NASA/TM–2009–215949

Turbulent Wing-Leading-Edge

Correlation Assessment for the

Shuttle Orbiter

Rudolph A. King and Matthew P. Vaughan

Langley Research Center, Hampton, Virginia

December 2009
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NASA/TM–2009–215949

Turbulent Wing-Leading-Edge

Correlation Assessment for the

Shuttle Orbiter

Rudolph A. King and Matthew P. Vaughan

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

December 2009
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Available from:

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443-757-5802
Abstract

This study was conducted in support of the Orbiter damage assessment activity that takes

place for each Shuttle mission since STS-107 (STS - Space Transportation System). As part

of the damage assessment activity, the state of boundary layer (laminar or turbulent) during

reentry needs to be estimated in order to define the aerothermal environment on the Orbiter.

Premature turbulence on the wing leading edge (WLE) is possible if a surface irregularity

promotes early transition and the resulting turbulent wedge flow contaminates the WLE

flow. The objective of this analysis is to develop a criterion to determine if and when the

flow along the WLE experiences turbulent heating given an incoming turbulent boundary

layer that contaminates the attachment line. The data to be analyzed were all obtained as

part of the MH-13 Space Shuttle Orbiter Aerothermodynamic Test conducted on a 1.8%-

scale Orbiter model at Calspan/University of Buffalo Research Center in the Large Energy

National Shock Tunnels facility. A rational framework was used to develop a means to assess

the state of the WLE flow on the Orbiter during reentry given a contaminated attachmentline flow. Evidence of turbulent flow on the WLE has been recently documented for a few

STS missions during the Orbiter’s flight history, albeit late in the reentry trajectory. The

criterion developed herein will be compared to these flight results.
Contents

1 Introduction 3

2 Overview of MH-13 WLE Data 3

3 Analysis Approach 4

4 MH-13 Correlation Results 5

5 Review of Flight Results 6

6 Conclusions 7

References 8

APPENDIX: NASA Internal Document A-1
1 Introduction

This document addresses the issue of turbulent heating on the wing leading edge (WLE) of

the Shuttle Orbiter and was requested by the Entry Aeroheating Working Group in support

of the Orbiter damage assessment activity. For the purpose of clearing the Orbiter’s thermal

protection system for safe reentry, the established baseline procedure used by the Data

Assessment Team for assessing the state of the flow on the WLE is the same as that used

for the windward surface, which incorporates the boundary layer transition (BLT) and wedge

tools. Further details of the Shuttle Program approved BLT Tool V.2 and wedge tool are

discussed in Refs. [1,2] and Ref. [3], respectively. This process for predicting WLE turbulence

on the Orbiter may be overly conservative and is the focus of this document. Turbulence

on the WLE is possible if a cavity or protruding gap filler promotes early transition and the

resulting turbulent wedge flow contaminates the flow in the WLE region. To the authors’

knowledge, there is no definitive evidence of turbulent flow in the WLE region of the Orbiter

throughout its flight history early in the reentry trajectory. A recent review of the flight

data [4] indicates that turbulent heating on the WLE may be occurring late in the trajectory

(Mach numbers less than 14). The intent here is not to develop a correlation to predict the

onset of WLE transition to turbulence. The objective of this analysis is to develop a criterion

to determine if and when the flow along the WLE experiences turbulent heating given an

incoming turbulent boundary layer that contaminates the attachment line. The data to be

analyzed were all obtained as part of the MH-13 Space Shuttle Orbiter Aerothermodynamic

Test conducted at Calspan/University of Buffalo Research Center (CUBRC) in the Large

Energy National Shock Tunnel facility (LENS). Refer to the test report [5] for details of

the MH-13 test program and results. Laminar and turbulent boundary layer flow states on

the Orbiter model were inferred from heat flux measurements. Based on observations made

during the test program, it was the first author’s belief that the flow divergence along the

attachment line was, at least partially, responsible for what appears to be a relaxation of

the flow back to the laminar heating values along the WLE, i.e., the flow conditions at the

attachment line did not enable self-sustained turbulence.

2 Overview of MH-13 WLE Data

The data used in this analysis were all acquired in the CUBRC LENS-I Shock Tunnel

during the MH-13 test program [5, 6]. The highly instrumented 1.8%-scale Orbiter model

(Lre f = 23.04 inch – distance from nose to body-flap hinge) was tested at conditions similar

to reentry flight conditions (no high temperature effects). Figure 1 shows a schematic

of the sensor layout on the model. The sensors of primary focus for this portion of the

test program are the leading-edge heat transfer gauges on the port side of model. The

gauges were installed on pyrex inserts (labeled as sections A – M) where detail layouts are

given on the lower left corner of the figure. Diamond-shaped boundary layer trips were

placed at upstream locations on the model and tested at flow conditions such that the flow

transitioned from a laminar state to a turbulent state immediately downstream of the trips.

Some configurations included a series of staggered trips on either the centerline (CL) region,

the attachment-line (AL) region, or both regions on the model. A list of the set of runs

and conditions used in this analysis for the test cases conducted with boundary layer trips

to evaluate the WLE heating is provided in Table 1 (for a complete list see Ref. [5]). The

numbers in columns CL and AL in the table represent the number of trips used in a staggered

arrangement. As an example, a photograph of the model with the trip configuration for run

78 is shown in Figure 2. All conditions analyzed in this report were conducted at zero yaw

and 40° angle of attack. Spreading of the turbulent boundary layer flow ensued downstream

of the trip on the windward acreage surface and eventually contaminated the attachment-
line regions. A necessary condition here for turbulent WLE heating is the ability of the

attachment-line flow to maintain turbulence as the flow diverges along the WLE. The data

demonstrated that the state of the boundary layer on the WLE not only depends on the

state of the incoming boundary layer flow but on the tunnel flow conditions. In some cases

with the same trip configurations and an incoming turbulent boundary layer, the WLE flow

was laminar and under other tunnel conditions it was turbulent. The data suggested that

the state of the WLE boundary layer has at least a Reynolds number dependence.

3 Analysis Approach

The analysis looks at several parameters with the main emphasis being on the attachmentline Reynolds number as developed by Poll [7]. For incompressible flow, Poll defined the

attachment-line Reynolds number R as

R = uerl/νe . (1)

Here, ue is the spanwise boundary layer edge velocity along the attachment line and νe the

kinematic viscosity at the boundary layer edge. The local length scale rl is defined as

^ 1/2

νe

rl =(2) (dve /dy) y=0

where (dve/dy)y=0 is the velocity gradient normal to the attachment line evaluated at the

edge of the attachment-line boundary layer, y = 0. A sketch depicting the attachment-line

flow, coordinate system, and relevant parameters along the leading edge of a long swept

wing is given in Figure 3. This sketch represents a classical attachment-line flow for an

essentially zero angle-of-attack configuration where the attachment line coincides with the

WLE. All parameters in Eqs. 1 and 2 are local to Figure 3. Poll demonstrated that at

relatively low values of R with incoming turbulence, the turbulent bursts decay rapidly

as the flow is convected in the spanwise direction. It becomes necessary to increase the

freestream Reynolds number to move the front (upstream of which turbulent bursts exist) to greater spanwise distances. The need to increase the freestream Reynolds number

ends dramatically when R approaches 245, as this is the critical Reynolds number beyond

which the turbulence is self-sustaining. Poll [8] later proposed that this incompressible criterion be applied to compressible flow with the use of a reference temperature given by

T. = Te + 0. 1(T,,, — Te ) + 0.6(TT — Te ) where Te , T,,, , and TT are the boundary layer edge

temperature, wall temperature, and recovery temperature, respectively. The compressible

form of the attachment-line Reynolds number is denoted as R* . Poll [9] suggested a critical

Reynolds number of R. = 245 f 35 beyond which the burst of turbulence is self-sustaining.

Poll’s criterion was later validated by Benard et al. [10] for attachment-line transition induced by gross disturbances at Me = 3. 28 in a low enthalpy hypersonic wind tunnel. Poll

demonstrated this criterion for edge Mach numbers up to Me = 6, which is well beyond the

Me values for the LENS data used in this study ( Me < 2 . 5) and Me values experienced by

the Orbiter during reentry.

Estimates of the attachment-line Reynolds numbers, R and R. were computed using

the existing LENS database for the test conditions given in Table 1. Tecplot ® and a

NASA-developed program that interpolated boundary layer edge conditions were the tools

used to estimate these Reynolds numbers. Details of the calculation approach are given

in a NASA internal document 1 which is included in the appendix of this document for

completeness. The Reynolds numbers were computed corresponding to the sensor locations

'Vaughan, M. P., Mazaheri, A., and Wood, W. A., “Calculating Similarity Parameters to Predict Boundary Layer Transition on the Space Shuttle Orbiter,” August 7, 2008.

4
given in Table 2. The locations X, Y, and Z are in the Orbiter coordinate system and

are consistent with coordinates given in Figure 1 ( X - streamwise distance with origin

upstream of Orbiter nose, Y - spanwise distance from plane of symmetry, and Z - wallnormal distance). Note that for simplicity the Reynolds numbers were not computed for

every insert (i.e., sections A, B, C – M) but were computed at every other sensor to include

the full spatial extent of the insert locations. R and R. were computed on the attachment

line so it was necessary to project a streamline from the attachment line to each sensor

location provided in the table. A plot depicting the computed attachment lines for the

three nominal Mach numbers tested relative to the desired sensor locations (see Table 2)

is shown in Figure 4. A detail view of section A is also included in the figure to give

additional perspective. The coordinates x and y are measured from the nose and centerline,

respectively. Note that the attachment-line locations in the region of interest are insensitive

to freestream Mach number for the range of Mach numbers tested. Also, note the location

of the attachment line relative to the WLE at 40 ° angle of attack in comparison to Figure 3.

For section A, the sensor depicted in the figure just outboard of the attachment line is sensor

102 (attachment line located between sensors 102 and 103).

4 MH-13 Correlation Results

Plots of normalized heat flux, St • RenLref, versus the zwle were plotted for all three nominal

Mach numbers, M = 10, 14 and 16, at each insert section. For the normalized heat flux,

St is the Stanton number and ReLre f is the freestream length Reynolds number. Following

the scaling analogy for boundary layers on flat plates, the exponents n = 1/2 and n = 1/5

are for laminar and turbulent scaling, respectively (see for example Ref. [11]). The abscissa

is defined as zwle = (Z — Zwle )/Lre f; consequently, zwle < 0 represents locations on the

lower surface, zwle > 0 on the upper surface and zwle = 0 on the WLE of the Orbiter. As a

demonstration example, Mach 10 data for a range of Reynolds numbers, with and without

trips, are presented for insert section E in Figures 5 and 6 corresponding to laminar and

turbulent scaling. As expected, in both figures the heating is higher on the lower surface

with peak heating occurring just two to three sensor locations below the WLE ( zwle = 0). In

Figure 5 with the laminar scaling, there is data collapse of the normalized heat flux between

runs 71 and 74 (laminar baseline runs with smooth OML - outer mold line) and run 30 (run

with effective boundary layer trips), except for the few inboard sensors on the windward

surface. This suggests laminar WLE heating for run 30 even with an incoming turbulent

boundary layer on the windward acreage. Note that the normalized heat fluxes for all runs

tend to collapse with the laminar baselines on the upper leeward surface (this is consistent

for all Mach numbers tested) indicating laminar flow on the leeward side. Similarly for

Figure 6 with the turbulent scaling, the data of the normalized heat flux for runs 35, 79, and

81 (runs with effective boundary layer trips) and run 132 (high Reynolds number turbulent

baseline run with smooth OML) tend to collapse indicating a turbulent WLE. This process

of plotting the laminar and turbulent normalized heat flux for each insert section (A –

M) and for all Mach numbers tested was conducted to evaluate the state of the boundary

layer near the WLE region. It is important to note that the interpretation of the state of

the attachment-line boundary layer is based on the laminar versus non-laminar/turbulent

normalized heat transfer data near the attachment-line region and not over the entire insert.

A more complete set of plots can be found in Section 4.2 of Ref. [5] (i.e., Figures 121 - 145).

All the data to be presented from this point forward are for test cases with effective

boundary layer trips as listed in Table 1. Values of the attachment-line Reynolds number R

are plotted versus x/Lref values along the attachment line in Figure 7 for the three Mach

numbers tested. The open symbols in all subsequent plots represent predominantly laminar

heating in the WLE region. Similarly, the filled symbols represent predominantly turbulent

5
(or non-laminar) heating in the WLE region. There is some variation in the R values with

streamwise location as seen in Figure 7. A simple arithmetic mean of the attachment-line

Reynolds number, < R >, for the eight locations in Table 2 is computed for each run and a

similar plot is presented in Figure 8. The uncertainty of the threshold value is large due to

the limited number of freestream unit Reynolds numbers tested during the WLE turbulent

heating phase of the test program. From this sparse set of data, run 30 at M = 10 provides

an R value where the flow over the WLE had predominantly laminar heating values, i.e., the

WLE flow reverted to laminar flow. Conversely, run 126 at M = 14 provides a value of R

where the WLE flow remained predominantly turbulent. It should be noted that the Mach

14 data, runs 78 and 126, are predominantly turbulent in the WLE region but clearly show

evidence of relaxing to laminar heating levels downstream of insert section I. At Mach 10, run

35 demonstrated turbulent flow (or at least non-laminar heating) along the entire measured

WLE region (sections A – M). These figures suggest that a threshold value for self-sustaining

turbulence on the Orbiter exists somewhere in the range of 261 < R < 291 (values from runs

78 and 35, respectively) assuming no Mach number dependence [9] for the current Me range.

Similarly, to account for compressibility, plots of the attachment-line Reynolds number R.

evaluated at the reference temperature T. are presented in Figures 9 and 10. These figures

indicate a threshold value exists somewhere in the range of 211 < R. < 232. Remarkably,

this Orbiter threshold value is within the range reported by Poll [8] of R. = 245 f 35

(210 < R. < 280). Based on the limited sub-scale Orbiter data, the results suggest that

Poll’s R. formulation may be a viable approach to assess the state of the flow in the WLE

region. However, conservatism needs to be built in to the threshold value of R. ,: 245 as

this represents a Reynolds number that enables self-sustained turbulence. That is, limited

runs of turbulent flow along the WLE can exists for values of R. < 245 that can expose

portions of the WLE to significantly higher heating levels.

Because of the added complexity in computing the R and R., is it possible to correlate

with a parameter already available in the wind-tunnel and flight tools? It can be shown that

R. is related to the momentum thickness Reynolds number RB , which is readily available.

Figures 11 and 12 show plots of RB and < RB >, respectively, along the attachment line.

These figures suggest that a threshold value exists somewhere in the range of 120 < RB <

133. Similarly, plots of the version 1 BLT parameter [12], RB /Me , are presented in Figures 13

and 14. These figures suggest that a threshold value exists somewhere in the range of

61 < RB /Me < 69. The relationship between the parameters R. and RB is clearly geometry

specific and depends on how the length scales η and θ are connected. Clearly, more Orbiterspecific data are necessary to evaluate this RB approach, particularly any historical flight

data.

5 Review of Flight Results

As a result of the findings in this study, the Entry Aeroheating Working Group requested a

review of the historical Orbiter flight data to evaluate if any evidence of non-laminar/turbulent

heating on the WLE has been experienced during reentry by the Shuttle Orbiter [4]. To

recap Ref. [4], a limited set of WLE heating measurements has been obtained on past STS

missions. These flights were limited to OV-102 (Columbia) and OV-103 (Discovery) vehicles which were instrumented with a radiometer embedded in panel 9 (near the location of

maximum WLE heating) of the RCC (reinforced carbon-carbon) panels on the port wing.

The study also corroborated measurements of thermocouple data on the windward surface

in the vicinity (both upstream and downstream) of the port wing and post flight reports to

identify if earlier-than-nominal transition occurred on the windward acreage that eventually

contaminated the WLE region. For flights that satisfied those conditions, the transition onset times from entry interface (EI) based on abrupt increases in radiometry measurements
attributed to laminar-to-turbulent transition were documented and R. values computed (see

Ref. [13] for computation details).

Three missions were identified in the report, STS-48, STS-56, and STS-102 (all on OV103). As a baseline configuration with nominal reentry transition, the results for STS-114

was also documented in the report. The results are succinctly summarized in Table 3. For

the three flight cases documented in the table with earlier-than-nominal transition, turbulent

heating on the Orbiter was observed at R. values (283 < R. < 401) larger than for Poll’s

criterion (R. = 245 ± 35) and the analysis presented herein (211 < R. < 232). No historical

Orbiter flight cases have been identified where transition occurred very early in the reentry

trajectory such that computed R. values are less then 245 as a means to anchor a threshold

value with historical flight data.

6 Conclusions

The objective of this analysis was to develop a criterion to determine if and when the flow

along the WLE experiences turbulent heating given that an incoming turbulent boundary

layer contaminates the attachment line. The data analyzed were all obtained in the LENS

facility. It is believed that the R. framework is a promising/workable approach to this

problem as it is well documented in the literature. In this framework, one may need to

assess how to compute a reference temperature T. for non-equilibrium reacting-flow with

species for actual flight conditions. A process was developed in Ref. [13] to evaluate R. on

the Orbiter WLE using existing reacting-flow CFD simulations. Concerns and questions

raised by a peer-review panel about the procedure used to compute R. are addressed in

Ref. [14]. The recent review of turbulent WLE heating experienced in flight at earlier-thannominal Orbiter transition indicates turbulent heating for R. > 283, consistent with the

findings in this report. An alternative RB framework was presented that does not necessitate

the need to recompute any new parameters. Additional data are strongly recommended

before adopting this RB framework and, if possible, any future WLE turbulence data must

be acquired at more refined unit freestream Reynolds number increments to reduce the

threshold uncertainties. Any additional high-Mach-number flight data, where the WLE

was contaminated with incoming turbulence from the windward surface, will be greatly

instrumental in validating the R. criterion which was formulated on ground-based data.

7
References

1. King, R. A., Kegerise, M. A., and Berry, S. A., “Version 2 of the Protuberance

Correlations for the Shuttle-Orbiter Boundary Layer Transition Tool,” NASA

TP-2009-215951, December 2009.

2. Kegerise, M. A., King, R. A., and Berry, S. A., “Development of Cavity Induced

Boundary-Layer Transition Correlations for Version 2.0 of the BLT Tool,” Engineering Note EG-SS-07-05, NASA Johnson Space Center, March 2007.

3. McGinley, C. B, Berry, S. A., Kinder, G. R., Barnwell, M., Wang, K. C., and

Kirk, S. K., “Review of Orbiter Flight Boundary Layer Transition Data,” AIAA

Paper 2006-2921, June 2006.

4. Berger, K. T., “Space Shuttle Wing-Leading-Edge Flight Data,” Engineering

Note EG-SS-09-04, NASA Johnson Space Center, July 2009.

5. Cassady, A. M., Bourland, G., King, R., Kegerise, M., Marichalar, J., Kirk, B.

S., and Trevino, L., “MH-13 Entry II: Space Shuttle Orbiter Aerothermodynamic  ̃

Test Report,” NASA TP-2007-214758, July 2007.

6. Wadhams, T. P., Smolinski, G. J., Holden, M. S., and MacLean, M. G., “Experimental Space Shuttle Orbiter Studies to Acquire Data for Code and Flight

Heating Model Validation,” AIAA Paper 2007-551, January 2007.

7. Poll, D. I. A, “Transition in the infinite swept attachment line boundary layer,”

Aero Quarterly, Vol. 30, pp. 607-629, 1979.

8. Poll, D. I. A, “The development of intermittent turbulence on a swept attachment

line including the effects of compressibility,” Aero Quarterly, Vol. 34, pp. 1-23,

1983.

9. Poll, D. I. A, “Boundary Layer Transition on the Windward Face of Space Shuttle

During Re-Entry,” AIAA Paper 85-0899, June 1985.

10. Benard, E., Gaillard, L., and Roquefort, A. D., “Influence of roughness on attachment line boundary layer transition in hypersonic flow,” Experiments in Fluids,

Vol. 22, pp. 286-291, 1997.

11. Kays, W. M., and Crawford, M. E., “Convective Heat and Mass Transfer,” 2nd

ed., McGraw-Hill, New York, 1980.

12. Berry, S. A., Horvath, T.J., Greene, F. A., Kinder, G. R., and Wang, K. C.,

“Overview of Boundary Layer Transition Research in Support of Orbiter Return

To Flight,” AIAA Paper 2006-2918, June 2006.

13. Padilla, Jose F., and Wood, William A., “Calculation of Attachment Line

Reynolds Number from Orbiter CFD Solution,” NASA/TM 2009-215762, June

2009.

14. Wood, William A., “R-bar-star peer-review follow-up on calculation procedure,”

Engineering Note EG-SS-09-05, NASA Johnson Space Center, June 2009.

8
Table 1. MH-13 test conditions analyzed in this note with upstream diamond-shaped trips

to induce turbulent WLE heating (CL - centerline and AL - attachment line).

Run

No.

Nominal

M

Re/ ft

10- 6

Trips & Locations

x/LTef CL* AL*

30 10 1.44 0.5 1 4 @ ea.

35 10 3.33 0.5 1 4 @ ea.

81 10 4.11 0.2 7 0 @ ea.

126 14 3.06 0.1 5 0 @ ea.

78 14 3.17 0.2 7 0 @ ea.

48 16 0.78 0.1 5 0 @ ea.

* Multiple trips attached in a staggered arrangement.

Table 2. Locations on MH-13 Shuttle Orbiter model used to compute relevant flow parameters.

Section Sensor No. X (inch)* Y (inch)* Z (inch)* x/LTef y/LTef

A 102 19.125 -4.099 5.254 0.6459 -0.1779

C 130 19.381 -4.324 5.271 0.6570 -0.1877

E 158 19.618 -4.557 5.285 0.6673 -0.1978

G 166 19.855 -4.796 5.299 0.6776 -0.2082

I 214 20.093 -5.034 5.312 0.6879 -0.2185

K 242 20.332 -5.274 5.326 0.6983 -0.2289

L 256 20.452 -5.395 5.333 0.7035 -0.2342

M 273 21.801 -6.738 5.396 0.7620 -0.2924

*Locations for sensors adjacent to WLE sensors on windward surface.

Table 3. Summary of flight cases from Ref. [4].

Flight Vehicle Port Thermocouple BLT Radiometer

EI Time (sec)

R*

EI Times (sec) Mach Number

STS-48 OV-103 1005 13.7 1020 283

STS-56 OV-103 1125-1225 10.2-7.5 1250 401

STS-102 OV-103 1065-1075 12.7-12.4 1080 307

STS-114* OV-103 1230-1269 7.9-7.0 1275 431

* Flight with nominal transition.
10
Figuree2. 1 Tripr configuration for t

runa78 where sevene large diamond-shaped ttrips swere in a

staggered arrangement around the model centerline at x/Lre f

. = 0.2.

11
Figure 3. A classic sketch of flow near the attachment line of an infinitely swept wing at

zero angle of attack.

AL @ Mach 10

AL @ Mach 14

0.5

• Sensor Locations

AL @ Mach 16

97

Leeward side 1 99

99

0.4 199 01 (LEADING EDGE)

02

0a

Windward side 10 1oa

0a 105

109 105

0.3 110

SECT: A

(19.115 X,-4.107 Y, 5.290 Z) /•

0.2

0.1

0

0.5 0.6 0.7 0.8 0.9 1.1

x/Lref

Figure 4. Sketch showing heat flux sensors (sensors adjacent to leading-edge sensors on the

windward surface) relative to the attachment lines with an insert detail of section A. The

attachment-line locations are insensitive to Mach number for the range shown.

12
Insert E (54%)

Q O Run=71, M.=10.5, Re/ft=1.04e+06

Q q Run=74, M.=10.6, Re/ft=3.61e+06

Q

Q

A Run=30, M.=10.6, Re/ft=1.44e+06

Q + Run=35, M.=10.7, Re/ft=3.33e+06

D Run=79, M.=10.8, Re/ft=3.50e+06

Q

v 0 Run=81, M.=10.6, Re/ft=4.11e+06

^

0

a Run=132, M.

= 1 0. 7 Re/ft=1.14e+07

Ak" Open Symbols − Baseline

........... A ..O...... . ................a .................. Filled Symbols − Tripped -

AA

−0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

z wle

Figure 5. Example plot of normalize heat flux around the WLE at insert E to demonstrate

laminar collapse at M = 10.

Insert E (54%)

0.5

0.4

w

rl

0.3

0.2

0.1

O Run=71, M.=10.5, Re/ft=1.04e+06

0 0 O q Run=74, M.=10.6, Re/ft=3.61e+06

Q A Run=30, M.=10.6, Re/ft=1.44e+06

a

A

V S Run=35, M.=10.7, Re/ft=3.33e+06

- 4

D Run=79, M.=10.8, Re/ft=3.50e+06

17 Run=81, M.=10.6, Re/ft=4.11e+06

e - a Run=132, M.

=10.7, Re/ft=1.14e+07

Open Symbols − Baseline

Filled Symbols − Tripped

0

−0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

z wle

Figure 6. Example plot of normalize heat flux around the WLE at insert E to demonstrate

turbulent collapse at M = 10.

13
400

350

400

350

300

250

I^ 200

150

100

50

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 7. Attachment-line Reynolds numbers versus the attachment-line streamwise locations in the vicinity of the WLE sensors.

--e R030, M10, Re/ft=1.44x 106

f R035, M10, Re/ft=3.33x 106

R081, M 10, Re/ft=4.11 x 106

- R126, M14, Re/ft=3.06x 106

R078, M14, Re/ft=3.17x 106

$ R048, M16, Re/ft=7.77x 105

I 1:^ 200

V

150-...............................:..........:............ Open Symbols − Laminar

Filled symbols − Turbulent

100

50

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 8. Average attachment-line Reynolds numbers versus the attachment-line streamwise

locations in the vicinity of the WLE sensors.

14
300

250

200

Ic^ 150

100

50

R030, M10, Re/ft=1.44x 106

n R035, M10, Re/ft=3.33x 106

A R081, M 10, Re/ft=4.11 x 106

f R126, M14, Re/ft=3.06x 106

R078, M14, Re/ft=3.17x 106

0 R048, M16, Re/ft=7.77x 105

Open Symbols − Laminar

Filled symbols − Turbulent

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 9. Attachment-line Reynolds numbers (evaluated at the reference temperature T*)

versus the attachment-line streamwise locations in the vicinity of the WLE sensors.

300 •f R030, M10, Re/ft=1.44x 106

f R035, M10, Re/ft=3.33x 106

R081, M 10, Re/ft=4.11 x 106

250 ...........:.......... :......... ... • V R126, M14, Re/ft=3.06x 106

R078, M14, Re/ft=3.17x 106

$ R048, M16, Re/ft=7.77x 105

I 1:* 150

V Open Symbols − Laminar

Filled symbols − Turbulent

100

50

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 10. Average attachment-line Reynolds numbers (evaluated at the reference temperature T* ) versus the attachment-line streamwise locations in the vicinity of the WLE

sensors.

15
200

180

160

140

120

100

80

60

40

20

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 11. Momentum thickness Reynolds numbers versus the attachment-line streamwise

locations in the vicinity of the WLE sensors.

200

R030, M10, Re/ft=1.44x 106

180 f R035, M10, Re/ft=3.33x 106

R081, M 10, Re/ft=4.11 x 106

160 ......... .......... ...... .....

R126, M14, Re/ft=3.06x 106

R078, M14, Re/ft=3.17x 106

$ R048, M16, Re/ft=7.77x 105

140 :....... ...:.........................................

120

m

100 ........... :.......... :.......... :.......... :.......... :...................

80 Open Symbols − Laminar

Filled symbols − Turbulent

60

40

20

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 12. Average momentum thickness Reynolds numbers versus the attachment-line

streamwise locations in the vicinity of the WLE sensors.

16
100

90

80

70

60

50 m

40

30

20

10

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 13. Momentum thickness Reynolds numbers normalized by edge Mach number versus

the attachment-line streamwise locations in the vicinity of the WLE sensors.

00

R030, M10, Re/ft=1.44x 106

90 f R035, M10, Re/ft=3.33x 106

R081, M 10, Re/ft=4.11 x 106

80 ......

R126, M14, Re/ft=3.06x 106

R078, M14, Re/ft=3.17x 106

$

5 M16, Re/ft=7.77x 10

70

R048,

60 V M

50

40 Open Symbols − Laminar

Filled symbols − Turbulent

30

20 ,

10

0

0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82

(x/Lref) AL

Figure 14. Average of the momentum thickness Reynolds numbers normalized by edge Mach

number versus the attachment-line streamwise locations in the vicinity of the WLE sensors.

17
(THIS PAGE INTENTIONALLY LEFT BLANK)

18
APPENDIX: NASA Internal Document

Calculating Similarity Parameters to Predict

Boundary Layer Transition on the Space

Shuttle Orbiter

Matthew P. Vaughan

Alireza Mazaheri

William A. Wood

Aerothermodynamics Branch

Research and Technology Directorate

Space Operations Mission Directorate

August 7, 2008

A-1
Abstract

The purpose of this project was to develop a method for calculating Reynolds number based

similarity parameters, R and R* , in an effort to more accurately predict boundary layer

transition on the Wing Leading Edge (WLE) of the Space Shuttle Orbiter. These Reynolds

numbers are based on boundary layer edge conditions and the velocity gradient normal to the

attachment line, the line at which flow diverges toward either the leeward or windward sides

of the Orbiter. The similarity parameters were calculated for several wind tunnel conditions

at locations corresponding to gauges along the WLE. For the calculations, streamlines were

first plotted through these locations using a program called Tecplot ®. Then, attachment line

points were found for each gauge location by following the streamlines until they converged

to within a pre-determined threshold of 1 . 25 ± .05 mm, corresponding to roughly three cells

of the surface grid used for the analysis. Using a NASA-developed program that interpolated

boundary layer edge conditions from existing wind tunnel databases, flow properties at the

attachment line locations were calculated and recorded. Finally, this data yielded the desired

Reynolds numbers after a few additional calculations.

After refining the method of calculation in order to reduce inconsistency and error, the

two similarity parameters were easily calculated at each point for several freestream Reynolds

numbers and Mach numbers. The results of the project are currently being analyzed to determine the viability of using R and R* as predictors of boundary layer transition along

the WLE of the Orbiter. If they correlate well to current wind tunnel data, the calculation

process described in the report should be automated to rapidly characterize transition at

flight conditions. An accurate prediction of boundary layer transition would allow for a less

conservative but still safe approach to damage assessment, potentially saving an additional

extra-vehicular activity in an already strict Space Shuttle Orbiter mission schedule to complete the construction of the International Space Station before the retirement of the fleet

in 2010.

Introduction

Upon reentry into the atmosphere, the WLE of the Space Shuttle Orbiter experiences the

most severe thermal stresses on the vehicle. Thus, fast and reliable methods for characterizing the flow over the wing leading edge are critical for mission safety. One problem

associated with this characterization is the transition of the boundary layer from laminar

to turbulent flow, which greatly increases the rate of heat transfer to the structure. One

method being investigated involves the use of two Reynolds numbers based on boundary

layer edge conditions at the WLE attachment line. The attachment line marks the divergence of airflow to either the windward or leeward side of the Orbiter (see Figures A-1 and

A-2). These parameters are given by the following equations (Poll, 1985):

"

2

1/2

Ue R

v

(A-1)

e (dVe /dy) v=0

"

2

1/2

Ue R*

v

(A-2)

*(dVe /dy)v=0

In these equations, Ue is the velocity along the attachment line, (dVe/dy)v=0 is the crosswise velocity gradient at the attachment line, ve is the kinematic viscosity at the boundary

layer edge, and v* is the kinematic viscosity evaluated at the turbulent reference temperature, given by

T* Te + 0.10(Tw — Te ) + 0.60(TT — Te ) (Poll, 1985) (A-3)

A-2
where TT is the recovery temperature, given by Benard, Cooper, and Sidorenko (2005) as

TT = Tel 1+ ry

2 

1

Me

I (A-4)

For the calculation of R and R., y is taken to be 1.4, r = Pr, and a value of 0.72 is

used for Pr (White, 1974). In order to determine the dynamic viscosity at the turbulent

reference temperature, Sutherlands Law was used to give

μ0

^l 

T0

I T + S

where the subscript indicates a reference variable. For air, T0 = 273 . 11K, μ0 = 1. 72 x

10-5Pa • s and S = 110. 56K (White, 1974).

The purpose of the research was to determine the feasibility of calculating R and R*

for several points near the WLE of the Space Shuttle Orbiter. The attachment line along

the wing shifts towards the centerline of the Orbiter at high angles of incidence, deviating

significantly from the attachment line of the infinite swept cylinder described by Poll (1985)

and increasing the complexity of the calculation. Because the actual attachment line for the

Orbiter is not precisely on the WLE, the possibility of obtaining meaningful results from

any calculation method developed was unclear before the research was conducted.

All boundary layer flowfield properties used in this work were obtained from an existing

database of CFD simulations. The simulations modeled the Orbiter at 40-degrees angle of

attack, for various freestream Reynolds numbers corresponding to conditions tested as part

of the MH-13 experiment (Cassady et al., 2007). The CFD simulations were performed

using the viscous flow solver Data-Parallel Line Relaxation algorithm (DPLR) (Wright et

al., 1998) using a 5-species air model and a constant-temperature, fully-catalytic surface.

Data Extraction

Calculating the two similarity parameters R and R. required two distinct steps. First, a

plotting tool called Tecplot was used to display the windward side of a wind tunnel model of

the Orbiter along with surface and boundary layer edge conditions at a particular freestream

Reynolds number and Mach number. Tecplot allows precise plotting of streamlines, which is

useful to locate the attachment line. Second, a NASA developed program called Blvolprops 1

was used to calculate surface and boundary layer edge conditions at user-specified points at

a variety of Mach numbers and Reynolds numbers. The program interpolates these conditions from a database of CFD simulations of Orbiter flowfields at wind tunnel conditions,

spanning the tunnel operational Reynolds-number range. Figure A-3 shows the Reynolds

numbers, Mach numbers, and angles of attack used for the calculations. A Microsoft ® Excel

spreadsheet was also employed, facilitating data storage from the other two programs and

expediting the actual calculation of R and R. .

The process of calculating the two similarity parameters began with the plotting of

streamlines near the tip of the Orbiters wing. The convergence of the upstream streamlines

revealed the approximate location of the attachment line. Then, eight points at Mach 10,

Mach 14, and Mach 16, and an additional four points at Mach 14 corresponding to gauges

on a wind tunnel model were plotted along with streamlines passing through each (see

Figure A-4). These streamlines rapidly converged to the position of the attachment line

as they were followed upstream, and a threshold separation distance between the two of

'Meyer, B., “A Boundary Layer Probing and Reynolds Number Interpolation Tool: Blvolprops v3.0,”

Swales Technical Note 06-488, Hypersonic Vehicle Analysis Group, NASA Langley Research Center, November 2006.

A-3
approximately 1 . 25 f . 05 mm was chosen, corresponding to approximately three cells on

the surface grid used to analyze the model. This threshold was chosen because of the need

to balance the practical application of the method and the asymptotic convergence of the

streamlines upstream of gauge locations. Too small of a threshold would lead to attachment

line points near the nose of the Orbiter, but a threshold that is too large would cause

unacceptable discrepancies between conditions along the streamline and conditions at the

attachment line. Once this threshold was crossed, the point on the attachment line was

recorded in the spreadsheet and used to determine relevant parameters such as boundary

layer edge temperature, pressure, viscosity, and density.

Calculating the crosswise velocity gradient at the attachment line locations found above

presented the most technical difficulty as there was no automatic method for obtaining accurate values of the gradient at specific points. An initial attempt to calculate the gradient

approximated the vector normal to the attachment line velocity by visual inspection. Two

points were chosen along this vector, and the components of the velocity along the approximated normal at each point were recorded. The gradient was then calculated using the

following relation:

^

dVe _ ΔVe,2 — ΔVe,1

(A-6)

dy v=0 Δy

where Δy is the distance between the two points. However, the error associated with

approximating the normal vector was too large and unpredictable, so a new method was

developed to make the calculation more consistent.

In the new method, a vector normal to the surface was calculated through the cross

product of two arbitrary vectors on the grid starting from the attachment line point. A

Tecplot utility that automatically calculated the surface normal vector was later used to

verify the accuracy of this method. The surface normal vector was then crossed with the

velocity vector along the attachment line to produce a vector in the direction of the desired

crosswise gradient. Finally, this vector was used to obtain one point on either side of the

attachment line at a fixed distance of 1. 25 mm. Decreasing the magnitude of the surface

normal vector reduced the error resulting from the projection of the two points onto the

curved surface of the wing.

Once these points were obtained, Blvolprops was used to determine the boundary layer

edge velocity at each point, yielding the gradient after a few additional calculations according

to equations A-1 through A-6. With this gradient and the other parameters acquired at

the attachment line point, R is easily calculated. However, the viscosity term of R. must

be evaluated at turbulent reference conditions. Using Sutherlands Law and assuming that

air is an ideal gas, the turbulent reference temperature, density, and dynamic viscosity were

determined, allowing R. to be calculated.

Conclusion

The calculation of R and R. proceeded smoothly once the method described above was

fully developed, and the research exceeded expectations due to the rapid development and

implementation of the method. The requested values of the two parameters were passed on

to be analyzed for potential correlations to boundary layer transition along the WLE of the

Space Shuttle Orbiter. If the parameters correlate well, they could potentially be used as

an additional means to assess damage on the Orbiter. Early boundary layer transition is a

serious risk to the structural integrity of the Orbiter, so an accurate prediction of transition

due to a damaged and irregular surface would be valuable towards determining whether

repairs are needed. However, despite the relative simplicity of the calculation method, the

process is tedious to perform by hand and should be automated before it is used in a real

time scenario.

A-4
References

Anderson, (2000). Anderson, J. D., Jr. (2000). Fundamentals of Aerodynamics (3rd ed.).

New York: McGraw-Hill.

Benard, et al., (2005). Benard, E., Cooper, R. K., and Sidorenko, A. (2005). Transition and

turbulent heat transfer of swept cylinder attachment line in hypersonic flow. International Journal of Heat and Mass Transfer, 49, 836–843.

Cassady, et al., (2007). Cassady, A. M., Bourland, G., King, R., Kegerise, M., Marichalar,

J., Kirk, B. S., and Trevino, L. (2007). MH-13 Entry II: Space Shuttle Orbiter Aerother-  ̃

modynamic Test Report. NASA TP-2007-214758.

Poll, (1985). Poll, D. I. A. (1985). Boundary layer transition on the windward face of Space

Shuttle during re-entry. AIAA Paper No. 85-0899.

White, (1974). White, F. M. (1974). Viscous fluid flow. New York: McGraw-Hill.

Wright, et al., (1998). Wright, M. J., and Candler, G. V. and Bose, D. (1998). Data-Parallel

Line Relaxation Method for the Navier-Stokes Equations. AIAA Journal, 36, 9, 1603–

1609.

A-5
Figure A-1. Attachment line on an idealized infinite swept cylinder.

FigurerA-2.S Streamlinesvdiverg ing fromathe attachmentnline on the(Orbiteru (Plotted using

Tecplot).

A-6
Figure 3: Table showing the wind tunnel conditions used to calculate and Figure A-3. Table showing the wind tunnel conditions used to calculate R and R*.

g g p g p g

Figure A-4. Gaugeitlocations (blue) with rcorrespondingl Machi 10Tattachment line points

(green). The additional four Mach 14 points are shown in red (Plotted using Tecplot).

A-7

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01-12-2009 Technical Memorandum

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

Turbulent Wing-Leading-Edge Correlation Assessment for the Shuttle Orbiter

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

Rudolph A. King and Matthew P. Vaughan t

tWork performed under the Langley Aerospace Research Summer Scholar 5e. TASK NUMBER

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599489.02.07.07.04.11.01

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14. ABSTRACT

This study was conducted in support of the Orbiter damage assessment activity that takes place for each Shuttle mission since STS-107

(STS - Space Transportation System). As part of the damage assessment activity, the state of boundary layer (laminar or turbulent)

during reentry needs to be estimated in order to define the aerothermal environment on the Orbiter. Premature turbulence on the wing

leading edge (WLE) is possible if a surface irregularity promotes early transition and the resulting turbulent wedge flow contaminates

the WLE flow. The objective of this analysis is to develop a criterion to determine if and when the flow along the WLE experiences

turbulent heating given an incoming turbulent boundary layer that contaminates the attachment line. The data to be analyzed were all

obtained as part of the MH-13 Space Shuttle Orbiter Aerothermodynamic Test conducted on a 1.8%-scale Orbiter model at

Calspan/University of Buffalo Research Center in the Large Energy National Shock Tunnels facility. A rational framework was used to

develop a means to assess the state of the WLE flow on the Orbiter during reentry given a contaminated attachment-line flow. Evidence

of turbulent flow on the WLE has been recently documented for a few STS missions during the Orbiter’s flight history, albeit late in the

reentry trajectory. The criterion developed herein will be compared to these flight results.

15. SUBJECT TERMS

Shuttle Orbiter, hypersonic boundary layer transition, attachment-line transition

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