User's Manual for the One-Dimensional Hypersonic Aero

75 Pages·1999·0.73 MB·English

NASA Contractor Report 4691
User(cid:213)s Manual for the One-Dimensional
Hypersonic Aero-Thermodynamic
(1DHEAT) Data Reduction Code
Brian R. Hollis
Grants NAG1-1663 and NAGW-1331
Prepared for Langley Research Center, Hampton, Virginia
August 1995
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NASA Contractor Report 4691
User(cid:213)s Manual for the One-Dimensional
Hypersonic Aero-Thermodynamic
(1DHEAT) Data Reduction Code
Brian R. Hollis
North Carolina State University ¥ Raleigh, North Carolina
National Aeronautics and
Space Administration
Langley Research Center
Hampton, Virginia 23681-2199
August 1995

TABLE OF CONTENTS
ACKNOWLEDGMENTS....................................................................................................v
ABSTRACT.......................................................................................................................1
INTRODUCTION...............................................................................................................1
SYMBOLS.........................................................................................................................2
ONE-DIMENSIONAL HEAT TRANSFER............................................................................3
TEST-TIME AND THE SEMI-INFINITE ASSUMPTION............................................4
HEAT TRANSFER MODELS..................................................................................5
Constant thermal properties...........................................................................5
Variable thermal conductivity.......................................................................6
Variable thermal conductivity and thermal diffusivity.......................................7
Finite-volume..............................................................................................7
1DHEAT CODE DESCRIPTION..........................................................................................8
OVERVIEW...........................................................................................................8
INSTALLATION AND SETUP................................................................................8
NAMING CONVENTION AND DIRECTORY TREE...............................................9
FILE DESCRIPTIONS.............................................................................................9
Input files....................................................................................................9
Output files.................................................................................................10
Error log......................................................................................................11
UNITS...................................................................................................................11
HEAT TRANSFER COMPUTATIONS.....................................................................12
STATISTICS...........................................................................................................13
DATA REDUCTION AND ANALYSIS...................................................................14
FINITE-VOLUME APPLICATIONS.........................................................................19
CONCLUDING REMARKS................................................................................................20
REFERENCES....................................................................................................................22
APPENDIX A. ANALYTICAL HEAT TRANSFER MODELS...............................................24
APPENDIX B. FINITE-VOLUME HEAT TRANSFER MODEL.............................................30
APPENDIX C. MATERIAL THERMAL PROPERTIES..........................................................34
MATERIAL PROPERTY CURVE FITS....................................................................34
Type-E Thermocouple...................................................................................34
Chromel......................................................................................................35
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Constantan..................................................................................................35
Macor.........................................................................................................35
Quartz........................................................................................................36
Pyrex..........................................................................................................37
17-4 Stainless Steel......................................................................................37
CORRECTION FACTORS......................................................................................38
ADDITIONAL MATERIALS...................................................................................40
VALIDATION OF THERMAL PROPERTIES DATA................................................40
APPENDIX D. 1DHEAT INPUT FILES...............................................................................42
SETUP FILE "1Ddemocoax.inp"...............................................................................42
Listing of sample setup file "1Ddemocoax.inp"................................................42
Description of "1Ddemocoax.inp" file............................................................42
FINITE-VOLUME SETUP FILE "1Ddemocoax.fvinp".................................................44
Listing of sample setup file "1Ddemocoax.fvinp".............................................44
Description of "1Ddemocoax.fvinp" file..........................................................44
INPUT TEMPERATURE FILE "1Ddemocoax.degk"...................................................45
Listing of sample input file "1Ddemocoax.degk"..............................................45
Description of "1Ddemocoax.degk" file..........................................................45
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ACKNOWLEDGMENTS
This research was supported by grants NAGW-1331 and NAG-1-1663 to the North Carolina State
University Mars Mission Research Center.
iii

ABSTRACT
A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has
been developed. This code can be utilized to determine heat transfer rates from surface temperature
measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an
analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical
solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant
substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The
finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly
incorporates the effects of variable substrate thermal properties and does not require the semi-infinite wall
thickness approximation used in the analytical model. This model also includes the option of a multiple-layer
substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce
several sets of aerodynamic heating data, of which samples are included in this report.
INTRODUCTION
Information on aerodynamic heating rates is a critical factor in the design of hypersonic vehicles. A
common experimental technique for the determination of aerodynamic heat transfer rates is wind tunnel
testing of models which have been instrumented with surface temperature sensors such as thin-film resistance
gages or coaxial surface thermocouples. These sensors are used to measure surface temperatures during a
wind-tunnel test, and the surface heat transfer rates are then calculated from the recorded time histories of the
surface temperatures.
An analytical relationship between the heat transfer rate and the measured surface temperature-time
history was developed by Vidal (ref. 1), and Schultz and Jones (ref. 2). This relationship is based on the
model of one-dimensional heat transfer to a semi-infinite substrate which has constant thermal properties.
Cook (ref. 3) extended this theory to include substrate materials with variable thermal conductivity. Hartunian
and Varwig (ref. 4) and Miller (ref. 5) developed approximate correction factors to account for substrate
materials with variable thermal conductivity and thermal diffusivity. The one-dimensional heat transfer
problem with variable thermal properties has also been solved numerically by many authors, for example
White (ref. 6), Patankar (ref. 7) and Dunn et al (ref. 8). Pittman and Brinkley (ref. 9) and Bradley and
Throckmorton (ref. 10) have extended the numerical method to multiple-layer substrate problems.
In this report, the One-Dimensional Hypersonic Experimental Aero-Thermodynamic data reduction
code, 1DHEAT, will be detailed. 1DHEAT is an fast, user-friendly FORTRAN code for heat transfer data
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reduction which incorporates both analytical and numerical models. Variable thermal properties are
accounted for in both models, and both models can be used to reduce either thin-film gage data or coaxial
thermocouple data. Additionally, multiple- layer substrates can be dealt with using the finite-volume model.
SYMBOLS
[ ]
C Stanton number (dimensionless heat transfer coefficient), q˙/ r u (h - h )
h ¥ aw ¥
c specific heat (J/kg-˚K)
p
E sensor voltage (mV or V)
h enthalpy (J/kg)
H dimensional heat transfer coefficient q˙/(h - h )
aw ¥
k thermal conductivity (W/m-˚K)
L( ) Laplace transform of ( )
q˙ heat transfer rate (W/m2)
Q heat addition (J/m2)
R sensor resistance (W )
r adiabatic wall recovery factor
RMS( ) root-mean square of ( )
S( ) standard deviation of ( )
s Laplace transform variable
T temperature (˚K)
t time (sec)
u velocity (m/s)
x depth through substrate(m)
x* dimensionless penetration depth
a thermal diffusivity, k/(r c ) (m2/s)
p
a coefficient of resistance (1/˚R)
R
b thermal product, r c k (W-s1/2/m2-˚K)
p
b ' correction factor
q
f transformed temperature, f =(cid:242) k dq (˚K)
k
0 0
l dummy time integration variable (s)
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