Expendable, slug-type calorimeter probes were developed for measuring high heat-flux levels of 10-30 kW/sq cm in electric-arc jet facilities. The probes were constructed with thin tungsten caps mounted on Teflon bodies. The temperature of the back surface of the tungsten cap is measured, and its time rate of change gives the steady-state absorbed heat flux as the calorimeter probe heats to destruction when inserted into the arc jet. Design, construction, test, and performance data are presented

Russell, L. D.

English

NASA Technical Reports Server

N,ASA T~chnical Memorandum 78573 
(NASA-TO-78573) CALORINETER PROBES FOB 
8EASUBING H I G H  TBERKAL FLUX (NASI) 13  p HC 
AOZ/t?P A O ;  CSCL l4B 
Calorimeter Probes for Measuring 
High Thermal Flux 
Larry D. Russell \ 
April 1979 
Nat~onal Aeronautcs and 
Space Adminlstrat~on 
https://ntrs.nasa.gov/search.jsp?R=19790011994 2020-03-21T23:06:03+00:00Z
NASA Teclmical Memorandum 78573 
Calorimeter Probes for Measuring 
High Thermal Flux 
- - - . . - -- - -  - . -. - . - -- . -- - -- 
Larry D. Rbssell, Ames Research Center, Moffett Fieid, Cal 
National Aerc mut !ss  and 
Space Adrnln~sr-~t~on 
Ames Research Center 
Moffctt Field. Callforna 5,4035 
SYMBOLS 
C specific heat, ~ / g  OC 
d slab thickness, cm 
at F dimensionless time parameter,- 
d2 
k thermal conductivity, W/cm O C  
Q absorbed heat flux, kw/cm2 
S thermocouple sensitivity at given temperature, mv/OC 
T' temperature rise above ambient, OC 
TM' aelting temperature above ambient, OC 
t time from application of heat flux, sec 
X relative depth into slab, X = 0 front, X = 1 back surface 
a thermal dif fusivity , cm2/sec 
p density, g/cm3 
iii 
Larry D. Russe l l  
Ames Research Center 
Expendable, slug-type ca lo r imete r  probes have been developed f o r  measur- 
i n g  h igh  hea t - f lux  l e v e l s  of 10-30 kw/cm2 i n  e l e c t r i c - a r c  jet f a c i l i t i e s .  The 
probes a r e  const ructed with t h i n  tungsten caps  mounted on Teflon bodies.  The 
temperature of t h e  back s u r f a c e  of the  tungs ten  cap i s  measured, and i ts time 
r a t e  of change gives  t h e  s t eady-s ta te ,  absorbed hea t  f l u x  a s  t h e  ca lo r imete r  
probe h e a t s  t o  d e s t r u c t i o n  when i n s e r t e d  i n t o  t h e  a r c  j e t .  Design, construc- 
t i c n ,  test, and performance d a t a  a r e  presented.  
INTRODUCTION 
Expendable, slug-type ca lo r imete r  probes have been developed f o r  measur- 
ing  t h e  extremely high hea t  f l u x e s  i n  a r c  j e t  f a c i l i t i e s  used f o r  s imula t ing  
hea t ing  cond i t ions  dur ing p lane ta ry  en t ry .  A tungsten cap is u t i l i z e d  f o r  i t s  
high mel t ing temperature a s  a ca lo r imete r  s lug .  The s l o p e  of t h e  temperature 
vs  time curve of t h e  back s u r f a c e  of t h e  cap i n d i c a t e s  t h e  absorbed steady- 
s t a t e  hea t  f l u x  a s  the  probe h e a t s  t o  d e s t r u c t i o n .  
The high heat- f lux l e v e l s  t o  be measured a r e  beyond what can be withstood 
by cooled,  s t eady-s ta te  c a l o r i m e ~ e r s .  Another type of ca lo r imete r ,  the  n u l l -  
point  o r  g rad ien t  ca lo r imete r ,  could be used by sweeping i t  through the  a r c  
j e t  f o r  a f lyby i n d i c a t i o n  of t h e  hea t  f l u x  and thus  avoid being destroyed 
( r e .  1 )  I n  t h e  g rad ien t  o r  nul l -point  ca lo r imete r  one o r  more thermocouples 
a r e  imbedded i n  a t h i c k  s l a b  t o  measure e i t h e r  temperature g r a d i e n t s  o r  t h e  
approximate mean temperature of the  s l a b  t o  deduce t r a n s i e n t ,  time-varying 
heat  f l u x  by means of i n v e r s :  h e a t - t r m s f e r  a n a l y s i s .  A fundamental problem 
with us ing a t r a n s i e n t  ca lo r imete r  i n  t h i s  a p p l i c a t i o n ,  however, i s  t h e  p res -  
ence of a l a r g e ,  high-frequency-induced n o i s e  s i g n a l  from t h e  a r c  j e t  r e s u l t -  
ing  from t h e  proximity of t h e  a r c  j e t ' s  cathode t o  t h e  ca lo r imete r  probe. 
With a slug-type ca lo r imete r  t h a t  can wi ths tand a longer  exposure t ime 2 t  
these  high heat- f lux l e v e l s ,  a low-pass f i l t e r  can be used t o  g r e a t l y  reduce 
the  e l e c t r i c a l  no i se  i c t e r f e r e n c e .  
The complexity of  the  cons t ruc t ion  and d a t a  reduct ion required f o r  
imbedded thermocouple ca lo r imete r s  a l s o  discourages  t h e i r  use by t h i s  method. 
The tungsten cap ca lo r imete r  with a s i n g l e  thermocouple loca ted  a t  i t s  back 
sur face  is r e l a t i v e l y  e a s i l y  const ructed and is expendable f o r  each 
appl. ication.  
The use  of tungsten wi th  i t s  high mel t ing temperature r e s u l t s  i n  a slug- 
type ca lo r imete r  t h a t  a t t a i n s  t h e  s t eady-s ta te  cond i t ion  of a l i n e a r  
t e m p e r a t u e  s l o p e  long enough t o  be  measured b e f o r e  f r o n t  s u r f a c e  of t h e  calo-  
rimeter melts. For a 1-nun-thick tungs te -  cap,  t h e  time of l i n e a r  temperature 
s l o p e  p r i o r  t o  mel t ing is on t h e  o r d e r  o t  40 m s  a t  f l u x  l e v e l s  of 20 kbI/cm2. 
By us ing t h e  l i n e a r  p o r t i o n  of  t h e  c a l o r i m e t e r ' s  response,  one can apply  t h e  
simple c a l o r i m e t r i c  heat-balance equat ion w i t h  known m a t e r i a l  pmameters  t o  
c a l c u l a t e  heat - f lux measurements above t h e  l e v e l  of 10 kw/crn2 where c a l i b r a -  
t i o n  f a c i l i t i e s  a r e  n o t  genera l ly  a v a i l a b l e .  
The e f f o r t s  of W i l l i a m  Carlson,  Warren Winovich, and George Liu i n  t h 2  
des ign  and t e s t i n g  of t h e s e  calor.imeters are g r a t e f u l l y  acknowledged. 
DESIGN AND COKSTRUCTION 
A drawing of a t y p i c a l  ca lo r imete r  probe is shown i n  f i g u r e  1. rhe probe 
c o n s i s t s  of a cap, body, and thermocouple assembly. The ca lo r imete r  cap is  
machined from wrought, s i n t e r e d  tungsten and is  a t t ached  t o  a Teflon body by 
two s t e e l  p ins .  Copper has a l s o  been used f o r  t h e  cap, but t h e  high mel t ing 
temperature +3f tungsten allows f o r  more than double t h e  l i n e a r  response time. 
The cap lias a b lun t  shape l i k e  t h e  t e s t  models t h a t  a r e  used i n  t h e  f a c i l -  
i t y ,  which enhances t h e  r a d i a t i v e  h e a t i n g  from t h e  shock l a y e r  ahead of t h e  
probe. A s l i g h t  curva tu re  ensures  t h a t  the  s t a g n a t i o n  po in t  of t h e  a r c  j e t  
flow w i l l  be near  t h e  c e n t e r  of t h e  probe r a t h e r  than near  t h e  edge i f  t h e  
probe is not  a l igned  p e r f e c t l y  normal t o  t h e  flow. The cap diameter is  s i z e d  
according t o  t h e  d e s i r e d  blockage f o r  a given a r c  j e t  nozzle.  The t y p i c a l  cap 
diameter is  4.1 cm and 1 mm th ick.  Probes have been cons t ruc ted  wi th  diam- 
e t e r s  of 2.0-5.5 cm and th icknesses  of 0.5-2.5 mm. The th ickness  is  optimized 
f o r  t h e  heat- f lux l e v e l  a s  w i l l  be explained.  
The Teflon body is d r i i l e d  t o  accommodate t h e  thermocouple, which is 
pressed a g a i n s t  t h e  back s u r f a c e  of t h e  cap by a spring-loaded ceramic holder .  
The thermocouple junc t ion  is  f l a t t e n e d  t o  provide uniform con tac t  a r e a ,  and 
t h e  s p r i n g  f o r c e  is set f o r  approximately 48.3 ~ / m m ~  (7000 l b / i n .  2). This  
method of a t t a c h i n g  t h e  thermocouple was found t o  be more r e l i a b l e  than spo t  
welding. A robus t  probe cons t ruc t ion  is required t o  wi ths tand t h e  acce le ra -  
t i o n  f o r c e s  and thermal shock r e s u l t i n g  from t h e  rap id  i n s e r t i o n  of t h e  probes 
i n t o  t h e  a r c  j e t  flow. The thermocouple t y p i c a l l y  used it; c11romel.-alumel, 
a l though platinum thermocouples have been used f ~ r  h igher  hea t  f l u x e s  when t h e  
back s u r f a c e  temperature may exceed t h e  thermal l i m i t  of  chromel-alumel. 
ANALY S I S 
The rap id  i n s e r t i o n  of t h e  ca lo r imete r  probe and t h e  uniform hea t  f l u x  
over  i ts l a r g e  diameter-to-thickness r a t i o  cap a l lows one-dimensional heat  
t r a n s f e r  a n z l y s i s  t o  be used. The f a m i l i a r  equat ion f o r  t h e  temperature r i s e  
of a semi - in f in i t e  s l a b  a s  a func t ion  of t ime and d i s t a n c e  through t h e  s l a b  
a f t e r  a p p l i c a t i o n  of  a s t e p  inpu t  of  hea t  f l u x  is given by equat ion 1 ( r e f .  2) .  
This equation is plotted in figure 2 for front and 
The curves illustrate the surface temperature rise 
heat flux and exposure time. The useful region of 
analysis of a probe used as a slope calorimeter is 
back surface temperatures. 
as a function of absorbed 
the curveR for steady-state 
the linear portion of the 
back surface curve up to the time when the front surface curve reaches the 
melting temperature. The linear slope portion starts at the time when the 
dimensionless time parameter or Fourier number F exceeds 0.4. Above this 
value, the transient series term of equation 1 becomes insignificant. The 
time derivative then gives the simple, steady-state calorimetric heat balance 
equation in te-ms of the temperature slope. 
and in terms of the observed thermocouple voltage slope it is 
This lumped parameter equation is used with constant coefficients C, k, and S. 
The variation of these values with temperature is minimized by selecting mean 
values for the temperature range corresponding to the linear slope region. 
The usable steady-state, linear slope response can be calculated from the 
steady-state portion of equation 1. The time to melt is given by 
The time to the steady-state, linear response from the 3ourier number is 
The time of linear response is the difference 
This desired response time may be maximized with respect to the slab thickness 
for 
and 
for 
a given material and heat flux by differentiating and solving for d: 
Table 1 gives the parameter values selected for tungsten 
table 2 gives the cap thicknesses for the maximum time of 
several heat-flux levels. 
and copper caps, 
linear response 
TESTING 
A heat- f lux source  s u i t a b l e  f o r  t e s t i n g  and c a l i b r a t i o n  of c a l o r i m e t e r s  
ai: l e v e l s  of  10  kw/cm2 was not  a v a i l a b l e .  Conventional sources  can produce 
h e a t  f l u x e s  up t o  about 1 kw/cm2. A c a l i b r a t i o q  test source  a l s o  r e q u i r e s  a 
uniform h e a t  f l u x  over a t  l e a s t  1 cm2 t o  minimize r a d i a l  conduction e f f e c t s  
and a s h u t t e r  c o n t r o l  t o  provide f o r  a f a s t - r i s e  h e a t i n g  pulse .  
For t e s t i n g  t h e  ca lo r imete r s ,  t h e  h e a t  f l u x  source  p r i m a r i l y  used was a 
h igh- in tens i ty  r a d i s t i o n  source  s i m i l a r  t o  t h a t  descr ibed i n  r e f e r e n c e  3. I t  
cons i s ted  of a high-pressure xenon-arc lamp i n  an e l l i p s o i d a l  r e f l e c t o r  w i t h  
an o p t i c a l  i n t e g r a t o r  and a high-speed s n u t t e r .  Heat f l u x e s  up t o  1 kw/cm2 
were used and had a uniformity  v a r i a t i o n  of 15% over 1 cm2. 
The tuqgsten s lope  ca lo r imete r s  were exposed t o  a 0.2-sec h e a t  pu l se  and 
t h e i r  s l o p e  responses recorded. 7rom equat ion 3 t h e  absorbed h e a t  f l u x  was 
c a l c u l a t e d  us ing parameter values  f o r  t h e  average temperature range,  Compari- 
son of the  measured f l u x  va lues  t o  secondary r e f e r e n c e  ca lo r imete r s  provided 
a r e l a t i v e  c a l i b r a t i o n .  The r e f e r e n c e  d e t e c t o r s  included a c a v i t y  radiornecer 
and s e v e r a l  commercial Gardon-type ca lo r imete r s .  The accuracy of t h e  r e f e r -  
ence ca lo r imete r s  was approximately 15%, inc lud ing  a b s o r p t i v i t y  e f f e c t s .  
The measured heat- f lux values  were t y p i c a l l y  70-85% of the  re fe rence  
calorimexer values .  This r e d w t i o n  is a t t r i b u t e d  t o  thermal coxitact l o s s e s  of 
t h e  spricg-loaded thermocouples. The r e l a t i v e  c a l i b r a t i o n  va lues  measured a t  
low-heat f l u x e s  a r e  n o t  e x t r a p o l a t i v e  t o  h e a t  f l u x e s  of a f a c t o r  of approxi- 
mately 20-fold o r  h igher ,  bu t  a r e  used f o r  t e s t i n g  t h e  ca lo r imete r s  f o r  d e f e c t s  
and r e l a t i v e  uniformity  of response. 
PERFORMANCE 
The tungsten cap ca lo r imete r s  have been used i n  t h e  Giant P lane t  P i l o t  
F a c i l i t y  ( r e f .  4). This f a c i l i t y  is a 100 MW a r c  h e a t e r  cgpable of producing 
hea t ing  r a t e s  up t o  30 kw/cm2. Tes t s  wi th  t h e  ca lo r imete r s  have been made a t  
powers t o  25 kw/cm2. Both r a d i a t i v e  and convective hea t ing  occurs ,  wi th  radia-  
t i v e  h e a t i n g  predominating a t  h igher  powers f o r  blunt-nosed ca lo r imete r s .  
The ca lo r imete r  is mounted a t  t h e  end of a swing-arm s t i n g ,  which posi-  
t i o n s  i t  i n  t h e  a r c  j e t  flow, and a sabo t  cover ing the  ca lo r imete r  i s  r e l e a s e d  
by t h e  flow r e s u l t i n g  i n  an exposure rise time of l e s s  than 1 0  msec. Th= 
thermocouple s i g n a l  is recorded on a high-speed o s c i l l o g r a p h  a f t e r  pass ing 
through a low-pass f i l t e r  and l ight-coupled i s o l a t i o n  ampl i f i e r .  The f i l t e r  
reduces n o i s e  induced by the  a r c ,  and t h e  a m p l i f i e r  provides gain  and high- 
vo l tage  i s o l a t i o n .  
A t y p i c a l  run record is shown i n  f i g u r e  3. The thermocouple response has  
a l i n e a r  response occur r ing  from about 20 rns a f t e r  the  s t a r t  of i n s e r t i o n  of  
t h e  probe t o  about 40 ms a f t e r  i n s e r t i o n ,  when t h e  onse t  of mel t ing of t h e  
tungsten cap and thermocouple occurs. This  ca lo r imete r  had a 4-cm diameter 
tungsten cap l-mm thick with a chromel-alumel thermocouple. The linear slope 
of the response indicates an absorbed heat flux of 14 kw/cm2. The incident 
heat flux would be approximately 35% higher after corrections are applied for 
the radiative component of the heat flux and the absorptivity of the calorim- 
eter. The radiative component is determined from independent radiometer mea- 
surements, and the absorptance of the tungsten cap surface has been measured 
to be approximately 75%. 
CONCLUSION 
Tungsten cap calorimeters with diameters from 2-5 cm have been developed 
and used to measure arc jet heat fluxes up to 30 kw/cm2. Their relatively 
simple construction allows them to be expendable and heated to destruction to 
obtain a measurable temperature slope at high heating rates. Absorbed heat 
fluxes can be calculated directly from the temperature slopes by using 
selected material parameters of the calorimeters. 
REFERENCES 
1. Powars, C. ; Kennedy, W. ; Rindal, k. : Heat Flux Measurement Using Swept 
Null Point Calorimetry. J o  Spacecraft, vol. 9, no. 9, Sept. 1972, 
pp. 668-672. 
2. Carslaw, H.; Jaeger, J.: Conduction of Heat in Solids. 2nd Ed., Oxford 
Univ. Press, Inc., 1959, pp. 112. 
3. Sheets, R.; Pierce, R.: Transient Calorimeter Calibration System. 
AFFDL TR-75-24, 1975, 
4. Winovich, W.; Carlson, W.: The Giant Planet Pilot Facility. Presented at 
the 25th Instrument Society of America Meeting, Anaheim; CA, May 7-10, 
1979. 
TABLE 1.- CALCULATION VALUES 
i 
TABLE 2.- THICKNESS FOR MAXIMUM TIME OF LINEAR 
RESPONSE 
\ 1 
Material 
Tungsten 3410 I 1 1083 Copper 
Absorbed power Copper 
dm,, cm I A ~ L ,  set I 
. .- Parameters at 1000 *C 
19.2 
8.93 
TM, O C  
0.16 
. 475 
p,  g/cm3 a, cm2/sec 
i 
C, ~ / g  OC
1.13 
3.5 
k, W/cm O C  
0.37 
.83 
7EFLON BODY 
PINS (2) 
CERAMIC SPACER SPRING 
THERMOCOUPLE 
PLUG \ 
\ TUNGSTEN CAP 
20 cm RADl US 
LENGTH = 6.86 cm 
Figure 1.- Tungsten-cap calorimeter probe. 
TUNGSTEN 
d = 0.010 cm 
p n 19.2ghma 
K = 1.13 W/cm°C 
a = 0.36 cm2/sec 
10 20 30 40 50 
TIME, msec 
Figure 2.- Calorimeter surface temperature versus absorbed heat flux and 
exposure time. 



Calorimeter probes for measuring high thermal flux

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