Average temperature time history calculations of the test media and tunnel walls for cryogenic wind tunnels have been developed. Results are in general agreement with limited preliminary experimental measurements obtained in a 13.5-inch pilot cryogenic wind tunnel

Lamb, M.

Stallings, R. L., Jr.

English

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A SIMPLIFIE q METH09 FOR CALCULATINI G TEMPERATURE
TIME HISTORIES IN CRYOGENIC WIND TUNfIELS
ROBERT L. STALLINGS, JR,
AND MILTON LAMB
LANGLEY RESEARCH CENTER
HAMPTON, VA, 23665
This informal documentation medium is used to provide accelerated or
special release of technical information to selected users. The contents
may not meet NASA formal editing and publication standards, may be re-
vised, or may be incorporated in another publication.
AN
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 	 DEC 19'F
LANGLEY RESEARCH CENTER, HAMPTON, VIRGINIA 23665	 RECE111'ED
';AS Sn FAtim
December 1976
	
INPUT R ,°.MQ(
ti
I Rep ri No
	 IGovernment2 Go 	 Ac,an.on No.
	
I 3 Rec,wmnt 's Catalog No
NASA TM X-73949	 +i	 i
4 Tale and Subtitle
A Simplified Method for Calculating Temperature
Time Histories in Cryogenic Wind Tunnels
7 Author(s)
Robert L. Stallings, Jr. and Milton Lamb
9 Perlo,mrngOrganiratron Name and Address
NASA Langley Research Center
Hampton, VA 23665
5 Report Date
December 1976
6 Perlorming Organization Code
8 Performing Orgomtataw Repcwl No
10 Work Unit No
505-11-15-02
11 Contract or Grant No
_	 —	 13 Type of Report and Period Covered
12 Sponsoring %,$mcv Name and Address	
Technical Memorandum
National Aeronautics and Space Administration
	 14 Sponsoring Agency code	 —^
Washington, D.C.
	 20546
15 Supplementary Notes
Special technical information release, not planned for formal NASA publication
16 Abstract
A simplified method for calculating average temperature time histories
	 !
of the test media and tunnel walls for cr y o genic wind tunnels has been
developed. Results from th r
 method are in qeneral agreement with limited
prelimina ry ex perimental m(.jsurements obtained in the Langley 13.5-Inch
^ilot Cr yogenic Wind Tunnel.
17 Key Words (Suggested by Authorls) l (STAR category undert ned'
Facilities, research and SuoSport
Heat transfer, cryogenic, wind tunnel
18 Distribution Statement
Unclassified - Unlimited
19 Security Uasuf (of this report)
'lnclassified
20 Security Clasuf lot this page)	 21. No of Pages122 Price*
Unclassified	 15	 11
`The Nat+onai technical Information Service, Stxingfreld, Virginia 22151
'Available from
+STIF/NASA Scientific and Technical Information Facility, P O. Box 33, College Park ,
 MD 10740
a
A SIMPLIFIED METHOD FOR CALCULATING TEMPERATURE
TIME HISTORIES IN CRYOGENIC WIND TUNNELS
Robert L. Stallings, Jr.
Langley Research Center
Milton Lamb
Langley Research Center
SUMMARY
A simplified method for calculating average temperature time histories of
the test gas and tunnel walls for cryogenic wind tunnels has been developed.
Results from the method are ,n general agreement with limited preliminary
experimental measurements obtained in the Langley 13.5-Inch P i lot Cryogenic
Win: Tunnel.
INTRODUCTION
The advantages of operating a wind tunnel at cryogenic temperatures in
order to obtain high test Re y nolds number has been well documented in recent
years.	 (See, for example. refs. 1 and 2.) The major advantages of operating
at an extremely low temperature are reduced dynamic pressure for a given
Re ynolds number and, for fan-driven tunnels, greatly reduced drive-power
requirements as compared to conventional wind tunnels. The need for improved
Reynolds number capability, the advantages of a cr yogenic tunnel with regard
to . capital cost, and the current national need to reduce energy consumption
(ref. 3) were factors which contributed to the United States Government's
decision to construct a large transonic tunnel at the Langley Research Center
ca p able of operating at cryogenic temperatures. This facilit y , to be known as
the National Transonic Facility, will have a 2.5 by 2.5 meter test section and
will have a Reynolds number capability based on typical model chord of
ap p roximately 120 x 10 6 when operating in the cryogenic mode at its maximum
operating pressure of 8.8 atmospheres.
I	 I
Some early preliminary studies conducted at the Langley Research Center 	 1
related to the feasibility of operating at cryogenic temperatures were
concerned with the time required for tunnel "cool down" for cryogenic operation,
the amount of coolant required to maintain the cryogenic temperatures during
a cryogenic run, and the time required for tunnel "warm up" after completion of
a cryogenic run.	 in order to estimate these parameters for various insulation
thicknesses, structural weights, and test gas properties, a simplified method
for calc=ulating average conditions for the entire tunnel system was developed.
This method is described in this report and some results are compared with
preliminary measurements obtained in th? Lan g ley 13.^-Inch Pilot Cryogenic
Wind T Annel .
SYMBOLS
A	 surface area of tunnel interior wall, m2
ATS	 test section cross-sectional area, m2
b	 width of air gap, m
c	 specific heat
*
 of 
+
test g as,	 Jp	 kg - K
h	 average heat transfer coefficient for tunnel interior wall
J	 __
M2 - sec - K
h 
	 average heat transfer coefficient for natural convection over
tunnel exterior- wall ,
	 -- J ---
m2
 - sec - K
kair	
thermal conductivity of air, m - sec - K
m	 coolant mass flow rate, k^
sec
MTS	 test section Mach number
P t	 stagnation pressure, N2m
9
1	 I
PTS	
test section static pressure, 2
rn
heat flux,q	 sec
t	 time, sec
TAMP	 atmospheric temperature, K
T S	saturation temperature of coolant, I'
T T	test gas temperature, K
T	 tunnel interior wall surface temperature,
Tw,6w
	
temperature of external wall surface,
T oy 1 , -W,^	 wall temperatures across air gap, K
w	 mass of test gas, kg
latent heat of vaporiza(ion of coolant,	 J-
kg
power coefficient ( 0.2 for 0.1- 
MTS 
=1.0)
ANALYSIS
The simple heat balance usej in this analysis is based on average
conditions throughout the tunnel system. For example, heat convected from the
system is based on an average heat transfer coefficient, conduction through the
tunnel walls is based on an averaqe wall thickness, and the test gas
temperature is calculated as an average temperature. With this in mind the
heat balance equation becomes
g test gas	 q N,)	 g conv.	 gcomp.
wherE g test gas is the heat stored in the test gas, q  
2 
is the cooling
.
available from the liquid nitrogen, 
gconv. 
is the heat exchanged with the
3
1	 i
rtunnel w, ► II, (ind q
C Gillp .	 is the energy flux transferred to the test gas by
the drrv ► —f,rn. Expressin(t the heat flux parameters in terms of the average
spacial temperatures and thermal properties (the expression for q 	 is
COMP.
from ref. 2), equation (1) becomes:
-WC	 dTT-	 ' + c (T T - T S )	 -hA(T w
 - TT)
P dt-
	 p
	
- 1 e . 05 PTS M ^TS `v T T ATS	
(2)
where T T is the average test gas temperature at time 	 t. the variation of
T T
 with time was obtained by solving equation (2) using a finite difference
scherie resultin q in the following e^.cation:
	
hN	 T
-) n + 1	 = (T T ) n
 + -
	 [ w n	 (1T)n
wncp
-x.05- P M 3	 ^'(T )	 A T	 t —	 -	 ` co	 (T T } n -	 1	 (3)TS TS
	
T ri	 S -	 -
wncp	 wnc^^
Therefore, if conditions at some initial `.ime t are known the tunnel test gas
ei-icerature after a time increment 't can be calculated. After the tunnel
tes t_ g as temperature is calculated at ti-E	 t + 't the change in tunnel wall
tem perature for this time increment can be calculated. For the present method,
the ^A! temperatures were calculated from the program of reference 4 modified
to include equation (3).
The finite difference solution of reference 4 applies to the case of a
thermally thick wall with various modes of heat transfer, including convection,
occurring at the exterior surface; however, the interior surface or back wall
is assumed to be insulated. When applied to the tunnel wall case, the exterior
surface as defined in reference a is actually the tunnel wall interior surface
whereas the back wall as defined in reference 4 would he the exterior surface
4
TT
f
of the tunnel wall which is exposed to atmospheric or, room condition.	 In tnis
discussion terminology applicable to th? tunnel wall case is used. Since an
exchange of heat from the exterior wall and its surrounding environment will
definitely occur, it is necessary that it be accounted for in the calculation.
The desired noninsulated exterior wall boundary conditions were artifically
,, btained by making the proper choice of variables and modes of heat transfer
available as options in the program that would be representative of the actual
transfer of heat.
Two noninsulated conditions were considered For the present method. First
and simplest of the two is the case where the exterior wall temperature is held
constant at ambient room temperature. This condition was simulated in the
Urogram by locating a fictitious block having a large thermal mass adjacent to
the exterior wall surface. The conduction o f heat to his fictitious block
maintains the exterior wall surface temperature at an essentially constant
value and therefore correctly simulates the flow of heat through the tunnel
wall for this hypothetical constant temperature boundary condition.
The second noninsulated condition considered for the exterior wall is
the case of free convection to a standard atmospheric environment. The flow
of the heat for this condition is governed by the equation
q	 h  A(T vi, Bw	 TA`9B)
	
(4)
where h 	 is the coefficient of heat transfer for free convection Conditions,
Tw,Bw	
is the temperature of the exterior wall, and IAMB is the ambient
atmospheric temperature. Equation (4) is very similar in form to the following
equation (eq. (7), ref. 4):
	
k
airA(Tw,l	 Tw)	 (5)
air  cond.
	 b
rJ
1	 I	 1	 II 	 ^	 !	 ^
for heat conduction across an air gap. The symbol k air is the conductivity
of air, 
Tw,l 
and 
Tw,2 
are the wall temperatures of the blocks on each side of
the gap, and b is the width of the gap or the distance between the two blocks
1 and 2.
	
If k 
air 
/b is set equal to hF, 
Tw,l 
set equal to 
Tw,aw, 
and Tw'?
set equal to	 T AMS , then equations (4) and (5) are equal.
	 If b is assumed	
.r• 1
to have unity value, then the value of 
kair will equal the value of hF
Therefore, free convection at the exterior wall can be artificial] ysimulated in
the program by assuming an air gap separates the exterior wall from a fictitious
block having a very large density and specific heat. The initial temperature of
the fiCtitioUS block is set equal to the ambient temperature and its mass and
specific heat are fixed at sufficiently large values such that it remains at
ambient temperature for the maximum time span of interest. The tunnel wall
temperatures computed from the program would then represent the proper values
for the case where the exterior wall is exchanging heat by free convection to
an atmos p heric environment.
RESULTS
In order° to determine if the present method qave realistic estimates of
temperature-time histories for the operation of a cryogenic tunr;el, comparisons
were made between calculations and experimental measurements of the test gas
temperature obtained in the Langley 13.5-Inch Pilot Cryogenic Wind Tunnel
(ref. 5). Tunnel specificiations that were used as inputs to the program are
shown in Table 1. Calculations were made for the p re-run cool-down period and
the post-run 4i?r;,,-up period. Ourinq these periods, the exterior wall
temperature was assumed to remain constant at 294 K and was incorporated into
6
Ithe p eogram using the first noninsulated method previously discussed.
Typical calculated cool-down temperature time histories are shown in
figure 1 for MTS = 0.4 and P t = 1 atmosphere. Temperatures are shown for
the test gas, the interior wall, and the exterior wall (= 2 04 f:). The
calculations indicate that the test gas temperature and interior wall
temperature decrease approximately linearly with time and reach the desired 	
dm- i
78 K iperating temperature in approximately 30 minutes. Also shown in figure 1
is a measured data point `or the facility from reference 5 for similar test
corditions. This measurement indicates the time required to cool the facility
ft-or- aoproximately 29 P K to 106 K is approximately 30 minutes as compared to
aporoximately 24 minutes predicted by the p resent method.
.alculated temperature distributions through an average tunnel wall
se;; ^n are shown in figure 2 for several values of t. during thu ccol-down
pe ri od. Due to the large thermal-conductivity of aluminum, the temperature is
esse n tiall y constant from the interior wall to the aluminum-urethane interface.
Large temperature Gradients occur through the urethane with the largest gradients
occ., ­ , inq at the aluminum-urethane interface.
Shown in figure 3 is the effect of test section Mach number on calculated
cool-down temperature-time histories for the test gas at a constant tunnel
total oressure equal to 1 atmosphere. At the higher test-section Mach numbers,
the results indicate a ra p id increase in time required for cool-down with
increasing Mach number. Although, cool-down time measurements have not been
obtained in the pilot tunnel over a wide range of Mach number, the trend of
increasing cool- Ho.,r time with increasing Mach number has been observed in
the facility.	 This increase in ` i me is a direct result of the increasing
enere, flux transferred by the fan to the stream with increasing Mach number.
7
-T
r I
I^ '
As shown in equation (3), this energy varies as M3TS*
Shown in figure 4 are calculated temperature-time histories for the test
gas in the Pilot Cryogenic Tunnel during warm-up periods for stagnation
pressures of 1 and 2 atmospheres and a test section Mach number of 0.6. During
the warm-up perio ,' which occurs after completion of a cryogenic run, the flow
of liquid r;-itrogen is terminated and the flow of heat through the tunnel walls
and from the drive-fan increases the test gas temperature as indicated in
figure 4. The calculated warm-up time for the case of 2 atmosp)eres tunnel
pre , sure can be compared with measurements from reference 5 that are shown in
figure 4 for similar conditions. The measured warm-up time from 1 5 K to 300 K
is a p proximately 53 minutes as compared to a p proximately 60 minutes calculated
from the present method. The calculations indicate that the warm-up time varies
inversely proportional to the tunnel stagnation pressure.
The general agreement shown between calculations and Teasurements in
f igures 1 and 4 indicates that the p resent method does give realistic trends
for the variation of averaae temperatures in a cryogenic wind tunnel.	 It
should be recognized, however, that the results are for average conditions and
can vary significantly from local conditions throughout the tunnel.
CONCLUDING REMARKS
A simplif i ed method for calculating average temperature-time histories of
the test gas and tunnel walls for cryogenic wind tunnels has been developed.
Results from the method are in general agreement with limited preliminar;
experimental measurements obtained in the Langley 13.5-Inch Pilot Cryogenic
Wind Tunnel.
8
Langley Research Center
National Aeronautics and Space Administration
Hampton, Virginia 23665
December 6, 1976
_-r
3• 1
9
r
REFEF r `ICES
1. Polharnus, E. C.; Kilgore, R. A.; Adcock, J. B.; and Ray, E. J.:	 The
Langley Cryogenic High Reynolds Number Wind-Tunnel Program. ACtronautiCS
and Aeronautics, Vol. 12, No. 10, October 1974.
2. Kilgore, R. A.; Goodver, M.J.; Adcock, J.B.; and Daven port, E. E.: The
Cryogenic Wind-Tunnel Concept for High Reynolds Number - estina. NASA
TN 0-7762, November 1914.
3. Kilgore, P,.A.; .Adcock, J. 6.; and Ray, E.J.: 	 The Cryogenic Transonic
Wind Tunnel for High Reynolds 'lumber P,esearch. Presented at the 4GARD
Fluid Dynamics Panel Symposium on Wind-Tunnel Design and Testing
Techniques, London, Engla;id, October 6-8, 19 7 5. AGARD Conference
Proceedings No. 174.
4. Garrett, L.B.; and Pitts, J.I.: A General Transient Heat T-ansfer Computer
Program for Thermall y Thick Walls. "NASA TM X-2058. August 1970
5. Kilgore, R.A.:	 Design Feature.., and Operational Characteristics of the
Langley Pilot Transonic Cr yogenic Tunnel.	 NASA TM X-72012, Se p t. 1974.
__• ,
10
i	 I	 i	 I	 i
Table 1. - PROGRAM INPUTS FOR 13.5-INCH PILOT CRYOGENIC WIND TUNNEL
1) Structural Material, Aluminum
(a) Mass = 3175kg
(b) Surface Area = 55.74 m?
=(c) Average Thickness =	 Mass--	 —
2.11 cm
Surface Area x Density
	
2)	 Insulation (External), Urethane
Average Thickness = 12.7 cm
3) Volume = 17 m3
	
4)	 Coolant, Liquid
(a) T T 78	 !'. Flow rate =	 1.02 sec
(t) T T	 = 78	 K: Flow rate regulated to maintain this	 temperature.
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A simplified method for calculating temperature time histories in cryogenic wind tunnels

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