September 2010 

NASA/TM–2010-216846 

Aero-Heating of Shallow Cavities in 

Hypersonic Freestream Flow 

Joel L. Everhart, Karen T. Berger, N. Ronald Merski, and William A. Wood 

Langley Research Center, Hampton, Virginia 

Kevin E. Hollingsworth 

Aerospace Computing, Inc., Hampton, Virginia 

Andrew J. Hyatt 

Boeing Space Exploration, Houston, Texas 

Ramadas K. Prabhu 

Lockheed Martin Engineering & Sciences Company, Hampton, Virginia 
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September 2010 

NASA/TM–2010-216846 

Aero-Heating of Shallow Cavities in 

Hypersonic Freestream Flow 

Joel L. Everhart, Karen T. Berger, N. Ronald Merski, and William A. Wood 

Langley Research Center, Hampton, Virginia 

Kevin E. Hollingsworth 

Aerospace Computing, Inc., Hampton, Virginia 

Andrew J. Hyatt 

Boeing Space Exploration, Houston, Texas 

Ramadas K. Prabhu 

Lockheed Martin Engineering & Sciences Company, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
 i

Table of Contents PAGE

List of Tables.................................................................................................................................................................... i 

List of Figures.................................................................................................................................................................. ii 

Abstract ...........................................................................................................................................................................1 

Introduction .....................................................................................................................................................................1 

List of Symbols................................................................................................................................................................2 

Literature Assessment ....................................................................................................................................................3 

Supersonic/Hypersonic Cavity Flow Physics ..................................................................................................................4 

Establishing the Testing Environment.............................................................................................................................5 

Experiment Design..........................................................................................................................................................6 

 Design Philosophy and Constraints .....................................................................................................................6 

 Two-Dimensional Surface Modeling.....................................................................................................................7 

 Test Condition Selection and Cavity Design ........................................................................................................7 

Experimental Method ......................................................................................................................................................7 

 Facility ..................................................................................................................................................................8 

 Models..................................................................................................................................................................8 

 Thermographic Phosphor Measurement System.................................................................................................9 

 Data Reduction.....................................................................................................................................................9 

Presentation of Test Data .............................................................................................................................................10 

Uncertainty Analysis......................................................................................................................................................11 

Results ..........................................................................................................................................................................12 

Conclusions...................................................................................................................................................................13 

Acknowledgment...........................................................................................................................................................14 

References....................................................................................................................................................................14 

List of Tables PAGE

Table 1.- Typical range of windward surface flow conditions at Mach 18. ....................................................................19 

Table 2.- Nominal flow conditions for the 31-Inch Mach 10 Air Tunnel.........................................................................19 

Table 3.- As-built cavity geometries. .............................................................................................................................19 

Table 4.- Baseline model run matrix from Test 406 ......................................................................................................19 

Table 5.- Test 404 run matrix for cavity-plate model 1..................................................................................................20 

Table 6.- Test 404 run matrix for cavity-plate model 2..................................................................................................21 

Table 7.- Cavity flow conditions and parameters, Xcav=8 inches.................................................................................22 

Table 8.- Variable uncertainty values............................................................................................................................24 

Table 9.- Summary Cavity Data. ...................................................................................................................................25 
 ii

List of Figures PAGE

Figure 1.- Cavity flow regimes.......................................................................................................................................27 

Figure 2.- Schematic of model mounting. .....................................................................................................................27 

Figure 3.- Flat plate surface flow properties for Re=1x106

............................................................................................28 

Figure 4.- Flat plate performance chart.........................................................................................................................28 

Figure 5.- Schematic of cavity locations. Design width is W/H=3.6. All dimensions are in inches................................29 

Figure 6.- Test model installed in 31-Inch Mach 10 Air Tunnel with TGP lighting and camera system. .......................29 

Figure 7.- Baseline Bump Factor Images......................................................................................................................30 

Figure 8.- Global heating images of Cavity Model 1 .....................................................................................................34 

Figure 9.- Global heating images of Cavity Model 2. ....................................................................................................37 

Figure 10.- Bump factor distributions for Cavity S11 - L/H=6.6, W/H=3.33...................................................................39 

Figure 11.- Bump Factor images for Cavity S12 - L/H=9.3, W/H=4.58. ........................................................................42 

Figure 12.- Bump Factor images for Cavity S13 - L/H=8.7, W/H=4.29. ........................................................................46 

Figure 13.- Bump Factor images for Cavity S14 - L/H=8.1, W/H=3.95. ........................................................................50 

Figure 14.- Bump Factor images for Cavity S21 - L/H=10.7, W/H=4.0. ........................................................................54 

Figure 15.- Bump Factor images for Cavity S22 - L/H=10.7, W/H=3.74. ......................................................................58 

Figure 16.- Bump Factor images for Cavity S23 - L/H=15.0, W/H=3.92. ......................................................................63 

Figure 17.- Bump Factor images for Cavity S24 - L/H=20.3, W/H=4.21. ......................................................................66 

Figure 18.- Bump Factor uncertainties for Cavity S12 - Run 03 - L/H=9.3, W/H=4.58, H/δ=0.185...............................71 

Figure 19.- Bump Factor uncertainties for Cavity S14 - Run 16 - L/H=8.1, W/H=3.95, H/ δ =0.992. ............................72 

Figure 20.- Bump Factor uncertainties for Cavity 24 - Run 28 - L/H=20.3, W/H=4.21, H/ δ =0.345..............................73 

Figure 21.- Variation of Average Bump Factor on cavity floor with H/ δ. .......................................................................74 

Figure 22.- Variation of Average Bump Factor on cavity floor with L/ δ.........................................................................75 

Figure 23.- Variation of maximum centerline endwall Bump Factor with H/ δ. ..............................................................75 

Figure 24.- Variation of maximum centerline endwall Bump Factor with L/ δ ................................................................76 
 1

Abstract 

The purpose of these experiments and analysis was to augment the 

heating database and tools used for assessment of impact-induced 

shallow-cavity damage to the thermal protection system of the Space 

Shuttle Orbiter. The effect of length and depth on the local heating 

disturbance of rectangular cavities tested at hypersonic freestream 

conditions has been globally assessed using the two-color phosphor 

thermography method. These rapid-response experiments were 

conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated 

immediately prior to the launch of STS-114, the initial flight in the Space 

Shuttle Return-To-Flight Program, and continued during the first week 

of the mission. Previously-designed and numerically-characterized 

blunted-nose baseline flat plates were used as the test surfaces. Threedimensional computational predictions of the entire model geometry 

were used as a check on the design process and the two-dimensional flow 

assumptions used for the data analysis. The experimental boundarylayer-state conditions were inferred using the measured heating 

distributions on a no-cavity test article. Two test plates were developed, 

each containing 4 equally-spaced spanwise-distributed cavities. The first 

test plate contained cavities with a constant length-to-depth ratio of 8 

with design point depth-to-boundary-layer-thickness ratios of 0.1, 0.2, 

0.35, and 0.5. The second test plate contained cavities with a constant 

design point depth-to-boundary-layer-thickness ratio of 0.35 with lengthto-depth ratios of 8, 12, 16, and 20. Cavity design parameters and the 

test condition matrix were established using the computational 

predictions. Preliminary results indicate that the floor-averaged Bump 

Factor (local heating rate nondimensionalized by upstream reference) at 

the tested conditions is approximately 0.3 with a standard deviation of 

0.04 for laminar-in/laminar-out conditions when the cavity length-toboundary-layer thickness is between 2.5 and 10 and for cavities in the 

depth-to-boundary-layer-thickness range of 0.3 to 0.8. Over this same 

range of conditions and parameters, preliminary results also indicate 

that the maximum Bump Factor on the cavity centerline falls between 2.0 

and 2.75, as long as the cavity-exit conditions remain laminar. Cavities 

with length-to-boundary-layer-thickness ratio less than 2.5 can not be 

easily classified with this approach and require further analysis. 

Introduction 

The Final Report of the Columbia Accident Investigation Board (CAIB) was released in August 2003. 

The CAIB identified “a breach in the Thermal Protection System of the leading edge of the left wing, 

caused by a piece of insulating foam ...” as the probable event resulting in the loss of the Space Shuttle 

Columbia during flight STS-107 on February 1, 2003. Many possibilities were investigated prior to 

reaching this assessment, among them the creation of impact-induced cavities in the thermal protection 

system (TPS) tiles, resulting in local augmentation of the heating and eventual burn-through of the 

aluminum substructure. Though impact-induced damage to the tiles was eventually excluded as the cause, 

the CAIB recommended that NASA “Develop, validate, and maintain physics-based computer models to 
 2

evaluate Thermal Protection System damage from debris impacts. These tools should provide realistic 

and timely estimates of any impact damage from possible debris from any source that may ultimately 

impact the Orbiter. Establish impact damage thresholds that trigger responsive corrective action, such as 

on-orbit inspection and repair, when indicated.” Langley Research Center, operating in concert with the 

Damage Assessment Aeroheating Team at Johnson Space Center, has provided for analysis and modeling 

an experimental cavity heating database consisting of nearly 775 wind tunnel runs1,2,3, along with many 

computational simulations of this complex fluid dynamic and aeroheating environment. The 

predominance of these data and simulations are for non-surface-breaching, impact damage situations 

where near-zero pressure gradients occur, such as on the windward surface tile acreage. Additionally, 

most of the data were acquired in the Langley 20-Inch Mach 6 Wind Tunnel4

 for cavities with depth-toboundary-layer-thickness ratios greater than 0.5 where the surface temperature rise is higher because the 

cavity disturbance is larger for these conditions, resulting in higher accuracy heating measurements. 

Recognizing the over-conservatism in the application of the initial heating data that could force 

unnecessary extra-vehicular activity (EVA, i.e., spacewalk) for repair in some scenarios, a rapid-response 

experiment addressing these concerns was planned and executed immediately prior to the launch of STS114, the first Return-To-Flight (RTF) Space Shuttle mission, and testing continued through the first week 

of the mission. The experiment was conducted on an extremely compressed schedule, occurring over a 

two-week period from conception through model design, fabrication, testing, and data delivery. Because 

there was insufficient time to complete the normal review and certification processes required by the 

Space Shuttle Program, the experimental results were to be used initially for “guidance-only” in case 

damage occurred on launch. 

The purpose of this report is to present wind test results focusing on the local heating augmentation of 

shallow cavities of depth-to-boundary-layer-thickness ratios less than 0.5. They were acquired in the 

Langley 31-Inch Mach 10 Tunnel4

 where the freestream temperatures are higher than those of the 

previous cavity flow studies conducted in the 20-Inch Mach 6 Tunnel. These higher freestream 

temperatures result in a greater surface temperature rise on the model, yielding lower data uncertainties. 

Based on the outcome of the analysis, allowances for these effects will be required in the engineering 

modeling tools5

 developed to assess potential heating augmentation resulting from damaged surfaces. 

Results from these analyses directly impact Damage Assessment Team decisions during a mission. 

List of Symbols 

Cp pressure coefficient 

h heat transfer coefficient, h=q/(Haw-Hw), (lbm/ft2

/s) 

L, W, H cavity length, width, and depth (in) 

M Mach number 

Mj Wind tunnel test models, j=1, 2 

p pressure (psi) 

q surface heat transfer rate (btu/ft2

/s) 

Rn model reference nose radius (in) 

Re unit Reynolds number (1/ft) 

Reθ momentum thickness Reynolds number 

Sij Shallow cavity designator with j=1,2,3,4 representing the cavity number on test model 

number i=1,2 

s distance along the streamline (ft) 
 3

T temperature (R) 

t time (s) 

U velocity magnitude (ft/s) 

x axial distance from model leading edge (in) 

y spanwise distance from model centerline (in) 

z distance normal to x-y plane (in) 

α angle-of-attack (deg) 

γ ratio of specific heats 

δ boundary layer thickness (in) 

θ boundary layer momentum thickness (in) 

Θ Normalized temperature in heating equation 

Λ Normalized time in heating equation 

ρ density (lbm/ft3) 

Acronyms 

BF Bump Factor. Local heating normalized by upstream reference heating. 

BFfloor avg Bump Factor average on cavity floor. 

BFCL maximum Bump Factor on the cavity end wall 

CAIB Columbia Accident Investigation Board 

LAURA Langley Aerothermodynamic Upwind Relaxation Algorithm 

RTF Return-to-Flight 

Subscripts 

avg average 

aw adiabatic wall conditions 

FR stagnation point conditions from Fay-Riddell calculation for a hemisphere 

local local condition 

ref reference condition 

t1 reservoir conditions 

w wall conditions 

∞ freestream static conditions 

Literature Assessment 

The supersonic/hypersonic cavity flow literature (particularly that for laminar test conditions), while 

helpful, is particularly sparse on both the local and downstream effects of many fundamental flow 

parameters. Fletcher, et al.6 published the survey paper “A Review of Heat Transfer in Separated and 

Reattached Flows” in 1970. Nestler7

 updated this survey with more recent work in 1985 in “The Effects 

of Surface Discontinuities on Convective Heat Transfer in Hypersonic Flow.” Together, these papers 

include much of the existing, pertinent cavity flow literature. They cited theoretical models of cavity flow 

developed by Burggraf8, Chapman9, Carlson10, Chang11, and Lamb12; however, none of the theories 

adequately capture the physics of laminar and turbulent three-dimensional cavity flows as will be 

demonstrated via global surface heating distributions presented herein, though they offer a framework for 

experimental studies. 

Numerical studies were conducted by Adams13, Morgenstern and Chokani14, Zhang, et al.15, and more 

recently for the CAIB and the Shuttle RTF program by (for example) Wood, et al.16 and Pulsonetti, et 
 4

al.17. The computational work presented by Wood uses the recently acquired RTF experimental open 

cavity results of References 2 and 3 for CFD comparison and validation of the numerical modeling, while 

Pulsonetti’s work deals with flight traceability. 

Experimentally, laminar two-dimensional flows were addressed by Galenter18 and Nestler19; laminar 

axisymmetric flows were addressed by Nestler20, Nicoll21,22, and Wyborny, et al.23; and, laminar threedimensional flows were examined by Cheatwood, et al.24, Hahn25, and Nestler26. The impact of a known, 

controlled pressure gradient on laminar-entry cavity heating was presented by Everhart, et al.1

. 

Experimental studies with cavities tested in transitional boundary layers or to determine the onset of 

transition were presented by Charbonnier and Boerrigter27, Boerrigter and Charbonnier28, Hollis and 

Liechty29-31, Larson and Keating32, Liechty, et al.33, and Rhudy and Magnan34. Turbulent two-dimensional 

experiments were presented by Charwat, et al.35,36, Chin and Seban37, Emery38, Hunt39, Lamb40-42, 

Nestler43-45,20, Shchukin, et al.46, and Stallings and Wilcox47; turbulent axisymmetric experiments were 

conducted by Hunt48 and Netterfield49; and turbulent three-dimensional experiments were published by 

Wilcox50,51. In general, the heating measurements were obtained with sparsely-spaced discrete sensors, 

the exception being those global phosphor thermography measurements presented by Cheatwood, et al., 

and Hollis and Liechty for circular cavities. Because of this spatial measurement sparseness, much of the 

three-dimensional nature of the surface heating profile is missed, as is in many cases the important peak 

heating value. While most of the idealized cavity geometries are rectangular with a flat bottom profile (a 

few have an arc bottom), the paper by Emery is of particular significance because heating profiles are 

presented for models with notched, cutback profile geometries that may be more representative of 

potential impact damage conditions. Two papers by Blair and Stallings52 and Stallings, et al.53 are 

significant because they present oil flow visualizations in and around the cavity and vapor screen 

visualizations of the cavity crossflow plane, clearly showing the growth and development of the cavity 

vortex structure. Gaps are an important class of cavities that have a length-to-depth ratio less than 1. Gaps 

have been examined by Coats, et al.54, Johnson55, Throckmorton56, and Weinstein, et al.57. 

As demonstrated above, many cavity research studies are available in the published literature. 

However, until recently there existed only a limited amount of laminar flow experimental data for 

evaluating heating effects in supersonic/hypersonic cavities, and most of the existing parametric 

variations and correlations were developed using turbulent heating measurements. Further, turbulent 

methods have typically been used for thermal assessments of damage on the Space Shuttle, even though 

much of the re-entry trajectory provides laminar edge conditions on the vehicle. The use of these 

turbulent methods may be overly conservative and restrictive for thermal assessment of shuttle tile 

damage for the laminar conditions. 

Supersonic/Hypersonic Cavity Flow Physics 

Based on the literature survey, the following overview of cavity flow physics is presented. Length- todepth ratio is typically used to distinguish between and classify different cavity flow regimes, as depicted 

in Figure 1. Very short or deep cavities with L/H<1 are known as gaps. In this case, shearing induced by 

the main stream flow causes the development of a column of counter-rotating vortices within the gap 

numbering approximately H/L. Alternating hot spots occur in the gap when the vortices directionally 

align and impinge on the sidewall. Two stable flow conditions exist for cavities with length L/H>1. The 

first is a short cavity of length 1≤L/H≤10, known as an open cavity. The mainstream flow does not enter 

the cavity directly, though there may be some mass interchange with the low-energy vortical flow inside 

the cavity. In this case, the cavity pressure is typically above the ambient and climbs to a peak at the 

downstream lip. The heating drops significantly below the undisturbed value and rises slowly to a peak on 
 5

the downstream lip. The other stable solution is a long cavity, known as a closed cavity, with length 

L/H>14. In this case, three distinct flows may develop if the cavity is long enough. First, the upstream 

flow is able to turn into the cavity and impinge on the floor, creating an aft-facing-step flow field. Next, a 

boundary layer on the floor may develop and recover to the ambient level outside the cavity. Finally, as 

the flow approaches the end wall it will turn outward and create a forward-facing-step flow field. For 

long, deep cavities, the pressure gradients may be severe where the flow turns and strong expansion and 

shock waves will be generated. Viscous shearing generated by this flow turning will augment the heating 

to levels significantly higher than the ambient levels on both the cavity floor and the end wall. The 

pressure in these long cavities will decrease below the ambient and steadily increase downstream, 

reaching large values of over-pressure behind the shocks. Vortices will develop on the cavity sidewalls as 

the flow expands around the corner into the cavity and on the floor after flow impingement, further 

augmenting the heating, which may extend laterally around the cavity in the most severe cases. These 

vortices will interact with the cavity end wall and spill into the downstream region beyond the cavity. 

Given laminar inflow, analysis of the heating profiles indicates that most any type of outflow may occur, 

depending on the cavity and its environmental state. The in-cavity flow may remain laminar, become 

transitional, or transition to fully turbulent flow; the downstream possibilities are equally varied and are 

currently the subject of extensive analysis and testing58 in support of Shuttle RTF. Cavities for the range 

10≤L/H≤14 are typically unsteady as the flow alternates between the two bounding conditions; these are 

known as transitional cavities. 

Boundaries between different cavity flow regimes are nominal, at best. For example, L/H values have 

been measured from 9 to 11 as the upper limit for open cavities and from 12 to 15 as the lower limit for 

closed cavity flow. These limits should therefore be taken only as a guide. Also, it is important to note 

that most of the reported cavity data were acquired in air (γ =1.4) with some in helium (γ =1.67). Since 

turning angle is a function of both Mach number and γ, conceivably, open/closed cavity boundaries will 

vary during re-entry as vehicle boundary layer edge conditions change. At present, experimental data are 

insufficient to estimate the strength of this effect on the aeroheating. 

Establishing the Testing Environment 

When few (if any) direct measurements of the cavity geometry are available and when the exact 

location of the cavity (implying local flow conditions) is unknown, defining the heating environment of 

an Orbiter damage-scenario cavity presents a significant challenge. Many possible variables and 

parameters exist. Following the literature, the gross geometric parameter space includes: length (L), width 

(W), and depth (H), and planform, cross-sectional, and profile variations. Sidewall and upstream end-wall 

entry angles may play an important role on the flow expansion into the cavity, while sidewall and endwall exit angles may affect recompression on the downstream wall and further expansion around the endwall corner – all parameters having a direct influence on the heating. The depth distribution along the 

cavity profile may potentially affect how or if the flow enters the cavity and impinges on the floor. The 

impact of roughness caused by irregular surfaces, protuberances, gap fillers between tiles (present or 

missing), embedded objects, etc. in and upstream of the cavity is unknown, but the roughness may 

significantly impact the shear layer/boundary layer transition process59. Local flow conditions and 

parameters include boundary layer thickness (δ), momentum thickness (θ), edge Mach number (Me), 

momentum thickness Reynolds number (Reθ), stream direction with respect to the cavity major axis, 

chemistry effects reflected in the ratio of specific heats (γ), wall temperature ratio (Tw/Taw), boundary 

layer state (laminar, transitional, or turbulent) entering/leaving the cavity, and pressure gradient. 

Shuttle Orbiter windward surface flow conditions are presented in graphical format in Reference 60. 
 6

Recently, surface flow conditions for the Shuttle Orbiter61 have been computed using the DPLR code62 for 

the STS-107 re-entry trajectory. The range of surface edge flow conditions from these sources over the 

windward acreage at Mach 18 where the pressure gradients are small (nominally zero) are presented in 

Table 1. 

Given the infinite number of potential geometric variations for impact damage, the Shuttle Damage 

Assessment Team has defined a simplified cavity representation. This rectangular geometry (called the 

“shoebox” geometry due to its shape) consists of a flat bottom bounded by straight sides and end walls. 

Entry, exit, and sidewall angles are prescribed for the general case. However, for the sake of simplicity, 

vertical sides and ends are used for the present designs. According to existing literature, the governing 

parameters for a cavity are the length-to-depth ratio L/H, and the depth-to-boundary-layer-thickness ratio 

H/δ. Lack of detailed width-effect information in the literature leads to the decision to scale the width by 

the depth W/H. 

Two different surveys of the shallow-cavity depth effect are desired. The nondimensional design 

conditions for the first are a variation of nondimensional depth H/δ at constant nondimensional length 

L/H; the design conditions for the second is a variation of length L/H at constant depth H/δ. For the first 

variation, the non-dimensional length of the cavity is chosen as 8 to ensure an open cavity flow field and 

to allow for dimensionally deeper cavities and physically longer cavities to enhance the optical access. 

Four cavities of non-dimensional depths of 0.1, 0.2, 0.35, and 0.5 were selected. For the second variation, 

a non-dimensional depth of 0.35 was selected with non-dimensional lengths of 8, 12, 16, and 20. 

Theoretically, this length variation will yield an open cavity, a transitional cavity, and two closed cavity 

flow fields, respectively. A cavity design width W/H of 3.6 was selected for all cavities to enhance the 

optical access. 

Experiment Design 

This section outlines the experiment design process. First, the design philosophy is presented, along 

with physical constraints imposed on the process. This is followed by the characterization of the model 

test surface using two-dimensional CFD simulations. Finally, the cavity design is generated, yielding the 

corresponding, available test space for these models. 

Design Philosophy and Constraints 

A flat-plate geometry where dCp/dx is approximately 0 was selected for installation of the cavities, 

allowing consistency with existing data. A tunnel-installation schematic of the model is presented in 

Figure 2 that will be further discussed in the models section. A blunted nose model was required to reduce 

the edge Mach numbers to target values at smaller angles of attack, thus minimizing the possibility of 

partial or complete tunnel-flow blockage63. Several different leading-edge-radius nose values were 

evaluated, and the variation of the surface flow properties of the plate were mapped for each as a function 

of model test conditions and attitude (i.e. Pt1, Tt1, α, Me, and Reθ). Based on an analysis of these 

computations, a nose radius, Rn, of 0.125 inches was selected. For this nose, the actual leading edge point 

will occur at 0.8245 inches downstream of the virtual origin defined at the x=0 inch station. The shoulder 

intersection between the nose and the beginning of the flat upper surface occurs at the 0.9495-inch station. 

According to Micol4

, the 31-Inch Mach 10 Tunnel test core is safely 10 inches at the smallest freestream 

Reynolds number. Therefore, a model width of 10 inches was selected to minimize possible interference 

of side-edge vortices on the model test region and to minimize spanwise flow-gradient effects across the 

model. With proper mounting, models as long as 30 inches can be injected through the tunnel sidewall. 
 7

Model length was defined during the design as nominally 20 inches. Finally, the cavity test location on 

the plate, Xcav, was established at the 8-inch station, downstream of the rapidly varying pressure gradients 

that occur as flow expands over the leading edge. This location was selected so that the desired scaled 

cavity with prescribed H/δ, W/H, and L/H yielded reasonable dimensions in geometric space (H, W, L) 

for measurement resolution. Since computational solutions were used to design the test articles, the 

available test domain was developed naturally as a part of the design process. 

Two-Dimensional Surface Modeling 

Two-dimensional baseline surface characterization was performed using the LAURA computational 

fluid dynamics code64,65. Best practices as defined in Ref. 66 were used to define the computational grid. 

Solutions for the flat surface were computed for leading edge nose radius values of 0.0625, 0.1250, and 

0.1875 inches for a range of stream conditions covering tunnel Re = 0.5 x106

, 1.0 x106, 1.8 x106, and 

2.0x106

 per foot at anticipated model angles of attack, α, ranging from -25 to 10 degrees. Boundary layer 

thickness, δ, was determined at the location where the enthalpy ratio had achieved 99.5 percent of the 

freestream value. As presented in Ref. 67, boundary layer thickness values computed with the LAURA 

code are typically 2-4% lower than experiment with a 10% standard deviation. Most of the expected 

initial large change in the pressure was completed by the 5-inch station for all conditions, particularly for 

the expanding flow conditions that occur around the test surface for positive angles of attack, though 

some slight gradient effects remain as the boundary layer continued to grow on the plate. The smallest 

nose radius was not selected because of fabrication concerns. Overall, relatively small differences were 

observed when comparing the effects of the 0.1250-inch nose radius to the 0.1875-inch nose radius on the 

boundary layer edge conditions. For consistency with other experiments, the 0.1250-inch nose was 

selected. Sample surface flow computations for the flat surface are presented in Figure 3. 

Test Condition Selection and Cavity Design 

The flow conditions at the location of the leading edge of the cavity are needed to determine the final 

cavity dimensions. The 8-inch station was selected as the cavity leading edge position based on the 

following factors: 1) the constant pressure gradient location begins at approximately 5 inches (see Figure 

2), 2) thicker boundary layers allow larger cavities, 3) the target-condition requirement for the magnitude 

and range of Reθ, and 4) the downstream narrowing of the plate side-edge vortices. Test conditions at this 

location were interpolated from the CFD surface flow distributions, and they are presented in terms of 

performance charts for the flat surfaces in Figure 4. In this figure, Me, Reθ, δ, and θ are plotted versus PT1

for various angles of attack. The effect of TT1 for the range of conditions considered was second order; 

therefore, it was neglected when determining the boundary layer edge properties. For each test surface, 

three nominal edge Mach number conditions (2.25, 2.50, and 2.85) covering the target range were 

specified. At each edge Mach number condition, the available Reθ space was determined from the curves, 

along with the α required to achieve these entry conditions; then, the corresponding δ and θ were 

determined to help scale the cavities. The boundary layer edge conditions were re-evaluated using the 

actual test conditions, and these conditions were used for final data reduction and post-test analysis. The 

resulting boundary layer thickness at this condition was used as the scaling factor for the cavity depth, 

H/δ. 

Experimental Method 

The experimental methods are presented, beginning with a description of the test facility and nominal 
 8

tunnel flow conditions. This is followed by a description of the model fabrication process, a discussion of 

the phosphor coating used for making the heating measurements, and the model mounting. An overview 

of the phosphor data system used to acquire the global heating measurements is next presented, followed 

by a discussion of the post-test data mapping and scaling. 

Facility 

The 31-Inch Mach 10 Air Tunnel was selected as the test facility because the higher surface 

temperature rise during a run would provide lower uncertainties in heat transfer measurements68. This is a 

blowdown facility in which heated, filtered air is used as the test gas. The tunnel has a square, contoured 

nozzle, which opens into a 31-inch square test section. Models are supported on a hydraulically operated, 

sidewall-mounted injection system that can transfer a model from the sealed isolation box outside the 

flow to the tunnel center-line in less than 1.5 seconds. Tunnel run times of approximately 60 seconds can 

be achieved, but typical heating studies require only a few seconds. The nominal reservoir conditions are 

stagnation pressures of 150 psi to 1450 psi at stagnation temperatures of about 1825°R. These reservoir 

conditions very nearly produce perfect gas (γ = 1.4) freestream flows with a Mach number of 

approximately 10 and Reynolds numbers of 0.2x106

/ft to 2.2x106/ft. Nominal flow conditions are 

provided in Table 2 and a detailed description of this facility is presented by Micoll4. 

Models 

The general manufacturing process for ceramic test articles is described in Buck, et al.69. Specific 

changes to this process for previous cavity heating experiments2,3 are described in Buck, et al.70. In this 

later manufacturing method, a rapid prototyping stereolithography (SLA) system at NASA Langley 

Research Center was used to make a resin mold pattern for casting cavities in flat 4-inch wide by 18-inch 

long ceramic insert models. These ceramic inserts were then installed in a 10-inch wide by 28-inch long 

steel flat-plate model for testing. 

The present experiment further improves this manufacturing process by eliminating the insert 

requirement. Here, the flat plate models were nominally 10-inches wide by 20-inches long and they were 

cast as a single piece to remove the step and gap mounting problems experienced with the previous 

method. Referring to Figure 2, all models had a 0.125-inch radius nose with a 15o

 aft-swept wedge on the 

lower nose surface. As schematically shown, the ceramic castings were then bonded to an aluminum 

backing plate that is at 0o incidence relative to tunnel centerline for the flat plate. 

Using the previously described cavity design process, three ceramic models were developed: 

1) a baseline flat plate model with no cavities; 

2) a model with four spanwise-distributed L/H=8 cavities with design-point depths of H/δ of 0.1, 

0.2, 0.35, and 0.5; and 

3) a model with four spanwise-distributed design-point-depth H/δ=0.35 cavities of lengths L/H of 

8, 12, 16, and 20. 

The models (shown schematically in Figure 5) were laser-ablated at a longitudinal location of x=8 inches, 

yielding the as-built cavity dimensions and spanwise location as presented in Table 3. Shallow-cavity 

model M1 represented the depth variation at constant design length L/H=8, while shallow-cavity model 

M2 represented the length variation at constant design depth H/δ=0.35. Also noted in Figure 5 is the 

nomenclature used for cavity identification. Here, each cavity is identified as Sij where i is 1 or 2, 
 9

depending on the model, and j is 1 to 4, depending on the cavity. For example, S23 represents model 2 

cavity 3. Note that cavity S11 is on the starboard side of M1 and that S21 is on the port side of M2. The 

common-geometry L/H=8, H/δ=0.35 reference cavities (S13 and S21) are highlighted in black. 

Both models were coated with a 27μm68 thick mixture of phosphors suspended in a silica-based 

colloidal binder and sent to quality assurance for measurement and application of small circular locating 

markers, known as fiducial marks. These fiducial marks aid in data reduction and model orientation, and 

they can be seen in the run images as dark dots. Even though fiducial marks do not influence the flow 

over the model surface, they will influence the local heating measurement because the ink used in the 

process will wick into the phosphor coating over a small circular region about the application point and 

locally change the calibration. Their influence on the data, notably in line cuts passing through them, is to 

produce a very short, very sharp-peaked sinusoidal signature covering the diameter of the marking. 

When mounted in the tunnel, the aluminum backing plate was attached to a 0°

 spacer block surface 

used to position the model on tunnel centerline and align the model to zero incidence. Finally, this entire 

assembly was attached from the leeward side to an existing model support strut and mounted to the tunnel 

sidewall injection plate. An offset angle wedge is placed under the strut base when required to extend the 

angle testing range of the model. A picture of the model mounted in the 31-Inch Mach 10 Tunnel with the 

phosphor thermography camera and lighting system is given in Figure 6. 

Thermographic Phosphor Measurement System 

Global surface heating distributions were calculated using the two-color, relative-intensity, phosphorthermography aeroheating measurement method71. This is the standard method for obtaining aeroheating 

data in NASA Langley’s hypersonic wind tunnels, and it can be used to identify the surface heating 

effects of complex three-dimensional flow phenomena, which are difficult to examine using conventional 

discrete-sensor methods. With this method, ceramic wind tunnel models are coated with phosphor crystals 

that fluoresce in the red and green regions of the visible light spectrum when illuminated by ultraviolet 

(UV) light. During a wind tunnel run, the phosphor-coated model is exposed to the heated flow of the 

tunnel, and the resulting changes in fluorescence intensity of the model are recorded and digitized through 

a 640 by 480 resolution color-CCD (charge coupled device) camera and a state-of-the-art video 

acquisition system. The fluorescence intensity is dependent on both the intensity of the incident UV light 

and the local model surface temperature. The UV dependence is removed by taking the ratio of the green 

to red intensity images, from which surface temperature distributions are determined through prior 

calibrations. Images are acquired before the wind tunnel run and after injection of the model to the tunnel 

centerline during a run. 

Data Reduction 

Global mappings of the surface temperature obtained with the thermographic phosphor data 

acquisition system were reduced to surface heating distributions using the IHEAT data reduction 

software71. In this method, phosphor images are acquired shortly after injection of the model to the tunnel 

centerline. With this software, temperature images acquired through the run are used to obtain heat 

transfer images. This is done by applying one-dimensional, semi-infinite-solid heat conduction theory 

assuming a constant heat-transfer coefficient, and by making empirical corrections to account for 

temperature changes in model substrate thermal properties. The results are presented in terms of a nondimensional heat transfer coefficient ratio, h/href, where href is generally taken as hFR, the theoretical 

stagnation-point heating computed with the Fay-Riddell72 theory. For this experiment, hFR was computed 
 10

using a 0.125-inch radius sphere (the test model nose radius) and a reference stagnation temperature of 

540oR. At this point, IHEAT was used to extract preliminary analysis data along lines from the twodimensional heating images. Also, these images were mapped onto a three- dimensional representation of 

the test article using IHEAT’s MAP3D photogrammetry program68 for further global analysis. 

Data for this experiment were translated such that the leading edge of the cavity is at x=0. The (x, y, z) 

data were then scaled to (x/H, y/H, z/δ) using the measured cavity depth and the computed boundary layer 

thickness. This yields a scaled-geometry cavity of (L/H, W/H, H/δ). Note again that the boundary layer 

edge conditions for each run are determined from the LAURA computations for matching tunnel and 

model conditions. 

The impact of the cavity on the local undisturbed environment was assessed by converting the local 

heating data to heating augmentation or bump factor (BF) format by normalizing hlocal/href by a referencelocation average heating havg/href, yielding BF=hlocal/havg. The reference-location heating on the baseline 

models (no cavity) is computed over a plate-centered strip located -2 ≤ x/ δ ≤ 0 by 

-2 ≤ y/ δ ≤ 2. (Note that x/ δ = 0 corresponds to the location of the cavity leading edge when cavities are 

present, since the coordinates have been translated.) In this format, BF=1 is the nominal undisturbed 

condition for a flat plate. For analysis consistency and to avoid the heating peak due to expansion into the 

cavity at the upstream edge, (havg/href) is computed ahead of each cavity over an area two cavity depths 

long by one cavity width wide, and this region is located at -3 ≤ x/H ≤ -1 by -0.5 ≤ y/H ≤ -0.5. 

Presentation of Test Data 

The as-run test matrix for the baseline flat plate model, including tunnel conditions, is presented in 

Table 4. These runs were obtained during Test 406 following the acquisition of the shallow cavity test 

data during Test 404. The shallow cavity test used two flat plates, each containing 4 discrete cavities. The 

test matrix for Shallow Cavity Model 1 containing a depth sweep at constant length is presented in Table 

5, while the test matrix for Shallow Cavity Model 2 containing a length sweep at constant depth is 

presented in Table 6. Computationally-generated boundary layer edge conditions and parameters at 

station x=8 inches (the cavity entrance) are presented in Table 7. This table provides the computed cavity 

entry conditions Me, Reθ, Reθ/Me, δ, and θ, as well as the cavity depth, width, and length normalized by 

the boundary layer thickness. Three types of runs were made for each cavity plate. The first type is a 

global heating run with the phosphor camera set to view the entire plate; the second type is a view of the 

plate with the camera capturing only the top two cavities; and, the third type is a view of the plate with the 

camera capturing only the bottom two cavities. Constraints on the cavity views were that upstream and 

downstream fiducials must be in each image for reference. 

Bump Factor images for the baseline runs acquired during Test 406 are presented in Figure 7. The data 

represented in these images provide the undisturbed heating profile of the entire plate, allowing an 

assessment of the flow uniformity and the boundary layer state. The global heating images for the cavity 

model plates are presented in Figure 8 and Figure 9. These images allow an assessment of the extent of 

the cavity flow field interactions over the plate surface. Because most cavities were very small, these 

global image data were of insufficient resolution for mapping; therefore, they are presented in terms of 

h/hFR. Also noted on the first image of each figure is the cavity identifier (ex. S21 on Figure 8a). This 

nomenclature was previously discussed in the Models section. Finally, the local, mapped, scaled Bump 

Factor distributions for each cavity are presented in Figure 10 through Figure 17. Here, x/δ is referenced 

from the cavity-entrance location using local conditions. The first image in Figure 10 identifies the 

location of the cavity and the fiducial marks for reference for all other figures. 
 11

Uncertainty Analysis 

Merski68 published the uncertainties for the phosphor thermography method as a whole in 2001. A 

more quantitative understanding of the uncertainty levels for this experiment were obtained by adding 

phosphor heat-transfer bump-factor uncertainty algorithms to the MAP3D code, resulting in global 

uncertainty surface maps similar to the three-dimensional heat transfer maps. The process is outlined 

below. 

The solution of the heat conduction equation (i.e. the data reduction equation) used in the IHEAT code 

is given by 

Θ

Haw

Tw

Hw

−Tinit

⎛

⎝

⎜ ⎞

⎠

⎟

= 1− eΛ2erfc ( ) Λ

where 

Θ( ) x,y,t = T x( ) ,y,t −T x( ) ,y,0 = T x( ) ,y,t −Tinit and Λ =

h Haw

Tw

⎛

⎝

⎜

⎞

⎠

⎟

β

h is the convective heat transfer coefficient, Haw is the adiabatic wall enthalpy, Hw is the wall enthalpy, Tw 

is the corresponding wall temperature, and t is the effective time of data acquisition. β is the thermal 

product of the substrate materials and it is equal to the square root of the product of the material density, 

specific heat, and thermal conductivity. 

Bias and precision uncertainty values for the time, temperature, and thermal product used in the data 

reduction equation were developed at the 95 percent confidence level and they are given in Table 8. The 

5.9% bias uncertainty quoted there for β is the maximum deviation observed across the temperature 

range. Uncertainties for each free parameter in the heat transfer coefficient resulting from the variation in 

each parameter were determined by individually inserting the parameter uncertainty range endpoints into 

the data reduction equation. The bias uncertainty, B, and the precision uncertainty, P, for the heat transfer 

coefficient were determined by obtaining the root-sum-square (RSS) from each of the component 

uncertainties using 

B = Bj

2

j

∑

⎛

⎝

⎜

⎞

⎠

⎟

1

2

 and P = Pj

2

j

∑

⎛

⎝

⎜

⎞

⎠

⎟

1

2

where j is the number of component uncertainties. Total uncertainties are obtained by taking the RSS of 

the bias and precision uncertainties. Bias and total uncertainties of the heat transfer coefficients are 

determined at every pixel point imaged on the model. 

Bump factors extracted from the mappings were used in two ways: 1) as line cuts when selecting 

specific data, and 2) as regions of interest over which all of the data were averaged. In the first case, the 

total uncertainties are applicable and in the latter, bias uncertainties are applicable. Precision uncertainties 

are removed during averaging, since they are primarily due to random pixel scatter. Accordingly, the 

average heat transfer coefficient havg used to compute bump factors was assumed to have only a bias 
 12

uncertainty. Typically, as shown in Ref. 73, total uncertainties in the bump factors are determined using 

UBF

BF

⎛

⎝

⎜

⎞

⎠

⎟

2

= Uhlocal

hlocal

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

2

+

Uhavg

havg

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

2

For nominally flat models of this type, very low heating rates are obtained during a run and the resulting 

uncertainty calculations were initially very high. Yet, comparisons of line cuts were more consistent than 

the uncertainty analysis seemed to suggest. While conservatism is important, excessive conservatism is 

undesirable. Therefore, the phosphor temperature lookup table data were re-examined and it was 

determined that since there was minimal variation of incident UV intensities on the models during the 

tunnel runs, and because of the low heating measurements, the data were typically confined to one very 

small segment of the temperature range. Thus, the bias uncertainties for the data used in calculating hlocal

and havg were unidirectional and determinate. Therefore, the bias uncertainties in hlocal had to be excluded 

from the bias uncertainties in havg when computing bias uncertainties for the bump factors. Similarly, total 

uncertainties in bump factors were then obtained simply by taking the RSS of the bias and precision 

uncertainties in havg and by excluding the bias uncertainties in hlocal. 

Representative bias uncertainties for cavity S12 (Run 03) are shown in Figure 18a, corresponding total 

uncertainties are shown in Figure 18b. Similarly, uncertainties for cavity S14 are shown in Figure 19. 

These open cavity flows represent some of the more challenging measurement configurations from an 

accuracy standpoint because the flow does not directly enter the cavity, resulting in a very small floor 

temperature rise relative to the pre-run condition. Here, total and bias uncertainties are typically less than 

10% over the plate surface. In the cavity where the lowest temperatures are experienced, the bias 

uncertainties are about 10%, while the total uncertainties approach 20%. A closed condition is presented 

for cavity S24 for Run 28 in Figure 20. As expected, the temperature rise is generally greater, resulting in 

lower bias uncertainties (3-4 percent or lower) with the exception of the low temperature regions on the 

cavity floor. Total uncertainties are in the 10-20 percent range. 

Results 

The objective of the present report is to provide a data set focused on the heating augmentation in the 

near field region of impact-induced shallow cavities. The results presented in this section represent a 

preliminary evaluation of the test data, recognizing that more extensive analysis and certification must be 

conducted prior to its inclusion in the engineering tools developed for damage assessment during flight 

operations. Two metrics are used. The first is the average bump factor on the entire cavity floor obtained 

by using the Region-of-Interest tool contained in the IHEAT data reduction program. The second is the 

endwall maximum bump factor obtained from centerline data slices through the cavity, again from the 

IHEAT program. A tabulation of these metrics is presented for each run in Table 9. 

Considering the open (L/H=8) cavity data presented first in Figure 21a, the BFfloor avg is plotted as a 

function of H/δ. The results from each cavity are color coded and a line representing a least-squares fit is 

provided. Length L/H=8 cavity data from Model 1 (S13) are compared with L/H=8 cavity data from 

Model 2 (S21) as a consistency check on the manufacturing, measurement, and data reduction processes. 

An exceptionally good comparison is demonstrated by the overlap of most of the discrete data at 

matching conditions and by the line-fit results. Recall that each test point generates data from two 

cavities, either S11 and S12 or S13 and S14, and that two runs are required to generate matching entry 

conditions for all four cavities on a single plate. Also, recall that the data for each cavity were acquired 
 13

over a wide range of Me and Reθ and, as shown, that overlapping depth conditions were acquired for 

adjacent cavities. Prior to the test, it was anticipated that BFfloor avg would regularly vary from 1 at zero 

depth to some asymptotically realized average value at larger depths. This has not occurred. The cavityfloor average data from each cavity are constant with depth and different cavities tested at the same depth 

generate a different constant. It is appropriate to note that no correlation was found when plotting this 

metric versus other flow parameters, including H/θ, W/H, Re, Reθ, and Reδ. A consistent stratification in 

H/δ (longitudinal shift) for each cavity was found when the data were identified according to Me; 

however, further analysis is required for the inclusion of this effect in a correlation. 

The variation of BFfloor avg for different L/H cavities is plotted as a function of H/δ in Figure 21b. These 

data exhibit the expected variation in that long cavities (L/H>14) allow the hotter external flow to enter, 

thereby increasing the heating. BFfloor avg values for the open cavities cluster around 0.3, while values for 

the closed cavities cluster near 0.5. Data from cavity S23 (L/H=16) are clearly transitional, switching 

from the open to the closed BFfloor avg levels. While not definitive and only after examining the behavior of 

S23, data from cavity S22 appear to be at least partially transitional. For comparison, cavity S13 from 

Model 1 and cavity S21 from Model 2 again generate nearly the same results, establishing consistency as 

previously discussed for Figure 21a. 

Poor correlation of the BFfloor avg data was demonstrated when plotted versus H/δ and L/H (not shown). 

However, the correlation was much improved when the cavity floor averaged data were plotted as a 

function of viscous length parameter L/δ, which is equivalent to (L/H)(H/δ), as shown in Figure 22. This 

presentation implies that BFfloor avg=0.291 with a standard deviation of 0.041 for fully-laminar flow 

conditions (i.e. laminar-in/laminar-out) conditions when 2.5 ≤ L/δ ≤ 10. Using Figure 21 and working 

backwards, if cavities are restricted in depth to the range 0.3 ≤ H/δ ≤ 0.8, then potentially, the relationship 

3 ≤ L/H ≤ 33 is also a valid constraint - if the L/δ constraint is maintained. 

The maximum values of the endwall centerline Bump Factor, BFCL, plotted as a function of H/δ are 

presented in Figure 23 for all cavities. No clear correlation exists with this parameter. However, plotting 

BFCL versus L/δ in Figure 24 is more revealing. Cavities that maintain a laminar-in/laminar-out boundary 

layer state typically have a BFCL values clustering between 2.0 and 2.75 for L/δ ≥ 2.5. A close 

examination of the S24 (L/H=20) data when L/δ ≥ 7 indicate that the boundary layer state on exit is either 

transitional or turbulent, generating BFCL values of 3.5 or larger. Cavity S23 with L/H=16 exhibits two 

distinct BFCL variations indicated by the dashed fairing lines: open flow characteristic values of 2.3 and 

closed flow characteristics trending toward transitional/turbulent boundary layer heating values on exit. 

This behavior is consistent with this cavity being near the upper end of the transitional-cavity limit. Solidline power-law fairings through the Model 1 (L/H=8) results (cavities S11, S12, S13 and S14) provide an 

apparent trend with increasing physical size. Since each line represents a matching range of Me and Reθ

test conditions and since H/δ variations do not collapse the data, additional research is required to 

understand this behavior at small L/δ. 

Conclusions 

An experiment to evaluate the heating augmentation induced by shallow cavities under fully laminar 

flow conditions has been conducted in the NASA Langley 31-Inch Mach 10 Tunnel in support of the 

Space Shuttle Return-to-Flight Program. Two-dimensional viscous flow solutions on a flat plate model 

were determined using the LAURA code, providing boundary-layer edge properties that were used to 

design a family of rectangular-planform cavities. Three ceramic models were developed: 
 14

1) a baseline flat plate model with no cavities; 

2) a model with four spanwise L/H=8 cavities with depths H/δ of 0.1, 0.2, 0.35, and 0.5; and 

3) a model with four spanwise H/δ=0.35 cavities of lengths L/H of 8, 12, 16, and 20. 

Phosphor thermography was used to map the heating distribution over the model surface. The heating 

data for each cavity and its surrounding field were converted to augmentation or Bump Factor format by 

referencing the measurements to a site upstream of each cavity. Test results are presented in graphical and 

tabular formats in this report, and they have been electronically transmitted to the Damage Assessment 

Aeroheating Team at Johnson Space Center. Preliminary results indicate that the floor-averaged Bump 

Factor is 0.291 with a standard deviation of 0.041 for fully-laminar flow conditions when 2.5 ≤ L/δ ≤ 10

for cavities in the depth range 0.3 ≤ H/δ ≤ 0.8. Over this same range of flow conditions and parameters, 

preliminary results also indicate that the maximum centerline cavity Bump Factor falls between 2.0 and 

2.75. Cavities with L/δ ≤ 2.5 can not be easily classified with this approach and, accordingly, require 

further analysis. 

Acknowledgement 

The authors gratefully acknowledge the contributions of NASA Langley Research Center employees 

Mr. Gary Wainwright for the design and fabrication of the stereolithography models, Mr. Mark Griffith 

and Mr. Michael Powers for fabrication of the ceramic models, Mrs. Kathy Kuykendall, Mr. Peter 

Veneris, and Mr. Ed Covington for the quality assurance measurements. A special recognition is accorded 

Mr. John Hopkins for his efforts to rapidly setup and laser-ablate the cavities. These individuals 

performed magnificently in the high-intensity environment of this test. 

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45 Nestler, D.E., “Hypersonic Boundary Layers and Selected Heat Flux Problems,” Short Course on Technology of Space Shuttle 

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46 Shchukin, V.K., Gortyshov, Yu. F., Varfolomeev, I.M., and Nadyrov, N.A., “Influence of Relative Depth and Reynolds 

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47 Stallings, Robert L., Jr. and Wilcox, Floyd J., Jr., “Experimental Cavity Pressure Distributions at Supersonic Speeds”, NASA 

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50 Wilcox, Floyd J., Jr., “Experimental Investigation of Porous-Floor Effects on Cavity Flow Fields at Supersonic Speeds,” 

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52 Blair, A.B., Jr. and Stallings, R.L., Jr., “Supersonic Axial-Force Characteristics of a Rectangular-Box Cavity with Various 

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54 Coats, Jack D., Rhudy, R.W., and Edmunds, E.W., “Effects of Surface Gaps and Steps on Laminar Heat-Transfer Rates at 

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56 Throckmorton, D.A.: “Heat Transfer to Surface and Saps of RSI Tile Arrays in Turbulent Flow at Mach 10.3,” NASA-TM-X71945, April 1974. 

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66 Palmer, Grant; Alter, Steve; Everhart, Joel; Wood, William; Driver, Dave; Brown, Jim; and, Prabhu, Ramadas: “CFD 

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June 25-28, 2007, AIAA-2007-4254. 

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Johnson Space Center Engineering Note, EG-SS-06-1, 2005. 

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Aeroheating Measurements,” NASA CDTP-1017, February 2001. 

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Ceramic Models,” U.S. Patent 5,266,252, November 1993. 

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Plate Cavity Phosphor Thermography Test Models for Shuttle Return-to-Flight Aero-Heating,” NASA TM 2006-214508. 

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Method,” Journal of Spacecraft and Rockets, Vol. 36, No. 2, 1999, pp. 160-170. 

72 Fay, J.A. and Riddell, F.R., “Theory of Stagnation Point Heat Transfer in Dissociated Air,” Journal of Aeronautical Sciences, 

Vol. 25, No. 2, 1958, pp. 73-85. 

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New York, 1989. 
Tables 

Table 1.-Typical range of windward surface flow conditions at Mach 18. 

Me 2.2 - 3.2 

Reθ 120 - 700 

δ 1 - 6 inches 

Table 2.- Nominal flow conditions for the 31-Inch Mach 10 Air Tunnel.

PT1

psi

TT1

oR

P∞x102

psi

T∞ oR q∞

psi

V∞

ft/s

M∞ R∞x10-6

ft-1

PT1 psi Test Core 

in.

348 1800 0.992 95.2 0.650 4628 9.67 0.568 1.205 10x10 

723 1825 1.867 94.2 1.259 4670 9.81 1.104 2.334 12x12 

1452 1800 3.509 90.7 2.430 4643 9.94 2.240 4.503 12x12 

Table 3.- As-built cavity geometries.

Cavity y (inch) H (inch) W (inch) L (inch) W/H L/H

Model M1 S11 3 0.018 0.060 0.118 3.33 6.6 

S12 1 0.036 0.165 0.333 4.58 9.3 

S13 -1 0.063 0.270 0.550 4.29 8.7 

S14 -3 0.099 0.391 0.800 3.95 8.1 

Model M2 S21 -3 0.068 0.272 0.530 4.00 7.8 

S22 -1 0.074 0.277 0.793 3.74 10.7 

S23 1 0.071 0.278 1.065 3.92 15.0 

S24 3 0.067 0.282 1.360 4.21 20.3 

Note: Cavities S13 and S21 were designed as a common reference cavity between Models M1 and M2. 

Table 4.-Baseline model run matrix from Test 406.

Run Zoom Model 

View Config PT1

(psia)

TT1

(oF)

Re 

(x10-6) 

(ft-1)

α

(deg) Comments

68 35 Global Base 602.66 1314.80 0.94 -7.77 

69 35 Global Base 823.28 1323.09 1.23 -7.20 

70 35 Global Base 1096.83 1333.19 1.59 -6.53 

71 35 Global Base 1377.99 1337.74 1.96 -6.29 

74 35 Global Base 1152.81 1319.22 1.69 -11.42 

73 35 Global Base 782.86 1319.56 1.18 -17.89 

72 35 Global Base 1215.85 1338.86 1.74 -15.57 

75 35 Global Base 1379.18 1330.20 1.97 -6.29 Random Repeat 
Table 5.- Test 404 run matrix for cavity-plate model 1. 

Run Zoom Model 

View Config PT1

(psia)

TT1

(oF)

Re 

(x10-6) 

(ft-1)

α

(deg) Comments

1 18 Global M1 641.28 1324.51 0.985 -7.77 Re high. Lower Pr 

2 18 Global M1 593.04 1329.40 0.914 -7.77 

3 70 Top S11 592.44 1324.56 0.916 -7.77 

 70 Top S12 592.44 1324.56 0.916 -7.77 

4 70 Bottom S13 593.04 1332.72 0.911 -7.77 

 70 Bottom S14 593.04 1332.72 0.911 -7.77 

7 18 Global M1 802.11 1336.51 1.193 -7.20 

6 70 Top S11 802.40 1328.00 1.203 -7.20 

 70 Top S12 802.40 1328.00 1.203 -7.20 

5 70 Bottom S13 801.64 1328.44 1.202 -7.20 

 70 Bottom S14 801.64 1328.44 1.202 -7.20 

8 18 Global M1 522.97 1343.67 0.806 -14.18 

9 70 Top S11 523.16 1346.34 0.804 -14.18 

 70 Top S12 523.16 1346.34 0.804 -14.18 

10 70 Bottom S13 523.35 1344.15 0.806 -14.18 

 70 Bottom S14 523.35 1344.15 0.806 -14.18 

13 18 Global M1 834.57 1331.40 1.243 -12.39 

12 70 Top S11 834.66 1329.63 1.245 -12.39 

 70 Top S12 834.66 1329.63 1.245 -12.39 

11 70 Bottom S13 834.66 1329.32 1.247 -12.39 

 70 Bottom S14 834.66 1329.32 1.247 -12.39 

14 18 Global M1 1194.51 1335.36 1.725 -15.57 Re low. Raise Pr 

15 18 Global M1 1218.78 1328.26 1.768 -15.57 Re slightly high - use 

17 70 Top S11 1214.31 1345.15 1.736 -15.57 

 70 Top S12 1214.31 1345.15 1.736 -15.57 

16 70 Bottom S13 1216.02 1343.06 1.740 -15.57 

 70 Bottom S14 1216.02 1343.06 1.740 -15.57 

24 70 Top S11 1082.78 1328.56 1.585 -6.53 

 70 Top S12 1082.78 1328.56 1.585 -6.53 

23 70 Bottom S13 1083.54 1332.89 1.579 -6.53 

 70 Bottom S14 1083.54 1332.89 1.579 -6.53 

25 144 Top S11 1082.02 1332.61 1.578 -6.53 Examining zoom and 

pixelation 

 144 Top S12 1082.02 1332.61 1.578 -6.53 Examine zoom and 

pixelation 

20 70 Top S11 1126.56 1333.84 1.636 -11.42 

 70 Top S12 1126.56 1333.84 1.636 -11.42 

21 70 Bottom S13 1125.42 1335.16 1.631 -11.42 

 70 Bottom S14 1125.42 1335.16 1.631 -11.42 

18 70 Top S11 773.85 687.63 2.269 -17.89 TT1 too low during run 

 70 Top S12 773.85 687.63 2.269 -17.89 TT1 too low during run 

19 70 Top S11 782.41 1329.20 1.174 -17.89 

 70 Top S12 782.41 1329.20 1.174 -17.89 

22 70 Bottom S13 781.84 1331.32 1.172 -17.89 

 70 Bottom S14 781.84 1331.32 1.172 -17.89 
Table 6.- Test 404 run matrix for cavity-plate model 2.

Run Zoom Model 

View Config PT1

(psia)

TT1

(oF)

Re 

 (x10-6) 

(ft-1)

α

(deg) Comments

26 18 Global M2 - - - -7.77 No tunnel conditions. 

27 18 Global M2 591.21 1324.55 0.92 -7.77 Repeat of run 26 

29 70 Bottom S21 591.78 1323.87 0.92 -7.77 

 70 Bottom S22 591.78 1323.87 0.92 -7.77 

28 70 Top S23 592.45 1324.41 0.92 -7.77 

 70 Top S24 592.45 1324.41 0.92 -7.77 

30 70 Bottom S21 - - - -7.20 Heater problem 

 70 Bottom S22 - - - -7.20 Heater problem 

31 70 Bottom S21 802.21 1319.50 1.21 -7.20 Repeat of run 30 

 70 Bottom S22 802.21 1319.50 1.21 -7.20 

32 70 Top S23 801.26 1322.53 1.21 -7.20 

 70 Top S24 801.26 1322.53 1.21 -7.20 

36 70 Bottom S21 522.21 1346.69 0.80 -14.18 

 70 Bottom S22 522.21 1346.69 0.80 -14.18 

37 70 Top S23 523.16 1349.63 0.80 -14.18 

 70 Top S24 523.16 1349.63 0.80 -14.18 

33 18 Global M2 835.33 1326.14 1.25 -12.39 

35 70 Bottom S21 834.57 1324.02 1.25 -12.39 

 70 Bottom S22 834.57 1324.02 1.25 -12.39 

34 70 Top S23 837.71 1328.62 1.25 -12.39 

 70 Top S24 837.71 1328.62 1.25 -12.39 

38 18 Global M2 1214.41 1345.21 1.73 -15.57 

40 70 Bottom S21 1217.74 1337.28 1.75 -15.57 

 70 Bottom S22 1217.74 1337.28 1.75 -15.57 

39 70 Top S23 1215.36 1332.45 1.76 -15.57 

 70 Top S24 1215.36 1332.45 1.76 -15.57 

47 70 Bottom S21 780.89 1332.37 1.17 -17.89 

 70 Bottom S22 780.89 1332.37 1.17 -17.89 

48 70 Top S23 780.32 1325.80 1.77 -17.89 

 70 Top S24 780.32 1325.80 1.77 -17.89 

46 70 Bottom S21 1125.61 1331.86 1.64 -11.42 

 70 Bottom S22 1125.61 1331.86 1.64 -11.42 

45 70 Top S23 1125.70 1333.29 1.64 -11.42 

 70 Top S24 1125.70 1333.29 1.64 -11.42 

42 70 Bottom S21 1082.78 1328.89 1.58 -6.53 

 70 Bottom S22 1082.78 1328.89 1.58 -6.53 

41 70 Top S23 1083.26 1335.78 1.58 -6.53 

 70 Top S24 1083.26 1335.78 1.58 -6.53 

43 70 Bottom S21 1356.21 1327.07 1.95 -6.29 

 70 Bottom S22 1356.21 1327.07 1.95 -6.29 

44 70 Top S23 1355.45 1328.13 1.95 -6.29 Camera misalignedCavities 22 and 23. 

 70 Top S24 1355.45 1328.13 1.95 -6.29 Camera misalignedCavities 22 and 23. 

49 70 Top S23 1356.31 1338.32 1.93 -6.29 

 70 Top S24 1356.31 1338.32 1.93 -6.29 
Table 7.- Cavity flow conditions and parameters, xcav=8 inches. 

Run Cavity y, cavity 

(inch) Me Reθ Reθ/Me

δ

(inch) θ (inch) H/δ W/ δ L/ δ

GLOBAL 

1 M1 Global 2.78 170 61 0.1882 0.0226 

2 M1 Global 2.78 165 59 0.1942 0.0233 

7 M1 Global 2.81 182 65 0.1768 0.0211 

8 M1 Global 2.37 191 80 0.1505 0.0200 

13 M1 Global 2.43 210 86 0.1343 0.0176 

14 M1 Global 2.19 260 118 0.1004 0.0140 

15 M1 Global 2.19 262 119 0.0997 0.0139 

27 M2 Global 2.78 260 94 0.1945 0.0234 

38 M2 Global 2.19 261 119 0.0999 0.0139 

CAVITY S11 

3 S11 3 2.78 165 59 0.1943 0.0233 0.09 0.31 0.61 

6 S11 3 2.81 182 65 0.1768 0.0211 0.10 0.34 0.67 

9 S11 3 2.37 191 80 0.1505 0.0200 0.12 0.40 0.78 

12 S11 3 2.43 210 86 0.1343 0.0176 0.13 0.45 0.88 

17 S11 3 2.19 261 119 0.0999 0.0139 0.18 0.60 1.18 

18 S11 3 2.12 241 114 0.1118 0.0159 0.16 0.54 1.06 

19 S11 3 2.12 242 114 0.1113 0.0159 0.16 0.54 1.06 

20 S11 3 2.48 228 92 0.1247 0.0161 0.14 0.48 0.95 

24 S11 3 2.85 200 70 0.1623 0.0192 0.11 0.37 0.73 

25 S11 3 2.85 200 70 0.1624 0.0192 0.11 0.37 0.73 

CAVITY S12 

3 S12 1 2.78 165 59 0.1943 0.0233 0.19 0.85 1.71 

6 S12 1 2.81 182 65 0.1768 0.0211 0.20 0.93 1.88 

9 S12 1 2.37 191 80 0.1505 0.0200 0.24 1.10 2.21 

12 S12 1 2.43 210 86 0.1343 0.0176 0.27 1.23 2.48 

17 S12 1 2.19 261 119 0.0999 0.0139 0.36 1.65 3.33 

18 S12 1 2.12 241 114 0.1118 0.0159 0.32 1.48 2.98 

19 S12 1 2.12 242 114 0.1113 0.0159 0.32 1.48 2.99 

20 S12 1 2.48 228 92 0.1247 0.0161 0.29 1.32 2.67 

24 S12 1 2.85 200 70 0.1623 0.0192 0.22 1.02 2.05 

25 S12 1 2.85 200 70 0.1624 0.0192 0.22 1.02 2.05 

CAVITY S13 

4 S13 -1 2.78 165 59 0.1942 0.0233 0.32 1.39 2.83 

5 S13 -1 2.81 182 65 0.1768 0.0211 0.36 1.53 3.11 

10 S13 -1 2.37 191 80 0.1505 0.0200 0.42 1.79 3.65 

11 S13 -1 2.43 210 86 0.1343 0.0176 0.47 2.01 4.10 

16 S13 -1 2.19 261 119 0.0998 0.0139 0.63 2.70 5.51 

21 S13 -1 2.48 228 92 0.1248 0.0161 0.50 2.16 4.41 

22 S13 -1 2.12 242 114 0.1113 0.0159 0.57 2.43 4.94 

23 S13 -1 2.85 200 70 0.1623 0.0192 0.39 1.66 3.39 
Table 7.- Continued. 

Run Cavity y, cavity 

(inch) Me Reθ Reθ/Me

δ

(inch) θ (inch) H/δ W/ δ L/ δ

CAVITY S14 

4 S14 -3 2.78 165 59 0.1942 0.0233 0.51 2.01 4.12 

5 S14 -3 2.81 182 65 0.1768 0.0211 0.56 2.21 4.52 

10 S14 -3 2.37 191 80 0.1505 0.0200 0.66 2.60 5.32 

11 S14 -3 2.43 210 86 0.1343 0.0176 0.74 2.91 5.96 

16 S14 -3 2.19 261 119 0.0998 0.0139 0.99 3.92 8.01 

21 S14 -3 2.48 228 92 0.1248 0.0161 0.79 3.13 6.41 

22 S14 -3 2.12 242 114 0.1113 0.0159 0.89 3.51 7.19 

23 S14 -3 2.85 200 70 0.1623 0.0192 0.61 2.41 4.93 

CAVITY S21 

29 S21 -3 2.78 165 59 0.1944 0.0234 0.35 1.40 2.73 

30 S21 -3 2.81 182 65 0.1768 0.0211 0.38 1.54 3.00 

31 S21 -3 2.81 182 65 0.1769 0.0211 0.38 1.54 3.00 

35 S21 -3 2.43 210 86 0.1343 0.0176 0.51 2.03 3.95 

36 S21 -3 2.37 191 80 0.1506 0.0200 0.45 1.81 3.52 

40 S21 -3 2.19 262 119 0.0998 0.0139 0.68 2.73 5.31 

42 S21 -3 2.85 200 70 0.1623 0.0192 0.42 1.68 3.26 

43 S21 -3 2.86 218 76 0.1502 0.0177 0.45 1.81 3.53 

46 S21 -3 2.48 228 92 0.1248 0.0161 0.55 2.18 4.25 

47 S21 -3 2.12 242 114 0.1114 0.0159 0.61 2.44 4.76 

CAVITY S22 

29 S22 -1 2.78 165 59 0.1944 0.0234 0.38 1.42 4.08 

30 S22 -1 2.81 182 65 0.1768 0.0211 0.42 1.57 4.49 

31 S22 -1 2.81 182 65 0.1769 0.0211 0.42 1.57 4.48 

35 S22 -1 2.43 210 86 0.1343 0.0176 0.55 2.06 5.91 

36 S22 -1 2.37 191 80 0.1506 0.0200 0.49 1.84 5.26 

40 S22 -1 2.19 262 119 0.0998 0.0139 0.74 2.78 7.95 

42 S22 -1 2.85 200 70 0.1623 0.0192 0.46 1.71 4.89 

43 S22 -1 2.86 218 76 0.1502 0.0177 0.49 1.84 5.28 

46 S22 -1 2.48 228 92 0.1248 0.0161 0.59 2.22 6.36 

47 S22 -1 2.12 242 114 0.1114 0.0159 0.66 2.49 7.12 

CAVITY S23 

28 S23 1 2.78 165 59 0.1943 0.0233 0.37 1.43 5.48 

32 S23 1 2.43 210 86 0.1342 0.0176 0.53 2.07 7.93 

34 S23 1 2.43 210 87 0.1341 0.0175 0.53 2.07 7.94 

37 S23 1 2.37 191 80 0.1505 0.0200 0.47 1.85 7.08 

39 S23 1 2.19 261 119 0.0998 0.0139 0.71 2.78 10.67 

41 S23 1 2.85 200 70 0.1623 0.0192 0.44 1.71 6.56 

44 S23 1 2.86 218 76 0.1502 0.0177 0.47 1.85 7.09 

45 S23 1 2.48 228 92 0.1247 0.0161 0.57 2.23 8.54 

48 S23 1 2.12 242 114 0.1114 0.0159 0.64 2.49 9.56 

49 S23 1 2.15 218 101 0.0943 0.0123 0.75 2.95 11.30 
Table 7.- Concluded. 

Run Cavity y, cavity 

(inch) Me Reθ Reθ/Me

δ

(inch) θ (inch) H/δ W/ δ L/ δ

CAVITY S24 

28 S24 3 2.78 165 59 0.1943 0.0233 0.34 1.45 7.00 

32 S24 3 2.43 210 86 0.1342 0.0176 0.50 2.10 10.13 

34 S24 3 2.43 210 87 0.1341 0.0175 0.50 2.10 10.14 

37 S24 3 2.37 191 80 0.1505 0.0200 0.45 1.87 9.03 

39 S24 3 2.19 261 119 0.0998 0.0139 0.67 2.82 13.62 

41 S24 3 2.85 200 70 0.1623 0.0192 0.41 1.74 8.38 

44 S24 3 2.86 218 76 0.1502 0.0177 0.45 1.88 9.05 

45 S24 3 2.48 228 92 0.1247 0.0161 0.54 2.26 10.90 

48 S24 3 2.12 242 114 0.1114 0.0159 0.60 2.53 12.20 

49 S24 3 2.15 218 101 0.0943 0.0123 0.71 2.99 14.43 

Table 8.- Variable uncertainty values. 

Uncertainty Type Bias Uncertainty Precision Uncertainty 

Initial model wall temperature 1.43 oC 1.0 oC 

Model run wall temperature at reference

location 1.93 o

C n/a 

Model run wall temperature 3.36 oC 1.0 oC 

Effective time 0.02 s 0.05 s 

Thermal product, β 5.9% n/a 
Table 9.- Summary Cavity Data.

Run Cavity δ

(inch)

L 

(inch)

H 

(inch) L/δ H/δ L/H

Avg 

Floor 

BF

Max CL 

BF

3 S11 0.2504 0.1500 0.0187 0.599 0.075 8.02 0.652 3.26 

3 S12 0.2504 0.2977 0.0396 1.189 0.158 7.52 0.446 3.00 

4 S13 0.2504 0.5296 0.0662 2.115 0.264 8.00 0.328 3.74 

4 S14 0.2504 0.7578 0.1021 3.026 0.408 7.42 0.248 2.26 

5 S13 0.2245 0.5296 0.0662 2.359 0.295 8.00 0.352 2.13 

5 S14 0.2245 0.7578 0.1021 3.375 0.455 7.42 0.318 2.49 

6 S11 0.2245 0.1500 0.0187 0.668 0.083 8.02 0.720 1.73 

6 S12 0.2245 0.2977 0.0396 1.326 0.176 7.52 0.391 4.59 

9 S11 0.1903 0.1500 0.0187 0.788 0.098 8.02 0.634 1.85 

9 S12 0.1903 0.2977 0.0396 1.564 0.208 7.52 0.421 1.44 

10 S13 0.1903 0.5296 0.0662 2.783 0.348 8.00 0.264 2.03 

10 S14 0.1903 0.7578 0.1021 3.982 0.536 7.42 0.254 2.69 

11 S13 0.1663 0.5296 0.0662 3.185 0.398 8.00 0.269 2.23 

11 S14 0.1663 0.7578 0.1021 4.558 0.614 7.42 0.269 2.41 

12 S11 0.1663 0.1500 0.0187 0.902 0.112 8.02 0.704 1.58 

12 S12 0.1663 0.2977 0.0396 1.791 0.238 7.52 0.415 2.61 

16 S13 0.1220 0.5296 0.0662 4.342 0.543 8.00 0.316 2.10 

16 S14 0.1220 0.7578 0.1021 6.212 0.837 7.42 0.330 2.73 

17 S11 0.1220 0.1500 0.0187 1.230 0.153 8.02 0.664 1.68 

17 S12 0.1220 0.2977 0.0396 2.441 0.325 7.52 0.462 1.59 

19 S11 0.1463 0.1500 0.0187 1.025 0.128 8.02 0.630 1.27 

19 S12 0.1463 0.2977 0.0396 2.035 0.271 7.52 0.469 1.89 

20 S11 0.1501 0.1500 0.0187 1.000 0.125 8.02 0.662 1.19 

20 S12 0.1501 0.2977 0.0396 1.984 0.264 7.52 0.455 1.91 

21 S13 0.1501 0.5296 0.0662 3.529 0.441 8.00 0.272 1.85 

21 S14 0.1501 0.7578 0.1021 5.050 0.680 7.42 0.239 2.09 

22 S13 0.1463 0.5296 0.0662 3.620 0.453 8.00 0.321 2.08 

22 S14 0.1463 0.7578 0.1021 5.180 0.698 7.42 0.269 2.49 

23 S13 0.2009 0.5296 0.0662 2.636 0.329 8.00 0.247 2.54 

23 S14 0.2009 0.7578 0.1021 3.771 0.508 7.42 0.198 2.25 

24 S11 0.2009 0.1500 0.0187 0.747 0.093 8.02 0.711 2.05 

24 S12 0.2009 0.2977 0.0396 1.482 0.197 7.52 0.410 2.62 

25 S11 0.2009 0.1500 0.0187 0.747 0.093 8.02 0.689 2.51 

25 S12 0.2009 0.2977 0.0396 1.482 0.197 7.52 0.434 3.31 
Table 9.- Concluded.

Run Cavity δ

(inch)

L 

(inch)

H 

(inch) L/δ H/δ L/H

Avg 

Floor 

BF

Max CL 

BF

28 S23 0.2504 1.0616 0.0676 4.239 0.270 15.70 0.415 2.35 

28 S24 0.2504 1.3277 0.0670 5.302 0.268 19.82 0.521 2.29 

29 S21 0.2504 0.5246 0.0666 2.095 0.266 7.88 0.342 2.00 

29 S22 0.2504 0.7971 0.0652 3.183 0.260 12.23 0.397 2.08 

31 S21 0.2245 0.5246 0.0666 2.336 0.297 7.88 0.255 2.14 

31 S22 0.2245 0.7971 0.0652 3.550 0.290 12.23 0.328 2.67 

32 S23 0.2245 1.0616 0.0676 4.728 0.301 15.70 0.440 2.73 

32 S24 0.2245 1.3277 0.0670 5.913 0.298 19.82 0.546 2.45 

34 S23 0.1663 1.0616 0.0676 6.385 0.407 15.70 0.486 3.23 

34 S24 0.1663 1.3277 0.0670 7.986 0.403 19.82 0.553 4.43 

35 S21 0.1663 0.5246 0.0666 3.155 0.401 7.88 0.275 2.34 

35 S22 0.1663 0.7971 0.0652 4.794 0.392 12.23 0.275 2.08 

36 S21 0.1903 0.5246 0.0666 2.756 0.350 7.88 0.301 2.04 

36 S22 0.1903 0.7971 0.0652 4.188 0.343 12.23 0.320 2.05 

37 S23 0.1903 1.0616 0.0676 5.578 0.355 15.70 0.343 2.92 

37 S24 0.1903 1.3277 0.0670 6.976 0.352 19.82 0.552 4.36 

39 S23 0.1220 1.0616 0.0676 8.703 0.554 15.70 0.345 2.26 

39 S24 0.1220 1.3277 0.0670 10.885 0.549 19.82 0.501 3.50 

40 S21 0.1220 0.5246 0.0666 4.301 0.546 7.88 0.301 2.20 

40 S22 0.1220 0.7971 0.0652 6.535 0.535 12.23 0.342 2.34 

41 S23 0.2009 1.0616 0.0676 5.283 0.336 15.70 0.349 2.33 

41 S24 0.2009 1.3277 0.0670 6.608 0.333 19.82 0.525 2.58 

42 S21 0.2009 0.5246 0.0666 2.611 0.331 7.88 0.288 2.62 

42 S22 0.2009 0.7971 0.0652 3.967 0.324 12.23 0.267 2.08 

43 S21 0.1854 0.5246 0.0666 2.830 0.359 7.88 0.302 2.44 

43 S22 0.1854 0.7971 0.0652 4.300 0.352 12.23 0.284 2.28 

45 S23 0.1501 1.0616 0.0676 7.075 0.450 15.70 0.305 2.19 

45 S24 0.1501 1.3277 0.0670 8.848 0.446 19.82 0.502 4.64 

46 S21 0.1501 0.5246 0.0666 3.496 0.444 7.88 0.270 2.14 

46 S22 0.1501 0.7971 0.0652 5.312 0.434 12.23 0.282 2.12 

47 S21 0.1463 0.5246 0.0666 3.586 0.455 7.88 0.291 2.22 

47 S22 0.1463 0.7971 0.0652 5.449 0.446 12.23 0.363 2.90 

48 S23 0.1463 1.0616 0.0676 7.257 0.462 15.70 0.488 3.59 

48 S24 0.1463 1.3277 0.0670 9.076 0.458 19.82 0.580 3.67 

49 S23 0.1854 1.0616 0.0676 5.727 0.365 15.70 0.346 2.49 

49 S24 0.1854 1.3277 0.0670 7.162 0.361 19.82 0.523 2.85 
Figures 

Figure 1.- Cavity flow regimes. 

Figure 2.- Schematic of model mounting. 
Figure 3.- Representative flat plate surface flow properties. Re=1x106

 per foot. 

Figure 4.- Flat plate performance chart. 
a) Shallow Cavity Model M1: Depth Variation. 

b) Shallow Cavity Model M2: Length Variation. 

Figure 5.- Schematic of cavity locations. Design W/H=3.6. All dimensions are in inches. Filled 

cavity is common to both models. 

Figure 6.-Test model installed in 31-Inch Mach 10 Tunnel with TGP lighting and camera system. 
a) Test 406 Run 68. 

Figure 7.- Baseline Bump Factor Images. 

b) Test 406 Run 69. 

Figure 7.- Continued. 
c) Test 406 Run 70. 

Figure 7.- Continued.

d) Test 406 Run 71. 

Figure 7.- Continued. 
e) Test 406 Run 72. 

Figure 7.- Continued.

f) Test 406 Run 73. 

Figure 7.- Continued. 
g) Test 406 Run 74. 

Figure 7.- Continued.

h) Test 406 Run 75. 

Figure 7.- Concluded. 
a) Test 404 Run 02 −− M∞=9.7, α=-7.77°

, Re∞=0.92x10

6

/ft. 

Figure 8.- Global heating images of Cavity Model 1. 

b) Test 404 Run 07 −− M∞=9.7, α=-7.20°, Re∞=1.19x10

6

/ft. 

Figure 8.- Continued. 
c) Test 404 Run 08 −− M∞=9.5, α=-14.18°

, Re∞=0.80x10

6

/ft. 

Figure 8.- Continued. 

d) Test 404 Run 13 −− M∞=9.7, α=-12.39°, Re∞=1.24x10

6

/ft. 

Figure 8.- Continued. 
e) Test 404 Run 14 −− M∞ =9.8, α=-15.57°

, Re∞=1.73x10

6

/ft. 

Figure 8.- Continued.

f) Test 404 Run 15 −− M∞ =9.8, α=-15.57°, Re∞ =1.77x10

6

/ft. 

Figure 8.-Concluded. 
a) Test 404 Run 27 −− M∞=9.6, α =-7.77°

, Re∞=0.92x10

6

/ft. 

Figure 9.- Global heating images of Cavity Model 2.

b) Test 404 Run 33 −− M∞ =9.7, α=-12.39°, Re∞ =1.25x10

6

/ft. 

Figure 9.- Continued. 
c) Test 404 Run 38 −− M∞=9.8, α=-15.57°

, Re∞=1.74x10

6

/ft. 

Figure 9.-Concluded.
a) Test 404 Run 03 - H/δ=0.093. 

Figure 10.- Bump factor distributions for Cavity S11 - 

L/H=6.6, W/H=3.33. 

b) Test 404 Run 06 -H/δ=0.102. 

Figure 10.- Continued. 
c) Test 404 Run 09 - H/δ=0.120. 

Figure 10.- Continued.

d) Test 404 Run 17 -H/δ=0.180. 

Figure 10.- Continued. 
e) Test 404 Run 20 - H/δ=0.144. 

Figure 10.- Continued.

f) Test 404 Run 24 - H/δ=0.111. 

Figure 10.- Continued. 
g) Test 404 Run 25 -H/δ=0.111. 

Figure 10.- Concluded.

a) Test 404 Run 03 - H/δ=0.185. 

Figure 11.- Bump Factor images for Cavity S12 - 

L/H=9.3, W/H=4.58. 
b) Test 404 Run 06 -H/δ=0.204. 

Figure 11.- Continued.

c) Test 404 Run 09 - H/δ=0.239. 

Figure 11.- Continued.
d) Test 404 Run 17 -H/δ=0.360. 

Figure 11.- Continued.

e) Test 404 Run 20 - H/δ=0.289. 

Figure 11.- Continued.
f) Test 404 Run 24 - H/δ=0.222. 

Figure 11.- Continued.

g) Test 404 Run 25 - H/δ=0.222. 

Figure 11.- Concluded.
a) Test 404 Run 04 - H/δ=0.324. 

Figure 12.- Bump Factor images for Cavity S13 - 

L/H=8.7, W/H=4.29. 

b) Test 404 Run 05 - H/δ=0.356. 

Figure 12.- Continued.
c) Test 404 Run 10 - H/δ=0.419. 

Figure 12.- Continued.

d) Test 404 Run 11 - H/δ=0.419. 

Figure 12.- Continued.
e) Test 404 Run 16 - H/δ=0.631. 

Figure 12.- Continued. 

f) Test 404 Run 21 - H/δ=0.505. 

Figure 12.- Continued.
g) Test 404 Run 22 - H/δ=0.566. 

Figure 12.- Continued. 

h) Test 404 Run 23 - H/δ=0.388. 

Figure 12.- Concluded. 
a) Test 404 Run 04 - H/δ=0.324. 

Figure 13.- Bump Factor images for Cavity S14 - 

L/H=8.1, W/H=3.95. 

b) Test 404 Run 05 - H/δ=0.356. 

Figure 13.- Continued. 
c) Test 404 Run 10 - H/δ=0.658. 

Figure 13.- Continued. 

d) Test 404 Run 11 -H/δ=0.737. 

Figure 13.- Continued.
e) Test 404 Run 16 - H/δ=0.992. 

Figure 13.- Continued.

f) Test 404 Run 21 - H/δ=0.794. 

Figure 13.- Continued.
g) Test 404 Run 22 - H/δ=0.889. 

Figure 13.- Continued.

h) Test 404 Run 23 - H/δ=0.610. 

Figure 13.- Concluded.
a) Test 404 Run 29 - H/δ=0.350. 

Figure 14.- Bump Factor images for Cavity S21 - 

L/H=10.7, W/H=4.0. 

b) Test 404 Run 31 - H/δ=0.384. 

Figure 14.- Continued.
c) Test 404 Run 35 - H/δ=0.506. 

Figure 14.- Continued. 

d) Test 404 Run 36 - H/δ=0.451. 

Figure 14.- Continued.
e) Test 404 Run 40 - H/δ=0.682. 

Figure 14.- Continued.

f) Test 404 Run 42 - H/δ=0.419. 

Figure 14.- Continued.
g) Test 404 Run 43 - H/δ=0.453. 

Figure 14.- Continued.

h) Test 404 Run 46 - H/δ=0.545. 

Figure 14.- Continued.
i) Test 404 Run 47 - H/δ=0.610. 

Figure 14.- Concluded.

a) Test 404 Run 29 - H/δ=0.381. 

Figure 15.- Bump Factor images for Cavity S22 - 

L/H=10.7, W/H=3.74. 
b) Test 404 Run 31 -H/δ=0.418. 

Figure 15.- Continued.

c) Test 404 Run 35 - H/δ=0.551. 

Figure 15.- Continued.
d) Test 404 Run 36 - H/δ=0.491. 

Figure 15.- Continued. 

e) Test 404 Run 40 - H/δ=0.742. 

Figure 15.- Continued.
f) Test 404 Run 42 - H/δ=0.456. 

Figure 15.- Continued. 

g) Test 404 Run 43 - H/δ=0.493. 

Figure 15.- Continued.
h) Test 404 Run 46 - H/δ=0.593. 

Figure 15.- Continued.

i) Test 404 Run 47 - H/δ=0.664. 

Figure 15.- Concluded.
a) Test 404 Run 28 - H/δ=0.365. 

Figure 16.- Bump Factor images for Cavity S23 - 

L/H=15.0, W/H=3.92. 

b) Test 404 Run 32 - H/δ=0.529. 

Figure 16.- Continued.
c) Test 404 Run 37 - H/δ=0.472. 

Figure 16.- Continued. 

d) Test 404 Run 39 - H/δ=0.711. 

Figure 16.- Continued.
e) Test 404 Run 41 - H/δ=0.437. 

Figure 16.- Continued. 

f) Test 404 Run 45 - H/δ=0.569. 

Figure 16.- Continued.
g) Test 404 Run 49 - H/δ=0.753.

Figure 16.- Concluded.

a) Test 404 Run 28 - H/δ=0.345. 

Figure 17.- Bump Factor images for Cavity S24 - 

L/H=20.3, W/H=4.21. 
b) Test 404 Run 32 - H/δ=0.298. 

Figure 17.- Continued. 

c) Test 404 Run 34 - H/δ=0.403. 

Figure 17.- Continued.
d) Test 404 Run 37 – H/δ=0.472. 

Figure 17.- Continued. 

e) Test 404 Run 39 - H/δ=0.671. 

Figure 17.- Continued.
f) Test 404 Run 41 - H/δ=0.413. 

Figure 17.- Continued. 

g) Test 404 Run 45 - H/δ=0.537. 

Figure 17.- Continued.
h) Test 404 Run 48 - H/δ=0.458. 

Figure 17.- Continued.

i) Test 404 Run 49 - H/δ=0.711. 

Figure 17.- Concluded.
a) Bias uncertainties (% Uncertainty/100). 

b) Total uncertainties (% Uncertainty/100). 

Figure 18.- Bump Factor uncertainties for Cavity S12 - Run 03 -

L/H=9.3, W/H=4.58, H/δ=0.185. 
a) Bias uncertainties (% Uncertainty/100). 

b) Total uncertainties (% Uncertainty/100). 

Figure 19.- Bump Factor uncertainties for cavity S14 - Run 16 -

L/H=8.1, W/H=3.95, H/δ=0.992.
a) Bias uncertainties (% Uncertainty/100). 

b) Total uncertainties (% Uncertainty/100). 

Figure 20.- Bump Factor uncertainties for cavity S24 - Run 28 -

L/H=20.3, W/H=4.21, H/δ=0.345.
a) Open Cavities - Depth Effect. 

b) Closed Cavities - Length Effect. 

Figure 21.- Variation of Average Bump Factor on cavity floor with H/δ. 
Figure 22.- Variation of Average Bump Factor on cavity floor with L/δ. 

Figure 23.- Variation of maximum centerline endwall Bump Factor with H/δ. 
Figure 24.- Variation of maximum centerline endwall Bump Factor with L/δ. 
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Aero-Heating of Shallow Cavities in Hypersonic Freestream Flow

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Everhart, Joel L.; Berger, Karen T.; Merski, N. Ronald, Jr.; Wood, 

William A.; Hollingsworth, Kevin E.; Hyatt, Andrew J.; Prabhu, Ramadas 

K.

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The purpose of these experiments and analysis was to augment the heating database and tools used for assessment of 

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depth on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally 

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