The infrared (IR) testing of the Olympus thermal model has provided a capability to perform cost effective thermal balance testing of satellites and satellite components. A high-accuracy monitored background radiometer was developed for the measurement of absorbed radiation heat flux encountered during IR thermal vacuum testing of spacecraft. The design, development, and calibration of this radiometer is described

Donato, M.

Larouche, M.

Ruel, C.

English

NASA Technical Reports Server

N88-10831 32 - 3s- 
I 
MONITORED BACKGROUND RADIOMETER* 
by 
C. Ruel, M. Larouche, and M. Donato 
Spar Aerospace Limited, 
-1 
f ' , j  :'r . 
i c--, I 
I' Ste-Anne-de-Bellevue, Quebec, Canada. 
INTRODUCTION 
The infrared (IR) testing of the Olympus thermal model at the David 
Florida Laboratory in Ottawa has provided Spar Aerospace Ltd a 
capability to perform cost-effective thermal balance testing of 
satellites andsatellite components. 
One of the requirements of the IR test technique is to accurately 
measure the radiant flux absorbed by the spacecraft surfaces. Most 
of t h e  commercially available radiometers did not meet the high 
accuracy and quick time response required, or were too complex to 
implement in the test set up because of the presence of fluid loops 
or power supplies. To overcome this obstacle, a high-accuracy, 
monitored background radiometer (MBR) was developed at Spar 
Aerospace Ltd for the measurement of absorbed radiation heat flux 
encountered during IR thermal vacuum testing of spacecraft ( S / C ) .  
This paper describes the design, development, calibration of this 
radiometer. 
BACKGROUND AND DESCRIPTION 
Various radiometer designs have been used for IR testing. Flat 
plate calorimeters, which represent one class of radiometer, 
consist of a control surface with a thermocouple and insulation on 
its backside (1,2). Many attempts have been made to optimize its 
design but the major drawbacks of this type of sensor remain the 
inadequate time response, and the accuracy in conditions different 
from the calibration conditions due to heat leaks from the sensor 
plate to the background environment. 
* This work was supported in part by the Canadian federal 
government's Department of Communictions, contract no. 1ST84- 
00275. 
15 
https://ntrs.nasa.gov/search.jsp?R=19880001449 2020-03-20T08:55:44+00:00Z
Thermopile type devices have also been used but they require fluid 
loops or an external power source and therefore increase the 
complexity of the test set up (3). 
A third type of radiometer currently available is the controlled 
background radiometer. It consist of a sensor surface mounted to a 
body which is kept at a constant temperature via a heater and 
control circuit. This type of radiometer also requires an external 
power source. 
As an extension to the above concepts, the MBR was developed to 
account for heat transfer from the back surface of the sensor 
plate. This is accomplished by monitoring the temperatures of both 
the sensor plate and body. 
The MBR consists of an aluminum sensor plate (SP) and body. 
Aluminum was chosen because its high thermal diffusivity ensures 
uniform temperatures and quick time responses. The SP is attached 
to the body with insulating teflon stand-offs to limit heat flow, 
and its outside surface is covered with the same material as the 
surface whose absorbed flux is to be measured. 
To accommodate the various coatings with which the sensor is to be 
covered, two basic versions of the MBR are currently in use as 
shown in Figure 1. Rectangular control materials like second 
surface mirrors, kevlar or graphite fiber epoxy (GFEC) samples can 
be bonded to rectangular MBR's, and paint or kapton films can be 
applied to the cylindrical MBR's. Except for their shape, the 
construction of the two types of MBR is identical. 
A flexible foil heater is bonded to the inner surface of the SP to 
supply the heat input required for calibration, and an aluminized 
mylar sheet covers the exposed surface of the heater to limit 
radiation heat loss from the back of the SP to the body. 
A very important aspect of the MBR design was to insulate the back 
of the SP as well as possible from the body and the environment to 
ensure that the ratio of the radiation heat transfer from the top 
SP surface to the heat transfer from the back of the SP was large. 
At the same time, to accurately account for heat transfer from the 
back of the SP, it was necessary design the MBR in a way that the 
heat transfer from the back of the SP was mainly to the body with 
little or no heat loss to the environment. This was done by bonding 
all the sensor plate leads to the body before they were fed through 
t h e  body wall. The length of the leads bonded to the body was 
determined by analysis to prevent any conductive heat loss from the 
sensor plate to the environment. 
Black paint is applied on the inside surface of the body to limit 
the reflection of incident radiation passing through the gap 
between the SP and body as shown in Figure 2 .  
16 
Two high accuracy thermocouples, respectively soldered to the SP 
and the body, are used to monitor temperatures. 
PRINCIPLE OF OPERATION 
In a conventional flat plate calorimeter the flux absorbed by the 
sensing surface equals the flux radiated and conducted to the 
surrounding environment. The sensing surface reaches an equilibrium 
temperature, from which the absorbed flux can be computed through a 
calibration curve. For the computation to be valid the radiometer 
must be used in conditions equivalent to the calibration 
conditions. Otherwise, the heat leaks to the environment implicitly 
included in the calibration curve cause an error to be introduced 
in the computation. Another peculiarity of a conventional flat 
plate calorimeter is that the flux measurements can be made only 
when the temperature of the sensing plate has reached steady state. 
The MBR can be classified as a flat plate radiometer but differs 
from the conventional type in that a second thermocouple is used to 
measure the background temperature. With this information, both the 
heat leaks to the background environment and the energy stored in 
the SP can be evaluated. These values are then used in the heat 
balance equation of the sensor plate to determine the heat flux 
absorbed. Because of this the sensor can be accurately used in a 
wide ranging temperature environment and the absorbed heat flux can 
be calculated even when the sensor plate temperature has not 
reached steady state. 
A heat balance performed on the sensor plate yields: 
Qcap + Qcond + Qrad/in + Qrad/out + Qabs = 0 (1) 
where Qcap represents the energy stored in the sensor plate, Qcond 
the SP-to-body conductive heat transfer through the leads and 
stand-offs, Qrad/in the radiative heat exchange between the sensor 
and body, Qrad/out the radiative heat loss from the SP to the 
environment, and Qabs the radiant energy absorbed by the sensor 
plate. 
To characterize the thermal behavior of the radiometer the MBR was 
mathematically modelled with two nodes. One of the node represents 
the sensor plate and the second one the body. A two-node model 
representation was chosen based on the simplifying assumption that 
temperatures are uniform along the SP and body. The assumption that 
material properties (specific heat, conductivity and surface 
emissivity) are constant with temperature was also made. Thus, 
17 
I equation 1 can be rearranged: 
F1 dT/dt + F2(Ts-Tb) + uF3(Ts4+Tb4) + a A s  %(Ts4) - Qabs = 0 (2) 
where Ts and Tb are the sensor and body temperatures respectively. 
F1, F2, and F3 are calibration factors which are experimentally 
determined by measuring Qabs and the resulting Ts and Tb for 
different Qabs values. 
CALIBRATION 
The purpose of the calibration activity was to evaluate factors F1, 
F2 and F3 of equation 2. 
The calibration tests were performed in a thermal vacuum (TVAC) 
chamber with LN2 cooled shrouds. For each MBR, five different power 
levels were supplied to the SP calibration heater to simulate the 
heat absorbed by the sensor plate, and the SP and the body 
temperatures were recorded as a function of time. 
For the calibration process the heat absorbed by the sensor plate 
Qabs can be expressed to account for heat radiation from the 
chamber wall: 
4 
Qabs = Qm + a A s E ,  Tw 
I where Qm is the measured heater power and Tw the chamber wall temperature, and Qabs here is the simulated absorbed flux. 
Equation 2 can then be rewritten: 
Qcalc - Qabs = 0 
where: 
(3) 
( 4 )  
4 4 4 
Qcalc = F1 dT/dt + F2 (Ts-Tb) + aF3 (Ts -Tb ) + a A s  E S T S  ( 5 )  
and Qcalc is the heat flux value calculated from the SP and body 
I temperatures. 
I For each MBR the difference between the measured absorbed flux 
18 
(equation 3) and the calculated flux (equation 5) at time i is 
defined: 
= Qabsi - Qcalci 4; 
Function @ is the summation of the square of the $,,‘A . 
n 
@ = 2 
c c  I 
where n is the number of selected data points for each MBR. 
F1, F2, and F3 were computed by minimizing 0 with the constraint 
that upper and lower bounds were defined for F1, F2, and F3. These 
bounds were centered about nominal values which were physically 
representative of the SP capacitance, conductive conductance and 
radiative conductance from the SP to the body. These bounds were 
necessary, because a least square minimization without constraints 
on the independent variables can result in calibration factor 
values with no physical significance. 
The minimization of function @ was performed using a simplex 
optimization code ( 4 ) .  
ERROR ANALYSIS 
The total uncertainty of the MBR arises from the calibration 
uncertainty and the uncertainty for usage outside the calibration 
conditions. 
CALIBRATION UNCERTAINTIES 
The total calibration uncertainty of the MBR can be expressed as 
the sum of the RMS deviation of the calculated flux from the 
measured absorbed flux, and the uncertainties in the absorbed flux 
measurement. 
DEVIATION OF THE CALCULATED FLUX 
The goal of the calibration was to obtain an expression which could 
be used to calculate the flux absorbed by the sensor plate by 
measuring the SP and body temperatures. 
The deviation of the calculated flux was defined as the RMS value 
of the difference between the calculated and the measured absorbed 
flux. This deviation can be attributed to the thermocouple 
uncertainty, the optimization process tolerance, and the 
simplifying assumptions of the MBR mathematical model. 
19 
The typical RMS deviation of an MRR was found to be less than 1% 
when calibrated with quasi-steady state data (dT/dt 5 0.5 C). 
UNCERTAINTY IN THE ABSORBED FLUX MEASUREMENT 
The uncertainty in the measured absorbed flux is due to 
inaccuracies in measuring the heater power and the sensor plate 
surface area. 
The measured absorbed flux consists of the heater power and the 
test chamber wall radiation (equation 3). The absorbed heat flux 
density is calculated from: 
qabs = Qabs/As 
where As is the sensor plate surface area. 
The inaccuracy in the absorbed flux density can be calculated from: 
where (from equation 3) 
3 
AQabs/Qabs = (AQm + 4 (J As %Tw ATw)/Qabs (10) 
The contribution of the Tw inaccuracy to the measured absorbed flux 
inaccuracy can be neglected, and equation 10 is rewritten: 
The power dissipated by the heater is measured from the voltage 
drop across the heater V1 and across a shunt resistance V2 such 
that: 
Qm = Vl*V2/R (12) 
where R is the shunt resistance value. The error in R is 5 1%, in 
V1 << 0.1%, and in V2 5 1%. Thus the total error in Qm is 
AQm/Qm = AVl/Vl + AV2/V2 +A R/R 
- ., 2% 
20 
, The error on the sensor area was estimated to bePAs/As = 0.5% such 
, that the uncertainty on the absorbed flux density due to the heater 
power and sensor area measurement uncertainties is 2.5%. 
I 
The total calibration uncertainty is the sum of the measured flux 
inaccuracy (2.5%) and the deviation of the calculated flux from 
the measured ( <  1%). This results in a total calibration 
uncertainty of less than 3.5% for the MBR. 
UNCERTAINTIES FOR USAGE OUTSIDE CALIBRATION CONDITIONS 
An additional source of error during the usage of the MBR is the 
I heat transfer between the sensor plate and the environment via the 
I gap between the SP and body. This error was shown to be < 0.1% by 
analysis. 
During the usage of the MBR the temperature difference Ts-Tb varies 
between O'C and 30'C, which is less than the temperature difference 
in calibration, where Ts-Tb varied from 1 O O ' C  in rapidly changing 
conditions to 40'C at steady state. Larger Ts-Tb values in 
calibration result in higher accuracies of the calibration factors 
F2 and F3. However, as can be seen from equation 1, for the 
limiting case when the Ts-Tb values approach 0 the contribution of 
factors F2 and F3 is decreased, in which case the absorbed heat 
flux value can be calculated from: 
I 
4 
qabs = a%Ts 
I 
The total error is then given by: 1 
i Aqabs/qabs = A E)/ E~ + 4 A T s / T s ,  (15) 
Therefore an uncertainty of _+. 1% in Es , and of 2 0.2'C in Ts 
results in a total error of +_ 1.2% for Ts = 130'C and f: 1.5 % for 
Ts = - 1 O O ' C .  Usually during testing, Ts-Tb varied from 0 to 30'C at 
steady state resulting in a total error between 2 3.5% and f. 1.5%. 
RESULTS 
Results of a typical MBR calibration are presented in Table 1. It 
shows that the RMS error between the calculated and measured flux 
is 0.85 % for a range of flux values varying from 8 % to 100 116 of a 
solar constant (absorbed). 
Results from an actual test where the MBR was used to measure the 
shows the time response of the MBR to a step change of 320 W/m**2 
I absorbed flux radiated from IR lamps are presented in Figure 3. It 
I 
21 
in the incident flux intensity. For curve 1 the capacitance term F1 
was included in the flux calculation process, and for curve 2 it 
was omitted. At the first data point available, after 5 minutes, 
the flux prediction was 2.8% off for curve 1 from the final 
stabilized value of 700 W/m**2, and it was 17% off for curve 2 
where the flux prediction was made without the capacitance term. 
CONCLUSION 
This paper has presented the design, development and calibration of 
a simple , light and accurate radiometer. This radiometer can be 
used in infrared or solar illumination testing of spacecraft, and 
requires no fluid loops or power supplies. Results highlighting the 
quick time response of the device to step heat inputs and the 
accuracy over a wide range of incident flux were presented. 
The monitored background raiometer design was shown to be adequate 
and reliable during the infrared testing of the Olympus ( 5 )  
satellite thermal model where 80 MBR's were used to measure the 
flux absorbed by spacecraft surfaces. 
22 
SYMBOLS 
A s  
F1 
F2 
F3 
q 
Q 
T 
sensor plate surface area (m**2) 
capacitance calibration factor 
conduction calibration factor 
radiation calibration factor 
power density (watts/m**2) 
power (watts) 
temperature (Kelvin) 
Greek Symbols : 
E surface emissivity 
0 Stefan-Boltzman constant 
Subscripts : 
abs absorbed 
b body 
calc calculated 
cap capacitance 
cond conductive 
m measured 
rad radiative 
S sensor plate 
W tesf chamber wall 
23 
REFERENCES 
1. 
2. 
3. 
4 .  
5. 
Bachtel, F.D. and Loose, J.D., "Design and Control of an 
Orbital Heating Simulator", AIAA paper 71-432, AIAA 6th 
Thermophysics Conference, April 1971. 
Gilcrest, A.S. and Mon, G.R., "A Calorimeter for Determining 
Thermal Radiation Fluxes in Space Simulation Chambers", Proc. 
Inst. of Environmental Sciences, 1963, p. 369. 
Redman, R.S. and Wolff, C.M., "Development of a Multipurpose 
Radiometer", Vol 16, #5, Journal of Spacecraft and Rockets, 
Sept./Oct. 1979, p. 350. 
Siddall, J.N., ' I  'OPTISEP' Designers' Optimization Subroutines 
ME/?l/DSN/REPl", Faculty of Engineering, McMaster University, 
Canada, 1970, pp. 28-32. 
Donato, M. et al., "Design of an Orbital Heating Simulator 
Using IR techniques", Fourteenth AIAA-NASA/ASTM/IES Space 
Simulation Conference, NASA CP- ,1986. 
24 
Qm/As 
(W/m 1 
N 
RMSe 
NOTES : 1 )  Qm/As is the measured flux in the calibration heater 
divided by the sensor surface area 
538 897 1220 COMBINED FOR 93 166 
ALL DATA 
7 11 13 26 11 68 
2.1 0.59 0.75 0.67 0 . 4  0.85 
2) N is the number of data points at each power level 
3) RMSe is the RMS error in per cent between Qm and 
Qcalc 
Table 1 - Typical Calibration Results Versus Power Level 
25 
nF POOR Q 
SENSOR PLATE 
Figure 1 - MBR 
-SENSOR PL 
-BODY 
RECTANGUL 
TYPE MBR 
.ATE 
AR 
'? 
Figure 2 - R e f l e c t e d  I n c i d e n t  
Rddiat ion  
750 
650 - 
550 k 
m z 
w 
0 
[L 
W z a 
15c 
35c 
01 
~ 
01 Flux calculated wtth 
(32 Flux calculated without 
capacitance 
capacitance 
0 
085489  TIME I HOURS 1 
Figure 3 - R s p n s e  to  Infrared Lamp Step Heat Input  
26 


Monitored background radiometer

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