39th AIAA Thermophysics Conference, Miami, Florida, June 25-28 2007

Computational and Experimental Investigation of

Supersonic Convection over a Laser Heated Target

Eric C. Marineau ∗

and

Joseph A. Schetz †

Virginia Polytechnic Institute & State University, Blacksburg, VA, 24061

and

Reece E. Neel ‡

AeroSoft, Inc., Blacksburg, VA, 24061

This research concerns the development and validation of simulation of the beam-targetinteraction to determine the target temperature distribution as a function of time for agiven target geometry, surface radiation intensity and free stream flow condition. Theeffect of a turbulent supersonic flow was investigated both numerically and experimentally.

Experiments were in the Virginia Tech supersonic wind tunnel with a Mach 4 noz-zle, ambient total temperature, total pressure of 1.1× 106 Pa and Reynolds number of5× 107/m. The target consisted of a 6.35 mm stainless steel plate painted flat black. Thetarget was irradiated with a 300 Watt continuous beam Ytterbium fiber laser generating a4 mm Gaussian beam at 1.08 micron 10 cm from the leading edge where a 4 mm turbulentboundary layer prevailed. An absorbed laser power of 65, 81, 101, 120 Watts was usedleading to a maximum heat flux between 1035 to 1910 W/cm2. The target surface andbackside temperatures were measured using a mid-wave infrared camera. The backsidetemperature was also measured using eight type-K thermocouples.

Two tests are made, one with the flow-on and the other with the flow-off. For the flow-on case, the laser is turned on after the tunnel starts and the flow reaches a steady state.For the flow-off case, the plate is heated at the same power but without the supersonicflow. The cooling effect is seen by subtracting the flow-on temperature from the flow-offtemperature. This temperature subtraction is useful in canceling the bias errors such thatthe overall uncertainty is significantly reduced.

The GASP conjugate heat transfer algorithm was used to simulate the experiments at 81and 65 Watts. Most computations were performed using the Spalart-Allmaras turbulencemodel on a 280, 320 cell grid. A grid convergence study was performed.

Compared to the 65 Watt case, the 81 Watt case displays more asymmetry and aregion of increased cooling is found upstream. The increased asymmetry was also seenon the backside by both the thermocouple and infrared temperature measurements. Thecomputation underpredicts the surface temperature by 7% for the flow-off case. For boththef 65 and 81 Watt cases, cooling is underpredicted at the surface near the center. Forall power settings, convective cooling significantly increases the time required to reach agiven temperature.

∗Currently Postdoctoral Scholar, Graduate Aeronautics Laboratory, California Institute of Technology, Pasadena, CA, 91125,Member AIAA†Holder of the Fred D. Durham Chair, Department of Aerospace and Ocean Engineering, 215 Randolph Hall, Blacksburg,

VA, 24061, Fellow AIAA‡Research Scientist, AeroSoft, Inc., Blacksburg, VA, 24061, Member AIAA

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39th AIAA Thermophysics Conference25 - 28 June 2007, Miami, FL

AIAA 2007-4147

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I. Introduction

Directed energy weapons have been of interest ever since Antiquity. Archimedes is said to have repelleda Roman attack by focusing sunlight using an array of parabolic mirrors causing the approaching ships tocatch fire. In recent decades, remarkable progress has been made since the first invention of the solid statelaser in the 1960’s through gas dynamic, chemical, free electron and advanced solid state lasers pushingtoday’s state-of-the-art1 such that the use of directed energy as an effective weapon is a reality that is nowbeing implemented through programs like the Airborne Laser2 a system used to destroy ballistic missiles intheir boost phase close to their launch area.

Contrary to conventional weapons which inflict damage through massive heat release and pressure waves,directed energy weapons rely on the absorption of thermal energy at the target surface. The kill mechanismis therefore fundamentally different. For missiles, Leonard3 has identified two kill mechanisms, namely thesublimation of the target skin and structural failure from skin weakening through heating. Using a simpleenergetic analysis, the flux of energy required to destroy a North Korean Taepo Dong 2 missile from structuralfailure is 2.4kJ/cm2, an order of magnitude lower than that required to sublimate the skin. For a structuralfailure to occur within 4 seconds, an average of 600W/cm2 must be absorbed which is much too low to geta laser supported detonation (LSD) wave at the surface and/or plasma formation shielding the target.

This research is concerned with the development and validation of modeling and simulation of the beam-target interaction. To our knowledge and that of the staff of Arnold Engineering Development Center,no experimental study of the lethality mechanism and temperature measurements of a laser heated targetsubjected to a supersonic flow the has ever been performed. The problem at hand can be defined in thefollowing way:

For a given target geometry, surface radiation intensity and free stream flow condition, what isthe target temperature distribution as a function of time?

II. Experimental Apparatus and Methods

A. Design Methodology

The objective of the experiment is to investigate the effect of a supersonic flow field over a laser irradiatedtarget, which is a difficult task due to the large temporal and spatial gradients over a very small area.Preliminary simulations showed a small convective cooling varying from 20 to 40 K between flow-on andflow-off such that the experimental uncertainties can reach the same magnitude as the predicted cooling.

Analytical methods and numerical simulations were used to design an experiment able to generate reliablemeasurements. In order to lower the experimental uncertainties, the convective cooling has to be maximized.This implies a maximization of the conjugate Peclet number ΛL first introduced by Cole4 and the beamgeometric ratio w/L as shown by Marineau.5 This introduces the following requirements: a thin turbulentboundary layer, a low solid thermal conductivity and a thin plate and/or a large beam diameter.

To get a thin boundary layer, a flat plate must be inserted into the flow a configuration referred to asa splitter-plate. It was determined by Marineau5 using experimental data6 for similar conditions that theboundary layer is fully turbulent at 0.09m from the leading edge such that the laser beam center was locatedafter 0.1m from the leading edge.

The effect of the material was investigated by Marineau5 where it was found that stainless steel leadsto a much greater conjugate Peclet number due to it’s low thermal conductivity. Stainless steel also as theadvantage of sustaining high temperature. AISI-303 stainless steel was chosen as the plate material.

The geometric ratio w/L can be made large by increasing the beam width or by making the plate thin.Here to facilitate repeatability, we chose to avoid using any external optics. The thickness of the plate nearthe target center is fixed to 2.54 mm.

B. Overview of Components

To our knowledge, no experimental study of the temperature distribution on a laser heated target submittedto a supersonic flow is available in the literature. Experiments on a laser heated ceramic disk have beenperformed at Oak Ridge Laboratory.7,8

Experiments were performed in the Virginia Tech 23× 23(cm) blow-down supersonic wind tunnel with aMach 4 nozzle, ambient total temperature, total pressure of 1.1× 106 Pa and Reynolds number of 5×107/m.

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The main components are depicted in Fig. 1. As we can see, the system uses both infrared thermographyand thermocouples. Three data acquisition and control modules are present. Each are linked to a differentcomputer.

Figure 1: Overall experimental layout

A drawing of the splitter plate is shown in Fig. 2 (a). The plate contains two inserts that can be removedif damaged. The laser hits the upstream insert. The second insert downstream is used to mount a Pitottube. The strut-mounted plate can be located on the side wall or on the test section floor plate which allowstaking Schlieren or shadowgraph images.

The inserts are mounted on a 6.25 mm thick plate. Since metals oxidize at high temperature, a pro-tective coating must be used to insure good repeatability. The plate was painted using Pyromark 2500 flatblack paint. This silicon based paint has an absorptivity of 95% and emissivity of 0.859 and can sustain atemperature of 1350 K.

A 300 W single-mode, continuous-wave Ytterbium fiber laser at 1080 micron from IPG Photonics wasused. The beam is Gaussian and its 4 mm diameter (e−2) does’t significantly change with distance as shownin Marineau.5 The laser was controlled using a labVIEW program developed in-house and the collimatorwas mounted on an optical table where it was positioned with two degrees of freedom using two translationstages each with a resolution of 3µm.

The Indigo Merlin mid-wave infrared camera has a 256× 320 cells Indium antimonide detector sensitivebetween 3 and 5 microns, a 12 bit dynamic range and a maximum frame rate of 50hz. A ND2 filter is avoidingsaturation for high temperature measurements. For each integration time, filter and lens combination, aradiometric calibration is performed by comparing the digital output of the camera to the known temperatureof a uniform blackbody. The variability of each cell is corrected using a non-uniformity correction table(NUC). The NUC are generated during the calibration process. The precision of the system is thereforedependant on the uniformity of the blackbody. Six calibrations, NUC, are performed for a 25 mm lens bythe manufacturer and checked in-house using a blackbody. Positioning the lens at about 6 inches from thetarget gave a spatial resolution of approximately 0.240 mm.

Since the temperature range due to heating is larger than the dynamic range of the camera, many runsmust be repeated to get the totality of the temperature field. For a power of 81 watts, the NUC0, NUC2,NUC3, NUC4 and NUC5 are used such that 5 runs are required. At each instant, the images must be

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(a) Splitter Plate (b) Backside thermocouples position

Figure 2: Splitter plate and backside thermocouples position

combined to give a single image. Also, each pixel must be mapped to a given physical coordinate. Adata reduction program written in Matlab was designed to perform those tasks, further details are found inMarineau.5

Two type-K surface temperature thermocouples from Medtherm corporation10 were used to make surfacemeasurements. One of 0.381 mm in diameter was located at the center of the heated insert. The other of1.549 mm in diameter was located upstream to provide an accurate wall temperature boundary conditionfor our numerical simulations. A fast response time is made possible by the two micron thickness junctionformed by a vacuum deposited metallic coating over the sensing end of the probe. During the test thecenter Medtherm thermocouple developed problems. Since the surface temperature was kept lower than thethermocouple maximum operating temperature, we believe that the failure can be attributed to a reactionbetween the thin thermocouple junction and the silicone-based paint.

Eight, type-K thermocouples (SRTC-TT-K-40-36 from Omega) made of 0.076 mm (gage 40) wires werefixed to the backside of the plate using Omegabond 400 high temperature cement. Positions are shown inFig 2(b). Such fine wires enable precise, pin-point measurements and fast response time. The NationalInstrument 6036E 16-bit analog-to-digital converter with the AMUX-64T multiplexer was used for thermaldata acquisition.

A BK7 glass window of 12.7 mm in diameter with an antireflection coating for the laser wavelength wasmounted on the tunnel wall allowing the laser access to the target. A Calcium fluoride (CAF2) window wasused to view the target. Calcium fluoride is ideal for mid-wave infrared measurements since it possesses ahigh and constant transitivity between 3 and 5 microns as well as an intrinsically low reflectivity. Opticalproperties of both windows are found in.5

III. Uncertainty Analysis

To cancel the bias errors, the temperature difference between the flow-off and flow-on cases was taken.For that strategy to be effective, the tests must be highly repeatable. Repeatability was quantified andthe uncertainty of temperature difference between the flow-off and flow-on case was determined for boththe thermographic and thermocouples measurements. A detailed uncertainty analysis was performed byMarineau.5 The uncertainty on the temperature is equal to 5.35% as computed by considering the uncertaintyin the laser power, the surface absorptivity, emissivity and the calibration error. The uncertainty on the

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thermocouple measurement is equal to 3.8%. To evaluate the uncertainty on temperature difference, therandom error was quantified using the backside temperature repeatability for three runs. A Student’s t-distribution was used to compute the uncertainty of the mean considering the limited number of samples.The effects of the alignment and timing errors are computed using an analytical solution developed byMarineau5 and combined using the mean root square formula. For the thermocouple, the repeatability fromsix runs was used to compute the random error. The uncertainties on the temperature difference for theinfrared camera and the thermocouple are plotted at Fig. 3 (a) and (b).

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)

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Figure 3: (a) Uncertainty on the temperature difference measured by the infrared camera on the surface andbackside as a function of distance for t = 1s and t = 10s. (b) Uncertainty on the temperature differencemeasured by the thermocouples as a function of time

We notice that uncertainty is a function of position and time. For the infrared measurements at thecenter on the surface, the uncertainty is smaller due to the absence of the positioning error. The positioningerror is approximatively equal to zero at the center since it corresponds to a maximum in the temperaturedistribution. On the surface, the positioning error is the greatest at 1 mm from the center due to the largeradial temperature gradient. From that position, the positioning error progressively decreases with distancesuch that away from the center the uncertainty is mainly due to the random errors. The uncertainty is greaterfor thermocouples 3 and 8, which are the closest to the center. For most thermocouples, the uncertaintyincreases with time.

IV. Experimental Results

A. Flow Survey

The boundary layer thickness was estimated with a Schlieren image, whereas the shock on the plate leadingedge is visualized best by using the Shadowgraph method. Fig. 4 (a) shows that the boundary layer isturbulent over the plate as eddies are identified. The boundary layer thickness is equal to 4 mm. Using theshock angle seen on Fig. 4 (b) the edge Mach number Me is estimated to 3.8. A value of Me = 3.75 wasobtained using static and pressure measurements.

B. Test Matrix

The test matrix is presented in Table 1. Different values of laser power were used to evaluate the effects of thepower on the temperature difference. At each power, two tests are made, one with the flow-on and the otherwith the flow-off. For the flow-on case, the laser is turned on after the tunnel starts and the flow reaches asteady state. For the flow-off case, the plate is heated at the same power but without the supersonic flow.The cooling effect is seen by subtracting the flow-on temperature from the flow-off temperature. No infraredmeasurements were made at 101 Watts, and only the high temperature calibration was used at 120 Watts.

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(a) Boundary layer Schlieren (b) Leading edge shock Shadowgraph

Figure 4: Flow visualization used to determine the edge Mach number and boundary layer thickness

Table 1: Test Matrix

Power (W ) Maximum Intensity (W/cm2) Time on (s)

65 1035 10.881 1289 10.8101 1607 10.8120 1910 10.8

C. Thermocouple Results

The backside temperature was measured for 6 runs at 81 Watts. Overall, repeatability was good as therun-to-run difference is less that 5 K. Fig. 5 (a) shows the temperature increase for the flow-on test. Slightasymmetry was found in the temperature distribution for the flow-off case which is most likely due to thelaser misalignment. However, since the alignment was kept the same for the flow-on and flow-off cases,misalignment should have a minor effect when the temperature difference between the flow-off and flow-oncases is taken. The temperature difference between the flow-off and flow-on cases for run 1 is plotted in Fig.5 (b). The greatest cooling is seen close to the center for thermocouples 3 and 8. The maximum cooling isbetween 20 K and 25 K at the center. We clearly notice some asymmetry by looking at the thermocouplepairs 1-6 and 2-5. The difference between thermocouples 2 and 5 reached almost 10 K at t = 10s. Asexpected, thermocouple 5 cools less than thermocouple 2, since heat is convected downstream. The samesituation arises when comparing thermocouples 1 and 6, as the difference in cooling is close to 10 K att = 10s. Clearly, a steady state was not achieved during the run as the temperature difference for all thethermocouples keep increasing.

D. Infrared Camera Results

Fig. 6 shows the surface temperature contours for the flow-on and flow-off cases at different times for 81Watts of power. The flow is directed from left to right. The upper half of each contour plot corresponds tothe flow-off case, and the lower part corresponds to the flow-on case. Some disturbance in the temperaturecontours can be seen on the upper part around r = 4 mm due to paint damage. Over the damaged area, theemissivity is less, which explains the disturbance. For the flow-off, case the temperature reaches 1175 K after10 seconds. The maximum temperature reaches 1115 K after 10 seconds for the flow-on cases. Maximumcooling was achieved at the center. More cooling can be seen upstream of the heated spot compared todownstream where the isolines almost coincide.

Fig. 7 shows the temperature distribution on the backside. The asymmetry is difficult to notice from thetemperature plots. The maximum temperature at the center reaches 675 K after 8 seconds for the flow-offcase and 650 K for the flow-on case. At the center, the infrared camera gets saturated past t = 8s for the

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Figure 5: Backside thermocouple temperature measurements for run 1 at P=81W

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Figure 6: Surface temperature for P=81 W with the flow going from left to right (flow-off on top half, flow-onon bottom half)

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flow-off case such that the t = 9s plot is not shown.

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Figure 7: Backside temperature for P=81 W with the flow going from left to right (flow-off on top half,flow-on on bottom half)

The asymmetry in cooling is better seen with the temperature difference between the flow-on and flow-offcases. The surface temperature difference is found in Fig. 8, and Fig. 9 gives the backside temperaturedifference. On the surface, a region of increased cooling is seen upstream, which is followed by a regionof reduced cooling right before the center. At the center, the cooling reaches about 50 K after 9 seconds.At t = 1s, the maximum temperature difference reaches 60 K. As seen in the uncertainty analysis, theuncertainty is greater at a small value of time due to the increase in the timing error from the large time rateof change of the temperature. Also, the flow-on and flow-off cases are on a different calibration for that valueof time such that the bias error does not cancel. It is, therefore, believed that the temperature difference isoverpredicted at t = 1s.

The asymmetry is also seen on the backside as clearly, more cooling occurs upstream than downstream.The effect of the mismatching calibration can be seen on all the backside images. For instance, at t = 1, adisk of high cooling is seen at r = 4mm. This cooling isn’t real as it is produced from the non-cancellationof the bias error for mismatching integration time. As time increases, the radius of the disk increases. Dataover that area must therefore be discarded.

The 120 Watt case displayed the greatest difference between flow-off and flow-on. The maximum surfacetemperature is plotted as a function of time for flow-on and flow-off in Fig. 10. After 10 seconds, atemperature difference of 90 K was measured. As seen in Fig. 10, the difference between the flow-off andflow-on case remains almost constant between 6 and 10 seconds. For times below 2 seconds, the signal istoo weak to get an accurate measurement (as only the high temperature calibration was used). Fig. 10also shows that convective cooling significantly changes the time required to reach a given temperature. Forexample for the flow-off case, only 5 seconds are required to reach 1500 K compared to 10 seconds for theflow-on case.

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(a) t=1s

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Figure 8: Surface temperature difference for P=81 W with the flow going from left to right

(a) t=1.5s

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Figure 9: Backside temperature difference for P=81 W with the flow going from left to right

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1100

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Figure 10: Maximum surface temperature for flow-on and flow-off conditions at P = 120W

E. Experimental Results Summary

A summary of the experimental results is shown in Table 2. We notice that the maximum temperaturedifference at the center increases with the power. A linear relation is found between the maximum surfacetemperature and the laser power. On the backside, a similar temperature difference is observed between the65 Watt and 81 Watt cases.

Table 2: Results summary for temperature and temperature difference of Surface (|s) and Backside (|b)

P (W ) Tmax|s(K) t(s) ∆Tmax|s(K) t(s) Tmax|b(K) t(s) ∆Tmax|b(K) t(s)

65 975 10 50 9 600 10 27 1081 1175 10 65 10 675 10 25 8101 NA NA NA NA NA NA 12 4.5120 1589 10 90 10 NA NA NA NA

More asymmetry was found at 81 Watt compared to 65 Watt. This was observed on the surface andbackside with both the infrared camera and thermocouple measurements. For the 81 Watt case, a regionof increased cooling is seen upstream where a coherent structure clearly appears. More testing would berequired to explain why such a difference is seen between the 81 Watt and 65 Watt cases.

V. Computational Model and Results

A. Computational Model

GASP version 4.3 from AeroSoft was used for this study. The integral form of the time-dependent Reynolds-Averaged Navier-Stokes (RANS) equations in three dimensions are solved. A solver for the three-dimensionalheat conduction equation has been added to GASP in order to perform conjugate heat transfer problems.The conjugate heat transfer algorithm which insured continuity of the temperature and conservation ofenergy at the fluid-solid interface was described and validated for high speed flow by Marineau et al.11 TheRoe flux-difference splitting12 is used to compute the inviscid flux with third-order spatial accuracy using theMUSCL reconstruction.13 The viscous flux is computed with second-order spatial accuracy using a centraldifference. Unsteady solutions are obtained using the dual-time stepping method with third order accuracy.

The free stream Mach number was set to 3.75, the static temperature to 77.4 K and the static pressureto 9770.5 Pa. A boundary layer profile from a flat plate simulation ran up to the measured thickness wasspecified at the inlet with a pointwise boundary condition.

To simulate the experiment, the fluid portion of the mesh is solved with a constant wall temperatureuntil a steady state is achieved. The steady state solution becomes the t = 0 solution for the time-accurate

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run. The steady state problem is solved using an infinite time step such that the system is solved with aNewton iteration5 and converged to a global residual of 10−12. Ten iterations are used on the inner problem.

The laser takes one second before reaching its selected power. The startup is modelled using the followingfunction:

g(r, t) =

{g(r) sin

(πt2Ts

)0 ≤ t ≤ Ts

g(r) t > Ts(1)

where r is the distance from the beam center, the startup time of the laser,Ts equals 1 second, g(r) is theintensity (heat flux per unit area) distribution for a Gaussian beam defined as:

g(r) = I0 exp(−r2/w2

)=

P

πw2exp

(−r2/w2

)(2)

Here, w is the radius where the intensity decreases by a factor equal to e−1, I0 the maximum surface intensityand P the absorbed power. Simulations were performed at 65 and 81 Watts of absorbed power. The surfaceintensity was specified with a pointwise boundary condition.

The time-accurate simulation was performed using a physical time step of 3× 10−4 seconds. Within thedual-time-stepping formulation, 10 inner cycles are performed for each time step. The inner pseudo timestep is set to infinity (ie, 1015). All cases were solved with the one-equation Spalart-Allmaras turbulencemodel. However, to assess the sensitivity to turbulence modelling, some cases were solved using Willcoxk − ω and Menter’s SST turbulence models. It was noticed that turbulence modeling has a small effect onthe maximum surface temperature.

The grid was generated with Gridgen. Only one half of the geometry is modelled due to symmetry.Three grid densities, coarse, medium and fine were generated, and the generalized Richardson extrapolationmethod14 was used to compute the spatial and temporal discretization errors which were combined intothe total discretization error using the root-mean-square formula. With flow-on, the total relative error onthe maximum temperature for the medium grid is 2.2 % and 1.2 % with flow-off. The uncertainty on thetemperature difference (flow-off - flow-on) at the target center is 5.9% (of the temperature difference) for themedium grid. The details of the grid and time convergence study are presented in Marineau.5

The medium grid for the fluid domain is shown in Fig. 11.An H-C-H topology is used allowing localizedclustering. The conjugate heat transfer boundary condition was used at the fluid-solid interface. An adiabaticboundary condition was used on the edge and on the backside of the solid. Convective and radiative boundaryconditions on the backside were tried, but the effect on the temperature is insignificant (less that 0.01 K). Inthe fluid, hyperbolic tangent clustering was used in the z-direction to properly capture the boundary layers.For the medium grid, more than 40 points are located in the boundary layer. The center of the first cell ofthe wall is located at 2.5× 10−6m from the wall to get a value of y+ of 0.5. In the solid, hyperbolic tangentclustering was also used in the z-direction.

Y X

Z

Figure 11: Medium grid for the fluid domain composed of four blocks. Half of the geometry is modelled dueto symmetry

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B. Computational Results

The use of CFD makes it possible to visualize the change produced by the wall heating on the flow field.Results for 65 Watts of laser power are presented next. Similar results are observed for the 81 Watt case.Moving away from the wall, note that that temperature contours get elongated in the flow direction as seenin Fig. 12. The temperature disturbance is localized in a thin, near-wall region such that for a maximum walltemperature of 900 K, the maximum temperature in the flow decreases to 400 K at 0.1 mm from the wall.Other flow variables are also affected by the heated region. A reduction of 60% in density is observed andam increase in laminar viscosity exceeding 100% is observed. The vorticity in the y-direction is significantlydecreased due to fluid dilation. Detailed results are found in Marineau.5

(a) wall (b) z = 0.04 mm

Figure 12: Temperature contours in the x-y plane dimensions are in m

The pressure disturbances emanating from the wall get convected downstream along Mach lines as seenin Fig. 13 (b) . The intensity of the disturbances is progressively reduced with increasing distance fromthe wall due to three dimensional effects. Fig. 13 (a) shows the streamlines and w-velocity contours in thesymmetry plane. To improve the visualization of the flow features, the scale is stretched by a factor of 20in the z-direction. Clearly, the heated spots acts as a ”bump” which slightly turns the flow upward. Veryclose to the wall, the flow is turned downward behind the bump, as a region of negative w-velocity is seen.The positive disturbance in the w-velocity component is convected along Mach lines, whereas the negativedisturbance is quickly damped out such that it remains near the wall.

VI. Comparison of Experiment and Computation

Comparisons between the experiment and the computations are presented for the P = 81 Watt case. Figs.14 (a) and (b) show the temperature profiles on the target surface with flow-off and flow-on. Comparisonon the backside are found in Fig. 15 (a) and (b). For both the backside and surface, the temperatureis underpredicted by the computation with the exception of t = 0.5s for the flow-off case. However, thisdifference is contained in the uncertainty margin when taking into account the bias error. Here, the laserpower is probably greater than what is reported by the manufacturer. The temperature difference of 60 Kobserved between the computation and the experiment at t = 10s corresponds to a difference of only 7% in thepower level. The dependence of the emissivity on the temperature could also explain the discrepancy betweenthe measurement and experiment. However, since the value of emissivity as a function of temperature forthe paint is not known, this remains speculation. A rise in emissivity of 10% would lead to an increasein temperature of 30 K. The difference between the experiment and the computation is less for the flow-on case since the measured temperature decrease due to the flow is greater than the one computed. Att = 0.5s, significant asymmetry is found in the measured temperature for the flow-on condition contrary to

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(a) Pressure iso-contours (b) Streamlines

Figure 13: (a) Pressure iso-contours at t = 10s for P=65 W. A high pressure region is created upstream ofthe heat spot and a low pressure region is created downstream dimensions are in m (b) Streamlines in thex-z plane at t = 10s dimensions are in m. The heat source acts like a ”bump”

the computation which appears almost perfectly symmetric. With an increase in time, this asymmetry isconvected further downstream between x = 4 mm and x = 6 mm.

The temperature difference profiles on the surface at t = 10s and on the backside at t = 8s are shown inFig. 16 (a) and (b).The temperature is underpredicted at the center. At t = 10s the measured temperaturedifference exceeds 60 K compared to 30 K for the computation. At 65 Watts, the underprediction was lessas the measured difference reached 50 K compared to 31 K for the computation. Upstream of this intensecooling region, good agreement is found between the computation and the experiment. This situation isclearly visualized in Fig. 17 (a) were the computed surface temperature is plotted on the upper half and themeasurement is on the lower half.

This means that the level of cooling before the perturbation introduced by the strong heating seems to bewell modelled. Downstream, away from the center, good agreement is also seen which leads one to think thatthe boundary layer relaxes quickly from its heat induced perturbation. On the backside, good agreementis generally found but more cooling is measured upstream as seen in Fig. 17 (b) this is consistent with thesurface prediction.

As seen in Fig. 16 (a), the measured temperature displays an oscillatory behavior close to the center. Theinterface between the region of cooling and heating isn’t probably as sharp as the measurements indicate,since heat diffusion should smooth the gradient out unless a strong flow feature such as a vortex is ableto maintain it. For instance, one can imagine strong heat extraction dragging the heat aft such that thedownstream wall temperature is increased. The oscillation in the temperature distribution at the centershould damp out with diffusion inside the solid. This can be explained to some extent that a differentsurface temperature distribution can lead to a similar temperature distribution on the back. Also, we havenoticed that for both the 65 Watt and the 81 Watt cases the greatest temperature difference arises near thecenter over a very small area. Moreover, the area of intense cooling is surrounded by an area of heating suchthat the difference in cooling near the center is not as large as it appears.

On the backside, good agreement is also seen between the infrared measurements, thermocouple mea-surements and computation as seen in Fig. 18 (a) and (b) where the temperature difference as a functionof time is plotted. The similarity between the two independent measurement methods demonstrates thereliability of the measurement systems.

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Figure 14: Comparison between infrared measurement and computed surface temperature as a function oftime at P=81 W

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Figure 15: Comparison between infrared measurement and computed backside temperature as a function oftime at P=81 W

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Figure 18: Comparison between infrared and thermocouples measurement and computed backside temper-ature difference as a function of time for P=81 W

VII. Conclusions

An experiment to assess the effect of supersonic flow over a laser heated target was designed and per-formed. Numerical simulations and analytical methods have been used extensively in the design of theexperiment. We strongly believe that numerical simulations and experiments are symbiotic and that thiswork corroborates that assertion.

The experimental results have been compared with a numerical model. Good agreement was foundon the backside and on the surface away from the center. Close to the center the measurements displaysignificantly more cooling than the computations. We believe the disagreement at the center could bedue to the incapacity of the turbulence model to respond to the strong distortion of the boundary layer.Moreover, in the turbulence models, only the solenoidal part of the dissipation rate is modelled, and theterms due to the fluctuation in viscosity are neglected as well as the compressible term. Since there is alarge temperature gradient inside the boundary layer, we can expect large viscosity fluctuation such thatthe viscosity fluctuation terms in the dissipation rate equation may become important. The same can besaid about the density, as a large density gradient exists in the boundary layer. Therefore, the validityof Morkovin’s hypothesis15 which assumes small density fluctuation is questionable for a flow over a laser-heated wall. The assumption of a constant turbulent Prandtl number is also questionable as it implies asimilarity between the velocity and thermal fields. One can compute a variable turbulent Prandtl numberby solving two extra transport equations,16,17 namely one for the variance of the temperature fluctuationand the other for its dissipation rate. Future work regarding such a model could be pursued in trying toimprove the prediction for laser heated flows. However, this might not provide an effective solution sinceto our knowledge, all of the two-equation turbulence models available for the computation of the turbulentPrandlt number in a compressible flow are extensions of their incompressible counterparts made possiblethrough Morkovin’s hypothesis.

The developed experimental methodology could be applied to full scale testing at AEDC. The compu-tational model can be extended to missile/laser interaction problem since a more complex geometry can behandled. For instance, the temperature due by a laser beam on a rotating missile could be modelled. Forthat situation, the flow field would likely play a more important role as cooling should significantly increase.

Acknowledgment

This work was funded by Arnold Engineering Development Center (AEDC) through the Air Force SBIRproject under contract FA9101-04-C-0035.

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Physics, Vol. 43, 1981, pp. 357–372.13GASP 3.0 User Manual , AeroSoft, 1997, ISBN 0-9652780-0-x.14Roache, P., Verification and Validation in Computational Science and Engineering, Hermosa, Albuquerque, NM, 1998.15Morkovin, M., “Effect of Compressibility on Turbulent Flows,” Mecanique de la Turbulence, 1962, pp. 369–380.16Sommer, T., So, R., and Zhang, H. S., “Near-Wall Variable-Prandtl-Number Turbulence Model for Compressible Flows,”

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Aeropropulsive Flows,” AIAA 43rd Aerospace Sciences Meeting, Reno. Nevada, 10-13 Jan 2005.

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