a typical centrifugal compressor are the surge line to the far left, the choke line on the far right, and the maximum speed line located at the top of the map. Therefore, engine designers have to make sure that the mass flow rate and pressure ratio requirements are within the range of compressor operation. Also, a significant goal of designers is to improve low engine speed torque.
At low engine speeds, the compressor is operating at a low mass flow point, and the maximum obtainable pressure ratio is limited by the surge line. Surge is an instability that causes self-sustained oscillations in the compression system that may be extremely damaging to turbochargers and engines. Typical forms of turbocharger surge failure are low cycle fatigue on the impeller as well as the shaft while the engine has to deal with the large pressure fluctuations and vibrations that are a result of surge.
Cumpsty (1989) further explores instabilities in axial compressors by graphically identifying the scenarios of stall and surge in Fig. 1.5 where the solid lines represent the compressor characteristics. The typical operation for compressors is as mass flow rate is reduced, the pressure rise across the compressor is elevated. Therefore, stability exists due to the restoring force of the fluid in the compressor duct. Eventually, the maximum pressure rise is reached and a further reduction in mass flow rate leads to a distinct change in the performance of the compressor as it enters either stall or surge. In the progressive stall case, Fig. 1.5a, the reduction of the mass flow rate below that at the peak
7 pressure rise results in only a small change in performance. Cumpsty (1989) mentions that its presence is often only captured by high-frequency instrumentation inside the machine. Abrupt stall, Fig. 1.5b, on the other hand, is extremely detrimental to the performance of the machine. Often, an entirely different characteristic for the compressor is observed in the stall region and performance is greatly reduced. For both progressive and abrupt stall, the flow is no longer circumferentially uniform as areas of very little flow, known as stall cells, exist even though the annulus average mass flow rate remains constant. For progressive stall, part-span stall is observed as the cells do not occupy the full blade radius, whereas for abrupt stall, full-span stall is created as the cells do occupy the full blade radius. In part-span cases, multiple stall cells can exist; however, in full-span cases there is typically only one cell. In both part- and full-span cases, the stall cells rotate in the same direction as the impeller at about 50% of the impeller speed for part-span and 20-40% of the impeller speed for full-span. Two forms of non-rotating stall are tip and volute stall. In some cases, the instability of surge, which is depicted Fig. 1.5c, is observed. In this case, stall is often the precursor to surge at which point the annulus averaged mass flow varies with time. Surge is categorized as mild or deep depending upon the amplitude of the annulus averaged mass flow rate oscillations. Mild surge is defined as self-sustained mass flow variations that always remain positive through the annulus, whereas deep surge is defined as self-sustained mass flow variations that reverse flow direction, or become negative. Cumpsty (1989) further suggests that the severity of the surge oscillations as well as if the stall is part- or full- span depends upon the compressor and its accompanying compression system.
8
Figure 1.5: Stall and Surge Characteristics (Cumpsty, 1989)
Typically, axial compressors enter an abrupt stall characteristic while centrifugal compressors experience a progressive stall characteristic. Greitzer (1976) states that once an axial compressor enters abrupt stall, it may not be able to obtain stable performance again because of the hysteresis effects. Day (1994) shows the hysteresis loop for two different axial compressors, a C106 and Greitzer‟s (1976) compressor and notes that between the two different axial compressors, significantly different hysteresis loops exist, allowing Greitzer‟s (1976) compressor to exit stall much easier than Day‟s (1994) C106 compressor. Emmons (1955) collected stall and surge data for both an axial and centrifugal compressor showing abrupt stall for the axial compressor and progressive stall for the centrifugal compressor with both able to enter surge. Since axial compressors may not be able to exit stall, stall operating points are typically the limit on the range of operation. However, as centrifugal compressors can typically tolerate operation in stall conditions, the surge operating points are typically the limit on the range of operation.
As centrifugal compressors are the primary components used in turbochargers, surge will be the focus for the remainder of this research through the experimental facility design, experimental results, and model comparison.
9 A schematic of a typical compression system is presented in Fig. 1.6. The system contains a compressor, an outlet duct, a plenum, and a throttle. The compressor, duct length, plenum volume, and throttle are the four main components that define surge characteristics in an axial or centrifugal compression system. Numerous studies are available in literature regarding the effect of these parameters on surge in a centrifugal compression system. These studies have often coupled the experimental and model results with different duct and volume geometries as well as the compressor and throttle characteristics to predict the effect of these parameters on the stability of an axial or centrifugal compression system.
Figure 1.6: Typical Centrifugal Compression System
Greitzer (1976) laid some of the foundations for surge studies in axial compression systems through the development of a model and comparisons with experimental data. Much like Emmons (1955), Greitzer likened the compression system to a Helmholtz resonator or spring-mass system with the motion of the fluid in the compressor duct with kinetic energy and the compression of the gas in the plenum with the potential energy. Using this analogy, Greitzer created a zero-dimensional (0-D) 10 model with four ordinary differential equations assuming a constant compressor speed to predict transient operation of an axial compression system. The four equations include conservation of momentum in the compressor duct, mass in the plenum, momentum in the throttle duct, and a first order time lag equation for the compressor pressure rise.
Greitzer also introduced the critical “B” parameter defined by
U V B P , (1.1) 2a Acc L
where U is the compressor tip speed, a is the speed of sound, Vp is the plenum volume,
Ac is the compressor duct reference cross-sectional area, and Lc is the equivalent compressor duct length. Greitzer (1976) found that “B” values greater than 0.7 resulted in surge. Greitzer (1976) also used a linear stability analysis to predict if surge will occur by comparing compressor and throttle characteristics as
dC 1 , (1.2) dm 2 dF c B dmT
where C is the compressor characteristic, mc is the mass flow rate through the
compressor, F is the throttle characteristic, and mT is the mass flow rate through the throttle. Therefore, Eqs. (1.1) and (1.2) show the importance of the compression system geometry and how it dictates if a compression system will enter surge. Equation (1.2) specifically determines the slope of the compressor characteristic where the rotating stall transitions to surge. Finally, Greitzer compares his numerical model and experimental results at multiple “B” values, including 0.65, 0.75, 0.84, 1.00, 1.03, 1.29, and 1.58. 11 Hansen et al. (1981) applied Greitzer‟s (1976) model to a small centrifugal compression system and compared with experimental results. Fink (1992) applied
Greitzer‟s (1976) work to a centrifugal compression system after eliminating the assumption of constant compressor speed and neglecting the momentum in the throttle duct. Therefore, Fink‟s model to predict transient performance in the compression system used four ordinary differential equations, including conservation of momentum in the compressor duct, mass in the plenum, angular momentum of the turbocharger spool, and a first order time lag equation for the compressor pressure rise. Fink also compared experimental results with the model predictions at a “B” value of 2.74 with a reasonably good accuracy, especially in the frequency domain. Yano and Nagata (1970) also developed a lumped parameter model using ordinary differential equations for conservation of mass in the plenum and momentum in the compressor duct as well as a plenum isentropic compression relationship to predict surge in a diesel engine compression system and compared the results to experimental data with fairly good agreement.
Theotokatos and Kyrtatos (2001) modified Fink‟s (1992) model such that inlet temperature and pressure change during reverse flow in deep surge. They also provided equations for extrapolation outside of the typical compressor operating range.
Theotokatos and Kyrtatos (2003) applied their model along with a one-dimensional (1-D) engine simulation code to a high speed diesel engine and were able to match the experimental results closely. Galindo (2008) developed a surge model for the compression system much like Greitzer (1976) and Fink (1992), and used it in
12 conjunction with a 1-D simulation code for an automotive engine. This allowed the detailed analysis of compression system stability and wave dynamics within the system.
In parallel to the modeling effort of compression systems, a review of current experimental setups was performed in order to help design a facility to test turbochargers with an emphasis on acoustics. Depending on how the compressor is powered, designs can be classified into four main categories:
a. Hot gas generated by a burner or electric heater passed through the turbine
with temperatures similar in magnitude to engine exhaust gas
temperatures.
b. Cold gas passed through the turbine with temperatures significantly lower
in magnitude than engine exhaust gas temperatures.
c. An engine to provide hot gas to the turbine while the compressor operates
in an independent compression system.
d. An electric motor driving the common shaft of the turbocharger.
Stemler and Lawless (1997) developed a hot gas facility that can elevate the turbine inlet temperature to 1200 F for a study of engine operating transients on turbochargers typical for diesel powertrain systems. Young and Penz (1990) developed a hot gas facility to allow all types of turbocharger testing on up to five turbochargers simultaneously with maximum turbine inlet temperatures of 815 C . Venson et al. (2006) built a compact turbocharger test bench using hot gas generated by a custom fuel burner. Naundorf et al. (2001) developed a modular turbocharger test stand with temperatures up to 1050 C that Kratzer Automation currently sells. Finally, Clay and
13 Moch (2002) operate a hot gas turbocharger test facility for Holset that specializes in evaluating turbocharger noise emissions.
Several others implemented a cold gas test stand due to its reduced cost and simplicity. Hansen et al. (1981) and Filho et al. (2002) used only cold, pressurized air to drive the turbine. Dale et al. (1988), Capobianco and Marelli (2005), and Rammal and
Abom (2007, 2009) all use electric heaters on cold air to elevate the turbine outlet temperature sufficiently that condensation is not a concern. Kirk et al. (2008) outline the thermodynamic principles for the design of a cold gas turbocharger test facility.
Galindo et al. (2006) use a six cylinder diesel engine to power a turbocharger to study surge and wave dynamics in the compression system. Lujan et al. (2002) power the turbine with a six cylinder diesel engine as well to perform a turbine efficiency study.
Torregrosa et al. (2006) use a four cylinder diesel engine to power a turbocharger such that maps can be recreated and acoustic reflection and transmission coefficients of the compressor and turbine can be measured.
Andersen et al. (2008) use an electric motor to power a compressor for an experimental investigation of the compression system surge characteristics. Finally, Sens et al. (2006) discuss the importance of measurement accuracies of certain quantities to ensure accurate calculation of all turbocharger map information for any test facility design. Having provided a brief introduction to earlier research on surge modeling and the experimental facilities, the objectives of the current research is discussed next.
14 1.3 Objective
The primary and secondary goals of the present research are to (1) construct a turbocharger test facility, and (2) develop a compression system model to compare predictions with experimental measurements, respectively. The test facility is a unique capability envisioned to serve dual purposes: (a) mapping compression systems within a typical operating range, and (b) measuring both mild and deep surge compression system performance. To enhance the understanding of mild and deep surge, the compression system geometry will be modified to observe its effect. Finally, acoustic data will be acquired both during surge and stable operation.
The objective of the analytical effort is to predict the compression system performance during surge. Therefore, a 0-D model much like Greitzer (1976) and
Fink (1992) will be developed in a simulation environment isolated from engine physics.
The model will have the ability to quickly modify the compression system geometry or performance parameters and study their effects. Finally, the experimental observations will be compared with the analytical results.
Chapter 2 describes the development of the turbocharger test facility and
Chapter 3 the analytical model. Experimental results are presented in Chapter 4, which are then compared with analytical predictions in Chapter 5. The study ends with concluding remarks in Chapter 6.
15
CHAPTER 2
DESIGN of EXPERIMENTAL SETUP
The experimental setup was designed to allow primarily the study of turbocharger compression system physics and the acoustics for a wide variety of turbochargers. To achieve these goals, many subsystems are incorporated into the experimental setup. This chapter first discusses turbocharger compressor operating ranges of interest and a thermodynamic analysis of the necessary turbine pressures and temperatures to achieve those ranges. Then, the design and selection of subsystems such as the screw compressor for the turbine air, flow control valves, flow measurement devices, turbocharger oil system, and the data acquisition and control system will be explained. Finally, geometric sketches of the implemented compressor outlet systems, small and large “B,” will be presented.
2.1 Turbocharger Operating Ranges and Thermodynamic Analysis
Typical operating ranges of diesel and gasoline engine turbocharger compressors are portrayed by Baines (2005) in Figs. 2.1a and 2.1b, respectively. Figure 2.1 shows diesel engine turbochargers are limited by the power available in the exhaust while those
16 of gasoline engines are confined by knock limits requiring the wastegate to open, bypassing exhaust energy around the turbine. Also, the low mass flow rate regions for both diesel and gasoline engines are very close to the surge line of the compression system. Therefore, since engine operating points force the compression system close to surge, the turbocharger test facility must be able to place the compression system in surge as well as reach a good portion of the stable operating region so that their physics can be studied.
Figure 2.1: Typical Turbocharger Compressor Operating Ranges (Baines, 2005)
The designed experimental setup must serve multiple purposes by allowing the ability to map compression systems within the operating range in Fig. 2.1, measure both mild and deep surge performance, and acquire acoustic data during surge and stable operation. As stated in Chapter 1, hot gas, cold gas, engine-driven, and motor-driven test benches exist for a variety of different goals. The motor-driven system has been
17 eliminated from consideration as motors and gear trains that allow speeds upwards of
150,000 RPM are not cost effective. An engine-driven test bench was not implemented as it requires additional compression equipment to maintain a positive pressure ratio across the engine, adding cost, complexity, and reducing flexibility. Also, in an engine- driven test bench, engine physics make it more difficult to study compression system physics in isolation. Therefore, the test bench at Ohio State University can be classified as a cold gas facility with a future goal to add hot gas capability.
In order for the turbocharger compressor to operate in the desired region, the turbine must be able to develop sufficient power. The turbocharger used for this investigation is a BorgWarner K03 variable turbine geometry (VTG) turbocharger with rotating guide vanes at the inlet to the turbine. The inlet guide vanes have a variety of open positions allowing the turbine to achieve a range of operation rather than one discrete line of operation. The turbocharger‟s turbine efficiency and mass flow rate maps
are presented in Figs. 2.2 and 2.3, respectively, with p, T, mt , and tm corresponding to pressure, temperature, turbine mass flow rate, and turbine times mechanical efficiency.
Subscripts 3 and 4 indicate turbine inlet and outlet conditions with the additional subscript “t” representing total quantities. The individual speed lines correspond to discrete turbine wheel tip speeds in m/s. Using these maps, a thermodynamic analysis can be performed, as illustrated next, to calculate the power developed by the turbine and the power available to the compressor.
18
BorgWarner K03 Turbine Efficiency Map Turbine K03 BorgWarner Efficiency
: : Figure 2.2 Figure
19
BorgWarner K03 Turbine Mass Flow Map Turbine K03 BorgWarner Flow Mass
: : Figure 2.3 Figure
20 A number of assumptions are used to simplify the turbine power calculation:
1) The turbine outlet static temperature, T4 , must always be greater than 0 C to
prevent any condensation that forms in the air stream from freezing on the
turbine and possibly causing mechanical failure.
2) The largest pressure ratio at the turbine for each VTG position in Figs. 2.2 and
2.3 will be treated as the maximum possible pressure ratio for this analysis.
3) The backpressure in the turbine outlet duct for the designed experimental
setup is assumed to be minimal, therefore, the turbine total outlet pressure,
p04 , is assumed to be 1 bar.
p3t As the pressure ratio, , of Fig. 2.3 contains the turbine outlet static pressure, p4 , the p4 difference in total and static pressures needs determined. The ratios of total (designated by subscript „0‟) to static values for pressure and temperature depending on the Mach number are calculated as
1 p0 1 2 1 M (2.1) p 2 and
T 1 0 1M 2 , (2.2) T 2 where is the air specific heat ratio with a value of 1.4 and M is the Mach number.
Using the maximum turbine inlet guide vane position at its maximum pressure, the mass
21 flow rate is approximately 0.25 kg/s, resulting in a Mach number of 0.39 with a temperature of 273 K, pressure of 1 bar, and a pipe diameter of 0.0438 m. This Mach number results in a total pressure 11.1 % higher than the static pressure and a total temperature 3.0 % higher than the static temperature. As this is the maximum flow rate
through the system, it allows for a good approximation for the outlet static pressure, p4 ,
and total temperature, T04 , at maximum turbine power. Using assumptions 1 and 2, the
outlet static pressure, , and total temperature, T04 , are calculated to be 0.90 bar and
281 K, respectively. The turbine inlet total temperature to avoid freezing of any condensation in the air stream is calculated from
T T 04 , (2.3) 03 1 p 11 4 t, ts p03
where p03 is the turbine inlet total pressure and T04 is the turbine outlet total temperature.
Since turbocharger mechanical efficiencies, m , are near 100 %, the turbine total to static
efficiency, t, ts , is the efficiency, tm, presented in Fig. 2.2. Using the turbine total inlet
temperature, T03 , from Eq. (2.3), the mass flow rate can then be determined by
p m MFP03 , (2.4) T T03 where MFP is the mass flow parameter presented as the vertical scale in Fig. 2.3. Using
this mass flow rate, the turbine total inlet temperature, T03 , from Eq. (2.3), the desired
22 p03 pressure ratio, , and the turbine total to static efficiency, t, ts , from Fig. 2.2, the p4 turbine power is calculated as
1 p P m c T 14 , (2.5) T T p03 t , ts p03
where cp is the specific heat of air at the turbine inlet temperature, T03 . The maximum power created by the turbine for each VTG position is calculated using Eq. (2.5) and presented in Table 2.1. The maximum power of 10.92 kW occurs at a VTG position of
40% open.
Open Position T04 (K) p4 (bar) p03 (bar) T03 (K) MFP mT (kg/s) PT (kW) set min. - Position 281 0.9 2.97 327.3 0.51 0.084 3.90 min. - therm. 281 0.9 2.97 334.1 0.62 0.101 5.37 20% - Position 281 0.9 3.06 342.7 0.79 0.131 8.09 40% - Position 281 0.9 2.97 351.0 0.98 0.155 10.92 60% - Position 281 0.9 2.70 344.0 1.17 0.170 10.78 80% - Position 281 0.9 2.61 337.7 1.30 0.185 10.51 max. - Position 281 0.9 3.06 320.8 1.48 0.253 10.10 Table 2.1: Turbine Power Calculation Results
It is assumed that all 10.92 kW of the power developed by the turbine is available to the compressor as the power lost in the shaft and seal assembly is very small relative to the turbine power. Fig. 2.4 is the BorgWarner 1880 DCF compressor map with an additional red line indicating the 10.92 kW operating line of the compressor calculated using only the turbine operating points presented on the turbine maps in Figs. 2.2 and 2.3. The 23 p compressor pressure ratio, 2t , is depicted against the reduced volumetric flow p1t
(corrected for inlet temperature) in the compressor inlet. Subscripts 1 and 2 indicate compressor inlet and outlet conditions with the additional subscript “t” representing total quantities. The individual speed lines correspond to discrete compressor impeller tip speeds in m/s. Also, compressor efficiencies are given by the contour lines.
Figure 2.4: BorgWarner 1880 DCF Compressor Map and 10.92 kW Line
This operating boundary can be extended upward if higher pressure ratios are used on the turbine allowing it to generate more power. At VTG positions of 40% to fully open, the
24 maps in Figs. 2.2 and 2.3 have the same maximum turbine speed of 430 m/s. Higher powers are developed using the 873 K inlet air of BorgWarner rather than the 320-351 K used in the calculations thus far. Therefore, higher pressure ratios can be used in the cold flow facility without reaching the 430 m/s maximum speed. Also, since this turbocharger was designed for pulse turbocharging and higher temperatures, mechanical and thermal stresses are lower. Therefore, the turbine should be structurally capable of handling elevated pressure ratios. For example, using a pressure ratio of 4.5 across the turbine, a
VTG position of 80%, and a turbine inlet temperature of 362 K to avoid freezing any condensation, provides approximately 22.5 kW of available power. This analysis suggests that using a cold flow test facility, with sufficient turbine inlet temperature to avoid freezing, easily allows the exploration of the compression system region of interest.
Upgrading to a hot gas test bench using a combustion burner to elevate the turbine inlet temperature to typical engine exhaust temperatures will allow exploration of more of the compression system operating region.
A schematic of the facility at the Ohio State University is presented in Fig. 2.5.
The facility was designed such that it could operate as a cold gas facility and then upgrade to a hot gas facility with minimal change of equipment and additional cost. A compressor and accumulator provide high pressure air, which is metered by a control valve, to the turbine. An orifice flow meter measures the mass flow rate and a burner or heater system can be used to elevate the turbine inlet temperature. The compressor loop is independent of the turbine loop allowing for more control and flexibility and also has a control valve for load control and an orifice flow meter for mass flow rate measurement.
A custom oil system was designed and implemented such that the turbocharger is 25 sufficiently lubricated. The operator uses a data acquisition and control system to monitor the facility. The turbocharger itself is located inside a hemi-anechoic room to facilitate external acoustic measurements.
26
: Facility Schematic Facility : Figure 2.5 Figure
27 2.2 Compressor Selection
As mentioned in Section 2.1, a pressure of at least 3.06 bar at the turbine inlet and
0.25 kg/s of air is needed to explore the BorgWarner turbocharger‟s compression system operating range of interest. To allow for larger turbochargers, the mass flow rate requirement was doubled to 0.5 kg/s, while the required turbine inlet pressure was assumed to remain constant. Blowers, reciprocating compressors, and screw compressors were the three main sources of pressurized air considered to provide flow to the turbine.
Suppliers Gardner-Denver and Continental Blower state that blowers have the ability to create large amounts of flow but can only achieve pressures of 2.5 bar at maximum flow with reduced pressures at lower flows in standard, cost effective units, therefore, they were eliminated from consideration. Reciprocating compressors have the ability to create pressures upwards of 9 bar with sufficient flow rate capability, however, they become extremely large and costly at these sizes as well as have relatively high maintenance costs. Screw compressors can achieve the same pressures and mass flow rates as reciprocating units but do so in smaller, more reliable, and cost effective packages.
Therefore, a Quincy QSI-750 screw compressor was installed to provide the high pressure air for the turbine loop. A picture of the screw compressor and its performance characteristic are presented in Figs. 2.6 and Fig. 2.7, respectively. The maximum and minimum screw compressor outlet pressures are 11.2 bar and 6 bar due to overpressure and oiling limitations, placing the flow range from 0.355 kg/s to 0.52 kg/s as the screw compressor is a constant power device. The internal air cooling system was bypassed allowing for 320 K turbine inlet temperatures to be achieved without the use of a burner or alternative heater. As the installed VTG position of the turbocharger is near fully 28 open, the 320 K turbine inlet temperature places the turbine pressure ratio at which condensation in the air stream will freeze at 4.48. A power calculation using Eq. (2.5) provides 10.1 kW, allowing for the majority of the 10.92 kW compressor operating range in Fig. 2.4 to be explored without additional heat input to the turbine inlet air.
A 30.02 m3 accumulator was installed downstream of the screw compressor. The screw compressor uses a regulator to modulate a throttle, maintaining a constant outlet pressure in the accumulator volume. The volume provides air storage as a buffer and minimizes fluctuations in the system prior to the compressed air reaching the rest of the test facility. The pipe size that carries the compressed air from the accumulator to the turbocharger was selected such that Mach numbers were low enough to reduce pressure losses. The screw compressor supplier recommended a 2.315 in inner diameter tube for the air supply to the turbine control valve and a 3.325 in inner diameter tube from there to the turbocharger. Using the screw compressor maximum output mass flow rate of
0.52 kg/s and minimum outlet pressure of 6 bar, the maximum Mach number in the tube to the control valve is 0.082. Assuming ambient pressure and the maximum screw compressor flow rate of 0.52 kg/s through the 3.325 in tube, the maximum Mach number to the turbocharger is 0.24. The pressure drop can be determined by applying these Mach numbers and diameters as
L 2 p g z f u , (2.6) 2gD where is the fluid density, g is the gravitational constant, z is the elevation change across the pipe length, L , D is the pipe diameter, and u is the fluid velocity in the pipe.
29 The Darcy friction factor, f , is a function of the Reynolds number and pipe roughness.
From the Moody Diagram, f 0.050 for the tube to control valve and 0.024 for the control valve to turbocharger resulting in pressure drops of 37.8 kPa and 12.03 kPa, respectively. These values account for 6.3% and 12.03% of the absolute pressure in the duct at those locations. Therefore, the pipe sizes are suitable for implementation into the test facility as they ensure small pressure drops.
Figure 2.6: Quincy QSI-750 Screw Compressor
30 Compressor Map for QSI-750 (0.42 kg/s at 8.48 bar - 298 K and 1 bar inlet) 12
11
10
9
8 Outlet Pressure (bar) 7
6
5 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 Mass Flow Rate (kg/s) Figure 2.7: QSI-750 Screw Compressor Performance Characteristic (0.42 kg/s at 8.48 bar – 298 K and 1 bar inlet)
2.3 Control Valve Design
The screw compressor does not regulate the flow rate to the turbocharger, rather, it maintains a constant pressure head in the accumulator. Therefore, a control valve is needed to control the mass flow rate from the constant pressure accumulator to the turbine. Also, a control valve is needed to throttle the turbocharger compressor for a given turbine power. Since turbochargers operate over wide ranges of mass flow rates and pressure ratios, the control valves need to have a large range of control with a good resolution. Ball and gate valves were immediately eliminated as they are typically selected for on/off control. Butterfly valves are typically used for on/off control and flow regulation in large pipe diameters. However, in the pipe sizes used in this application, 31 butterfly valves do not have a satisfactory resolution, especially at low flow rates, making them difficult to implement. Needle and globe valves provide excellent flow control but are only readily available in duct diameters less than 1 in. Since none of these valves fits the application, a hybrid valve was considered. The segmented ball valve was chosen as shown in Fig. 2.8 with accompanying actuator and positioner. The ball valve has a V-cut that provides a better resolution at low flow rates, while still allowing high flow rates with a minimal pressure drop across the valve.
The next step is to size the valves for the appropriate flow ranges that will be observed in both the turbine and compressor. As the facility must be able accommodate a variety of turbochargers, it is important to consider their performance characteristics in the sizing analysis. In Figs. 2.9 and 2.10, multiple turbine maps ranging from the
GT1241-756068 designed for a 130-150 HP engine to the GT3071R for a 300-460 HP engine are plotted within the flow capability limitations of the 1.5 in segmented ball valve selected for turbine flow control. Pressures of 110 and 75 psig in the accumulator are selected for comparison. The flow capability limitations, boundary ABCD, are the maximum and minimum effective valve open percentages of 90% and 7%: lines AB and
CD; a manufacturer specified Mach number of 0.5 at the valve outlet: line CD; and the maximum flow rate capability of the screw compressor described in Section 2.2 at the selected accumulator pressure: line BC. Even though the valve can fully close and shutoff flow in the loop, line AD represents the realistic lower limit of the mass flow rate through the valve such that the valve area gain is low enough to provide suitable control.
32
Figure 2.8: Segmented Ball Valve with Actuator and Controller
120 Valve Opening = 90% A B Screw 100 Note: GT = Garrett, BW = Borg Maximum Pressure Compressor Minimum Pressure Warner; Area of operation Limitation encompassed by black lines GT1241-756068-1 50-130 HP defined by control valve GT1544-454082-2 100-150 HP 80 limitations GT2052-727264-1 140-225 HP BWK03 160 HP GT2560R-466541-1 200-330 HP GT2252-452187-6 150-260 HP 60 GT2871R-771847-1 280-460 HP GT3071R 300-460 HP
40 Pressure (psig) Pressure
20
Valve Opening = 7%, C Valve Outlet Flow Mach Number = 0.50 0 D 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Mass Flow Rate (kg/s) Figure 2.9: Turbine Flow Control Valve Capability with Accumulator at 110 psig 33 80 A Valve Opening = 90% Screw Compressor Limitation B 70 Note: GT = Garrett, BW = Borg Maximum Pressure Warner; Area of operation Minimum Pressure 60 encompassed by black lines defined GT1241-756068-1 50-130 HP by control valve limitations GT1544-454082-2 100-150 HP GT2052-727264-1 140-225 HP 50 BWK03 160 HP GT2560R-466541-1 200-330 HP GT2252-452187-6 150-260 HP 40 GT2871R-771847-1 280-460 HP GT3071R 300-460 HP
30 Pressure (psig) Pressure
20 C 10
Valve Opening = 7%, Valve Outlet 0 D Flow Mach Number = 0.50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Mass Flow Rate (kg/s) Figure 2.10: Turbine Flow Control Valve Capability with Accumulator at 75 psig
Figure 2.11 performs a similar analysis for the compressor load control valve.
Multiple turbocharger compressor performance maps are plotted in Fig. 2.11 ranging from the GT1241-756068 designed for a 130-150 HP engine to the GT2871R for a
280-460 HP engine. The same limitations as in Figs. 2.9 and 2.10 apply regarding the maximum and minimum valve open position and valve outlet Mach number, lines BC,
B‟C‟, AD, and A‟D. The arbitrary maximum and minimum pressure, line AB or A‟B‟ and CD or C‟D‟, are the realistic limitations of the application and were imposed even though the valve can continue to perform at higher and lower pressures. The 2 in segmented ball valve was selected over the 2.5 in valve as it provides better resolution at low mass flow rates improving control for surge studies on the majority of the compressors.
34 Pneumatic actuators use compressed air from the accumulator to provide torque to rotate the segmented control valves for both the turbine and compressor loops. The torque is transferred using a common shaft between the valve, actuator, and the 32-bit position controller, which uses a PID algorithm and position sensor to obtain the desired valve position. The controller has five user selectable gain values ranging from conservative to aggressive. Since the controller is 32-bit, it can achieve 4.29 109 points within its full operating range, providing sufficient resolution to explore discrete operating scenarios such as mild surge. Therefore, the selected control valves achieve the goals of a wide range of operation while still maintaining good resolution.
Figure 2.11: Compressor Load Control Valve Capability
35 2.4 Flow Meter Design
Sharp edged orifice flow meters are a cost effective method to measure the flow rate through a system and can achieve relatively high accuracies when used properly.
Orifice flow meters were therefore implemented, instead of other more expensive solutions, downstream of the turbine and compressor control valves. Figure 2.12 shows a typical installation of an orifice flow meter with tolerances and flange locations.
Concentric orifices as well as D and D/2 port locations, shown in Fig. 2.12, were chosen because of easy installation. The flow rate is calculated by using the ANSI 2530 code presented by Miller (1996) and then calibrated against the Ford Flow Bench at the Ohio
State University to improve accuracy.
Figure 2.12: Orifice Flow Meter Installation (Miller, 1996)
36 The flow equations are derived from the Bernoulli equation
p u2 p u 2 u 2 1 1 gz 2 2 gz K 1 , (2.7) 212 2L 2
where p1 is the upstream pressure, u1 is the upstream velocity, z1 is the upstream
pressure port height, p2 is the downstream pressure, u2 is the downstream velocity, z2 is the downstream pressure port height, is the fluid density, g is the universal gravity
constant, and KL is a loss coefficient. Equation (2.7) is for incompressible flow and may be modified for compressible flow as
u2 u 2p2 dp u 2 1gz 2 gz K 1 , (2.8) 212 2 L 2 p1
p2 dp where accounts for the compressibility of the fluid from the upstream to p1 downstream port locations. As the flow media is air, the effect of elevation change can be ignored. Therefore, applying isentropic expansion and mass flow continuity to
Eq. (2.8) yields
2 2 Cdf Y1 d m p p , (2.9) 4 4 1 1 2 1 f
where m is the mass flow rate, Cd is the orifice discharge coefficient, Y1 is the
compressibility coefficient, d f is the corrected orifice diameter, f is the corrected
orifice to pipe diameter ratio, and 1 is the upstream fluid density. The discharge
37 u2 coefficient, C , accounts for the flow vena contracta and the loss term, K 1 , in d L 2
Eq. (2.8). Corrections for thermal and internal pressure influences on the orifice and pipe diameter are implemented for improved accuracy. The corrected orifice diameter is
0.5 3 D 2 f 0.135MM 0.1555 pp Ftad d d d F 1,12 (2.10) f M ad 2 Ed 1.3 Df 1.06M 1.17 Ft ad d where
pD 1 f D DDFf M ad 11 (2.11) 22ED F ad t D
is the corrected pipe diameter, ED is the pipe modulus of elasticity, Ed is the orifice modulus of elasticity, t is the pipe wall thickness, t is the orifice thickness, is the D d D
pipe Poisson‟s ratio, DM is the measured pipe diameter, dM is the measured orifice
diameter, FTTad1 P 1 M with D as the pipe coefficient of thermal expansion, T1
the upstream fluid temperature, and TM the temperature when the pipe diameter was
measured, and FTTad1 d 1 M with d as the orifice coefficient of thermal
expansion, T1 the upstream fluid temperature, and TM the temperature when the orifice diameter was measured.
38 The ANSI 2530 code [1991] is used to determine the discharge coefficient, Cd ,
and compressibility coefficient, Y1 , for a given operating point. The pipe diameter, DM , being used is 71.76 mm and the corresponding discharge coefficient is given by
28 0.7 Cxd0.5961 0.0291 f 0.229 f 0.000513 f 1 4 0.35 8.5 6 0.021 0.0049x31 f x 0.0433 0.0712 e 0.1145 e , (2.12) 1.1 1.3 1 0.23x3 x 2 0.0116 f 1 4 x 3 x 4 0.52 x 4
66 4 10 10 0.8 2 0.47 x f where 1 , x2 4 , xx31 0.019 f , and x4 . Using ReD m 1 f 1 f 4Df
Eq. (2.12) yields typical discharge coefficients around 0.6. The compressibility coefficient is given by
4 pp12 Y1 1 0.41 0.35 f , (2.13) p1
where is the specific heat ratio of the fluid. If the fluid is incompressible, Y1 1, as expected. Substituting Eqs. (2.10-2.13) into Eq. (2.9) allows the calculation of the mass flow rate through a sharp edged orifice.
Suitable straight lengths before and after the orifice, and pipe taps within ±0.1 and
±0.01 pipe diameters for upstream and downstream locations, respectively, are needed to ensure reasonable accuracy with the equations. The seven orifice sizes used in the present study are listed in Table 2.2. Note that the maximum and minimum diameter ratios, , are 0.796 and 0.216, respectively.
39 Orifice 1 2 3 4 5 6 7 Pipe Diameter (mm) 71.76 71.76 71.76 71.76 71.76 71.76 71.76 Orifice Diameter (mm) 57.15 50.80 41.91 31.75 22.86 17.27 15.49
β 0.796 0.708 0.584 0.442 0.319 0.241 0.216 Table 2.2: Orifice Sizes
Assuming there will be one elbow upstream and downstream of the orifice installation, suitable straight lengths can be determined using Fig. 2.13. Since the maximum diameter ratio, , is 0.796, the ideal upstream and downstream lengths are 20 and 5 pipe diameters, respectively. However, this makes the orifice flow meter extremely difficult to package. Therefore, a compromise between accuracy and packaging had to be made.
The next largest diameter ratio is 0.708 placing upstream and downstream lengths at 14 and 4 pipe diameters, respectively. An extra diameter was added to the upstream and downstream straight lengths to ensure flow development, making lengths 15 and 5 pipe diameters, respectively. Therefore, an additional ±0.5% uncertainty due to geometry effects exists for the largest orifice only. Using the tolerance specified in Fig. 2.12, four holes, circumferentially located 90º apart, are placed 71.8 mm upstream and 35.9 mm downstream of the orifice leading edge for pressure measurement. A K-type thermocouple for inlet temperature measurement is located 97.16 mm upstream of the orifice.
40
Figure 2.13: ANSI 2530 Straight Length Req. for Maximum Accuracy (Miller, 1996)
To check the accuracy of Eqs. (2.9-2.13) as well as the selected straight lengths, a flow meter was placed on the Ford Flow Bench and each orifice was tested from 0.75 kPa to the maximum pressure drop that the Ford Flow Bench could provide. The mass flow rates calculated from Eq. (2.9) were compared with the Ford Flow Bench mass flow rate calculated as
mQbench1.1694 bench , (2.14)
3 where Qbench is the volumetric flow rate from the Ford Flow Bench and 1.1694 kg/m is the reference density. Figures 2.14-2.20 present the mass flow rate vs. pressure drop comparison for Orifices #1-7. As the mass flow rates calculated by Eq. (2.9) and (2.14) deviate slightly, the next step is to look into calibration.
41 Meter and Flow Bench Mass Flow Rate Comparison - Orifice 1 0.45 Orifice Mass Flow - Eq. (2.9) 0.4 Bench Mass Flow - Eq. (2.14)
0.35
0.3
0.25
0.2 Mass (kg/s)Rate Flow 0.15
0.1
0.05 0 5 10 15 20 25 Pressure Drop (kPa) Figure 2.14: Orifice #1 (57.15 mm) Comparison
Meter and Flow Bench Mass Flow Rate Comparison - Orifice 2 0.3 Orifice Mass Flow - Eq. (2.9) Bench Mass Flow - Eq. (2.14)
0.25
0.2
0.15 Mass (kg/s)Rate Flow
0.1
0.05 0 5 10 15 20 25 Pressure Drop (kPa) Figure 2.15: Orifice #2 (50.80 mm) Comparison
42 Meter and Flow Bench Mass Flow Rate Comparison - Orifice 3 0.18 Orifice Mass Flow - Eq. (2.9) Bench Mass Flow - Eq. (2.14) 0.16
0.14
0.12
0.1 Mass (kg/s)Rate Flow 0.08
0.06
0.04 0 2 4 6 8 10 12 14 16 18 20 Pressure Drop (kPa) Figure 2.16: Orifice #3 (41.91 mm) Comparison
Meter and Flow Bench Mass Flow Rate Comparison - Orifice 4 0.1 Orifice Mass Flow - Eq. (2.9) Bench Mass Flow - Eq. (2.14) 0.09
0.08
0.07
0.06
0.05 Mass (kg/s)Rate Flow 0.04
0.03
0.02 0 2 4 6 8 10 12 14 16 18 20 Pressure Drop (kPa) Figure 2.17: Orifice #4 (31.75 mm) Comparison
43 Meter and Flow Bench Mass Flow Rate Comparison - Orifice 5 0.05 Orifice Mass Flow - Eq. (2.9) Bench Mass Flow - Eq. (2.14) 0.045
0.04
0.035
0.03
0.025 Mass (kg/s)Rate Flow 0.02
0.015
0.01 0 2 4 6 8 10 12 14 16 18 Pressure Drop (kPa) Figure 2.18: Orifice #5 (22.86 mm) Comparison
Meter and Flow Bench Mass Flow Rate Comparison - Orifice 6 0.03 Orifice Mass Flow - Eq. (2.9) Bench Mass Flow - Eq. (2.14)
0.025
0.02
0.015 Mass (kg/s)Rate Flow
0.01
0.005 0 2 4 6 8 10 12 14 16 18 Pressure Drop (kPa) Figure 2.19: Orifice #6 (17.27 mm) Comparison
44 Meter and Flow Bench Mass Flow Rate Comparison - Orifice 7 0.024 Orifice Mass Flow - Eq. (2.9) 0.022 Bench Mass Flow - Eq. (2.14)
0.02
0.018
0.016
0.014
0.012
Mass (kg/s)Rate Flow 0.01
0.008
0.006
0.004 0 5 10 15 Pressure Drop (kPa) Figure 2.20: Orifice #7 (15.49 mm) Comparison
Both Miller (1996) and Doebelin (2004) indicate that the most accurate method to designing orifice flow meters is to calibrate them against a known flow source.
Therefore, in an effort to remove the deviation in Figs. 2.14-2.20 and maintain
ANSI 2530 code, the orifice mass flow rates were calibrated to the Ford Flow Bench data by
m C Y a p p b , (2.15) d 1 1 1 2
where Cd and Y1 are the ANSI 2530 discharge and compressibility coefficients calculated in Eqs. (2.12) and (2.13) while a and b are the curve fit coefficients presented in Table 2.3.
45 Orifice a b 1 0.004397 0.5021 2 0.003062 0.5065 3 0.001992 0.5044 4 0.001052 0.5103 5 0.0005569 0.5086 6 0.0003094 0.5133 7 0.0002529 0.5134 Table 2.3: Orifice Calibration Coefficients
Calculating the orifice mass flow rate with this method reduces the error relative to the
Ford Flow Bench within ±1.25 %, achieving the goal of measuring the mass flow rate inexpensively and efficiently in both the turbine and compressor loops.
2.5 Oil System Design
An oil system was designed and built so the shaft and bearing system of the turbocharger have sufficient lubrication during operation. As many turbochargers will be tested on this facility, the oil system must be able to provide sufficient flow rate and operating pressure for a range of turbochargers. Discussions with knowledgeable individuals indicated that a reasonable oil consumption would be 2 L/min at 90 C . As this was the only design information that could be obtained at the time, the maximum flow rate of the system was set as at least 3 L/min to provide a reasonable factor of safety. The oil pressures that turbochargers observe are the same as the engine, which vary with engine speed. At low engine speeds, oil pressures can be as low as 8 psig while
46 at higher engine speeds they can reach values upwards of 60 psig. Oil temperatures can also exceed 100 C depending upon the how long the engine operates at high loads.
For these reasons, a system with a pump, bypass pressure regulator, and controllable oil heater was designed as illustrated schematically in Fig. 2.21. The Tuthill oil pump is coupled to a ½ HP motor, delivering 3.6 L/min at an 80 psig outlet pressure.
The pump is located outside the hemi-anechoic room to reduce noise contamination.
Using this pump provides a 1.8 to 1 factor of safety over the 2 L/min value. The outlet flow is passed through a standard engine oil filter and then regulated to the desired operating pressure between 15-75 psig using a spring-loaded pressure regulator while the dial gauge displays the operating pressure. The bypass pressure regulator was sized such that it could bypass the full flow rate of the oil pump back to the tank if necessary. The oil is then passed through the turbocharger and is returned to the tank. Both the bypass and return lines enter the tank below the oil level to minimize oil aeration which can cause mechanical damage to the shaft and bearing system. The oil tank is 30.5 in x 8 in x
4 in with a 0.25 in wall thickness and can hold 13.6 quarts of oil, eliminating the need to change oil frequently. A 1 kW immersion heater and controller heats the oil in the tank to a desired temperature set by a front panel display within 10 minutes. Overall, this system provides sufficient flow rate capability and easily adjustable operating pressures and temperatures to replicate those observed in engine systems.
47
Figure 2.21: Oil System Schematic
2.6 Data Acquisition and Control System and Instrumentation Selection
For performance and acoustic measurements, the instrumentation as well as the data acquisition and control system was configured as described next. The pressure and temperature at the compressor and turbine inlet and outlet, compressor and turbine mass flow rates, and the turbocharger speed need to be measured to perform turbocharger performance mapping. To improve surge studies, the plenum pressure and temperature must be captured. The data acquisition and control system is configured such that these signals can be acquired and the control valves discussed in Section 2.3 can be controlled simultaneously.
48 The compressor inlet and turbine outlet are instrumented with Kistler 4045A2 piezoresistive pressure transducers with a natural frequency of 30 kHz, providing linear measurement of oscillations up to 6 kHz, a maximum compensated operating temperature of 120 C , and a maximum pressure of 2 bar absolute. The compressor outlet and plenum pressure transducers are Kistler 4045A5 piezoresistive models, also with a natural frequency of 30 kHz and a maximum compensated operating temperature of
120 , but with a maximum pressure of 5 bar absolute. As compressor outlet and plenum temperatures can exceed 120 C , the transducers are installed within water jackets to prevent damage. As the dominant frequencies of interest during surge are typically below 200 Hz, these transducers allow for performance and surge measurements. Above 6 kHz, the transducers are non-linear and not recommended for use by Kistler as the linear sensitivity values are no longer applicable. The turbine inlet pressure is measured with a Validyne P55D differential pressure transducer referenced to barometric pressure using an 80 psi diaphragm. This provides better control relative to barometric pressure and allows one of the two available Kistler 4045A5 transducers to be installed in the plenum. The Validyne P55D differential pressure transducer can measure frequencies up to 250 Hz and will mainly be used for bench control and map data. K- type thermocouples are installed at each location near the Kistler or Validyne transducer.
To measure the steady state mass flow rate in the compressor and turbine, one of the orifice flow meters discussed in Section 2.4 was installed in each loop. For both meters, a Validyne P55D differential pressure transducer measures the pressure drop across the orifice and the inlet pressure relative to barometric pressure. A 90 in H2O diaphragm is selected for each orifice pressure drop as well as an 8 psi and an 80 psi 49 diaphragm for the compressor and turbine meter inlet pressure relative to barometric pressure. Also, a K-type thermocouple was installed upstream of the orifice in both meters.
The turbocharger speed is measured with a PicoTurn BMV6 based on the principle of attenuation by eddy currents and can provide digital pulse or analog voltage outputs. The speed sensor can measure speeds between 200 RPM and 400 kRPM and is capable of operating temperatures up to 230 C . As the orifice flow meters only measure steady state mass flow rate, another device, such as a hot wire anemometer, is needed to obtain the instantaneous mass flow rate in the compressor loop. However, from research into hot wire suppliers, the flow velocity, pressure, and temperature fluctuations during deep surge require an expensive, dynamically compensated system.
Therefore, instantaneous mass flow rate measurement is currently not implemented. For acoustic information above 6 kHz, microphones would have to be implemented.
To configure a data acquisition and control system, the number of channels and sample rate for each type of input signal must be determined. Using the Nyquist
Theorem, the minimum sample rate must be twice the maximum frequency of interest for frequency analysis. Typically, for waveform analysis in the time domain, a sample rate of at least ten times the maximum frequency of interest is recommended (Doebelin,
2004). As simultaneous pressure signals will be analyzed, each high frequency voltage channel will have its own A/D converter (the channels will not be multiplexed) such that signal comparison is accurate in the time domain. A summary of current as well as possible future input and output signals is provided in Table 2.4.
50 Description Number Input/Output Type Sample Rate Simult. Kistler 4 Input 0-5 V, 0-10 V 60 kHz Y Validyne 5 Input 0-5 V 2.5 kHz Y
Thermocouple 7 Input Thermocouple 100 Hz N Current Valve Control 2 Output 4-20 mA 100 Hz N Pressure Transducer 4 Input 0-100 mV to 0-10 V 400 kHz Y Microphones 4 Input 0-7.1 V 800 kHz Y Hot Wire Anemometer 1 Input 0-5 V 10 kHz Y
Future Thermocouple 5 Input Thermocouple 100 HZ N Additional Control 2 Output 4-20 mA 1 kHz N Table 2.4: Predicted Input and Output Channels for DAQ/Control System
Using Table 2.4, the data acquisition system was configured as a two chassis system due to the wide variety of measurements and channel count. A National
Instruments (NI) cDAQ-9178, 8-slot, chassis with NI 9213, NI 9203, and NI 9265 modules provides 16 channels of thermocouple measurement, 8 channels of 0-20 mA input at a 200 kHz multiplexed sampling rate, and 4 channels of 0-20 mA output at a
100 kHz multiplexed sampling rate. Also, a NI PXIe-1073, 5-slot, chassis with NI PXIe-
6358 and NI PXI 6143S modules allow for 16 channels of variable input voltage (settable to 0-1 V, 0-2 V, 0-5 V, or 0-10 V) at a 1.25 MHz simultaneous sampling rate and 8 channels of input 0-5 V at a 250 kHz simultaneous sampling rate. This configuration accommodates all of the current needs as well as the potential future needs with a wide amount of flexibility.
51 2.7 Turbine and Compressor System Geometry
The turbine inlet geometry is a 31.75 in piece of straight steel tube, a sufficient length to ensure developed flow at the entrance to the turbine. The turbine inlet tube has an inside diameter of 1.37 in (identical to turbine inlet), outside diameter of 1.50 in, and a
1 in radius inlet bellmouth that is connected to the 3.325 in pipe downstream of the turbine flow control valve mentioned in Section 2.3. The K-type thermocouple and
Validyne P55D pressure tap locations are 1 and 1.25 in upstream of the flange interface, respectively. The turbine outlet is connected using a three bolt flange to an 18 in long pipe with a 1.725 in inside diameter (identical to the turbine outlet) and a 1.975 in outside diameter. The flush mounted Kistler 4045A2 pressure transducer and K-type thermocouple are located 2 and 2.5 in downstream of the flange interface, respectively.
The compressor system geometry can be broken up into two systems: small and large “B.” A picture of each system is provided in Figs. 2.22 and 2.23. A sketch of the compressor outlet geometry for the large “B” system is provided in Fig. 2.24 while a sketch for the compressor inlet geometry used for both the large and small “B” systems is provided in Fig. 2.25. The large “B” compressor outlet system consists of an outlet adapter, duct, duct to plenum adapter, variable volume plenum, pipe elbow assembly, and the compressor flow control valve. The outlet adapter connects the volute exit to the duct which contains the flush mounted Kistler 4045A5 transducer and K-type thermocouple.
The duct then connects to the variable volume plenum via the adapter. The flush mounted plenum Kistler 4045A5 transducer and K-type thermocouple are located in the duct to plenum adapter such that the piston can be fully closed during the volume
52 adjustment. Finally, the pipe elbow assembly connects the plenum to the compressor
flow control valve. The duct length, LCO , and the plenum volume, which will be used to control “B” values, will be presented in Chapter 4 along with the experimental data. As the large “B” system does not allow low enough “B” values to measure far left of the stability limit, surge line, a small “B” system was implemented. As Fig. 2.26 illustrates, the small “B” system eliminates the plenum volume, pipe elbow assembly, and the longer duct of the large “B” system. Therefore, the “B” value of the system is reduced, allowing performance data left of the surge line to be measured.
53
Figure 2.22: Small “B” System
Figure 2.23: Large “B” System
54 The geometry at the compressor inlet and downstream of the valve in the compressor outlet system are the same for the small and large “B” systems. The compressor inlet system consists of an inlet bellmouth duct that contains the flush mounted Kistler 4045A2 transducer as well as the K-type thermocouple and connects to
the compressor inlet directly. The compressor inlet duct length is defined as LCI as it will be specified in Chapter 4 along with the experimental data. The geometry downstream of the valve in the compressor outlet systems consists of 3 in inside diameter PVC pipe to the orifice flow meter made out of PVC as discussed in Section 2.4. After the orifice flow meter, 3 in inside diameter PVC pipe routes the air to an exhaust duct that vents outside the building. Temperatures above 125 ˚C (257 ˚F) are observed in the orifice flow meter and the connected pipe, high enough to cause damage. Therefore, an air to water intercooler was installed directly after the valve before transitioning to PVC, reducing temperatures in the PVC components to below 30 ˚C (86 ˚F). The intercooler causes a maximum air pressure drop of 0.1 psi, hence minimally affecting the flow system.
55
tic
tic
Compressor Inlet Schema Inlet Compressor
: :
2.25
Large “B” Compressor Outlet Schema “B” Outlet Large Compressor
: :
Figure Figure Figure 2.24 Figure
56
Figure 2.26: Small “B” Compressor Outlet Schematic
57
CHAPTER 3
LUMPED PARAMETER MODEL
In Chapter 1, the physics of mild and deep surge as well as the stability criterion defining the location of the surge line in a compression system was discussed. This stability criterion only provides some insight into when the compression system will transition from a stable operating point into a self-sustaining surge oscillation rather than the overall system dynamic behavior (Fink, 1992). Therefore, it is desirable to create a model that predicts the overall system dynamic behavior, especially while operating in self-sustained surge. This chapter will discuss the available models in the literature, their derivation and assumptions, model inputs, and a comparison to previously published results. The latter will include two different forms of the lumped parameter model:
(1) one without a compressor time lag (Section 3.3.2), and (2) another with a compressor time lag (Section 3.4.2). In addition, a parametric study will be performed for the time step and time lag constants.
58 3.1 Literature Review
As stated in Chapter 1, Greitzer (1976) laid some of the foundations of compression system surge studies by creating a lumped parameter model to predict overall system physics for an axial compressor. The simplified compression system geometry used in the model is shown in Fig. 1.6 and consists of a compressor duct, plenum, and throttle with a duct. Greitzer (1976) used the following assumptions to develop the system of equations that define the model:
1. One-dimensional, incompressible flow in a constant area compressor and throttle
duct.
2. The compressor and throttle are modeled by actuator discs with zero length.
3. Duct Mach numbers are low and the pressure rise across the compressor is small
compared to ambient pressure, allowing ambient density to be used for the
compressor and throttle ducts.
4. Isentropic compression and expansion in the plenum.
5. Negligible velocity in the plenum.
6. Constant compressor speed.
The governing equation for the conservation of momentum in the compressor duct is
Lcc dm pp2 P , (3.1) Ac dt
where t is time, Lc is the compressor duct length, Ac is the compressor reference area,
mc is the mass flow rate in the compressor duct, p2 is the pressure in the compressor
59 duct, and pP is the pressure in the plenum. The sum of the ratio of the length to area for
L L all of the actual ducting, , is taken as the lumped c ratio for the model. Applying A Ac the same conservation of momentum derivation to the throttle duct yields
LTT dm ppP , (3.2) AT dt
where LT is the throttle duct length, AT is the throttle duct area, mT is the mass flow
rate in the throttle duct, and p is the ambient pressure. The third balance equation, conservation of mass in the plenum, is derived as
VPP dp 2 mmcT , (3.3) aP dt
dPP1 dp where 2 has already been implemented from the isentropic plenum dt aP dt
compression and expansion assumption, VP is the plenum volume, P is the plenum
density, and aP is the speed of sound in the plenum. Using these three equations, the system dynamics without a compressor time lag can be modeled. However, in reality there is a time lag, or delay, in the compressor response that allows deviation from the steady state performance characteristics. Applying this concept yields the first order time lag equation
dp 2 pp , (3.4) dt 22ss
60 kr2 where 2 is the time lag constant presented by Greitzer (1976), k is some U
number of revolutions (typically two), r2 is the impeller tip radius, U is the impeller tip
speed, p2ss is the compressor duct pressure calculated using the steady state
characteristic, and p2 is the instantaneous compressor duct pressure.
In Fig. 3.1, Greitzer (1976) compared the experimental results (open circles) and model predictions (dashed line) with solid line representing the compressor characteristic.
The model captures the overall trends but fails to match experimental data closely.
Greitzer (1976) states it is difficult to model systems in the reverse flow and unstable, positive (+) slope regions due to the lack of knowledge and experience at the time of publication. Therefore, improving the compressor characteristic in the reverse flow and
(+) slope regions should improve the comparison between the model predictions and experimental results.
61
Figure 3.1: Experimental and Theoretical Results for B = 1.29 (Greitzer, 1976)
Hansen et al. (1981) applied Eqs. (3.1) - (3.4) to a centrifugal compression system with satisfactory results presented in Fig. 3.2. Solid and dashed lines indicate model predictions and the compressor steady state characteristic, respectively, while dots and circles present pressure transducer data vs. flow rates as inferred from inlet and outlet hotwires, respectively. The somewhat improved accuracy relative to Greitzer (1976) is because Hansen et al. (1981) measured the characteristics for reverse flow and the region with (-) slope right of the surge line. The two measured characteristics were connected with a cubic polynomial in the (+) slope region left of the surge line. Arnulfi et al. (1999) applied Greitzer‟s (1976) model to a multistage centrifugal compressor with improved accuracy as they measured the compressor steady state characteristic in the entire (+) and reverse flow region. Therefore, Grietzer‟s (1976) model is applicable to centrifugal compression systems.
62
Figure 3.2: Experimental and Theoretical Results (Hansen et al., 1981)
Fink (1988) modified Greitzer‟s (1976) model to allow speed to change and assumed the throttle duct is short and inductance free. This eliminates the throttle conservation of momentum, Eq. (3.2). To allow speed to change, Fink added a conservation of angular momentum equation for the turbocharger shaft assembly as
I dU TTDc , (3.5) r2 dt
where I is the turbocharger shaft assembly inertia, TD is the turbine drive torque, and
Tc is the compressor torque. Adding the energy storage of the turbocharger speed variation significantly changes the physics of the compression system during mild and deep surge. A quiescent period was introduced between deep surge flow reversals with a variable speed, Fig. 3.3b, unlike the fixed speed case, Fig. 3.3a. Fink (1988) also stated 63 that by introducing a variable shaft speed, the mild to deep surge transition flow rate was reduced and the mild surge amplitudes were elevated.
Figure 3.3: Compression System Model Results for T =0.235, (a) Fixed Speed, (b) Variable Speed (Fink, 1992)
L Fink (1988) used the compressor through flow time for the time lag constant, mer , C
where Lmer is the meridonial length of the compressor and C is the average flow velocity through the compressor. Therefore, Fink‟s (1988) model consists of Eq. (3.1) and
Eqs. (3.3) - (3.5) and alters Greitzer‟s (1976) assumptions as follows:
1. The throttle duct length is now short and inductance free.
2. The quasi-steady throttle nozzle is choked.
3. The gas angular momentum in the compressor passages is negligible compared to
the wheel angular momentum.
64 4. Ambient density is no longer used for the duct since the compressor pressure rise
is not small relative to ambient pressure.
5. The compressor speed is no longer constant.
Fink (1988) measured the entire (+) flow region of the compressor pressure ratio and torque characteristics. The reverse flow characteristics were determined by calculating instantaneous compressor mass flow rate and pressure ratio with plenum conditions using Eq. (3.3) and (3.1), respectively. These characteristics are displayed in non-dimensional form in Fig. 3.4.
Figure 3.4: Non-Dimensional Pressure Rise and Torque Characteristics (Fink, 1992)
65 The compressor flow coefficient is determined as
Cmxc c , (3.6) UAU1 c
where Cx and 1 are the axial velocity and density at the compressor inlet, respectively.
For forward flow through the compressor (designated by subscript f ), the non- dimensional pressure rise and compressor torque are determined by
1 p 2 1 p1 f 2 (3.7) 1 M to and
Tc f 2 , (3.8) 12Ac r U
U respectively, where is the fluid specific heat ratio, M to is the compressor tip a1
Mach number relative to inlet conditions, and a1 is the speed of sound at the compressor inlet. In reverse flow (designated by subscript b ), the characteristics are defined as
1 p 1 1 p2 b 2 (3.9) 1 M tp
and
66 Tc b 2 , (3.10) 22Ac r U
U respectively, where M tp is the compressor tip Mach number relative to outlet a2
conditions, 2 is the density at the compressor outlet, and a2 is the speed of sound at the compressor outlet. As the fluid in the duct is considered incompressible and the Mach
number is assumed low, 1 , aa1 , 2 P , and aa2 P . Therefore, plenum conditions can be used in Eqs. (3.9) and (3.10) to determine the non-dimensional pressure ratio and torque coefficients.
Theotokatos and Kyrtatos (2001) implemented Fink‟s (1988) model into their 1-D code to better predict compression system performance. However, they only measured steady state characteristics in the region with negative (-) slope to the right of the deep surge line. Then they developed a method to extrapolate the steady state characteristics to the left of the deep surge line in the (+) slope and reverse flow regions. The pressure ratio characteristics in the (+) slope and reverse flow region are determined using
3 p2 p20 mCC m pr 1 1.5 1 0.5 1 , (3.11) pp 1 10 and
p2 p20 2 2 pr 2 mc , (3.12) pp1 10 2
67 p respectively, where 20 is the pressure ratio at zero flow while and are parameters p10 shown in Fig. 3.5. The pressure ratio at zero flow can be calculated using radial equilibrium as
2 1 p20 U 1 22 1 2 rr21 , (3.13) p102 RT 1 r 2
where R is the ideal gas constant, T1 the compressor inlet temperature, and r1 as the impeller mean geometric radius, dividing the inlet area into two sections with equivalent areas. Non-dimensional pressure ratio is calculated using Eqs. (3.7) and (3.9) for the (+) and reverse flows, respectively. Theotokatos and Kyratos (2001) then calculated the torque for the stable region right of the surge line of the compressor map as
1 r Rm T p T 21c 2 1 , (3.14) c Up1 c 1
where C is the compressor efficiency. The mass flow rate and torque are then non- dimensionalized using Eqs. (3.6) and (3.8), respectively. The dimensionless torque, ,
versus flow coefficient, c , is then fit by a line for the entire (+) flow region as
cc12 c , (3.15)
where c1 and c2 are the fit coefficients. In the (-) flow region, the even extension (mirror image) of Eq. (3.15) is applied. The non-dimensional extrapolated characteristics can be converted back to dimensional form through Eqs. (3.6) - (3.10), while using Eq. (3.14) to 68 determine compressor efficiency. By implementing these extrapolations, Theotokatos and Kyrtatos (2001) were able to predict system performance when operating outside of the measured data.
Figure 3.5: Characteristic Extrapolation Values (Theotokatos and Kyrtatos, 2001)
3.2 Selected Model, Assumptions, and Method of Calculation
Fink‟s (1988) model was selected as it allows the compressor speed to vary, better capturing mild and deep surge physics. Therefore, the assumptions used are those stated in Section 3.1 with Fink‟s (1988) model and Eq. (3.1) and Eqs. (3.3) - (3.5) as the system of ordinary differential equations. The calculation of the conditions at each location of the compression system will be discussed in the remainder of this section.
The ambient conditions are assumed to be STP with p 101,325 Pa and
T 298 K . As the duct fluid is assumed incompressible with low Mach numbers, the
69 conditions at state 1 are the same as ambient. Initially, an equilibrium flow coefficient,
mc T , is defined, and the non-dimensional pressure ratio and torque are PcAU determined from the characteristics in Fig. 3.4. Using Eqs. (3.6) - (3.10), the compressor
p2 pressure ratio, , mass flow rate, mc , and torque, Tc , are calculated. The drive torque, p1
TD , is set equal to the compressor torque and is assumed constant. The compressor
efficiency, c , can be determined using Eq. (3.14) with the compressor torque and
pressure ratio. Using the compressor efficiency, pressure ratio, and inlet temperature, T1 , the compressor outlet temperature can be calculated as
1 p 2 1 p1 TT211 . (3.16) c
As the initial point is in equilibrium, the plenum pressure, and temperature, TP , are the same as the compressor duct pressure and temperature. Also, the compressor duct steady
state pressure, p2ss , is initially set equal to the instantaneous pressure, p2 . Using the
choked flow assumption and the equilibrium flow rate, mT T P AU c , the throttle effective area is
mT AT 1 , (3.17) 2 21 PPa 1
70 which is kept constant throughout the simulation. The lumped parameter model temporal, or time, scale is broken into steps. The system of ordinary differential equations is solved using a 4th order Runge-Kutta method for each step. The output U ,
mc , pP , and p2 at the current time step are used to calculate the Tc , p2ss , aP , and mT for the next step. This process is repeated for a user-defined number of time steps.
3.3 Model Results without a Time Lag
The time lag equation, Eq. (3.5), is disregarded and only Eqs. (3.1), (3.3), and
(3.4) are solved simultaneously for each time step to solve the model without a compressor time lag. The model results will be created using Fink‟s equilibrium tip
2 speed, U = 322 m/s, tip radius, r2 = 0.0639 m , shaft inertia, I = 0.001 kg/m ,
2 compressor duct length, Lc = 1.27 m, reference area, Ac = 0.0036 m , and plenum
3 volume, VP = 0.2078 m . The model is still the one presented in Section 3.2, except the
compressor outlet pressure, p2 , is now calculated directly from the characteristics in
Fig. 3.4 rather than using the time lag equation. As mentioned in Section 3.2, the time step size dictates the number of steps needed to capture the physics for a desired time duration. Therefore, a study of the effect of step size on the model results without a time lag will be performed to ensure accuracy prior to comparing results with Fink (1988).
71 3.3.1 Time Step Validation
In numerical models, errors are typically due to the combined effects of the scheme characteristics and their spatial and temporal discretization (Dickey et al., 2003).
Therefore, the numerical scheme selection and its discretization values are a compromise between accuracy, stability, and computational requirements (Dickey et al., 2003). As mentioned in Section 3.2, the numerical scheme is a 4th order Runge-Kutta method solved using MATLAB. This scheme is known to be an accurate scheme with suitable computational requirements. Therefore, only the discretization values need to be carefully selected for an appropriate compromise between accuracy, stability, and computational requirements. Since the lumped parameter model has a temporal but no spatial variation, only the effect of the temporal discretization needs to be evaluated. The time step was varied from a small value, 6 microseconds in this case, to one that forced
numerical instability. The equilibrium flow coefficient, T , defines the throttle area,
A , and drive torque, T , which are kept constant throughout the duration of each T D
simulation. T 0.1000, 0.2350, and 0.2400 are used for the time step parametric study.
A curve was fit to these results to better show the trends of the numerical results which are presented in Figs. 3.6-3.9. These results show the percent change relative to
converged values for the c and amplitudes as well as frequencies. A solid square was placed on the point in each figure that indicates the time step values for a 5% deviation from the converged values. The 5% value was selected as the convergence criterion for the time step size to account for the error associated with the assumptions and lumping process. This value yields a good approximation to mild and deep surge as
72 will be discussed in Section 3.3.2; however, it could be further reduced to improve
convergence. The % frequency deviation for c and , Figs. 3.7 and 3.9, is smaller than their % amplitude change, Figs. 3.6 and 3.8, for a given time step size. This is consistent with the observation made earlier by Dickey et al. (2003). The deviation is
largest for T in the following order: 0.2400, 0.1000, and 0.2350. The frequencies for
T 0.2400, 0.2350, and 0.1000 are 10.55 Hz, 0.254 Hz, and 3.765 Hz, respectively.
Therefore, the higher the frequency, the smaller the time step must be to ensure accuracy.
Dickey et al. (2003) and Radavich (2000) support this finding. Radavich (2000) provides a predictive equation for the necessary time step as
1 t , (3.18) nf where n is some integer constant and f is the frequency of interest. Radavich (2000) mentions that n values of 2,000 to 4,000 are typical. As seen in Figs. 3.6-3.9, the largest time step that still provides less than a 5% deviation is 25 microseconds from the
c and amplitudes at T 0.2400. Applying Eq. (3.18) with a dominant frequency of 10.55 Hz yields n 3,791 which lies in the range indicated by Radavich (2000).
Therefore, this time step will be used when comparing model results without a time lag with Fink (1988) in Section 3.3.2.
73
Figure 3.6: Flow Coefficient Amplitude Time Step Study – Without a Time Lag
Figure 3.7: Flow Coefficient Frequency Time Step Study – Without a Time Lag
74
Figure 3.8: Head Coefficient Amplitude Time Step Study – Without a Time Lag
Figure 3.9: Head Coefficient Frequency Time Step Study – Without a Time Lag
75 3.3.2 Comparison of Model Results without a Time Lag with Fink (1988)
Fink (1988) solved his lumped parameter model both with and without the compressor time lag. Predictions without a time lag from the model developed here and
Fink (1988) are compared in Figs. 3.10-3.16 using T 0.2400, 0.2398, 0.2397, 0.2350,
0.2300, 0.2000, and 0.1000. Each figure presents three plots, including the instantaneous
flow coefficient, c , impeller tip Mach number, M to , and non-dimensional pressure rise,
, vs. the Helmholtz resonator period, t H , over a range of 0 to 95. The results for 2
each T match Fink‟s (1988) model well in amplitudes as well as frequencies. The
model results are in a decaying mild surge oscillation when T 0.2400 (Fig. 3.10a),
just like Fink‟s (1988) results (Fig. 3.10b). Moving to T 0.2398 (Figs. 3.11a and
3.11b), placed both model results into a self-sustained mild surge oscillation. Deep surge is noticed by both at 0.2397 (Figs. 3.12a and 3.12b) with the first flow reversal T
occurring at t H 70 . The amplitudes of , , and M are also identical. Again, at 2 c to
T 0.2350 (Figs. 3.13a and 3.13b), the results match closely, except for a small deviation in cycle frequency. Such a deviation in the period between flow reversals can be attributed to the potential differences that were approximated here from Fink (1988) rather than having the actual data. This deviation in the period between flow reversals is
most evident at T 0.2350 (Figs. 3.13a and 3.13b), since the system spends a large
amount of time in the mild to deep surge transition region. However, at T 0.2300
(Figs. 3.14a and 3.14b), 0.2000 (Figs. 3.15a and 3.15b), and 0.1000 (Figs. 3.16a and
76 3.16b), the predictions appear to be identical. As these results match well, the next step is to add the time lag equation, Eq. (3.5), and compare the predictions with the experimental results of Fink (1988).
77
Figure 3.10: Predictions without Time Lag for T =0.2400; (a) Present Model, (b) Fink’s Model (1988)
78
Figure 3.11: Predictions without Time Lag for T =0.2398; (a) Present Model, (b) Fink’s Model (1988)
79
Figure 3.12: Predictions without Time Lag for T =0.2397; (a) Present Model, (b) Fink’s Model (1988)
80
Figure 3.13: Predictions without Time Lag for T =0.2350; (a) Present Model, (b) Fink’s Model (1988)
81
Figure 3.14: Predictions without Time Lag for T =0.2300; (a) Present Model, (b) Fink’s Model (1988)
82
Figure 3.15: Predictions without Time Lag for T =0.2000; (a) Present Model, (b) Fink’s Model (1988)
83
Figure 3.16: Predictions without Time Lag for T =0.1000; (a) Present Model, (b) Fink’s Model (1988)
84 3.4 Model Results with a Time Lag
The time lag equation, Eq. (3.5), is added to Eqs. (3.1), (3.3), and (3.4) and solved simultaneously to allow the compressor pressure ratio to deviate from the steady state characteristic. With the addition of Eq. (3.5), the model is solved as described in
Section 3.2, where the compressor outlet pressure, p , is calculated using the time lag 2 equation. Similar to the preceding section, a time step comparison will also be performed for the time lag model to ensure accuracy prior to comparing with experimental results.
Finally, a parametric study is performed by implementing time lag constants previously used in literature.
3.4.1 Time Step Validation
Fink‟s (1988) time lag constant, presented in Section 3.2, is used here for the time step study. Therefore, much like the model without a time lag, three equilibrium flow
coefficients, T 0.1000, 0.2350, and 0.2400 , were selected. The step size was varied from a value of 6 milliseconds to either 3 seconds or instability, whichever occurred first. A curve fit was applied to these points such that a trend could be observed. The results are presented in Figs. 3.17-3.20 with solid squares indicating the necessary time step to ensure 5% accuracy, which provides a reasonable compromise between computational time and accuracy. As in the model without a time lag, the time
step has a much larger effect on the amplitudes of the c and oscillations than their frequencies, consistent with observations of Dickey et al. (2003) and Radavich (2000).
To meet the 5% accuracy criterion for any T , a 6 millisecond time step was selected. A
85 mild surge flow coefficient, T 0.2400 , requires a smaller time step than the deep
surge cases with T 0.1000 and 0.2350. This follows the observations of the model
without the compressor time lag as T 0.2400, 0.1000, and 0.2350 have the highest frequency in that order. Therefore, the higher the frequency, the smaller the time step must be to ensure accuracy. Applying Eq. (3.18) with a dominant frequency of 9.76 Hz yields n 17,076, which is significantly larger than that suggested by Radavich (2000).
Figure 3.17: Flow Coefficient Amplitude Time Step Study – Time Lag
86
Figure 3.18: Flow Coefficient Frequency Time Step Study – Time Lag
Figure 3.19: Head Coefficient Amplitude Time Step Study – Time Lag
87
Figure 3.20: Head Coefficient Frequency Time Step Study – Time Lag
3.4.2 Time Lag Constant Study and Comparison with Experimental Results
Fink (1988) presented experimental data for two equilibrium flow coefficients,
T 0.235 (deep surge) and 0.236 (mild surge), as shown in Figs. 3.21a and 3.21b, respectively. The time lag model used by Fink (1988) was able to match these experimental results closely. Therefore, the model developed here was implemented using Fink‟s (1988) time lag constant.
88
Figure 3.21: Experimental Results; (a) T =0.236, (b) =0.235 (Fink, 1988)
At T 0.236 (Fig. 3.22), the predictions are in deep surge while Fink‟s (1988) experimental results are in mild surge (Fig. 3.21a). The flow coefficient was increased to
T 0.2398 , at which point mild surge was predicted. However, this was also the same
T for mild surge in the model predictions without a time lag (Fig. 3.11b). Therefore, the predictions using Fink‟s (1988) time lag constant do not appear to transition from
mild to deep surge at the same T as his experimental results. At T 0.235 , the deep surge predictions (Fig. 3.23) have similar periods, amplitudes, and overall characteristics relative to Fink‟s (1988) experimental results (Fig. 3.21b). Hence, the model developed here with Fink‟s (1988) time lag constant matches his deep surge experimental results reasonably well. In Eq. (3.5), the only variable is the time lag constant itself as the
89 steady-state pressure, p2ss , is determined from the measured performance characteristics
and the instantaneous pressure, p2 , is provided from the previous time step. Therefore, a time lag constant parametric study was performed to understand its influence on the
system and the T for transition from mild to deep surge.
Figure 3.22: Time Lag Model Results, T =0.2360, τ = Fink (1988)
90
Figure 3.23: Time Lag Model Results, T =0.2350, τ = Fink (1988)
Since Fink‟s (1988) and Greitzer‟s (1976) time lag constants are both used in literature, Greitzer‟s (1976) time lag constant is next implemented with the results shown
in Fig. 3.23. This implementation did not yield the mild surge at T 0.236 (Fig. 3.24) either which was observed in Fink‟s (1988) experimental data (Fig. 3.21a). Varying the
flow coefficient led to mild surge at T 0.2398 , similar to observations with the previous time lag constant. At 0.235 (Fig. 3.25), the deep surge predictions have T slightly reduced periods, but similar amplitudes and overall characteristics relative to
Fink‟s (1988) experimental results (Fig. 3.21b). Further analysis shows that
Fink‟s (1988) time lag constant approaches infinity at zero mass flow rate, while
Grietzer‟s (1976) fluctuates as a function of impeller tip speed. Neither time lag constant
yielded predictions that transition from mild to deep surge at a similar T as 91 Fink‟s (1988) experimental results. However, a time lag constant needs to be selected for the implementation later in Chapter 5 when Fink‟s (1988) model is applied to the experimental facility described in Chapter 2. Since both Greitzer‟s (1976) and
Fink‟s (1988) time lag constants yielded similar predictions, Fink‟s (1988) will be used to maintain consistency with his model.
Figure 3.24: Time Lag Model Results, T =0.2360, τ = Greitzer (1976)
92
Figure 3.25: Time Lag Model Results, T =0.2350, τ = Greitzer (1976)
93
CHAPTER 4
EXPERIMENTAL RESULTS
In Chapter 3, the lumped parameter model was discussed and compared with previously published data from Fink (1988). This chapter will present the experimental data acquired from the facility discussed in Chapter 2. The data is discussed in two main sections: (1) small and large “B” performance characteristics; (2) mild and deep surge temporal behavior at multiple volumes and speeds. The temporal behavior will consist of compressor inlet, outlet, and plenum pressures as well as turbocharger shaft speeds.
Therefore, this chapter will first discuss the compression system geometries (lengths and volumes) used throughout the experiments. Then, the performance maps from the small and large “B” data will be presented as well as how they were calculated. Finally, the mild and deep surge temporal behavior at a variety of speeds and volumes will be presented.
4.1 Small and Large “B” Compression System Geometries
Throughout this chapter, data will be presented from the small and large “B” systems discussed in Section 2.7. An image of the small “B” system and a sketch of its geometry are presented in Figs. 2.22 and 2.26, respectively. This system was 94 implemented as it allowed for smaller “B” numbers (0.14, 0.18, and 0.20 for tip speeds of
230, 310, and 370 m/s, respectively) than the large “B” system (0.67, 0.87, and 1.02 for tip speeds of 230, 310, and 370 m/s, respectively). The smaller “B” values allow acquisition of data to the left of the deep surge line of the compressor, whereas the large
“B” system would enter into deep surge. Therefore, the small “B” system was well suited for the measurement of the performance characteristics of the compression system, which will be further discussed in Section 4.2.
An image of the large “B” system and a sketch of its geometry are presented in
Figs. 2.23 and 2.24, respectively. As noted in Section 2.7, the compressor outlet and plenum length were left undefined until this chapter. The compressor outlet duct length,
LCO , was kept fixed at 14 in (0.356 m) during the entire data acquisition. However, the plenum length, which defines the volume, was set at four different values presented in
Table 4.1. During the large “B” experiments for the performance characteristics, the volume was at the full setting, yet, all volumes were used when capturing mild and deep surge temporal behavior. Finally, the compressor inlet system, which remained the same
for both the small and large “B” systems, is depicted in Fig. 2.25 and its length, LCI , is kept constant at 15 in (0.381 m) throughout the experiments.
Full 1/2 1/4 1/8 Length (m) 0.857 0.429 0.214 0.107 3 Volume (m ) 0.00924 0.00462 0.00231 0.00115 Table 4.1: Plenum Volume Settings
95 4.2 Small and Large “B” Performance Characteristics
The compressor operating range was swept with both the small and large “B” systems to determine the performance characteristics of the BorgWarner turbocharger within the regions of interest. As stated earlier in Chapter 1, most compressor characteristics are defined with a pressure ratio, corrected mass flow rate, and reduced
speed. Therefore, the measured static pressure at the compressor inlet and outlet, p1 and
p2 , static temperature at the compressor inlet and outlet, T1 and T2 , turbocharger speed
in rev/min, N , and the compressor mass flow rate, mc , need to be converted in order to produce the compressor map.
To convert static quantities to total quantities, the velocity at each measurement location needs identified. For a cross-sectional area, A , the velocity is given by
m u c , (4.1) A
where mc is the measured compressor loop mass flow rate from the orifice flow meter
p and is the density at the measurement location. Equation (4.1) is applied at the RT compressor inlet and outlet, locations 1 and 2. Using the velocity at each location, the static pressure, p , can be converted to total pressure by
1 p p u2 , (4.2) 0 2
96 p which yields the total to total pressure ratio, 02 , used in the compressor map. The p01 compressor inlet total temperature is then calculated as
1 1 p01 TT01 1 . (4.3) p1
The reduced tip speed in the compressor map can then be calculated by
2 Tref Ured r2 N , (4.4) 60 T01
where r2 is the impeller tip radius, N is the turbocharger speed in rev/min, and Tref is the reference temperature (typically 298 K). Finally, the corrected mass flow rate used in the compressor map is
Tref
T01 mmc, cor c , (4.5) p01
pref
where pref is the reference pressure (typically 1 bar) and mc is the measured compressor mass flow rate. The next step is to determine the compressor total to total efficiency as
1 p 02 1 p 01 . (4.6) c, tt T 02 1 T01
97 Finally, the compressor torque can be determined using Eq. (3.14) with the total to total
efficiency, c, tt , compressor inlet total temperature, T01 , corrected mass flow rate, mc, cor ,
p and the total to total pressure ratio, 02 . Using Eqs. (3.14) and (4.1) - (4.6), the p01 compressor pressure ratio, efficiency, and torque characteristics can be created from measured data.
The small and large “B” systems with a full volume setting were swept within the
region of interest to create the 230, 310, and 370 m/s reduced speed, Ured , lines. These speed lines are plotted in Figs. 4.1-4.3 using data points within a reduced speed,
Ured 0.62 m/s, of the target 230, 310, or 370 m/s. The large “B” system with full volume was swept from the maximum open position of the compressor load control valve to the point at which deep surge occurred for each speed line. The small “B” system was swept from the maximum open position of the compressor load control valve to the minimum allowable pressure drop for a reasonable accuracy across the smallest orifice discussed in Section 2.4. Figures 4.1-4.3 present the total to total pressure ratio, total to total efficiency, and the compressor torque as a function of the corrected mass flow rate, respectively. The large and small “B” data are in agreement. Also, the small “B” system allows the compressor map to be measured significantly further left than the large “B” system with full volume due to improved stability with lower “B” numbers. The small
“B” system allowed mapping further right, closer to a pressure ratio of unity, than the large “B” data due to the lower pressure drop across the system. The agreement of the small and large “B” performance characteristics and the extended map region of the small
98 “B” data was also observed by Fink (1988). Finally, the far left points of the large “B” data define the deep surge line of the compressor. The application of these maps within the lumped parameter model will be further expanded upon in Chapter 5.
Figure 4.1: Measured Pressure Ratio Characteristics; Magnified view in * will be discussed in Section 4.3.3
99
Figure 4.2: Measured Efficiency Characteristics
0.7 Small B Data Large B Data 0.6
0.5
370 m/s
m] -
0.4
[N
c T
0.3 310 m/s
Torque [N-m] Torque Torque,
0.2
230 m/s 0.1
0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Mass Flow Ratem [kg/s] Mass Flow Rate, c , cor [kg/s] Figure 4.3: Measured Torque Characteristics
100 4.3 Mild and Deep Surge Temporal Behavior
Temporal behavior during mild and deep surge for each volume in Table 4.1 was taken with the large “B” system at each speed. This temporal behavior will be presented here along with frequency analyses to provide a better understanding of the system physics. Prior to presenting the data, a system geometry calculation will be performed to predict the expected frequencies at each volume.
Greitzer (1976) and Fink (1988) present the Helmholtz frequency as
waHPAc fH , (4.7) 22LVcP
where wH is the Helmholtz angular frequency, aP is the speed of sound in plenum, Ac is
the compressor reference area, Lc is the compressor duct length, and VP is the plenum volume. In the discussion of Greitzer‟s (1976) model in Chapter 3, it was stated that the
L L sum of the ratio of the length to area, , is taken as the lumped c ratio for the A Ac model. This method is applied for the compressor inlet duct, compressor, diffuser, volute, compressor outlet duct, plenum, and valve inlet sections in Table 4.2. Also, the compressor and duct have no volume in lumped parameter theory. Therefore, to accurately capture the energy storage of the experimental system, the sum of the compressor, diffuser, volute, outlet duct, plenum, and valve inlet duct volumes is
considered the lumped plenum volume, VP . The inlet duct volume is ignored in the summation process as it is not pressurized by the compressor. The volute was the most
101 difficult to capture due to its circular and semi-conical geometry. The average area over the volute length, assuming a constant rate of diameter expansion, is calculated as
sf 2 2 s d d di f i A ds , (4.8) v 4 s 4ss f f 0 where s is some axial length along the volute, d is the diameter, and subscripts i and f indicate initial and final quantities. The volute used in the experiments had a small
initial diameter, di 3.8 mm (0.15 in) due to the casting and a final diameter,
d f 30.0 mm (1.18 in). By performing a circumference calculation at the mean volute diameter and adding in the exit volute length yielded a final volute length, s f 0.3269 m (12.869 in). Applying these inputs to Eq. (4.8) provided an average area,
42 Av 2.97 10 m , and multiplying by the volute length, s f 0.3269 m yielded a volume of 9.70 1053 m . To verify this calculation, the diffuser was plugged with clay and the volute was filled with water. Water was then poured into a graduated cylinder to determine the volute volume as 94 mL (9.40 1053 m ) which is quite close to the result from Eq. (4.8). The volume was then divided by the volute length, s f 0.3269 m to yield an average area of 2.90 1042 m . The area and volume measured by the water test
L will be used for the lumped c ratio; however, Eq. (4.8) would also yield a good Ac
L approximation. Table 4.2 shows the importance of a careful calculation for the volute A
102 L as it accounts for 46.95, 47.74, 48.14, and 48.34% of the overall c ratio at plenum Ac volume settings of full, 1/2, 1/4, and 1/8, respectively. Using the calculated geometry in
Table 4.2 and an average plenum temperature at each point of Table 4.3, the expected
Helmholtz frequency for the full, 1/2, 1/4, and 1/8 volumes are 12.2, 16.9, 22.6, and
28.9 Hz, respectively.
Inlet Duct Compressor Diffuser Volute Outlet Duct Plenum Valve Inlet Sum Length (m) 0.3810 0.0508 0.0140 0.3269 0.4360 0.8573 0.1752 - Area (m2) 0.00096 0.00086 0.00074 0.00029 0.00071 0.01080 0.00157 -
Full Volume (m3) - 0.000044 0.000010 0.000094 0.000308 0.009258 0.000275 0.009989 L/A Ratio 397.70 58.80 18.88 1136.85 618.00 79.38 111.59 2421.19 Length (m) 0.3810 0.0508 0.0140 0.3269 0.4360 0.4286 0.1752 - Area (m2) 0.00096 0.00086 0.00074 0.00029 0.00071 0.01080 0.00157 - 1/2 Volume (m3) - 0.000044 0.000010 0.000094 0.000308 0.004629 0.000275 0.005360 L/A Ratio 397.70 58.80 18.88 1136.85 618.00 39.69 111.59 2381.51 Length (m) 0.3810 0.0508 0.0140 0.3269 0.4360 0.2143 0.1752 - Area (m2) 0.00096 0.00086 0.00074 0.00029 0.00071 0.01080 0.00157 - 1/4 Volume (m3) - 0.000044 0.000010 0.000094 0.000308 0.002315 0.000275 0.003045 L/A Ratio 397.70 58.80 18.88 1136.85 618.00 19.84 111.59 2361.66 Length (m) 0.3810 0.0508 0.0140 0.3269 0.4360 0.1072 0.1752 - Area (m2) 0.00096 0.00086 0.00074 0.00029 0.00071 0.01080 0.00157 - 1/8 Volume (m3) - 0.000044 0.000010 0.000094 0.000308 0.001157 0.000275 0.001888 L/A Ratio 397.70 58.80 18.88 1136.85 618.00 9.92 111.59 2351.74
Table 4.2: Calculated Ratios
Temporal behavior will be presented by first comparing the three tip speeds, 230,
310, and 370 m/s, at the full plenum volume. Then, the 310 m/s speed will be compared at the remaining 1/2, 1/4, and 1/8 plenum volumes. With each point, a time averaged
(denoted by – over a quantity) mass flow rate, mc, cor , flow coefficient, c , pressure ratio,
103 p 02 , non-dimensional pressure ratio, , rotational speed in rev/min, N , tip speed, U , p01 and “ B ” parameter will be provided in Table 4.3 with deep surge points shaded in a light
gray color. With each operating point, the time averaged mass flow rate, mc, cor , flow
coefficient, c , and “ ” parameter will be provided in the figure caption. The operating points will be presented while moving right to left along the speed line, going from stable, to mild surge, and into deep surge.
104
Table 4.3: Experimental Matrix (with Calculated c , , U , a p , fH , and B )
To ensure the mild surge pressure trace can be easily observed within the overall pressure signal, a zero-phase filter was applied using the filtfilt function in MATLAB.
The impact of the filter can be seen by observing, for example, a mild surge point at the compressor inlet for a 310 m/s impeller tip speed and full plenum volume. An FFT of the signal up to 10 kHz, the Nyquist frequency, and temporal behavior are presented in Figs.
4.4 and 4.5, respectively. In Fig. 4.4, the mild surge oscillation frequency and amplitude 105 are 12.8 Hz and 141.2 dB, respectively. In the unfiltered signal, amplitudes are also significant around 1.8 and 9.5 kHz. This makes it difficult to observe the mild surge oscillations in the unfiltered temporal behavior of Fig. 4.5. For this instance, all information below 120 Hz is unfiltered, or passed, without attenuation, which makes the mild surge trace in Fig. 4.5 clearly visible. Therefore, this method will be used to better observe the time variation of pressure. Pass frequencies are selected such that the surge data is not attenuated. Therefore, a 120 Hz low-pass filter was implemented for mild surge as the predominant low frequency information will not be attenuated regardless of the plenum volume setting. Deep surge temporal behavior possesses information at harmonics of the dominant frequency; therefore, a 200 Hz low-pass filter is implemented to capture the predominant low frequency information.
Frequency Domain of Compressor Inlet Pressure 160 X: 12.8 Unfiltered Y: 141.2 Filtered 140
120
100 SPL [dB]
80
60
40 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Frequency [Hz] Figure 4.4: Typical Mild Surge Frequency Analysis – Compressor Inlet SPL
106 Static Pressure at the Compressor Inlet 1.06 Unfiltered Filtered 1.04
1.02
1 Pressure Pressure [bar] 0.98
0.96
0.94 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] Figure 4.5: Typical Mild Surge Temporal Behavior - Static Pressure at the
Compressor Inlet, p1
4.3.1 Temporal Behavior - U 230 m/s, Full Plenum Volume
Figures 4.6-4.29 present the first impeller tip speed, 230 m/s, at a full plenum volume. A stable operating point right of the peak pressure rise is presented in Figs. 4.6-
4.8 at a time averaged corrected mass flow rate, mc, cor 0.0205 kg/s ( c 0.0873).
Stability is evident as the FFT does not yield elevated amplitudes in the 10-20 Hz region, where the Helmholtz frequency is expected. Moving left on the speed line to
c 0.0847 in Figs. 4.9-4.11, a slight increase in the frequency-domain amplitudes can be noticed in the 10-20 Hz region for the compressor inlet, outlet, and plenum. This may
be viewed here as the beginning of mild surge. Progressing further left to c 0.0826
(Figs. 4.12-4.14), the pressure oscillations begin to more fully develop at 11.6 Hz in the 107 plenum, compressor outlet, and compressor inlet, which is nearly identical to the
calculated Helmholtz frequency, fH 11.75 Hz (Table 4.3). At c 0.0792 (Figs. 4.15-
4.17), the oscillations have grown further to 137.4 dB in the plenum and the frequency has slightly shifted to 12 Hz. The mild surge is more visible in the compressor outlet and plenum pressure traces in Fig. 4.15a as well as visible for the first time in the compressor inlet and speed traces at the same frequency, Figs. 4.16 and 4.17, respectively. At
c 0.0749, the plenum pressure oscillations have grown to 145.6 dB at 12.0 Hz in
Figs. 4.18-4.20 and the speed fluctuations to almost 500 rev/min peak to peak. The final
mild surge point, c 0.0720, is presented in Figs. 4.21-4.23. Plenum pressure oscillations are now 150.4 dB at 11.2 Hz, again still close to the 11.75 Hz calculated
Helmholtz frequency, fH , in Table 4.3 at this operating point. The pressure amplitudes are becoming somewhat inconsistent due to the system being on the threshold of instability to deep surge. The speed fluctuations have grown to 700 rev/min and also possess the same inconsistency. A reduction in throttle area results in the deep surge
oscillations presented in Figs. 4.24-4.26. The time averaged flow coefficient, c , has dropped significantly to 0.0588. The dominant peak of 166 dB in the plenum occurs at
8.8 Hz, which is significantly lower than the calculated Helmholtz frequency,
fH 11.75 Hz, in Table 4.3 at this operating point. The compressor outlet and inlet oscillations occur at the same 8.8 Hz frequency but at lower amplitudes of 165 and
158.4 dB, respectively. Unlike mild surge, significant surge amplitudes are observed at harmonics of the primary surge frequency. The plenum and compressor outlet pressures are nearly identical except at the minimum and soon after the maximum pressures. This
108 deviation drives the change in flow direction of the system due to the momentum equation. When the compressor outlet pressure is lower than the plenum pressure, just after the peak plenum pressure, a flow reversal happens in the system causing the high pressure outlet air to exhaust through the inlet duct. This is evident in Fig. 4.25a as the compressor inlet pressure spikes to 1.04 bar at the same time. The flow remains reversed until the minimum plenum pressure, at which point the compressor outlet pressure is higher than the plenum pressure, accelerating the flow in the forward direction and returning it to (+). Also, in Fig. 4.25a, the compressor inlet pressure has now returned to just under 1 bar, typical for forward flow. Finally, the speed fluctuations have grown significantly to 1,500 rev/min (peak to peak) with the highest and lowest speed occurring simultaneously with the lowest and highest compressor outlet and plenum pressure, respectively. Further closing the valve, thereby dropping the time averaged flow coefficient to 0.0409 in Figs. 4.27-4.29, elevates the surge frequency to 9.2 Hz c from 8.8 Hz, while increasing the mean speed to N 94,052 rev/min from
93,651 rev/min (Table 4.3). Otherwise, the pressure and speed oscillation amplitudes are very similar to Figs. 4.24-4.26. In summary, mild and deep surge frequencies were 11.2-
12 Hz and 8.8-9.2 Hz, respectively. The measured mild surge frequencies are nearly
identical to the calculated Helmholtz frequencies, fH 11.75-11.76 Hz (Table 4.3), similar to the results presented by Fink (1988). The deep surge frequencies are 74.9-
78.3% of the calculated Helmholtz frequencies, fH 11.75-11.76 Hz, which also coincides with the findings of Arnulfi (1999) that the deep surge frequencies are 74-80% of the Helmholtz frequency. One important observation is the lack of a quiescent period
109 in the deep surge trend relative to Fink‟s (1988) results presented in Fig. 3.21b. Finally, the transition point from mild to deep surge occurs at a time averaged flow coefficient,
c 0.0720, and corrected mass flow rate, mc, cor 0.0169 kg/s .
110 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 130 120 110 100
SPL[dB] 90 80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 140
120
100
80 SPL[dB]
60
40 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.6: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
111 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 120 110
100
SPL [dB] SPL 90
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.7: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
4 x 10 9.35
9.3
9.25 Speed[rev/min] 9.2 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 60
40
20
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.8: U = 230 m/s, Full Volume, mc, cor0.0205 kg/s, c 0.0873, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N
112 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 120
110
100
90 SPL[dB]
80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 140
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.9: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
113 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 120 110
100
SPL [dB] SPL 90
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.10: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
4 x 10 9.35
9.3
9.25 Speed[rev/min] 9.2 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 60
40
20
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.11: U = 230 m/s, Full Volume, mc, cor0.0199 kg/s, c 0.0847, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 114 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 11.6 130 Y: 122.5 120
110
100
SPL[dB] 90
80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 140 X: 11.6 Y: 124 120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.12: U = 230 m/s, Full Volume, mc, cor0.0194 kg/s, c 0.0826, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
115 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 140 X: 11.6 Y: 124.9 120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.13: U = 230 m/s, Full Volume, mc, cor0.0194 kg/s, c 0.0826, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
4 x 10 9.35
9.3
9.25 Speed[rev/min] 9.2 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 30
20
10
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.14: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 116 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s]
X: 12 (a) 140 Y: 135.6
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] X: 12 (b) Y: 137.4 140
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.15: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
117 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 140 X: 12 Y: 137.6 120
100 SPL [dB] SPL
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.16: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.17: U = 230 m/s, Full Volume, mc, cor0.0186 kg/s, c 0.0792, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 118 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a)
160 X: 12 Y: 143.8 140
120
100 SPL[dB]
80
60 0 20 40 60 80 100 120 Frequency [Hz] (b) 160 X: 12 Y: 145.6
140
120
100 SPL[dB]
80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.18: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
119 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5
X: 12 Time [s] Y: 145.4 (a) 150
100 SPL [dB] SPL
50 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.19: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.20: U = 230 m/s, Full Volume, mc, cor0.0176 kg/s, c 0.0749, B 0.67 ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 120 1.34
1.33
1.32
1.31 Pressure [bar] Pressure 1.3 Compressor Outlet Plenum 1.29 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 160 X: 11.2 Y: 148.8
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b) X: 11.2 160 Y: 150.4
140
120
100 SPL[dB]
80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.21: U = 230 m/s, Full Volume, mc, cor0.0169 kg/s, c 0.0720, B 0.67 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
121 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 11.2 (a) 160 Y: 148.7 140
120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.22: U = 230 m/s, Full Volume, mc, cor0.0169 kg/s, c 0.0720, B 0.67 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.23: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 122 Compressor Outlet Plenum 1.35
1.3
1.25 Pressure [bar] Pressure
1.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 8.8 180 Y: 165 160 X: 18 Y: 142.2 140
120
SPL[dB] 100
80
60 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (b) X: 8.8 180 Y: 166 160 X: 17.6 Y: 144.7 140
120
SPL[dB] 100
80
60 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.24: U = 230 m/s, Full Volume, mc, cor0.0138 kg/s, c 0.0588, B 0.68;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
123 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 160 X: 8.8 140 Y: 158.4
120
SPL [dB] SPL 100
80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.25: U = 230 m/s, Full Volume, mc, cor0.0138 kg/s, c 0.0588, B 0.68;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.26: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 124 Compressor Outlet Plenum 1.35
1.3
1.25 Pressure [bar] Pressure
1.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 180 X: 9.2 Y: 164.1 160 X: 18.8 140 Y: 135.1
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (b) 200 X: 9.2 Y: 165.3
X: 18.8 150 Y: 138.5
SPL[dB] 100
50 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.27: U = 230 m/s, Full Volume, mc, cor0.0096 kg/s, c 0.0409, B 0.68;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
125 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 X: 9.2 Time [s] Y: 157.9 (a) 160
140
120
SPL [dB] SPL 100
80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.28: U = 230 m/s, Full Volume, mc, cor0.0096 kg/s, c 0.0409, B 0.68;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.29: U = 230 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 126 4.3.2 Temporal Behavior - U 310 m/s, Full Plenum Volume
Figures 4.30-4.44 present a similar stable to deep surge (right to left) study for the impeller tip speed, U 310 m/s, at a full plenum volume. Figures 4.30-4.32 present a
stable point at c 0.0894 like Figs. 4.6-4.8 did for 230 m/s. This stable point is also just right of the peak pressure rise. Figures 4.33-4.35 show the early symptoms of
mild surge at a flow coefficient, c 0.0843, as pressure oscillations at the compressor inlet, outlet, and plenum in the 10-20 Hz region begin to grow. In Figs. 4.36-4.38, mild
surge has fully developed at c 0.0815 with a plenum pressure amplitude of 140.4 dB
at 12 Hz, which is close to the calculated Helmholtz frequency, fH 12.23 Hz
(Table 4.3), at this operating point. Also, this is a similar frequency to the 11.2-12 Hz mild surge frequencies at the lower impeller tip speed, U 230 m/s, and a full plenum volume. Peak to peak speed oscillations in Fig. 4.38a are 200 rev/min, similar to mild surge amplitudes for the 230 m/s cases. This operating point is also very close to the final mild surge condition, as a further reduction in throttle area to a time averaged flow
coefficient, c 0.0660, results in deep surge as presented in Figs. 4.39-4.41. The compressor outlet and plenum pressures follow the same trends as those presented in
Figs. 4.24. Also, the quiescent period observed by Fink (1988) is still nonexistent. The pressure amplitude in the plenum is 171.1 dB at 8.4 Hz, 69% of the calculated Helmholtz
frequency, fH 12.19 Hz (Table 4.3), at this operating point. The compressor inlet and outlet amplitudes, however, are 163.7 and 170.2 dB, respectively. The 8.4 Hz plenum pressure frequency is very similar to the 8.8 and 9.2 Hz plenum pressure frequencies during deep surge for 230 m/s in Figs. 4.24-4.29. The amplitudes, however, have 127 elevated slightly from the 166 dB deep surge values for U 230 m/s. Turbocharger shaft speed oscillations have also grown to N 3,000 rev/min (peak to peak). A further
reduction in throttle area to c 0.0499 results in a slightly higher plenum pressure frequency, 8.8 Hz, for the deep surge oscillations presented in Figs. 4.42-4.44. Again, this throttle reduction results in an increase of the mean speed value, from N 126,243 to 127,684 rev/min in this case (Table 4.3). The mild surge oscillations are again close to
the calculated Helmholtz frequencies, fH (Table 4.3), while the first and second plenum pressure deep surge frequencies are 69% and 72% of their calculated Helmholtz
frequencies, fH 12.19 and 12.18 (Table 4.3), respectively.
128 1.64
1.62
1.6
Pressure [bar] Pressure 1.58 Compressor Outlet Plenum 1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 120
110
100
90 SPL[dB]
80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 120 110 100 90
SPL[dB] 80 70
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.30: U = 310 m/s, Full Volume, mc, cor0.0283 kg/s, c 0.0894, B 0.87;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
129 1.02
1 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 120
100 SPL [dB] SPL
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.31: U = 310 m/s, Full Volume, mc, cor0.0283 kg/s, c 0.0894, B 0.87;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.254 1.252 1.25 1.248 1.246 1.244 0 0.1 0.2 0.3 0.4 0.5 Speed[rev/min] Time [s] (a) 20
10
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.32: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 130 1.64
1.62
1.6
Pressure [bar] Pressure 1.58 Compressor Outlet Plenum 1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 130 120 110 100
SPL[dB] 90 80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 140
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.33: U = 310 m/s, Full Volume, mc, cor0.0267 kg/s, c 0.0843, B 0.87;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
131 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 140 120
100
SPL [dB] SPL 80
60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.34: U = 310 m/s, Full Volume, mc, cor0.0267 kg/s, c 0.0843, B 0.87;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.254 1.252 1.25 1.248
1.246 Speed[rev/min] 1.244 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 80 60
40 20
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.35: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 132 1.64
1.62
1.6
Pressure [bar] Pressure 1.58 Compressor Outlet Plenum 1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 12 (a) Y: 138.9 140 130 120 110
SPL[dB] 100 90
80 0 20 40 60 80 100 120 Frequency [Hz] (b) X: 12 150 Y: 140.4
100 SPL[dB]
50 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.36: U = 310 m/s, Full Volume, mc, cor0.0258 kg/s, c 0.0815, B 0.86;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
133 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 160 X: 12 Y: 143 140
120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.37: U = 310 m/s, Full Volume, mc, cor0.0258 kg/s, c 0.0815, B 0.86;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.254 1.252 1.25 1.248
1.246 Speed[rev/min] 1.244 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 150
100
50
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.38: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 134 Compressor Outlet Plenum 1.65
1.6
1.55
1.5
1.45 Pressure [bar] Pressure 1.4
1.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 8.4 180 Y: 170.2
160 X: 16.8 Y: 146.5
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (b) X: 8.4 180 Y: 171.1
X: 16.8 160 Y: 150.1
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.39: U = 310 m/s, Full Volume, mc, cor0.0209 kg/s, c 0.0660, B 0.88;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
135 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s]
X: 8.4 (a) 180 Y: 163.6 160 140 120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.40: U = 310 m/s, Full Volume, mc, cor0.0209 kg/s, c 0.0660, B 0.88;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.41: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 136 Compressor Outlet Plenum 1.65
1.6
1.55
1.5
1.45 Pressure [bar] Pressure 1.4
1.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 8.8 180 Y: 170.8
160 X: 17.6 Y: 143.1 140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz]
X: 8.8 (b) 180 Y: 171.7
160 X: 17.6 Y: 146.6
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.42: U = 310 m/s, Full Volume, mc, cor0.0158 kg/s, c 0.0499, B 0.89;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
137 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 8.8 (a) 180 Y: 164.9 160 140 120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.43: U = 310 m/s, Full Volume, mc, cor0.0158 kg/s, c 0.0499, B 0.89;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.44: U = 310 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 138 4.3.3 Temporal Behavior - U 370 m/s, Full Plenum Volume
Figures 4.45-4.65 present the mild and deep surge temporal behavior for the impeller tip speed, 370 m/s, at a full plenum volume in the same manner as the previous two speed lines. Figures 4.45-4.47 present a stable point as no amplitude is
noticeable in the FFT results. Note that the time averaged flow coefficient, c 0.1371,
is now much larger than the stable flow coefficients, c 0.0873 and 0.0894 of
230 and 310 m/s, respectively. Closing the throttle by a small amount to
c 0.1305, causes slight mild surge in Figs. 4.48-4.50 as a small increase in amplitude is observable in the 10-20 Hz region of the FFT results. By examining the magnified view in “ ” of Fig. 4.1 closely, a small hump or local maximum can be seen in the
370 m/s small “B” speed line just to the right of the deep surge line at approximately
mc, cor 0.05 kg/s ( c 0.13). The slightly (+) slope of the small “B” speed line just left
of this local maximum causes the mild surge. Progressing further left to c 0.1141, the slope is now (-) again, promoting stability. This can be seen in Figs. 4.51-4.53 as the elevated amplitude in the 10-20 Hz region of the FFT results is now eliminated. Further
throttling the system to c 0.0950 in Figs. 4.54-4.56 initiates a weak mild surge again at a frequency of approximately 12 Hz. The system is now operating near the far left point of the large “B” data, the surge line, of the compressor map in Fig. 4.1. Reducing
the flow coefficient to c 0.0871 (Figs. 4.57-4.59) causes the mild surge amplitudes to grow slightly to 129.6 dB and 12.4 Hz in the plenum, which is similar to the calculated
Helmholtz frequency, fH 12.68 Hz (Table 4.3), at this operating point. The speed
139 oscillations in Fig. 4.59a are not observable as they are smaller than the discretization limit of the sensor. This operating point is the final location (among the acquired data) before deep surge, as a slight reduction of the throttle area to a time averaged flow
coefficient, c 0.0725, causes deep surge in Figs. 4.60-4.62. During deep surge, the pressure amplitudes have grown to 173, 172.2, and 163.2 dB at 8 Hz in the plenum, compressor outlet, and compressor inlet, respectively, with harmonics observed in the
FFT. The 8 Hz frequency is 63% of the calculated Helmholtz frequency, fH 12.62 Hz
(Table 4.3). The compressor inlet and outlet and the plenum pressures exhibit a deep surge behavior similar to the previous two speed lines. The compressor inlet pressure trace, Fig. 4.61a, rapidly rises during flow reversal and returns to just below 1 bar when the flow becomes (+) again. The time of the elevated compressor inlet pressure corresponds with the compressor outlet pressure being lower than the plenum pressure, or flow reversal. Also, the time of the rapid compressor inlet pressure drop corresponds with the compressor outlet pressure being higher than the plenum pressure, or flow acceleration in the forward direction. In the meantime, the speed and compressor inlet pressure fluctuations have grown to N 5,000 rev/min and 0.2 bar peak to peak,
respectively. A throttle reduction to a time averaged flow coefficient, c 0.0450
(Figs. 4.63-4.65), increases the deep surge frequency to 8.8 Hz and the mean speed value from N 149,265 to 151,588 rev/min (Table 4.3).
140 1.96 Compressor Outlet 1.94 Plenum
1.92
1.9 Pressure [bar] Pressure 1.88
1.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 130 120 110 100
SPL[dB] 90 80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 130 120 110 100
SPL[dB] 90 80
70 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.45: U = 370 m/s, Full Volume, mc, cor0.0518 kg/s, c 0.1371, B 1.01;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
141 1.01 1
0.99
0.98 Pressure[bar] 0.97 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 120
100
SPL [dB] SPL 80
60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.46: U = 370 m/s, Full Volume, mc, cor0.0518 kg/s, c 0.1371, B 1.01;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.496 1.494 1.492 1.49
1.488 Speed[rev/min] 1.486 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 80 75
70 65
Magnitude[rev/min] 60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.47: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 142 1.94 Compressor Outlet Plenum 1.92
1.9
Pressure [bar] Pressure 1.88
1.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 130
120
110
100
SPL[dB] 90
80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 130
120
110
100
SPL[dB] 90
80
70 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.48: U = 370 m/s, Full Volume, mc, cor0.0493 kg/s, c 0.1305, B 1.01;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
143 1.01 1
0.99
0.98 Pressure[bar] 0.97 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 120
100
SPL [dB] SPL 80
60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.49: U = 370 m/s, Full Volume, mc, cor0.0493 kg/s, c 0.1305, B 1.01;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.496 1.494 1.492 1.49
1.488 Speed[rev/min] 1.486 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 300
200
100
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.50: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 144 1.94 Compressor Outlet Plenum 1.92
1.9
Pressure [bar] Pressure 1.88
1.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 130
120
110
100
SPL[dB] 90
80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) 140
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.51: U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
145 1.01 1
0.99
0.98 Pressure[bar] 0.97 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 110 100
90
SPL [dB] SPL 80
70 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.52: U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.00;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.496 1.494 1.492 1.49
1.488 Speed[rev/min] 1.486 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 200 150
100 50
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.53: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 146 1.94 Compressor Outlet Plenum 1.92
1.9
Pressure [bar] Pressure 1.88
1.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 12 130 Y: 125.7
120
110
100 SPL[dB]
90
80 0 20 40 60 80 100 120 Frequency [Hz] X: 12 (b) Y: 127.7 130
120
110
100
SPL[dB] 90
80
70 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.54: U = 370 m/s, Full Volume, mc, cor0.0359 kg/s, c 0.0950, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
147 1.01 1
0.99
0.98 Pressure[bar] 0.97 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 12 (a) 120 Y: 111
100
SPL [dB] SPL 80
60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.55: U = 370 m/s, Full Volume, mc, cor0.0359 kg/s, c 0.0950, B 1.00;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.496 1.494 1.492 1.49
1.488 Speed[rev/min] 1.486 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 200 150
100 50
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.56: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 148 1.94 Compressor Outlet 1.92 Plenum
1.9
Pressure [bar] Pressure 1.88
1.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 12.4 (a) Y: 127.7 130 120 110 100
SPL[dB] 90 80
70 0 20 40 60 80 100 120 Frequency [Hz] (b) X: 12.4 140 Y: 129.6
120
100 SPL[dB] 80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure 4.57: U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
149 1.01 1
0.99
0.98 Pressure[bar] 0.97 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 140 X: 12.8 Y: 119.3 120
100
SPL [dB] SPL 80
60 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.58: U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.496 1.494 1.492 1.49
1.488 Speed[rev/min] 1.486 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 600
400
200
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure 4.59: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 150 Compressor Outlet Plenum 1.9
1.8
1.7
Pressure [bar] Pressure 1.6
1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) X: 8 180 Y: 172.2
X: 16.4 160 Y: 154.6
140 SPL[dB] 120
100 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (b) X: 8 180 Y: 173 X: 16.4 Y: 157.5 160
140 SPL[dB] 120
100 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.60: U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.00;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
151 1.15 1.1 1.05 1
0.95 Pressure[bar] 0.9 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 8 (a) 180 Y: 165.2 160 140 120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.61: U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.00;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.62: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 152 Compressor Outlet Plenum
1.9
1.8
1.7
Pressure [bar] Pressure 1.6
1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 8.8 (a) 180 Y: 174.6
X: 17.6 160 Y: 148.4
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] X: 8.8 (b) Y: 175.5 180 X: 17.6 160 Y: 152.1
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure 4.63: U = 370 m/s, Full Volume, mc, cor0.0170 kg/s, c 0.0450, B 1.02;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
153 1.15 1.1 1.05 1
Pressure[bar] 0.95 0.9 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 8.8 (a) 180 Y: 168.7 160 140 120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure 4.64: U = 370 m/s, Full Volume, mc, cor0.0170 kg/s, c 0.0450, B 1.02;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure 4.65: U = 370 m/s, Full Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N
154 4.3.4 Temporal Behavior – Full Volume Summary
In summary, for the full volume, mild surge was in the range of 11.6 to 12.8 Hz while deep surge was between 8 and 9.2 Hz, depending upon the compressor load control valve, or throttle, setting. The frequency of mild surge increases slightly as a function of the rotational speed of the compressor because the pressure ratio elevates, increasing plenum temperature and therefore the speed of sound. This is further validated in the calculation of the Helmholtz frequency in Table 4.3. Deep surge frequency, on the other hand, seems to be relatively constant as a function of speed but varies with the load control valve setting. Evidence of the dependency on the load control valve (throttle) setting is found by comparing deep surge frequencies for a given tip speed and plenum volume. At U 370 m/s and a full plenum volume, the deep surge frequency is 8 Hz
(Figs. 4.60-4.62) and then 8.8 Hz after closing the throttle slightly (Figs. 4.63-4.65). For
U 310 m/s and a full plenum volume, the deep surge frequency is 8.4 Hz (Figs. 4.39-
4.41) and then 8.8 Hz after a slight reduction in throttle area (Figs. 4.42-4.44). Finally, at
U 230 m/s and a full plenum volume, the deep surge frequency is 8.8 Hz (Figs. 4.24-
4.26) and then 9.2 Hz after closing the load control valve slightly (Figs. 4.27-4.29). The deep surge frequency was observed to elevate with a reduction in throttle area for all measured impeller tip speeds and plenum volumes. For impeller tip speeds, U 230 and
310 m/s, moving from right to left (decreasing the compressor flow coefficient) results in growing mild surge amplitudes until deep surge occurs at or slightly left of the compressor peak pressure rise. However, the impeller tip speed, U 370 m/s, has an additional hump (or local maximum) in the speed line that caused the system to progress through stable, mild surge, stable, mild surge, and finally deep surge as the compressor 155 mass flow rate was reduced. This local maximum can be seen in the small “B”
performance characteristics in the magnified view in “ ” of Fig. 4.1 at mc, cor 0.05 kg/s
( c 0.13). The deep surge flow reversals are driven by the momentum equation as the compressor outlet pressure is higher than the plenum pressure when accelerating the flow in the forward direction and lower than the plenum pressure when reversing the flow.
Otherwise, the compressor outlet and plenum pressures are nearly identical. Also, unlike
Fink (1988), there was not a quiescent period observed between consecutive deep surge flow reversals. Other authors, including Hansen (1971) and Galindo (2008), have not observed the quiescent period either. This may be due to Fink‟s (1988) rather large volume relative to more practical configurations. As indicated earlier, the observed mild surge frequencies of 11.6-12.8 Hz are nearly identical to the calculated Helmholtz
frequencies, fH , in Table 4.3 while the deep surge frequencies of 8-9.2 Hz are between
63% and 77% depending upon the load control valve position.
4.3.5 Temporal Behavior – Variable Volume and Speed Study
Since the frequencies of mild and deep surge vary only slightly with speed as a function of the plenum temperature, the volume was varied at a fixed impeller tip speed,
U 310 m/s, to study its effect on the system. Experimentally measured mild and deep surge amplitudes and frequencies are summarized in Table 4.4. Also, the calculated
Helmholtz frequency, fH , with the measured plenum temperature, TP , for each point is presented in Table 4.3. The temporal behavior for the mild and deep surge cases for the
1/2, 1/4, and 1/8 volumes are provided in Appendix A as Figs. A.1-A.18 for further reference. 156 Mild Surge Deep Surge Amplitude Frequency % of Amplitude Frequency % of (dB) (Hz) Helmholtz Figures (dB) (Hz) Helmholtz Figures Full 140.4 12 98.1 4.36-4.38 171.1 8.4-8.8 68.7-72.0 4.39-4.41 1/2 148.8 16 94.6 A.1-A.3 172.7 12.4 73.4 A.4-A.6 1/4 156.7 21.2 93.8 A.7-A.9 175.1 18.4 81.5 A.10-A.12 1/8 156.5 27.2 94.2 A.13-A.15 175.6 23.6 81.7 A.16-A.18 Table 4.4: Variable Volume Mild and Deep Surge Frequency Summary – Experimental Results
A mild surge operating point for the impeller tip speed, U 310 m/s, with a 1/2
plenum volume and c 0.0783 (Figs. A.1-A.3), exhibits an amplitude of 148.8 dB at
16.0 Hz. During deep surge (Figs. A.4-A.6), at c 0.0685, the amplitude is 172.7 dB at a 12.4 Hz frequency in the plenum. The mild surge amplitude is slightly higher than the full volume case, while the deep surge amplitude is similar. The mild surge
frequency of 16 Hz is 94.6% of the calculated Helmholtz frequency, fH 16.91 Hz, in
Table 4.3 while the deep surge frequency of 12.4 Hz is 73.4% of the Helmholtz frequency. These percentage values are very comparable to those discussed in the variable speed study with a full plenum volume. Finally, the mild and deep surge frequencies have been elevated by factors of 1.33 and 1.38 relative to the study at full volume, respectively.
At a 1/4 volume setting and an impeller tip speed, U 310 m/s, the mild surge plenum pressure oscillations at 0.0761 (Figs. A.7-A.9) have an amplitude of c
156.7 dB at 21.2 Hz, while the deep surge oscillations at c 0.0606 (Figs. A.10-A.12) have an amplitude of 175.1 dB at 18.4 Hz. Again, the mild surge amplitude is slightly
157 higher than the full and 1/2 volume cases, while the deep surge amplitudes are similar.
The calculated Helmholtz frequency in Table 4.3 is 22.57-22.59 Hz at the 1/4 volume.
The mild and deep surge frequencies have been elevated by factors of 1.33 and 1.48 relative to the 1/2 volume case, respectively. The mild surge frequency of 21.2 Hz is
93.8% of the calculated Helmholtz frequency and the 18.4 Hz deep surge frequency is
81.5% of the Helmholtz frequency. The mild surge frequency relative to the Helmholtz frequency is comparable to that in the full and 1/2 volume cases, while the deep surge value is slightly larger.
The mild (Figs. A.13-A.15) and deep (Figs. A.16-A.18) surge points for
U 310 m/s with a 1/8 volume setting have time averaged flow coefficients,
c 0.0739 and 0.0644, respectively. These results show mild and deep surge plenum pressure oscillations at amplitudes and frequencies of 156.5 and 175.6 dB at 27.2 and
23.6 Hz, respectively. The mild surge amplitude is similar to the 1/4 volume amplitude but slightly elevated relative to the full and 1/2 volume cases; however, the deep surge amplitude is quite comparable to the full, 1/2, and 1/4 volume amplitudes. The calculated
Helmholtz frequency is 28.86-28.90 Hz at the 1/8 volume. The mild and deep surge frequencies have been elevated by a factor of 1.28 relative to those for the 1/4 volume case. The mild surge frequency of 27.2 Hz is 94.2% of the calculated Helmholtz frequency from Table 4.3, while the deep surge frequency of 23.6 Hz is 81.7% of the
Helmholtz frequency. Again, the mild surge frequency relative to the Helmholtz frequency is comparable to that in the full, 1/2, and 1/4 volume cases, while the deep surge value is slightly larger than the full and 1/2 volume cases, and comparable to the
158 1/4 volume. In an effort to better understand the effects of the impeller tip speed and plenum volume on surge frequencies, the dominant and Helmholtz frequencies for all of the experimental data points discussed in this chapter (Table 4.3) are plotted in Figs. 4.66 and 4.67, respectively. Both the Helmholtz and mild surge frequencies elevate slightly as a function of impeller tip speed (Fig. 4.66) due to the rising plenum temperature from the higher compressor pressure ratio, while the deep surge frequency decreases slightly. On the other hand, the Helmholtz, mild surge, and deep surge frequencies all increase as a function of decreasing plenum volume (Fig. 4.67). In summary, the mild surge frequency is close to the calculated Helmholtz frequency for all impeller tip speeds and plenum volumes, while the deep surge frequency is typically 63% to 82% of the Helmholtz frequency, depending upon the throttle setting.
159 14
13
12
Calculated Helmholtz frequency 11 Experimental - Mild Experimental - Deep
Frequency(Hz) Fit for calculated Helmholtz frequency 10
9
8 230 250 270 290 310 330 350 370 390 Tip Speed (m/s) Figure 4.66: Dominant Surge Frequencies as a Function of Tip Speed
35 Calculated Helmholtz frequency Experimental - Mild 30 Experimental - Deep Fit for calculated Helmholtz frequency 25
20
15 Frequency(Hz)
10
5
0 0 0.002 0.004 0.006 0.008 0.01 0.012 Volume (m3) Figure 4.67: Dominant Surge Frequencies as a Function of Plenum Volume
160
CHAPTER 5
COMPARISON BETWEEN MODEL and EXPERIMENTAL RESULTS
In Chapter 3, the theory of the lumped parameter model developed by
Greitzer (1976) and Fink (1988) was described in detail. Also, additional literature on compressor map creation and extrapolation was introduced. Finally, numerical stability and accuracy of the Fink (1988) model was examined. Chapter 4 presented the data from the experimental facility and the turbocharger system discussed in Chapter 2. In the present chapter, the experimental data will be converted into performance maps for input into the model discussed in Chapter 3. Finally, the lumped parameter model pressure and speed predictions will be compared to the experimental results for an impeller tip speed of U 370 m/s and full plenum volume operating under stable, mild, and deep surge conditions.
5.1 Performance Characteristic Input into the Model
p02 In Chapter 4, performance characteristics for pressure ratio, , efficiency, c, tt , p01
and torque, Tc , of the small and large “B” compression systems were presented in
161 Figs. 4.1-4.3, respectively. This information is input into the model so that the compressor pressure ratio and torque can be determined. Greitzer (1976) and Fink (1988) converted their maps into non-dimensional form with Eqs. (3.6) - (3.10) in an effort to converge characteristics for multiple speed lines into one, implement a curve fit, and use it as a model input. This is evident by Fink‟s (1988) non-dimensional pressure ratio, , and torque, , characteristics in Fig. 3.4. The same concept was applied to the performance characteristics measured for the small “B” data presented Figs. 4.1-4.3. The non-dimensional pressure ratio, , in the positive (+) flow region was calculated using
Eq. (3.7) and the flow coefficient, c , with Eq. (3.6) for the speed lines of 230, 310, and
370 m/s. Also, the non-dimensional torque, c , was calculated from the data using
Eqs. (3.8) and (3.14). Figures 5.1 and 5.2 show the resulting and c variation as a function of .
162
Figure 5.1: Non-Dimensional Pressure Ratio Characteristic
Figure 5.2: Non-Dimensional Torque Characteristic
163 In order to use the non-dimensional data as an input into the map, the data points were curve fit and extrapolations were performed in regions of the map that could not be measured with the experimental facility at the time. In the reverse mass flow portion of the map, the method proposed by Theotokatos and Kyrtatos (2003) in Eq. (3.12) is used
p for the pressure ratio. This pressure ratio, 02 , in the reverse flow region is converted to p01
non-dimensional form, , using Eq. (3.9) and a tip Mach number, M tp , relative to the speed of sound at a temperature of 298 K. For the (+) flow region of the non-dimensional pressure ratio map in Fig. 5.1, a curve fit was applied for each speed line from a zero mass flow rate, radial equilibrium, to a non-dimensional pressure ratio, 0 . A piecewise polynomial curve fit was applied to each speed line as they do not coalesce into one line like Fink‟s (1988) data. The order of each piece of the polynomial curve fit was selected such that the fit accurately captures all of the data points with R2 values greater than 0.99 and the slope of the characteristics. The (+) slope portion of the
230 m/s line uses a 5th order polynomial from the radial equilibrium point, Eq. (3.13), to the peak pressure ratio, . The negative (-) slope portion uses an 8th order polynomial from the peak pressure ratio to 0 . The same concept is applied to the 310 m/s speed line except a 7th order fit is used for the (-) slope portion. A different concept had to be applied to the 370 m/s speed line due to the additional hump, or local maximum, at a flow
coefficient of c 0.13, discussed in Chapter 4. Using just a two-piece polynomial fit made it difficult to capture this hump. Therefore, a three-piece fit was employed with a
5th order polynomial used from radial equilibrium to the first pressure ratio peak, 3rd order
164 from the first peak to the second peak, and an 8th order from the second peak to 0 .
The coefficients of these fits are provided in Table B.1 of Appendix B for further reference. These fits are superimposed on the data in Fig. 5.1 and a zoomed-in view of the peaks is presented in Fig. 5.3. The implementation of a piecewise curve fit for each speed line allows for a good representation of the location and magnitude of the non- dimensional pressure ratio peaks. Also, the three-piece fit captures the additional local maximum in the 370 m/s speed line quite well. The quality of these fits will help improve the comparison between the model and the experimental results. When using the model, if the tip speed is between the 230 and 370 m/s speed lines, linear interpolation is used. Otherwise, if the tip speed is above 370 m/s or below 230 m/s, the fits for those speed lines are used as the non-dimensionalization is expected to capture most of the effects of speed change.
165
Figure 5.3: Detailed View of Non-Dimensional Pressure Ratio Characteristic
The fit for the non-dimensional torque, c , superimposed on the data in Fig. 5.2, is simpler as the 230, 310, and 370 m/s speed lines coalesce essentially into one. This allows one fit to capture the non-dimensional torque, , for every impeller tip speed.
For the (+) flow region, a 9th order polynomial fit was applied and a value of zero was
forced at c 0 . In the reverse flow region, the even extension (mirror image) of the polynomial fit is applied as stated by Theotokatos and Kyrtatos (2003) in Section 3.1.
Since inlet conditions are used for the (+) non-dimensionalization, if the c (-) within the model, the non-dimensional torque, , from Fig. 5.2 is multiplied by the ratio of the
inlet density, 1 , divided by the plenum density, P . These maps allow the compressor
166 p02 pressure ratio, , and torque, Tc , to be determined for any mass flow rate, mc , and tip p01 speed, U , for input into the time lag model system of ordinary differential equations,
Eqs. (3.1), (3.3) - (3.5).
5.2 Model Inputs
This section will further expand on the geometric, inertia, ambient, time step, and time lag constant inputs to the model. The model was implemented at U 370 m/s
( N 149,086 rev/min) and a full plenum volume for comparison to the experimental
2 data. The compressor reference area, AC 0.000862 m , is calculated by subtracting the
L compressor hub area from the total inlet area. Multiplying the C ratio determined in AC
Table 4.2 by the compressor reference area gives the compressor duct length,
3 LC 2.087 m . The plenum volume, VP 0.009989 m , is already specified in Table 4.2.
The measured impeller exit radius, r2 23.7 mm. Finally, the turbocharger manufacturer provided the inertia as I 1.72 1052 kg-m .
Ambient conditions are set to the measured room temperature, T 298 K , and
barometric pressure, p 0.995 bar , respectively. Fink‟s (1988) model assumed that
pp1 . However, in the experiments, pp1 during forward flow due to the dynamic
1 head, u2 . Therefore, measured static pressures are implemented at the compressor 2
167 inlet as boundary conditions to account for the dynamic head. For the stable (Fig. 4.52a)
and mild surge (Fig. 4.58a) experiments, p1 0.984 and 0.987 bar, respectively, and will be the boundary conditions for these operating points. However, during deep surge
(Fig. 4.61a), pp1 1.014 bar 0.995 bar due to the system flow reversals.
Therefore, the minimum p1 0.950 bar will be used as the boundary condition for the deep surge operating point.
A brief time lag constant study was performed similar to Section 3.4.2.
Implementations of Fink (1988) and Grietzer‟s (1976) time lag constants yielded similar results. Also, fixed time lag constants were used ranging from values similar to the mean of Fink (1988) and Greitzer (1976) up to two orders of magnitude larger, at which point the system no longer entered deep surge. Otherwise, model predictions remained similar.
L Therefore, Fink‟s (1988) time lag constant, mer , is implemented with a meridonial C
length, Lmer 50.8 mm. In Section 3.4.1, the study of Fink‟s (1988) system yielded a time step of 0.006 seconds with a system frequency of 9.76 Hz. Equation (3.18) by
Radavich (2000) yielded n 17,076 . Applying to Eq. (3.18) with a
Helmholtz frequency, fH 12.6 Hz , the average of the U 370 m/s and full plenum volume values in Table 4.3, yields a time step of 0.0046 seconds. Therefore, a time step
of 0.004 seconds was implemented. The initial speed, N , and mass flow rate, mc , are
specified by the user to set the throttle area, AT , and drive torque, D , to their fixed values. At the beginning of the model, an instantaneous 2% disturbance in the mass flow rate is provided and the system is allowed to converge to its equilibrium point. This
168 equilibrium point may be stable, mild, or deep surge and will be used for comparison with experimental results. The system is solved as stated in Section 3.2 with a time lag and the aforementioned geometry.
5.3 Comparison between Model and Experiments
This section will provide a comparison between model predictions and experimental results of the setup described in Chapter 2 at U 370 m/s and full plenum
volume. Plenum pressure, pP , and turbocharger shaft speed, N , will be used for comparison with experimental results. Additional model predictions, such as instantaneous mass flow rate and compressor outlet, plenum, and steady state characteristic pressure with respect to instantaneous mass flow rate will be provided for further discussion. Three specific operating points, including stable, mild, and deep surge, as shown in Fig. 5.4 (time averages representing the surge locations) will be used for the comparison between the model and experiments.
As will be shown in this section, the stable point (1) yielded a good match between the experimental data and model predictions for the plenum pressure, speed, and mass flow rate. Also, the mild surge point (2) had comparable mean plenum pressures, mean speeds, and amplitudes with an 11.6% higher system frequency in the predictions relative to the experiments. Finally, the deep surge plenum pressure amplitudes were nearly identical with a 28.6% higher predicted system frequency relative to experimental results.
169
Figure 5.4: Comparison to Experiments for U 370 m/s
5.3.1 Stable - Point (1)
Stability was evident with the operating point in the (-) slope portion near point
(1) of the 370 m/s speed line shown in Fig. 5.4. The predicted plenum pressure is constant at 1.888 bar in Fig. 5.5 while the experimental value is fairly constant with a mean of 1.880 bar. The plenum pressure is slightly larger in the model relative to the experimental data due to neglected flow losses in the former. The measured and predicted turbocharger shaft speeds are constant at 149,100 rev/min in Fig. 5.6 as the small speed fluctuations in the experimental data are due to discretization limits of the
sensor. The instantaneous model mc 0.0431 kg/s shown in Fig. 5.7 is identical to the
experimental mc, cor 0.0431 kg/s. Also, no distinct frequency is observed in either set of
170 results, providing evidence of stability. Therefore, the model achieves a good match with the plenum pressure, speed, and mass flow rate.
1.94 Experimental Model
1.92
[bar] P 1.9
1.88
Plenum Pressure, p PlenumPressure, 1.86
1.84 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s]
Figure 5.5: Plenum Pressure, pP , Comparison, Stable;
U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.01
171 5 x 10 1.498 Experimental Model 1.496
1.494
1.492 Speed, N Speed, [rev/min]N
1.49
1.488 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s] Figure 5.6: Speed, N , Comparison, Stable;
U = 370 m/s, Full Volume, mc, cor0.0431 kg/s, c 0.1141, B 1.01
Figure 5.7: Predicted Mass Flow Rate for Compressor vs. Throttle, Stable
172 5.3.2 Mild Surge – Point (2)
Closing the load control valve to place the operating point in the (+) slope region near point (2) in Fig. 5.4 forces the system into mild surge. Initial conditions were
N 149,350 rev/min and mc 0.0372 kg/s. In the expanded view of Fig. 5.8, the mean
experimental and predicted plenum pressures are pP 1.886 and 1.902 bar, respectively.
Again, the mean experimental plenum pressure is below the predicted value due presumably to the neglect of flow losses in the latter. A structured oscillation, observable in both the experimental and model plenum pressures, becomes more evident in the FFT of these traces depicted in Fig. 5.9. The amplitude of the first (and dominant) peak is
127.5 dB at 12.8 Hz from measurements vs. 130.3 dB at 14.29 Hz of predictions. One reason for the elevated frequency may be the higher plenum temperatures, therefore higher speed of sound in the model due to the adiabatic system assumption. The average model plenum temperature was 406.03 K while the experimental value was 382.10 K.
As a result, the predicted speed of sound and Helmholtz frequency will be 3.1% greater due to temperature effects in view of Eq. (4.7). Also, in Table 4.4, the observed mild surge frequencies were 93.8-98.1% of the calculated Helmholtz frequency from the lumped parameter analysis. This difference could also occur in the model predictions and may be due to the difficulties in lumping complex experimental geometry, especially the volute, into a simplified form.
173 1.905 Experimental Model
1.9
[bar] P 1.895
1.89
Plenum Pressure, p PlenumPressure, 1.885
1.88 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s]
Figure 5.8: Plenum Pressure, pP , Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00
140 X: 14.29 X: 12.8 Y: 130.3 Experimental 130Y: 127.5 Model
120
110
100 SPL[dB] 90
80
70
60 0 20 40 60 80 100 120 Frequency [Hz]
Figure 5.9: Plenum Pressure, pP , FFT Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00
174 Measured and predicted speeds depicted in Fig. 5.10 have a mean value of
N 149,350 rev/min and peak to peak amplitudes of N 150 and 50 rev/min, respectively. This is reasonable since the experimental shaft speed has an additional
N 50 rev/min discretization amplitude due to limits of the sensor hardware. The predicted mass flow rates for the compressor and throttle are presented in Fig. 5.11.
Also, the compressor outlet, plenum, and steady state characteristic pressures vs. the instantaneous mass flow rate are depicted in Fig. 5.12. The instantaneous compressor mass flow rate fluctuates between 0.0360 and 0.0377 kg/s, remaining (+) at all times, and the plenum pressure “loop” oscillates in a counter-clockwise manner.
5 x 10 1.498 Experimental Model 1.496
1.494
1.492 Speed, N Speed, [rev/min]N
1.49
1.488 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s] Figure 5.10: Speed, N , Comparison, Mild Surge;
U = 370 m/s, Full Volume, mc, cor0.0329 kg/s, c 0.0871, B 1.00
175
Figure 5.11: Predicted Mass Flow Rate for Compressor vs. Throttle, Mild Surge
Figure 5.12: Predicted Pressure vs. Mass Flow Rate, Mild Surge
176 5.3.3 Deep Surge – Point (3)
Further closing the throttle places the system in deep surge as shown by the time averaged point (3) in Fig. 5.4. The model was matched to this operating point by
comparing the peak plenum pressure, pP 1.88 bar, and the mean speed,
N 149,265 rev/min. Initial conditions were N 147,400 rev/min and
mc 0.0350 kg/s. In Fig. 5.13, the experimental plenum pressure varies from 1.54 to
1.88 bar while the model plenum pressure varies from 1.57 to 1.88 bar. The FFT analysis in Fig. 5.14 yields experimental and predicted plenum sound pressure levels of 173 dB and 174 dB, respectively, which are also nearly identical. The predicted deep surge frequency of 10.29 Hz is 28.6% larger than the measured 8 Hz. In addition to the reasons mentioned earlier for the elevated mild surge frequency, deep surge cycle frequency is also dependent on the reverse flow characteristics. As described in Section 5.1, the reverse flow characteristics are extrapolated using methods by Theotokatos and
Kyrtatos (2003) and are likely to introduce error into the model since they are not actually measured. Also, as presented in Chapter 4, the compressor inlet pressure elevates from 0.95 to 1.10 bar during reverse flow rather than remaining constant at
0.95 bar.
177 1.95 Experimental Model 1.9
1.85 [bar]
P 1.8
1.75
1.7
1.65
Plenum Pressure, p PlenumPressure, 1.6
1.55
1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s]
Figure 5.13: Plenum Pressure, pP , Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01
X: 8 X: 10.29 180Y: 173 Y: 174 Experimental Model 160
140
SPL[dB] 120
100
80 0 20 40 60 80 100 Frequency [Hz]
Figure 5.14: Plenum Pressure, pP , FFT Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01
178 Measured and predicted turbocharger shaft speeds in Fig. 5.15 have similar time averaged values, but different peak to peak amplitudes. The experimental and predicted peak to peak amplitudes are N 5,000 and 3,600 rev/min, respectively. The smaller amplitude in the model predictions may be due to the higher cycle frequency. Additional predictions from the model are presented next with the compressor and throttle mass flow rates as a function of time in Fig. 5.16, and the compressor outlet, plenum, and steady state characteristic pressures vs. the instantaneous compressor mass flow rate in Fig. 5.17.
The compressor mass flow rate fluctuates from 0.095 to -0.035 kg/s while the throttle mass flow rate varies slightly around 0.035 kg/s as a function of plenum pressure. Also, the instantaneous mass flow rate provides insight into the overall flow direction in the system. Finally, in Fig. 5.17 the compressor outlet pressure is seen to deviate from the steady state characteristic due to the time lag constant, . When the flow rate is at its most (+) and (-) value, the time lag constant is at its smallest value and the compressor
outlet pressure is close to the characteristic. However, near mc 0, the time lag constant becomes large and the compressor outlet pressure deviates from the steady state characteristic considerably. In addition, the plenum pressure creates a well defined counter-clockwise “loop” (same as the direction of mild surge) as the system goes through its filling and emptying cycle.
179 5 x 10 1.54 Experimental 1.53 Model
1.52
1.51
1.5
1.49 Speed, N Speed, [rev/min]N 1.48
1.47
1.46 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s] Figure 5.15: Speed, N , Comparison, Deep Surge;
U = 370 m/s, Full Volume, mc, cor0.0274 kg/s, c 0.0725, B 1.01
Figure 5.16: Predicted Mass Flow Rate for Compressor vs. Throttle, Deep Surge
180
Figure 5.17: Predicted Pressure vs. Mass Flow Rate, Deep Surge
In summary, the deep surge operating point matched plenum pressure amplitudes well. However, the predicted deep surge frequency was 28.6% higher than the measurements. The experimental and predicted turbocharger shaft speeds had similar mean values, but different amplitudes, possibly due to the elevated system frequency.
Finally, the model provided instantaneous mass flow rate predictions that could not be measured without additional hardware.
181
CHAPTER 6
CONCLUDING REMARKS
The primary goal of this study was to design, develop, and construct an experimental turbocharger facility at the Ohio State University in order to measure steady state performance characteristics of the compression system and study mild and deep surge. The facility was designed as a cold flow system capable of working with a variety of turbochargers. An overall system performance analysis was performed while selecting and designing various subsystems for providing compressed air, flow control, turbocharger lubrication, and data acquisition. Finally, large and small “B” systems were implemented to provide the ability to measure performance over a wide operating range and to study mild and deep surge with a variable plenum volume.
The small and large “B” compression systems were swept within the range of
p interest of the implemented turbocharger to determine pressure ratio, 02 , efficiency, p01
c, tt , and torque, Tc , characteristics. The large “B” system performance characteristics extended from the surge line to the pressure ratio defined by the minimum pressure drop of the system. The small “B” system performance characteristics were identical to the large “B” data except it was able to measure left of the deep surge line and closer to the
182 choke limit of the compressor. The extended range and identical values from the small
“B” and large “B” systems were also observations previously made by Fink (1988).
The large “B” system was then used to study mild and deep surge with plenum settings of full, 1/2, 1/4, and 1/8 volume at impeller tip speeds, U 230, 310, and
370 m/s. For both 230 and 310 m/s speed lines, the system went from stable to mild surge followed by deep surge. Moving right to left along the 370 m/s pressure ratio characteristic yielded two local maxima. The system was stable right of the 1st local maximum at a (-) characteristic slope and entered mild surge left of the maximum when the characteristic obtained a (+) slope. The system regained stability between the 1st and
2nd local maxima when the characteristic attained a (-) slope. Mild surge occurred again left of the 2nd local maximum at a slightly (+) characteristic slope. A further reduction in throttle area from the mild surge point left of the 2nd local maximum yielded deep surge.
During deep surge, the compressor outlet and plenum pressures have similar magnitudes, except for when a change in flow direction occurs. The compressor outlet pressure spikes below the plenum pressure when a flow reversal occurs and above the plenum pressure when the flow becomes (+) again. The compressor inlet pressure elevates significantly during the flow reversal period as the high pressure and temperature air in the compression system exhaust through the inlet duct. Additionally, the speed fluctuates significantly with the peak shaft speed occurring simultaneously with the minimum plenum pressure. During mild surge, the pressure and speed amplitudes have significantly reduced relative to deep surge. Again, the compressor outlet and plenum pressures are nearly identical except for a small offset due to the pressure drop in the outlet duct. 183 The average experimental mild surge frequencies of the full plenum volume operating points at 230, 310, and 370 m/s impeller tip speeds were 11.8, 12, and 12.4 Hz, respectively. These are comparable with the 230, 310, and 370 m/s tip speed Helmholtz
frequencies, fH 11.74-11.76, 12.18-12.23, and 12.53-12.68 Hz, respectively, which were calculated using the experimental plenum temperature. The slight increase in frequency with speed is due to elevated temperatures in the plenum from the higher compressor pressure ratios. In the variable volume study, the mild surge and Helmholtz frequencies increased in light of Eq. (4.7) as the plenum volume was reduced. At the
310 m/s speed line, the measured frequencies of 12, 16, 21.2, and 27.2 Hz for the full,
1/2, 1/4, and 1/8 volumes matched the calculated Helmholtz frequencies of 12.23, 16.91,
22.59, and 28.86 Hz reasonably well. However, deep surge frequencies were 63-82% of the calculated Helmholtz frequency depending upon the load control valve setting.
In addition to the primary goal of the study, the performance characteristics measured with the small “B” system were converted into non-dimensional form and used for input into Fink‟s (1988) lumped parameter model applied to the current experimental setup. Experimental and model results were compared at an impeller tip speed,
U 370 m/s, and a full plenum volume for a stable, mild, and deep surge point. The stable point was accurately captured with nearly identical plenum pressure, speed, and mass flow rate values relative to the experimental data. The predicted and experimental mild surge mean plenum pressure, mean speed, and amplitudes were comparable; however, the predicted frequency was 11.6% higher relative to the experiment. Some reasons for this elevated frequency may include the higher plenum temperatures in the
184 model relative to the experiment and the difficulty in lumping complex experimental geometry, especially the volute. For the deep surge comparison, experimental and model plenum sound pressure levels were nearly identical at 173 and 174 dB, respectively, however, the model deep surge frequency was 28.6% higher than that of the experiment.
Contributing factors for this additional elevation in predictions relative to experimental measurements may be the extrapolated characteristics and the fixed compressor inlet pressure and temperature.
Therefore, the present work provides the following contributions:
A systematic study of a variety of turbocharger test benches previously published
in literature and a test facility selection process.
The development and construction of a cold flow turbocharger test bench and its
subsystems capable of working with a wide variety of turbochargers.
A thermodynamic performance calculation for the overall cold flow test facility
quantifying limits and capabilities.
A comprehensive experimental study and frequency analysis on a compression
system with varying speeds and volumes, improving the understanding of mild
and deep surge. Mild surge frequencies occur at the Helmholtz frequency and
deep surge at a reduced frequency, depending on the load control valve setting.
By comparing the difference between experimental compressor outlet and plenum
pressures, which drive the system mass flow rate, overall flow characteristics
during deep surge were identified.
185 A method was outlined to minimize the effect of time step on numerical results
and a time lag constant study was performed using Fink‟s (1988) system.
To further improve the understanding of steady state compression system performance, the radial equilibrium point and reverse flow region should be measured, eliminating the need for extrapolation. Also, an experimental investigation of the time lag constant could improve the understanding of its impact during transient operation.
The next phase of the analytical work should include further implementation of more complex system geometry into the model to yield better compressor outlet and overall comparisons. Also, the approximations associated with heat transfer, lumped geometry calculations, and the fixed compressor inlet pressure and temperature could be explored to improve model predictions.
186
APPENDIX A
EXPERIMENTAL RESULTS WITH VARIABLE VOLUME and U 310 m/s
Experimental data on the time variation of a number of variables, including
plenum pressure, pP , compressor outlet pressure, p2 , compressor inlet pressure, p1 , and turbocharger shaft speed, N , will be presented in this appendix for an impeller tip speed
in the following plenum volume order: 1/2, 1/4, and then 1/8. For each plenum volume, a mild surge point will be presented first, followed by a deep surge
point. Table 4.3 summarizes the time averaged mass flow rate, mc, cor , flow coefficient,
p02 c , pressure ratio, , non-dimensional pressure ratio, , rotational speed in rev/min, p01
N , tip speed, U , and “ B ” parameter for each operating point with deep surge points shaded in a light gray color. Also, in each figure caption, the time averaged mass flow
rate, mc, cor , flow coefficient, c , and “ ” parameter will be provided.
187 1.64 Compressor Outlet Plenum 1.62
1.6
Pressure [bar] Pressure 1.58
1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] (a) 160 X: 16 Y: 147.5
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b) 160
140 X: 16 Y: 148.8 120
100 SPL[dB]
80
60 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure A.1: U = 310 m/s, Half Volume, mc, cor0.0248 kg/s, c 0.0783, B 0.64 ;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
188 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 16 (a) 160 Y: 146.4 140
120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure A.2: U = 310 m/s, Half Volume, mc, cor0.0248 kg/s, c 0.0783, B 0.64 ;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.254 1.252 1.25 1.248
1.246 Speed[rev/min] 1.244 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 150
100
50
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure A.3: U = 310 m/s, Half Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 189 Compressor Outlet Plenum 1.65
1.6
1.55
1.5
1.45 Pressure [bar] Pressure 1.4
1.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s]
X: 12.4 (a) 180 Y: 171.7
X: 24.8 160 Y: 150.4
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz]
X: 12.4 (b) 180 Y: 172.7 X: 24.8 160 Y: 154.2
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure A.4: U = 310 m/s, Half Volume, mc, cor0.0217 kg/s, c 0.0685, B 0.64;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
190 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s]
X: 12.4 (a) 180 Y: 163.3 160 140
120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure A.5: U = 310 m/s, Half Volume, mc, cor0.0217 kg/s, c 0.0685, B 0.64;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure A.6: U = 310 m/s, Half Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 191 1.64 Compressor Outlet Plenum 1.62
1.6
Pressure [bar] Pressure 1.58
1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 21.2 (a) 160 Y: 155.5
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] X: 21.2 (b) Y: 156.7 160
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure A.7: U = 310 m/s, Quarter Volume, mc, cor0.0241 kg/s, c 0.0761, B 0.48;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
192 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 21.2 (a) 160 Y: 151.2 140
120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure A.8: U = 310 m/s, Quarter Volume, mc, cor0.0241 kg/s, c 0.0761, B 0.48;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure A.9: U = 310 m/s, Quarter Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 193 Compressor Outlet Plenum 1.7
1.6
1.5
Pressure [bar] Pressure 1.4
1.3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 18.4 (a) 180 Y: 174
160 X: 36.8 Y: 144.2 140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] X: 18.4 (b) Y: 175.1 180 X: 36.8 160 Y: 151
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure A.10: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
194 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 180 160 X: 18.4 140 Y: 164.1
120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure A.11: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure A.12: U= 310 m/s, Quarter Volume, mc, cor0.0192 kg/s, c 0.0606, B 0.49; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 195 1.64 Compressor Outlet Plenum 1.62
1.6
Pressure [bar] Pressure 1.58
1.56 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 27.2 (a) 160 Y: 155.3
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] X: 27.2 (b) Y: 156.5 160
140
120 SPL[dB] 100
80 0 20 40 60 80 100 120 Frequency [Hz] (c)
Figure A.13: U = 310 m/s, Eighth Volume, mc, cor0.0234 kg/s, c 0.0739, B 0.38;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
196 1.02 1.01
1
0.99 Pressure[bar] 0.98 0 0.1 0.2 0.3 0.4 0.5 Time [s] X: 27.2 (a) 160 Y: 149.9 140
120
SPL [dB] SPL 100
80 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure A.14: U = 310 m/s, Eighth Volume, mc, cor0.0234 kg/s, c 0.0739, B 0.38;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
5 x 10 1.25 1.249
1.248
1.247 Speed[rev/min] 1.246 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) 60
40
20
Magnitude[rev/min] 0 0 20 40 60 80 100 120 Frequency [Hz] (b)
Figure A.15: U = 310 m/s, Eighth Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 197 Compressor Outlet Plenum 1.7
1.6
1.5
Pressure [bar] Pressure 1.4
1.3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [s] X: 23.6 (a) 180 Y: 174.6
X: 47.2 160 Y: 148.6
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] X: 23.6 (b) Y: 175.6 180 X: 47.2 Y: 155.2 160
140
120 SPL[dB]
100
80 0 20 40 60 80 100 120 140 160 180 200 Frequency [Hz] (c)
Figure A.16: U = 310 m/s, Eighth Volume, mc, cor0.0204 kg/s, c 0.0644, B 0.38;
(a) Static Pressure at the Compressor Outlet, p2 , and Plenum, pP , (b) Frequency Domain Analysis of Compressor Outlet Pressure, , (c) Frequency Domain Analysis of Plenum Pressure,
198 1.1
1.05
1 Pressure[bar] 0.95 0 0.1 0.2 0.3 0.4 0.5 Time [s] (a) X: 23.6 180 Y: 162.9 160 140
120 SPL [dB] SPL 100 80 0 50 100 150 200 Frequency [Hz] (b)
Figure A.17: U = 310 m/s, Eighth Volume, mc, cor0.0204 kg/s, c 0.0644, B 0.38;
(a) Static Pressure at the Compressor Inlet, p1 , (b) Frequency Domain Analysis of Compressor Inlet Pressure,
Figure A.18: U = 310 m/s, Eighth Volume, ; (a) Turbocharger Rotational Speed, N , (b) Frequency Domain Analysis of Turbocharger Rotational Speed, N 199
APPENDIX B
NON-DIMENSIONAL CHARACTERISTIC FIT COEFFICIENTS for SECTION 5.1
Curve Fit Coefficients Fit Curve
: : TableB.1
200
REFERENCES
Andersen, J., Lindstrom, F., and Westin, F., 2008, “Surge Definitions for Radial Compressors in Automotive Turbochargers,” SAE Paper 2008-01-0296.
Arnulfi, G., Giannattasio, P., Giusto, C., Massardo, A., Micheli, D., and Pinamonti, P., 1999, “Multistage Centrifugal Compressor Surge Analysis: Part I – Experimental Investigation,” ASME Journal of Turbomachinery 121, 305-311.
Arnulfi, G., Giannattasio, P., Giusto, C., Massardo, A., Micheli, D., and Pinamonti, P., 1999, “Multistage Centrifugal Compressor Surge Analysis: Part I – Numerical Simulation and Dynamic Control Parameter Evaluation,” ASME Journal of Turbomachinery 121, 312-320.
Baines, N. C., 2005, Fundamentals of Turbocharging. Concepts NREC, White River Junction, Vermont.
Capobianco, M. and Marelli, S., 2005, “Transient Performance of Automotive Turbochargers: Test Facility and Preliminary Experimental Analysis,” SAE Paper 2005- 24-066, ICE 2005, 7th International Conference on Engines for Automobile.
Clay, D. C. and Moch, S. W., 2002, “Development of a New Test Facility for Evaluations of Turbocharger Noise Emissions,” Institute of Mechanical Engineers 32, 129-141.
Cumpsty, N. A., 1989, Compressor Aerodynamics. Krieger Publishing Company, Malabar, Florida.
Dale, A., Watson, N., and Cole, A. C., 1988, “The Development of a Turbocharger Turbine Test Facility,” Institute of Mechanical Engineers, Seminar on Experimental Methods in Engine Research and Development.
Day, I. J., 1994, “Axial Compressor Performance During Surge,” ASME Journal of Propulsion and Power 10(3), 329-336.
Dickey, N., Selamet, A., and Tallio, K., 2003, “Effects of Numerical Dissipation and Dispersion on Acoustic Predictions from a Time-Domain Finite Difference Technique for Non-Linear Wave Dynamics,” Journal of Sound and Vibration 259(1), 193-208. 201 Doebelin, E., 2004, Measurement Systems: Application and Design. McGraw-Hill, New York, New York.
Emmons, H. W., Pearson, C. E., and Grant, H. P., 1955, “Compressor Surge and Stall Propagation,” Transactions of the ASME 77, 455-469.
Filho, F. A., Valle, R. M., Hanriot, S. M., and Barros, J. E, 2002, “Automotive Turbocharger Maps Building Using a Flux Test Stand,” SAE Paper 2002-01-3542.
Fink, D., 1988, “Surge Dynamics and Unsteady Flow Phenomena in Centrifugal Compressors,” PhD Dissertation, Massachusetts Institute of Technology.
Fink, D., Cumpsty, N., and Greitzer, E., 1992, “Surge Dynamics in a Free-Spool Centrifugal Compressor System,” ASME Journal of Turbomachinery 114, 321-332.
Galindo, J., Serrano, J., Guardiola, C., and Cervello, C., 2006, “Surge Limit Definition in a Specific Test Bench For The Characterization of Automotive Turbochargers,” Experimental Thermal and Fluid Science 30, 449-462.
Galindo, J., Serrano, J., Climent, H., and Tiseira, A., 2008, “Experiments and Modelling of Surge in Small Centrifugal Compressor for Automotive Engines,” Eperimental Thermal and Fluid Science 32, 818-826.
Greitzer, E. M., 1976, “Surge and Rotating Stall in Axial Flow Compressors, Part I: Theoretical Compression System Model,” ASME Journal of Engineering for Power 98, 190-198.
Greitzer, E. M., 1976, “Surge and Rotating Stall in Axial Flow Compressors, Part II: Experimental Results and Comparison With Theory,” ASME Journal of Engineering for Power 98, 199-217.
Hansen, K., Jorgensen, P., and Larsen, P., 1981, “Experimental and Theoretical Study of Surge in a Small Centrifugal Compressor,” ASME Journal of Fluids Engineering 103, 391-395.
Kirk, R. G., Papke, W. J., East, J. T., Mueller, T., and Newman, A. S., 2008, “Development of a Bench Test Stand for High Speed Turbochargers,” STLE/ASME International Joint Tribology Conference, October 20-22, Miami, FL, 513-515.
Korpela, S., 2009, “ME 627– Lecture Notes: Principles of Turbomachinery,” The Ohio State University.
Lujan, J. M., Bermudez, V., Serrano, J. R., & Cervello, C., 2002, “Test Bench for Turbocharger Groups Characterization,” SAE Paper 2002-01-0163.
202 Miller, R. W., 1996, Flow Measurement Engineering Handbook, 3rd Edition. McGraw- Hill, New York.
Naundorf, D., Bolz, H., & Mandel, M, 2001, “Design and Implementation of a New Generation of Turbo Charger Test Benches Using Hot Gas Technology,” SAE Paper 2001-01-0279.
Peng, W. W., 2008, Fundamental of Turbomachinery. John Wiley & Sons, Inc., Hoboken, New Jersey.
Radavich, P., 2000, “Coupling Between Mean Flow and Acoustic Resonances of a Deep Side Branch,” PhD Dissertation, The Ohio State University.
Rammal, H. and Abom, M., 2007, “Turbocharger Acoustics,” SAE Paper 2007-01-2205.
Rammal, H. and Abom, M., 2009, “Experimental Determination of Sound Transmission in Turbo-Compressors,” SAE Paper 2009-01-2045.
Sens, M., Nickel, J., Grigoriadis, P., & Pucher, H., 2006, “Influence of Sensors and Measurement System Configuration on Mapping and the Use of Turbochargers in the Vehicle,” SAE Paper 2006-01-3391.
Stemler, E. and Lawless, P., 1997, “The Design and Operation of a Turbocharger Test Facility Designed for Transient Simulation,” SAE Paper 970344.
Theotokatos, G. and Kyrtatos, N., 2001, “Diesel Engine Transient Operation with Turbocharger Compressor Surging,” SAE Paper 2001-01-1241.
Theotokatos, G. and Kyrtatos, N., 2003, “Investigation of a Large High-Speed Diesel Engine Transient Behavior Including Compressor Surging and Emergency Shutdown,” Transactions of the ASME 125, 580-589.
Torregrosa, A., Serrano, J., Dopazo, J., and Soltani, S., 2006, “Experiments on Wave Transmission and Reflection by Turbochargers in Engine Operating Conditions,” SAE Paper 2006-01-0022.
Venson, G. G., Barros, J. E. M., and Pereira, J. F., 2006, “Development of an Automotive Turbocharger Test Stand Using Hot Gas,” SAE Paper 2006-01-2680.
Yano, T., and Nagata, B., 1970, “A Study on Surging Phenomena in Diesel Engine Air- Charging System,” Japanese Society of Mechanical Engineers 14(70), 364-376.
Young, M. Y., & Penz, D. A, 1990, “The Design of a New Turbocharger Test Facility. SAE Paper 900176.
203