DESIGN STUDY OF THE UTIA LOW DENSITY PLASMA TUNNEL
by
J. B. FRENCH AND E. P. MUNTZ
(~
MARCH. 1960 UTIA TECHNICAL NOTE NO. 34
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-4DESIGN STUDY OF THE UTIA LOW DENSITY PLASMA TUNNEL
by
J. B. FRENCH and E. P. MUNTZ
The authors wish to thank Dr. G. N. Patterson for his
assistance in initiating and guiding this study. The supervision of Drs. 1. 1. Glass and J . H. deLeeuw. and their interest and assistance in the various phases of this study, are gratefully acknow ledged.
The assistance of Dr. A. C. Hallett of the Department
of Physics of the University of Toronto. who provided both advice and
the laboratory facilities during the cryogenic experiment, is gratefully
acknow ledged.
The financial assistance of the Defence Research Board
A design study of a low density plasma tunnel has been
eompl.eted. A eombination of an electric-are-powered souree of high energy plasma, and a eryogenic pumping system, has been ehosen to pro
-vide high energy flows at low pressure. The work reported covers a p re-liminary investigation of the arc souree operating characteristics, scme limit estimates of the expansion process. an experimental investigation of a lIpilot plant" cryogenie pump, and the design of the overall tunnel and
pumping system based on these results. It is concluded that a versatile facility ean be built, which will be able to produce the following test section eharacteristies-hypersonie flow, statie pressures less than 10 microns at 5 lb/hr mass flow, mean free paths of the order of 111, stagnation
temperatures up to 10, OOOoK, and low levels of stream fluctuation and
TABLE OF CONTENTS
NOTATION
1. INTRODUCTION
Il. PRELIMINARY PLASMA JET STUDIES
2. 1 Description of Plasma Source 2.2 Operating Characteristics
2.2.1 Experimental Arrangement 2.2.2 Operating Envelope
2.2.3 Electrode Life and Stream Contamination 2.2.4 Residual Swirl
2.2.5 Fluctuations in the Flow 2.2.6 Reproducibility of Conditions iii 1 5 5 6 6 6 7 8 8 9
lIl. THE EXPANSION PROCESS 9
3. 1 Limits of the E xpansion Process 9
3. 2 Boundary Layer Growth 10
3.3 Discussion of Expansion Process 10
3. 3. 1 Arc Equilibrium 10
3.3.2 The Recombination Process 11
3.3.3 The Deionization Process 11
3. 4 C onc lusions 13
IV. EXPERIMENTAL INVESTIGATION OF THE PERFORMANCE OF A LOW DENSITY CRYOGENIC PUMPING SYSTEM 13
4. 1 Theoretica1 Princip1es 13
4.2 Description of the Experiment and the Experimenta1
Results 16
4.2.1 Simulation of Conditions to be Encountered
in the Proposed Plasma Tunnel 16
4.2.2 Experimental'Program and Procedure 18
4.2.3 Experimental Apparatus 18
4.2.4. Experimenta1 Results and Their Reduction 19
4.2.4.1 Pressure Measurements 4.2.4.2 Pressure History 4.2.4.3 Therma1 Conductivity 4.2.4.4 Vapour Pressure 19 19 20 24
(ii) 4.2.5 Discussion of Results 4.2.5.1 Pumping Performance 4.2.5.2 Therma1 Conductivity 4.2.5.3 Vapour Pressure 4.2.6 Conc1usions
V. THE CRYQGENIC PUMPING SYSTEM VI. TUNNEL DESIGN
6.1 General Considerations
6.2 Details of the More Important Sections of the Design 6.2.1 Test Section
6.2.2 Isolation Va1ve
6.2.3 Auxiliary Pumping Fdcilities VII CONCLUSIONS REFERENCES 24 24 25 25 26 26 29 28 30 30 31 31 32 33
a A c cm f K A K 2)3~ L m M 6 M n N p q Q q R Re S T t
S
NOTATIONcoefficient of deioniza tion surface area
radiation coefficient
most probable random molecular speed Maxwellian velocity distribution function thermal conductivity
thermal conductivity for runs 2, 3 and 4 based on density measured for run number 1.
nozzle length
mass of an air molecule
total mass of condensate deposited up to a given time mass of condensate within any given layer
At
number density of moleculestotal number of partic les pressure
bulk ve locity of gas specific energy flow energy flow
s pecific gas constant Reynolds number
molecular speed ratio
=
q/Cm absolute temperaturetime
boundary layer thickness density factor
w
r
(iv) emissivity
ratio of specific heats (C p/C v)
absolute velocity components of gas molecules evaporation or condensation coefficient
net interphase mass transfer (mass/unit area/unit time) evaporation rate .(mass/unit area/unit time)
condensation rate (mass/unit area/unit time)
S'l.
l
e - -
~
J
1f (, -
e
~f
s)
J
unit of pressure 1 ~ = . 001 mm Hg relaxation time
Subscripts For Section IV )1 )2. 3.4 )0· )1 )s )c ( )effective
refers to run number 1 or to conditions at a position w i thin the c ondensa te
refers to runs 2 or 3 or 4
refers to gas condition remote from condensate surface refers to gas condition a few mean free paths from condensate surface
refers to gas condition at the temperature of condensate surface
condition at the copper condensing surface va1ues based on actual condensate surface area
1. INTRODUCTION
In 1956 the Institute of Aerophysics put into operation a low density wind tunnel (Ref. 1) which is capable of providing free-molecule flow conditions around small bodies, at subsonic and moderately super-sonic Mach numbers. This facility has been of great value in implement-ing a series of experimental investigations which accompanied theoretical
studies (Refs. 2, 3), in particular the development of the orifice type
probe and long tube probe for pressure measurement under free-molecular flow conditions. The present program of studies in this tunnel includes force and drag measurement on bodies, extending from free-molecular conditions into the transition regime, and the development of the electron gun technique (Ref. 4) as a means of obtaining point measurements of density.
At the same time. however. it is recognized that there exists an area of ihcreasing practical and theoretical interest in the field of high energy. low density flows. This field includes the initial stages of
atmospheric entry and sustained flight at great altitudes, proposed plasma and ionic space propulsion systems. and in general. the study of
phenomena pertaining to the extension of the kinetic theory to plasmas. Adapting the present tunnel to high energy flows was considered. but this was found impractical for several reasons. In the first place, it would interrupt the experimental program laid out for this tunnel. Further, the present pumping capacity placed an undesirable restriction on the plasma source mass flow and tunnel pressure level. Another advantage of ha ving separate low and high energy facilities is that as free-molecular flow instrumentation is developed in the existing low energy facility it can be applied directly or with little modifipation to the high energy facility.
In order to make a logical choice of a source of high energy
plasma. and of the high vacuum pumping system, it is necessary to list the desired capabilities of the proposed tunnel. These are as follows.
(1) The test section mean free path should be at least 0.5".
This magnitude is selected to provide free-molecular conditions for probes and small test models.
(2) The test section flow should contain controllable amounts of dissociation and ionization. These are important characteristics of high energy flows. and in order to be
able to study them separately the tunnel should be able to run on different gases - for example nitrogen at intermed-iate temperatures is convenient for studying flows with dissociation, and a monatomic gas like argon is convenient for studying flows with ionization.
(2)
(3) The test section flow should be hypersonic. It is always true that flight at extreme altitudes involves hypersonic flight speeds, so that if simulation' of flight conditions is
considered Mach numbers abov.è 5 should be available. It
is noted that exact simulation of Mach number is not necessary, since flow patterns vary little throughout the
whole hypersonic range.
(4) It is more important that high directed stream velocities be obtainable since satellite velocities are of the order of 20. 000 ftl sec. An important area of investigation will
involve the interaction of particles of this velocity with a '
surface. and of plasmas of this velocity with magnetic and
electrostatic fields. It is apparent that in order to pro-vide flow s with this high directed energy the plasma should have a large stagnation enthalpy.
(5) The available running time should exceed five minutes. Low density flows involve low static pressures, and the
response time of gauges available at present is of the order of minutes. Further. spectrographic studies to date have shown the need for photographic exposures of several minutes duration.
These desired capabilities taken together fopm the basis of the choice of the high energy plasma source and the necessary vacuum
pumping system. It is felt that if these capabilities are achieved, a facility
useful for two basic types of investigation should result. First. it would be capable of simulating various combinations of the parameters of high speed. high altitude flight. although not all of them simultaneously. Actually. because of the complexity of the physical and aerodynamic phenomena involved, studies of the basic physics are facilitated by pro-ducing and investigating the influence of various parameters separately. Additionally. the fact that above the tropopause the atmosphere is far from
thermodynamic equilibrium makes its simulation very difficult.
Second. and perhaps more important, the basic physics of high energy low density plasmas. and their interactions with solid bodies and fields, can be investigated.
An arc-powered plasma source. or plasma jet. appears
to be the only means of producing high energy plasma which satisfies the various requirements. Shock tube and "hot-shot" systems provide running times which are many orders of magnitude too short (poin1:.5).
Electrode-less r - f heating may provide controllable amounts of dissociation and ionization, but the total enthalpy addition possible at present seems to be very modest (Ref. 5), and faUs far short of providing the enthalpy which would result in the high directed velocities required. Pebble bed heaters
provide higher enthalpies, but still not sufficient to produce appreciable ionization or dissociation.
As a result of these considerations, it was decided to study a plasma jet in order to determine its suitability as a high energy
source for the proposed tunnel. This study is detailed in sections II and lIl. It was soon apparent that, while the plasma jet satisfied the
capabilities previously listed, it introduced two severe problems - con-tamination of the plasma stream by evaporated electrode material and fluctuations in the energy addition to the stream because of instabilities in the arc process. A simple solution to both these problems was found (Sec. 2.2.3 and 2.2.5), when it was established that running at arc
chamber peripheral static pressures below 100 mm Hg virtually eliminated both contamination and fluctuations. This study also established
an optimum cathode orifice diameter (nozzle-throat diameter) for maximum
energy addition and stability under this reduced operating pressure. From this study the operating mass flow for maximum specific energy addition
was found to be about 1 lb/hr, although flows up to 5 lb/hr at reduced specific energies could also be useful. The mass flow requirement for
the pumping system design was chosen as 5 lb/hr.
The test section mean free path requirement of 0.5"
together with the chosen mass flow, defines the design pumping performance.
The results of Sec. 3.l and 3.2 indicate that, for the specific initial
conditions indicated and using a conventional nozzle, at nozzle exit pressures of about 10 micron Hg any uniform core of the flow wiU have been eliminated by the boundary layer. Hence this pressure level could be chosen as the minimum desired for the vacuum pumping system, if the
facility were to be used only for flight simulation.
However, many basic investigations can be made in
non-uniform flow and the larger mean free paths assoc:iated with somewhat
lower pressure levels may be very desirable. Therefore, the minimum
desired test section pressure has been estabUshed as 1 micron Hg.
C onventional high vacuum pumping systems are incapable of handling these relatively large mass flows at pressures of a few microns. unless a system of inordinate size and cost is used. Since this low
pressure region is of primary interest. the design of the proposed facility
hinged on finding a more effective pumping system.
A recently proposed possibility in high vacuum pumping is
the cryogenic pump. which operates by condensing the air, or whatever working fluid is being used, on an extremely cold surface. A comparison on a thermo dynamic basis of the efficiency of the cryogenic system with other more conventional systems is given in Ref. 6; the much greater efficiency of the cryogenic system at low pressures shown in that report is reflected in ' a greatly reduced capital outlay for a system of a given capability.
( 4)
One problem connected with the wind tunnel application of cryogenic pumping is the disposal of the condensed phase. For air or argon, the normal working pressure of the proposed facility is below the triple point, so that while the pump is in operation a steadily thickening layer of solid builds up on the condensing surface. The energy liberated during the condensation process must be removed through this layer; thus a temperature drop will exist between the gas-solid interface and the metal surface. This temperature drop will depend on the thickness and the thermal conductivity of the condensate. The condensate has an effective
vapour pressure corresponding to its surface temperature. This vapour
pressure will be the lowest pressure the pumping system can attain. The vapour pressure curve of most solidified gases, of which nitrogen is typical, is astrong function of temperature, (Fig. 1), and relatively high pressures might be reached very quickly as the condensate builds up, if the temperature rise across it were excessive. Accordingly, for a
cryogenic pump to be effective, the surface temperature of the condensate must, for a reasonable length of time, stay below some specific value, corresponding to a given pressure level. This time requirement wiU vary depending on the application, but for the UTIA plasma tunnel, times of the order of ten minutes would be satisfactory. Between runs, the condensing surface would be defrosted by simply raising the temperature
50 that the condensate evaporates and can be removed by the roughing pumps
(Sec. 6. 2.4).
To obtain the available time for a run at a specified mass flow per unit condensing area, the vapour pressure curve of the working medium, the condensate density, and the thermal conductivity of the con-densate must be known. Of these, for most gases, only the vapour pressure curve is known. In order to obtain more information for the design of a suitable cryogenic pump, a pilot scale experiment was under-taken, in which the mass flow per unit area, metal surface temperature Tc' and incoming gas temperature were the same as those in the fuU scale case. Simulation of full scale conditions ';via-s:; stressed because it was felt that the rate of deposition might have an effect on the solidity and bulk thermal conductivity of the solid phase.
The condensing surface temperature Tc is determined by
the choice of· cool~J1t pJ.ediuh1 in the cryogénic pump. To condense air, this choice is effeètively limited tv helium, hydrogen, or neon. At present the Institute has available two compressor units capable of liquefying hydro-gen or neon when combined with a Joule-Thomson throtUing valve, but not capable of liquefying p.elium because the lowest available temperature in the cycle before the joule-Thomson valve is above the invers ion tempera-ture of helium, so that use of this gas would result in net heating instead
of cooling over a complete Joule-Thomson cycle. These units each consist
of a 2000 psi compressor and a freon regrigerant system used for inter-cooling - they are described in Ref. 7. Neon was preferred to hydrogen
for safety reasons, although this choice raised the minimum Tc attainabie from 20.4 oK to 27. 30K. For cases where a reduced heat removal capacity is acceplabIe, e. g. an absolute minimum test section pressure at somewhat '. lower mass flows is desired. the minimum Tc can be lowered to 24. 57~
by boiling the liquid neon at a pressure just above that of the triple point. Having chosen neon as the working fluid in the heat removal system, the design study of the proposed tunnel follows logically.
First. the chosen arc source was investigated to define an envelope of operating conditions, especially wUh regard to mass flow. Secondly, a cryogenic pumping system was studied both theoretically and with a "pilot plant" model pumping system. The experiments with the model pumping system, were designed to predict the pressure rise with time in the pumping chamber of the full scale pump, for a wide range of values of the specific mass flow, i. e. the iniet mass flow per unit con-densing surface area.
Using these results, together with the requirements of desired running time and test section pressure, the cryogenic pump is discussed. This report covers all three aspects of this work . .
II. PRELIMINARY PLASMA JET STUDIES 2. I Description of Plasma Source
The problem of obtaining a current-free plasma fr om an arc discharge depends on the stability of the arc with an imposed fluid flow through it. Perhaps the most highly developed type is that pioneered in Germany (Refs. 8. 9) in which the fluid is arranged to flow axially down
the arc path and is discharged through a perforation in one electrode. The earIy German work was on swirl- stabilized arcs using water as a working fluid; recently a commercial model has been produced which can use nearly any gas as the working fluid. The model studied in this report is the 25 KW plasma arc source or "plasma jet" marketed by the Plasmadyne Corpor a-tion as model L-20.
A cross-sectional view of this unit is given in Fig. 2. The fluid is introduced tangentially at the periphery of the arc chamber, resulting in a high rotational speed at the throat even at low mass flows. This swirl constrains the very much less dense arc to a central position.
The electrodes are a sleeve cathode and a button anode made of thoriated tungsten and held in water cooled copper mounts. It is suggested that the sleeve cathode is able to survive because direct contact with the 10, OOOoK stream is prevented by the magnetogasdynamic pinch effect (Refs. 10. 11).
(6)
The power supp1y for this plasma jet consists at present of two 12.5 KW transformer-rectifier power packs, equipped with
inductive smoothing and ha ving a feedback control winding for varying the output amperage and voltage. The current and voltage are variable up to the limits of 600 amps and 80 volts, within the 25 KW limitation.
2.2. 0 Operating Characteristics 2.2.1 Experimenta1 Arrangement
An overall view of the apparatus used is shown in Fig. 3. The plasma head with its cooting water and power leads is seen attached to the left end of a cylindrica1 pyrex test section. This in turn is
connected to a vacuum chamber which could be maintained continuously at a pressure of about 2 mm Hg. by a Kinney KDH 130 vacuum pump, at mass flows of approximately 2 lbs/hr. The instrumentation consisted of current, voltage, and water flow meters and instruments to measure the static pressure at the periphery of the arc chamber (in the following shortly called arc chamber pressure) pressure, vacuum chamber static pressure, and working fluid mass flow. Fig. 4 shows a typical picture of the plasma jet running on argon. A simp1e conical brass nozz1e of 11/2" exit diameter was used. The detached bow shock wave around the b1unt body is c1ear1y visible.
The arc could be initiated at low pressure by producing a 9000 volt, 60 cycle/ sec discharge between the anode and a metal sting placed about 6" axially downstream.
The operation of the system was also examined for time fluctuations with a Tektronix type 535 oscilloscope, arranged to display either the fluctuation in arc current, or the fluctuation in total visible light output from various regions of the efflux downstream of the cathode as measured by an RCA 929 photocell.
2.2.2 Operating Envelope
The interim vacuum facitity shown in Fig. 3 served the purpose of providing a choked jet from the plasma head, over the whole range of arc chamber pressures at which it may be desired to operate the final tunnel. . An initial and comp1etely empirical survey showed that the best front orifice diameter fr om the viewpoint of arc stability was about 0.4" for air or nitrogen and 0.3" for argon, minor changes from these dimensions having no appreciable effect. These results hold true over an arc chamber range from 10 to 80 mm Hg. The head can be operated at pressures up to several atmospheres, but because of considerations of electrode life, stream contamination and time fluctuations, (Sections 2.2.3, 2.2.5) reduced pressure operation of the plasma head is favoured.
The plasma head was operated to determine the maximum possible energy addition to the air mass flow through it. For the pressure range of interest it was found that the optimum internal diameter of the
cathode was 0.4". Using this cathode size the plasma head was run over
a range of air mass flows from 0.5 lb/hr to 2.0 lb/hr. The object of
each run was to add to the air stream the greatest amount of energy
without either producing an imstable arc or exceeding the ratings of the
power supply. For each run the arc chamber pressure, air mass flow, and power input were observed. Thus each maximum power operating
point for the head consisted of an arc chamber pressure, mass flow,
and maximum obtainable energy addition.
In order to calculate enthalpy addition to the stream.
allowance was made for heat lost to the cooling water by using a curve
based on the manufacturer's data for reduced pressure operation (Fig. 5).
This curve indicates that energy losses to the cooling water increase
as mass flow decreases - at mass flows below 1 lb/hr approximately one
half of the input energy is lost. Knowing the net energy addition to the
stream at each mass flow, the corresponding enthalpy per unit mass of
gas could be calculated, based on the simplifying assumption of a uniform
stream. The temperature corresponding to this maximum enthalpy
addi-tion was found using Mollier charts for high temperature air (ReL 8).
The resulting operating envelope of mass flow versus maximum
obtainable temperature is shown in Fig. 6, together with a cross plot
of the head pressures corresponding to each mass flow.
The operating points shown in Fig. 6 are scattered. but they still indicate the operating region fairly clearly. The maximum
temperature curve is defined by the open circle points. The whole area
beneath this curve is available as stable operating region. so that for
instance at 1 lh/hr mass flow any temperature up to 90000K is obtainable.
Above 1 lb/hr, the full 600 amps available can be applied, so that this
limits the energy addition and hence upper temperature. Below 1 lb/hr,
the arc process goes unstable before the full 600 amps can be appli~d,
and the temperature is limited as shown. The head pressure level is
defined by the half-filled circles; at 1 lb/hr and maximum power input
the head pressure will be about 31 mm Hg.
It is emphasized that these curves are the result of an
initial investigation only. The purpose of this was primarily to find out
the operating range of mass flows of the plasma head. and further to
check at least qualitatively that the head could produce plasma at
tempera-tures approaching 10, OOOoK.
2.2.3 Electrode Life and Stream Contamination
i
The problem of stream contamination due to 10ss of
(8)
chamber pressures. By weighing the electrodes before and after a run, and knowing the working fluid mass flow, the stream was estimated to contain up to 10 mole % metallic impurities, coming from the molten anode spot and erosion from the sleeve cathode. However, .this probl:äm
was virtually eliminated when the head was run at pressures below 100 mm Rg., even at very high power settings, for nitrogen or argon. The oxygen in air again made the contamination significant even at these low pressures. The very low level of conta.mination may be inferreà from the fact that
after running the arc for 30 minutes almost continuously no change in the shape or weight of either electrode wa.s apparent. Further, spectrograms obtained during these runs showed a corresponding reduction in intensity of the s pec tra 1 lines of the impurities.
2.2.4 Residual Swirl
Under certain running conditions. the emerging jèt had a residual swirl corresponding to a helix angle of a-bQut 700• as indicated by
marks on several simple conical nozzles that were used. These marked nozzles were for small expansion ratios, and no e~perimental evidence is available at present for the amount of swirl rema.ining after expansion down to pressures less than 1 mm Hg. This remains to be investigated. 2.2.5 F luctuations in the Flow
It has been found that as a result of instabilities in the arc, the plasma generated is characterized by time fluctuations in its properties . Arc current, arc voltage, and the total light emitted across the centre line of the jet at the nozzle exit have been monitored and displayed on an
oscilloscope. The power input to the stream, and the total light emitted, have been found to vary . widely. "'" Further investigation has shown that operation below 100 mm Hg arc chamber pressure decreases the severity of the fluctuations markedly. The head has several stable types of operation, each characterized by differences in the arc mechanism as indicated by differences in the fluctuation pattern. At a mass flow of 1 lb/hr, a current of 500 amps and wUh new, smooth electrodes, the
plasma jet may be run consistently with no current and voltage fluctuations greater than
t
5% of the mean value. This is considered acceptable for preliminary work.A discussion of suggested mechanisms for this fluctuation is given in Ref. 9. It is suggested that secondaryarcs are present
between the main central arc channel and the sle~ve wall, and that these secondary arcs and their attachment points to the sleeve wall are rotated and blown downstream by the cooler gas near the wall. When they reach the end of the sleeve they are broken and renewed upstream. Lower pressures tand to make these secondary arcs less constricted, possibly even allowing them to diffuse into a stationary radial sheet discharge.
20206 Reproducibility of Conditions
It was found empirically that so long as the head was run at reduced pressures, it could be operated for extended periods of time, maintaining steady values of current ~voltage and arc chamber pressure. The arc starts best at reduced power and mass flow settings, but upon'
adjustment of these parameters to previous settings, these variables regained their previous valueso Starting and adjustment of settings to
predetermined values req uires several seconds, so that a pumping system must be at least semi-continuous in operation.
lIl. THE EXPANSION PROCESS
The expansion of the plasma to a pressure of a f~;w microns is an extremely complex processo The complicating factors
rnay be listed as:
1) non-uniformity of the initial stream
2) the probability of relaxation effects
3) the extremely rapid boundary layer growth because of the
very low Reynolds number 0
Additionally, there may be swi:t11, ambipolar diffusion of ions and elect-rons, (as inentionedin Sec 0 3. Jo 3) and a non-adiabatic nozzle wall to '
contend witho
Perhaps the most rational approach is to determine the possible limits of the expansion process corresponding to completely equilibrium and completely frozen flow. The use of air is considered. 30 1 Limits of the Expansion Process
One limiting case that could exist in the nozzle expansion
is that the flow be in complete thermodynamic equilibrium. Assuming an
adiabatic frictionless wall and a uniform one- dimensional stream, calcu-lation of the expansion involves an isentropic mov~ment on a Mollier chart
(Ref. 12) from an initial point determined by the plasma head operating
curve (Figo 6). Mean free paths at various stages in the expansion were deduced from transport proper ties of air given in Ref. 13. The head
conditions chosen as typical were: air mass flow
=
1. 2 lb/hr., stagnationpressure
=
3605 mm., and stagnation temperature = 91000KoFor the same initial conditions, a frozen expansion was calculated.. This assumes that the initial levels of ionization and dissocia-tion are unchanged during the expansion. Since dissociadissocia-tion is virtually
complete at 91000K, the gas may be taken as monatomic throughout, with
a specific heat ratio
't
=
L 67. Thus the only energy modes providing energy for the directed velocity as the expansion proceeds are tlrbse(10)
corresponding to the three translational degrees of freedom.
The results of the calculations for these two extreme
cases are presented in Fig. 7, in which the equilibrium limit is shown
dotted and the frozen limit as asolid line.
3.2 Boundary Layer Growth
It is suggested 'in Ref. 1 that a first approximation to the
laminar boundary layer growth in a nozzle may be obtained by using the
Blasius formula for a flat plate, based on the flow parameters at the
nozzle exit, i.. e .•
5-2.
L
Calculations based on this formula were made to obtain an order-
of-magnitude comparison of the boundary layer growth for the two limiting
cases for the expansion process. The throat diameter was taken as 0.4", and the flow was assumed to expand through a pressure ratio of 1000, from 36.5 mm to 36.5 microns, with corresponding area change.
For the frozen case the isentropic exit diameter is L. 89";
a nozzle length of 6" provides a reasonable maximum expansion angle,
and for that length the boundary layer displacement thickness is about 0.6".
By comparison, the equilibrium case has an isentropic
exit diameter of 5", and at a nozzle length of l' has a displacement
thickness of 6", indicating not only that the Blasius approximation is
completely inadequate, but also that there is probably little uniform core
left at this pressure level.
3. 3 Discussion of Expansion Process
3.3.1 Arc Equilibrium
Before proceeding with the discussion of the expansion
process, it is noted that the arc itself may be far from thermodynamic
equilibrium. Ref., 14 presents a review of arc researches, and suggests
that equilibrium depends upon pressure level. At atmospheric pressure
or greater, the electron mean free path is so short compared with the
arc length that virtual equi-partition of energy exists, the electrons
transmitting their energy (picked up by acceleration in the electric field)
to the gas almost instantly. Thus one temperature may be used to
describe plasma random kinetic motion, rotational and vibrational
temperatures if molecules still exist, ionization level (through the Saha
Between atmospheric pressure and 30 mmo Hg • a region of uncertainty exists, and below 30 mm .• the arc is far from equilibrium, the
temperatures now existing being divided into two ma in groups. The lower temperature group consists of the ion, atom and molecular
random translational temperatures, molecular vibrational and rotational
temperatures~ and these may be taken as equal. The upper group
con-tains electron temperature. electronie excitation temperature and ionizatio.n level. Thus, for example, care must be taken in relating spectroscopic data to temperature. If hydrogen is introduced as a
thermometer gas, the second order Stark shift of the 1-1 fJ line affords
a reasonably accurate method of determining the number density of electrons and ions, but it is not permissible to use the Saha equation to obtain translational temperature from this. No discus sion of
spectroscopie techniques is included in this report, but it is apparent
that several approaches must be used to characterize fully the arc efflux.
3.3.2 The Recombination Process
In order to avoid confusion, the term recombination is used in this report to mean recombination of atoms to form molecules,
as distinct from electrons and ions forming atoms, which wi11 be referred
to as deionization.
Recent studies (Refs. 15, 16) on the flow in hypersonic
nozzles indicates that the flow in nozzles planned for the proposed
tunnel will be foo'zen in dissociation. An approximate criterion (ReL 15)
which may be applied to nozzles is that if
('..Lr)
d...Z-é
(~~J~
\O-:s thenozzle will be near equilibrium where T may be considered as the averaf.e
temperature in the nozz le, and t/Jl?C::I\.)( the maximum relaxation time for
the chemical process. As is pointed out in Ref. 16, the expression' is
strictly applicable only to nozzles with sm all expansion ratios. HoweveI'. it can be applied in our case to give a rough indication whether freezing
wi11 be encountered or not. For an expansion from 36.5 mm. to 36.5
microns in a 1. 5 ft. long nozz1e,
(Y
T ) r;{ ~t(~~)~ 500 whichindicates that the nozzle flow would be frozen. (A value of 1:",«.,)( = 3 x 10- 4
sec. was obtained from Reference 15 assuming T = 65000}( and 0.1 atms.
pressure).
3.3.3 The Deionization Process
There can be several processes operative during the expansion leading to electron and ion 10ss. These are reviewed at some length in ReL 17; for the case of a decaying arc plasma they can be
reduced to
1) classical two-body deionization (radiative deionization)
2) dissociative deionization
(12)
In estimating the rate of change of ionization level, the forwa d process
of ionization has been neglected.
For process (1), which inv01ves the simple coHision of
an ion and an electron. it might be though that the greatly increased
collision cross-section due to the long range Coulomb forces would
increase the rate of deionization, but this is largely offset by the fact that in the vast majority of encounters the particles are simply deflected and no deionization results. This is reflected in the very low values
of the deionization co fficient ex.. in the classical rate equation (Ref. 17)
where
dN
d~
-
oe.
N is the number per cu. cm. of electrons or ions, of which there are essentially equal numbers
dN/dt is theLagrangian time derivative
oe.
is expressed in cm3I
sec.Typical values of oe reported (Ref. 17) for argon at approximately 70000K are of the order of 2.5 x 10- 11 cm 3
I
sec. If an initial ion d nsi yof 6 x 1015 ions/cm3 is assumed, which is about 25% greater than the
thermal equilibrium value for argon at lO, OOOoK, about 45 micro seconds
are required to reduce the ion concentration by a factor 10 to 6 x 1014
Thus if the plasma travels in a tubular extension of the cathode orifice
with no expansion at a typical velocity of 10, 000
ft
l
sec. about 14 cm~are req uired for this change. When aUowance is mad for th simua l-taneous decrease in N due to nozzle expansion, for instance by a step expansion of a 10/1 area ratio, th ionization level becomes essentia.!.ly frozen for any reasonab1.e nozzle length.
Dissociative ionization' (process 2) occurs when the electron is captured by a mo ecular ion which is dissociated in the pro -cess. This type is not applicable therefore to argon. For nitrogen, a combined coefficient for (1.) and (2) is about four orders-of-magnitude
greater than for argon, and hence the ionization level wHI drop rapidly during the initial stages of the expansidn.
Ambipolar diffusion mayalso affect the number density of ions and electrons during the expansion. This is due to the very high mobilities of the electrons, which diffuse radiaUy outward more rapidly
than the ions. This charge separation produces a space charge which slows down the electrons and accelerates the ions in their radial outward movement. A combined diffusion constant can be defined for the wh01e
process. If a 'wall is present it wiU acquire a negative potential
increases the rate of deionization at the wall.
3. 4 C onc lusions
The foregoing results and discussion indicate that a
practical and useful facility can be built. utilizing the plasma produced by
the arc source expanded to low pressures.
The combination of the plasma jet and an adequate
pumping system. should provide all of the desired capabilities listed in the introduction. The test section mean free paths will be of the order of 0.5". a most useful feature in ensuring free-molecular conditions around a model. The flow produced will be weU suited to studying the various
aspects of dissociation and ionization. The flow will also be hypersonic, so that simulation of the flow patterns of high speed flight will be obtainable.
The low density plasma stream will be available at very high directed
velocities. so that many high speed interactions could be studied.
The following sections present details of the mechanical design of the complete facility and in addition present the basic
considera-tions involved in designing a cryogenic pumping unit to satisfy the
requirements of 5 lb/hr mass flow of air, nitrogen or argon, test section
pressures down to 1 micron Hg , and running tinies of at least 5 minutes.
IV. EXPERIMENTAL INVESTIGATION OF THE PERFORMANCE OF A
LOW DENSITY CRYOGENIC PUMPING SYSTEM
This section gives details of the pilot plant experiment
used to determine the feasibility and performance of the projected cryogenk
pumping system.. Simulation of full scale conditions was stressed.
Because of the somewhat complicated nature of the condensation process.
which involves both interphase mass transfer and energy flow, a brief
theoretical discussion is given.
4. 1 Theoretical Princîples
The condensing system is idealized to a unit area of the
condensed phase at temperature T s. in contact with a condensing gas
phase whose distant temperature. pressure and density are T o. Po and
~ O. Following Ref. 18. if condensation is occurring the gas phase is
approaching the solid surface with a speed ratio S where
S
=
directed (bulk) ve locity
random kinetic velocity
:: ( 1)
Under equilibrium conditions S
=
O. and the absolute evaporation rate(14)
transfer occurs. No net transfer of heat occurs either, because the two phases are in equilibrium. The "evaporation rate" may thus be obtained by replacing the solid surface with a gas with a Maxwellian velocity distri
-=-bution function fs corresponding to the surface temperature T s. Then the evaporation rate W~+ is
W S
+ =
;<0[",,/: ,.,
is
.t;
ti;;
oI~
ot
J;
( 2)- DO :-Cl() 0
where m
=
molecular mass, n=
number density in real space and1;
:J%,.
~3:1
are absolute velocity components,r
is normal 0 thecon-densate surface. This integrates to
~
(.IJSt -
Ps
j
:27T
IR
Ts
(if we accept Ps = (' sRT s' which will be true for very low densities even though the temperature is low).
(3)
Note that Ps is the pressure of the hypothetical gas
which would be in equilibrium with the surface, and hence is virtually the
vapour pressure of the soUd phase at temperature T S. There can be a small difference between the actual vapour pressure of asolid existing
under some higher equilibrium pressure, Pe' and its true vapour
pressure. This may be due to the presence of another but non-condensing molecular species in the gas phase. According to Keenan (Ref. 19) this
difference is given by
; ; =
Sa..cfuq./
(4)
e
Since the interphase mass transfer which occurs in this study always takes
place at pressures near the true vapour pressure of the condensed phase,
as will be seen later, this distinction is unimportant for our purposes. We next define an evaporation (or condensation)
coefficient C'" • This is the fraction of the u,)~ stream which
arises by spontaneous emission from the surface. Then c:r'WS
-+
=
absoluteevaporation rate and (1 - a-)
w
s+ is the reflected stream of moleculesthat hit the surface and rebound.
The absolute evapo~at.ion rate cr" wS-t may be assumed
to be independent of the gas phase c-onditions, depending only on the solid surface conditions. Thus, although the ws-&- expression was developed for complete equi.librium conditions, the value of O""'W
s
+
will beheat flow are aUowed. Reliable experimental evidence from many sourees
indicates that cr' is approximately unity for most metals, and larger than
0.9 for many materials (i. e. 0.94 for ice). (Ref. 18, p. 30)
If net mass transfer to the solid occurs, then at a short
distance from the interface the gas phase should be moving as a uniform
gas (i. e. at enough mean free paths distance for the incoming and outgoing
streams to interact). It is safe to assume that heat transfer in the gas
phase will be occur:ring. since the distant gas temperature is T O' In our
case, for instanee, the gas is precooled by a liquid nitrogen intercooler
to approximately 800K and the evaporatirig. : stream is at a lower
temperature T s (in our case at temperatures from 270K to 4BOK). These
streams interact, so that at a few mean free paths from the surface some
temperature T x exists, less than T O' We assume that this heat
trans-fer is not too violent, so that the velocity distribution function of the gas
closely approximates a MaxweUian distribution. Then the rate of
conden-sation is given by
ob rIJ 0
W1 _
=
L
[t(J
L
n
YhFr
~
dS;
ol),..
ot
3
3 (5)where
3
3 now contains the bulk componentS;t
C m.J: of the incoming gas continuumwhere
C
lt1 = most probabie random speedI Eq. 5 integrates to W:r. - -
Pr
12.
rr~
Tr
and if-
[
then-
-and the "absolute condensation rate" will be
er'
W-x.- The same valueof
cr
may be used here for the non-equilibrium condensation coefficientsince, although cr' probably varies with incident particle energy, the
gross mass interchange between phases in the situations encountered in
cryopumping applications is much larger than the net interphase mass
transfer, and incoming particles wiU thus have energies very near to the
equilibrium values. The net interphase mass transfer is the sum of the
(16)
W
~ 0-w
S+
+
cr-
W:.c _w
.tiL (6)[ / - (lL)(:&)
Ps
7;
fl]
orWe may make some safe approximations to this general expression. P is the actual vapour pressure of the sblid phase at
temperature T s: and this will be taken as being its true vapour pressure. A quick estimate will show that under any reasonable condition of tunnel
operation or design, SI
<
O. Ol, so thatT'
may be taken as unity~ A result of this is that the 11 equilibrium" or gross mass flow to and fruin thesurface far outweighs the fresh incoming stream at temperature T o' Thus
the temperature of the fresh incoming stream is brought very close to the condensate surface temperature so that to a good approximation T s = TI' Under these conditions Eq. 6reduces to
-w
(Pr -
Ps)
( 7)the minus sign signifying condensation.
Consequerttly there is necessary a driving pressure or pressure above the vapour pressure to cause the non-equilibrium process
of net condensation to occur. Using the vapour pressure curve for nitrogen, insertion of typical numberical values shows that only a very
slight overpressure is required for areasonabie mass flow. For example, for a condensing surface area of 180 sq. ft. and a mass flow of 5 lb/hr the driving pressure required would be O. 095 micron Hg.
Ref. 18 provides a detailed discus sion of the condensation of a binar?' system (such as nitrogen-oxygen). Qua litative ly, this d: scussion ::;hows that if one gas is not condensing at the same proportionate rate as the other. an accumulation of this gas in the vapour phase immediately above the. soliçl will quickly raise lts net condensation rate until
propor-tionality is again achieved.
4.2 Description of the Experiment and the Experimental Results 4. 2. 1 Simul'j3.tion of Conditions to be E ncountered in the Proposed
Plasma Tunnel
While it may be desirable to use various gases in the plasma
tunnel, the greatest use is likely to be with air, nitrogen or argon. Air
was chosen as the gas to be used in the present experiments. Argon and
nitrogen and their l.ikely effect on the pumping performance as compared
From the vapour pressure curves of Fig. 1. it may be
seen that the temperature difference between the boiling temperature at
P
=
1 atm. (27. 30K) of liquid neon and the condensate surface temperaturewhich will result in a condensate vapour pressu.re of 1 micron is only
about 5. 20K. This leaves a modest allowable temperature margin for the
temperature rise across the condensate before the minimum design
I
w orking pressure is reached. It was. therefore very important that the
full scale conditions be closely simulated by the present experiment.
In order to maintain a condensing surface at 27. 30K':< the
experimental set-up shown in Fig. 8 was used. The condensing surface
was a copper rod. The rod could be held at any desired temperature by
adjusting the current either in a heat er winding around its base. or in a
heater immerse·d in the liquid helium. The rod was cooled by cold (40K)
helium vapour. if the liquid helium was boiled using its, heater. more
vapour was available for cooling the rod.
In the proposed tunnel, the air entering the pumping
chamber would be between 80 and 1000K. To simulate this, the walls
of the test chamber were maintained at a constant temperature between
80 and 100ql< for each of the experimental runs; this also prevented
material condensing anywhere but on the rod. The incoming air was
baffled (Fig. 9) so that the air molecules would have at least one collision
with the chamber walls before striking the condensing surface.
I
The simulation of the pumping duty was attained by
adjust-ing the air mass flow in the ,experiment so that the ratio of mass flow to
condensing surface area
(
ti.;
)
was comparable to the U.) values whichappeared practical for the fuil scale tunnel. The condensing surface
area A, strongly affects the pumping performance of a cryogenic pu
mp-ing system; the larger the area the more thinly the condensate is spread
and thus the slower the condensate surface temperature risee Since the
required area was unknown. a wide range of w · values was chosen for
the experiments. The table appearing below summarizes the experimental
conditions under which the runs were conducted.
Run Rod Temp. 0 K. W (lb/ft2hr)
1 34.3 1. 200
2 28.7 0.430
3. 28.7 0,0494
4 28. 7 0.00794
*
In the experiments, owing to an error in a rough initial calibration ofthe thermocouples the condensing surface was actually maintained at
28. 75~. The 1. 450K difference may be co'nsidered to be a slighLsafety
(18)
4.2.2 Experimental Program and Procedure
For each of the selected W values a pressure history was determined. i. e., at t
=
0, and -P=
10-7 mmo Hg. the desired mass flow was started into the test chamber and the auxiliary pumping units turned off. The test chamber pressure was then read at equal time interva Is for a pproxima te ly one hour. F rom this pres s ure history the pumping performance of the fuU scale pump could be predicted for the specific CA) value of the experiment.An attempt was made at obtaining a vapour pressure curve for air. It was expected to be very close to that för nitrogen. The vapour pressure was measured by turning off the mass flow and maintaining the rod and a layer of condensate at a constant temperature until the pressure in the test chamber appeared to have stabilized. This pressure was then considered to be the vapour pressure of the condensate at the temperature of the rod. This procedure was repeated for several temperatures.
4.2. 3 Experimental Apparatus
A schematic drawing of the experimental apparatus
appears in Fig. 8. A cross-sectional view of the test dewar and condens-ing surface is shown in Fig. 9. The dewar c\onstruction was necessary in order to insulate the walls of the test chamber from the cold (40K)
he li urn va pour .
The test dewar was made of two concentric stainless steel cylinders at the bottom of which were attached, by means of two 3/64 in. thick stainless steel plates, two concentric cylinders made of kovar and kovar sealing glass. The bottom of the two cylinders was sealed with a single 3/64 in. thick stainless steel plate through which the
copper rod, used as the condensing surface, passed into the test chamber.
The dimensions and general configuration are shown in Fig. 9. Both the
inner and outer glass cylinders were silvered except for two thin strips
on each, which were left clear. These clear strips were aligned 50 that the interior of the test section was visible. The temperature of the walls of the test chamber could be controlled by the heater windings indicated in the draw ing.
A small oH diffusion pump backed by a mechanical pump was used in leak hunting and in evacuating the apparatus before each run. The ultimate vacuum measured was 1 x 10- 7 mmo Hg. The leak rate was measured as approximately 0.05 micron litre/hr.
The condensing surface was a copper rod 2 3/4 in. long by 0.25 in. diameter with a standard machined finish. The rod tempera-ture could be controlled by the heater windings shown in Fig. 9.
The inlet mass flow of air was controlled by a needle valve and measured by a positive displacement method using a low vapour
pressure oil. The inlet air was dried by passing it through a liquid air cold trap. The air was then passed through the measuring apparatus and needle valve and into a 34.0 in. length of stainless steel hypodermic tub-ing which lead the air down the inner tube of the dewar stem and directed
it against a baffle in the chamber (see Fig. 9) .
Two pressure measuring gauges were used. One was a C. V. C. Philips type PHG 09 gauge used to give an indication of very low pressures. The other was a triple range (0-50 micron, 50 micron - 1 mm., 1 mmo - 5 mm.) McLeod gauge. The McLeod gauge was used to measure the pressures during the experimental runs.
Temperature was measured at two stations (Fig. 9) by gold-silver thermocouples. A calibration curve for these is given in Fig. 11.
4~ 2".4 Experimental Results and Their Reduction 4. 2.4.1 Pressure Measurements
At chamber pressures below approximately 10 micron Hg significant thermal transpiration existed in the inner stem of the test dewar which acted as the pressure lead to the McLeod gauge (Ref. 20). The thermal transpiration effect, while not always at the free-molecular (Kn ~ 10) value, could be accounted for to within the accuracy of the
pressure measurements using experimental data quoted in Refs. 21 and 22. For the
w
value used in the experiments the gas mass velocity will everywhere be small (as is shown for the gas mass motionat the condensate surface in Sec. 4. 1) and thus PI
=?(i).
The pressures measured by the McLeod gauge during the experiment were effectively p=
Po
=
PI4.2.4.2 Pressure History
The primary results desired from the present experi-ments, was the prediction of the pressure~o versus time for the fuH scale cryogenic pump, for various W values. The fuU scale system was simu1ated by the experimental apparatus described in the previous sections.
Each run (see Sec. 4.2. 1) was conducted at a constant in1et mass flow. Some difficulty was encountered owing to the growth of the condensate thickness being greater than had been anticipated. Since the condensing surface was cylindrical, the deposition of an appreciable amount of solid air, increased the effective diameter of the condensing surface significa ntly . Thus, during each run the W effective varied
(20)
somewhat, whereas in the fuU scale case, owing to the much larger
dimensions involved, the change of condensing surface area, and thus the change in W effective' would be negligible.
The difficulty of the varying surface area is not tO-f>
serious, because at pressures below 5 micron Hg the effective value
changed by not more than 2%. So, in the pressure region where the
pump-ing system gives the lowest, and therefore the most critical pumping times,
the changes in uJ effective would be negligible. Even at pressures of 20 micron Hg the errors averaged only 20%.
Then for each run, the pressure in the test chamber'
versus time may be plotted directly from the experimental results, after therma 1 transpiration effects have been accounted for. These plots appear in Figs. 12 - 15.
To put the results in a more useful form. equivalent mass
flow, calculated from the value of (w )c' was plotted against time to reach various pressure, levels (Fig. 16). From these curves the time to
reach a given pressure at any arbitrary mass flow may be read. An
accuracy of ± 10% for the times has been estimated.
4.2.4.3 Thermal Conductivity
At low temperatures the thermal conductivities of solids are known to be strongly dependent functions of temperature (Ref. 23).
In addition, the thermal conductivity of a condensate may be considered to be a function of the macroscopic (as opposed to microscopic) density of the condensate. That is, the condensate conductivity may depend on how closely, or loosely, the crystals in the condensate are packed. It
was thought likely that the macroscopic density and therefore the thermal conductivity would depend on the effective rate of deposition.
To accurately determine the values of {)J effective
during each run wou1d require a record of the condensate thickness. The
experimental apparatus was designed basically to give the pressure
history curves described previously and was not at all weU suited to the determination of condensate thickness which is also required for the
determination of condensate density. The thickness of the deposit was
measured visually through the various dewars surrounding the test chamber. The method employed was to note the diameter of the
conden-sa te coated rod and subtract from this the known rod diameter. The condensate appeared as a white solid, with the surface having a shine associated with it which made it appear almost waxen. It was also noted
that the surface had a granular texture.
The density of the condensate could only be measured for
run number 1, since in the other runs difficulty was encountered in
of the glass walls of the outer dewars due to condensation. The accuracy of the average density measured for run number 1 was probably no better than
±
20%.The difficulties encountered in the measurement of the condensate thickness make the ca1culation of thermal conductivities from the results of the experiments rather uncertain. Owing to the cylindrical nature of the condensing surface and the rather thick layers of condensate which were deposited during the runs (especially runs 1 and 2), the
effective condensing surface area increases significantly during the runs, reducing -{JJ ff t' . lf the density of the condensate were known at all
e ec lve
points in the condensate, then accurate thermal conductivities could be calculated as a function of uJ effective and temperature. Unfortunately the only density which is known is the average density of run number 1.
Despite the considerations outlined above it was decided
that an approximation to the therma1 conductivity of the condensate would
be of some value as an aid to the fuller understanding of the performance of the cryogenic pumping system. The method of approximating the
thermal conductivities for the various runs, as a function of temperature,
is presented below. It should be remembered that the numerical values are only of low accuracy.
It was assumed that the change in uJ effective values
during a single run was small compared to the changes between the runs
themselves, so that each run may be considered to have taken place at a
constant density. This assumption of constant density for each run allows an approximate study of the factors affecting the thermal conductivity of
the condensate and therefore of the performance of the cryogenic pumping
system.
Since the average density of the condensate during run number 1 is known, the average density measured for run number 1 is
used for all the runs as a first approximation. With the help of an
expression developed below based on an assumed relationship between density and thermal conductivity. the values calculated from this first approximation are used to find the average densities of the other runs.
Having made the above assumptions, the thermal
conductivity was ca1culated as follows.. From Sec. 4. l.
I
- w
(8)In this expression VU and PI were measured. which leaves an expres sion in T s and Ps. Using the vapour pressure curve for air (Fig. 1) Ps is a known function of T S' Hence Ps and T s may be
(22)
obtained at arbitrarily selected times throughout the run. The energy flow through the condensate may be ca lcu,lated from the appropriate heats of condensation and fusion. the mass flow and temperature of the incoming air. and the radiative heat transfer which. as may be seen by reference to table I, becomes significant for run 3 and 4.
In Sketch I, a cross section is shown of the condensate covering the condensing surface. Say the condensate surface
V'
-~
/
=AL
______________ - -____ - - - -____ --_______ Jz V s-
.
-
. -
.
@
--- . ---~.·
0
7
7
777777777777
71
7777777777
SKETCH 1- --
~-
-
.f.:--
]
-
-
~
)'
;
_ jin ._. - [ _had a temperature T sI at a thickness Yl and a temperature T s2
=
T sI+
..ó. T at a thickness Y2. where ,6, T was of the order of 10K. Since
energy flow through the layer is constant the temperatures of the two
faces of the condensate 1ayer with thickness A.f!. are known. Knowing this and the thickness of the layer from the density which was assumed to be that of run number 1, then a first approximation to the therma1
conductivity corresponding to the temperature T = T sI
+
T s2 may be found using the relation 2..A.
K
CT)
=
(9)A
where K
(T)
represents the therma1 conductivity based on the density measured for run 1. A plot of these conductivities for the various runs is shown in Fig. 17. For a discussion of Fig. 17 see Sec. 4.2.5.To approximate the influence of the changes in average densities between runs on the values shown in Fig.
n
the following approach was used. It was assumed that the thermal conductivity varied directly as the condensate density, that isK
(T)
-
C
(T)
e
(10) Then, sinceAL
--
~M
IA
e
(11)KA(T)
-
GA
Al..
6 MAf
A
.AT
A A orKA
(
-,-)
-
-
QA
L;),./VIA
(12)'1-
11
~
L
'1.. (R
1... f M
A)
e.A~~
~L
tA. AJl..7T1..L
l.(/(.2.+
H~
)e.ATr.
..". Leg
8 6where subscript A refers to run 1, and subscript B refers to runs 2, 3,
or 4.
Now
'11fLL
z.(.n2.+
Ha
_
\ "
AT, ~..,,-
L PA
j (A B-'"
where KBrorepresents the therma1 conductivities of runs 2,
based on the ave rage density of run number 1 (
f'
A ).Frorn Eq. 10
where
and from Eqs. 13 and 14
2-oe
Me]
]
(14) 3 and 4 (15)Frorn Eq. 15
oe..
may be ca1cu1ated for runs 2, 3 and 4 using the datapresented in Figure 17.
The values of oe., have been deterrnined for runs 2
and 3 and are given in Table Il.
From the values ofcc.and the densities so determined,
new values of the therma1 conductivities may be calculated. These are 'shown in Fig. 18, from which it may be seen that while the original
differencesbetween the thermal conductivities for the separate runs have
been reduced sornewhat (Figs. 17 and 18), significant differences still
remain, presumably owing to the different deposition rates.
There are two extreme cases for the re1ation of therma1
conductivity to density which should . . be considered for the i
nterpre-tation of the experimental results. In the first place, if the density did
not change between runs 1, 2, 3 and 4, then the curves of Fig. 17 would
be the conductivity va1ues versus temperature at the various values of
However, it seerns unlikely that the density did not change between runs,
for the measured density of run number 1 (33 lb/ft3) is very nearly half
that of the density of solid nitrogen frozen from the 1iquid form (64.1 lb/ft3,
Ref. 24). Thus it would seem reasonab1e to assume that the density of
