SUMMARY OF RESULTS AND SUGGESTIONS FOR FUTURE WORK

Flow

IV. SUMMARY OF RESULTS AND SUGGESTIONS FOR FUTURE WORK

IV. 1 Surnpary of Results

The work c a r r i e d out in this experimental investigation in- clude s the building of a low density, high enthalpy continuous -flow t e s t facility; the development of a probe which can be used f o r m e a s - urements of impact p r e s s u r e , m a s s f l u x and total enthalpy and a

stagnation-point heat -transfer probe to withstand a n extremely hostile plasma environment; and the use of these probes in a n attempt to define the flow field of a highly ionized, supersonic f r e e jet.

Test Facility

T h e t e s t facility has the flexibility of operating a t low gas flowrates (< 0.5 gm/sec) when using the diffusion-ejection pumping

system and operating a t highef flowrates when the wind tunnel com- p r e s s o r facility i s used. One version of the so-called Magneto- Plasma-Dynamic a r c heater was used to heat the gas to average

total enthalpies ranging from between about 5000 to 10,000 B T U / I ~ ~ . Operation of the a r c heater a t 0.5 $m/sec argon flowrate, over a

range of current from 200 to BOO8 amp., provided a stable discharge and a flow field of high purity. The atom-ion number density was

15 - 3

about P O c m a t the exit plane of the a r c heater, Probe Development

All probes were water cooled to allow continuous operation in the hostile plasma envirornment encountered here. Probe tips made of molybdenum, tungsten and carbon were used for the com- bined impact p r e s s u r e ^# m a s s flux and total enehafpy probe, in o r d e r to maintain a sharp Peading edge, This feature was necessary to

insure swallowing of the shock wave while making the m a s s flux

measurements in supersonic flow. It also delays the onset of viscous effects which complicate the interpretation of p r e s s u r e measurements, The m a s s flux sampling technique was developed in the supersonic flow field of an unheated f r e e jet.

An important feature incorporated into the design of the

stagnation point heat t r a n s f e r probe was a 0.001 in. "airtt gap which thermally isolated the outer heat shield cooling passage from the inner calorimeter. Stagnation point heat transfer r a t e s ranged as high a s about l 3 BTU/' i n ²sec,

Heated F r e e J e t Investigation

These probes were used in am attempt to define the flow field of a highly ionized a r c heated f r e e jet. Based upon eke Chapman (36) viscosity f o r a fully-ionized gas, the Reynolds number was about

2508 a t the exit plane and remained at about this value along the centerline of the f r e e jet, The total p r e s s u r e ranged betv6een about .. . .. 28 and 35 mmHg. The impact p r e s s u r e and m a s s flux measurements indicated that the flow was source-like, chemically frozen, and in other details very much like the underexpanded f r e e jet flow of a perfect gas. Near the exit plane,

X/D* =

^1.where the f r e e shear 1aye.r is small, the validity of f i e pu measurements was demon- s trated.

The enthalpy measurements made on the centerline, a t x / ~ * = l , ranged from between 18,000 B T U / ~ ~ ~ a t 200 amp. to 32,000 BTu/lbm at 1008 amp, These values a r e about a factor of P O higher than those reported by others, who used this size probe o r smaller (0,47 in,

dia. inlet), in supersonic flow. These centerline values were ap- proximately three times the m a s s average total enthalpy deduced from a heat balance on the a r c heater. Thus, use of the average total enthalpy to infer local flow field quantities in the f r e e jet, i s

completely misleading.

By combining these total enthalpy measurements with the impact pressuFe and m a s s flux measurements just mentioned, the fraction of the total energy contained inionization was shown to

range between

q.

7 a t 200 amp. and 0.6 a t 1000 amp, Using equilibrium conditions for reference purposes, the total temperature ranges from between 12, O O o O a t 200 amp. to 20, OOOOK a t 1000 amp.

FOP this same c u r r e & range9 the species m a s s fraction ranges from 0,2 f o r the atoms and 8.8 f o r &he singly-ionized ions, to 0.8 for the singly-ionized ions and 0.2 for the doubly-ionized ions respec- tively, Reasonable approximation to other flow quantities along the centerline i s obtained by assuming that the gas i s fully singly- ionized and chemicaUy frozen to recombination, and that the flow i s hypersonic. The electron energy equation was examined, and it was concluded that within a few diameters from the exit the electrons become energetically isolated from the ions and the electron heat

conduction t e r m dominates. These conclusions substantiate the results of electron temperature

(TE)

measurements made (by others (15 and 20)) at the exit plane and 3 diameters downstream, which show that to a f i r s t approximation,

TE

constant. Solution of the electron heat conduction equation, for tihis simple case, indicates a very weak deaay of

TE

dong the axis.

Radial profiles of stagnation point heat t r a n s f e r were obtained between one and twelve diameters downstream of the exit plane. No theory exists which accounts f o r the effect on heat t r a n s f e r of unequal species temperature f o r the conditions encountered here. A prelirni- nary attempt to correlate the results along the axis in the supersonic

region (1 S X/D+ 4

a),

shows that the electron temperature (TE# TI in general) plays a n important role. If i t i s assumed that TE i s

nearly independent of current level, the data at the two current levels correlate quite well. Elevated electron temperature was taken into account in the evaluation of the thermal conductivity (in the Prandtl number) i n o r d e r that the data could be compared to the heat transfer prediction by Finson and Kemp (391, Their prediction i s only

strictly valid for equal species temperatures throughout and chemical equilibrium a t the edge of the boundary layer. In this regard, the one fluid modef. cannot provide the exact solution to this problem;

however, it may establish the trend of the data a s a result of unequal temperature.

lev.

2 Suggestions for Future Work

A s a result of the present investigation, a number of problems a r e suggested for future w o r k

(1 ) A n experimental investigation to determine the electron temper

-

a t u r e and density in the supersonic portion of the f r e e jet used here.

Near the exit plane ( x / D * ~ 3) the electron temperature can be measured spectroscopically, F o r a l l Bocations the possibility exists for measuring TE and n by

E

swinging a small uncooled Langmuir probe through this jet.

(2) A theoretical and a continued experimental investigation to solve the stagnation point heat transfer problem. In particular a two-fluid model must be used to determine the effect on the stagnation point heat transfer rate of unequal species temperature and of probe potential which i s , in general, d s f e r e n t from the plasma potential.

(3) An experimental investigation of the d a r k space which exists upstream of the disk shock (see Fig. 15) in the f r e e jet a s well a s upstream of the bow shockwave from the total enthalpy probe (see Fig. _25). With regard to the f o r m e r instance, the Langmuir probe measurements (suggested as (1) above) in this region and through the disk shock of the f r e e jet should answer some fundamental ques

-

tions about the variation of electron temperature, Of particular interest, in'the l a t t e r instance, i s the possibility of altering the structure of this d a r k space by changing the potential on the body.

-79

-

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"Partition Functions and Thermodynamic P r o p e r t i e s of Argon P l a s m a t t , ~ r n d d Engineering Development C e n t e r , AEDC

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TDR-63-146, Aug. 1963.

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S.: P r i v a t e Communication.

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APPENDIX A: MASS FLUX SAMPLING TECHNIQUES A. 1 Mass flux measurement

Mass flux, pu, can be measured in a supersonic s t r e a m if the shock wave can be I ' swallowed1' in the diffusor section of a probe thereby capturing the undisturbed streamtube bounded by the probe tip perimeter. This technique h a s been used successfully by s e v e r a l investigators (54, 55, 5 6 ) who measured pu in much lower enkhalpy flows than reported here. The probe must have a s h a r p leading edge of small enough' included angle so a s to insure shock attachment while taking the m a s s sample thereby eliminating m a s s spillage a t the tip.

In addition the vacuum supply for the probe must have sufficient pumping capacity, with line l o s s e s included, so that the p r e s s u r e a t the probe tips? a t the required flowrate, is l e s s than the static p r e s s u r e downstream of the shock, Both a steady-state sampling technique using a vacuum pump and a transient sampling technique

. using a 4 f t evacuated collector tank were employed. 3

The purpose of this appendix is to establish the operating range of the pu sampling technique in hot flow, To do this, models of the two sampling techniques used h e r e a r e developed to allow calculation of their operating ranges in t e r m s of jet conditions and sampling conditions. The centerline pu measurements made in the known flow field of the cold f r e e jet a r e shown to be valid a s long a s

conditions fall within the calculated operating range. This same model of the sampling technique is then used to predict the pu probe operating range in hot flow.

Since the m a s s flux measurement involves flowrates

typically between 1 0-8 and 1

o m 5

lbm/sec, the probe line Reynolds number range between l o m 2 to 10/in. Knudsen number based on probe tip conditions i s no greater than about .01. Thus the Hagen-

Poiseuillelaminar flow result is used to relatb probe line p r e s s u r e drop to flowrate. This solution i s ,

To introduce m a s s flowrate, Ifi, and to account for @e change in density the expression i s rewritten in t e r m s of the average density

-

( P ~ + P ~ ) P = i

R T

⁹

where q = - D~

L ^and

9 Bbm f t

=

256pR T = 1.30-0

-

sec 0bfl2 for argon a t 5 2 ~ ~ ~ .

Now if this result i s applied to a s e r i e s of 3 tubes of different lengths Lo, L1, L 2 and diameters DO, Dl

D2,,

the result is.

A. 2 Steady State Mass -flux Measurement Technique

With valves A and B open and valve C closed (see Fig. 6 ) the m a s s flux sample i s pumped from the probe inlete through the probe lines, through the vacuum pump and finally into an inverted water -filled calibrated beaker. The time elapsed to displace the water from the calibrated beaker to the f r e e surface of the water

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