NASA/TP–2009–215951

Version 2 of the Protuberance

Correlations for the Shuttle-Orbiter

Boundary Layer Transition Tool

Rudolph A. King, Michael A. Kegerise and Scott A. Berry

Langley Research Center, Hampton, Virginia

December 2009

https://ntrs.nasa.gov/search.jsp?R=20090042976 2018-05-17T09:06:52+00:00Z
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NASA/TP–2009–215951

Version 2 of the Protuberance

Correlations for the Shuttle-Orbiter

Boundary Layer Transition Tool

Rudolph A. King, Michael A. Kegerise and Scott A. Berry

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

December 2009
The use of trademarks or names of manufacturers in this report is for accurate reporting and does not

constitute an offical endorsement, either expressed or implied, of such products or manufacturers by the

National Aeronautics and Space Administration.

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802
Abstract

Orbiter-specific transition data, acquired in four ground-based facilities (LaRC 20-Inch Mach

6 Air Tunnel, LaRC 31-Inch Mach 10 Air Tunnel, LaRC 20-Inch Mach 6 CF 4 Tunnel, and

CUBRC LENS-I Shock Tunnel) with three wind tunnel model scales (0.75, 0.90, and 1.8%)

and from Orbiter historical flight data, have been analyzed to improve a pre-existing engineering tool for reentry transition prediction on the windward side of the Orbiter. Boundary

layer transition (BLT) engineering correlations for transition induced by isolated protuberances are presented using a laminar Navier-Stokes (N-S) database to provide the relevant

boundary-layer properties. It is demonstrated that the earlier version of the BLT correlation

that had been developed using parameters derived from an engineering boundary-layer code

has improved data collapse when developed with the N-S database. Of the new correlations

examined, the proposed correlation 5, based on boundary-layer edge and wall properties,

was found to provide the best overall correlation metrics when the entire database is employed. The second independent correlation (proposed correlation 7) selected is based on

properties within the boundary layer at the protuberance height. The Aeroheating Panel

selected a process to derive the recommended coefficients for Version 2 of the BLT Tool. The

assumptions and limitations of the recommended protuberance BLT Tool V.2 are presented.
Contents

List of Tables 3

List of Figures 4

1 Introduction 7

2 Analysis Approach 8

2.1 Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Data Overview 11

3.1 LaRC 20-Inch Mach 6 Air Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 LaRC 31-Inch Mach 10 Air Tunnel . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 LaRC 20-Inch Mach 6 CF4 Tunnel . . . . . . . . . . . . . . . . . . . . . . . . 13

3.4 CUBRC LENS-I Shock Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.5 Historical Flight Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Correlation Results 14

4.1 LATCH versus N-S Database . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Proposed Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 PC#1: Reθ /Me = C x (k/6) n.. . . . . . . . . . . . . . . . . . . . . 17

4.2.2 PC#2 & 3: Reθ /Me = C x (k/6* ) n & C x (k/θ)

n

. . . . . . . . . . . 17

4.2.3 PC’s#4 & 5: Reθ /Me = C/[(k/6)(Te /Tw )

m

] & C/[(k/6)(He /Hw )

m

] . 18

4.2.4 PC’s#6 & 7: Rek-Type Correlations . . . . . . . . . . . . . . . . . . . 18

4.3 Correlation Down Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.4 Selection of Correlation Constants . . . . . . . . . . . . . . . . . . . . . . . . 19

4.4.1 Option 1 Correlation (PC#5) . . . . . . . . . . . . . . . . . . . . . . . 20

4.4.2 Option 2 Correlation (PC#7) . . . . . . . . . . . . . . . . . . . . . . . 21

4.5 Correlations Revisted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.6 Assumptions and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Summary 23

References 24

2
List of Tables

1 Relevant correlation parameters for data obtained in the NASA LaRC 20-Inch

Mach 6 Tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1 Relevant correlation parameters for data obtained in the NASA LaRC 20-Inch

Mach 6 Tunnel – (Cont).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 Relevant correlation parameters for STS-121mission support data obtained

in the NASA LaRC 20-Inch Mach 6 Air Tunnel.. . . . . . . . . . . . . . . . . 27

3 Relevant correlation parameters for new data obtained in the NASA LaRC

20-Inch Mach 6 Air Tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Relevant correlation parameters for data obtained in the NASA LaRC 31-Inch

Mach 10 Air Tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Relevant correlation parameters for data obtained in the NASA LaRC 20-Inch

CF4

Tunnel.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Relevant correlation parameters for data obtained at a nominal M = 10 in

the CUBRC LENS-I Shock Tunnel.. . . . . . . . . . . . . . . . . . . . . . . . 31

7 Relevant correlation parameters for data obtained at a nominal M = 16 in

the CUBRC LENS-I Shock Tunnel.. . . . . . . . . . . . . . . . . . . . . . . . 31

8 Historical flight cases as documented in Refs. [5] and [26]. . . . . . . . . . . . 32

9 Relevant correlation parameters for historical flight cases. . . . . . . . . . . . 33

10 Side-by-side comparison of facility dependent metrics for a correlation in the

form of the approved BLT Tool V.1 protuberance correlation. . . . . . . . . . 34

11 Down-select table for most promising correlations investigated. . . . . . . . . 35

12 Tabulated correlation coefficients for proposed correlations 5 and 7.. . . . . . 35

13 Computed transition times for the ten accepted flight cases using proposed

correlations 5 and 7 with the recommended correlation coefficients. . . . . . . 36

14 Revisited correlations and the respective metrics. . . . . . . . . . . . . . . . . 37

3
List of Figures

Focused inspection image of a protruding gap filler on STS-121.. . . . . . . . 38

Generalized correlation approach used in this report. . . . . . . . . . . . . . . 38

Complete database (ground-based and flight) projected onto windward surface. 39

Complete database (ground-based and flight) in the form of Reθ

/Me versus

x/LTef . ....................................... 40

Complete database (ground-based and flight) in the form of Re k versus k/6. . 40

6 Existing LaRC 20-Inch Mach 6 Air Tunnel data used to develop BLT Tool V.1. 41

7 Existing LaRC 20-Inch Mach 6 Air Tunnel data reanalyzed to estimate the

incipient transition Reynolds number. . . . . . . . . . . . . . . . . . . . . . . 41

8 Ensemble of facility dependent data based on N-S database. . . . . . . . . . . 42

9 Ensemble of facility dependent data based on LATCH database. . . . . . . . 42

10 Calibrated flight data analyzed using N-S database. . . . . . . . . . . . . . . 43

11 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ /Me x k/6 = C . . . . . . . . . . . . . . . . . . . . . . . . . 43

12 Ensemble of facility dependent data based on N-S database for correlation

Reθ /Me x k/6* = C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

13 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ /Me x k/6* = C . . . . . . . . . . . . . . . . . . . . . . . . 44

14 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ/Me x k/B = C . . . . . . . . . . . . . . . . . . . . . . . . . 45

15 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ /Me x (k/6)(Te /T,,,)

0.16 = C . . . . . . . . . . . . . . . . . . 45

16 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ /Me x (k/6)(He /H,,,)

0.30 = C . . . . . . . . . . . . . . . . . 46

17 Ensemble of facility dependent data based on N-S database for correlation

Re k (reference to μ,,,) = C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

18 Ensemble of facility dependent data and flight data based on N-S database

for correlation of the Rek-type . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

19 Flight data plotted in correlation space (PC#5) along with correlation curves

derived from ensemble of facility dependent and flight data (N-S database). . 47

20 Flight data plotted in correlation space (PC#7) along with correlation curves

derived from ensemble of facility dependent and flight data (N-S database). . 48

21 Plot showing flight data and correlation curves with constants recommended

by the Aeroheating Panel for PC#5 . . . . . . . . . . . . . . . . . . . . . . . . 48

22 Plot showing ground-based data, flight data, and correlation curves for PC#5. 49

23 Plot showing flight data and correlation curves with constants recommended

by the Aeroheating Panel for PC#7 . . . . . . . . . . . . . . . . . . . . . . . . 49

24 Plot showing ground-based data, flight data, and correlation curves for PC#7. 50

25 Ensemble of facility dependent data and flight data based on N-S database

for correlation Reθ /Me x (k/B)(He /H,,,

)

0.44 = C . . . . . . . . . . . . . . . . . 50

26 Plot showing ground-based data, flight data, and derived correlation curves

for correlation Reθ/Me x (k/B)(He /H,,,)

0.44 = C . . . . . . . . . . . . . . . . . 51

4
Nomenclature

C Correlation constant (see Eq. 1)

H Total enthalphy

k Protuberance height

LTe f Orbiter reference length from nosetip to body-flap hinge line

M Mach number

R Correlation coefficient of regression

Re unit Reynolds number

Rek Reynolds number based on conditions at k, pk uk k/μk

Reθ Momentum thickness Reynolds number, peueB/μe

SˆY

Standard error of regression

T Temperature

u Resultant velocity

U Uncertainty

x axial distance from Orbiter nosetip

X Distubance parameter (see Eq. 1) or axial distance in Orbiter structural reference system

y spanwise distance from Orbiter centerline symmetry plane

Y Transition parameter (see Eq. 1) or spanwise distance in Orbiter structural reference system

Z Vertical distance in Orbiter structural reference system

δ Boundary layer thickness

δ

* Displacement thickness

B Momentum thickness

μ Viscocity

p Density

Q Standard deviation

Subscript

1 last fully laminar condition

2 first condition with laminar departure

e edge conditions

flt flight

gb ground based

inc incipient conditions

k conditions at height k

00 freestream conditions

Superscript

n Correlation exponent (see Eq. 1)

m Exponent

() mean value

(ˆ) = log( )

Acronyms

BLT Boundary layer transition

CFD Computational fluid dynamics

CUBRC Calspan-University of Buffalo Research Center

DPLR Data-Parallel Line Relaxation

EI Entry interface

LaRC Langley Research Center

LATCH Langley Approximate Three-Dimensional Convective Heating

LAURA Langley Aerothermodynamic Upwind Relaxation Algorithm

N-S Navier-Stokes
PC Proposed correlation

STS Space Transportation System

TPS Thermal protection system
1 Introduction

The Entry Aeroheating Working Group led by Boeing Houston and NASA Johnson Space

Center was created as a result of the Columbia Accident Investigation to develop analysis

tools and plans and to execute ground testing in order to monitor the health of the Orbiters

thermal protection system (TPS) during reentry. Members of this working group and the

associated Aeroheating Panel (see Ref. [1] for details) also provide real-time support to

the Damage Assessment Team during each Shuttle mission since STS-107 (STS- Space

Transportation System). During Shuttle ascent, the TPS on the Orbiter can experience

debris strikes and displacement of TPS components (such as the gap fillers that are placed

between the TPS tiles) resulting in cavities and protuberances in the heat shield system. An

example of an on-orbit image for a gap filler protruding from the TPS is shown in Figure 1

(image taken during STS-121 mission). This gap filler is somewhat atypical as many rips,

tears, and frays are associated with this proturberance (most gap fillers are simply dislodged

and do not exhibit rips or tears). Part of the on-orbit process is to determine if cavities

and/or protuberances resulting from the ascent stage can cause premature boundary-layer

transition resulting in increased thermal loads that can ultimately affect the safety margins

during reentry. The Boundary Layer Transition (BLT) Tool, which is one of the suite of

tools developed for the Damage Assessment Team, is an engineering tool used in a rapidturnaround environment to assess if and when these damage sites can cause early transition.

The original version of the BLT Tool approved by the Orbiter Project Office in the Space

Shuttle Program for this process is Version 1 (see Refs. [1]- [6]).

This report explores potential protuberance correlations to be used for the next-generation

Orbiter BLT Tool (Version 2) utilizing ground-based data and calibrated historical flight

data (i.e., previous Orbiter flights where protuberance sources were identified as the cause

for early boundary-layer transition as inferred from thermocouple measurements) [5]. Proposed correlations due to cavity damages are discussed in a separate report [7]. As a brief

recap on the development of the original protuberance correlation, hypersonic boundarylayer transition data were acquired in three ground-based facilities (LaRC 20-Inch Mach 6

Air Tunnel, LaRC 31-Inch Mach 10 Air Tunnel, and LaRC 20-Inch Mach 6 CF 4 Tunnel)

on 0.75%-scale wind tunnel models with diamond shaped protuberances. Various correlations were examined using the ground-based measurements and flow parameters derived

from an engineering code called LATCH (Langley Approximate Three-Dimensional Convective Heating) [8], which utilized a two-layer approach with inviscid LAURA (Langley

Aerothermodynamic Upwind Relaxation Algorithm) [9] solutions. The implementation of

LATCH for the BLT Tool V.1 is discussed in Ref. [4]. Most of correlations investigated were

not useable due to unsatisfactory data collapse between the three facilities as well as when

compared against flight data. Due to these inconsistencies, a simpler correlation utilizing

data from one facility, LaRC 20-Inch Mach 6 Air Tunnel, and flight was implemented as the

protuberance correlation for the BLT Tool V.1.

There are a few key objectives for the development of a new version of the BLT Tool.

Firstly, the LATCH flow properties used in the development of the BLT Tool V.1 are limited

to boundary-layer edge properties and wall conditions such that correlations dependent on

flow properties within the boundary layer (e.g., Rek = pkukk/μk where k is the height at

which these parameters must be defined) are not possible. The first goal was to reexamine

the protuberance correlation utilized in BLT Tool V.1 and evaluate alternate correlations

using a database derived from full laminar Navier-Stokes solutions. The two viscous CFD

solvers used for the present analysis were LAURA [9] and DPLR (Data-Parallel Line Relaxation) [10] codes. The implementation of the viscous CFD database for the next-generation

BLT Tool is given in Refs. [11] and [12]. Secondly, the BLT Tool V.1 protuberance correlation was developed using ground-based data obtained in a single facility with a single

protuberance type and compared against a few historical flight cases. The correlations pre7
sented herein are developed using a more expansive database to include data obtained in

four ground-based facilities and reexamined flight data. This database includes the effects

of protuberance shape and orientation, a larger range of trip height normalized by the local

boundary-layer thickness ( k/S), and a larger ground-based Mach number range. And lastly,

the Orbiter Project Office baselined BLT Tool V.1 protuberance correlation includes only

one correlation with no redundancy. So, the final objective was to develop a new protuberance BLT Tool which utilizes two independent correlations, where the primary correlation

will be the correlation with the highest level of confidence based on the regression metrics

for the entire database (ground-based and flight data).

This report includes a background of the analysis approach, an overview of the protuberance correlation approach (highlighting the protuberance BLT Tool V.1), and a brief

review of the entire database. The correlation results are then presented and the findings

are summarized. Version 2 of the protuberance BLT Tool approved for future flights by the

Orbiter Project Office is presented. From this point forward, reference to the BLT Tool will

be synonymous with the protuberance component of the BLT Tool.

2 Analysis Approach

In this section, the general correlation and regression analysis will be discussed and will

include details of the approved protuberance correlation for the BLT Tool V.1. The general

regression approach along with the metrics used for goodness of fit will follow. The section

closes with a discussion of the error analysis used for the ground-based data.

2.1 Correlation Analysis

Transition correlation approaches generally attempt to relate or scale ground-based (wind

tunnel and ballistic range) data to flight test conditions. It is important to note that the correlations are not intended to provide a fundamental contribution of the transition physics.

Ref. [13] has an extensive review of boundary-layer transition correlation development as

it pertains to reentry vehicles. Early correlation results were for the most part based on

wetted length transition Reynolds number, but these Reynolds numbers obtained in flight

were usually larger than those achieved in ground-based experiments. Also, large data scatter were associated with these results presumably due to factors like local Mach number,

wall cooling, surface roughness, wetted length, freestream tunnel disturbance, etc. Later

correlations involving Reynolds numbers based on local boundary-layer thicknesses showed

marked improvement over those based on wetted length Reynolds numbers. With the advent of high-speed computing, correlations based on reasonably accurate computed local

boundary-layer flow properties became practical, particularly for flows that involve entropy

layer swallowing dictated by bluntness ratios (e.g., Shuttle Orbiter). The local boundarylayer flow properties are usually computed for laminar flow conditions and these flow and

fluid properties are used to develop the correlations. So clearly there is a need for consistent

boundary-layer solutions when developing and applying these correlations.

The generalized correlation approach used in this report follows the work summarized

in Ref. [14]. Figure 2 shows a schematic of the generalized correlation approach where the

abscissa is the logarithm of a disturbance parameter X and the ordinate the logarithm of a

transition parameter Y. The line in the plot represented by

Y = CXn (1)

delineates a best estimate boundary for the correlation such that data below the line denote

laminar flow and data above denote turbulent flow. For small disturbance parameters X, the

transition parameter Y should asymptote to a smooth-wall limit, which is facility dependent.

8
Similarly, for large X values, Y asymptotes to a limiting lower value. This limited lower value

is referred to as the so called protuberance limit (i.e., further increases in roughness height has

no additional effect on transition) or a lower threshold limit (i.e., the unit Reynolds number is

too low to produce and/or maintain the turbulence). Use of a correlation method represents

a simplified engineering approach to a complicated physics-based problem. The BLT Tool

V.1 was developed using incipient transition data, i.e., data indicating the first evidence

of laminar-to-turbulent transition on the windward surface of the Orbiter. The BLT Tool

V.1 [2,3] assigns as the disturbance parameter X = k/δ where k is the protuberance height

and δ the boundary-layer thickness and the transition parameter as Y = Reθ /Me where Reθ

(= pe ueB/μe ) and Me are the momentum thickness Reynolds number and boundary-layer

edge Mach number, respectively. The curve coefficient, C = 27, was selected as a lower

bound to the transition Reynolds number data, such that statistically most of the incipient

transition data lie above the correlation curve, which introduces some conservatism into the

tool. An exponent value of n = —1 was used so that the BLT Tool V.1 is expressed as

Mθ 

X 6 = C. (2)

e

The data used in the development of Eq. 2 are presented later in the report.

2.2 Regression Analysis

The power-law form of the generalized correlation can be expressed as

log Yi = n log Xi + log C (3)

or

Yˆ

i

 = nXˆ

i + Cˆ

(4)

where Yˆ

i = log Yi, Xˆi = log Xi and Cˆ = log C. Applying least-squares regression to Eq. 4

in the Xˆ-Yˆ space provides expressions for the slope n and intercept C. ˆ The regression

equations are

n = 

N

E

XiYi —

E

Xi

E

Yi

N EˆX2i — (EˆXi

)

2

and E

C = 

Yi — n E Xi

(6) N

where the E’s imply summation from i = 1 to N with N being the number of data points.

In general, the regression analysis for Eq. 1 has two degrees of freedom to specify the best

fit, i.e., n and C (= 10 ˆC ). If the exponent n is specified in Eq. 1, then Eq. 5 is replaced

by n = constant so that there is only one degree of freedom, C. ˆ The BLT Tool V.1 is an

example where the exponent was specified as a constant, i.e. n = —1.

The standard error of the regression [15] is given by

SˆY 

= p

Yˆ

i — (nXi + ˆC)] 2

12 1/2

.

(7)

N —2

Throughout this document, the upper and lower limits of the 95% confidence limit are

assumed to be bounded by the 2 SˆY value about the best fit C. ˆ For small sample sizes ( N <

31), it is more appropriate to assume that the 95% confidence limits for a T-distribution

are bounded by tSˆY. Here the numerical value of t is a function of the sample size N. For

example, ten historical flight cases are discussed in this document. For a sample size of

(5)
N = 10, a value of t = 2. 26 (1.13 times the assumed value) is the recommended value to

provide a 95% confidence limit. Or stated another way, the use of 2SˆY for the ten flight

cases only provides a 92% confidence level. With the above caveat, the upper and lower 95%

confidence coefficients assumed in this document (i.e., the 2SˆY value) in the X-Y space are

C+95% = 10 ˆC+2SYˆ (8)

and

C-95% = 10 ˆC-2SYˆ

 , (9)

respectively. The correlation constant can be selected to be either C-95%, C+95%, or C with

C-95% being the most conservative (i.e., with respect to transition prediction capability)

and C+95% the least conservative constant. As a measure of the goodness of the data (Xˆ

and Yˆ

), the correlation coefficient R is defined as

-1< R = 

QXˆYˆ <1 (10)

Q ˆX Q ˆY

where QXˆ and QˆY are the standand deviations of Xˆ and Yˆ

, respectively, and QXˆYˆ is the

covariance of Xˆ and Yˆ . Values of 1R1 —> 1 are desirable and implies a strong correlation for

the dataset. The other metric used to evaluate the goodness of the regression is

ΔC C+95% - C-95% (11)

C C

where ΔC/C is a measure of the scatter in the data about the best fit coefficient C.

2.3 Error Analysis

This section briefly discusses the methodology used to estimate uncertainties incurred in the

determination of the disturbance, X, and transition, Y, parameters as a result of groundbased measurement uncertainties. The uncertainty analysis is conducted by a Monte Carlo

(MC) simulation method [15] and is applied only to the ground-based data. The assumed

true value of each input variable is applied to the data reduction equations. All of the

associated uncertainties for each of these variables are input. Here, 95% confidence estimates

(2Q for Gaussian distributions) are assumed for each uncertainty and a random number

generator is used to compute individual error values. The individual error values are added

to the corresponding assumed true value of each variable to obtain a measured value. The

measured values are applied to the data reduction equations to obtain the result variables.

The process is repeated Nj times such that a distribution is obtained for each result variable.

The input uncertainties under consideration here are the Reynolds number uncertainties

and uncertainties in the measurement of protuberance height k. In this report, the assumed

true incipient transition unit Reynolds number, Ree,inc, is defined as the average between

the last fully laminar value (Ree,1) and the first non-laminar value (Ree,2) for all the

ground-based data. The values of Ree,1 and Ree,2 are computed directly from recorded

tunnel conditions and have associated uncertainties, URe_,1 and URe_,2. These uncertainties are represented by a Gaussian distribution such that URe_ = 2QRe_ . The incipient

transition Reynolds number for realization “j” is in the range Re(j)

e,1 < Re(j)

e,inc < Re(j)

e,2

provided that the uncertainties URe_,1 and URe_,2 are much less than the percent difference

between Ree,1 and Ree,2 (typically larger than 20%). A uniform distribution is assumed

for the measured Re(j)

e,inc since this value is equally likely to be any value in the interval

between Re(j)

e,1 and Re(j)

e,2. The uncertainties for the protuberance height k are represented

10
by a Gaussian distribution where Uk = 2σk . The measured value, k

(j)

, is the assumed true

k value plus the individual uncertainty for each “j” realization.

The nominal Reynolds number percent uncertainty (based on the range of Reco,inc

tested) used for NASA Langley Research Center’s 20-Inch Mach 6 Air Tunnel is estimated

at 3% based on data reported in Ref. [16]. Similarly, nominal Reynolds number uncertainty

for the NASA Langley Research Center’s 31-Inch Mach 10 Air Tunnel is estimated at 1.2%

based on unpublished data. 1 No information was available for the other NASA facility, the

20-Inch Mach 6 CF4 Tunnel, so the nominal value was assumed to be the same as that

for the 20-Inch Mach 6 Air Tunnel (i.e., 3%). For the CUBRC LENS-I Shock Tunnel, the

nominal Reynolds number percent uncertainties estimated are 4% and 5% for Mach 10 and

Mach 16, respectively [17]. These values are considerably less than the percent difference

values between Reco,1 and Reco , 2 . The uncertainty used for the protuberance height k in all

measurements is estimated to be Uk = 0.0005 in. based on repeated measurements. All error

analysis presented in this document were conducted using Nj = 500, 000 realizations. Take

as an example the BLT Tool V.1, the flow properties in both X (= k/6) and Y (= Reθ /Me )

have been approximately scaled relative to Reynolds number. The flow properties at the

assumed true value, Reco,inc, are known, thus a scaling relationship is required to obtain

the results in flow properties based on uncertainties in Reco. The values of Reθ /Me and 6

are thus scaled using

Reθ

= 

Reθ,inc ×^Reco

M

(12)

e

Me co,inc

and

6 = 6inc × RRe

Reco ,inc (13)

co

respectively. Distributions of (Reθ

/Me )

(j) and k(j)/6(j) are obtained using these techniques

and the corresponding uncertainties, URe,/m. and Uk/δ, are computed based on 2σ values.

3 Data Overview

The data used to develop the correlations in this report were obtained in four groundbased facilities and on several historical Shuttle missions. The bulk of the data to be

presented were based on measurements obtained in NASA Langley Research Center (LaRC)

Aerothermodynamic Laboratory (LAL) which consist of three hypersonic wind tunnels [18].

The three tunnels are the 20-Inch Mach 6 Air Tunnel, the 20-Inch Mach 6 CF 4 Tunnel, and

the 31-Inch Mach 10 Air Tunnel. The high Mach number ground-based data were obtained

in the Calspan-University of Buffalo Research Center (CUBRC) LENS-I Shock Tunnel [17,

19]. The ground-based transition data were derived from heat transfer measurements. A

departure in the normalized mean heat transfer rate from the laminar baseline was used

as the primary transition criterion. The ground-based tests were conducted over a range

of unit Reynolds numbers as the heat transfer measurements were acquired to evaluate the

state of the boundary-layer flow. As discussed already in the Section 2.3, an estimate of

the incipient transition unit Reynolds number, Reco , inc (= ρcouco/μco), is defined as the

average Reynolds number between the last fully laminar condition (Reco,1) and the first

condition with evidence of laminar departure (Reco,2). This basis for defining the incipient

conditions will be used throughout this document. The results to be presented as part of the

BLT Tool V.2 development were derived from the N-S database extraction tool [11] using

the experimental test conditions as inputs. The N-S solutions are fully laminar solutions

on a smooth Orbiter geometry (i.e., without the protuberances). All the ground-based data

'Rhode, M. N., Private communication, January 2007.

11
reported in this document were acquired at a nominal angle of attack of 30 ° or 40° and a

nominal yaw angle of 0 ° .

3.1 LaRC 20-Inch Mach 6 Air 'Tunnel

The existing M = 6 data obtained prior to the development of the BLT Tool V.1 are

presented in Table 1. The measurements were acquired on 0. 75%-scale Orbiter models.

Most of the data were acquired at a nominal angle of attack of 40° and a few cases at

30° . A phosphor thermography system was used to infer global heat transfer rates on

the windward model surface for hypersonic boundary-layer transition detection. Details of

the experimental setup and test conditions are available in Ref. [20]. The flow parameters

presented in the table are those required for the correlations examined during this study. For

the coordinate system given in the table, axial distance from the nosetip is represented by

x and spanwise distance from the centerline (CL) symmetry plane is y. The flow properties

are probed at (x/Lref, y/Lref) which corresponds to the location of the protuberances

(diamond-shaped trips for this database) with heights k. The data in Table 1 correspond to

those at the estimated incipient transition Reynolds number (based on the average between

the last fully laminar value and first value with laminar departure). The test conditions

for the data presented on the first page of this table (first 30 data points) were the only

ground-based conditions used in the development of the BLT Tool V.1. The range of the

current disturbance parameter for this Mach 6 data is 0. 2 < k/S < 1. 6 based on the N-S

database. All k/S values reported in this section were derived from the N-S database.

The data presented in Table 2 were obtained in support of the STS-121 mission on a

0. 75%-scale Orbiter model at a nominal angle of attack of 40 ° . All transition measurements

were acquired with raised diamond-shaped (“pizza-box”) trips at x/L locations more aft

than the previous data. Details of the experimental setup and test conditions are provided

in Ref. [21]. Later in the document, the combined test conditions characterized in Tables 1

and 2 are referred to as “existing Mach 6 data.” The range of k/S for the STS-121 mission

support data is 0. 2 < k/S < 0. 5.

Table 3 presents recently acquired Mach 6 data obtained as part of a technical expert

investigation study. The funding was allocated to the BLT Team as a discretionary resource

to support potential studies that the team deemed important with concurrence from the

Aeroheating Panel. The BLT Team decided to use the resources to conduct a protuberance

study, and this data will be referred to as the new Mach 6 data. The measurements were

acquired on 0. 9%-scale Orbiter models at a nominal angle of attack of 40 ° . The larger

model scale (20% larger than the 0. 75%-scale model) facilitated improved manufacturing

capabilities of the protuberance geometry and size. The data expanded the existing Mach

6 database by acquiring data for other representative protuberance shapes (e.g., gap fillers

and shapes resulting from tile repair concepts), for protuberances at aft locations on the

Orbiter and for protuberances at outboard locations inboard of the shock interaction region.

Details of the experimental setup, test conditions, and results are provided in Ref. [22]. The

range of k/S for the new data is 0. 2 < k/S < 0. 6.

In summary, all the Mach 6 data were acquired for protuberance heights in the range

of 0. 2 < k/S < 1. 6. The corresponding boundary-layer edge to wall temperature ratios for

these conditions at the location of the trips are in the range 0 . 7 < Te /Tw < 1 . 4.

3.2 LaRC 31-Inch Mach 10 Air 'Tunnel

The existing M = 10 data obtained prior to the development of the BLT Tool V.1 are

presented in Table 4. The transition measurements were acquired on 0. 75%-scale Orbiter

models using a phosphor thermography system. Most of the measurements were acquired

at a nominal angle of attack of 40 ° and a few cases at 30 ° . In all cases, transition was forced

12
with raised diamond-shaped protuberances. Details of the experimental setup and test

conditions are available in Ref. [20]. These M = 10 data were not used in the development

of the BLT Tool V.1 derived with the LATCH database due to unsatisfactory collapse in the

correlation space with the M = 6 data and historical flight data. However, the BLT Tool

V.2 includes these data and it will be shown that use of a N-S database for the correlation

parameters leads to an acceptable data collapse. The range of k/S for the Mach 10 data is

0. 2 < k/S < 2. 1. The temperature ratios are in the range 1 .6 < Te/T,, < 2.4, larger than

the ratios at Mach 6.

3.3 LaRC 20-Inch Mach 6 CF4 'Tunnel

The LaRC 20-Inch Mach 6 CF 4 Tunnel uses tetrafluoromethane (CF4 ) as the test gas. CF4

has a larger normal shock density ratio and smaller ratio of specific heats (gamma) than air.

This simulates an important aspect of dissociative high-temperature effects associated with

the reentry of blunt vehicles, i.e., the increase in normal shock density ratio or the decrease

in the ratio of specific heats that occurs within the shock layer of the vehicle [23]. Existing

Mach 6 CF4 data are presented in Table 5 for data acquired on 0 . 75%-scale Orbiter models

with raised diamond-shaped protuberances. Most of the data were acquired at a nominal

angle of attack of 40 ° and a few cases at 30°. Heat transfer data were inferred using a

phosphor thermography system. Details of the experimental setup and test conditions are

available in Ref. [20]. These data were not used as part of the development of the BLT Tool

V.1 derived with the LATCH database due to unsatisfactory collapse in the correlation space

of the database with the M = 6 data and historical flight data. As for the case with data

acquired in the LaRC 31-Inch Mach 10 Air Tunnel, the BLT Tool V.2 will include the CF 4

database when the N-S database is used for the deriving the correlation parameters. The

range of k/S for the CF4 data is 0. 2 < k/S < 2. 7. The corresponding temperature ratios

are 1 . 3 < Te/T,, < 1 .8 and tend to bridge the range between the LaRC Mach 6 and Mach

10 Air Tunnels.

3.4 CUBRC LENS-I Shock 'Tunnel

Recently acquired transition data were obtained at Mach 10 and 16 in the LENS-I Shock

Tunnel on a 1 . 8%-scale Orbiter model. Data were acquired for protuberance shapes in the

form of raised diamond-shaped trips and fence trips. All of the data were acquired at a

nominal angle of attack of 40° . Heat transfer measurements, inferred by thin-film gauges,

and temperature sensitive paint measurements were used to assess the state of the flow.

The data collected in the CUBRC facility extended both the ground-based Mach number

and k/S ranges. Details of the experimental setup, test conditions, and results are available

in Ref. [24] (see also Ref. [25] for experimental setup). The Mach 10 data are presented in

Table 6 where the range of k/S is 0.3 < k/S < 0. 4 and Te/T,, is 2 . 7 < Te/T,, < 2.8 (somewhat

larger temperature ratios than the LaRC Mach 10 Air Tunnel). Two Mach 16 test cases

(configurations 4 and 5 as noted in Ref. [24]) were tested at large k/S values in order to

acquire transition onset data at low unit Rem’s. Transition onset due to both starboard and

port attachment-line trips was not realized for configuration 4 but, based on supplementary

measurements (i.e., unsteady heat transfer data), transition appeared to be imminent (see

Ref. [24] for discussion). Table 7 presents the correlation parameters for the Mach 16 data.

The last two lines of Table 7 provide the properties at the highest unit Rem tested for the

laminar attachment-line flow for configuration 4. These laminar results are documented in

the table for the purpose of qualitative interpretation (to be discussed later). The range of

k/S for the Mach 16 data is 0 . 2 < k/S < 3. 5. The temperature ratios are significantly larger

than those for the other ground-based facilities, namely 4.9 < Te/T,, < 5. 4

13
3.5 Historical Flight Data

Actual flight data are essential to calibrate and anchor the BLT Tool as the ground-based

data cannot accurately simulate the reentry atmospheric conditions experienced by the

Orbiter. As a result, historical flight data were reexamined to better determine the root

causes of the occasional early transition times realized on some of the past Shuttle missions.

Details of the analysis are given in Ref. [5] and further refined in Ref. [26]. Ten flight cases

were identified as having early transition times due to protruding gap fillers: STS-28 (2

cases), STS-41, STS-55 (2 cases), STS-73, STS-81, STS-94, STS-99 and STS-103. These

flight cases are tabulated in Table 8 along with their respective measured transition times

from entry interface, EI (EI is arbitrarily defined as the altitude at which the Orbiter enters

the discernible atmosphere at 400,000 feet). In the Orbiter structural reference system

given in this table, axial distance is represented by X (X = 236 in. represents the nosetip),

spanwise distance from the centerline symmetry plane is Y, and distance in the vertical

direction is characterized by Z (Z = 338. 5 in. represents the nosetip). The estimated

uncertainties in the post-flight measurements of the gap filler protrusion heights, k, are

also indicated in the table and provide a measure of uncertainty for the flight data. The

reported uncertainties in k were obtained from different sources and methodologies (refer

to Ref. [26] for details). Note that three interpretations are available for STS-73. The gap

filler for STS-73 was bent over during post-flight measurements with a bent over height

of k = 0.6 in. and an unbent height of k = 1. 4 in. Also, two likely transition times were

extracted from the thermocouple data detected on the windward surface of the Orbiter (refer

to Refs. [5] and [26] for more details). The interpretation accepted by the Aeroheating

Panel is the first STS-73 line shown in the table which assumes a k consistent with the

bent height and the earlier of the two transition times from EI (880 seconds). The two

alternate interpretations are indicated in the table with asterisks for completeness. The

relevant correlation parameters are presented in Table 9 where x is the axial distance from

the nosetip of the Orbiter. The range of k/S for the historical flight cases is 0 . 1 < k/S < 0. 3,

i.e., all submerged protuberances. The corresponding range in freestream Mach number is

7 < M < 19. The corresponding temperature ratios are 2 . 6 < T,

/Tw < 4.3, which are

bracketed by the ground-based values.

4 Correlation Results

In this section, the BLT Tool V.1 protuberance correlation is compared using the LATCH

and Navier-Stokes databases. Proposed correlations are then presented followed by a downselect process. The agreed upon correlation constants for the down-selected correlations are

presented. Assumptions and limitations of the down-select correlations are discussed.

Before proceeding, three graphical illustrations of all the data to be used in the development of the next-generation BLT Tool are shown in Figures 3 through 5. The first plot,

Figure 3, overlays the database onto the Orbiter’s windward surface. The existing databases

(LaRC’s M6, M10 & CF4 data) use only positive y/LT,f values, but data were acquired with

protuberances on both the starboard and port sides of the Orbiter. For the other databases,

positive y/LT,f values denote the starboard side and negative y/LT,f values denote the port

side. The historical flight data (plotted as y/LT, f > 0) are all captured within the spatial

extent of the ground-based data. The plot of N-S based Reθ /M, versus the normalized

streamwise coordinate x/LT,f in Figure 4 demonstrates the range of the experimental data.

Some values of Reθ /M, for flight are larger than those for the ground-based data. Similarly,

Figure 5 shows a plot of N-S based Re k (= ρkuk k/μk ) versus k/S where the subscript ‘k’

denotes that the properties are evaluated at the trip height k. It should be noted that

not all the data are for submerged protuberances ( k/S < 1), since the relevance of Re k for

protuberances larger than the local boundary thickness is unclear. The values of Re k for

14
flight are larger than the corresponding ground-based data at similar k/S values; however,

the overall Re k values for flight are within the range of those obtained in the ground-based

facilites. Note that the use of correlations in the format of Reθ /Me and/or Rek equal a

constant, demonstrate uncertainties more than a factor of ten for the Orbiter’s windward

surface. Due to this large uncertainty, the correlations used in the BLT Tool V.1, and those

implemented for the BLT Tool V.2 have additional correlating parameters to mitigate large

uncertainties.

4.1 LATCH versus N-S Database

The data analysis done in this report is slightly different from the analysis done in the

development of the BLT Tool V.1 [2, 3]. As noted earlier, the incipient transition unit

Reynolds number, Rem,inc, in this report is defined as the average between the last fully

laminar value (Rem,1) and the first non-laminar value (Rem,2) for all the ground-based

data. With this consistent framework, the percent error between the actual and estimated

Rem,inc is bounded by one-half the percent difference between Rem,1 and Rem,2. For the

development of the BLT Tool V.1, a different approach was used, in which Rem,inc was

usually taken as the last laminar value. With that approach, the percent error in Rem,inc

can be as large as the percent difference between Rem,1 and Rem,2, and the estimated

Rem,inc values are consistently biased to low values. The percent difference between Rem,1

and Rem,2 in some cases can be as large as 50%. Plots showing both approaches are shown

in Figures 6 and 7 where C(“Best Fit”) refers to the best estimate of the regression fit.

The data plotted are based on the LATCH solutions and are the only ground-based data

used to develop the BLT Tool V.1. Using the previous framework for estimating Rem,inc

(see Figure 6), the best fit and −2Q fit are C = 38.6 and C_95% = 28. 4, respectively. The

accepted coefficient for Version 1 is C = 27 which was selected as the conservative bound

akin to the C_95% coefficient value of 28.4 in this analysis. A percent difference of 5%

between these two coefficients is realized and is mainly attributed to the analysis used, i.e.,

the Version 1 analysis used a trial and error approach to conservatively bound the results

versus the more rigorous regression approach applied here. Using the current framework

(see Figure 7), the corresponding values are C = 40.4 and C_95% = 27. 8. This translates to

a 4.6% and a 2.1% difference in C and C_95% between both frameworks. The uncertainties

represented by the cross-hairs in the Figure 7 are from contributions due to the uncertainties

in Rem,inc as discussed in Section 2.3 (computed using MC method). The error bars here

are used to demonstrate that the consistent analysis approach introduces uncertainties that

are bounded for the most part by the 95% confidence levels of the data. The uncertainty in

k was set to zero (Uk = 0) since only the contributions due to the uncertainties in Reynolds

numbers were intended. From this point forward, the consistent framework to estimate

Rem,inc is used exclusively.

Correlation plots for the ensemble of the ground-based data are shown in Figures 8 and

9 for the N-S and LATCH databases, respectively. The plots include error bars to denote

resulting uncertainties in Reθ /Me and k/S (refer to Section 2.3 for discussion). These uncertainties account for uncertainty contributions due to Rem,inc selection and protuberance

height, k, measurements. An estimated uncertainty in k based on measurements is taken as

Uk = ±0. 0005 in. for all ground-based data. Note that the scatter is larger for the new Mach

6 data than for the existing Mach 6 data using both the N-S and LATCH databases. Protuberance shape effects and orientation effects were investigated in the new study thereby

increasing the variability in the data. Protuberance orientation effects on Rem,inc could be

significant but no first-order shape effects were realized (refer to Ref. [22] for details). Significant variability also exist for the LENS-I Mach 16 data. The circled data points on the right

of the plot (4 data points but appear as 3 data points) were obtained for large k/S ( > 1 .3)

values. The inference was made in Ref [24] that these low Rem conditions tend to suggest a

15
lower threshold at Mach 16 necessary to sustain turbulent flow. The regression analysis for

the ensemble data do not include the four LENS-I Mach 16 data points at k/S > 1 .3. These

data points will introduce some bias into the results as Ree /Me asymptotes to a threshold

limit for large k/S values. Both measures of goodness, R and ΔC/C, show improvement

from the LATCH framework to the N-S framework. Table 10 shows a comparison of the

facility dependent metrics between the LATCH and N-S databases. Overall improvement in

the metrics (decrease in ΔC/C and increase in |R|) is observed for the N-S database except

for the LENS-I Mach 16 data. A new ensemble metric, QC /C, is introduced in the table

where QC is the sample standard deviation and C the mean of the facility constants. Note

that this new measure is only applied when each facility regression uses the same numeric

value for n. The calculation of QC/C does not include the LENS-I Mach 16 data since the

regression fit is flawed (see comment above). This metric is a measure of the facility-tofacility regression variability. Again, the N-S database show better results than the LATCH

database, i.e., reduced variability.

A plot of the historical flight data in the correlation space is presented for completeness

in Figure 10. Each datum has the associated STS mission identified in the figure. The

ten flight cases accepted by the Aeroheating Panel are shown along with the two alternate

interpretations of STS-73 (refer to Section 3.5 for details). The metrics, R and ΔC/C, are

computed based on the ten accepted flight cases. Recall from the discussion in Section 2.2

for small sample sizes that it is more appropriate to assume a T-distribution for the 95%

confidence limits, i.e., ftSˆY uncertainty band. If t = 2. 26 is assumed for N = 10, then

(C-95%, C+95%) = (31 . 1, 55. 6) instead of (C-95%, C+95%) = (32. 2, 53 . 8) as reported in the

figure. It is evident that the percent differences in the confidence limits are small (less than

3.5%), and thus supports the assumption of using a consistent value of t = 2 in this report

as appropriate. The horizontal error bars shown in the plot represent the uncertainties in

protrusion heights, k (see Table 8). Based on the available documentation, it is not clear if

the uncertainties in k are representative of a 95% uncertainty band, a value typically used

in engineering applications. Throughout this baselining process, 95% confidence limits have

been used for the uncertainties. Recall that for a Gaussian distribution, the 95% confidence

limits are consistent with f2 Q uncertainties about the mean. Similarly, fQ uncertainties

are representative of 68% confidence limits. However, based on the relative magnitudes

of some of these uncertainty values given in Table 8, the values do not appear to have

a consistent uncertainty basis. All but two of the uncertainties quoted for the accepted

flight cases are greater than f18%; hence, the quoted uncertainty bands are most likely

representative of 95% confidence limits (f2 Q) than, for example, 68% confidence limits

(fQ). The uncertainties in transition times reported in Refs. [5] and [26] are less than a

few seconds. These time uncertainties represent small percent errors in Ree /Me and S and

consequently were not included in the flight uncertainty analysis. The error bars shown in

Figure 10 assumes the k uncertainties in Table 8 represent 95% confidence levels.

4.2 Proposed Correlations

All proposed correlations, PC, are developed using the Navier-Stoke database. For all the

proposed correlations, the regression analysis for the ensemble data, both with and without

flight data, does not include the LENS-I Mach 16 data for k/S > 1 . 3 (see discussion in

Section 4.1). As a reminder, these excluded transition onset data points are circled red in

the correlation plots to follow. Data points for the laminar LENS-I Mach 16 data (refer to

Section 3.4) are enclosed using a green circle with a tail when plotted. The laminar data

(two data points but appear as one) are obviously not used in the regression analysis but

are presented to reinforce the observed departure of the large k/S, Mach 16 data from those

at lower Mach numbers.

16
Various correlating parameters were examined that took advantage of the fluid and flow

variables available or derivable from the existing N-S database. Correlations were assessed

for the ensemble of ground-based data as well as for the entire database (ground-based +

flight data). A representation of the correlations investigated are discussed below. In addition, protuberance correlations with independent correlating parameters were examined

to achieve the goal of obtaining redundant independent correlations. The primary protuberance correlation will be the correlation with the highest level of confidence based on the

regression metrics for the entire database. In the following subsections, the reader will be

pointed to correlation plots that include some of the regression metrics but not the ensemble

metric, uC/C. These are summarized in Table 11.

4.2.1 PC#1: Reθ /Me = C X (k/S)

n

The form of the BLT Tool V.1 correlation with all the ground-based and historical flight data

is presented in Figure 11. This correlation will serve as a baseline for future comparison.

For the plot shown, the exponent was kept constant, n = —1. A value of n = —1 .04 for

the exponent was obtained when it was allowed to vary in the regression analysis. The

flight data are bounded by the best fit curve, C = 32. 6, and the least conservative curve,

C+95% = 58. 8. Note that the transition onset Mach 16 data for k/S > 1 . 3 (symbols enclosed

with red circles) depart from the observed trends of the lower Mach number data. Similarly,

the laminar Mach 16 data for k/S ;::Li 1 . 8 (symbols enclosed with a green circle) also support

the observed trends and are in the same family as the transition onset Mach 16 data for large

k/S. The ensemble metric for this database (ground-based and flight data) is uC/C = 21 . 2%.

4.2.2 PC#2 & 3: Reθ /Me = C X (k/S*) n & C X (k/B) n

For hypersonic flows, the boundary-layer thickness, S, can be overly sensitive to the methodology used to define the boundary-layer edge [27]. Also, it was thought that the displacement

thickness, S*, or momentum thickness, B, may provide some level of improved facility-tofacility collapse as they account, somewhat indirectly, for temperature differences between

the facilities. As a first attempt, the disturbance parameter was changed to X = k/S* to

mitigate the sensitivity observed with S. As before, the exponent was assumed constant,

n = —1 (a value of n = —0. 96 was obtained for the entire database when n was allowed to

vary in the regression analysis). A plot of the proposed correlation, for ground-based data

only, is presented in Figure 12. The ensemble metric for this correlation is uC/C = 7. 3%.

This correlation clearly demonstrates better collapse of the ground-based data when compared with the baseline correlation in Figure 8 where uC /C = 19.9%. When the flight

data is added to the database as shown in Figure 13 (the ensemble metric increases to

uC/C = 34. 9%), the proposed correlation becomes less attractive when compared to the

baseline in Figure 11. All the metrics, ΔC/C, 1R1, and uC/C, indicate a less robust correlation than that of the baseline when both ground-based and flight data are utilized. Whether

this ground-based versus flight data discrepancy should be attributed to differences in test

versus flight environment, or some other factor, is unclear.

As a second attempt, the disturbance parameter was changed to X = k/B to mitigate the

sensitivity observed with S. Again, the exponent was assumed constant, n = —1 (n = —0. 92

was obtained for the entire database in the regression analysis). A plot of the proposed

correlation for the ground-based and flight data is presented in Figure 14. The ensemble

metric for this correlation is uC/C = 23. 3%, slightly larger than the baseline value of

uC/C = 21. 2% (see Figure 11). All the metrics, ΔC/C, 1R1, and uC/C, indicate a less

robust correlation than that of the baseline when both ground-based and flight data are

utilized.

17
4.2.3 PC’s#4 & 5: Reθ /Me = C/[(k/S)(Te /T,,,

)

m] & C/[(k/S)(He /H,,,

)

m]

The next correlation approach investigated the implementation of either a temperature ratio,

Te /T,,,, or total enthalpy ratio, He /H,,,, to mitigate the facility variability. At the time the

BLT Tool V.2 was being developed, the decision was made to implement this approach

with the most promising of the proposed correlations. As a result, this implementation

was conducted for PC#1. To obtain values of the exponent m that provided best values

of the metrics, the regression was conducted recursively for values of the exponent in the

range —1 < m < 1. Note that a value of n = —1 was used for the regression exponent.

The values of m using both the ground-based and flight data for Te /T,,, and He /H,,, , which

yielded the lowest values of ΔC/C, were found to be m = 0. 16 and m = 0. 30, respectively.

Figure 15, which includes both ground-based and flight data, shows the correlation plot

for the disturbance parameter X = [(k/S)(Te /T,,,

)

m] where σC/C = 23. 6%. A similar plot

using the total enthalpy ratio is presented in Figure 16. The ensemble metric using the

total enthalpy ratio is σC/C = 19. 9%. All the metrics (ΔC/C, JRJ, and σC/C) for the

correlation with disturbance parameter, X = [(k/S)(He /H,,,

)

m], are better than both the

baseline correlation (PC#1) and the correlation with X = [(k/S)(Te /T,,,

)

m] when both the

ground-based and flight data are utilized.

4.2.4 PC’s#6 & 7: Rek -Type Correlations

In the first correlation considered in this section, the disturbance and transition parameters

were selected as X = (pk uk k) /(pe ueB) and Y = peueB/μ,,,, respectively [14]. The subscripts

‘k’ and ‘w’ denote properties evaluated at height k in the undisturbed laminar boundary

layer and at the wall, respectively. The correlation was evaluated with an exponent n = —1

(i.e., pk uk k/μ,,, = C) using all the ground-based data and is shown in Figure 17. It becomes

obvious looking at the plot and metrics that an exponent of n = —1 is not appropriate.

The metrics for this correlation are undesirable (relatively large ΔC/C and small JRJ) and

do not improve significantly if n becomes a free parameter in the regression analysis. With

the addition of the flight data, the metrics for this correlation become worse. As a result,

this correlation approach was not pursued further. Ref [14] shows a similar plot (Figure 2

in the reference) with data reported in Ref [28] that were obtained only on the centerline of

a Shuttle-Orbiter model. The plot reported there shows a good correlation, unlike the data

presented here. Note that the best fit constants for both plots are in excellent agreement

(C = 343 for the current data and C = 344 for the data reported in Ref [14]), which

serves as a sanity check for the current analysis. It should be noted that the current data

includes results obtained away from the centerline in the influence of crossflow. Additionally,

data with k/S > 1 are also part of the current dataset and the interpretation of Rek -type

correlations for protuberances extending beyond the boundary layer is unclear.

The next correlation considered defines as the disturbance and transition parameters

X = (pk uk k) /(pe ueB) and Y = pe ueB/μk , respectively. Note that the only difference between this correlation and the previous correlation is the location at which the viscosity

is evaluated (at height k versus at the wall). Substituting into Eq. 1 gives the following

expression,

1+n

Rek

n x 

L

Ree • 

μe 11 = C. (14)

L

μk

For the special case of n = —1, Eq. 14 degenerates to Rek = C, the scenerio discussed in

Ref [14]. Figure 18, which includes ground-based and flight data, presents the correlation

plot where the exponent was selected as n = —0. 6 (best fit exponent, n = —0. 573, rounded

to nearest tenth). The ensemble metric is σC/C = 35. 0%, larger than the baseline value

of σC/C = 21 . 2% (refer to in Figure 11). The flight data are biased toward the C+95%

18
line. Note that the large k/S, LENS-I Mach 16 data fall within the 95% confidence limits

unlike the previous correlations. It is not clear why the large k/S data are in family for this

correlation.

4.3 Correlation Down Select

The correlations are summarized in the Table 11. Based on the correlation metrics, proposed

correlation 5 provides the best collapse of the total ensemble data (ground-based + flight).

Proposed correlations 1 - 5 are not sufficiently independent correlations since they share the

same disturbance parameter Reθ

/Me. Consequently, PC#7 is the next best independent

correlation based on the correlation metrics in the table. The recommended engineering

correlations for the next-generation BLT Tool are therefore proposed correlations 5 and 7,

where PC#5 uses an Reθ /Me versus (k/S) • (He /Hw )

0.30 correlation,and PC#7 an pe ueB/μk

versus (pk uk k) /(pe ueB) correlation. The correlation constants for proposed correlations 5

and 7, based on the regression analysis applied to the ground-based and flight data, are

[C-95%, C, C+95%] = [25. 3, 42 .8, 72 . 5] and [118. 0, 217. 6, 401 . 3], respectively.

4.4 Selection of Correlation Constants

As per the down-select process in Section 4.3, the recommended options 1 and 2 for the

BLT Tool V.2 protuberance correlations are proposed correlations 5 and 7, respectively.

The recommended ensemble correlation plots, which includes both ground-based and flight

data, were presented in Figures 16 and 18. For clarity, the recommended correlations are

re-plotted in Figures 19 and 20 with only the flight data. Error bars due to uncertainties

in protrusion heights, k, assuming 95% confidence limits for the quoted uncertainties (refer

to Table 8), are also presented in the figures (see end of Section 4.1 for details). For both

recommended options, the flight data are consistently biased towards the C+95% curve. This

will result in overly conservative correlations, with respect to the tool’s transition predictive

capabilities, if the selected best estimate correlation coefficients, C, are used. A methodology

was decided upon by the Aeroheating Panel to derive a new set of correlation coefficients

using the entire database. Stated briefly, the best estimate correlation coefficient will be

derived from the nominal flight data, and the 95% confidence limits will be based on the

extensive ground-based data. It should be noted that the k values measured on the ground

upon landing for the nominal flight cases were assumed to have the same values during

reentry, i.e. aerodynamic forces, landing forces, and ablation of the gap-filler material do

not appreciably change the height of the protruding gap filler.

The rationale for this methodology, agreed upon by the Aeroheating Panel, can be summarized with the following statements. As is evident from the preceding sections, extensive

ground-based measurements have been acquired for a range of Mach numbers and k/S values

to examine the effects on transition onset of protuberance geometry, orientation, and spatial

location all on the windward surface of sub-scale Orbiter models. The recommended correlations clearly indicate a bias between the best fit of the flight data and ground-based data

(see Figures 19 and 20). It should be noted, however, that correlations based on the nominal

flight data have very similar slope values, n, as correlations based on the entire ensemble

database, i.e. similar correlation trends. Whether these differences should be attributed

to the ground test versus the flight environment, uncertainties in the flight protrusion geometries (see discussion in Secton 3.5), numerical modeling inconsistency, scaling issues, or

some other factor is unclear. For example, the ground-based facilities do not accurately

simulate the reentry flight conditions experienced by the Orbiter (e.g., high-temperature

effects). Secondly, the ground-based facilities inherently have a noise environment, due to

radiation from the turbulent nozzle-wall boundary layers, not realized in flight. Taking into

account the aforementioned comments, the decision was made to use the best fit correlation

19
coefficient derived from the nominal flight data (ten accepted cases) as the best estimate

coefficient for the recommended correlations. This removes the unwanted bias between the

best estimate coefficients of the correlations and the flight data. The 95% confidence limits

are derived using the extensive ground-based data as it includes more protuberance geometry and location effects than the flight data. The confidence limits are derived by equating

the ground-based uncertainty to the desired uncertainty about the best estimate coefficient

for the respective correlations (details to follow).

4.4.1 Option 1 Correlation (PC#5)

Recall for the option 1 correlation (i.e., proposed correlation 5), the disturbance and transition parameters are (k/δ) (He /Hw )

0.30 and Reθ /Me , respectively, where the slope is n = −1.

Regression analysis was applied to the nominal flight data accepted by the Aeroheating

Panel. The analysis results in very good metrics for the correlation. The best fit correlation

constant for the accepted flight data is taken to be C = Cflt = 61 .3, where the subscript

‘flt’ denotes flight data. The new 95% confidence limits are derived based on the uncertainty values obtained from the ensemble of the ground-based data. The analysis is easily

done in the regression space, i.e., Xˆ

-Yˆ space (refer back to Section 2.2). For the current

correlation approach applied to the ensemble ground-based data, the best fit is Cgb = 41 . 6,

where the subscript ‘gb’ denotes ensemble ground-based data. Recall from Section 2.2 that

Cˆ = log C. The newly derived uncertainty, 2SYˆ/C, ˆ

is equated to the ground-based uncertainty, 2SˆY ,gb/Cˆ

gb, where SˆY is defined in Eq. 7 and SˆY,gb = 0. 109. The newly derived

standard error becomes SˆY = SˆY ,gb x C/ˆ Cˆ

gb . The 95% confidence coefficients are then

computed using Eqs. 8 and 9. The newly derived coefficients for option 1 correlation are

(C-95%, C, C+95%) = (35.3, 61 . 3, 106 . 4) versus (C-95%, C, C+95%) = (25. 3, 42 . 8, 72 . 5) for

the total ensemble of ground-based and flight data. Both sets of coefficients are tabulated

in Table 12 for convenience.

A plot showing the newly derived correlation coefficients and the flight data with associated error bars, assuming 95% confidence limits for the quoted uncertainties in k, is

presented in Figure 21. In the following plots, C(“BF Flight”) denotes best fit coefficient

for the flight data. It should be noted that the uncertainties in the accepted flight data are

all contained within the 95% confidence limits of the correlation. If 68% confidence limits for

the quoted uncertainties in k are assumed, then the errors bars are twice those in Figure 21

due to the linear dependence of the disturbance parameter to k. For this assumed larger

uncertainty band, five of the accepted flight cases can potentially lie below the C-95% line,

i.e., STS-55 (2 cases), STS-94, STS-99, and STS-103. These flight cases represent the largest

quoted k uncertainties (f25% to f30%) and most likely already represent approximate 95%

confidence limits (≈ f2u uncertainty bands) instead of the assumed 68% confidence limits

(see discussion at the end of Section 4.1). Figure 22 shows a plot with all the available data

and the newly derived correlation curves. The large k/δ, Mach 16 data, both laminar and

transitional, are indicated in the figure. These data are out of family from the observed

correlation trends. As expected, some of the ground-based data lie below the C-95% curve.

To put this correlation in perspective, the historical flight data with the measured EI transition times are shown in Table 13. Results from one post STS-107 flight, i.e. STS-121, are

included at the end of the table as an added flight case. The predicted transition times using

the associated flight trajectories for this correlation are shown in the table. The predicted

times are based on the correlations coefficients recommended by the Aeroheating Panel (see

Table 12). Note the good agreement between the measured transition times and the best

estimate (BE) transition times for PC#5 with the recommended coefficients.

20
4.4.2 Option 2 Correlation (PC#7)

The discussion for the option 2 correlation (i.e., proposed correlation 7) is very similar to the

above discourse for the option 1 correlation. The disturbance and transition parameters are

(Pkuk k)/(PeueB) and PeueB/μk, respectively, where the slope is n = — 0. 6. The regression

analysis applied to the nominal flight data accepted by the Aeroheating Panel resulted in a

new best fit correlation constant of C = Cflt = 396.8. As before, the new 95% confidence

limits are derived based on the uncertainty values obtained from the ensemble of the groundbased data. The best fit constant and standard error for the ground-based ensemble data are

Cgb = 207. 5 and SˆY ,gb = 0. 114, respectively. The newly derived standard error becomes

SˆY = SˆY ,gb x C/ˆ Cˆ

gb . The 95% confidence coefficients are then computed using Eqs. 8

and 9. The newly derived coefficients for option 2 correlation are ( C_95%, C, C+95%) =

(220. 7, 396. 8, 713. 4) versus (C_95%, C, C+95%) = (118. 0, 217. 6, 401 . 3) for the total ensemble

of ground-based and flight data. Both sets of coefficients are tabulated in Table 12 for

reference.

A correlation plot utilizing the newly derived coefficients and the flight data with associated error bars is presented in Figure 23. The errors bars in this figure assume 95%

confidence limits for the quoted uncertainties in k. Note that all the uncertainties in the

accepted flight data are all contained well within the 95% confidence limits of the correlation. Figure 24 shows a plot with all the available data and the newly derived correlation

curves. The large k/δ, Mach 16 data, both laminar and transitional, are indicated in the

figure. These data points are in the same family with the lower Mach number data and

the observed correlation trends. As expected, some of the ground-based data lie below the

C_95% curve. Table 13 also shows the predicted transition times using this correlation.

4.5 Correlations Revisted

Recall from the analysis in Section 4.2, that improved data collapse in the correlation parameters was obtained with the implementation of a temperature or total enthalpy ratio.

Specifically in Section 4.2.3, the inclusion of the total enthalpy ratio in the disturbance parameter, X = [(k/δ)(He /Hw )

m], provided improved correlation metrics as compared with

X = k/δ (compare PC’s#1 and #5 in Table 11). A similar procedure using the entire

database was conducted during the development of the BLT Tool V.2 for X = k/δ

* , but the

improvements in the correlation metrics with the addition of these ratios were secondary to

the proposed correlation #5. Due to the relative lack of collapse (poor correlation metrics)

when correlating with a disturbance parameter, X = k/B (see Table 11), the implementation of the temperature or total enthalpy ratio was not pursued during the development

of the BLT Tool V.2. More recently, this was examined for both X = [(k/B)(Te /Tw )

m]

and X = [(k/B)(He /Hw )

m] with interesting results for regression exponents of n = —1.

The improvements made in the correlation metrics with the inclusion of the temperature

ratio are still not as good as those with PC#5; however, improvements better than PC#5

are observed with the addition of the total enthalpy ratio. The correlation metrics are

summarized in Table 14 for the entire database (ground-based + flight data). Note the

improvements in the metrics between PC#5 and the total enthalpy ratio implementation

of X = k/B (line with right arrow) in the table, albeit small for R and ΔC/C. A 25% improvement in the facility-to-facility variability ( QC /C) is observed. A plot of this correlation

is shown in Figure 25. Two observations with this revised correlation are that the flight

data are consistently biased towards the C+95% line and that the Mach 16 data for the large

k/δ are out of family for this correlation, similar to observations made for PC#5. Upon

applying the methodology of the Aeroheating Panel as described in Section 4.4, the flight

and ground-based data are re-plotted with the newly derived coefficients in Figure 26. The

newly derived coefficients for this correlation are ( C_95%, C, C+95%) = (268. 0, 450. 7, 758. 1)

21
versus (C_95%, C, C+95%) = (212.0, 350. 3, 578.8) for the total ensemble of ground-based

and flight data.

4.6 Assumptions and Limitations

There are a few key assumptions employed in the development of the proposed BLT correlations that need to be mentioned.

• The main underlying assumption is that the ground-based transition database provides

an adequate representation for the flight database. Firstly, the ground-based facilities are incapable of simulating the actual flight conditions experienced during reentry.

These include, but are not limited to, high-temperature effects, appropriate freestream

Mach number range, and environmental noise conditions. All conventional hypersonic

facilities are known to radiate noise from the transitional/turbulent nozzle-wall boundary layers. This radiated noise has been shown to affect transition measurements for

a range of transition mechanisms.

• The protuberance heights, k, used in the sub-scale ground-based tests assume a scaling

based on local boundary-layer flow parameters like Reθ , Rek , Me , S, etc.

• BLT correlations developed with ground-based data and simplified protuberance geometries are assumed directly scaleable to flight.

• The nominal flight data are used to select the recommended best estimate correlation

coefficient even with the known geometry uncertainties in flight. Recall that geometry

measurements were all acquired upon Shuttle landing. In addition, the possibility of

the protuberances (gap fillers) bending or deforming under the aerodynamic loads of

reentry are unknown.

• The extensive ground-based data are used to estimate the 95% confidence limits of

the recommended correlation coefficients.

With the assumptions above, it should be noted that the historical flight data, for most of

the proposed correlations, lie within the 95% confidence limit of the entire database (refer

to Sections 4.2 and 4.4 for details).

The limitations of the BLT correlations need to be clearly stated. Caution needs to be

exercised to insure that the correlations are applied within the range of parameters used in

the development.

• The correlations are applicable on the windward surface of the Orbiter for protuberances inboard of and on the attachment lines.

• The ratio of protuberance height to local boundary-layer thickness is 0 . 1 < k/S < 3. 5.

For large k/S and M values (e.g., k/S > 1.3 and M > 16), preference should be

given to PC#7 (Rek -type approach) since it collapses the data better than PC#5

(Reθ/Me

- type approach).

• Apply BLT correlations using a consistent computational framework to that utilized

during development.

The BLT correlations were developed within a limited parameter range due to restricted

range in facilities and available data. As a result, there is no data to validate and/or anchor

the correlations outside of the limited parameter range so the end user must be cognizant

when exceeding the following bounds.

• The correlations were developed with protuberances located at x/LTef values in the

range of 0. 1 < x/LTef < 0. 85.

22
• The correlations were developed using transition data with freestream Mach numbers

in the range of 6 < M,,^ < 19.

5 Summary

Boundary layer transition data specific to the Space Shuttle Orbiter, acquired in four groundbased facilities (LaRC 20-Inch Mach 6 Air Tunnel, LaRC 31-Inch Mach 10 Air Tunnel, LaRC

20-Inch Mach 6 CF4 Tunnel, and CUBRC LENS-I Shock Tunnel) using three wind tunnel

model scales (0.75, 0.90, and 1.8%) plus Orbiter historical flight data, have been analyzed

to develop an engineering tool for windward-side Orbiter reentry transition prediction. BLT

engineering correlations were presented using a N-S database developed for both groundbased and flight conditions. It was demonstrated that the BLT Tool V.1 applied with the

N-S database provided better data collapse than with the LATCH database. In all the

regression analysis, the large k/S ( > 1. 3) data at Mach 16 were not included in the analysis

and are excluded from the correlation metrics. Of the correlation tools examined during the

development of the BLT Tool V.2, the proposed correlation 5 with X = (k/S) x (He /Hw )

0.30

and Y = Reθ /Me was found to provide the best overall correlation metrics when the entire

database of ground-based and flight data is employed. The large k/S, Mach 16 data were

out of family for this correlation. The second independent correlation (proposed correlation

7) selected uses X = (pkuk k)/(peueB) and Y = peueB/μk as the disturbance and transition

parameters, respectively. This correlation, developed using the entire ground-based and

flight database, provided an overall data collapse to include the Mach 16, large k/S data, but

the metrics were not as good as proposed correlation 5. The Aeroheating Panel adopted an

approach to select the recommended correlation coefficients for version 2 of the protuberance

BLT Tool. The coefficients for the BLT Tool V.2 are summarized in Table 12. The BLT

Tool V.2 has been baselined and approved by the Orbiter Project Office in the Space Shuttle

Program as part of the transition prediction tool for use by the Damage Assessment Team for

real-time evaluation of the Orbiter’s TPS prior to reentry. The protuberance correlations

were recently revisited and an improved correlation with X = (k/B) x (He /Hw ) 0.44 and

Y = Reθ /Me was obtained. The improved metrics are marginally superior and have similar

trends to the proposed correlation 5. Consequently, there is not a strong justification for

re-baselining of the protuberance correlation for the BLT Tool V.2.

23
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T. J., Berry, S. A., Gnoffo, P. A., Wood, W. A., Reuther, J. J., Driver, D.

M., Chao, D. C., Hyatt, J., and Picetti, D., “Orbiter Return To Flight Entry

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

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

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6. Berry, S. A., Horvath, T.J., Cassady, A. M., Kirk, B. S., Wang, K. C., and

Hyatt, A. J., “Boundary Layer Transition Results From STS-114,” AIAA Paper

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7. 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.

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for Calculating Heating Rates on Three-Dimensional Vehicles,” Journal of Spacecraft and Rockets, Vol. 31, No. 3, 1994, pp. 345-354.

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B., Saunders, D. K., Mazaheri, A., and Calloway, R. L., “Viscous-CFD Space

Shuttle Orbiter Boundary Layer Data and Probe Software,” Engineering Note

EG-SS-07-10, NASA Johnson Space Center, March 2007.

13. Berkowitz, A. M., Kyriss, C. L., and Martellucci, A., “Boundary Layer Transition

Flight Test Observations,” AIAA Paper 1977-125, January 1977.

24
14. Reda, D. C., “Review and Synthesis of Roughness-Dominated Transition Correlations for Reentry Applications,” Journal of Spacecraft and Rockets, Vol. 39,

No. 2, 2002, pp. 161-167.

15. Coleman, H. W. and Steele, W. G., “Experimentation and Uncertainty Analysis

for Engineers–2nd Edition,” John Wiley & Sons, Inc., 1999.

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Between DSMC and Navier-Stokes Solutions and Measurements in Regions of

Laminar Shock Wave Boundary Layer Interaction in Hypersonic Flows,” AIAA

Paper 2002-0435, January 2002.

18. Miller, C. G., “Hypersonic Aerodynamic/Aerthermodynamic Testing Capabilities

at Langley Research Center,” AIAA Paper 1992-3937, July 1992.

19. AAEC Research Staff, LENS Brochure, Capabilities and Technologies, Buffalo,

NY 2004.

20. Liechty, D. S., Berry, S. A., and Horvath, T. J., “Shuttle Return To Flight Experimental Results: Protuberance Effects on Boundary Layer Transition,” NASA

TM-2006-214306, June 2006.

21. Kegerise, M. A., King, R. A., and Berry, S. A., “Wind Tunnel Test in Support

of STS-121: Protuberance Effects on Boundary-Layer Transition,” Engineering

Note EG-SS-07-06, NASA Johnson Space Center, March 2007.

22. King, R. A., Berry, S. A., and Kegerise, M. A., “Effect of Protuberance Shape

and Orientation on Space Shuttle Orbiter Boundary-Layer Transition,” NASA

TM-2008-215103, February 2008.

23. Micol, J. R., Midden, R. E, and Miller, C. G., “Langley 20-Inch Hypersonic CF 4

Tunnel: A Facility for Simulating Real-Gas Effects,” AIAA Paper 1992-3939,

July 1992.

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

B. S., and Trevino, L., “MH-13 Space Shuttle Orbiter Aerothermodynamic Test  ̃

Report,” NASA TP-2007-214758, 2007.

25. 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.

26. McGinley, C. B, Berry, S. A., “Orbiter Historical Flight Boundary Layer Transition,” Engineering Note EG-SS-07-09, NASA Johnson Space Center, March 2007.

27. Wood, W. A., Erickson, D. W., and Greene, F. A., “Orbiter Entry Aeroheating

Working Group viscous CFD boundary layer transition trailblazer solutions,”

NASA TM-2007-214882, June 2007.

28. Bouslog, S. A., Bertin, J. J., Berry, S. A., and Caram, J. M., “Isolated Roughness

Induced Boundary-Layer Transition – Shuttle Orbiter Ground Tests And Flight

Experience,” AIAA Paper 1997-0274, January 1997.

25
26
27
28
29
30
31
Table 8. Historical flight cases as documented in Refs. [5] and [26].

Flight Gap

Filler

X - 236

(in.)

Y

(in.)

Z

(in.)

k

(in.)

Transition

time (s)

STS-28 A-28 329.00 -21.00 278.00 0.5 f 0.1 (f20%) 902

STS-28 B-28 528.00 -94.00 282.00 0.5 f 0.1 (f20%) 912

STS-41 C-41 274.90 -45.60 281.60 0.11 f 0.01 (f9%) 1201

STS-55 A-55 225.10 -2.10 278.00 0.20 f 0.05 (f25%) 1060

STS-55 C-55 181.60 -20.20 282.90 0.20 f 0.05 (f25%) 1060

STS-73 A-73 279.18 7.43 278.61 0.60 f 0.11 (f18%) 880

*STS-73 A-73 279.18 7.43 278.61 0.60 f 0.11 (f18%) 982

*STS-73 A-73 279.18 7.43 278.61 1.40 f 0.19 (f14%) 880

STS-81 A-81 235.16 9.02 279.79 0.32 f 0.03 (f9%) 966

STS-94 A-94 211.20 4.24 280.74 0.30 f 0.08 (f27%) 993

STS-99 A-99 267.50 -6.40 278.80 0.35 f 0.09 (f26%) 1012

STS-103 A-103 270.70 7.43 278.78 0.250 f 0.075 (f30%) 958

* Alternate interpretation of data.

32
33
34
Table 11. Down-select table for most promising correlations investigated.

Proposed

Equation

Correlation Equation

C =

Ground-Based Ground-Based + Flight

R ΔC/C σC/C R ΔC/C σC/C

1 Reθ /Me k/6 -0.87 1.26 19.9% -0.88 1.25 21.2%

2 Reθ /Me k/6* -0.90 1.08 7.3% -0.87 1.32 34.9%

3 Reθ

/Me k/B -0.84 1.41 25.9% -0.86 1.36 23.3%

4 Reθ /Me (k/6) (Te /Tw )

0.16 -0.89 1.14 14.5% -0.89 1.20 23.6%

⇒5 Reθ

/Me(k/6)(He/Hw )

0.30 -0.91 1.04 8.9% -0.91 1.10 19.9%

6 pkukk/μw -0.79 2.51 30.9% – – –

⇒7 *Rek.6 [Reθ (μe /μk )]

0.4 -0.87 1.09 14.8% -0.84 1.30 35.0%

* Results are for n = −0.6 for all data (see Eq. 14).

⇒ Recommended correlations.

Table 12. Tabulated correlation coefficients for proposed correlations 5 and 7 based on the

approach adopted by the Aeroheating Panel and the use of the entire ensemble (groundbased and flight) database.

Approach Correlation C-95% C (Best Fit) C+95%

BF(flight) + 2σ(ground-based)* PC#5 35.3 61.3 106.4

Ensemble(ground-based & flight) PC#5 25.3 42.8 72.5

BF(flight) + 2σ(ground-based)* PC#7 220.7 396.8 713.4

Ensemble(ground-based & flight) PC#7 118.0 217.6 401.3

Approach adopted by Aeroheating Panel (BLT Tool V.2).

35
36
Table 14. Revisited correlations and the respective metrics.

Correlation Equation Ground-Based + Flight

R OC/C uC/C

*Reθ/Me (k/6)(He /Hw )

0.30 = C -0.91 1.10 19.9%

Reθ /Me (k/6*) (Te /Tw ) -

0.27 = C -0.89 1.20 23.5%

Reθ/Me(k/6*) (He/Hw )

-0.10 = C -0.87 1.31 33.2%

Reθ /Me (k/B)(Te /Tw )

0.33 = C -0.89 1.17 23.5%

⇒ Reθ /Me (k/B)(He /Hw )

0.44 = C -0.92 1.05 15.5%

* Proposed correlation #5 used as baseline reference.

⇒ Improved correlations.

37
Figure 1. Focused inspection image of a protruding gap filler on STS-121.

Turbulent Flow

d^

a0

Laminar flow Leo

eel ~bell Y = CX, ^00

C>0

n<0

Log (disturbance parameter)

Figure 2. Generalized correlation approach used in this report.

38
39
103

m

M 102

• LaRC M6: Existing Data

n LaRC M6: New Data

.... .... A LaRC M10: Existing Data

......................................... ... .........

N—S Database 0 LaRC CF4: Existing Data

LENS M10: New Data

o LENS M16: New Data

~ Smooth Limit 4 Flight: Data

^^^^ , '

f

, • • fit •'

i • 0 n •

•::g4 ...

v

n

- A 4 0

0 _a n

o Q ♦ •

0 0 o

........ ..................................................

♦ QD

101

0 0.2 0.4 0.6 0.8 1

x/Lref

Figure 4. Complete database (ground-based and flight) in the form of Reθ /Me versus

x/LTef .

104

N −S Database

Y

103

7Y

Q

Y

N^ LL

102

10

−1

10

0

10

1

k/8

Figure 5. Complete database (ground-based and flight) in the form of Rek versus k/S.

40
.................... A C, /C =0.625 • LaRC M6: V.1 Analysis -

... ......... ... 95/0

-

— C("Best Fit")=38.6

R=-0.942 --- C+95 %

=52.5

Uk=±0.0000 in - - - C-95%

=28.4

0 ON `s

• 3.

..................................:......... ...... .... ...`...............,.........;............_ .

. • •.

(Ree/Me)x(k/S)-n=C

n=-1.000

LATCH Database `,

101

L

_

10-1

m

m 102 Q

M

100

103

k/S

Figure 6. Existing LaRC 20-Inch Mach 6 Air Tunnel data used to develop BLT Tool V.1.

103

A C 95%/C =0.765 • LaRC M6: V.2 Analysis

C("Best Fit")=40.4

R=-0.842 - - - C+95%

=58.8

` `

Uk ±0.0000 in ....... - - - C-95%

=27.8

...... ..:....................................:............_

....... .....}........................... .......................

+.

.....................................:..........:.....

(Ree/Me)x(k/S)-n=C

n=-1.000 ` . `

101 LATCH Database '^,

10-1

k/S

Figure 7. Existing LaRC 20-Inch Mach 6 Air Tunnel data reanalyzed to estimate the

incipient transition Reynolds number as the average of the last laminar value and the first

value with laminar departure.

m

m 102

a^

100

41
103

m

m 102

a^

A C /C =1.560 • LaRC M6: Existing Data

95% n LaRC M6: New Data

R=-0.618 • LaRC M10: Existing Data .

Uk= ±0.0005 in o LaRC CF4: Existing Data

> LENS M10: New Data

o LENS M16: New Data

.............................:...:.... —C("Best Fit")=30.6

- - - C+95%

=62.6

-

..

... ..... , ... ..

C-95%=14.9

_. .

... ......... ......

(Re 0/Me)x(k/S)-n=C

n=-1.000

LATCH Database

100

101

10-1

103

m

m 102

a^

A C /C -1.257 ................... . 95% - .....

• LaRC M6: Existing Data

LaRC M6: New Data

`^ R=-0.868 • LaRC M10: Existing Data

o LaRC CF4: Existing Data - Uk

= ±0.0005 in > LENS M10: New Data

`, o LENS M16: New Data

— C("Best Fit")=31.9

+ - - - 

C+95% =57.8

C %=17.6

-95

... ......... ......

..

(Re6/Me)×(k/S)-n=C

,. \. .... ............

.... ......`............

n=-1.000

N-S Database

100

k/S

Figure 8. Ensemble of facility dependent data based on N-S database.

101

10-1

k/S

Figure 9. Ensemble of facility dependent data based on LATCH database.

42
103

m

m 102

Q

M

A C /C =1.251

95%

• LaRC M6: Existing Data

n LaRC M6: New Data

R=-0.880 LaRC M10: Existing Data

* LaRC CF4: Existing Data

> LENS M10: New Data

^. o LENS M16: New Data

• ` '

,

-4 Flight: Data f

nn C("BF Flight")=32.6

`

- - - 

C+95%=58.8

`^. ` 'i n / `:

OL

60o.....;A..

C-95%=18.0

p...,.

,

o 1 ` •

(Reθ/ M

e

)x(k/S)-n=C

, 

o

♦ • \`

n=-1.000 °p Q `.

N-S Database

100

101

10-1

103

N

m 102

Q

M

101

10-1

............... A C 95%/C 

=0.520 ;:::;:::: • Flight Data

n STS-73: Alternatives

R=-0.935 C("Best Fit")=41.6

- - - 

C+95 % =53.8

TS -94

- - - 

C-95%=32.2

` STS-28

515-55

,

.............. STS-73.... .^.. ......... .... ... ..._

........................... .......:..^.....'. . ...........................:

.. ,

, ,

(Reθ/ M

e

)x(k/S)=C

N-S Database

100

k/S

Figure 10. Calibrated flight data analyzed using N-S database.

k/S

Figure 11. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ

/Me x k/S = C.

43
100

101

103

m

m 102

A C /C =1.324 • LaRC M6: Existing Data

111111 ,95% n LaRC M6: New Data

R=-0.867 A LaRC M10: Existing Data

`^ ♦ o LaRC CF4: Existing Data

`, ` ♦ > LENS M10: New Data

`, ; ♦ 7 LENS M16: New Data

` . Flight: Data

` ^•^ n© — C("Best Fit")=103.1

`` ♦

'^n ^`^

- - C+95%

=191.8 ,^ ♦

♦, ♦ ` C =55.4 --- -95% -

♦ .....................................:.:♦.... ..A .;... ♦;...;..:...

(Re ./Me) x(k/S*)-n=C

`. op `♦ p

` ♦ • o ^ ♦ O

n=-1.000 # #

N-S Database

101

L

10-1

103

m

m 102

Q

M

1 01

• . 4 C /C =1.083 • LaRC M6: Existing Data -

..... 95% n LaRC M6: New Data

R=-0.903 A LaRC M10: Existing Data

^A .....:.. ..:..'.^..:..;....;...;............ # LaRC CF4: Existing Data

` ♦ `. > LENS M10: New Data ..........., ....... ........^..., .:.:.:.

♦ ♦ o LENS M16: New Data

...........:.. :....:..... ^.'..i .............:. C("Best Fit")=97.9

^ ♦ % w C+95%

=164.3

.• ♦ - - C-95%

=58.3

... ..

..„ 0 ...;

... ...._

... ......:.. .......:... ....

,.. VvNv

 .

,^

_

(Ree. . /M/Mee) x( k/S* n

........) =C ..... . ...................

.`. ♦ of ` ♦ :..0 ... .;... ..

♦ `,^ • ♦^

n=-1.000 `, # ♦ ^♦

N-S Database ♦ 

` ' ♦ `.

10-100101

k/S*

Figure 12. Ensemble of facility dependent data based on N-S database for correlation

Reθ /Me x k/S* = C.

k/S*

Figure 13. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ

/Me x k/S* = C.

44
0 1

(k/ 8)

(T

e

/T

w

)

m 10

m

102

M

103

101

10-1

4 C /C =1.203 • LaRC M6: Existing Data

............. 95% n LaRC M6: New Data

R=-0.890 LaRC M10: Existing Data

o LaRC CF4: Existing Data

` > LENS M10: New Data

° LENS M16: New Data

Flight: Data

! n — C("Best Fit")=34.9

n '^^. - -

C+95%=61.8

`^^ • .

°,^. C-95%=19.8

(Re 0 /Me

 )(k/8)(T 

e 

/T 

w

)

m

=C' 0

m=0.16 0

N-S Database

103

N

m 102

Q

It

1

4 C/C =1.363 • LaRC M6: Existing Data

95% n LaRC M6: New Data

R=0.862 ♦ LaRC M10: Existing Data

o LaRC CF4: Existing Data

LENS M10: New Data

LENS M16: New Data

• ';^ ^` n Flight: Data

• C("Best Fit")=234.2

n

j

n^n C+95% =443.0

.....o°^►:......^.^. ^.. •. `... - - _. ,

° ......^.... ♦..^

- C 95% 

=123.8

-

(Re θ/M

e

) × (k/θ) n=C

... ......... ............

n=1.000 o °

NS Database

100

10

k/θ

101

Figure 14. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ /Me x k/B = C.

Figure 15. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ

/Me x (k/δ)(Te /Tw )

0.16 = C.

45
100 1

(ρku

k

k)/(ρ

e

u

e

θ)

10

104

103

m

N

N

.^ Q 102

101 L

10

-1

Δ C95%/C =2.505 • LaRC M6: Existing Data

` ..:. ........... n LaRC M6: New Data ...........; `.... R=0.788 ♦ LaRC M10: Existing Data -

o LaRC CF4: Existing Data

........ .............. :. ....................... > LENS M10: New Data

o LENS M16: New Data

` ..

........... C("Best Fit")=343.1 ^... C+95%

=979.5

C 95%=120.1

(ρku

k

k)/μ

w

=C

n _

.,

NS Database

103

AC /C =1.102 • LaRC M6: Existing Data

95% n LaRC M6: New Data

R=-0.906 ♦ LaRC M10: Existing Data

........ .....:....:...:...........i. s LaRC CF4: Existing Data

^. > LENS M10: New Data

^.\ o LENS M16: New Data

Flight: Data

C("Best Fit")=42.8

n

C+95% m =72.5

m ^. ♦ 102

A N C- =25.3 ^:.•.. ^. - - - 95%

.......... ......... n

^♦. Q.:...............

Q

M

`

..... `^ ` , .Q^...`. ..(D..

........... :...... :.... :... ...:.....^:.:..... ..... ..... ... ............ :......

(Re 

0 

/Me ) (k/S) (H

e

 /H

w

) m =C

m=0.30 ^^o

N-S Database

101

0 1

^k/S) (H

e

/H

w

)

m

10

Figure 16. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ /Me x (k/δ)(He /Hw)

0.30 = C.

10-1

Figure 17. Ensemble of facility dependent data based on N-S database for correlation

Rek (reference to μw) = C.

46
n LaRC M6: Existing Data

n LaRC M6: New Data

A LaRC M10: Existing Data

LaRC CF4: Existing Data

LENS M10: New Data

o LENS M16: New Data

Flight: Data

C("Best Fit")=217.6

- - - C+959/ 6

=401.3

C-959/6=1 18.0

A C 959/6 /C =1.301

R=-0.841

0

(k/8) (H/H 

w

)

0.30

e

101

104

103

Y

m

m

m

.^ Q

102

(P

e

u

e

e)/(#k)X[(Pku

k

k)/(P

e

u

e

e)]-n=C

n=-0.600

N S D b

101

10-1 100 1

(Pku

k

k)/(P

e

u

e

e)

10

Figure 18. Ensemble of facility dependent data and flight data based on N-S database for

correlation of the Rek-type.

103

Flight Data

n STS-73: Alternatives

... ................. C("Best Fit")=42.8

`.,......... ............ - - - C+959/ 6........... =72.5

- - - C-959/6=25.3

.....................: ........::.................

......................^..... ...............

.....

..............

,

.............. ^...;..............

(Re 0 /Me ) (k/8) (H 

e 

/H 

w

)

0.30=C

N-S Database

101

10-1

Figure 19. Flight data plotted in correlation space (PC#5) along with correlation curves

derived from ensemble of facility dependent and flight data (N-S database).

m

m 102

Q

M

47
0

(k/8) (H°H

w

)

0.30 101

104

103

Y

m

N

NQ

102

1

• Flight Data

• STS-73: Alternatives

C("Best Fit")=217.6

- - - C+959/ 6

=401.3

- - - C-959/6=1 18.0

\ \

...........:...... ... ...:.. :...:.... ^..... ,...... :....

\

... ...... ..:.\..::....: ...............

Rek

0.6x [Ree-(1x.

e

/1x.

k

)]0.4=C

\ \ \ \

N-S Database ' i\ 10

10-1 100 1

(P

k

u

k

k)/(P

e

u

e

e)

10

Figure 20. Flight data plotted in correlation space (PC#7) along with correlation curves

derived from ensemble of facility dependent and flight data (N-S database).

\ ........................................:............ • Flight Data

n STS-73: Alternatives

.. ....... \ C("BF Flight")=61.3

C+95%=106.4

` - - 

C-95 % =35.3

.............. ......... .......:::....

.............................

............ ...............

.

(Re 0 /Me )(k/8)(H

e

 /H

w )

0.30=C

N-S Database

101

10-1

Figure 21. Plot showing flight data (assumes 95% confidence levels for quoted k values) and

correlation curves with constants recommended by the Aeroheating Panel for PC#5.

103

m

m 102

a^

48
103

`. • LaRC M6: Existing Data

n LaRC M6: New Data

^.^ A LaRC M10: Existing Data

♦ LaRC CF4: Existing Data

LENS M10: New Data

`. o LENS M16: New Data

m 102

^.^.,....^... .^ 4 Flight: Data

A • ' C("BF Flight")=61.3

• t ^► - - - C-95%

=35.3

S C+95%=106.4

.............. ............. ^.^>0....

ti

(Reθ/M

e

)(k/δ)(H

e

/H

w

)

0.30=C • .............

.o

N—S Database

101

0

(k/δ) (H/H

w

)

0.30

Figure 22. Plot showing ground-based data, flight data, and correlation curves (using constants recommended by the Aeroheating Panel) for PC#5.

.... • Flight Data

- n STS-73: Alternatives

— C("BF Flight")=396.8

- - - C +95%

=713.4

^.^:..

- - - C-95%

=220.7

... ...` .... ... ...... ....

........... .... .. ......... ... ..... ^. ^...

Rek

0.6x [Ree.(['

e

/['

k

)]0.4=C

101 L N-S Database

10-1

Figure 23. Plot showing flight data (assumes 95% confidence levels for quoted k values) and

correlation curves with constants recommended by the Aeroheating Panel for PC#7.

10—1 101

104

103

Y

i

m

N

N

Q

102

100 1

(Pku

k

k)/(P

e

u

e

e)

10

49
104

103

Y

m

N

Q

102

........... ............................:..................

.... • LaRC M6: Existing Data

...:......:....:.:.:...........:...... n LaRC M6: New Data

• LaRC M10: Existing Data

0 LaRC CF4: Existing Data

LENS M10: New Data

` o LENS M16: New Data

A Flight: Data

` - C("BF Flight")=396.8 ..,`.... - - C

+95%

=713.4

.... - - - C-95%

=220.7

... • 0 ... ....

^

.. ...... ... ..... .....

• 0^

^, n -

... ... n 17 n ^ . 0 0

... .... • fl •.•0

Rek

0.6x [Reo.(I'

e

/I'

k

)]0.4=C

101 L

N-S Database

10-1

Figure 24. Plot showing ground-based data, flight data, and correlation curves (using constants recommended by the Aeroheating Panel) for PC#7.

100 1

(P

k

u

k

k)/(P

e

u

e

o)

10

N

m 102

103

101

100

Δ C /C =1.047 • LaRC M6: Existing Data

95% n LaRC M6: New Data

R=0.915 • LaRC M10: Existing Data

......^.^........................................... o LaRC CF4: Existing Data

` > LENS M10: New Data

` o LENS M16: New Data

N

...; I Flight: Data

` 2 • n — C(" Best Fit")=350.3 t'4n _ C+95%=578.8

^`~ •

r.

^^^ C 95%

=212.0

` 0

(Re θ/Me)(k/θ)( H

e

/H

w

)

m

=C ^` • ^^._

m=0.44 • ^`

NS Database

101

m

(k/θ) (H

e

/H

w

)

Figure 25. Ensemble of facility dependent data and flight data based on N-S database for

correlation Reθ

/Me x (k/θ)(He /Hw )

0.44 = C.

50
103

m

102

It

101

.....................................................

• LaRC M6: Existing Data

n LaRC M6: New TEI Data

... ........ • LaRC M10: Existing Data

........... o LaRC CF4: Existing Data

LENS M10: New Data

` Io LENS M16: New Data

' 4 Flight: Data

J ti •• • n ' C(" BF Flight")=450.7

"

 C- - - +95% =758.1

• •!yam C 95% Wl •' =268.0

- -

AV

-.-.-.... -.-.

n ` ` O ti

CR ^

(Re /M )(k/θ)(H /H )0.44

=

θ

C

^.,.^. .

e e w

•.. . .. ....

o

NS Database

0 1

10

(k/θ) ( H

e

/H

j0.44

Figure 26. Plot showing ground-based data, flight data, and correlation curves for correlation

Reθ/Me × (k/θ)(He/Hw )

0.44 = C based on coefficients derived from the methodology of the

Aeroheating Panel.

51
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01-12-2009 Technical Publication 10/2000–9/2002

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

Version 2 of the Protuberance Correlations for the Shuttle-Orbiter Boundary

Layer Transition Tool

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

Rudolph A. King, Michael A. Kegerise and Scott A. Berry

5e. TASK NUMBER

5f. WORK UNIT NUMBER

599489.02.07.07.04.11.01

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

NASA Langley Research Center REPORT NUMBER

Hampton, Virginia 23681-2199 L–19791

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)

National Aeronautics and Space Administration NASA

Washington, DC 20546-0001

11. SPONSOR/MONITOR’S REPORT

NUMBER(S)

NASA/TP–2009–215951

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 16

Availability: NASA CASI (443) 757-5802

13. SUPPLEMENTARY NOTES

An electronic version can be found at http://ntrs.nasa.gov.

14. ABSTRACT

Orbiter-specific transition data, acquired in four ground-based facilities (LaRC 20-Inch Mach 6 Air Tunnel, LaRC 31-Inch Mach 10 Air

Tunnel, LaRC 20-Inch Mach 6 CF4 Tunnel, and CUBRC LENS-I Shock Tunnel) with three wind tunnel model scales (0.75, 0.90, and

1.8%) and from Orbiter historical flight data, have been analyzed to improve a pre-existing engineering tool for reentry transition

prediction on the windward side of the Orbiter. Boundary layer transition (BLT) engineering correlations for transition induced by

isolated protuberances are presented using a laminar Navier-Stokes (N-S) database to provide the relevant boundary-layer properties. It

is demonstrated that the earlier version of the BLT correlation that had been developed using parameters derived from an engineering

boundary-layer code has improved data collapse when developed with the N-S database. Of the new correlations examined, the proposed

correlation 5, based on boundary-layer edge and wall properties, was found to provide the best overall correlation metrics when the

entire database is employed. The second independent correlation (proposed correlation 7) selected is based on properties within the

boundary layer at the protuberance height. The Aeroheating Panel selected a process to derive the recommended coefficients for

Version 2 of the BLT Tool. The assumptions and limitations of the recommended protuberance BLT Tool V.2 are presented.

15. SUBJECT TERMS

Shuttle Orbiter, hypersonic boundary layer transition, roughness-induced transition

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

ABSTRACT

18. NUMBER

OF

19a. NAME OF RESPONSIBLE PERSON

a. REPORT b. ABSTRACT c. THIS PAGE STI Help Desk (email: help@sti.nasa.gov)

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