DESIGN, CALIBRATION AND TESTING OF A FORCE BALANCE FOR. A HYPERSONIC SHOCK TUNNEL by. PRAVIN VADASSERY. Presented to the Faculty of ...
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
Copyright © by Pravin Vadassery 2012 All Rights Reserved
ACKNOWLEDGEMENTS 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 1. INTRODUCTION ……………………………………..………..…....................................... 1 1.1 Literature Survey .............................................................................................. 1 1.2 Force Measurement Techniques ..................................................................... 2 1.2.1 Internal Force Balance ..................................................................... 3 1.2.2 External Force Balance .................................................................... 3 1.2.3 Strain Gages .................................................................................... 4 1.2.4 Piezoelectric Film ............................................................................. 4 1.2.5 Accelerometer .................................................................................. 5 1.3 Convolution ...................................................................................................... 5 1.4 Objective of Research ...................................................................................... 7 2. FACILITY........................................................................................................................ 8 2.1 UTA Hypersonic Shock Tunnel at the Aerodynamics Research Center .......................................................................................... 8 2.2 Reconstruction of the UTA Hypersonic Shock Tunnel ........................................................................................................ 13 2.3 Diaphragm Test .............................................................................................. 13 3. DESIGN AND EXPERIMENTAL SETUP .................................................................... 15 3.1 Force Balance Design .................................................................................... 15 v
3.1.1 Finite Element Analysis ................................................................. 18 3.1.2 Force Balance Construction .......................................................... 24 3.2 Calibration Technique .................................................................................... 29 3.2.1 Static Calibration ............................................................................ 29 3.2.2 Dynamic Calibration ...................................................................... 32 3.3 Shock Tunnel Testing ................................................................................... 42 4. RESULTS AND DISCUSSION .................................................................................... 43 4.1 Force Measurement Prediction ..................................................................... 43 4.1.1 Modified Newtonian Theory .......................................................... 43 4.1.2 Coefficient of Drag Calculation using Pitot Pressure .......................................................................... 46 4.2 Experimental Results ..................................................................................... 48 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
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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 vii
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 viii
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
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LIST OF TABLES Table
Page
2.1 Rupture properties of diaphragm tests .................................................................................... 14 3.1 Properties of some metals/alloys ............................................................................................ 16 3.2 Static calibration results .......................................................................................................... 31 3.3 Test condition .......................................................................................................................... 42 4.1 Force prediction using modified Newtonian theory condition 1 .............................................. 46 4.2 Force prediction using modified Newtonian theory condition 2 .............................................. 46 4.3 Comparison of experimental to theoretical drag ..................................................................... 52
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CHAPTER 1 INTRODUCTION The forces acting on a flight vehicle are critical for determining its performance. Of particular interest is the hypersonic regime. Research in hypersonics has led to successful tests of scramjet (supersonic combustion ramjet) based vehicles, such as, NASA X-43A. In hypersonic vehicle design, significance is laid on propulsion system integration, engine performance, aerodynamics and thrust measurements. Specifically ground-based test facilities have limited steady test time thus making force measurement complex in this very short duration of time. 1.1 Literature Survey Hypersonic wind tunnels have been in use since the 1950’s and have developed into different types, namely, continuous and impulse types. Impulse facilities include shock tubes, reflected shock tunnels and expansion tunnels. The basic principle of these impulse facilities is to suddenly release a highly compressed gas in the so-called driver tube through rupturing a diaphragm. The sudden release of the compressed gas propagates a shock wave into a so-called driven tube filled with the test gas at low pressure.
The shock
compresses and heats the test gas to the desired conditions, after which, it is expelled by a nozzle to hypersonic conditions. For example, the T4 free piston shock tunnel at the University of Queensland is an impulse-type facility that simulates hypersonic flows [1].
1
1.2 Force Measurement Technique Throughout this thesis, force measurements refer to techniques for impulse facilities unless noted otherwise. Force measurement is complicated in impulse facilities due to the short test duration that will likely prevent the force balance from attaining a steady state. This limitation of short test times in such facilities was overcome by applying the stress wave force measurement technique (SWFM), proposed by Sanderson and Simmons [2]. Due to impulsive aerodynamic loading, stress waves that are created, propagate and reflect through the model and support structure, which are measured and analyzed by this method. Extension of this work by Daniel and Mee [3] using finite element modeling led to the design of a threecomponent force balance. The SWFM technique is based on the principle that, when stress waves travels, no force equilibrium is reached in such a short duration of time so that the strain histories are the crucial feature for developing force measurement techniques. An investigation into internal and external force balances was undertaken by Robinson et al. [4] which showed that a higher accuracy of the recovered force and moment loads was attained using an external force balance. Also, for a blunt body, these authors found that the interaction of external balance on the model forces was negligible when compared to that of an internal balance. Some of the recent developments include comparing the experimental measurements with CFD calculations by Boyce and Stumvoll [5], which showed good agreement for a range of Mach numbers and test gases. On the other hand, accelerometer-based force balance were used by Kulkarni and Reddy [6] and Sahoo et al [7], which was a single-component accelerometer force balance. The data were in accordance with modified Newtonian theory. Sahoo et al. [8], found that the drag measured on a 30 degree semi-apex angle blunt cone model at Mach 5.75 with an acceleratorbased balance agreed closely to the SWFM technique.
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1.2.1 Internal Force Balance Internal force balances are defined as those that have the measuring instruments like strain gages, accelerometers placed inside the model. The mounting system (sting) has to adapt depending on the location of the force balance. Models are generally attached to a long sting and placed in the test section of the tunnel. The geometry of the model has to accommodate the sting. A common way to measure forces is by strain gages. Strain gages work on the principle that when a load is applied, the stretching or deformation of the gage causes a change in electrical resistance, details can be found in Section 1.2.3. 1.2.2 External Force Balance External balances are those where the measuring instruments are located outside the model but may be within the test section. The definition of external balances used to be restricted those that are mounted outside the test section, which has been updated to balances that are specifically external to the model, but which can be within the test section. The principle of external balances is similar to that of internal balances but the difference is that the measuring devices are placed on a supporting structure, such as a sting. The forces on the model are transmitted as stress waves to the sting, which on deformation or bending creates strain that is measured by the attached strain gages. Specifically for hypersonic shock tunnels, external force balances that use stress wave propagation are named as Stress Wave Force Balances (SWFB) [2]. During a run in an impulse facility, the sudden aerodynamic load initiates stress waves in the model. The stress waves propagate and reflect between the model and the support structure. A steady state of force equilibrium cannot be achieved between the model and the support structure, since the duration of steady flow time is very minute. The SWFB concept operates on the principle that no steady-state force equilibrium is achieved [9]. The force balance forms a linear system, where the forces can be obtained by a deconvolution technique, which is discussed further in a later chapter. A SWFB is suspended from the test section by 3
means of thin wires, with the strain gages mounted on the supporting sting. Different kinds of materials have been used for SWFB construction such as brass, aluminum or steel. 1.2.3 Strain Gages Strain gages are sensors that are used to measure strain or deformation. Strain gages work by the principle that a strain in a metal or semi-conductor causes a change in resistance, which when measured can be related to the strain. There are different types of strain gages, namely, metallic foil gages and semiconductor strain gages, which can be either piezo-resistive or piezoelectric. All resistance-based strain gages require an excitation voltage. A Wheatstone bridge arrangement increases the sensitivity of the strain gage, thus allowing small changes in strain to be measured. 1.2.4 Piezoelectric Film Piezoelectric film gages are a type of transducer for measuring dynamic strain and are used in high-frequency applications .Some of the features of piezo film are its flexibility, varying thickness, lightweight and easy application. These gages have a large frequency range of up to the order of 1 GHz. Some other properties include its dynamic range, high mechanical strength, and temperature and humidity stability. Piezoelectric film can be adapted to various shapes and can be bonded with commercial adhesives. Another feature is high voltage output, that can be as high as 10 times higher than normal strain gages. Some disadvantages of piezoelectric films are that they are sensitive to electromagnetic radiation, in such cases shielding becomes important to avoid any kind of interference and ensuring a good signal-to-noise ratio. Piezoelectric film gages do not require an external power source or excitation voltage. Marineau [11] showed that a piezoelectric force balance has a higher frequency response than a strain gage force balance. Both balances showed comparable levels of accuracy. The piezoelectric balance shows a 350% increase in frequency response and 400% increase in sensitivity.
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1.2.5 Accelerometer An accelerometer as the name suggests is a device that measures acceleration of an object. It measures the rate of change of the velocity of the object relative to an inertial frame of reference. The most common measuring unit is “g.” An accelerometer can also measure a quantity of weight per unit mass (test mass), which has the dimensions of acceleration and is also known as the g-force. Accelerometers are used in force measurements due to their high sensitivity to vibrations and their high-frequency range. 1.3 Convolution Convolution is mathematically an operation that involves multiplication, shifting and addition. The reverse operation called deconvolution is used to calculate the input signal, when the system's impulse response and its output signal are known. It can be difficult to understand the convolution and deconvolution concepts in the time domain. More often, deconvolution is carried out in the frequency domain. Multiplication in the frequency domain is equivalent to the convolution operation in the time domain and likewise division in frequency domain acts like the deconvolution operation in the time domain. The expression for convolution is given by the formula
∗
(1.1) (1.2)
where, y(t) is the output of the system , x(t) input to the system and h(t) is the transfer function of the system. Convolution expressed in both continuous and discrete form is represented in figure 1.1.
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x(t)
Linear system h(t)
y(t)
(a)
x(n)
Linear system h(n)
y(n)
(b)
Figure 1.1 A linear input-output system a) continuous, b) discrete. Due to the large number of multiplications and additions that must be performed in the convolution algorithm, it can be inefficient when a large amount of data needs to be processed. As stated above, the convolution could be made easy by multiplication in the frequency domain via Fourier and inverse Fourier transforms, represented in equation (1.3).
(1.3)
A block diagram showing the input-output relationship in the time and frequency domains is depicted in Fig. 1.2. Fourier transform is used to change a signal from time domain to frequency domain. The reverse is done by inverse Fourier transform. The frequency response is a complex function of frequency that can be expressed by a magnitude and a phase spectrum.
x(t)
y(t)
h(t)
x(f)
h(f)
FT
FT
IFT
Frequency Domain
IFT
Time Domain
y(f)
Figure 1.2 The relationship of convolution in time domain and in the frequency domain [12]. 6
1.4 Objective of Research The goal of this research is to design, calibrate and test a simple force balance system that is capable of measuring drag on various models. As the test time is of very short duration, force measurement becomes a challenge. To design this force balance system, an approach is utilized to model the response of the balance using FEA. ANSYS Explicit Dynamics solver is used for the dynamic analysis. Piezoelectric films were used to measure stress waves due to aerodynamic loading. Deconvolution was used to determine the system transfer function and to recover the force. The drag on a spherically blunted cone was measured and the drag coefficient was compared with that obtained from modified Newtonian theory. Future efforts would consist of extension of the force balance to measure other components of force, such as lift and pitching moment. Force measurement on other models, such as conical model, inlets and scramjet vehicles would be included.
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CHAPTER 2 FACILITY 2.1 UTA Hypersonic Shock Tunnel at the Aerodynamics Research Center The Hypersonic Shock Tunnel at the UTA Aerodynamics Research Center is a reflected type. It was designed and built in the late 1980’s [13]. The main components of the hypersonic shock tunnel include the driver section, driven tubes, nozzle, test section, diffuser and dump tank, which are shown in figure 2.1. This facility is able to simulate high Mach numbers and high enthalpy flows. The main parts of this shock tunnel are:
Driver tube
Diaphragm section
Driven tubes
Nozzle
Test section
The shock tube is fabricated in four sections for ease of transportation, installation and maintenance [14]. The driver tube is a single section which is designed for a maximum operating driver pressure of 41.4 MPa (6000 psi) and hydrostatically tested to 62.1 MPa (9000 psi). The driver tube is 3 m (10 ft.) long with an internal diameter of 15.24 cm (6 in.) and a wall thickness of 2.54 cm (1.0 in.). One end is closed off with a hemispherical end cap.
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Figure 2.1 Schem matic of the UTA Hypersonic H Shock Tunnel and its dimensions d
9 Figure 2.2 Pan norama photogra aph of the UTA Hy ypersonic Shock Tunnel
The other o end has s a 48.26 cm (19 in.) diam meter 11.43 cm m (4.5 in.) thicck flange, which allows the e drive er tube to be bolted b to the diaphragm d se ection and the e driven sectio on [15]. The fllange has two o O-rin ng grooves machined in them to accom mmodate two O-rings O to en nsure a tight, high-pressure e seal [15]. ble diaphragm m section se eparates the driver from the driven tu ube, so-called d The doub d to hold two diaphragms. This section has the sam me dimension as that of the e because it is used ges. Steel boltts of 2 in. diam meter are use ed to bolt the flanges togetther. flang
Figurre 2.3 Schem matic of the do ouble diaphrag gm section be etween the drriver and drive en tube [15].
ograph of the e double diap phragm section (middle), driver sectio on (right) and d Figurre 2.4 Photo drive en section (lefft). The steel pipe p is used to t pressurize the double diiaphragm secction. 10
The driven tube is constructed in three segments of 2.74 m (9 ft) length each. The three segments are connected to each other with a flange at each end identical to the one on the driver section. The internal diameter is the same as the driver tube. Two O-rings are located between each connection to provide a good high-pressure seal. The expansion nozzle was developed by LTV Aerospace and Defense Company, presently a part of Lockheed Martin Missiles and Fire Control. It was part of an arc-driven hypervelocity wind tunnel facility and was subsequently donated to UTA. The end of the driven tube has a special coupling for the nozzle insert and secondary diaphragm. The coupling consists of several parts that form a locking system for the throat insert. The nozzle has interchangeable throat inserts to provide a discrete test section Mach numbers of 5 to 16. The nozzle has a length of 2.57 m (101 in), with an exit diameter of 33.6 cm (13.25 in) at the test section [15]. The test section has a dimension of 53.6 cm (21.1 in.) in length and 44 cm (17.5 in.) in diameter. It has circular access windows of 23 cm (9 in.) diameter facing each other on either side. These two ports can be used as mounting ports or for optical windows [10]. The rear of the test section has a conical converging section which leads into the diffuser. The dimensions of the converging section are 38.1 cm (15 in) in diameter within the test section and it contracts to a diameter of 31 cm (12.2 in) to the entrance of the diffuser. The flow is captured by the converging section and generates the first shock wave necessary to slow the flow down in the diffuser [15]. The dump tank is located outside the building and has a volume of 4.25 m3 (150 ft3). The vacuum system vacuums the shock tunnel from the tank to the secondary diaphragm. A 35.6 cm (14 in) vacuum pipe is connected directly from the dump tank by a flange joint with a double O-ring seal. A smaller 7.62 cm (3 in) diameter piping is used for connecting the vacuum pump to the vacuum tank.
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A high-pressure system is used to pressurize the driver tube. Another lower pressure system is used to operate the remote control valves and the booster pump (Haskel model55696) on the high-pressure system. The high-pressure system consists of a 5-stage compressor and a booster pump. The 5-stage compressor (Clark Model CMB-6) which is located in the adjacent compressor building can provide dry air at up to 14.5 MPa (2100 psi). The booster pump (Haskel Model 55696) is a two-stage booster pump which is used to attain pressures of up to 41.4 MPa (6000 psi) in the driver tube. The Haskel pump uses dried, filtered compressed air from the main compressor or helium supplied from 2200 psi bottles. The pressurized gas is stored in a one meter diameter spherical storage tank which can hold pressures up to 41.4 MPa (6000 psi). The low pressure is generated by another compressor (Kellogg American inc. modelDB462-C) which supplies dry air at 1.2 MPa (175 psi). Regulators are used to reduce the pressure to 689.5 kPa (100 psi), which is needed for the booster pump operation. The lowpressure compressed air (175 psi) is used by both the vacuum pump isolation valves and the booster pump in the high-pressure system. A secondary diaphragm separates the driven section from the test section. Both the driven section and the test section including the nozzle have their own vacuum pumps. The driven tube is vacuumed by a vacuum pump (Sargent-Welch Model 1376). This pump has a free-air displacement of 300 liters per minute and is able of pumping down to 0.001 mmHg. The test section is vacuumed by another vacuum pump (Sargent-Welch Model 1396) which is connected to the dump tank. This pump is capable of a free-air displacement of 2800 liters per minute and is able of achieving low pressures of up to 0.0001 mmHg. Vacuum is measured in both the driven tube and the dump tank by a pressure gauge (MKS Baratron Type 127A). The gauge has a full-scale range of 1000 mmHg and an accuracy of 0.1 mmHg.
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2.2 Reconstruction of the UTA Hypersonic Shock Tunnel The hypersonic shock tunnel had not been in use for many years and had been disassembled for a long time due to other research activities. Reconstruction was needed and began in 2010, where some of the parts had to be repaired or replaced with redesigned parts. The hypersonic shock tunnel began full operation by mid 2011. The first steps involved were setting up the driven tube sections which included removal of corrosion and cleaning the inner tube. The diaphragm section was attached back to the driver segment. For obtaining a good vacuum, the system had to be rechecked to ensure good seal. A schedule 40-steel pipe of 76 mm (3 in.) internal diameter and 2.13 m (7 ft.) length had to be replaced and customized for convenient attachment to the external dump tank. Safety valves from the dump tank had to be replaced. Due to corrosion of the inner surface of the tank, it was cleaned and treated with Enrust™ to prevent further occurrence. Some components had to be refabricated or redesigned. The throat locking mechanism for the nozzle inserts had to be fabricated in 4340-stainless steel. A diffuser section was designed for convenient sting installation. This section has five ports used for model mounting and instrumentation purposes. 2.3 Diaphragm Test As mentioned before, the driver and driven tube are separated by double diaphragms made of 1008 steel (10/12gage, 0.03 in. thickness). New thickness tests had to be conducted for higher pressure in the range of 20~30MPa (3000~4500 psi). Thickness and scoring play important roles for achieving proper rupture. In some tests, the petals were torn off, which are undesirable. These steel diaphragms must be scored with a cross pattern on each run, for perfect rupture. Several tests were conducted on the scoring depth and thickness of the plate, to improve the quality of the rupture and to contain the needed pressure. The tests ensured a clean rupture and minimal petal fragmentation. Detailed drawing is given in appendix A. The special cross pattern, known as a cross potent in heraldry was made [15] with a CNC machine for quick manufacturing and reduced cost. Moreover, CNC machining helps in maintaining 13
conssistent scoring g depths. The e figure 2.5 shows s the ste eel diaphragm m before and after the testt. Table e 1.1 specifie es the differen nt rupture presssures for diffferent scoring g depths.
Table 2.1 Ruptu ure propertiess of diaphragm m tests.
High-pre essure Test
Diaphrag gm scoring de epth (inches)
Rupture Presssure R (Psia)
1 2 3
0.040 0.035 0.030
2200 2548 3050
Figurre 2.5 Steel diaphragms, d (a) Scored Dia aphragm, (b) Ruptured dia aphragm afterr a successfu ul test.
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CHAPTER 3 DESIGN AND EXPERIMENTAL SETUP 3.1 Force Balance Design An investigation was conducted by Robinson et al. [4] on both internal and external balances to measure forces and moments using FEA (finite element analysis). Their analysis showed that greater accuracy of the recovered forces and moments could be obtained with the external force balance design. For the present work, the design of an external force balance (stress wave force balance) was investigated. This balance has the ability of mounting a variety of models. Some of the conceptual design requirements included: 1. Size constraint. 2. Strength of Balance and other components. 3. Model and support attachment 4. Strain gage and transducer placement. 6. Calibration ease 7. Machining simplicity
The force balance can only be accommodated in the limited room given by the dimension of the test section, including the model. The design should be able to adapt to the test section of the UTA Hypersonic Shock Tunnel, which has a dimension of 53.6 cm (21.1 in.) in length and 44 cm (17.5 in.) in diameter. The strength of the balance is important in deciding on the type of material. Different type of metals including steel, stainless steel, brass and aluminum were investigated.
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Table 3.1 shows some properties of specific metals/ alloys. Material
Young's Modulus (GPa)
Maximum tensile strength (MPa)
Density (kg/m³)
Aluminum-6061-O
69
310
2700
Brass
97-105
550
8000-8730
Stainless steel, AISI 302 cold-rolled
207
860
8190
Steel, API 5L X65
200
531
7600
For ease of manufacture, reduced weight and high strength, aluminum (Al-6061) was chosen as a suitable material. Other materials used for the model and support bolts include hardened steel and stainless steel. An FEA was used to assist in selecting a suitable force balance design amongst a number of candidates. The first step was modeling simple stress bars to understand the propagation of stress waves in solids. These stress bars were analyzed in ANSYS using the Explicit Dynamics solver. All preliminary conceptual designs were modeled using Catia V5 and analyzed using the FEA solver. Many other types of designs were analyzed, as shown in figure 3.1.
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Fig gure 3.1 Different prelimina ary designs.
n gage placem ment the slan nt faces are the t preferred stress bars. The differen nt For strain prelim minary designs were ana alyzed using FEA by appllying a simullated impulse e force to the e front, at the mode el mount locattion, details limited to (f) iss explained in n section 3.1.1 1. Designs (a) and (b) showed a large stresss concentratio on where the e bolts are loccated. Design ns (c) and (d) show wed higher in nternal reflecttions of stresss waves tha an (f). Design n (e) was co omplex, which h would not be prac ctical. FEA de emonstrated that t most stra ain is seen on n the stress bars b of design n (f). Design D (f) was s chosen con nsidering all th he factors tha at are mentioned above. Itt was decided d to mo odel the force e balance as a single solid piece for fabrication ease. The force e balance wass fabricated in n 6061 alumin num alloy from m a single so olid block. The e single block desig gn helped in reducing the e stress concentration, which w tends to o accumulate e more e at joints wh here memberrs are fastened together. Figure 3.2 shows s the fab bricated force e balan nce. The force balance has a dimension n of 20.9 cm (8.25 in.) in le ength, 10.8 cm (4.29 in.) in n heigh ht and 2.5 cm m (1 in.) in wid dth. The stresss bars have a 0.88 cm (0.35 in.) thickn ness. Detailed d draw wing of the forc ce balance iss given in appendix A.
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Figure 3.2 Fabricated forcce balance (6 6061- aluminu um alloy)
3.1.1 1 Finite Eleme ent Analysis Finite elem ment analysiss which helpss to determine e stress distriibution, displa acements and d deforrmations, was s used to verify the stresss concentration and respo onse of the force f balance e. The ANSYS A Explicit Dynamics solver is use ed to understa and the dynam mic response of a structure e unde er a time-vary ying load typiccally with dura ations of less than 1 secon nd. This solve er can also be e used d for impact analysis, sho ock propagattion and stre ess wave pro opagation. Th he differentia al equa ation of motion n in structural dynamic ana alysis is given n by,
(3.1) wherre m iss the mass off the system, c iss the damping g coefficient , k iss the stiffness s constant , u iss the displace ements vectorr p(t) iss the vector of o the time-varying load.
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At each point in time, the vectors of displacement , velocity
and acceleration
are
of particular interest to determine stress concentration of the balance and understand its dynamic response. A mesh was generated using the explicit meshing feature. Tetrahedral elements were used to mesh the force balance. A total number of 34088 elements was used in the simulation. A uniform mesh was generated with default size elements to respond to high frequencies of the stress wave. Mesh refinement was used for computational efficiency, by maintaining larger elements to insignificant areas and increasing relevance to areas of higher stress concentration. Care was taken in this process, as a coarse mesh was not able to transmit high-frequency information to the finer mesh [1]. Damping was not used in the simulation, so as to acquire high frequency stress waves. For computational ease, the balance was analyzed without the other small components. Figure 3.3 shows the mesh of the force balance.
Figure 3.3 Generated mesh of the force balance using explicit dynamics.
The force balance was modeled as a rigid body, the top surface, a fixed support and the simulated force was applied from the front face, which is shown in figure 3.4. The time step 19
is co ontrolled by th he smallest element e size, which is use ed to progresss the solution n in time. The e soluttion time step was 0.085 µss.
ure 3.4. Analysis settings, force is applied from the front f surface. Figu
Fig gure 3.5 Strain concentratio on in stress bars b of the forrce balance. 20
From the solution of the stress analysis, it can be seen that stresses are prominent on the two stress bars, figure 3.5. Animation results show that stress waves move from the front of the axial bar towards the stress bar and then to the rear of the axial bar. Reflections of stress waves occur in the stress bars. These results are shown in figure 3.9. First analysis was to determine the response of the force balance to a simulated impulse force, figure 3.6. The pulse of 220 µs width, was applied to the front surface, with maximum amplitude of 350 N (78.6 lbf). Strain was monitored on two locations, on the top surface of the axial bar (location 1) and on the stress bar (location 2), as shown in figure 3.4. Figure 3.7 (a) shows the strain output on location 1, which resembles the input impulse. The response of location 2 is shown in figure 3.7 (b). Many reflections are seen in the response of this location due to various wave reflections in the stress bar. From the simulation, a transfer function was obtained from the strain-history of locations 1 and 2. The next analysis was to find the response of the force balance to a simulated step load. The step load (100 µs rise time) of 222.4 N (50 lbf) was applied to the model for a period of 4 ms. The step load and step response on location 2 can be seen in figure 3.8.
Figure 3.6 Simulated input load of 350 N. The pulse starts at 90 µs. 21
The input step lo oad was reco overed by de econvolution of o the step response r with h the transfe er functtion. FEA sho owed the dyn namic behavio our of the forcce balance to o impulsive fo orces and also o demo onstrated pos sitions to placce the strain gages. g It helpe ed in showing g that input fo orces could be e successfully recov vered.
(b)
(a)
onse to the simulated s imp pulse at (a) lo ocation 1 and d (b) location n 2.The pulse e Figurre 3.7 Respo startss at 90 µs. .
(a)
(b)
8 (a)Simulated d step load off 222.4 N and d (b) step resp ponse of locattion 2. Figure 3.8 22
Figure 3.9 Animated result shows the e stress wave propagation in the force balance.
23
3.1.2 2 Force Balan nce Constructtion A 12.7 mm m (1/2-in.) threaded hole in the fro ont of the ba alance is use ed for mode el attacchment. Two 12.7 mm 1/2--in. threaded holes were available at the e top to attacch the balance e convveniently into the test secction. Two 6.3 3 mm (1/4-in n.) threaded holes were lo ocated at the e botto om for attachm ment as need ded. Figure 3..2 shows the fabricated forrce balance with w a detailed d draw wing given in appendix a A. A blunt co one model wa as chosen to o validate the force balancce by measuring the forcess and comparing th hem to the prrediction, which will be disscussed in se ection 5.2. Th he blunt cone e mode el was made e of steel with h a base radius of 40 mm m (1.575 in.) and a semi--angle of 18.5 5 degre ees. The mod del was 88.9 mm (3.5 in.) long and it we eighs about 907.1 9 g (2 lbss). Figure 3.10 0 show ws a photogrraph of the blunt b cone. For F simultane eous pitot pre essure measurements the e mode el was design ned to hold a PCB 113A21 1 pressure tra ansducer. A pressure p transducer holde er was designed to firmly embracce the transd ducer. This ho older was tigh htened from the centerline e throu ugh the base of the mode el to the nose e of the cone e. The pitot pressure p transducer had a recesss of 4.5 mm m (0.18 in.). The T design specification s of both the blunt b cone model m and the e presssure transduc cer holder are e given in the Appendix A.
Figure 3.10 0 Blunt cone model m (a) side e view (b) fron nt view. 24
Another component that was used was a two-sided bolt, with a hole drilled through it. This bolt was used to connect the model to the force balance and take out the coax cable from the pressure transducer. A 12.7 mm (1/2 in.) thread on one side was used for balance attachment and a 17.4 mm (11/16 in.) thread was used for model attachment. The overall length of the bolt was 96.5 mm (3.8 in.). Another feature of this bolt is its hinge design, so that the angle of attack of the model can be changed, from 5 to +5 deg. Due to this feature, the bolt made of 4140 steel was additionally hardened and drawn, making it strong enough to withstand high impact loading. Detailed drawings of parts of the bolt are given in appendix A.
Figure 3.11 Hardened steel bolt, the larger pin is used to change the angle of attack and the other pin is used to lock the position.
The hardened steel bolt was screwed into the base of the model with required wiring lead taken out. This assembly consisting of the model and the hardened steel bolt was attached 25
to the front of the force balance, thus in the centerline. Piezoelectric film gages (Measurement Specialties Model DT1-052k) were used to measure the stress waves. Two gages were used, one on the stress bar and the other behind the model on the balance aligned with the axis. The gages were shielded with copper foil to prevent EMI (electromagnetic interference). Care was also taken to protect the gages from direct pressure exerted during flow by wrapping PVC/ rubber around them, which was then sealed with electrical tape.
Figure 3.12 Installed model and balance in the test section. The support structure can be seen on the top. Additional strain gages (Omega Model SGD-3/120-LY13) were used for static calibration. These gages were installed on the centerline of the first stress bar in a Wheatstone bridge arrangement. A full-bridge mode was chosen since it gives maximum sensitivity to strain and also provides temperature compensation. M-bond 200 adhesive and conditioner were used as adhesive for attaching the strain gages. The finished gages were then given a protective coating of M-coat c. Figure 3.13 shows the installed gages on the front bar. The strain gage
26
signal was amplified with a strain gage amplifier (Paine Model strain gage amplifier) with a gain of 100 and an excitation of 10 V.
Figure 3.13 Two strain gages are seen on the stress bar, the other two gages of the full bridge are attached to the lower surface of the stress bar.
Two holes of 12.7 mm (1/2-in.) diameter, a distance of 11.6 mm (4.6-in.) apart, were drilled from the top of test section. The force balance assembly was attached to the ceiling of the test section by two hardened steel bolts. A 5.5 mm (7/32-in.) diameter hole was drilled into each bolt for channeling wiring from the test model and force balance to outside the tunnel. These holes were later sealed from both inside and outside. For adjusting the alignment and 27
height of the force balance an aluminum block of dimensions 2.5 cm × 2.5 cm × 15.2 cm (1 in. × 1 in. × 6 in.) was installed between the balance and the ceiling. The model-balance assembly was attached to the aluminum block by two 12.7 mm (1/2-in.) steel bolts. Steel washers and rubber washers/bushings where placed in all bolt connections for damping. Figure 3.14 shows the force balance-model assembly attached in the test section.
Figure 3.14 The force balance with the model, view from front of the nozzle.
28
3.2 Calibration Techniques 3.2.1 Static Calibration Static calibration is done by loading the force balance system with known weights and measuring the output for each increasing load. After loading the balance unloading is performed in like manner. This procedure helps to characterize the linearity and the possibility of hysteresis in the system. Figure 3.15 shows a sketch of the static calibration procedure.
Figure 3.15 Schematic of the static calibration procedure.
Static calibration was performed on a thrust stand by holding the force balance rigidly. Steel wire rope was attached to the blunt cone using the pressure transducer holder by tightening the holder inside the cone. The steel wire was tied to a digital scale (AWS model-TL440), which had a maximum load range of 1957 N (440 lbf). A turnbuckle was used to connect the weighing scale rigidly to an anchor bolt in the thrust stand. Tension was applied to the model-balance assembly by tightening the turnbuckle. The force was progressively applied, up to a maximum of 1423 N (320 lb). The strain was noted down for each load. Table 3.2 shows 29
the applied loads. For this calibration the foil strain gages were used as they can measure the applied static loads. The same procedure was done for unloading the force. Figure 3.16 shows the strain gage output voltage versus applied force on the balance system, for both the loading and unloading case. No significant hysteresis was seen in the static calibration. The trendline equation V=0.003F+0.003, R2=0.999, for loading and the trendline equation is V=0.0003F +0.009, R2=0.995 clearly show a linear relationship between the applied load and strain.
0.45 0.40
Voltage , (V)
0.35 0.30 0.25 0.20 0.15 0.10
Loading
0.05
Unloading
0.00 0
200
400
600
800 1000 Force (N)
1200
1400
1600
Figure 3.16 Static loading and unloading of force balance.
30
Table 3.2 Static calibration results. Mass (lbs)
Force (N)
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320
0.0 88.9 177.9 266.8 355.8 444.8 533.7 622.7 711.7 800.6 889.6 978.6 1067.5 1156.5 1245.5 1334.4 1423.4
Strain gage output voltage (V) Loading of weight Unloading of weight
0.000 0.025 0.047 0.071 0.097 0.119 0.141 0.167 0.188 0.212 0.232 0.254 0.276 0.298 0.320 0.349 0.369
0.000 0.030 0.054 0.077 0.101 0.132 0.156 0.178 0.209 0.232 0.257 0.280 0.304 0.321 0.339 0.355 0.373
Another approach that was performed for static calibration was using an impulse hammer (PCB Model 086C01) and averaging the output for different input hammer forces. For this method, piezoelectric films were used to measure the dynamic strain. Since these piezoelectric films measure dynamic forces, the output forces were averaged. Given that the output of the piezoelectric film gages oscillates around zero, the average would give values close to zero, therefore the rms value of the output voltage was calculated. Thus the sensitivity constant can be determined. The trendline equation of V=7E-05F +0.003, R2=0.953 of figure 3.17, shows the linear relation formed by averaging output of different hammer hits, with different force values.
31
0.050 0.045 Averaged Voltage (V)
0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000 0
100
200
300
400
500
Force (N) Figure 3.17 Plot of average film output versus applied hammer force. 3.2.2 Dynamic Calibration Dynamic calibration is performed to characterize the balance behavior when a sudden load (impulse force) acts on a system. Dynamic calibration is performed by different methods including hammer impulse excitation. A perfect impulse will excite all the frequencies of a system, which consist of the model and the force balance. Other ways of calibrating is creating a step load by hanging weights from a wire and cutting the wire. This type of calibration can be done both horizontally and vertically. Drop test calibration is a procedure of suspending the balance and cutting the wire above the balance, thus creating a step response. For the drop test calibration, care must be taken to prevent damage from impact. Figure 3.18 is a sketch of a cut weight test. The balance and model system are attached from the top and a known mass is suspended from the end of the model through a pulley. The wire is then cut near to the model creating a step response, measured with the gages.
32
Figure 3.18 Sketch of a cut weight test. Cut weight test was also performed vertically, since vibrations can occur in the step response when using a pulley as support. This arrangement is seen in figure 3.19.
Figure 3.19 Vertical cut weight test 33
Dynamic calibration is performed to o find the forrce balance characteristics c s, also known n as th he transfer fun nction. Calibra ation is done by striking th he model with h an instrumen nted hammerr. A scchematic of th his calibration n is shown in n figure 3.20. A PCB Model 086C01 impulse force e hamm mer was used d with the mo odel installed in the test se ection. A signa al conditionerr (PCB Model483A A) was utilize ed for the ham mmer signal. The piezoelectric films were w used to measure the e outpu ut strain. Da ata were reco orded using an oscillosco ope (Tektronix Model DP PO 4054, see e Appe endix C for details). d The sampling s rate e for the calib bration was 25MS/s. 2 Diffe erent hamme er tips, consisting off metal, plastic and rubberr were tested to determine e one that is most m suitable e. Testss showed tha at the metal tip excited the system with w higher fre equencies. The T rubber tip p damp ped higher fre equency and created impu ulses of largerr pulse width. Both the mettal and plasticc tips were w used to create the im mpulse. Figurre 3.21 illustra ates the raw data of a ham mmer impulse e and the t strain output. A detail of o the pulse with w the metal tip is shown in figure 3.22 2, the hamme er signa al takes more e than 1 ms to o reach back to its steady state, right after a the pulse e. When using g the im mpact hammer care was taken t to obta ain a good pu ulse. A poor strike s will crea ate a string of o small pulses due to t the bounce e of the hamm mer.
Figure 3.2 20 Schematicc of impulse hammer h calibrration
34
Figurre 3.21 Raw data of a ha ammer impulsse (above) an nd the respon nse of the ha ammer impacct taken n over duratio on of 150 ms (below).
F Figure 3.22 Sa ample hamme er impulse cre eated by strikking the metall tip on the mo odel cone. 35
To form the transfer function (impulse response), the obtained strain output is deconvolved with the hammer impulse. As mentioned before, a poor hammer strike can result in obtaining an inaccurate transfer function. The hammer strike can be verified, since theoretically convolution of an ideal impulse with a unit step results in a perfect step response. Matlab™ was used to create a unit step (start at t=0) as shown in figure 3.25. The hammer impulse was convolved with this unit step. The resultant convolved signal is illustrated in figure 3.23. This signal was compared with a simulated step response, which is formed by convolving a modified impulse with the unit step [9]. This modified impulse was created by padding zeroes right after the pulse of the hammer strike, as shown in figure 3.26. The pulse was identified to have a width of approximately 487µs, as illustrated in figure 3.27.
Figure 3.23 Check signal of both raw hammer signal and modified hammer signal.
A detailed view of the check signal is shown in figure 3.24. The error bar shows the deviation of the signal from the modified pulse signal. The hammer check signal agrees with the perfect step response. An error estimate on the signal shows variation of ± 0.6 %. It may be 36
conccluded that the ese variationss in the hamm mer check sig gnal is becausse the mean right after the e pulse e of the hamm mer strike, (fig gure 3.22) is not n zero.
Figure e 3.24 Detaile ed view of che eck signal witth error bar
Fiigure 3.25 Siimulated unit step input. 37
The pulse e width chang ges for each hammer impu ulse, the calib bration pulse width ranged d from 200 to 500 µs.
Fig gure 3.26 Mo odified hamm mer impulse.
Figurre 3.27 Enla arged view of o the pulse of the modiified hammerr impulse. Pulse width iss appro oximately 487 7µs. 38
Througho out this work, Matlab™ wa as used for data d processing. The impu ulse response e was found by dec convolution of o the pulse output o with th he hammer im mpulse. The deconvolution d n was tested in two o ways, one using u FFT alg gorithm and th he other itera ative deconvolution method d using g functional minimization m w extended with d conjugate gradient g algorithm (JMECG G) [16]. From m figure e 3.28 it can be seen tha at both the sig gnals, obtaine ed by FFT an nd JMECG ag gree well with h each h other. Both methods ca an be used in n determining g the impulse e response. The obtained d deco onvoluted sign nals had to be b filtered aga ain, since the e deconvolution method amplifies a highfrequ uency compon nents. A ten-p point moving--average filterr was used fo or this samplin ng rate.
Figurre 3.28 Com mparison of the impulse response ob btained using g two metho ods (FFT and d JMEC CG) The impu ulse response e in the frequ uency domain n is known as a the frequency response e functtion (FRF). From F the FRF F shown in fiigure 3.29, th he higher frequencies mig ght be due to o 39
intern nal reflection of stress waves. The re esulting frequ uency respon nse describess the balance e syste em characteristics. A deta ailed view of the t first 12 kHz k is shown in figure 3.30. The phase e specctrum of the siignal is illustra ated figure 3.31.
Figurre 3.29 Powe er spectral density plot off frequency response r function showing the variouss frequ uencies.
3 Enlarged d power specctral density plot of FRF forr the first 12 kHz. k Figure 3.30 40
Figure e 3.31 Enlarge ed view of phase spectrum m of FRF for the first 12 kH Hz.
Matlab™ was used to o create a spe ectrogram of the t frequencyy response fu unction (FRF)), which h is shown in n Figure 3.32 2. The spectrrogram was calculated c ussing the shorrt-time Fourie er transsform. The spectrogram shows s the fre equency variiation with tim me. At any point p of time e, frequ uencies are excited, this iss due to the hammer impullse. The modes of vibration are seen ass red. The T first mode shows the maximum am mplitude.
.
F Figure 3.32 Sp pectrogram of the FRF. 41
3.3 Shock Tunnel Testing The experiments were conducted with the UTA Hypersonic Shock Tunnel, using air as the driver gas. Steel diaphragms were used in the double diaphragm section as mentioned in chapter 1. The secondary diaphragm was made of mylar (0.010 in. thickness). For the tests, a Mach 10 nozzle insert was used. CEA (Chemical Equilibrium with Applications) was used in calculating reflected shock conditions. The flow was considered a frozen composition. Shock velocity was calculated using two pressure transducers (PCB Model-111A23), which were located 82.5 cm (32.5 in.) and 219.7 mm (86.5 in.) from the end of the driven section. The free stream flow conditions were found using the perfect gas relations, which are summarized in table 3.3. For the experiments all the signals including the pitot pressure, force data and pressure transducers in the driven tube (CH1 and CH2) were recorded simultaneously using an oscilloscope (Tektronix Model DPO 4054, see Appendix C for details). A rising edge trigger was used for the first pressure transducer (CH1) for a level of 300 mV. It was set to ensure no loss of data and capture all signals. The data were sampled at 25 MS/s and for a duration of 40 ms.
Table 3.3 Test conditions. Condition No:
M∞
P0 (MPa)
ρo (kg/m3)
T0 (K)
p∞ (Pa)
ρ∞ (kg/m3)
T∞ (K)
V∞ (m/s)
H0 (MJ/kg)
9.441
2.68
10.22
914.6
72.89
4.95E-03
51.3
1344.9
0.65
9.427
2.705
10.21
923.7
73.76
4.93E-03
52.0
1352.3
0.66
Condition 1 Condition 2
42
CHAPTER 4 RESULTS AND DISCUSSIONS 4.1 Force Measurement Prediction 4.1.1 Modified Newtonian Theory Newtonian theory assumes that the oncoming flow can be considered of as continuous stream of particles.
When the particles hit a surface at high speeds, they lose all their
momentum perpendicular to the surface. The pressure coefficient predicted by Newtonian theory is given by
2sin
(4.1)
This equation shows that the pressure distribution is related to the square of the inclination angle. The modified Newtonian theory was proposed by Lees in 1955 so that the pressure is a function of M∞:
,
1
(4.2)
where, Cp,max is the maximum pressure coefficient behind a normal shock wave, at the stagnation point.
∞
is calculated using the Rayleigh pitot formula [18] :
(4.3)
43
The axial force coefficient is calculated by the following relation [17],
2C
0.25 cos
,
0.125 sin
cos
cos
sin
⁄
cos
1
(4.4)
0.50 sin ⁄
cos
tan
sin
cos cos
2tan
where, RN is the nose radius of the blunt cone RB is the base radius of the blunt cone θc is the half cone angle α is the angle of attack The normal force coefficient is calculated by the following relation [17],
2C
0.25
,
⁄
cos
cos
(4.5)
⁄
2
The following relation is used to calculate Lift-to-Drag ratio:
44
(4.6)
Drag g is calculated d by using the e relation
D
ρv S C (4.7)
(4.8 8)
(4.9 9)
4.9) into (4.7) yields Eqnss. (4.8) and (4
(4.10)
The axial and norrmal force coefficients, coe efficients of liift and drag were w estimate ed for a range e of an ngles of attack k from 0 to 15 5 deg which are a summarize ed in Tables 4.1 4 and 4.2.
Figurre 4.1 Plot of (a) coefficien nt of drag vs. angle of atta ack and (b) co oefficient of lift vs. angle of o attacck. 45
Table 4.1 Force prediction using modified Newtonian theory using condition 1. Angle of Attack (α) 0 5 10 15
Ca
Cn
Cl
Cd
L/D
0.2697 0.2736 0.2852 0.3041
0 0.1427 0.2780 0.3991
0 0.1183 0.2243 0.3067
0.2697 0.2850 0.3291 0.3971
0 0.4152 0.6814 0.7725
Table 4.2 Force prediction using modified Newtonian theory using condition 2. Angle of Attack (α) 0 5 10 15
Ca
Cn
Cl
Cd
L/D
0.2692 0.2732 0.2848 0.3038
0 0.1427 0.2781 0.3991
0 0.1184 0.2244 0.3069
0.2692 0.2846 0.3287 0.3967
0 0.4160 0.6826 0.7736
4.1.2 Coefficient of Drag Calculation using Pitot Pressure The following equation shows how force coefficients are found by normalizing the force history by the pitot pressure using a suitable scaling factor [9],
From equation 4.7
(4.11)
The Rayleigh-pitot formula given in equation 4.5 can be also written as [9],
(4.12) 46
For high values of M∞, when 2
≫
1 , equation 4.12 can be approximated as,
(4.13)
(4.14)
(4.15) Substituting these into equation 4.13 we get
Substituting
(4.16)
in equation 4.16
(4.17)
For a given flow condition
and S remain constant, therefore drag coefficient is expressed as
(4.18)
Measuring the pitot pressure along with the force during an experiment can be used to estimate the force coefficient, which also varies with time. 47
4.2 Expe erimental Ressults The predicted values using the mo odified Newto onian theory and the reco overed forcess were e compared. Figure 4.2 is a plot of the coefficie ent of drag history h obtain ned from the e recovvered force of o condition 1. This data was w normalized with the pitot p pressure e as shown in n section 4.1.2. An average a taken from 175 µss to 275 µs iss also shown in the figure.
Figu ure 4.2 Coefficient of drag from the reco overed force (condition ( 1).
It can be seen that ap pproximately the t first 120 µs is the flow w commencin ng stage, after the fllow arrival the e drag coefficcient remains steady for a period of 100 0 µs and is th hen noticed to o decre ease. This is due to increa ase in pressure at the base e of the cone, which would d describe the e decre ease in the coefficient c of drag d [9]. A lo ow frequency oscillation was w found in the t test signa al which h would also account for the unsteadyy drag force. Further invesstigations nee ed to be done e on th his low freque ency vibration. Figure 4.5 shows s that the e recovered fo orce data follo ows the same e trend d as the pitot signal. s 48
Figure 4.3 3 Recovered drag d force an nd theoretical force. The raw r pitot pres ssure signal iss shown in fig gure 4.4, a de etail of the pito ot pressure fo or the first 400 0 µs is shown in figu ure 4.5. The data d was filterred using a 20 kHz low-pass Butterwortth filter.
Figure 4.4 4 Raw pitot signal.
49
Figurre 4.5 First 40 00 µs of the pitot p pressure and drag. A 20 2 kHz low pa ass filter was used. The results for condittion 2 are sh hown in figurres below. Figure 4.6 is a plot of the e Coeffficient of drag history obta ained from th he recovered force of condition 2. Figu ure 4.7 showss the re ecovered forc ce.
Figu ure 4.6 Coefficient of drag from the reco overed force (condition ( 2). 50
Figure 4.7 Recovered R dra ag force. The raw r pitot pres ssure signal iss shown in fig gure 4.8, a de etail for the firsst 400µs is sh hown in figure e 4.9. The T data was s filtered using g a 20 kHz low w-pass Butterworth filter.
Figure 4.8 8 Raw pitot signal. 51
Figure 4.9 9 First 400 µss of the pitot pressure. p A 20 kHz low-pa ass filter was used. u From m the experim mental resultss it is seen that the reco overed drag is in accorda ance with the e meassured pitot pressure. The e experimenta al to theoreticcal drag com mparison is su ummarized in n table e 4.3. Δ % is i the differeence betweeen the theorretical and experimental e values. The e varia ations seen in n the recovere ed drag, migh ht be due to several facto ors, which are e discussed in n detaiil in chapter 5. 5
Table 4.3 Comparison C o experimenta of al to theoreticcal drag
C Condition no :
Dragexp e (N)
Draagtheory (N)
Δ %
Coefficientt of drag coefficient
1
16.9 ± 8 8.9 %
1 17.9
5.9
0.199 ±± 7.8
2
13.6 ± 19.6 %
1 18.0
32.3
0.128 ±± 27.9
52
CHAPTER 5 CONCLUSION AND FUTURE WORK Due to the short duration in impulse hypersonic shock tunnels, it is difficult to measure accurately the aerodynamic forces. Since the test time is very small, force equilibrium may not be reached between the model and the balance structure. The stress wave force balance (SWFB) is a method used to analyze the stress waves formed during aerodynamic loading. 5.1 Force Balance in the UTA Hypersonic Shock Tunnel A force balance was designed for measuring forces on aerodynamic models. In the present work, drag was measured for a blunt cone using the force balance. The force balance system included the model, which was fabricated in steel and the force balance, made of 6061 aluminum alloy. Several designs were investigated before the actual fabrication. Some of the limitations in the design included the size of the balance, amount of load the balance must withstand, model and support attachment and machining simplicity. The force balance was designed to fit in the hypersonic shock tunnel test section, allowing room for support attachments, model attachment and wiring. FEA (Finite Element Analysis) was used to determine the dynamic characteristics of the force balance under high impact loading. It was also performed to be certain of the maximum loads the force balance could resist. Piezoelectric film gages and strain gages were used to measure forces. Both static and dynamic calibrations were performed. The static calibration involved loading the force balance with increments of known weights and measuring the strain for each weight. The same procedure was also done for unloading the weights. These results were plotted to obtain a linear relationship. Dynamic calibration was done by pulse excitation using an impulse force hammer. The input by a hammer hit and the output was obtained from the piezoelectric film 53
gages. From the impulse hammer tests an impulse response/ transfer function was determined. Another dynamic calibration carried out was vertical and horizontal cut weight tests. These tests involved hanging known weights to the model by steel wires and cutting the wire, thereby creating a step load. These step loads were deconvoluted with the obtained transfer function to recover the step input. The model used in experiments was a blunt cone made of steel. It was designed such that a pitot pressure measurement was taken simultaneously. The model and balance assembly was then installed from the top in the test section. The required wiring was taken out of the test section through drilled bolts, which were sealed. The instrumented gages were shielded to prevent electromagnetic interference and sealed in rubber and electrical tape. Tests were conducted with conditions mentioned in chapter 4. All the data signals including the pitot pressure, force data and pressure transducers in the driven tube (CH1 and CH2) were recorded simultaneously using an oscilloscope ( see Appendix C). The strain data was processed and deconvolved with the transfer function, to recover the drag. Deconvolution was performed using an iterative algorithm [16]. A low frequency vibration was noticed in the signal of the measured force, before the incident shock reached the pressure transducers in the driven tubes. From each of the primary tests, this mentioned vibration occurred, which led to the conclusion that a vibration is due to the test section movement. An approach was made to tighten down the test section using steel wire rope and turnbuckles. Tests showed that these oscillations persisted. Therefore, it may be concluded that stress waves formed by the sudden rupture of the diaphragms have affected the drag measurements.
54
5.2 Future Work and Recommendations The following points may be included for future work for force measurements:
Develop an isolation system to reduce the initial vibrations in the force signal.
Force measurement with other models
Analyzing the flow with CFD simulations.
Tests at different enthalpy levels.
Calculate three components of force, such as, lift, drag and pitching moment.
Compensation of inertial forces due to tunnel movement using accelerometers.
Analyze signals in time-frequency representation using wavelet transform.
From the recovered drag, it can be seen that the signal follows the pitot pressure but that there is also a fluctuation in drag, which is accounted by the occurrence of these low frequency vibration. Further investigations need to be done on developing methods to decrease these low frequency oscillations, by using springs, rubber dampers etc. Some of the recommendation include, but are not limited to tests with simple shield design and compare the results. Also, test the model at different angle of attacks and compare the drag. Care must also be taken with the piezoelectric films, since they are very sensitive to EMI (electromagnetic interference). Any power source close to the tunnel must be avoided, which can result in erroneous values.
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APPENDIX A
LIST OF DESIGN DRAWINGS
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57 Figure A.1 Force balance drawing.
58 Figure A.2 Blunt cone model drawing.
59 Figure A.3 PCB pressure transducer holder drawing.
60 Figure A.4 Hinge joint part 1 drawing.
61 Figure A.5 5 Hinge part 2 draw wing.
62 Figure A.6 Scoring pattern on steel diaphragm drawing (courtesy Tiago Rolim).
APPENDIX B MATLAB PROGRAM FOR FORCE ESTIMATION
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%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/(gamma1))*((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 elseif in==1
xxxxxxxxxxxxxxxxxxx
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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))).*((((dcosd(theta)).*cosd(theta))/tand(theta))+(((dcosd(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).*((((dcosd(theta)).*cosd(theta))/tand(theta))+(((dcosd(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 65
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
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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 Nom. Resistance – 120 Gage Factor – 2.0 ± 5% Operating temp – -75 to 200°C
C.4
Pressure Transducers 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.
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[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.
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