DESIGN, CALIBRATION AND TESTING OF A FORCE BALANCE FOR A HYPERSONIC SHOCK TUNNEL by PRAVIN VADASSERY Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN AEROSPACE ENGINEERING THE UNIVERSITY OF TEXAS AT ARLINGTON MAY 2012
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DESIGN, CALIBRATION AND TESTING OF A FORCE BALANCE FOR
A HYPERSONIC SHOCK TUNNEL
by
PRAVIN VADASSERY
Presented to the Faculty of the Graduate School of
The University of Texas at Arlington in Partial Fulfillment
Foremost, I am thankful to God for having blessed me throughout my life, without whom
nothing is possible. Next thanks go to Dr Frank Lu and Dr Don Wilson for their constant support
and for giving me the opportunity to work at the ARC (Aerodynamics Research Center). Again, I
am thankful to Dr Lu for his determination, enthusiasm and vast knowledge. His words of
encouragement, “Making mistakes is all part of the learning process”, helped me to overcome
the hardships during my research. A special thanks to Eric M Braun for his help, quick
suggestions and for always being around.
I acknowledge my fellow team mates in doing an excellent job of reconstructing the
UTA Hypersonic Shock Tunnel and getting it back on running condition. Special thanks go to
Tiago Rolim for his endless support and always assisting me in the times of repair, machining
and discussions. Thanks also to Derek Leamon, Nitesh K Manjunatha, Raheem Bello and
Dibesh Joshi.
I appreciate the work of all the technical staff involved in the Mechanical and Aerospace
Department. Special credit to Kermit Beird, Sam Williams and Rod Duke for fabrication of all
necessary parts and for sharing their practical knowledge. I sincerely thank everyone in the
ARC, also for making this place lively and ‘loud’.
Finally, I would like to thank my parents, family and friends for their patience and for
supporting me.
April 17, 2012
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ABSTRACT
DESIGN, CALIBRATION AND TESTING OF A FORCE BALANCE FOR
A HYPERSONIC SHOCK TUNNEL
Pravin Vadassery, M.S
The University of Texas at Arlington, 2012
Supervising Professor: Frank K. Lu
The forces acting on a flight vehicle are critical for determining its performance. Of
particular interest is the hypersonic regime. Force measurements are much more complex in
hypersonic flows, where those speeds are simulated in shock tunnels. A force balance for such
facilities contains sensitive gages that measure stress waves and ultimately determine the
different components of force acting on the model. An external force balance was designed and
fabricated for the UTA Hypersonic shock tunnel to measure drag at Mach 10. Static and
dynamic calibrations were performed to find the transfer function of the system. Forces were
recovered using a deconvolution procedure. To validate the force balance, experiments were
conducted on a blunt cone. The measured forces were compared to Newtonian theory.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................................................................................................ iii ABSTRACT ..................................................................................................................................... iv LIST OF ILLUSTRATIONS.............................................................................................................. vii LIST OF TABLES ............................................................................................................................. x Chapter Page
2.1 UTA Hypersonic Shock Tunnel at the Aerodynamics Research Center .......................................................................................... 8
2.3 Diaphragm Test .............................................................................................. 13
3. DESIGN AND EXPERIMENTAL SETUP .................................................................... 15
3.1 Force Balance Design .................................................................................... 15
vi
3.1.1 Finite Element Analysis ................................................................. 18 3.1.2 Force Balance Construction .......................................................... 24
5. CONCLUSION AND FUTURE WORK ........................................................................ 53
5.1 Force Balance in the UTA Hypersonic Shock Tunnel ................................... 53
5.2 Future Work and Recommendations ............................................................ 55
APPENDIX
A. LIST OF DESIGN DRAWINGS ..................................................................................... 56
B. MATLAB PROGRAM FOR FORCE ESTIMATION ..................................................... 63
C. INSTRUMENTATION DETAILS .................................................................................. 67 REFERENCES ............................................................................................................................... 70 BIOGRAPHICAL INFORMATION .................................................................................................. 72
vii
LIST OF ILLUSTRATIONS
Figure Page 1.1 Linear input-output system (a) continuous (b) discrete .............................................................. 6 1.2 Convolution in time and frequency domain ................................................................................ 6 2.1 Schematic of the UTA Hypersonic Shock Tunnel ..................................................................... 9 2.2 Panorama view of the UTA Hypersonic Shock Tunnel .............................................................. 9 2.3 Schematic of the double diaphragm section ........................................................................... 10 2.4 Photograph of double diaphragm section ............................................................................... 10 2.5 Steel diaphragms (a) scored diaphragm (b) ruptured diaphragm after test ........................................................... 14 3.1 Different preliminary designs .................................................................................................... 17 3.2 Fabricated force balance .......................................................................................................... 18 3.3 Generated mesh of the force balance ...................................................................................... 19 3.4 FEA analysis settings ............................................................................................................... 20 3.5 Strain concentration in stress bars .......................................................................................... 20 3.6 Simulated input load of 350 N .................................................................................................. 21 3.7 Response to simulated impulse at (a) location1 (b) location2 ......................................................................................................... 22 3.8 (a) Simulated step load of 222.4 N (b) step response of location 2 ........................................ 22 3.9 Animated result of stress wave propagation ............................................................................ 23 3.10 Blunt cone model (a) side view (b) front view ........................................................................ 24 3.11 Hardened steel bolt hinge ..................................................................................................... 25 3.12 Installed model and balance in the test section .................................................................... 26 3.13 Attached strain gages ........................................................................................................... 27 3.14 Installed model and balance in the test section, front view .................................................... 28
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3.15 Schematic of static calibration procedure ............................................................................. 29 3.16 Static loading and unloading of force balance ...................................................................... 30 3.17 Average film output versus hammer force ............................................................................ 32 3.18 Schematic of a cut weight test .............................................................................................. 33 3.19 Vertical cut weight test .......................................................................................................... 33 3.20 Schematic of impulse hammer calibration ............................................................................ 34 3.21 Raw data of hammer impulse test .......................................................................................... 35 3.22 Sample hammer impulse ...................................................................................................... 35 3.23 Check signal for both raw and modified hammer pulse ........................................................ 36 3.24 Detail view of check signal with error bar ............................................................................... 37 3.25 Simulated unit step input ....................................................................................................... 37 3.26 Modified hammer signal ......................................................................................................... 38 3.27 Enlarged view of the modified hammer pulse ....................................................................... 38 3.28 Impulse response obtained from FFT and JMECG .............................................................. 39 3.29 Power spectral density plot of FRF ....................................................................................... 40 3.30 Enlarged power spectral density plot of FRF for first 12 kHz ................................................ 40 3.31 Enlarged phase spectrum of FRF ......................................................................................... 41 3.32 Spectrogram of the FRF ........................................................................................................ 41 4.1 Plot of (a) coefficient of drag (b) coefficient of lift .................................................................... 45 4.2 Coefficient of drag from recovered force (condition 1) ............................................................ 48 4.3 Recovered drag force and predicted force .............................................................................. 49 4.4 Raw pitot pressure signal ....................................................................................................... 49 4.5 Detailed view of the pitot pressure signal and drag ................................................................. 50 4.6 Coefficient of drag from recovered force (condition 2) ............................................................. 50 4.7 Recovered drag force .............................................................................................................. 51 4.8 Raw pitot pressure signal ........................................................................................................ 51
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4.9 Detailed view of the pitot pressure signal ................................................................................ 52 A.1 Force balance drawing ............................................................................................................ 57 A.2 Blunt cone model drawing ...................................................................................................... 58 A.3 PCB pressure transducer holder drawing ............................................................................... 59 A.4 Hinge joint part 1 drawing ....................................................................................................... 60 A.5 Hinge joint part 2 drawing ....................................................................................................... 61 A.6 Scoring pattern on steel diaphragm drawing .......................................................................... 62 C.1 Amplifier circuit diagram for piezoelectric film ......................................................................... 69
x
LIST OF TABLES
Table Page 2.1 Rupture properties of diaphragm tests .................................................................................... 14
3.1 Properties of some metals/alloys ............................................................................................ 16
%xxx Program to calculate Axial, Normal force coefficient and L/D xxx% xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx clc clear all for j=1:4 in=input('*********************\nTo find Axial,Normal force coefficient and L/D press 1: \nTo find Cpt press 2:\nTo find Pressure ratio press 3:\n********************* '); Rb=1.65; Rn=0.355; theta=9; phi=asin(cos(theta)); r=0; L=0; d=Rb/Rn; gamma=1.4; M=4.3; if in==3 %%%xxxxxxxxxxxxxxxxxxx pressure ratio calculation xxxxxxxxxxxxx Cpt=input('Enter Cpt , if known : ') ; gamma=input('Enter specific heat ratio : '); M=input('Enter Mach no: '); pressure_ratio =(((gamma+1)*M^2)/2)^(gamma/(gamma- 1))*((gamma+1)/((2*gamma*M^2)-(gamma-1)))^(1/(gamma-1)) x=pressure_ratio; plot(M,x ,'*b'); xlabel('Mach no: ,M') ylabel('Pressure ratio , Pt2/P1') %xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Cpt calculation xxxxxxxx elseif in~=(1:3) return elseif in==2 x=input('Enter pressure ratio : '); gamma=input('Enter specific heat ratio : '); M=input('Enter Mach no: '); Cpt=(((x)-1)*(2/(gamma*M^2))) %%%xxxxxxxxxxxxxxxxxxxxxxx L/D xxxxxxxxxxxxxxxxxxx elseif in==1
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for i=1:1 Cpt= input('Enter Cpt: '); Rb=input('Enter Base Radius: '); Rn=input('Enter Nose Radius: '); theta=input('Cone half Angle : '); phi=asin(cos(theta)); r=0; x=0; L=0; d=Rb/Rn; gamma=input('Enter specific heat ratio : '); M=input('Enter Mach no: '); alpha=-15:0.5:15; Cp=Cpt*(sind(theta))^2 plot(alpha,Cp,'*r') hold on xlabel('Angle of Attack,Alpha') ylabel('Axial Force Coefficient, Ca') a=2*Cpt*((Rn^2)/Rb^2); b=0.25.*(cosd(alpha).^2).*(1-(sind(theta)^4))+(0.125.*(sind(alpha).^2)*(cosd(theta).^4)); c=((tand(theta).*((cosd(alpha).^2)*(sind(theta).^2)+0.5.*(sind(alpha).^2).*(cosd(theta).^2))).*((((d-cosd(theta)).*cosd(theta))/tand(theta))+(((d-cosd(theta)).^2)/(2*tand(theta))))); Ca=a*(b+c); plot(alpha,Ca,'*-r') hold on title('Axial Force Coefficient vs Angle of Attack (Alpha)') xlabel('Angle of Attack, Alpha') ylabel('Axial Force Coefficient, Ca') p=2*Cpt*((Rn^2)/Rb^2); q=0.25.*sind(alpha).*cosd(alpha).*(cosd(theta)^4); r=(sind(alpha).*cosd(alpha).*sind(theta).*cosd(alpha).*((((d-cosd(theta)).*cosd(theta))/tand(theta))+(((d-cosd(theta)).^2)/(2*tand(theta))))); Cn=p*(q+r); figure plot(alpha,Cn,'*-black') title('Normal Force Coefficient vs Angle of Attack (Alpha)') xlabel('Angle of Attack,Alpha') ylabel('Normal Force Coefficient, Cn') CL=((Cn.* cosd(alpha))-(Ca.*sind(alpha))); CD=((Cn.* sind(alpha))+(Ca.*cosd(alpha))); L_D= CL./CD figure
66
plot(alpha,L_D,'*-g') drawnow title('L/D ratio vs Angle of Attack (Alpha)') xlabel('Angle of Attack,Alpha') ylabel('L/D ') hold on end end end
67
APPENDIX C
INSTRUMENTATION DETAILS
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C.1 Data acquisition
Manufacturer: Tektronix Digital Phosphor Oscilloscope. Model: DPO 4054
Features: Analog bandwidth – 500 Mhz Sample rate – 2.5 GS/s Record length – 20 M points Analog channels – 4
C. 2 Strain measurements
Manufacturer: Measurement specialties Model: DT1-052k Features: Min. impedance – 1MΩ
Output voltage – mV to 100’s of volt Operating temp – -40 to 60°C
Manufacturer: Omega engineering, Inc. Model: SGD-3/120-LY13 Features: Max Vrms – 4.5
Manufacturer: PCB Piezotronics, Inc. Model: 111A23 Features: Measurement range – 10kpsi Sensitivity – 0.5mV/psi Maximum pressure – 15kpsi Operating temp – -73 to 135°C
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Manufacturer: PCB Piezotronics, Inc. Model: 113A21 Features: Measurement range – 200psi Sensitivity – 25mV/psi Maximum pressure – 1000psi Operating temp – -73 to 135°C
C.7 Strain gage amplifier
Manufacturer: Paine instruments, Inc. Model: Strain gage amplifier Features: Excitation voltage range – 0-10V
Gain – 100
Amplifier circuit diagram used for piezoelectric films
Figure C.1 Circuit diagram of piezoelectric film amplifier. Circuit uses a LM-386 IC.
70
REFERENCES
[1] Robinson, M., “Simultaneous Lift, Moment and Thrust Measurements on a Scramjet in
Hypervelocity Flow,” Ph.D. dissertation, University of Queensland, 2003.
[2] Sanderson, S.R. and Simmons, J.M., “Drag Balance for Hypervelocity Impulse Facilities,” AIAA Journal, Vol. 29, No. 12, pp. 2185–2191, 1991.
[3] Daniel, W.J.T. & Mee, D.J., “Finite Element Modelling of a Three-Component Force Balance
for Hypersonic Flows,” Computers and Structures 54 (1), 3548, 1995. [4] Robinson, M., Schramm, J.M. and Hannemann, K., “An Investigation into Internal and
External Force Balance Configurations for Short Duration Wind Tunnels,” Notes on
Numerical Fluid Mechanics and Multidisciplinary Design, Volume 96/2008,129-136, 2008. [5] Boyce, R. R. and Stumvoll, A., ”Re-entry Body Drag: Shock Tunnel Experiments and
[6] Kulkarni, V. and Reddy, K.P.J., ”Accelerometer-Based Force Balance for High Enthalpy
Facilities,” J. Aerosp. Engrg. 23, 276 doi:10.1061/(ASCE), 2010. [7] Sahoo,N, Mahapatra, D.R., Jagadeesh, G., Gopalakrishnan, S. and Reddy, K.P.J., ”Design
and Analysis of a Flat Accelerometer-based Force Balance System for Shock Tunnel Testing,” Measurement, 40 (1).pp.93-106, 2007.
[8] Sahoo, N., Suryavamshi, K., Reddy, K.P.J. and Mee, D.J., ”Dynamic Force Balances for
Short-Duration Hypersonic Testing Facilities,” Experiments in Fluids, 38 (5). pp. 606-614, 2005.
[9] Mee, D.J., “Dynamic Calibration of Force Balances,” Centre for Hypersonics, The University
of Queensland, Australia. Tech. Rep. 2002/6, Jan 2003.
71
[10] Smith, A. L.; Mee, D.J., “Drag Measurements in a Hypervelocity Expansion Tube,” Shock
Waves, Volume 6, Issue 3, pp. 161-166,1996.
[11] Marineau, E., “Force Measurements in Hypervelocity Flows with an Acceleration
Compensated Piezoelectric Balance,” Journal of Spacecraft and Rockets, 0022-4650
vol.48, no.4 (697-700), 2011.
[12] Smith, S.W., The Scientist and Engineer's Guide to Digital Signal Processing.
[Online],http://www.dspguide.com/, 2012.
[13] Murtugudde, R.G., "Hypersonic Shock Tunnel," Master's Thesis, Department of Aerospace Engineering, The University of Texas at Arlington, Arlington, TX, 1986. [14] Stuessy, W.S, "Hypersonic Shock Tunnel Development and Calibration," Master's Thesis, Department of Aerospace Engineering, The University of Texas at Arlington, Arlington, TX, 1989. [15] Stuessy, W.S., Murtugudde, R.G., Lu, F.K. and Wilson, D.R., "Development of the UTA
Hypersonic Shock Tunnel," Paper 90-0080, AIAA 28th Aerospace Sciences Meeting, January 8-11, Reno, Nevada, 1990.
[16] Prost, R., Goutte, R., “Discrete Constrained Iterative Deconvolution Algorithms with
Optimized Rate of Convergence,” Signal Process.7(3), 209–230,1984.
[17] Bertin, J.J. Hypersonic Aerothermodynamics. American Institute of Aeronautics and
Astronautics, Inc., Washington, DC, 1994.
[18] Anderson, J.D. Fundamentals of Aerodynamics. New York, NY: McGraw-Hill, 2001.
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BIOGRAPHICAL INFORMATION
Pravin Vadassery graduated with a Bachelors degree in Aeronautical engineering, his
endeavor to learn new things, lead him to the Masters degree in Aerospace engineering. His
passion for experiments and hands-on jobs helped him during his research at the Aerodynamic
Research Center. He has worked on many projects during his undergraduate and graduate
years, which included areas of design, analysis, and comparative studies. He plans to start his
career with all experience he gained and eventually establish his own company.