Identifying the Aerothermodynamic Environment of the Space Shuttle Orbiter, Columbia

Copyright © IFAC Identification and S\"Slem Parameter ESlimation 1982. Washington D.C .. L:SA 1982

IDENTIFYING THE AEROTHERMODYNAMIC ENVIRONMENT OF THE SPACE SHUTTLE ORBITER , COLUMBIA D. R. Audley* and

J. K. Hodge**

*Department of Mathematics, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohz'o 45433, USA **Department of Aeronautical and Astronautical Engineering, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohz'o 45433, USA Abstract _ \-Ie consider the system identification problem associated with determining the aerothermodynamic heating environment of the Space Shuttle Orbiter Columbia during reentry_ A mathematical characterization of this environment is required for mission capability assessment as well as operational flight planning_ The identification problem is one of estimating certain parameters in a fairly complete nonlinear, nonstationary partial differential equation (diffusion) model of the heat transfer characteristics of the orbiter thermal protection system (tiles) interacting with the surface boundary phenomena of aerodynamiC forced convection and radiation. Our solu tion uses a maximum likelihood technique that incorporates discrete, depth wise (thermocouple) temperature measurements and reentry trajectory data. Results of analyzing flight test data collected during the first flight of the Columbia are included for illustrative purposes _ Keywords_ Identification; space vehicles; partial differential equations; parameter estimation; thermal variables _

INTRODUCTION The following reports on one aspect of a capability assessment of the Space Transportation System (STS or Space Shuttle)_ Emphasis is on the reentry phase of flight _ This effort is different from the baseline assessment being conducted by NASA/Rockwell, though a close working relationship is maintained_ A revolutionary aspect of the STS is the reusability of the Space Shuttle Orbiter . It has been designed for more than one hundred missions. Among the many subsystems that are critical to its controlled, gliding reentry is the Thermal Protection System (TPS) _ An insulating sheath about the Orbiter, it has been designed to withstand the intense heat loads of atmospheric reentry, without degradation, for the life of the vehicle_ Aerothermodynamic performance, as limited by the TPS, is a dominating aspect of total system performance _ It affects the ability of the STS to perform a specified mission, with attendant reentry requirements such as cross range, in much the same way engine performance and airframe aerodynamics affect and limit the capability of high performance aircraft. Therefore, it is a main objective of this assessment to determine the aerothermodynamic capability of the Orbiter.

where surface temperatures exceed 2300 degrees F; Flexible Reusable Surface Insula tion (FRSI), a Nomex felt substance found on the upper surface where maximum surface temperatures do not exceed 700 degrees F; and two varieties of silicon based tiles, High/Low temperature Reusable Surface Insulation (HRSI/LRSI), used on the underside and other high heat load areas where RCC is not needed _ More than just acting as an insulator, the TPS also features a highly radiating surface (with emissivities on the order of _8 to _92) to reduce the effect of aerodynamiC forced convection on the heat transfer to the underlying aluminum structure _ The choice of TPS material and its design is dictated by vehicle geometry and aerodynamic flow _ Design parameters have been exclusively determined from ground tests and theoretical considerations: this type of TPS heat shield has never undergone a reentry flight test. For this reason, early flights in the Orbital Flight Test (OFT) program will have trajec tories designed so as to expose the Orbiter to the most benign aerothermal heating environment possible . In keeping with the flight test philosophy used in assessing the capability of flight vehicles for more familiar characteristics , such as aerodynamic performance and handling qualities, a scenario has been developed for aerothermodynamic assessment . A number of test maneuvers will be flown by the Or biter on reentry during the OFT program . Maneuver

The TPS consists of a variety of materials including Reusable Carbon-Carbon (RCC), used on the wing leading edge and other locations 1347

1348

D. R. Audley and J . K. Hodge

induced modulation of the surface aero - heating wi ll generate measurable transients in the TPS heat transfer behavior . Processing of test observations after each flight will expand and enhance the TPS development data base . This cumulatively enriched data base wil l be used in g round based mission/flight simulators in two modes . First, during the flight te st program, it will faci litate maneuver planning for subsequent test flights, consistent with a cautious , graduated build - up flight envelope expansion . Second, it will suggest true, flight based Orbiter reentry performance limitations which are crucial to a mission capa bility assessment . The overall nature of the STS aerothermodynamic fligh t test program is the subject of Hodge, Aud le y and Phillips

be made to extrapolate the findings at one point to another location outside a neighbor hood of the test point . This last assumption fo r ces the question of the scope of this STS aerothermodynamic assessment effort . Seven " control points" (see Fig . 1) have been established by ~ASA as critical location s that must be tracked fo r purposes of reentry trajectory shaping . Initially, these control points fo r m the basis of the investigation . Howeve r, many locations have been instrumented with thermo couples and pressure senso r s . Points with g ro ssly anomalous measu rements wi ll be ana l yzed and this cou ld lead to r eplacements and additions to the o riginal cont rol point set .

(1981) . In the following, a model of the TPS aerother modynamic environment will be described. When used with the existing aerothermodynamic TPS data base, it has been f9und apt for predicting aerothermal performance . Based on this model, a well - posed inverse problem is formu lated for identifying certain parameters that are useful for incorporating flight test objectives into the data base. The ultimate objective of the present discussion is to present a solution of the parameter identification (inverse) problem . Some preliminary analysis of data gathered on the 12 - 14 October 1981 flight of the Columbia is included for illus trative purposes . Fig . 1 . MODELS OF THE AEROTHERHODYNAMIC ENVIRONMENT A natural separation occurs in developing the models necessary for aerothermodynamic performance analysis . This separation occurs between the diffusion equation model of heat transfer in the TPS and the "surface" boundary condition for aerodynamic forced convection and rad iat ion . It is the boundary condition that consists of the primary unknown of aerothermo performance : the parametric characterization of aerodynamic forced convection and the emissivity of radiative transfer . However, they are observed via the heat transfer behavior of the TPS material . Hence an accurate TPS thermal model must be incorporated in any boundary condition identification effort . If there are any uncer tainties in this model, that could dominate behavior over the boundary condition , they must be parameterized for identification simul taneously with the aerothermo unknowns . The first assumption made is that the thermal character istics (conductivity, k; specific heat capacity , C; and density , 0 ) of the TPS materia l s are a priori known based on labora tory tests and theoretical consideration.

Representative Control Points.

In the following, a one- dimensional (depthwise) diffusion equation model is used. This is a main assumption . It is motivated in an effort to maintain computational tractability . However, it is claimed that there is no resulting degradation of solutions . This is based on two observations. First, predictive solutions over entire reentries do not differ from high-fidelity (3-D) solutions by more than a few percent when using a I-D model. In the identification algorithm, predictive solutions are not allowed to propagate for more than a few seconds. Second, and most important, the l - D model is incorporated in a closed loop recursive (Kalman) estimator . Here , thermocouple measurements located in the TPS material are used to "stabilize" the estimation of the temperature field via a statistical predictor - corrector scheme. Any resid ual error cau sed by neglec t ing "span-wise" heat transfer with the I - D model is effec tively eliminated . The diffusion model of TPS heat transfer is characterized by the stochastic partial dif ferential equation

a

aru(x , t)

2 C\2 ,a 2

u(x,t)

oX Next , the practical constraint is imposed that analyses will p r ovide only local r esul t s. In other words , all models will apply to spec i fic loca t ions on the Orbiter and no attempt will

+ T (X,t) where u(x,t)dR

1

i=A,B,C,D

is the TPS temperature

(1)

1349

The Aerothermodynamic Environment of the Space Shuttle u

2

= ki/ P ic is a heat transfer parameter; i i x E [O,l] is th e normalized sp a cial variable ; and t ET , a su b set of the real line , R, denoting a time set o f interest . Thi s differs from the usual heat equation by th e additive stochastic process T , whic h incorporates uncertainties in the model . Formall y , T = ' ( ' ,' , . ) is defined on the product s pa c e ( O, l)xTxn , where ~ is a probabilistic sample spa c e , and w(x , t,w)dR . A precise definition and mathematical develop ment of this stocha stic model is not justified at this point and i s deferred to references such as Balakrishnan (1973) or Sawaragi , Soeda , and Omatu (1978). As will be seen, the realities of the experimental situation allows a simple treatment o f this process . In the present context, the v ariable w is suppressed due to the nature of c omputationall y processing single time series samples of the stochastic process solution of equation (1) . The TPS material thermal properties are characterized as nonlinear functions of the independent parameters (temperature and pressure , P) such that k = ki(u(x ,t), P) and c = ci(u(x ,t» i i with density, P i' assumed constant for each material. Preflight values of the parameters are given in Rockwell (1977). Bou nd a r y conditions for (1) are formed using the geometry of the TPS shown in Fig . 2. This includes continuity of the t emper atu r e field across boundaries between material types, as we ll as the adiabatic condition a t t he heat sink (x=l) Cl Cl x u(l,t) + Yl(t) = 0

(2)

and the co ndit ion at the surface (x= O)

R[PRf S[ ~TATl

CO:\: TROL

\'E

BLOCK

~Ct:

1 SOS E CAP

2

~!AT E RIAI .s

P O I~ TS

C H I~ E

CO.\T1SC

3 wIs e L EADIS G EOCr: RCC 4 ELEVON CO.\1I '\G

C(\ATn:r. C(M TISG

S SOOY FU? 6 C[S TE RL ISE 7 o~s POD

FRS 1

RCC

RCC

HRS I

:-;IP

RCC

RCC

LRS I

SIP SIP SIP

L ~S I

lRS t FRS I

0

CO:-IPOS ITE

BLOCK A

R£US[ABL[ SURF ACE INSULATION

BLOC K B

( RSI)

BLOCK C

BLOCK 0

AOIABATl C WAL L

Fig . 2 .

TPS

~ode l

Cross Sec tion (Composite) .

con st r ained as fo ll ows : The spacia ll y dis tributed process T(X, t) is assumed t o be Gaussia n with zero mean a nd covariance EtT (X,t)T(y,S)T } = Q(x , y)Q (t,s) t

x , y E [O,l]

whe re Q(x,y) = E exp { -~I x - Y I} , an d Qt(t, s) embodies the temporal correlation of the process . The boundary processes are assumed t o be temp orall y white, Gauss ian with zero means a nd cova r ia n ces

Cl ' ,4 , ,4 k";\ u(O,t) - w [ t u(0 ,t )+460 ,
where 0 is Stefan - Boltzman constant , E is t hermal emissivity, and uoo (t) is free space or radiation sink temperature. Simila r to (1), Y and Y are stochastic processes that l O embody uncertainty at the bounda r ies. As shall be seen , Y is especiall y impo rt ant as O it includes all of the trajectory unce rtainties. The surface bounda r y condition (3) will be discussed further. The initial condition for the temperature field , at time to' is specified with a n asso -

Y and Y are independent and o (t-s) is the l O Dir ac delta function. The surface boundary co ndition includes forced convective heating. This term f( a )q q

ciated uncertainty xE[O ,l]

f(t), uses a reference heating model, re f(t), and a static transfer relation,

re f( a ). The purpose of this parameterization is to regularize the otherwise ill - posed inverse pro b lem of constructing a time series

Gauss ian with cova rian ce E{ ,"(X)T"(y)T } E"exp { - Ql x - y l} , where E; ' } denotes expectation and ~ is the correlation parameter.

f(t), re based on noisy measurements of the TPS tem perature at (spacial and temporal) discrete points.

The models for the stochastic processes T , Y ' O and Y are assumed to be stationary and are l

The reference heating is the stagnation heating that would occur on a one foot sphere at the same point on the flight trajectory .

where T "(X) is zer o mean , E{T "(X) } = 0 ,

of t he aero - heating rate, q(t) = f(a)q

D. R. Aud l ey and J . K. Hodge

1350

The NASA/Rockwell model (Sec 1 . 3 . 3 of the Rockwell (1978» report is used for stagnation heating :

uncertainties associated with the measure ments . These include sensor noise and instru mentation errors , especially quantization problems associated with 8 - bit data word length .

where

~

.24 T00

h

w

T

w

The model for

w~

is constrained to

be stationary , white Gaussian with zero mean i

i

"I

and covariance Ec\" k'-' . i = R. o (k - j) . J l sors have independent processes so

2

+ v /S0 , 063

All sen -

total enthalpy

E {W ~w t }

.24 T

su r face (wall) enthalpy

independent of model processes .

. (q

. 25

A large variance exists relative to the thermocouple configuration at the many meas urement locations . Most have a "surface" TC located at the interface of the RSI and the radiative surface coating and a TC that can be associated with the bondline temperature . There are also a relatively few locations (on the order of 40) that have TC ' s imbeded in the RSI materials at several depthwise loca tions . Some of these locations , with indepth TC ' s , do not have a surface TC. The prime TC configurations for analyzing transient test maneuvers are those that include a surface TC . The several TC variations are incorporated in Fig . 2 .

w

re

floE)

=

3 · 10 (q

re

f/ . 4761E)

. 25

wall temperature The static transfer relation , f(a), or heating ratio, summarizes the dependence of the con vective aero - heating on other parameters not included in,

qre f'

This includes body loca -

tion (there is an f(a) associated with each control point) ; angle a , of attack/slideslipl control su r face deflection (these effects pre dominate during test maneuvers) ; Reynolds number , Re ' effects (including bounda r y layer transition and turbulence) ; and Mach varia tions (which are not distinguished f r om r eal gas effects) . Test maneuvers a r e designed to maximally decouple the heating ratio f r om Re and Mach . However, sometimes f(a) is deter mined unde r other than controlled conditions . In any case , a family of maneuver s are needed at several Mach and R combinations t o com e pletely cha r ac t erize f(a) . Finally , the bifu r cation associated with laminar flow transi tion and turbulence a r e included as discontin uities i n the heating r atio . The p r eflight data base fo r f(a) may be found in the Rockwell (1978) report . The other p r ime unknown is emissivity , E , and is thought to be approxi mately . 85 (but may be . 8 ~ E ~ . 92) . Further discussion of the physical consitlerations in corporated in the reference heating model and heating r atio may be found in Hodge , Audley , and Phillips (1981) . There are a large numbe r of thermocouple (TC) measurements located throughout the TPS . These will form a prime source of data for TPS flight test . Haterial property characteris tics (conductivity) will be supported by local static p r essu r e measu r ements . The reference heating is constructed from trajectory estimates which are provided independent of the current task. This is the NASA BET (Best Estimate of Trajectory) product . It is con structed using on - boa r d iner tial measurements . The TC measurements , Yi(t ) , a r e time discrete k (frequency ~ 1 Hz) samples of the TPS tempera ture field at spacially discrete depth'''ise locations : (5) The random variable ,

w~,

incorporates the

=

0 , i f j, and sensor processes are

Temperatures measured by the surface TC ' s (on the HRSI/LRSI) may be seriously affected due to the imprecise manner with which the surface coating is applied to the RSI . Specifically , the thickness , 6x , of the coating can have a A relatively large deviation from the specifica tion value of 15 mils . Since error in 6 x A can have a significant effect on maneuver based parameter identification , it is treated as an unknmm and identified simultaneously with f( a ) and E . Summarizing , the following Aerothermodynamic Environment Identification Problem (AEIP) is stated : Given the TPS -aerothermodynamic model , equations (1) - (4) (including boundary and initial conditions); find the "best" estimate of the aerothermo environment parameters , E , fe Ci ), ox A

based on a specified trajectory esti mate , local pressure, a , and thermo couple measurements .

A SOLCTIO~ TO THE AERO THER'IODnA.'!IC DTIRO:-"'IE;\T IDENTIFICATIO~

PROBLE~

The existence and uniqueness of a solution to the AEIP is obtained by exploiting the more abstract f unctional analytic setting found in the Balakrishnan references. The proof given in Balakrishnan (1975) provides a solution technique that yields an as ymp totically un biased and asymptotically consistent estimate via the technique of a posteriori maximal likelihood for infinite dimensional systems . This technique consists of determining the

The Aerothermodynamic Environment of the Space Shuttle maximum of the likelihood function (LF) defined by a cer tain Radon-Nikodym derivative .

\~here y(t.) ER J

H -

~'

Fortunately , the special (finite) nature of the observation process (equation (5» leads to a tractable likelihood function. In thi s case the maximum of

provides the required "be s t" estimate of the aerothermo parameters at time t . The density i functionf() ( ) Io ( · ,· i ·),isthejoint u t i , Yt 'Cl i probability density func tion of u(t.) and l.

Y(t.) conditioned on 8 . l.

The measurements

fix the random va riable yeti); and u (t . )

J

~i

T n [u (t.)u (t.) .. . u (t.)] ER (superl 2 J J n J script "T" denotes vector or matrix transpose), and u.(t.)- u(x.,t.) l.

J

J

l.

(random variables for each x.ED) pro-

ki

1J

is the measurement vector ; and

(an mxn matrix) is defined by

1 if ith element of u (t . ) appears J as kth eler.lent o f y (t.) hki

(6)

h

m

1351

J

if ith element of u (t . ) does not J appear in y(t .) . J Th e vector \.I -- r. \.I 1 \.I j2 " . \" m]T j is composed of j j the individual components in equation (5) (an m-vector discrete-time white , stationary Gaussian process with zero mean and covari. T} ance, E\\.I .\.I . - R6 (i-j), R is an mxm , symmet l. J ric positive definite matrix) .

°

Haximizing the likelihood function (6) with respect to e and ; represents finding the set of parameters, 0 , and a consistent temperature field at time t , u(t ), that most probi i ably produced the measu r ement sequence ~ i'

l.

vides a representation of the TPS tempe rature profile, u(x,t); D

This approach makes good use of all the apriori models and statistics as well as the measured observations of the thermocouples.

{ XiE [O,l]: i-l,2, . .. ,n and xi are sufficiently "dense" in [0,1] such that the se t { u(x . ,t.) } ~ 1 is a "good" represenl. J l.tation of the temperature profile u(x,t.) : ; J

yeti)

[y(t )y(t ) ·· .y(t )] is the vector l 2 i of the measurement time history corre spo nding to equation (5);

Now the natural logarithm (In) of the exp r es sion (6) is now red efined as the likelihood function,

The maximum of 1[ ; , " ;

tji]

and the maximum of

f u (t . ),Y(t.) 18 (; ' Y i ie ) occur at the same l.

l.

values of 8 and u(t.) since the natural

~i

1~ l ~ .. . 'tJ

l.

is the set of realized

values of the measurements to be used as data;

8

[ ~ xA , E ,

logarithm is monotonic. These values can be obtained by solving for the roots of the gradients,

the parameters characterizing

9_0.*

f( c.)]TE;RP is the ae r othe rmod ynamic parameter vecto r (set); ~,A

the dummy variab les corresponding to u(t ) and S , respectively . i

~ote the criticality of the definition of the vector u(t.) in expression (6). This incor J porates the practical matter of eventually solving the (deterministic) partial differential equation associa ted with equation (1). Since a finite-difference scheme will be used, the node points are used to represent the temperature field in the specification of the LF . This, along with the temporal discretizati on of the measu remen ts in equation (5), accounts for t he simple random variable form of expression (6). Fo r convenience, the set of points D is furthe r constrained to include t he points used in the definition of the observations . The measurement equation (5) is now

y (t . ) J

Hu (t.) + \.I. J J

(7)

°

(9A)

°

(9B)

simultaneously. Constraining the maximization of L for some of the unknowns (for example emissivity, E ~ Z , ~ E ~ 1) has been con sidered, but found to be unnecessary .

°

Repeat application of Bayes' rule to (6) and incorporating the Gaussian form of the densi ties provides, through (9A), that u*(t.) l.

with associated covariance p(t.+) l ~

e "* ~ -

E ~ [u(t.) - ~(t.+)][u(t.) 1 1 1 (ll)

D. R. Audley and J . K. Hodge

1352

Thus, the a posteriori maximum likelihood estimate of the temperature profile of the TPS at ti is the conditional expectation gen -

at CP7 included a surface thermocouple (node 2, Fig . 2) and an in-depth thermocouple at . 32 inches.

erated using the a posteriori maximum likelihood estimate of the parameters, 9* . This temperature profile is generated using a (nonlinear) "Kalman filter" algorithm. See Maybeck (1979), Jazwinski (1970), or Sawaragi, Soeda, and Omatu (1978) for relevant theor y . Specific equations for the estimator used here are found in Audley (1981) (available from the author).

The parameter estimator was run in a sequential mode using a series of observation

, N

sequences { t\ ~ } , 1 (as defined for equation

-d 1

Summarizing to this point: the simultaneous solution of the p equations (9B) and the result of equation (10) yields the a posteriori maximum likelihood estimate of 0 (and the temperature profile u*(t )), the required solution to i the AEIP .

,

V1

~

'

tively with a resulting best estimate 9 *( ~ 1) . This estimate provided the initial 6* for the next

Simultaneous solution of (9B) and (10) requires an iterative technique since a closed form solution is generally not possible. A modified form of Newton-Raphson algorithm is used where an approximation technique known as "scoring" (see Rao (1952), Wilks (1962), or chapter 10 of Maybeck (1981)) reduces the computational burden associated with the Jacobian of the likelihood function.

J=

Each sequence 11 ~ was processed itera-

(6)).

~

0

" 1 b servatlon lnterva,

'+1 6 *( ~ 1 ) .

1J ' + j

l

'Id lng ' , Yle a

1

The sequence of resulting heating

ratios, f(a) , is shown in Fig. 3 , with asso ciated preflight wind tunnel data . Sensitiv ity to sideslip, B, in the wind tunnel data is clearly seen (most pronounced at a = 30 0 due to aerod ynamic flow characteristics). ~o correction has been made to co rrelate R e effects , though they certainly are present . The agreement between wind tunnel and flight is cons idered to be very good by aerothermo dynamicists.

SOME NUMERICAL RESULTS FROM THE MAIDEN VOYAGE OF COLUMBIA A large amount of data for testing the identification software has been processed . This consists primarily of computer gene rated data-- for which excellent results were obtained (as is often the case) -- and wind tunnel data-where the identification was not as sterling, but was still very good. These results are discussed elsewhere (see Hodge, Audley, and Phillips (1981)) . Here, the analysis of the AEIP fo r the space shuttle orbiter Columbia on its maiden flight of 12 - 14 April 1981 are presented for illustration. The first flight in the OFT program provided only meager data for AEIP analysis. Specifically, no aerothermodynamic flight test maneu vers were flown during reentr y because of normal first-flight safety conservativeness. Optimally designed test maneuvers are scheduled for later flights. Control point 7 (CP7) on the orbital maneuvering system (OMS) pod, provides a representative point. There are definite unknowns in aerothermodynamic theory that make theoretical predictions of lee (or upper) side heating a sportive task . However, some spa rse (raw) wind tunnel data is available for comparison wi th the identification results. The dominant independent parameter for f( a ) at CP7 is angle of attack . There is some effect of sideslip angle, but this is not identified here . Our heating ratio model is f( a ) = fO + fla where a is angle of attack.

Instrumentation

Fig . 3.

CP7 - OMS POD Heating Ratio .

CONCLUDING REMARKS A new approach to analyzing aerothermod ynamic flight performance has been developed . At the heart of this approach is a system identification problem for some parameters of a partial differential equation model of heat transfer. The maximum likelihood technique used has provided good preliminary results when applied to real data. REFERENCES Audley, D. R. (1981) . Parameter Identification of the Reentry Aerothermodynamic Envir onment . Balakrishnan, A. V. (1975) . Identification Proc. 6th IFIP Conf. on Optimization Novosibirs k, Springer - Verlag 1975. Hodge, J. K. (1981). Flight Testing a Manned Lifting Reentry Vehicle for Aerothermodynamic Performance. Paper AIAA-8l-242l, Pr oc. of t he First AIAA Flight Test Conf . Las Vegas. Maybeck, P. S. (1979-81). Stochastic Models, Estimation , and Control . Academic Press .