Effects of Disturbances on Quiet Flow in the Mach 4 Ludwieg Tube

Effects of Disturbances on Quiet Flow in the Mach 4 Ludwieg Tube AAE 50 Experimental Aerodynamics Final Report Matt Borg and Justin Smith May 5, 004

Abstract The PQFLT was used to determine the effects of disturbances on flow quietness. Initially, normal runs were performed to ascertain a range of quiet flow Reynold s Numbers. Runs were performed for initial driver tube pressures between 6 psia and 16 psia. While none of the cases tested yielded noise levels low enough to be considered quiet flow by the conventional definition, runs at Unit Reynold s Numbers between 5000 and 40000 (driver tube pressures between 8 psia and 1 psia) had noise levels below 0.07% of the mean pressure. Disturbances were then introduced downstream of the test section by bursting the diaphragm asymmetrically. This was done for the same range of driver tube pressures as for the normal bursts. It was determined that asymmetric bursting produces no effect on noise levels. Finally, upstream disturbances were introduced through a jet at the end of the driver tube. Four runs were made at driver tube pressures of 10. psia. With each run, the strength of the jet was adjusted by changing the voltage applied to a pressure regulator controlling the jet. Regulator voltages of 0. V, 0.4 V, 0.6 V, and 0.8 V were used for the four runs and a distinguishable difference in rms noise level between normal and jet bursts was established. Particularly, the increased noise level was found to vary linearly with jet strength (voltage), showing increases from about 0 % at the 0. V level up to about 40% for the 0.8 V setting. Introduction Although supersonic wind tunnels are used in a variety of aerodynamic applications, often the data collected in them cannot be correlated to flight data. Supersonic vehicles are usually exposed to laminar free stream flow. Such flow cannot be properly replicated in typical supersonic wind tunnels. Conventional tunnels have turbulent boundary layers, which radiate noise onto the test object. This noise changes the laminar-turbulent transition Reynold s number on the object, and makes correlation to real data difficult or impossible [1], The noise level in a quiet wind tunnel is on the order of those experienced in flight, ~ 0.05% of mean data [8], typically an order of magnitude less than that in conventional tunnels Quiet supersonic wind tunnels allow proper study of high-speed boundary layers and thus more accurate prediction and control of boundary layer properties such as skin friction and heat transfer. Such flow promotes transition on a model at a Reynold s number comparable to flight []. RMS noise is typically measured as pitot-pressure fluctuations with fast pressure transducers or as massflow fluctuations with hot-wires [1]. Quiet flow is hard to achieve because the mechanisms of transition are many and poorly understood [3]. Below Mach 4, first mode instabilities dominate the flow and initiate transition. The second mode of instability remains stable []. Three modes of disturbance fields in compressible, viscous, and heat - conductive gases have been identified: vorticity mode, entropy mode, and sound-wave mode. The three modes are non-interacting for small fluctuations, but do interact at larger intensities [4].

There are several criteria which a quiet facility must meet. There must be a supply of clean, dry air. The tunnel must also minimize disturbances in the settling chamber. Additionally, the nozzle must be smooth, so as to promote the starting of the tunnel and a laminar boundary layer in the nozzle. It is known that the absence of such criteria in conventional supersonic tunnels promotes earlier transition of the boundary layer from laminar to turbulent and thus precludes quiet flow []. The region of quiet flow in a quiet facility is called the test core. This region is defined downstream of the test core by Mach lines traced to the acoustic origin of turbulence in the nozzle-wall boundary layer. The upstream boundary of the test core is defined by Mach lines due to the attainment of the design Mach number for the tunnel. The size of the test core is influenced by free stream Reynold s number. As it increases, the boundary layer transition region moves upstream and the Mach lines from this disturbance move upstream as well, decreasing the test core size []. The PQFLT The Purdue Mach 4 Quiet Flow Ludwieg Tube (PQFLT) was developed between 199 and 1994. This facility is a short duration wind tunnel consisting of a driver tube with a nozzle on the end from which flow exits into a test section and a diffuser [5]. The driver tube is 68 feet long with a 1 in diameter. A smooth contraction runs from the driver tube to the first throat (1.368 sq. in with an area ratio of 83 for the driver tube), followed by a 3.8 x 4.3 in Mach 4 rectangular nozzle. The nozzle was fabricated at NASA Langley in the 1970 s, and was donated to Purdue in 1991. Although not designed as a quiet nozzle, it was used to achieve quiet flow in the Purdue Ludwieg Tube [6]. Quiet flow has been achieved in the PQFLT for Reynold s numbers up to about 400000 based on the length of the quiet-flow test core (approximately 4 in). This corresponds to stagnation pressures up to about 14 psia []. After achieving quiet flow to low Reynold s numbers, the facility was used to develop instrumentation, as well as to study instability waves in quiet flow [7]. A Mylar diaphragm is used to initially isolate pressurized air in the driver tube from vacuum downstream of the test section. Wires are attached to the diaphragm. It is burst by running a large current through these wires to melt the diaphragm at the points of contact. The thickness of Mylar used for the burst diaphragms depends on the initial driver tube pressure. In general, diaphragm thicknesses of.004 in,.007 in, and.010 in are used for driver tube pressures of 50-70 kpa, 70-15 kpa, and 15-170 kpa, respectively [5]. When the diaphragm bursts, a shock wave travels downstream and an expansion wave travels upstream through the test section and into the driver tube. The expansion wave propagates through the driver tube and induces flow through the nozzle. The wave is reflected back through the nozzle from the closed end of the driver tube (with a round trip time of about 10 msec [6]). Additional expansion waves propagate into the driver tube until the stagnation pressure is too low to maintain supersonic flow in the nozzle and test section. A typical run lasts between 3 and 5 seconds [5]. Between expansion wave cycles, the flow is in a quasi-static state. Calculations are thus

based on data collected between wave fronts. Motivation It was desired to measure the effects of disturbances on the quiet flow obtained in the Purdue Quiet Flow Ludwieg Tube (PQFLT). An effective range of unit Reynold s numbers providing quiet flow needed to first be established. Additionally, a lower threshold unit Reynold s number still allowing supersonic flow was measured. Disturbances were then introduced into the flow in two forms. It was desired to determine whether downstream disturbances would travel upstream through the subsonic portion of the boundary layer. Thus, the first disturbance investigated was downstream of the quiet test core. This disturbance was formed by bursting a diaphragm asymmetrically. This created a fairly large downstream obstruction to flow, and thus the desired disturbance. Additionally, this study sought to determine whether certain upstream disturbances could preclude quiet flow. An air jet of varying intensity was introduced far upstream of the throat at the back of the driver tube. Since quiet wind tunnel facilities are essential for the further development and testing of hypersonic vehicles, an understanding of quiet facilities is necessary to continue this development. As has been demonstrated, there are a number of factors in any wind tunnel that could preclude quiet conditions. It is desired to ascertain the effects of disturbances in a facility where quiet flow has been consistently demonstrated. The PQFLT facility provided an excellent facility for this study. Procedure Before the tunnel could be run, a cone and sting mount were removed from the test section and a hot wire probe inserted. After cleaning the tunnel and ensuring that no particulate had settled into it, the test section was closed. After several runs had been completed collecting data from the hot wire probe and a Kulite static pressure transducer on the side wall of the tunnel, it was determined that these instruments would not indicate whether the flow was quiet or noisy. The hot wire probe was removed, and a Kulite pitot probe was inserted into the flow. It was placed further forward in the nozzle, near the center of the first window, than the hot wire had been to ensure that it was in the test core of quiet flow. A Mylar diaphragm was then prepared. This involved tracing out a new diaphragm onto a sheet of Mylar, cutting it, and punching holes in it for bolts to go through. The new diaphragm was then inserted into the diaphragm rings. After the bolts were handtightened sufficiently, Nichrome wires were taped across the diaphragm at right angles to each other. At the intersection point, a small loop was made so that when the wires were heated they would not melt through the tape and short each other out. The wire setup can be seen in Figure 1. The diaphragm ring was then inserted into the diaphragm section of the tunnel. The two wire leads from a capacitor bank at the bottom of the diaphragm section were attached to the diaphragm rings. The tunnel was then closed by operating a small hand pump, and sealed by tightening a flange clamp.

Figure 1: Diaphragm wire setup Two vacuum pumps were then turned on so as to evacuate the 535 cubic foot vacuum tank on the downstream end of the tunnel. One of two valves were opened which either added filtered, dry air to the driver tube, or applied a vacuum to the driver tube. Using these valves, the driver tube was brought to the desired initial stagnation pressure. After the vacuum tank reached the desired back pressure, -4 torr, the run was initiated. In order to start a run, a bank of capacitors was charged to approximately 40 Volts. A circuit was then closed with an electronic switch, enabling the capacitors to dump their charge into the Nichrome wires in contact with the diaphragm. The wires dissipated approximately 10 Watts. This heated them very quickly and melted the Mylar with which they were in contact. The upstream pressure then burst the diaphragm and the run began. The signal output by the Kulite pitot sensor was run through a circuit that amplified the DC signal by a factor of 100. On a second output, the signal was high-pass filtered the signal to isolate the AC component of the signal and amplified it by a factor of 10000. Both of these signals were read by a LeCroy 9104 digital oscilloscope. After the approximately 3.5 second run was finished, a computer was used to save data via a GPIB card for later reduction. The tunnel and vacuum tank were brought up to atmospheric pressure by fully opening the compressed air valve so the tunnel could be opened. After data were saved, the diaphragm section was opened. The used diaphragm rings were removed, and a new diaphragm setup put in its place for the next run. The diaphragms typically petaled into four quadrants. A picture of a typical burst diaphragm can be seen in Figure. Figure : A typical symmetrically burst diaphragm. The pitot probe was then calibrated by pressurizing the driver tube to a known pressure, read from a Paroscientific 740-30A pressure gauge, and recording the corresponding output voltage measured by an HP 34401A digital multimeter. The first time the calibration was completed, the lowest driver tube pressure used in the calibration was approximately 1.8 psia. It was then decided that the pitot probe needed to be calibrated to lower pressures because the measured pitot

pressures during a run were near this lowest calibrated point. There was also a curious deviation from linearity for the three lowest points on the calibration curve. It was necessary to determine whether the linearity of the voltagepressure relationship broke down at sufficiently low pressures. Thus, a second calibration to lower driver tube pressure, with more data points taken was completed. The deviation from linearity in the case of the second calibration was determined to be too high. Upon attempting a third calibration, it was found that the Paroscientific pressure gauge would not read lower than approximately 1. psia. After connecting the pressure gauge to a different pressure vessel and comparing with a separate pressure gauge, it was determined that something was wrong with the setup of the pressure gauge on the PQFLT facility. The pressure gauge matched almost perfectly in comparison with the other. The Paroscientific was then reconnected to the PQFLT, and the driver tube was pressurized to approximately 1 psia. A bubble leak test confirmed a leak in a connection from the tunnel to the Paroscientific. The connection was tightened, and the leak was successfully stopped. A third pitot calibration was performed, both at high and low pressures. Runs were made with driver tube pressures of approximately 15., 14., 14.1, 13., 1., 11.3, 10.7, 10.1, 9.3, 7.9, 7., and 6.3 psia to determine the maximum driver tube pressure allowing quiet flow in the nozzle, and the minimum pressure allowing supersonic flow. After attempting to run the tunnel to a driver tube pressure of lower than 6.0 psia, it was discovered that there was a significant leak that did not permit driver tube pressures below 5.5 psia. Even with the vacuum line completely open, both vacuum tanks running, and the vacuum tank in the tens of torr range, the tunnel pressure would not drop below approximately 5.5 psia. The tunnel was then pressurized to approximately 3 psia, and a bubble leak test was performed. It was suspected that the leak was from around the windows. The bubble test showed that the windows were air tight. Two leaks were found in other locations, however. One was plugged with a bolt, in place of the RTV that had inadequately sealed before. The second leak was plugged by applying more RTV. A picture of the successful bubble test can be seen in Figure 3. Figure 3: Successful bubble leak test. It was then desired to ascertain whether a disturbance downstream of the test core would propagate upstream through the subsonic region of the boundary layer and cause it to transition from laminar to turbulent, thus upsetting quiet flow. The tunnel was run in the same manner, but the diaphragms were prepared to burst asymmetrically. The diaphragms were burst in such a way that the bottom half

remained intact and disturbed the flow. This was accomplished by insulating the bottom half of the vertical Nichrome wire from the Mylar by placing a piece of masking tape between the wire and the Mylar. This method generally worked quite well. A picture of a typical asymmetrically burst diaphragm can been seen in Figure 4. Asymmetric bursts were made at initial driver tube stagnation pressures of 6.8, 10.0, 10.3, 10.5, 10.7, 11., and1. psia. After observing the effects of downstream noise on quiet flow conditions, a disturbance in the form of an air jet was introduced upstream of the test section in the far end of the driver tube. The jet strength was controlled by varying the voltage on the pressure regulator that supplied air to the end of the driver tube. All jet runs were made at an initial driver tube stagnation pressure of approximately 10. psia as that was near the lowest % RMS value achieved during normal tunnel operations. Runs were made with the pressure regulator voltage set to.,.4,.6, and.8 volts. Above that voltage, an overpressure relief valve was tripped, which disallowed higher pressure regulator voltages to be used. Figure 4: Asymmetrically burst diaphragm Theory Pitot Probe Figure 5. Nozzle of the PQFLT (not to scale).

A diagram of the nozzle of the PQFLT adapted from [8] is given in Figure 5. Upstream of the test core, the stagnation pressure, p 0,1, is measured by the Paroscientific gauge, and the stagnation temperature, T 0, is measured with a thermocouple at the end of the driver tube. The quiet-flow region is bounded upstream by Mach lines that emanate from the onset of uniform flow, and downstream by Mach lines which radiate from the nozzle walls as the boundary layer transitions from laminar to turbulent []. These boundaries define the quiet-flow test core in the nozzle, prior to the constant-area test section. Stagnation pressure in the quiet flow test core was measured just behind the center of the first window in the tunnel (~1/4" behind center). This location was selected because it is well within the quiet flow core [8]. Since the flow is supersonic in the region where stagnation pressure measurements are made, a bow shock develops in front of the pitot tube, Figure 6. M>1 p 0,1 p 1 Shock p 0,, Pitot Probe Figure 6. Bow shock in front of a pitot tube in supersonic flow. The presence of a shock in front of the Kulite precludes the utility of Bernoulli's equation in determining the velocity, and ultimately the Mach Number of the incoming flow. A normal shock relation, Rayleigh's Pitot Formula [9] must then be used to find an implicit relation for the test-core Mach Number, M, provided that the stagnation pressure behind the shock, p 0, and the driver tube static pressure, p 1, are known, Equation (1). γ p γ 0, M p 1 = 4γ 1 ( γ + 1) M 1 γ + γ M ( γ 1) γ + 1 (1) The driver tube static pressure is obtained from the isentropic relation [10] of Equation () and must be solved simultaneously with Equation (1). This is done iteratively, i.e. a guess is made for M, and plugged into both Equations (1) and (). Dividing the two to get p 0, / p 0,1, this answer is then checked against the measured ratio. A new guess is then made on M and the process is repeated until the desired accuracy is reached. For this analysis, M was solved to three significant figures. p 1 p0,1 1 M γ γ 1 γ 1 = + () Unit Reynold s Numbers are calculated from Equation (3). ρ Re = U 1 (3) µ For this analysis, density is given by the isentropic relation [3], 1 γ 1 γ 1 ρ = ρ0 1+ M (4) where the driver tube density, ρ 0, is obtained from p 0,1, T 0, and the ideal gas law (with R=87 J/Kg/K for air at STP).

Dynamic viscosity, µ, was taken from Sutherland's Law [], run, the prerun fluctuations are smaller than those during the run. T + S T 3 / ref µ = µ ref T + S T (5) ref 10 9 8 7 A 68.9 55. For air, µ ref = 1.7894x10-5 kg/(m.s) for T ref = 88.16 K, and S = 110 K. Finally, the flow speed, U, is calculated from the speed of sound, c, in the following manner: U = cm = γrtm (6) with temperature computed from an additional isentropic relation [3]: Pressure [psia] 6 5 4 3 1 B 0 0 0.5 1 1.5.5 3 3.5 4 4.5 5 Time [s] Figure 7. Stagnation pressure in the test core for an initial driver tube pressure of 8.6 psia. C D 41.4 7.6 13.8 Pressure [kpa] 1 γ 1 T = T0 1+ M (7) Quiet Flow Measurements A typical DC pitot trace for an initial driver tube pressure of 8.6 psia is given in Figure 3. The accompanying AC trace follows in Figure 8. Data were collected for 5 seconds at 50 khz. The oscilloscope record of the data consists of four main sections. These sections, labeled in Figure 7, are A Prerun B Startup C Expansion Wave Cycles D Subsonic Flow The prerun portion of the DC trace gives the driver tube pressure before the run has started. The AC data during the prerun is used to determine the electronic noise level when the tunnel is not running, the prerun noise. Notice from Figure 8 that for a typical Figure 8. AC pitot data for an initial driver tube pressure of 8.6 psia. During the startup, pressure fluctuates greatly as uniform supersonic flow begins to establish itself in the test core. No useful data can be taken during this time. Following the startup, after quiet flow has been established, expansion waves emanate through the driver tube and reflect back towards the test core. During each wave cycle, quasistatic conditions of uniform supersonic flow exist within the test core. It is during the first expansion wave cycle that

measurements of "flow quietness" are obtained. RMS pressure fluctuations are obtained from Equation (8): p rms ( p p ) = (8) ac ac In this equation, symbols with bars denote average quantities. The condition for quiet flow is [11] p rms p p dc rms,prerun 0.0005 (9) In this calculation, the prerun noise is subtracted so that only fluctuations inherent to the tunnel operation are considered. After approximately 30 expansion wave cycles have passed, the driver tube pressure is no longer great enough to sustain supersonic flow. This event is marked by a dramatic increase in rms pressure fluctuation because the turbulent subsonic boundary layer radiates noise into the test core. the leak pressure was not negligible and skewed the results. Since for higher pressures the calibration remained the same, all initial stagnation pressure data recorded in previous runs was still accurate and usable. A linear fit of the third data set was used to determine the following formula for conversion from Kulite voltage to pressure: p 0,1 = 1.0736 V + 1.7651 (10) A sample calculation for a run with an initial driver tube pressure of 11.3 psia (77910 kpa) and temperature of 74.5 o F (96.8 K) is now given. For this run, the diaphragm was burst normally and data were sampled at 500 khz for 0.5 seconds. The collected data include 0.1 seconds of prerun and about 3 1/ expansion cycles of same duration. Figure 10 shows both the AC and DC pressure traces. Results Several calibrations of the pitot probe were performed and are shown in Figure 9. As can be seen, all three calibrations matched quite well for driver tube pressures above 4 psia. Below 4 psia, the third calibration deviated from the other two, but remained linear with the higher pressure data. This sort of behavior is to be expected. Since the leak was so small, at higher pressures, the leak pressure difference was very small compared to the mean pressure. It thus had a negligible effect. When the mean pressure dropped sufficiently, however, Figure 9. Kulite pressure transducer calibration curves in the PQFLT.

Plugging this and the Mach Number into Equation (6), U = 1.4 = 669 m/s ( 87 J / Kg K)( 74 K)( 3.88) Finally, viscosity is obtained from Equation (5) with variables for air: Figure 10. Sample pressure data for a driver tube pressure of 11.3 psia. For the first pressure step after startup, the mean pressure was computed to be p 0,1 = 1.73 psia. Using Equations (1) and (), this corresponds to a Mach Number of 3.88. From the ideal gas law, the stagnation density is computed in the following manner: ρ 0 p = RT 0,1 0 = 77910 Pa ( 87J/Kg K)( 96.8K ) 3 = 0.915kg / m Then, from Equation (4), 3 1.4 1 ρ = 0.915kg / m 1+ = 0.084 kg/m 3 ( 3.88) 1 1.4 1 From Equation (7), with T 0 = 96.8 K, 1.4 1 T = 96.8 K 1+ = 74 K ( 3.88) 1 µ = 3/ -5 88.16+ 110 74 1.7894 10 kg/m s = 5.039x10-6 kg/m.s 74+ 110 88.16 Plugging all of these values into Equation (3), the unit Reynold's Number is obtained for this run: 3 ( 0.084kg / m )( 669m / s) Re1 = 6 5.039 10 kg / m s = 37705 /cm From Equation (8), the rms pressure fluctuation was computed to be 0.001371, while the prerun rms was 0.00047617. Using these values and the mean stagnation pressure on the first step, Equation (9) yields a fractional rms pressure fluctuation of:.001371.00047617 1.73 = 0.000744 This is a noise level of 0.0744 % of the mean signal. While this level is typically an order of magnitude below that of conventional tunnels, it still does not meet the requirements of Equation (9) for a quiet run. Figures 11 and 1 summarize Unit Reynold s Number and Mach Number calculations for all tunnel runs, respectively. Reynold s Number is shown to vary linearly with initial driver

tube pressure. A range of 15000 to 50000 was found for operation with pressures from 6 psia to 16 psia. Figure 1. Mach Number vs. driver tube pressure. Figure 11. Unit Reynold s Number vs. driver tube pressure. Mach Numbers around 3.9 were obtained for the entire range of pressures examined. Higher Mach Numbers were obtained at higher driver tube pressures. This is expected because the boundary layer is thinner at the point of pressure measurement. Thus the expansion ratio in the nozzle is effectively larger and the Mach Number increases as well. Near driver tube pressures of 6-7 psia, three seemingly anomalous Mach Numbers were found. These points were also found to have the highest noise levels computed. For these runs, the first pressure steps were around 0.7 psia. It is unknown why these points differ from expected values. It is doubtful that the flow dropped to subsonic because the pressure drop was larger than would be expected in subsonic flow, and the oscilloscope trace showed clearly defined expansion wave steps. Runs at these conditions should be repeated to ensure that these results are anomalous. Flow noise levels for all of the runs performed in the PQFLT are summarized in Figure 13. These runs include normal bursts, asymmetric burst, jet bursts, and combinations of asymmetric and jet bursts. From the figure, it can be seen that none of the normal burst runs have rms noise levels below 0.05% of the mean. However, a relatively wide range of driver tube pressures (~8-1 psia) has noise levels below 0.07%. This result is consistent with [11]. This pressure range corresponds to Reynold s Numbers between 5000 and 40000. Figure 13. Flow noise levels in the PQFLT. The horizontal scale is Reynold s Number per cm.

It can be seen that asymmetric diaphragm bursting has no effect on noise levels. If anything, asymmetric bursting decreases the noise level near the optimum Reynold s Number (i.e. near the Reynold s Numbers with lowest noise levels for normal bursting). The application of jets increases noise levels by approximately 30-40% on average. This is evident from Figure 14, as jet runs were performed at Reynold s Numbers around 35000, p 0,1 ~ 10. psia. For these runs, the jet pressure was varied with a regulator. Four settings were used from 0. V to 0.8 V. For regulator voltages higher than this, the relief valve would no longer let air into the tunnel. A plot of the trend in rms noise vs. regulator voltage is shown in Figure 14. This indicates an approximate linear relationship between voltage and noise level, but more settings would need to be used to verify this. Conclusions 1) Quiet flow, according to convention (<.05%), was not achieved. This is possibly because the nozzle was slightly dirty and accumulated particulate increased noise levels. However, noise levels of <.07% were found for a significant range of Unit Reynold s Numbers, keeping with previous results. ) Downstream disturbances in the form of asymmetrically burst diaphragms did not propagate upstream with sufficient strength to trip the boundary layer to early turbulent transition. The disturbance caused by the asymmetric burst was damped out by the time it reached the test core. 3) Upstream disturbances caused by jets introduced into the plenum (driver tube) increased the RMS percent noise linearly with voltage applied to the pressure regulator. Thus, upstream jet disturbances do effectively cause the boundary layer to transition earlier and to radiate noise into the test core. 4) Quiet flow is not influenced as heavily by downstream disturbances as upstream. Upstream jets have a strong effect on tunnel noise level. Nozzle dirtiness (accumulate particulate) also influences boundary layer transition. Figure 14. RMS Noise vs. Regulator Voltage for jet runs in the PQFLT. 5) It is suspected that the lowest unit Reynold s Number providing supersonic flow is approximately 15000/cm as RMS noise increased markedly near this value. Schlieren imaging would help to ascertain whether this is the case.

References [1] Schneider, S. P. and Skoch, C. 001: Mean Flow and Noise Measurements in the Purdue Mach-6 Quiet-Flow Ludwieg Tube, AIAA 001-778. [] Haven, C. E., 1995: Measurements of Laminar-Turbulent Transition on Supersonic Wind-Tunnel Walls, MS Thesis, Purdue University, West Lafayette, IN. [3] Blaisdell, G. 003: Class Notes: Introduction to Aerodynamics, Purdue University, West Lafayette, IN. [4] Kovasznay, L. 1953: Turbulence in Supersonic Flow, Journal of the Aeronautical Sciences, 0(10), 657-68. [5] Ladoon, D. W., 1998: Wave Packets Generated by a Surface Glow Discharge on a Cone at Mach 4, Ph D Dissertation, Purdue University, West Lafayette, IN. [6] Schneider, S. P., Haven, E. 1994: Mean Flow and Noise Measurements in the Purdue Quiet-Flow Ludwieg Tube, AIAA 94-0546. [7] Schneider, S. P., Skoch, C., Rufer, S., Swanson, E., Borg, M. 004: Bypass Transition on the Nozzle Wall of the Boeing/AFOSR Mach-6 Quiet Tunnel, AIAA 004-050. [8] Salyer, T. R., Laser Differential Interferometry for Supersonic Blunt Body Receptivity Experiments, Dissertation, Purdue University, West Lafayette, 00, pp. 11. [9] Anderson, J. D., Fundamentals of Aerodynamics, 3 rd Edition, McGraw- Hill, New York, 001, pps. 448, 7-73. [10] Currie, I. G., Fundamental Mechanics of Fluids, 3 rd Edition, Marcel Dekker, New York, 003, pp. 455. [11] Schneider, S. P., and Haven, C. E., Quiet-Flow Ludwieg Tube for High- Speed Transition Research, AIAA Journal, Vol. 33, No. 4, 1995, pp. 688-693.