NBSIR 74-363

HEAT TRANSFER IN PULSED SUPERCONDUCTING MAGNETS

V. Arp, P. J. Giarratano, R. C. Hess, and M. C. Jones

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

January 1974

Interim Report

Prepared for:

Air Force Aero Propulsion Laboratory

Wright Patterson Air Force Base, Ohio 45433

NBSIR 74-363

HEAT TRANSFER IN PULSED SUPERCONDUCTING MAGNETS

V. Arp, P. J. Giarratano, R. C. Hess, and M. C. Jones

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

January 1974

Interim Report

Prepared for

Air Force Aero Propulsion Laboratory

Wright Patterson Air Force Base, Ohio 45433

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director

FOREWORD

This program was completed under the sponsorship of the

Department of the Air Force, Wright Patterson Air Force Base, Ohio,

and was fiinded with FY 197 3 AF Aero Propulsion Director's Funds.

It is divided into three parts. A fourth part, presenting advanced

information on liquid helium pumps, will be reported separately; it

is being delayed so that further information being developed tinder

another program can be used to assist in providing a more comprehensive data analysis.

Dr. C. E. Oberly

GS-12

Physicist

FOR THE COMMANDER

Dr. P. E. Stover

GS-15

Chief, Power Distribution Branch

Aerospace Power Division

iii
CONTENTS

Page

Li Research Needed for Pulsed Superconducting EnergyStorage Systems 1 1.1 Introduction 1

1. 2 The Present Art . 1

1. 2. 1 Operational Time Constants 2

1. 2. 2 Choice of Conductor 6

1. 2. 3 Forces 7

1. 2. 4 Heat Transfer 9

1. 2. 5 Composite Structures 13

1. 3 Extrapolation to Larger Systems 15

1. 4 Summary and Conclusions 17

1. 5 Acknowledgement 20

2. Deterioration of Heat Transfer to Supercritical Helium

at 2. 5 Atmospheres 21

2. 1 Introduction 21

2. 2 Experimental Results and Discussion 23

2.2.1 Heat Transfer Coefficients Profiles • • 23

2. 2. 2 Comparison of Supercritical and

Subcritical Helium Heat Transfer

Coefficient Profiles 25

2. 2. 3 Correlation of Experimental Results . . 27

2. 3 Conclusions 30

iv
CONTENTS (Continued)

Page

3. Forced Convection Heat Transfer to Subcritical

Helium I* 32

3. 1 Introduction 32

3. 2 Description of Experimental Apparatus and

Measurement 33

3.3 Heat Transfer Results 39

3.4 Conclusions 5 3

3.5 Appended Experimental Data , 54

4. ' Notation 126

5. References 127

This paper was presented at the 1973 Cryogenic Engineering

Conference in Atlanta, Georgia.

V
LIST OF FIGURES

Page

Figure 1. Approximate representation of magnet current

and magnet winding temperature as a function

of time, showing the times t , t , t , and

J. 2 3 as defined in the text 3 4

Figure 2. Heat transfer coefficient profiles at 2. 5 atm . . 24

Figure 3, Heat transfer coefficient profiles at subcritical

pressures (1. 05 and 1. 97 atm) 26

Figure 4. Ratio of experimental to predicted heat transfer

coefficients (h /h J versus correlating

exp pred

parameter, $ 28

Figure 5. Schematic of experimental apparatus 34

Figure 6. Typical wall temperature profiles for various

inlet conditions (pressure: 1. 1 and 1. 5 atm) . . 40

Figure 7. Typiccil wall temperature profiles for various

inlet conditions (pressure: 1, 4 and 2 atm) ... 41

Figure 8. Heat flux (q) vs temperature difference

(T ,,-T, ) in the nucleate boiling region

wall bulk

under forced flow conditions 42

Figure 9. Dimensionles s critical heat flux,

KU = q /^P^^^rag(p-p )]''^^'^vs correlating crv V

3 92 parameter ( 1 -x) ' 49

Figure 10. Comparison of various modes of helium

heat transfer 51

vi
LIST OF TABLES

Page

Table 1. Operational time constants for pulsed magnetic

energy storage 4

Table 2. Cryogenic design as related to operational time

constants ; 5

Table 3. Time constants of helium heat transfer and

flow systems 10

Table 4. Summary of program areas 18

Table 5. Experimental values of q where

0. 8 <h /h , < 1. 2 29

exp calc

Table 6. Values of $ from [14] 30

Table 7. Example of variation of critical heat flux and

critical quality, at L/D of 50 , with pressure,

mass velocity and inlet conditions

(using equation 5) . . . , . 50

vii
HEAT TRANSFER IN PULSED SUPERCONDUCTING MAGNETS

ABSTRACT

The first section of this report summarizes

design problems for the development of advanced

superconducting pulse magnets, leading to recommendations for future work, primarily in (1)

evaluation of eddy-current, hysteresis, and

frictional losses, and (2) transient heat transfer

between the superconductor and the helium. Two

subsequent sections report measurements of

forced convection heat transfer respectively to

subcooled liquid helium and to supercritical

helium just above the critical pressure.

Key words: Forced convection heat transfer;

pulsed power systems; pulsed superconducting

magnets; superconductor losses; supercritical

helium; transient heat transfer.

viii
1. RESEARCH NEEDED FOR

PULSED SUPERCONDUCTIVE ENERGY STORAGE SYSTEMS

V. Arp

1. 1 Introduction

Pulsed power systems under study use superconducting coils for

accumulating the energy which is delivered at each pulse. Such systems

are lighter in weight than equivalent capacitive systems when the stored

energy exceeds about 10 kilojoules [1], and so are importaxit for possible

airborne applications. Experience to date shows that the superconducting

coils dissipate less than 1% of the stored energy at each pulse, so that

high efficiencies are possible.

We have reviewed the current problems in developing useful

pulsed power systems for the sponsor's needs. In doing so, we have

held discussions with responsible technical people in three companies

under contract to the sponsor - Avco, Magnetic Corporation of America

(MCA), and Westinghouse - as well as with other researchers who are

recognized for contributions to superconducting technology. Included

among these are specialists in properties of materials, electrical

machinery, helium flow and heat transfer, and refrigeration. This

report is our perspective on the problems which must be considered as development proceeds.

1.2 The Present Art

Superconducting magnets of reliable steady- state performeince

have proven their value in many applications, in sizes ranging up to

g 10 joules of stored energy. Development of superconducting devices

is proceeding in several directions to include superconducting motors,

generators, power lines, pulsed synchrotrons, cind high-power pulsed

energy sources. The total of these development efforts, not including

materials electronics, instrumentation or auxiliary systems development

or basic studies, utilizes annual funding within the U. S. of about $26 M.
Many of these applications utilize superconductors in a. c. circuits, where heat generation from residual eddy-currents (proportional to frequency) and hysteresis (independent of frequency) are

importcint factors in the system design. At the lowest frequencies

are found synchrotron magnets, which are run from zero to full field

in a few seconds, corresponding to frequencies in the neighborhood

of 0. 3 Hz. Even at this low frequency, some designs have exhibited a

deterioration in critical current below steady state values due to the a. c. heating [2] . The design and eventual practicality of superconducting

power lines at 50 or 60 Hz is strongly dependent on minimizing the

a. c. heating in superconducting materials, and a major effort is being

expended to develop conductors having lower losses. The pulsed energy

coils under consideration in this report exhibit relatively high losses

typical of high frequencies, corresponding to pulse discharge times in

the neighborhood of 0. 05 milliseconds and pulse repetition rates of from

5 per second (at this date) to 200 per second (desired in the future). At

these highest frequencies, the losses are so large as to possibly quench

the superconductor during the discharge period, at least for magnets

operating close to their critical current.

1. 2. 1 Operational Time Constants

Figure 1 and tables 1 and 2 list the relevant time constants which

must be considered in developing a pulsed energy system for the sponsor's

needs. The ranges listed include, approximately, the existing values on

model coils and the desired values on the next generation of systems.

Table 2 summarizes the cryogenic design features which can be

associated with the listed time constants.

2
A A A., A A

O

\—

C_3 Z3O

o

UJ

o.

-T.

TIME

TIME

Figure 1. Approximate representation of magnet current and

magnet winding temperature as a function of time.

showing the times t^^ , t^, t„, and as defined

in the text.

3
Table 1. Operational Time Constants for Pulsed Magnetic

Energy Storage

Discharge time 0. 05 to 0. 3 ms

Charge time ^ 1 to 1 00 ms

Pulse repetition time 5 to 100 ms

Duration of pulse train ^ 20 to 200 s

Standby between pulse trains > 500 s

' ""' "' 4 Mission duration t, 10 s o

4
QQs

OQnooaao

•rf

n)

(0a,oo

<0

(D

fi •H

COvOaoU

0) I—

a

03

0)

OhaooU• 1-1 mQwo

>• U

"[1a d) B ^

CO

J3

O (U

m

!>

•1-1 uo

CD

tn

•tH o

Oh

0)o

a;

0) o ^ a;

CD

•1-1

f-i

CD

<u 5

cnU

(U •H

1—

I o

•S e:

(1)

CQo o

CQ

U ^ •H M CD

I-) 0) n-l u>

1:1

CD(to• H

CO • H o ^• H

rC! -U

V tJ CD • H

CD • rH <U T3 ^

0) H

0) I 0)

CD ^ S I

CD

CD -H

S- S ° g

Ql •H

4l>

—

o - •S

CD 13 o

-<-> og . O O O •rM

;h 'I

tl

«5 ^ rH 03 ^ s ^

{50 C• H• 1-1 ClO ,Q

u C! ^ d

5tj S • H (U

•2 ^ O 5 O ttJ ft

fl CO » 2

«§• iH a fx

Oh 2 TM >

'O •H

<U CD

IP (U o• H-(->

r £

•5 5

"d "J 5 ^ C (U <u 6 g 2

<U S O " P ^ TM 0 -

_g W)Oa>>

•iHCO

CO

d)o

>4

t-H

•iH>dGOUOC

•i-i a

&£) • H

CO

a; Q

T3T)

•rHO>a

•i-t i-Hoo

CD

CO

d)a• H

(tJ (U

•^ -5

•H -(->

to tH

CO S

•H>dOO• Hc

W)

•H

CD Q

73

CJ

ftao

(1)

^4

0) Q

aM

•rHg.0uo• H

-«->

;h

0)GO • rHU

(U 1 

2 S

ft O

H

tn 5
Successful system operation requires that the conductor temperature during (i. e„ , at the end of) the charge period, t^, be less than the

superconducting critical temperature for the given field and current.

It is preferable that the conductor temperature also remain below T

c during the discharge period, t^, but this is not necessary provided that

all the heat generated during and can be removed prior to the next

charging period, beginning after time, . More delicate is the requirement of equality between the heat generated per pulse and the heat

transferred to the helium per pulse, so that there occurs no slow rise

in average temperature which would finally drive the system normal

before the desired completion of pulsed operation at [4]. To accomplish this requires (1) adequate pulsed heat transfer during the interval,

T^, so that any deficit in pulsed heat trajisfer rate can be made up by a very small average temperature rise in the superconductor, and (2)

maintenance of the helium temperature and density, averaged over time,

T^, at or below a safe design value for the duration of the pulsed operation, . This latter requires that hot spots in the coil and excessive

vapor formation in the coolant passages not occur and was the motivation

for our studies of helium pumping and heat trajisfer problems for the

sponsor last year [5]. Finally, the very long time constants, and

T^, have little effect on the design problems considered here, smd we

do not discuss them further in this report.

1. 2. 2 Choice of Conductor

The dominajit design consideration of pulsed magnets, then,

involves the transfer of heat generated in the superconductor at each

pulse to the helium bath, and thus, the selection of a superconductor

of minimal losses is of great importajice [6,7]. Existing designs all

use some sort of braided cable superconducting winding to meet external

requirements of low inductance and high current along with minimum induced

6
currents in conductors in parallel . Beyond this point, however,

there are two noticeable differences in the coils used respectively by

Avco and MCA. Avco chooses a braid at which there is a solder (electrical) connection at each point where one strand within the braid touches

the next. MCA chooses to insulate each strand within the braid, Avco

chooses a multifilament superconducting strand, whereas MCA claims

that a copper -clad single large filament will have lower losses than the

multifilament conductor of the same outside diameter and current

capacity. Both select conductors of about 0. 12 mm diameter. In all

cases the intent is the same, to minimize the total losses.

Whichever of these configurations is used it appears that the integrated loss per pulse can be calculated from the conductor specifications

to within a factor of about two of the value obtained from helium boiloff

measurements. It would be desirable to increase the accuracy of the

loss predictions to something like the 20% which might be expected of

most other design parameters.

The significant amount of ongoing work on losses in superconducting

power lines is certain to generate information on losses which will be

useful in subsequent pulsed magnet designs. In the further discussions

in this report we assume implicitly that the eddy current and hysteresis

losses can be calculated or measured to an accuracy consistent with

the other design parameters,

1. 2. 3 Forces

Substantial mechanical stresses can build up within a coil due to

localized pressure of the magnetic field on the conductor windings.

Suppliers have not indicated any severe problems with the overall

containment of these forces on the pulsed energy coils to date.

However, as coil sizes increase, so will at least some of the stress

7
levels in the windings, assuming that the peak m.agnetic £ield is

essentially constant (being determined by superconducting properties).

This is best understood by considering the hydraulic analog, in which

container wall tensile stresses increase as container diameter increases,

for constant internal fluid pressure. Though the added stresses are not

expected to present severe problems in preventing gross coil rupture,

they could present problems in two areas (1) frictional heating from

release of mechanically stored energy in a slightly inelastic

coil structure as the forces are removed (during discharge), and

(2) frictional heating from relative motions of individual cable strands

by just a few micrometers [4]. In short, the relatively loose

or porous structures which provide excellent heat transfer

to helium may at the same time be subject to higher losses from

frictional movements. These movements can be reduced greatly by

impregnating the coil with epoxy or other filler chosen on the basis of

various thermal or mechanical properties. This is commonly done, in

fact, on small coils and/or coils wound with relatively stable superconductors. However, heat transfer from the conductor to the helium

is much impeded at the same time, and this could be decisively detrimental to pulsed coil operation. What is needed is to obtain definitive

information on frictional losses in coil structures during pulsed discharge, as distinct from hysteresis and eddy-current losses in the

superconductors themselves. The mechanical losses might in fact turn

out to be negligible, but there is insufficient information upon which to

make reliable advanced design decisions at the present time.

The cumulative effect of high repetitive mechanical stresses may

also lead to fatigue failure in the coil, though little data exists on this

topic. Copper (which is commonly used in stabilizing superconductors)

is well-known for its work-hardening. Necessary measurements on

8
epoxies or epoxy-copper laminates have never been made, so that

estimations of this mode of possible coil failure cannot be made at this

time. Fatigue failure has not been reported on the test coils, but it

probably will become important for continued field service.

1. 2. 4 Heat Transfer

The people who have designed the existing pulsed coils tell us that

if an effective heat transfer coefficient could be assured, they could

design the coil fairly accurately on that basis, obtaining a more compact

coil system if the design value were higher than (conservative) values

previously accepted. Magnet design for quasi -steady state performance

2

is commonly based upon heat transfer rates of 0. 2 to 0. 4 W/cm which

can be achieved in pool boiling. There is some evidence that higher

heat transfer rates in pool boiling can be achieved for short times [8, 9],

but the subject has not been investigated thoroughly in a way which is

useful for general cinalysis. The Avco design assumed higher values,

based on Jackson's paper.

We have reviewed the various thermal and kinetic factors which

may be important in determining heat transfer rates on the time scale

of the pulse repetition time in table 1. They are given in concise form

in table 3 and deserve elaboration here.

First, we consider nucleate boiling heat transfer. This involves

generation of low density vapor which must be allowed to escape from

the heated surface. In non-horizontal cooling passages of small L/D,

vapor removal may be accomplished by natural convection, driven by

the liquid-to-vapor density difference. This method was used on the MCA

model coil, though the Avco coil used forced circulation. It is questionable

that natural convection vapor removal would be successful on larger coils,

since L/D ratios will probably scale non-linearly with overall size (see

discussion on section 8); likewise, it is questionable on faster-pulsing

9
COO

COa• iH 1—

oOO

(Da

•i-i

O

PP- <;

CO

•I-I uBaooU

.—Icdo

1^ Ho o A in

(U Q o

CO

(D

O

rill ^ o o

•H

cu I—

o

*^ .1-1 o

f-l CO as o

vDO

-i-> os

•iH0

4-> o el

no

I—

o u O 0

—I CO o a;

0) Ph

0)GO

Q

CO

<u

•iH

-)-> oa• H

tiO <u

0) cj

fl o

CO

stai

O1—1 ed

a PI

O

CO o i-> O

1—1 o o CO o bO 1—

CI CO nJ to mi api Jh

-;-> 1—

^1 o CD c^J CO (U (U o C^ G o

!ha

1—1OO ?M

CD TJ

tsl

CO

CO

(1)

*' o O5 >^ H i5

1—

a oo

t3 o

PI

ci <^

0) >

HOT? 03o

COao

-4-> CD> u ^

0) mCO§

-i->

<u

-l-> d

CD

>^ T)

T)

(TJ (U

-i-> CO (UN o •i-i 0

CO

CO 0 (U

-(-> }-<

(Ua

•iH o

-•-> o

I—

CO

PiGO

•i-l CD

0) XI

a)

-i-> CO

CD

Gfl • H

1—

OOoa>

•H

15a

<0

CO

0)

ftum

•i-i y

CO o

CD

m i—

.r-l O o O

f-H

II GO

PJ

D • H4JO Q du

GJD ouu

(Uft CO pt

CO CO < ^1o I CO

.Si

0)

(UftOu

ft

a ^ ^ a

p)uo

ft>I XI

•1-1 g-o

XI

(U

CDo

ft

CD

-l->

0) H

(1) 2

pi

CO

CD

ft

PI oOu

<D

>->a

Q)u

GO

CD

<S) u

7iCO

COu

ft o

•H>

,P3

(U

COO

ft

10
coils, since the onset of film boiling would be determined largely by the

time -average rate of vapor formation, so that the total allowed heat transferred per pulse would be reduced as the pulse rate increased. Hence,

some form of forced flow superimposed on the natural convection

associated with nucleate heat transfer will probably be necessary to

avoid failure through vapor-lock in the channels, thus achieving the high

heat transfer rates which may be available on a short time scale. As

indicated in table 3, enhcinced nucleate -boiling heat transfer rates woxild

be associated with times, t , of roughly 0. 5 to 10 milliseconds, depending

n

strongly on the integrated heat transfer, surface conditions, and perhaps

other parameters. Our recent work [ 1 0] has shown that superimposed

flow does not measurably change the nucleate -boiling heat tremsfer rates

under steady state conditions, but its effect during pulsed heat transfer

has never been investigated. Surface roughness may be especially

importctnt on this time scale.

In time -dependent forced-convection heat transfer, we are able

to identify more parameters. In the shortest interval, t^, following

the heat pulse, the dominant mechanism is thermal diffusion into the

non-turbulent part of the boiindary layer. Assuming constant fluid

properties at a temperature about 4 K in the liquid region (for this discussion, the results are not very sensitive to fluid conditions provided

immediate vicinity of the critical point is excluded), Baylis [11] has

shown that

100 D

"^d F PrReU ' where f is the fluid friction factor, U is the fluid velocity. Re is the pipe

Reynolds number, D is the pipe diameter, and Pr is the fluid Prandtl

number, generally about 0. 7. If we normalize all of the calculations to

heliimi flowing at 3 meters per second in a 1 mm diameter channel,

5 corresponding to a Reynolds number of about 10 , t, )%jO. 05 milliseconds,

d

about the same as the coil discharge time, . However, preliminary

11
calculations [12] suggest that, at supercritical pressures, as the wall

temperature rises to not far above the critical temperature, an expanding

region of lower density fluid will be formed adjacent to the wall, such

that the effective boundary layer thickness increases with heat input. The

net effect is to increase markedly, perhaps by as much as one or two

orders of magnitude and to decrease the heat transfer rate during this

interval, since heat transfer is by thermal conduction over relatively

large distance without aid of turbulent convection.

The next forced convection time constant to consider is the equilibration time between thermal and velocity profiles, as controlled by turbulent effects. In essence, this is the time required to establish steady

state heat transfer. By eoialogy with the position-dependent development

of the thermal profile within the steady- state flow of fluid entering a heated conduit, we estimate that this time t 10 D/U, as 3 milliseconds

e using our previous normalization and assuming constant fluid properties.

The accuracy of this analogy is probably within a factor of two for constant

fluid properties, but the effect of variable fluid properties is unknown.

Another time constant of importcince is the time to reach local flow

equilibrium due to a flow perturbation (change in pressure gradient).

From a systems standpoint, this must be considered where the density

decreases and frictional pressure drop increases in a heated channel. It can be shown that this time constant is = D/4fU. Using our previous

normalization, this time is then «i 30 milliseconds.

Other thermal time constants for helium heat transfer in superconducting systems have been described. In a report on the Brookhaven

Superconducting Power Line Project [13], a time constant of 8. 6 seconds

is calcTilated for achievement of steady state after a perturbing thermal

overload. We tend to believe that this calculation is incorrect. Baylis [H]

has estimated the time for a heat pulse to travel in helium from the

laminar boundary layer through a layer of developing turbulence to a fully

12
turbulent core. This is a most difficult calculation to perform

convincingly, and the result must certainly be less than t . e As we look further into these time-dependent heat transfer

problems, various features are found which further complicate the

analysis. For example, the standard velocity and temperature profiles

for turbulent flow in a heated pipe have been derived for steady state flow

of a fluid having constant properties. In unsteady flow of a fluid with

variable properties, the local relationships between mean turbulent

velocities, viscous dissipation, eddy diffusivity, etc. , which are

implicit in the standard profiles, may no longer be good approximations,

and considerable care must be used in sorting out the appropriate

relationships.

1. 2. 5 Composite Structures

The time constant for diffusion of thermal energy a distance x through a solid having a thermal diffusivity q' is

T «(l/a) x^ , s where we neglect geometrical factors like rr, 1/2, etc. The

diffusivity of a typical composite superconducting wire will be some2 where between that of reasonably pure copper at 4K, a » 5000 cm /s

2

and stainless steel at 4K, <y ^ 3 cm /s, probably closer to that of copper.

For typical wire radii of about 0. 006 cm, the time constant will be in the

range of a few microseconds. Because this is much less than any other

time constant considered in this study, it is reasonable to assume for

these heat transfer calculations that the temperature of the wire surface

is equal to that of the active superconducting filament.

Since it may be necessary for structural reasons to impregnate

the windings, or portions of the windings, with non-conducting filler

(such as epoxy), we must consider the effect this has on the transient

13
heat transfer. For a typical polymer in the helium range, the

diffusivity is probably within a factor of 3 of the value

2 2

01 (cm Is) « 1. /T . From this we estimate that for the typical insulation thickness on a wire (about 0. 03 mm) at 4K, the thermal time constant is

T !=» 0. 1 millisecond,

s For a potted, braided cable where the smallest relevant value of x

may be ten times larger, and the time constant would rise to about

10 milliseconds or more; however, the effective diffusivity may also

change in this last case depending on the relative volumes of conductor

and epoxy along the heat transfer path, so that the time constant is

strongly dependent on the winding configuration.

The effect of this is to decrease the amplitude of the alternatin

temperature variations at the insulator to helium surface for those

frequencies much greater than 1/t , Thus, in order to transfer heat

s at a given average rate (equal to the integrated heat generated in the

superconductor per pulse rate divided by the pulse repetition rate),

this attenuation of the a.c, component is accompanied by an increase in

the d. c. component, i. e. , the average difference between the surface

temperature and the bath temperature.

If the helium could be regarded as a temperature-invariant heat

sink, the relative magnitudes of these steady and alternating heat

transfer rates would be determined by comparison of T with the

generating times T , t_, and T-. However, these are of the same

order of magnitude as t^, t , and T^, which characterize various fluid

heat transfer regimes related to the alternating component of thermal

flux. Further, the transient heat transfer rate would probably be

modified by the steady component of thermal flux. One can see that

14
the total problem becomes highly nonlinear, involving all of the named

constants. For analysis purposes, one could bracket real system

performance by assuming various approximations on the relative magnitudes of the operational, solid diffusion, ajid heat transfer time constants,

but this may not be very helpful for detailed system design. We do not

believe that the problem of calculating the overall, time -dependent heat

trajisfer rate is impossible, but neither is it going to be done on the back

of an envelope.

1.3 Extrapolation to Larger Systems

A major question to be considered is the extent to which the

superconducting coil performance can be analyzed in terms of separable

concepts: heat generation in superconductors, heat diffusion through

solids and potted windings, heat transfer at helium- cooled surfaces,

heat generation from mechanical motions and flexing of windings, fluid

flow through coolant channels, etc. The question is particularly relevant

to the complex relationships among all the short time constants

100 milliseconds) discussed above. There is no easy answer to it,

and it is appropriate to dwell briefly on it here. We discuss several

subsidiary questions.

Will unusual or irregular (e. g. , braided cable) windings make it

impossible to evaluate local heat transfer coefficients or flow fields to

the usual accuracy? The answer depends partly on the heat transfer

mode. Nucleate boiling heat transfer coefficients are relatively independent of any superimposed forced flow, whereas forced- convection

heat transfer analysis will probably have to rely on additional empirical

correlations between flow cind heat transfer as are commonly used in

heat exchanger analysis and design. We feel that experimental work

on typical braids (or other representative geometries) will be required,

ajid that appropriate ancdysis can be made in parallel with that for other

fluid heat transfer systems.

15
Will a realistic analysis require so many additional parameters,

such as the correlation above, or measures of surface conditions, as

to be not very dependable or useful for advanced design? There is no

reason to believe that this would be the case, in that the logical procedure

would be to determine such parameters in separate experiments, just as we now determine, separately, the specific heat of superconductor,

the thermal conductivity of helium, etc.

Because of the strong interaction between the various heat transfer

mechanisms on the millisecond time scale, will the subsequent nonlinear

dependence of system performance on the various parameters, and the

uncertainty in individual estimates of those parameters, combine to

reduce the accuracy of correlations between theory and experiment

to such low values as to be useless for subsequent design? This question

is most difficult to answer at this stage, primarily because of insufficient

knowledge of transient helium heat transfer. It should be reviewed when

and if work in this field progresses.

If the above complex interactions are not understood, can scaling

from a successful test coil allow reliable design of large-scale system

performance? We think that the answer is no, because the correct

scaling laws would not be known. For example, if the design limitation

was primarily that of obtaining adequate helium flow, the scaling would

be dominated by considerations of length to diameter ratios in the cooling

channels. If the primary design limitation was that of thermal diffusion

through a composite solid, then scaling could involve increased numbers

of flow channels, keeping diffusion distances about constant. If, as is

more likely, the design limitation involves some sort of delicate balance

between solid diffusion times and time -dependent heat trsinsfer to the

helium, it would be difficult to deduce the scaling laws without

understanding that balance.

16
1.4 Summary and Conclusions

The sponsor's goals for pulsed power systems are one to two

orders of magnitude beyond the existing coils in terms of both stored

energy and repetition rate, and we do not think that this gap can be

bridged efficiently without systematic evaluation of some of the more

important design elements. Further, we conclude that it is possible

to identify design elements which can be studied separately and then

integrated into advanced design. These elements are summarized in

Table 4. Item 1 relates to calculation of the total energy dissipation in the

superconductor at each pulse, and how this is influenced by the choice

of conductor, the winding tension, coil impregnation, etc. The total

losses will probably decrease as the structural regidity increases, but

by how much? An increase in rigidity will generally decrease the heat

transfer surface to the helium, and thus tend to raise the average temperature, of the coil. At the present time, the basic loss mechanisms

are understood, but evaluation as a function of specific design features

can be and needs to be done to better accuracy than at present. Appropriate laboratory measurements can be made on coils or samples which

need not be capable of operating at the high repetition rate required for

a working system. Also, there is considerable input to this problem

from ongoing studies of superconducting power lines and of large pulsed

magnets for high energy physics, though this will not answer all the

questions for these rapid pulse applications. We give this high priority

just under item 3 below.

Item 2 relates to possible degradation in the performance of an

initially successful design, due to mechanical fatigue failures from

repetitive pulsed forces on the windings. Fatigue stress limits are

largely unknown at low temperature^ and are a source of concern to

17
o

u

<-> o

,^o

o

CO

CO

ro O

13

o M

o

o ^

03 (U

m

I—

u

u

ft

CO

CO

• H o

° 2

3

cmo

.2 o o ^

ft o

ft Xi

CO O

O

o

o

fta

>

(U (U ft +^ 0) S o

=tfc ^-5 -tii ft

o O

« .2

(;3

ft

M 8

O

•HO

O

r—I

'

a

CD

>->

0)

o

-l->

o

-•-> -r-t

-l->

>

O

aO

o

r-l 4->

(Ufto > :^ -^u

X!

o

-l-> C!

(1) CD

<DU

ft

-4->

CXI

iUo

£»£) ao

(1) CO 1—1 •!-)

-l->

0) J

O

-

•iS >

CO nJ ^ +->

• H

•H m

a ^ w a

&0

+-> n XJ

(U CO "

.2 H

4-> o

-l-> o

o

^ .2

(u a

J. <^

•43 -43 S o

CJ rrt ^ ^3 qj > 0 O p3

(;5 U

•H 0)

(1) ro

O

CIo

•43

OS r—

>

COO

O

o

.5

rd CD

CD a

Q) CD

.iH •<-> V. ^

ft O X5 w ft a B=

I 0) m

(H CD ^ m

fi ^

•II <^ ^ rrt m -t-> C

.2 ^ -

g a

> ^ .2

•—I i-i-* CD S ftl

O

Pio

o 5P

S O

o

(U W t3 CO

CD

(c5 <3

O

• H-4->

0) .2

TO «+-! >->CO >

(Ct

CO

t3

CD

(U r-H

O

S ^ ;h X)

C CD 2 «

^

"J

<U r" w ^ -5

CO

18
superconductor motor and generator design. For pulsed energy storage

applications, this will probably be an important long-range consideration, but we give it lower priority at this date. Fatigue studies on

superconducting materials are being initiated now in support of Naval

ship propulsion studies.

Items 3, 4, and 5 relate to the general problem of providing

adequate cooling to the coil during pulsed operation. This general

category can be divided into two parts (a) time dependent heat transfer,

where variations in relevant parameters during the time must be

considered, and (b) maintenance of the helium temperature and density

in the flow passages, averaged over the time, , at or below

design values during the duration of the pulsed operation, t^. Part (a)

contains many mutually interacting subfactors, some of which are very

poorly understood at this time, including items 3 and 4. Part (b) has

motivated the helium pumping studies recently supported by the sponsor,

and further contains item 5. The evaluation of time -dependent heat transfer coefficients to

helium, item 3, deserves highest priority because least is known about

it, analysis is difficult and not to be obtained in brief programs, very

little active work is ongoing at the present time, and design data is

presently uncertain by factors of roughly half an order of magnitude or more. We recommend a comprehensive program of analytical and

experimental work on a practical geometry, e. g. , a single conducting

strand or surface cooled by helium under variable conditions, to obtain

time dependent heat transfer coefficients on time scales typified by t ,

T^, and T^. Because of the close proximity of the critical point, at

2. 2 atmospheres and 5. 2K, to helium conditions which may exist within

the coil structure, it may be necessary to take explicit account of the

non-ideal properties of helium in many of these studies. Evidence is

19
clear that they will be much different than steady state heat transfer

coefficients, and it is necessary to pin this down in order to make use

of (possible) enhanced values in advanced designs.

Item 4 relates to calculation of time -dependent thermal gradients

in composite structures, i, e. , insulating layers, possible impregnated

coil structures. Relevant information is being developed in this area

through other programs, and consequently we give this low priority as

a need of the pulsed energy program. Also the data can probably be

obtained with shorter lead time than that of item 3 above. Further,

results from item 1 may influence the type and detail of information

which is needed.

Item 5 relates to evaluation of time -independent flow friction

factors and effective heat transfer coefficients at braids or

other practical superconductor configuration. This is important in

determining the required flow conditions, channel sizes, etc, , to

maintain adequate cooling during all of the pulse repetition time, , The

study would be analogous to those which are performed on heat exchangers of special geometry, and is the logical evolution of the helium

pumping work previously supported by the sponsor. However, we give

this lower priority than items 1 and 3, since studies made there may

influence the configurations of most interest, and the lead time required

to develop the information is less than that for item 3,

1. 5 Acknowledgment

Dr. M. C. Jones has participated in valuable discussions of

many of these problems, particularly as a result of our joint trip to

Westinghouse, MIT, Magnetic Corporation of America, and Avco. Our

principle contacts at these locations were, respectively. Dr. Michael

Walker, Prof. Joseph Smith, Dr. Richard Thome, and Dr. Tim Hatch,

all of whom contributed valuable information.

20
HELIUM AT 2. 5 ATMOSPHERES

Patricia J. Giarratano and M. C. Jones

2. 1 Introduction

In a previous study of forced convection heat transfer to supercritical

helium in a vertical tube [14] a correlation was developed from the experimental

data to predict the heat transfer in this region. The correlation is:

'

^'"•^ 0. 0259 -ft"- ® C

°- 4/m,°- * (1)

qO. 8 \

J- B/ ' P

in which fluid properties |i, C and -ft have been collected together on the right

P

hand side. Equation (1) predicts a maximum in the heat transfer coefficient

when the bulk fluid temperature is equal to the transposed critical temperature.

For a given pressure, the transposed critical temperature is defined as the

temperature at which is a maximum. The prediction of equation (1) is consistent with the experimental observations of Johannes [15] and Ogata and Sato [16]

in their investigations of supercritical helium heat transfer under low to moderate heat flux conditions. Similar enhancement in heat transfer to carbon

dioxide as the bulk fluid approaches the transposed critical temperature has been

observed by Tanaka et al. [17].

In reference [14]wenoted that the peak in the properties parameter,

^0.6 Q

o-4/jj^o.4^ at the transposed critical temperature accounts for the enP

hanced heat transfer observed under the operating conditions of that study.

However, at high heat fluxes, a degradation, rather than enhancement,

in heat transfer in the transposed critical region has been observed by many

inv -stigators, e. g. Ogata and Sato[l6]for helium, Shiralkar and Griffith [ 18] for

carbon dioxide, Shitsman[19] for water, and Powell [20] for oxygen.

21
As summarized by Shiralkar and Griffith, the conditions under which

degradation occurred are:

1, The wall temperature must be above, and the bulk temperature

below the transposed critical temperature.

2. The heat flux must be above a certain value, dependent on the flow

rate and pressure.

Heat transfer degradation seems therefore to be a function of the

inhomogeneity of the fluid resulting from the temperature dependence of fluid

properties. Equation (1) when Tg , is essentially a homogeneous heat

transfer model.

With the experimental apparatus described in reference [ 14]for supercritical helium It was not possible to attain both criteria noted above. Because

of the inefficiency of the heat exchanger, as the heat flux to the test section'was

increased there was a corresponding increase in the inlet bulk fluid temperature.

Therefore high heat flux measurements were obtained only for high bulk temperatures (greater than Tjj.).

Subsequent revision of the experimental apparatus;, including the heat

exchanger, for subcritical helium heat transfer studies[21] has enabled us to

obtain supercritical helium heat transfer data under conditions described in

the above two criteria. We chose, therefore, in the present study to attempt

to verify the above criteria for the degradation of heat transfer to supercritical

helium and to quantify them as far as possible. An operating pressure of 2. 5

atm was selected as being one which could be comfortably controlled and

which would at the same time be close enough to the critical pressure of 2. 245

atm to give good definition to specifically supercritical effects.

In this paper we present the experimental data and discuss the conditions

under which departures of supercritical helium heat transfer from equation (1)

were observed. The probable limitations to the previously developed correlation,

equation (1), are also discussed..

22
" ine ranges oi experimental variaBTes are as follows:

Pressure - 2. 5 atra (T^c = 5. 4 K)

Mass velocity - 7, 12, 22 g/s-cm^

Test section inlet temperature - 4. 05, 5. 04 K

Heat flux - 0. 008 to 0. 713 W/cm^

Flow direction - vertically downward

Reference[2 1] contains a complete description of the experimental apparatus.

2. 2 Experimental Resiolts and Discussion

2. 2. 1 Heat Transfer Coefficients Profiles

The experimental results are shown first in the form of heat transfer coefficient profiles. Figure 2, for the uniformly heated 0. 213 cm i. d. x 10 cm long

stainless steel test section. The estimated systematic error in the measured heat

transfer coefficients varies from 55 percent for the worst condition (high flowrate

and low heat flux) to 8 percent for the most favorable condition (low flowrate and

high heat flux). However, the plot of Figure 4 which compares the experimental

heat transfer coefficient with that predicted by equation (1) suggests the systematic

error is much lower than the estimated upper bound of 55 percent. The major

source of error arises from the uncertainty in the outside wall temperature and

thickness of the stainless steel test section.

For a constant property fluid having a fully developed turbulent velocity

profile along the entire length of a uniformly heated tube, the typical variation of

the heat transfer coefficient h with position in the tube is one of rapid reduction

from a high value at the entrance of the tube (the thermal entrance region) to a

lower and essentially constant value at positions in the tube more than approximately 20 diameters from the beginning of the heated section. As can be seen in

Figure 2 for helium at 2. 5 atm and conditions noted, the variation of h with

position in the tube is generally in contrast with that expected for a fluid having

negligible property variation. Although the usual entrance effects are exhibited

in the profiles, the subsequent peaks (or in some instances further deterioration

in heat transfer coefficient) can be related to the rapidly changing properties in

the tube (in the vicinity of the transposed critical temperature, ) General trends can be noted by reference to Figures 2 (a) through 2(d).

At low heat flux, e. g. : 0. 028 W/cm^, Figure 2 (b;, and bulk fluid temperature

less than 4. 264 K a heat transfer coefficient profile typical of that expected

23
4 • 0.067 W/cm* -

% ' 0 029 W/cm*

A

q • 0 260 W/cm'

TBoutl.f3 329K

{a)l

2 4 6 8 10 12 LENGTH ALONG TEST SECTION, cm

.24

.22

.20

12

10 U»

oa

P • 2.5 olm 6 " II 2 - 12 5 g/i-cm*

T»i«l,» '^OAZ-AOeSK

q 0.25« W/cm'

TSoutl.f • 878K

q • 0.345 W/cm*

'•'outlet • 5.055 K V

q« 0.113 W/cm'

TBoutltt"**89K

q>0 7l3W/cm'

Taouil.f "5 3I8K

0 2 4 6 8 10 12 LENGTH ALONG TEST SECTION, cm (c)

P 2.5 otm G- 6.8-7.«q/t -cm'

Tb,„,„ • 4.056 - 4.064 K

q 0.177 W/cm*

T»ou.l.t-'*9^8'<

q • 0113 W/cm*

Tioutl.t' * 732K

q • 0.259 W/cm*

QTbo„,I„-5.I75K

q> 0.026 W/cm'

T»q«tl.t •'*-264K O

q • 0.401 W/cm'

Ti^„„ • 5.303 K

2 4 C • 10 LENGTH ALONG TEST SECTION, cm

(b)|

.48

.40

.36

.32

.24

P • 2.5 otm G • 20.5- 24 3 g/»-cm'

TBinUt • 4.060 - 4.066 K

q • 0 452 W/cm*

TBootUt 4801 K

q«05e2W/cm'

TBo„tl.t-'*9*«'< q- 0.253 W/cm*

TBoull.t • « 53' K

q « O 115 W/cm*

TBoutl.t"^300K O

q - 0 029W/cm*

T»outl,t • 4 |3I K _l I 2 4 6 8 10 LENGTH ALONG TEST SECTION, cm

12

Figure 2 . Heat transfer coefficient profiles at 2. 5 atm.

(E

24
for turbulent heat transfer to a constant property fluid is observed. An increase in the heat flux to 0. 113 W/cm^, and as a consequence, increase in

the temperature rise of the bulk fluid, produces a substantial change in the

shape of the h vs length curve. In addition to the overall increase in h,

after the initial redaction of heat transfer coefficient in the thermal entrance

region it rises to a maximum value at 37 diameters from inlet, deteriorating

again beyond. Further increase in heat flux produces a similar result until,

eventually, a heat flux somewhere above 0. 177 W/cm^ is reached where the

overall magnitude of the heat transfer coefficient decreases. However, the

characteristic shape remains the same (e. g. : 0. 259 W/cm^ curve). Finally, at

0. 401 W/cm^ the overall heat transfer coefficient is seen to be further reduced

and the peak exhibited at the lower heat fluxes has disappeared, the profile

generally exhibiting deterioration along the entire length of the test section.

2. 2. 2 Comparison of Supercritical and Subcritical Helium Heat Transfer

Coefficient Profiles

It has been suggested by Goldmann r22]that supercritical fluids exhibit

"pseudo boiling" like characteristics under high heat fluxes and low bulk temperatures. Figures 3(a) and 3(b) show heat transfer coefficient profiles for

subcritical helium at 1. 05 and 1. 97 atm (taken from data of reference [21]);

the transition from nucleate to film boiling at a critical heat flux is evidenced

by the sharp reduction in the heat transfer coefficient.

The critical heat flux phenomenon observed in the supercritical case

bears some analogy, but we note two striking differences. In the first place

the supercritical heat transfer coefficients are almost two orders of magnitude

lower than the subcritical coefficients before degradation or transition. Only

at high mass velocities (e, g. ~ 75 g/s-cm^) are comparable supercritical heat

transfer coefficients obtained (" 14], Secondly, the transition in the subcritical

case is much sharper, i. e. a small change in heat flux gives rise to a more

dramatic decline in the heat transfer coefficient than is observed for supercritical helium. This evidence does not therefore specifically substantiate the

pseudo boiling hypothesis, although qualitative simularities are undeniable.

25
26
2. 2. 3 Correlation of Experimental Results

We have examined the data for some indicator of heat transfer coefficient degradation in order to provide a quantitative criterion for this phenomenon. While the criteria of Shiralkar and Griffith were generally found to be

true when degradation took place, it was not possible for the present experimental conditions to relate the maximum in the heat transfer coefficient with

the bulk fluid temperature being at the transposed critical, as was found in

reference [14]. Neither was this true for a film temperature (defined as the

mean of wall and bulk fluid temperature) or wall temperature being at the

transposed critical. Although there are many possibilities which we have not

tried, we present in Figure 4 a plot of the ratio of the observed heat transfer

coefficient to that calculated from equation (1) versus a dimensionless parameter §. $ is defined as

^ heat per unit mass added to fluid up to a given point along the tube

enthalpy at transposed critical - enthalpy at inlet

Q(z)/m _ 4zq

~

iTc - ii N ~ (iic - Mn) GD

$ is thus the fraction of the heat required to bring the fluid to T^^ which has

been added up to point z. The data plotted are for two different inlet temperatures, 4 K and 5 K, and for three different thermometer stations clear of the

entrance region where z/D = 22, 31 and 45 respectively. This plot appears

to bring the data together fairly well and adds confirmation to our interpretation

of equation (1), developed in our earlier work. The data exhibit a clear deviation from the predicted heat transfer for $ > 0. 3 (relatively high heat flux

conditions) and show somewhat of a crisis as $ approaches 1. 0. However,

equation (1) is apparently a good representation of low heat flux data and

according to Figure 4 at least, should be valid for $ ^ 0. 3.

While it correlates the present data, the plot of Figure 4 may not be

universally applicable for all inlet conditions. For example, when inlet temperatures are very near the transposed critical, substantial values of $ could

27
5*: !^ 2«: ^ :^ ^ lo >t ir> vj- in

O • < ^

O

<

o

<

D

CVJn fO

nO

>vN

If)

II O

\

^4

<3

O

M n

p^Jd^

/

dx^^

O f3

M

b

lO'O

-t->

o

o

u

<0 «H

CQ

EJ«J

»^

-»->

-t-> n)o; J2

X

(Uoo

0^

bp

28
be achieved even under low heat flux (i. e. homogeneous) conditions and

significant deviation from equation (1) would not be expected. For the range

of the present inlet conditions table 1 contains the maximum heat fluxes above

which departures of more than 20 percent from equation (1) were observed

(i. e. $ > 0. 3).

Table 5 . Experimental values of q where 0. 8 < h /h < 1. Z. exp calc

G Tg INLET q

g/s- cm^ K W/cm^

5. 7 - 7. 6 4. 056 - 4. 064 less than 0. 177

6. 8 - 7. 6 5. 038 - 5. 043 less than 0. 187

11. 2 - 12. 5 4. 047 - 4. 085 less than 0. 345

20. 5 - 24. 3 4. 047 - 4. 085 less than 0. 582

We were not able to run the apparatus with $ > 1 for reasons which are not

entirely clear. Several things happened simultaneously as the fluid approached the

transposed critical temperature, including the problem that the superconducting power

leads to the test section went normal. It should be noted that similar experiences

occurred in our subcritical experiments in film boiling once the heat flux exceeded about I. 1 W/cm^ and this may simply he a limitation imposed by the transition temperature of the superconducting leads.

An unexpected feature of Figure 4 is the region 0. 07 < $ < 0. 3 which

shows clear enhancement above the value of h given by equation (1). It should

be remembered that equation (1) already accounts fairly well at higher pressures

for enhancement due to the temperature dependence of the fluid properties as well

as the non-linearity of the heat transfer process indicated by the term (Tyj/TB)°"

In view of the apparent significance of the parameter ? for the present

study at 2, 5 atm it is natural to inquire as to the values obtained in the experiments of ["14]since the correlation developed there seems to represent the low

29
heat flux limit. Table 6 lists the maximum values of $ for the pressures

investigated for those runs in which the fluid entered below the transposed

critical temperature. A value of $ for each thermometer is given.

Table 6 , Values of ^^ from [14]

x^res s ure rp / rp INLET' TC ^alm

(z/D=40)

3J . (So

r\ r\ AO U. U4o 0. 096

A

, OO 0. 74

r0 .97 0. 64 1. 28

7 . 86 0. 37 0. 74

8 . 69 0. 077 0. 15

9 .91 ' 0. 104 0. 208

10 . 76 0. 160 0. 320

14-15 . 44 0. 96 1. 92

19-20 . 97 0. 40 0. 80

Since substantial values of f were achieved in [12] at higher pressures one

can only surmise that degradation of heat transfer was not significant and

perhaps this is of concern only quite close to the critical pressure as is here

the case. Further experiments along the lines of those reported here would

be required to clarify this point. Judging from these observations at 2. 5 atm,

a safe range of application of equation (1) would be given by values of T,nlet/

Ty^ greater than those shown in table 6 with corresponding values of § less

than those shown in table 6

2. 3 Conclusions

The experiments reported here for heat transfer to supercritical

helium in forced flow at 2. 5 atm lead to the following conclusions:

1. For supercritical helium, both enhancement and deterioration in heat

transfer can occur as observed with other fluids. In general the criteria quoted

from Shiralkar and Griffith for the existence of an impaired heat transfer coefficient are verified. A good quantitative indicator of the particular behavior

30
to be expected for the inlet conditions of this experiment at 2. 5 atm is given

by the value of the dimensionless pararaeter $ defined in the text.

2. At 2. 5 atm and conditions noted Vv^ith heat fluxes below those given

by ? = ^ 0. 3 equation (1) gives heat transfer coefficients within ± 20 percent

of the experiments.

3. For 0. 3 < $ < 1. 0 the experimental heat transfer coefficient

deteriorates to as low as 12 percent of that given by equation (1), the value

§=1.0 appearing to be somewhat of a heat transfer crisis.

4. There is a strong indication from earlier results that this type of

behavior may not be observable at 4 atm and above. The estimated range of

applicability of equation (1) is given by information contained in table 6.

31
3. FORCED CONVECTION HEAT TRANSFER

TO SUBCRITICAL HELIUM I

Patricia J. Giarratano, R. C, Hess, a nd M. C. Jones

3. 1 Introduction

The intensive development of superconducting technology for electrical

power equipment calls for a good knowledge of heat transfer to helium. Traditionally, simple bath cooling is used to provide the necessary rates of heat

transfer to stabilize the conductor, and this appears still to be quite adequate

in d. c. applications. However, in a. c. applications and various applications

where large field sweep rates are experienced, either in normal operation or

under fault conditions, losses occur and there may be design benefits from

circulating the helium.

In a previous study at the Cryogenics Division of the National Bureau

of Standards, by Giarratano et al. [21]. heat transfer coefficients for forced

flow of supercritical helium were measured and a correlation was developed

to predict the heat transfer in this region. As an extension of that study we

have measured heat transfer coefficients under conditions of forced flow of

subc ritical helium. Particular emphasis has been placed on determination of

conditions under which a transition from nucleate boiling to film boiling occurs

(critical heat flux) since an unacceptable rise in wall temperature may occur

at this point (from the point of view of cooling superconductors).

It is hoped that the information developed in our program will go some

way towards broadening the designers choice and permitting closer design.

The data presented herein are a summary of over two hundred experimental

runs, including seventy four transition observations.

32
3. 2 Description of Experimental Apparatus

and Measurement

A schematic of the boiling heat transfer flow loop is shown in

figure 5. A centrifugal pump, previously described in [23] , circulates the

liquid around the flow loop. To maintain a constant inlet temperature to the

test section, heat is removed from the liquid as it passes through approximately 13 meters of 0. 32 cm i. d, copper tubing located in a heat exchanger

reservoir of approximately 2. 5 liter capacity. The heat exchanger reservoir

is continuously supplied with liquid helium from a storage dewar.

Test Section

The test section is a 0. 213 cm i. d. x 20 cm long stainless steel tube

with a wall thickness of 0, 016 cm. It is resistance heated along 10 cm of its

length (L/D - 50). A stainless steel-pyrex seal located in the bottom of the

loop provides electrical isolation of the test section. A wire wound preheater

upstream of the test section allows variation of quality at the inlet of the tube.

Accurate measurement of the current and potential drop across the two heaters

is used in the calculation of heat flux. At the lowest power levels the uncertainty is less than 2 percent.

Temperature Measurement

Outside tube wall temperatures are measured at ten points along the

heated test section length with calibrated carbon resistance thermometers.'

One lead of the carbon resistor is soldered to a small copper block which

also provides a tempering post for the resistor's electrical leads. The block

+ Identification of any materials or their manufacturer by the National Bureau

of Standards in no way implies a recommendation or endorsement by the

Bureau. Furthermore, use of other trade names in this paper is for the sake

of clarity and does not in any way imply a recommendation or endorsement by

the Bureau.

33
34
is thermally clamped to the test section but is electrically isolated from it by a

thin (0. 012 7 cm) Mylar film. The thermometers are positioned one cm apart

with the first thermometer located 0. 6 cm from the inlet. Inside wall temperatures are obtained by calculation of the temperature drop through the tube wall

using the thermal conductivity of stainless steel given by equation (Al) in the

appendix of reference [24], Bulk fluid temperatures are measured at four points

along the flow loop (upstream of preheater, upstream of test section and two

measurements downstream of the test section) with germanium resistance

thermometers. These thermometers are potted with vacuum grease in copper

wells which are soldered to the tube.

The carbon resistance thermometers and the germanium resistance

thermometers used in this study were calibrated in a separate apparatus,

over the range 4 - 20 K, against three germanium resistance thermometers

(GT 1011, 1027 and 1024), These three germanium thermometers had been

previously calibrated against NBS secondary standard germanium thermometers

(GT 722 and 734),

In our calibration, over the range 4 - 9 K the agreement between GT 1011,

1027, and 1024 was within 0, 01 K for the worst case and was generally within

0. 005 K. Above 9 K the agreement was within 0. 05 K. An average value of the

three germanium thermometer readings was taken to be the true temperature.

The calibration data for each thermometer were fit with a curve of

the form:

N

Log T = E A(N)(Log R)

N=0

with an rms percent error of 0. 06 in temperature over the range 4 - 19 K.

This corresponds to approximately 0, 003 K at 4. 2 K and 0, 01 K at 19 K.

However, in the heat transfer apparatus during preliminary runs, it became apparent that there were carbon thermometry errors that were bulk

temperature dependent and which partially decayed in time (time constant of

35
the order of hours). Extensive tests indicated that the time dependence of

the error was probably due to residual spurious radiation heat leaks, not

evident in the calibration apparatus but irapossible to totally eliminate in the

heat transfer apparatus, and the bulk temperature dependence was probably

due to shifts in calibration. Therefore, we adopted an In situ re-calibration

procedure which allowed correction of the carbon thermometers on the basis

of the germanium thermometer readings taking into account both time and

bulk temperature dependence.

The estimated uncertainty in outside wall temperature after correction

is at most 0, 02 K (the maximum shift in calibration of the germanium thermometers upon which corrections for carbon thermometers were based). However,

the error in temperature difference between the inside wall and the bulk temperature, due to uncertainty in the thermal conductivity of the stainless steel

wall, the wall thickness and bulk temperature, is of the order 0. 05 K at heat

2 2

fluxes of 0. 02 W/cm and is of the order 0. 15 K at heat fluxes of 0. 2 W/cm ,

In the two-phase region, since the pressure drop across the test section

was of the order of a few mm Hg for the data presented, the intermediate

bulk temperatures were taken to be the saturation temperatures corresponding

to the inlet static pressures. This approximation was within experimental error.

Pressure and Flow Measurement

Provision was made to measure pressure drop across the flow orifice,

preheater, and test section and the static test section inlet pressure using

calibrated pressure transducers and a static Bourdon tube pressure gauge

accurate to 0. 01 atm located outside the cryostat at room temperature.

The pressure transducers were located at room temperature which resulted in large temperature gradients along the pressure tap lines. Consequently

the pressure drop readings across the test section were unsteady (noise of the

same order as the pressure drop itself). However, generally when there was

no surging the AP across the test section was less than 7 mm Hg.

36
Since the fluid at the outlet of the preheater was slightly subcooled

for much of the data presented a calorimetric method determined the flow rate

under these conditions. The calorimetric flow rate from the preliminary

runs was also used to determine a discharge coefficient for the flow orifice so that the orifice may be used for flow measurement when calorimetric flow

determination is not possible, i. e. , two-phase out of the preheater. The

discharge coefficient so obtained agrees with that of an identical orifice

section which was calibrated in a separate apparatus.

For the calorimetric method, applicable for 75 percent of the runs,

accuracy of the flow rate ranges from 2 percent to 9 percent (more uncertainty

at the lower operating pressures due to less subcooling available). This is

due to uncertainty in measuring the temperature rise of the bulk fluid through

the preheater section. For 25 percent of the runs where the orifice was

used there is an additional maximum uncertainty of 35 percent (3(t limits) due

to fluctuations in the readings of pressure drop across the orifice.

Extraneous Heat Exchange

To minimize heat leak from room temperature to the test section by

conduction, all electrical leads and the thin walled, 0. 317 cm diam, stainless

steel pressure transmission lines are thermally anchored to the outside copper

surface of the liquid helium heat exchanger. A length of multifilament niobiumtitanium superconducting wire is used for power leads between the heat ex- changer and the preheater. The small diameter and low thermal conductivity

of this wire further minimizes heat leak due to conduction and joule heating in

the leads is eliminated. Error in heat flux due to axial conduction from the

ends is less than 2 percent for the worst condition. Extraneous heat to and

from the test section is therefore considered negligible. Boil-off from the

liquid helium heat exchanger is routed through coils soldered to the pump

housing and the radiation shield. This arrangement minimizes heat leak from

room temperature via conduction along the pump housing and provides a low

temperature radiation shield around the flow loop. The test section portion is

37
further protected from radiation by a copper shield thermally anchored to the

_7 heat exchanger. The evacuated copper enclosure (vacuum less than 10

mm Hg) which is submerged in a bath of liquid nitrogen provides first stage

radiation shielding from room temperature.

Experimental Measurement

For a fixed system pressure, pump speed and quality at the inlet of

the test section, the power to the test section was increased in steps from

zero. At a certain power level a discontinuous rise in the wall temperature

occurred at the outlet end of the test section (critical heat flux). Further

increase in power caused the discontinuity to move up the test section toward

the inlet. The upper limit of power was usually determined by excessive wall

temperatures at the outlet. After a change in test section power, thermometer

voltages stabilized generally within a few seconds and were recorded by a

digital voltmeter and automatically punched on paper tape together with all

other pertinent voltages and run information.

Since the flow loop is a closed system, as power was applied it was

necessary to vent the system to maintain a constant test pressure and conversely a decrease in power applied required adding and condensing gas in

the loop to maintain the pressure.

This procedure was repeated for different pump speeds, inlet quality

and pressure.

During a measurement the temperatures and pressure were stable to

within their accuracy prior to a transition in the heat transfer mechanism

(critical heat flux exceeded). When a transition occurred, it was accompanied

by fluctuations in temperature (for the wall stations in the transition region) of a rather random nature, and an amplitude of the order of 0. 5 K. Oscillations in pressure were not noticeable but this was at least partly due to

the pressure transmission line being heavily damped.

38
We have attempted to establish the variability of our data frora day

to day by limited repetition of a measurement under the same set of conditions

(e. g. same pressure, pump speed and inlet quality). For heat fluxes below

the critical heat flux typical deviations in wall temperatures, at a given position on the test section, were 0. 02 K. For heat fluxes above the critical

heat flux the wall temperature deviations were of the order of 0, 05 K and

the position of the transition was repeatable to the nearest thermometer, i. e.

to within 1 cm.

3. 3 Heat Trajisfer Results

Temperature profiles along the wall for subcritical helium heat transfer are shown in figures 6 and 7 for pressures from 1. 1 to 2. 0 atm' and mass

velocities from 4. 5 to 63 g/s-cm . A typical profile is extremely flat up to

some point at which a sharp rise is observed for the higher heat fluxes. This

we identify, with reference to a vast body of literature on boiling heat transfer, as indicating a hydrodynamic transition from wetted-wall, e. g. , nucleate

boiling, to dry-wall, e. g. , film boiling, heat transfer. Thus, at a particular

point along the test section there is a critical heat flux above which the wall

temperature rises quite steeply with heat flux.

Below the critical heat flux, heat transfer is very high as evidenced

by the wall temperatures being nowhere more than about 0. 3 K above the bulk

fluid temperature. Indeed this behavior is strongly reminiscent of boiling heat

transfer without forced convection, i. e. , pool boiling. In figure 4 we plot

the heat flux q against the difference between the wall and bulk fluid temperatures AT. The AT plotted is an average of the AT's for all positions on the

tube having an L/D > 20 to preclude possible entrance effects. Furthermore

since the wall temperature profile is so flat in this nucleate boiling region

and since the bulk temperature is not changing, such a plot gives an indication

of the average heat transfer in the nucleate boiling region. We have plotted as

solid lines, the nucleate pool boiling correlation of Kutateladze r25] for 1. 1 and

2. 0 atm and indicated at the upper extremities the critical heat flux for pool

boiling given by a second correlation due to Kutateladze [25]. As shown for

* 1 atm = 0. 1013 MN/m^

39
32

28

24

20

PRESSURE = I.I otm MASS VELOCITY = 45g/s-cm*

QUALITY @ INLET = -0 03 to -0.02

32

28

24

20

h- 16

12

d 16 t

q = 0.228 W/cm*^

J \ L J I I

PRESSURE = I.I atm MASS VELOCITY = 13 g/s-cm*

QUALITY @ INLET =-0.07

TbuLK q = 0.283'

J \ L J \ \ \ \ I

32

28

8 16 24 32 40 L/D

PRESSURE I.I otm MASS VELOCITY = 28 - 32 g/s-cm^ QUALITY (jD INLET = 0.0

q = 0.686 W/ cm*

48 16 24 32 40 48 L/D

d 8

Tbulk

J I \ L_J \ L

PRESSURE = I 5atm MASS VELOCITY = l4g/»-cm^ QUALITY (J) INLET = -0.07

^TSULK

q = 0256/

J \ I \ \ \ \ \ \ L

16 24 32 40 L/D

48 16 24 32 40 48 L/D

Figure 6, Typical wall temperature profiles for various inlet conditions,

(pressure: 1. 1 and 1. 5 atm)

IB- 107t.81 I

40
PRESSURE = 14 atm MASS VELOCITY = 63g/s-cm^

QUALITY (g) INLET = 0.0

7.5

7.0

6.5

10

' BULK q = O.I7r

J I L

24 L/D32 40 48

7.5

7.0

6 5

PRESSURE = 2 atm MASS VELOCITY = 27- 28 g/s-cm^

QUALITY @ INLET =-O.II to-O.IO

q = 0.328 W/cm ,

vt: 6.0

<^ 5.5

5.0

4.5

4,0

^Tbulk

J \ L

8 16 24 L/D

32 40 48

it: 6.0

S 5.5

5.0

4.5

4.0

PRESSURE = 2 atm MASS VELOCITY = 13 g/s- cm^ QUALITY (§) INLET = -0.05 to -0.03 —Q _ Q

^Tbulk

1

16

14 —

12

10

8 16 24 L/D

PRESSURE = 2 atm MASS VELOCITY = 47 g/s-cm^

QUALITY(5) INLET = -0.3

32 40 48

-<3:^ ^

^Tbulk

2 —

J \ \ \ L_J \ I 8 16 24 32 L/D

40 48

Figure 7. Typical wall temperature profiles for various inlet conditions

(pressure: 1. 4 and 2 atm).

IB- 1U7486~

41
KUTATELADZE CORRELATIONS FOR

NUCLEATE POOL BOILING a

CRITICAL HEAT FLUX [ 3 ]

VELOCITY PRESS. QUALITY at /s-cm atm INLET

3 - 15

26-37

12

28-42

I.I

14

> 2.0

2 )

-0.07 to 0

- 0.07 to 0

-0.04 to 0.1 -0.14 to 0.0

J. J I I I I I II J I I I II II

0.1 AT. K

10

8. Heat flux (q) vs temperature difference (T T ) in

wall bulk

the nucleate boiling region under forced flow conditions.

(1-107422 I

42
example by Brentari et al. [26] these correlations give a good average representation of nucleate pool boiling data for cryogenic fluids. The present data

for forced convection heat transfer are represented by the first of these correlations below the critical heat flux as well as any given set of pool boiling

data, which are notorious for their sensitivity to the precise nature and

preparation of the boiling surface, as well as its heating history (a strong

hysteresis effect is often observed).

The lack of reproducibility in the present data in this region is quite

in character with nucleate pool boiling data and has apparently masked any

trend with mass velocity. We conclude that forced convection has had no significant effect on the rate of heat transfer below the critical heat flux and that

the boiling mechanism itself is the primary determinant.

Above the critical heat flux wall temperatures are quite high and are

now a strong function of the mass velocity in addition to heat flux and pressure.

At 1. 1 atm the wall temperatures rise to unacceptable values from the point

of view of cooling of superconductors even at the highest mass velocities.

At 2 atm, however, it is clear that the temperature excursion above the critical heat flux has reached a limit which is of some practical value and at the

/ 2

highest mass velocity (47 g/s-cm ) it is even possible for the whole test

, 2

section to be in film boiling below 8 K, with a heat flux of 0. 755 W/cm . Even at 1. 4 atm and 63 g/s-cm a very useful heat flux can be supported

while wall temperatures remain in a useful range. It is noticed too that when

film boiling is well established throughout a good proportion of the test section,

wall temperatures tend to fall again toward the outlet. This may be due to an

increase in velocity as more vapor is generated as the fluid moves down the

section.

We have not been able to find a suitable correlation to give a unique

representation of the film boiling heat transfer coefficient even when we confined our attention to data for fully developed film boiling. This we defined

as data for which the given thermometer was downstream of the maximum

wall temperature. Correlations which were investigated for subcritical

hydrogen in reference [26]could not represent the available data to better than

43
an rms deviation of about 100 percent. We therefore have to rely for the

present on the data alone to describe the film boiling region for helium.

Our primary interest in the present work has been in the nucleate-tofilm boiling transition itself. The point of transition on the test section is

quite clearly indicated on the temperature profiles to the nearest wall thermometer station. We take a point mid-way between two adjacent thermometers

where one shows no significant temperature rise, and therefore presumably

is still in nucleate boiling, while the next thermometer does indeed show a

significant rise. In this way we have recorded 74 data points for the point of

transition. Our goal has been to provide a means of predicting the transition,

that is: given the state of the fluid at entry to the heated section, i. e. enthalpy

and pressure, the flow rate and the heat flux, we wish to know at what position

downstream the transition will occur. Alternatively, given the state and flow

rate we wish to know the heat flux - the critical heat flux - at which the transition will occur at a certain position. Here we list the observed trends. In the

next section we discuss the rationale for a correlation and describe the correlations that represent our data.

1 The first and most obvious trend is that, for a given pressure and mass

velocity the critical heat flux is a function of distance from the inlet to the

heated section. In experiments on heat transfer to subcritical helium under

conditions of natural convection Johannes and Mollard [27] found that most of

their data could be represented by a single curve when the critical heat flux

was plotted against the distance from the inlet to the heated section in diameters

(the equivalent diameter D was used for rectangular cross section, where

D = 4x cross-sectional area/heated perimeter). The equation which represente ed their data was — = 1. 7 + 0. 125(L/D (2)

q e cr

where q is the critical heat flux, L the tube length at which transition ocurcr

red, and D the equivalent diameter based on the heated perimeter. Under

44
conditions of natural circulation the mass velocities obtained by Johannes

/ 2

and Mollard were from 2 to 3 g/s_cm , For our lowest mass velocities

2

(4. 5 g/s-cm ) at 1. 1 atm pressure our critical heat fluxes are only about

10 percent higher than given by equation (2). However, a cursory examination of our data showed that there are considerable departures which may

be summarized as follows.

i. Critical heat fluxes may be as much as a factor 2 or 3 times

2 higher when mass velocities are in the range 30 - 60 g/s-cm .

ii. Critical heat fluxes may be as much as a factor of 2 lower at

2 atm pressure.

iii. Critical heat fluxes are enhanced by subcooling the liquid helium

at the inlet to the test section.

There are thus at least five interdependent variables which characterize the

transition: the heat flux, the thermodynamic state (2 variables), the mass

velocity and the position in the tube.

Critical Heat Flux Correlation

Two factors have influenced our approach to correlation of our transition data. The first is that considerable simplification of the problem is

possible if we adopt a local hypothesis. That is, we assume that transition

occurs at a point in the tube under conditions of local hydrodynamic similarity.

The second is the success which has been achieved for a very wide range of

liquids (from helium to water) in correlating the pool boiling transition on the

basis of the similarity criterion derived first by Kutateladze [25]. This criterion

= KU = constant (3)

was derived from an analysis of the equations of motion of the two phases and

equations for the dynamic interaction at the vapor-liquid interface when

45
turbulent transport predominates. In equation (3) X is the latent heat of

vaporization, cr the surface tension, and are vapor and liquid densities

respectively and g is the gravitational acceleration. The essential point in

the derviation of (3) is that in pool boiling the only scale of the velocity is the

quantity q/p^X and there is no scale for the pressure difference between phases,

AP. We have taken the point of view that in forced convection boiling a well

defined scale of velocity exists also in the direction of the tube axis as does

a pressure drop. Further, we require an added parameter to complete the

hydrodynamic description, namely the void fraction, or, equivalently, the

quality x and the ratio p^/ o . It is then straight forward to show that similarity

in forced convection boiling can be specified by the following groups:

T-x p L P gD G ""v

^

G is the mass velocity or mass flow per unit area. Now the ratio p. AP/G for

G D

given L/D is determined by a Reynolds number which we define as Re -

where y, is the liquid viscosity. Noting also that the first and second groups

are the Froude number and Weber number respectively we arrive at the following equivalent set of dimensionles s groups.

I Fr, We, Re, X , , KU

|

This is as far as the local hypothesis takes us and the above groups

should be adequate provided the point under consideration is remote from any

flow perturbing geometry eg: the entrance to this heated section. This would

be indeed a non-local effect. Now because some of our transitions were observed as close as three diameters distance from the entrance we included the

group ^1 + where L is again, as in (2), the length up to the transition point.

Since in the absence of forced convection we must again recover the criteria (3)

the following form suggests itself

[C C C C. /p vC C

1

Fr • We ^.(1+ D/L)^ • d-x) .

• Re

""J

(4)

46
We have replaced x by 1-x to avoid a negative term in the subcooled region.

Using non linear least squares fitting techniques [28]and the helium properties

data given by McCarty [29], it was possible to determine the constants, C^, in

equation (4) . The experimental data of Johannes and Mollard [27], with the

equivalent diameter based on the wetted perimeter instead of the heated

perimeter, were used to supplement our own. Those data provided low mass

2

velocity input (natural circulation with G's of the order 2g/s-cm ). The

standard deviation for the fit was 0. 017 in units of KU, which was approximately 19 percent for an average value of KU. The constants obtained were

^1 = 0. 04

^2 - 0. 36

^3 = 0. 40

^4 = essentially zero

^5 ^ -0. 73

^6 2. 72

= 0. 11 ^7

= -0. 30 ^8

Owing to the complexity of equation (4) and to the fact that some of

the exponents were quite small, suggesting some redundancy, we experimented

with several variants of (4) in which terms were removed. A good compromise between simplicity and goodness of fit was achieved with the expression

KU = + [1-x] ^ (5)

where

= 0. 031

=: 0. 078

- 3. 92

47
and the standard deviation was 0. 02 (approximately 22% for an average of

KU).

In arriving at a final selection of a correlation we plotted in addition

three data points of Jergel and Stevenson [30]and two of Keilin et al. [31].

The latter are particularly significant, because in their work these authors

observed transition under rather different circumstances; their L/D was

278 and transition occurred at a quality of about 0. 4 (e.g. our L/D < 48 and

X < 0. 2 for similar pressures and mass velocities). It was found that some

variants of (4) fitted to our own data and those of Johannes and MoUard were

quite unable to predict the Keilin et al. data to better than an order of magnitude, whereas equation (5) came within 5 percent. Equation (5) and all the

data discussed are shown plotted in figure 9.

To more pointedly illustrate the effects of mass velocity pressure and

inlet conditions on critical heat flux we have constructed table 1 for a 10 centimeter long X 0. 2 cm i. d. tube using equation (5) in the calculations. It is

apparent that, for a given pressure, increasing the mass velocity from natural

convection rates (2 g/s-cm ,2) to reasonable forced convection rates (50 g/s-cm ,2) results in a threefold increase in critical heat flux. Furthermore for a given

pressure the effect of increased subcooling at the inlet also results in an

increased critical heat flux. The maximum benefit from subcooling is obtained

at 2 atm where it is seen that for an inlet temperature of 4 K and mass velocity

2

of 50 g/s-cm the critical heat flux is approximately three times that at saturated inlet conditions. Note that at 2 atm equation (5) predicts that transition

can occur at negative values of x representing subcooled helium. Such a circumstance has been observed in our experiments; it is possible to have

subcooled film boiling under forced convection conditions. Table 7 can be

taken as a reasonable representation of the experimental results on transition

of this and other work.

48
49
o

inm

—. O ^ e §

0)

1—1 .w a ^ u .2^o SCo aj X fl 1—1 ^ fl X

1—1u 0) 5 > u S s - .2 j>

(t

d

(0CO

<u

Ph >o

rfl §w

CO

(JOI—I >

CO

COa

II O

II

Fl

.1-1

-t-> 1—1d

PC

a

1—1 1—( ao u

•p-i

.i-»

1-1 • 1-1

uO

u

II II o

CMd

II Q o

in

I—1 d

0.

07

atm o

CO

r—1 d

1—1 1—1 d

II 0.

tn 0.

09

0.

34

0.

07 0.

64 o

IT) 0.

32 0.08 6

atm o

CO 0.

29 (M

1—1 d

i-H

II in

in

1—1 CX) CO d d

(M 1—1 d

0.

73

O

in

l-H d

0.

08

atm o

CO 0.

37 1—1 d

l-H

II in o

rod

0.

38

in

i-H d

0.

73

Sat.

Inlet

Conditions

O cr

uu

(VJ (VJ o

in

d

d

in c o CO CO *->

(vj

d

d

II in o ^

in 1—1 o . o o

Qv o o 1—1 d d

in CO o in <—< in d d1 C

-*-> C o o

(ti CO

dd

sD 1

1—1 r—I

II in r—t

(Vj

(1, o O

CO CO 1—1

in

dd o o

in

dd o CX5 o o g

CO

dd

(t o in

II in (VJ CO O o

in

1—(

sD

d

d

r?I-H BH« II

u

fl —1

O

u

cr o B*->

(VJ

II Oha

(CJ

1—1

II 1—I

II

XId DC xt<

t/) fl (VJ

•"^ (VJ 1—I ^

(U o • ^ U II o

ino

COo

ino

CO

(VJ o

ino

CO

in

(VI o

CO

in

(VJ

oooo

COI—I d

(VI oo

(VI

in

50
51
Comparison of Modes of Heat Transfer

In figure 6 the present results of heat flux q as a function of wall temperature rise AT for L/D = 48 are represented by shaded areas for comparison

with other modes of heat transfer. We have included calculated values of the

nucleate pool boiling correlations of Kutateladze and calculated values of q vs. AT for supercritical helium heat transfer at 3 atm and at mass velocities of

2

10, 30, and 50 g/s-cm . These were computed from

0. 8 0. 4| Nu = 0. 0259 Re Pr ^-^^

where Nu is the Nusselt number, Re the Reynolds number, Pr the Prandtl

number, T^ the inside wall temperature, and T^ is the bulk fluid temperature.

The above correlation was developed in reference[24] which represented the

data of that reference (L/D = 20 and 40) with an rms deviation of 8. 5 percent.

We conclude from this comparison that for heat fluxes between 0. 01

and 0. 3 W/cm subcritical pressures are preferable to supercritical pressures

for equivalent mass velocities in forced convection. Above these heat fluxes,

, 2

up to about 1 W/cm and at pressures near one atmosphere, supercritical heat

transfer is superior to subcritical, which is now in a dry-wall regime and

shows very steep temperature rise for a small heat flux increment. However,

at subcritical pressures approaching the critical pressure (e. g. 2 atm), and

the highest flow rates observed the heat transfer rates are better or equivalent

for the whole range of heat flux (. 01-1 W/cm ). We note that even though

critical heat fluxes at 2 atm are relatively low, compared to 1 atm, the temperature excursion after transition is moderate if a reasonable flow rate is

used (see last wall temperature profile in figure 3).

Finally, judging by the slopes of the curves in figure 10, at heat fluxes

2

beyond the range of the present data (> 1 W/cm ) supercritical heat transfer

should be superior.

52
3. 4 Conclusions

i. The usual transition from wetted-wall to dry-wall heat transfer

is observed in heat transfer to subcritical helium I under forced

convection.

ii. Below the transition, forced convection has little effect on heat

transfer and the pool boiling correlation of Kutateladze for the

heat flux vs. temperature rise of the wall is sufficient.

iii. Above the transition, the heat transfer coefficient falls off drastically. For superconductivity applications and low operating

pressure (e. g. 1 atm) this will usually have to be avoided except

2

at mass velocities of the order of 60 g/s-cm or higher; but may

be tolerated if higher operating pressures are used (e. g. 2 atm).

iv. Transition is a function of many variables (see discussion of correlation) but may be predicted by a relatively simple function of

quality (equation 4) which implicitly contains those variables.

2

V. At heat fluxes between 0. 01 and 0. 3 W/cm subcritical heat transfer is superior to supercritical for the same mass velocity. Above

about 0. 3 W/cm the reverse is true, for an operating pressure

of 1 atm, and for an operating pressure of 2 atm the heat transfer

rates are comparable.

53
3. 5 Appended Experimental Data

For possible future reference in testing other methods of analysis, the

uncorrected data are given in the following table.

List of Symbols Used

P System pressure

Q Wall heat flux

G Mass velocity

^inletj X Quality at the test section inlet and local quality

4[3 Length to diameter ratio (position in the test section)

Local inside wall temperature

Tg Local bulk fluid temperature

H Local heat transfer coefficient

Due to uncertainty in temperature measurement (discussed

in text) in some instances a negative experimental heat

transfer coefficient is indicated. This obviously unrealistic

situation is denoted by an asterisk.

54
Table Al.

P(ATM) = 1.66 G (G/S- CM2) = 7. 7

0(W/CM2) = 0.032 XI>IlET = 0. 00

L/0 TW TB X H

( K) (K) (W/CH2- K)

2 . fl 81 3 '.8 11 0.00 19. 092

i+. 806 '.811 0.01

12.2 '.802 '.811 0.01

16.9 k, 801 '.811 0.02

21 . 6 U. 80 0 '.811 0.02

26. 3 85d '.811 0.03 0. 67'^

35

31

.

.'07 ^.

k,

8U0

802 '.811

'.a 11

0.

0.03

0*^ » ^4 G . H SOi* '.811 0.01+

^+5 . 1 809 ii.eii 0.05

P(ATM) = 1.70 G (G/S- CM2) - 7. 3

0(W/CM2) = 0.05*+ XlNuET = 0. CO

L/0 TW TP X H

( <) (K) (W/CH2- K)

2 .d i*. 85? 0.31 5. 6'+l

7.3 857 0.02 3. Sli*

12.2 816 0.02

16.3 i+. 819 0.03

21.6 i*. 856 ^.8'42 0 ,Qk 3. 782

26.3 k, 836 '.8'+2 0.05

31.0 t+. 852 k,6i*2 0. 06 5. ''0

35.7 t+. 85 (i '.8'*2 0.07 3. ''0

i+G . k 868 ' .8'42 0. 08 2. 113

^+5 .1 ^.870 '.6'^2 0.09 1. 96'^

P(ATM> = 1.76 G (G/S- CM2) = 7. 2

0(W/CM2) = 0.085 XIMLET = -0.02

L/0 TW TB X H

(K) (K) (W/CM2- K)

2.8 k. 888 '.866 -0.01 3. 888

7.5 838 '.879 0.00 10. 35'^

12.2 U. 8bi* '.879 0. 02 19. 131

16 . 9 385 '.879 0. a<+ 11+. 302

21 . 6 365 '.879 0. G5 lU. '81

26.3 t». 887 '.8 79 0. 07 10. 96<«

31.0 ^4 . 366 '.879 0. 06

35. 7 336 i^. 879 0.10 13. 100

1*0 . W '.895 '.879 0. 11 5. 377

k5 . 1 '.897 '.879 0. 13 '.988

55
P (ATM ) = 1 • 7 0 G (G/S- CM2) = 11. *

0 (W/CM2 ) = 0 . KINLET = -0.03

L / 0 TW TB X H

( <) ( K) (W/CM2-'K)

2,6 739 '.606 -0.02

7 . 5 '•737 '•8 21 - 0 • 0

1

<• 735 '.837 -0.00

16.9 '.7i+0 '.836 0.01

21.6 U - 7 3 9 '•836 0.02

26.3 t*. 737 '.8 38 0.03 ******

3 1 . Q U . 73 ? '.838 0. 0'^ ****** 35.7 *. 737 '.836 0.05 ****** ^•753 '.838 0.07 ******

i»5.1 '.751 '.838 0.08 ******

P(ATM) = 1.77 G (G/S- CM2) = 11 . 2

0(W/CM2) s 0.099 KINLET = -0.05

L/0 TW TB X H

( K) (K ) (W/CM2- K

)

2.8 *. 779 '.832 -0.05 ******

7.5 U. 777 '.8 '7 - 0 . 0'^ ******

12.2 77^ '.862 -0. 02 ******

16. J 780 '.8 77 -0.01 ****** 21.6 U . 778 '.892 -0.00 ******

2 6 . i U. 776 '.892 0 • 01

31.0 '.771 '.892 0.02

35.7 '•77'+ '•892 0 . 0*^ ******

kO » k 1* . 795 '.892 0.05 ******

tt5.1 792 ' . 8 *^2 0 . Q6 ******

G (G/ S- CM2) = 3 , 1

X ^ l» u. « = -0.03

L / D TW TB X H

( K) (K) (W/CM2- K)

2 . d '.271 '. 129 -0.03 0^ 0'^6

7.5 ' . 292 '•135 -0.02 0. 0*^2

12.2 ' . 335 '. l'+2 -0.02 0 • 0 3'^ 16.9 . 31 ' '. l'+8 -0.02 0» 0 39

21.6 '. 318 '.155 -0.02 0. Qt^O

26. 3 *. 332 '.161 -0. 02 0. 036

31.0 '.335 '•166 -0.01 0. 039

35.7 <. 3'^1 '.17'^ -O^ 01 0.039

. < <. 365 <f.l81 ^0.01 0.035

'5,1 '.375 '.187 -0.01 0. 035

56
P(ATM) = 0.98 3(&/S-CM?) = 3.1

G{W/CM2) = 0.016 XINLFT = -0.02

L/0 TW TB X H

(<) (K ) (W/CM2

2 . 3 k. kl3 i^. 135 -1]. 02 0.057

7.5 U. 373 ^.155 -0.01 0.071

12.2 4+. i»10 '.I 76 -0.01 0.068

16.9 373 ^.196 -0.00 0. 089

21 . 6 k. 376 i^. 207 0. 00 0. 09^^

26 . 3 '.'02 ^.207 0.01 0.081

31 . 0 ^.207 0.01 0.073

35 . 7 ^.207 0.02 0. 07'^

. k *. 3!i2 ^.207 0. 02 0.091

i*5 . 1 k, 388 . 2 C 7 C. 03 0.087

P(ArM) = 1. J i G (G/S- CM2) = 1 Q(W/CM?) = 0 . 031 XINLlT - -0.03

L ZD TW TB X H

(<) (K) (W/CM2

2 . 8 k. 399 '.118 -0.03 0.111

7.5 «. 'O 2 '.l'+8 -3.02 n. 123

12 , 2 «. 'Sb '.179 -0.01 0.112

16.':) '.2 09 -0.01 0.157

21 . 6 '+.'20 '.232 0. 00 0. 166

26.3 *. '' 7 ^.232 0.01 0. l'+5

31 . 0 i^. '73 £.232 0.02 0.130

35 . 7 '.'50 '.232 0.02 0. l'+3

i^. '27 '.232 0.03 0.160

^5 . 1 '.232 0. Ci+ C. l'+3

P(ATM) = 1. 0;+ G (G/S- CM2) = k. 3

C{H/CM2) = 0 . 069 XlNILtT = -C. 0'+

L/0

2 . 8 7.5

12 . 2

16 . 9

21 . 6

26.3

31.0

35 . 7 'O . ' '5.1

TW

(K)

i+. 1^77

'*. '69

'.533

«. '69

k75

k,52Z

«. '99

k. 506

'.539

TB

(K)

k. 13U

'.197

'.260

'.268

'.268

'.268

'.268

'.268

'.268

'.2 68

0.03

•0.02

0.00

0.01

0.03

0. OU

0. 06

0.07

0.09

0. 10

H

(W/CM2-K)

0.200

C. 253

0. 2'+7

0. 3'+2

0. 331

0. 285

0. 271

0.298

0. 289

57
P(ATM) = 0.9t G(G/S-CM2) = 3.5

0(W/CMZ) = Q.007 XIMLtT = -C.OC

L /D TW TP X H

(K) (K)

2.8 33 3 179

" -0.00 0. 056

7.5 i4. 320 '.ltJ6 0.00 0.053

12.2 t*. 322 1 86 0. OG 0.052

16.9 337 '.186 0.00 P. 0'+7

21 . 6 i+. 369 '.186 0.01 0. 0 39

2 6.3 '.3'*'i '.186 0.01 0. 0'+'+ 31.0 „• , J+.3!*5 '+. 1 86 0.01 0. 0'+5

35.7 ^.351 '.186 0.01 0.^+3

kC .k '+.373 '.186 0.01 0.038

^5 . 1 i+.372 '.186 0.02 0. 038

P{ATM) = i.O J &(G/S

Q(rt/CM2) = 0,023 XlMLi

L/0 TW

( K)

2 . i '.373

7.5 • i^. 37H

12.2 '. 373

16.9 . !. 3 8^

2 1.6 . '.39'}

26.3 '.'12

31 . J <. '32

35.7 . k,k27

H 0 . ^ ;^ . ' . < 0 G ^5 . 1 '.'10

C M 2 ) = 3.9

= -C.C2

Te X H

(K ) (W/CM2

'.17'+ -0. 01 0. Ilk

'.196 -0. 01 0. 125

'.219 -G. 00 0. it+a

^.225 0 . 00 0. l'+3

'.225 0. 01 0. 138

'.225 0. 01 G. 122

'.225 c

.

02 0. 109

'.225 0. 03 0. 112

'.225 0. 03 0. 130

'•225 0. 0'+ G. 123

F(ftTM) = 1.0-f 3(G/

C(H/CM?) = 0.063 XINL

L/0 TW

( K

)

2.6 '.^5 9

7.5 ','55

12.2 '+. '3 9

16.9 '5 6

21.6 '.'5 6

2 6.3 '.'9 3 31.0 i*. 50 :J 35.7 U,kdU

kO ,k U,m7

'5. 1 '.519

-CMZ) = '.3

T = - 0. 03

T^ X H

(K) (W/CM2

'.163 -0. 02 0. 228

'.2'*0 -0. 01 0. 29'+

'.262 0. 01 0. 358

'.262 0. C2 c. 326

'.262 0. 0'+ 0. 309

'.262 0. 05 0. 273

'.262 0. 06 0. 256

'.262 0. 08 0. 28'+

'.2 62 0. 09 0. 281

'.262 a. 10 0. 2'+6

58
P(ATM) = 1.0'+

G(W/CM?) = O.ilu

G(G/S-CM2) = 3.9

XINLF T = -0.03

L /D

2 . 3 7.5

12.2

16.9

21 . 6

26.3

31 . 0 35 . 7

C • 4

h5 .

1

TW

(K)

'.^+95

^.^81

if. '61

i*. '71

£. kbS

«. 51 0 *. 525

*. i+yu

'.513

k,5kb

TB

(K)

'.228

^•26^

'.2et»

'.26'^

0. 01

3.0 2

0.05

0.07

G. IC

C. 13

0 . 16

O.le

3. 21

C . 2U

H

(W/CM2-K)

0. '35

C • 5 56

0.588

0.560

0. 576

C. £^71

0. ''5

0.505

0. '67

0. '12

P(ATM) = 1.07 G (G/S- CM2) = 10.7

0{W/CM2) = 0. 176 = -c. 05

I/O TW TB X H (K) (<) (W/CM2

2 . 8 '.518 122 -0.0'+ 0 . kk5

7.5 i*, 50 3 '.187 -0 . 03 C.557

12 . 2 k7b '.252 -0.01 0.786

16 . 9 '.298 0.00 0.938

2 1.6 t^. '+82 '.298 0.02 0. 957

26.3 '.528 '.298 0.0'+ C. 765

31 . a 535 '.298 0.05 0. 7<+0

35 . 7 U. 522 '.298 0.07 0.785

t+O .

I* '.298 C. 08 0. 70'+

k5,l ^.576 '+.298 0.10 C. 633

F(ATf1) = 1.12 G (G/S- CM2) = 8.3

0(^J/CM2) = 0. 030 XINLET = -0. 05

L/0 TW TB X H

(K) (K) (W/CM2

2.8 '. '+17 t*. 167 -G. 05 C. 119

7.5 i*. '+12 '+.18'+ -0. 0'+ 0. 130

12.2 '. '+'6 '.202 -0. Ok 0.121

16 . 3 '. '66 '.219 -0. Ok 0,120

21 . 6 '.237 -0. 03 0. 129

26 . 3 h,kd2 '+.25'+ -Q. 03 C. 130

31 . 0 '. 50 3 '+.272 -0. 03 0.128

35 . 7 £+. '91 '.289 -0. 02 0, l'+7

'0 . <+ «+. 505 '.307 -0. 02 0. 150

45 . 1 '. 519 '.32'+ -0. 02 0.152

59
F^(ATM) = 1.13 G(G/S-CM2) = 8.8

C(W/CM2) = 0.062 XINLlT = -C.C5

L /O TW Te X H

(K) (K) (W/CM2

2 . 3 ^4.4+79 166 -0.05 0. 199

7.5 1+ . U'+3 ^4. 193 - 0

.

0. 2^48

12 . 2 ^4.220 -0. Oi4 0. 2'46

16 . 3 ^4.2^6 -0 . G3 C. 253

21 . D i4.273 -0.02 0.281

26.3 ^4 . 3 0 0 -0.02 0. 267

31,0 . ^+. 57^4 ^4. 326 -0.01 0. 251

35.7 , 14.525 U . 3 5 3 -a. 00 0. 362

i+ C . U. 53 7 ^4.359 0.01 0 . 3U8

5 . 1

• U.577 ^.359 0. 01 0.285

F(ATM) = 1. 1 1 G (G/S- C^2) = 8.8

G(>^/CM2) = J . 11^4 XIMLET = - 0. C5

L/D TW T9 X H

(K) (<) ( W/CM2

2.5 U. (497 ^4.177 -0. 0^4 0.357

7 . 5 U.226 -0. 03 0.52'*

: 12.2 U . :469 U. 275 -0. 02 0.587

16 .9 k,k'i6 U.32'4 -0. 00 0. 69^4

21.6 U .

i4 9 'J i4. 335 0. 31 0.733

26.3 ^. 537 i4.335 0. C2 0.553

3 1 . U '4.561 i4. 335 0. 03 0.506

35 . 7 u, 53 G ^4.335 0. 05 0. 536

^40.^4 U. 533 ^.335 0. 06 0. 561

^45 . 1 ^4. 58 7 U. 3 35 0 . 37 0. '52

P(aTM) = 1. 11 G (G/S- CM2) = 8, 6

0{^^/CM2) = 0 . 18 J X INLET = - C. 05

L/0 TW T9 X H

(K) (K ) (W/CM2

2.6 i4. 53 7 197 -0. ou 0.580

7.5 t4, t452 i4.2 7^4 -0.02 1. 0C8

12.2 i4 . 148 3 ^4.3^1 0.00 1. 268

16 . 9 513 44.3^41 0.02 1. 0^4 21 . 6 i4. 517 i4. 3i4l 0. Oi4 1.023

2 6.3 ^4. 532 i4. 3'4l 3. C6 C. 9^4^

31 . 0 ^4 . 5 5 '-f U. 3^41 0.08 0 . 8^4 44 35 . 7 ^4.530 i4.3'4l 0.10 0. gS't

i40 . ^ U. 571 ^4 . 3 1 0. 12 0 . 781

^45. 1

t4. 63^4 3U1 C. 1^4 0. 683

60
P{ATM) = 1.12 G(G/S-CM?) = 92.5

0(W/C^'2) = 0.0^*3 XINLET = -C.C5

L/0 T W (K)

2.

a

7.5 '.'56

12.2 k.klb

16.9 '.'19

21.6 k,kZk

26.3 '.'Oo

31. J k.kl^

35.7 '.'05

'O.'^ '.'29

'5.1 '.'32

P(ATf1) = 1.12 3(3/S

Q(W/CM2) = 0.113 XINlE

7 R X H

( K ) ( W/CM2

'.168 -0.05 0.175

'•17'+ -0.05 0. 170

'.180 -0.05 0.202

'.186 -0.05 0.205

'.192 -0.05 0.206

'.198 -0. 05 0. 228

- Q . 0 ' 0.223

'.21C -0,Qk C. 2'^5

'.216 -0. Oi^ 0. 225

'.222 -0. 0'^ 0. 228

CM?) = 58.8

L/D TW TB X H (K) (K ) ( W/CM2

2 . 8 '.196 -0.0'+ 0. 391

7.5 ', '85 '.202 -0.0'+ 0.398

12.2 k, kb6 '.208 0. '3'+

16.9 <. '80 '.21'^ -0.03 C.'+23

21 . 6 '. kSk '.220 -0.03 0. '27

26.3 '.225 -0.03 0.'+30

31 . 0 k. 507 '.231 -0.03 0. '09

35.7 *. 'as '.237 -0.03 0. '56

'0 . < !. 518 '.2'^3 -0.03 0. i+ll

'5. 1 U, 532 '.2i*9 -0.02 0. 399

F(ATM) = 1.09 G(G/S-CM2) = 3'+.8

C(W/CM2) = 0.259 XINLET = -0.02

L/U IW 13 X H

(<) (K) (W/CM2

2.8 '.512 £.273 -0.01 1.078

7.5 '. '97 '.299 -0.01 1.311

12 . 2 '. '97 '.321 0.00 1. '73

16.9 '.516 '.321 C. 01 1.-330

21.6 '.510 '.321 0.02 1. 371

26.3 '.520 '.321 0.02 1. 302

31 . J '. 526 '.321 0. 03 1. 265

35.7 U, 568 '.321 0.0'+ 1. 0'+7

'0 • ^ 7. 210 '.321 0.0'+ 0. 090

t*5. 1 10. 312 '.321 0.05 0,Qk3

61
P(ftTM) ' 1.12

C(H/CM2) = 0.067

S(G/S-CM2) s 86.0

XlfJLET X -0.02

L/D TW

(K)

2.8 i4,ki7

7.5 I*. 1*63

12. Z U.'490

16.9 ^.502

21.6 '.'85

26.3 '.'as

31.0 '.'sg

35.7 '.'29

P(ATM) = 1.52 G(G/S

G(W/CM2) = 0 . 007 XIvJlE

TT D X H

1

\

\K)

J ^ d T '•2 63 -0.02 0 . 301

'.270 -0.02 0.3'^7

'.276 -0.02 0. 313

'•262 -0.02 0.307

^.289 -0.02 0.3k3

^.295 -0.02 0. 355

(.302 -0.02 0.360

'•306 -0. 02 0.558

'.315 -0.02 0. 597

(.321 -0. C2 0. '97

-CM2) * 7.2

r = -0.09

L/D TW T3 X H

(<) (K) (W/CM2

2.8 '. 5'^9 '.'9'^ -0. 09 0.127

7.5 , '•S'^a -0.08 0.139

12.2 '.563 '.502 -0.08 0.112

16 . 9 '.563 '.505 -0. 08 0.118

21 . 6 '.56 8 '.509 -0.08 0.117

26.3 '.57'^ '.513 -0. 08 0. Ill

31 . 0 '.578 '.516 -0.08 0.111

35 . 7 (.sai '.520 -0. 08 0.112

'O . ' t*» 593 '.52'^ -0.08 0. 100

k5 . 1 '.592 (.527 -0.08 0.106

P(ATM) = 1.52 G(G/S-CM2) « 7.2

Q(H/CM2) = 0.028 XIMLET « -0.09

L/0 TH TB X H

(K) (K) (W/CM2-K)

Z»f\ <».693 (.'97 -0. 08 O.l'^O

^ 7.5 '.713 '.509 -0. 08 0. 13'^

12.2 '. 736 '.520 -0. 08 0. 128

16.9 '.7i^9 '.532 -0. 07 0. 127

21.6 k.7t*h k.Skh -0. 07 0. 138

26.3 '.758 '.556 -0. 06 0. 136

31.0 (^. 770 '.567 -0.06 0.135

35.7 '. 765 (•579 -0.05 fi.ikd

kG.i* '.781 '.591 -0. 05 0.1'»5

'5.1 '•796 V.603 -0.05 0.1<^2

62
P(ATM) X G (G/S- CM2) = 7 , 1 X INL ET = •0.07

L /n TW TB1 U y n

( K) (K) ( W/CM2

2.8 W. 75

3

<t.5D8 "•-'WW 0.265

7.5 ^« 7W2 '•5 33 0.310

12.2 !»• 757 '.557 -0,05 0.325

16.9 t».772 ^.582 -O.O** C. 3'^3

21*6 <».757 '.607 -0.03 0. '3'^

26,3 <».777 '•632 -0.02 O.'^'^S

31*0 <». 777 ^.657 -0.01 O.St^O

35.7 l».77d *».675 0.00 0. 629

<>.003 '.6 75 0.01 0.506

<»5.1 <»«612 '.675 0.02 0.'^73

P(ATM) = Q(H/CH2) c 0.116C(G/S-CM2) = 7.2

KISLET = -0.08

L/D TW TB X H

(K» (K) (W/CM2

2.8 '.7'^'^ '.515 -0.07 0.507

7.5 <».731 '.559 -0.05 0.67'^

12.2 '.752 '.603 -0.03 0.777

16.9 <. 770 ^.6'^7 -0.01 o.a'^i

21 .6 '.750 '.676 0.01 1.587

26.3 '. 769 '.676 0.02 1.25'^

31.0 '. 769 '.676 0.0'^ 1.251

35. 7 '. 769 '.676 0.06 1.258

'0.'« ^•810 '.676 0.08 0.871

'5.1 ^.815 i^.676 0.09 0. 837

P(ATM) = l.'^9

0(W/CM2) = 0.175

G(G/S-CM2) = 7.2

XISLET * -0.07

L/D

2.6

7,5

12.2

16.9

21.6

26.3

31.0

35. 7

'O . < '5.1

TW

(K)

'.728

'.715

'. 7'^0

763

736

<. 757

'. 759

<. 756

«• 81'^

'.817

13

(K)

'.539

'.606

'.672

'.675

'.675

'.675

'.675

'.675

'.675

'.675

•0.06

-0.03

-0.00

0. 03

0. 05

0.08

0. 11

0. 13

0.16

0.19

H

(W/CM2-K)

0. 930

1.60'^

2. 561

1.993

2.867

2.128

2.097

2. 156

1. 26 3

1.23'^

63
F(ATM> = 1.52 G(G/S-CM2) = li».8

Q{W/CH2) = 0 . 029 Xlf^LET = -C.C9

L/0 TW TB X H

(K) (K) (M/CM2

2.6 '.605 '.'85 -0. 09 0. 2'^1

7.5 620 '.'91 -0.09 0. 225

12.2 626 '.'97 -0.08 0.22'^

16.9 6'*1 '.502 -0.08 0.209

21.6 6t»3 '.508 -0. 08 0.215

26.3 '•650 '•51'+ -0.08 0. 213

31.0 65U '•520 -0. 08 0.216

35. 7 ^.653 '.526 -0.07 0.212

' O .

t* k,b76 '.532 -0.07 0. 199

*»5.1 U. 686 '.538 -0.07 0. 196

P(ATM) = 1.52

0(W/CM2) = 0.065

S((i/S-CM2) = 15.1

XINLET « -0.09

L/0 TM TB X H

(K) (K) (W/CM2

2.8 '.738 -0.09 0.258

7.5 <. 7W5 '•'98 -0.08 0. 266

12.2 '.7<»7 '.512 -0.08 0. 279

16.9 <• 756 '.526 -0. 07 0.285

21.6 '•753 '•5'^0 -0.07 0.306

26. 3 '.7&9 '.55'^ -0.06 0. 30'^

31.0 '•771 '•566 -0^06 0. 322

35.7 '•766 '•561 -O^ 05 0. 351

'0 •' '.786 '.595 -0^05 0. 3'^3

<*5.

1

*. 797 4.609 -O.O'^ 0.3'^8

P(ATM) = l.i»8

0(W/CM2) = 0.116

G(G/S-CM2) s 1*^.6

XINLET = -0.07

L/D

2.8

7.5

12.2

16.9

21.6

26. 3

31.0

35. 7

kS. 1

TW

(K)

'.758

<. 755

'. 756

'.768

'.761

'. 768

'.767

<. 766

'.797

<. 802

TB

(K)

'. '99

'.521

'.5'^3

'.565

'.586

'.608

'.630

'.652

'.669

'.669

0.07

0.06

0.05

Q,Qk

0.03

0.02

0.02

0.01

0.00

0.01

H

(W/CM2-K)

0. ''8

0. '95

C.5'^6

0.572

0. 665

0. 728

0.8'^9

1.021

0.871

64
P(ATM) = l,kQ 5(S/S- .2

C(W/CM2) = a. 256 XISLET - -C.C7

L/0 TW Te X H

(K) (<) (W/CH2

2 • a ^,730 H.533 •>0. 06 1. 293

7 . 5 727 '.SCI -0. 0(« 1. 757

12.2 '.730 '. 630 -0.02 2.551

16 . 9 k. 7kb ^.670 O.OB 3. 369

21 . 6 U. 737 ^,670 0.02 3. 855

26.3 '.670 0* 0<» 3. '7'»

31.0 U, 7'4d '.670 0. 16 3.296

35 . 7 i+. 733 '.670 0.01 3. 756

kC . h t*. 799 '.670 9.10 1.963

k5 ,

1

^+.889 '.670 0.12 1.168

P(ATM) = l.'^7

C(rt/CM2) = 0.250

5{S/S-CM2) = It^.l

XIMLET « -0. 06

L/IJ TW T9 X H

(K) (K) (W/CM2

2.4 k, 727 '. 53'^ -0.35 1. 298

7.5 h. 72k '.563 -0.03 1.763

12 . 2 '. 727 '.630 -0.01 2. 60'*

16.9 k,7ki '.66'» 0.01 3.273

21.6 '• 73'^ '•66<^ 0.63 3.611

26.3 k» 7'tl '.66'^ 0. 0(» 3. 28'^

31. C k, 7k3 '.66l^ 0. 06 3. 198

35 . 7 k, 7Zk '.66'* O.OS 3.592

^0 • ' '.793 '•66'+ 0*10 1. 95'+

k5.i '.81'* '•66<^ 0. 12 1.676

P(ATM) - l.itS

G(W/CM2) = 0.180

G(G/S-CM2) « 1'^.3

XISLET « -0.07

L /D

2 . 8

7.5

12.2

16 . 9

21 . 6

26.3

31.0

35 . 7 'O • k

'5.1

TW

(K)

'. 7kk

k.7kZ

k, 7k3

'.753

«. 7W8

*. 753

'. 75'^

'. 7'»9

*. 793

<. 800

TB

(K)

k»51S

'.583

'.618

'.652

'.668

'.668

'•666

'.666

'.666

•0. 06

•0.05

•0.03

•0.02

•0. 01

Q.Ol

0.02

0.9V

0.15

0. 06

H

(W/CM2-K)

0. 787

0. 93'^

1. 129

1. 327

1. as9

2. 121

2. 101

2.222

1. ''0

1. 365

65
F(ATM) = 1. <4d G (G/ S- CM2 ) = 1 £ , 5

0 . 115 XIMLET = - C . 07

L / D TW TG X H

( K) (K) (W/CM2

2 . 6 £+.757 £+.5C0 -G. 07 0. £+i+9 7 . 5 U, 757 £.522 -0.06 0. £+91

12.2 757 £+.5£+£+ -0. 05 0. 5£+2

16.9 U • 75 H £.566 -0. 0£+ 0.582

21 . 6 £.763 £.567 -0.03 0. 659

26.3 £.770 £.6 09 -0.02 0.718

31.0 76b £.631 -0.02 C. '\55

3 5.7 £+ . 76£* £.652 -0.01 1.035

ki .k 795 £.670 0. 00 0.92£+

k5, 1 £.302 £.670 0.01 0. 876

P(AT'i) = 1. 52 S (G/S- CMZ) - 1£+. 8

C{H/CM2) = 0 . C23 X I N L E T = -G.C9

L/D TW 73 X H

(K) (K) (W/CM2

2.8 £+.597 £+.£87 -0.09 0. 256

7.5 £. 613 £+.£93 -0.09 0. 23£+

12.2 £+.622 £+.£+99 -0.08 0 .229

16.9 £+.633 £+. 5C5 -0. oe C. 220

21 . 6 £.639 £+.511 -0.08 0.219

26,3 £+• 6£+6 £.517 -0.08 0. 218

31 . J £. 650 £+.522 -0.07 0.221

35 . 7 £+. 655 £+.529 - J. C7 C. 22£+

^ 0 . ' £+.672 £. 53£+ -0.07 0.206

£+5.1 £+.677 £+.5£+l -0.07 0.206

P{ATM) = 1.32

0{W/CM2) = 0.030

G (G/S-CM2) =60.2

XT^LET = -0.01

L/D TW TB X H (K) (K) (W/CM2

2 . 8 £+. 55£+ £+.507 -0.01 0. 626

7.5 £. 559 £•510 -0.01 0. 605

12.2 £. 560 £+.513 -0.01 0. 626

16.9 £+.558 £.515 -0. CI 0. 700

21 . 6 £+.563 £+.518 -0.01 0. 723

26 . 3 £+.562 £. 521 -0.01 0, 726

31 . 0 £+. 5bl £+.52't -0.01 0. 798

35.7 £+.560 £.527 -0.01 0.903

£+0 . k £.575 £.5 30 -0.01 0.658

£+5 . 1 U,575 £+.533 -0.01 0,712

66
P(ATM) = 1.31 G (G/S- CM2) = 60.9

Q(W/CM2) = 0.117 XINLCT = -C. 00

L/O TW TB X H

(K) (K )• (W/CM2-•K)

2. 8 U. 632 ^.512 -0.00 0.978

7.5 ^.518 -0.00 0.932

12.2 U, 6£»5 ^.522 0.00 0. 953

16.9 i4. 6'+6 ^.522 0.00 0.9'*7

21 . 6 <+. 639 1+.522 0.00 1.008

26. ? ^.522 0. CI 0. 965

31 . 0 U. 639 4^.522 C. 01 1.005

35 . 7 tf . 636 ^.522 0.01 1.028

U. 657 '.522 0.01 0. 812

U5 .

1

667 '.522 C. CI C. 811

P(aTM> = 1.33 G (G/S- CM2) = 58. 5

Q(W/CM2) = 0.262 XINLET = - C. 01

L/O TW TB X H

(K) (K) (W/CM2- K)

2 . 6 ^.532 -0. 30 1. 9'+0

7.5 i*. 669 -0.00 2.101

12.2 '.662 0.00

16.9 t*. 673 '.5i*5 0,01 2.05'+

21.6 i+. 670 0.01 2. 100

26 . 3 'f. 676 0.02 2.008

31 . 0 671 0.02 2.081

35 . 7 U, 657 0.03 2.1'+8

<iO . k 727 5^*5 G. 03 1. '''

k5 . 1 i*. 735 0.0'+ 1.380

P(ATM) = 1,32 G (G/S- CM2) = 59.

0 (H/CM2) = 0 . 351 xinlet = -C. 00

L/O TW TB X H

(K) (K) {W/CM2- K)

2 . 8 t*. 6'*6 k. 532 -0.00 3. 160

7.5 6'*9 '.532 3. Ql 3. 0<^k

12.2 U. 6'*0 '+.532 0.01 3. 329

16.9 '.657 ^.532 0.02 2.893

21.6 1*. 650 '.532 0.02 3. 066

26.3 U. 656 k, 532 G. 03 2.90'+

31.0 U. 659 ^.532 0. 0'+ 2.836

35.7 '.656 '.532 0. 0'+ 2.855

^0 . k k. 7k7 '.532 0.05 i.67'»

^5 . 1 U. 767 '.532 G. 06 1.533

67
P(ATM) = 1.33

0(W/CM2) = 0.363

3(G/S-CM2) - 60.5

XINLET - -O.Cl

1 / n T1 Rt3 yA n

Itv 1 2.8 't. 651 ^.526 -0.00 2.915

7.5 650 '•538 0.00 3.226

12.2 6«»2 '.538 0.01 3. '81

16.9 if. 662 '.538 G.Ol 2.921

21.6 1*. 651 '.538 0.02 3. 207

26.3 i+. 661 '.538 0.03 2.955

31 . 0 673 '.538 0. U3 2.683

35.7 667 ^.538 0. 2. 3C8

U 0 .

i+ '.757 '.538 0.05 1.658

U5. 1 79t* '+.538 0.05 l.'+16

P(ATM) = 1,3J G (3/S- CM?) = 59. 2

&(W/CM2) = 0.25'+ XINLET = -0. 01

L/Q TW TB X H

(K) (K) (W/CH2

2.8 '.671 '.526 -0.01 1. 753

7.5 !. 665 '• 538 «0. 00 1.998

12.2 '. 659 !. 5t^'^ 0.00 2. 20(»

16.9 '.677 '.5'^'^ O.Gl 1.905

21.6 '.671 0.01 2.009

26.3 '.677 0.02 1.916

31.0 k, 675 0. 02 1. 9'^0

35.7 '.673 C.C2 1. 978

<. 736 0.03 1. 312

'5.1 <. 7'»3 0.03 1.278

P(ATM) = 1.32

G(H/CM2) = 0.113

G(G/S-CM2) « 62.0

XINLET « -0.01

L/0 TW TB X H

(K) (K) (H/CM2

2.9 '.636 '.50i^ -0.01 0. 6'^6

7.5 '. 6'+5 '.509 -O.Cl 0.835

12.2 '. 6'^5 '.515 -Q.Ol 0.866

16.9 *. 65'+ U.520 -0.00 0. 839

21.6 *. 6«»5 '.525 -0.00 0.937

26.3 '.652 (.53C -0.00 0.925

31. 0 '.653 '.532 0.00 0.936

35.7 '•6(f5 <».5 32 0.00 1.003

'0 . < '.682 '.532 0.00 0.751

'5 .

1

686 '.532 0. 01 0. 735

68
F(ATM) = 1.32

0(W/CM2) = 0.029

Ci(5/S-CM2) = 60.9

XISLET - -0. 01

L/D TW TB X H

(K) (K) (W/CM2

2.8 555 ^.513 -0.01 0. 68'^

7.5 fi. 561 ^.515 -0.01 0.620

12.2 556 i^. 517 -0.01 0. 733

16.9 i*. 562 ^.519 -0. 01 C. 675

21 . 6 569 '.521 -0.01 0. 607

26.3 '4. 559 '.523 -0.01 0. 788

31 . 0 't. 56o '.525 -0.01 0. 82'^

35.7 i4. 562 '.527 -0. Cl C. 826

<40 . ^ '.586 1^.529 -0.00 0. 50'^

^5 . 1 i+. 592 '.531 -0.00 0. '76

P(ATM) = 1.08

Q(W/CM2) = 0.008

G(G/S-CM2) = ',0

XI^LET = -0.01

L/0 TW TB X H

(K) (K) (W/CM2

2 . 8 tt. ^35 '.266 -0.01 0.117

7.5 '.308 '.273 -0.01 0.231

12.2 <. 353 '.281 -0.01 0. 112

16.9 t^. 361 '.288 -0.01 0.111

21 .6 <. 323 '.296 -0.00 0. 298

26 . 3 1^ . 380 '.303 -0.00 0. 095

31 . a «. 387 '.310 -0.00 0.106

35.7 '.363 '.311 0.00 0.155

'0 . h *. 380 '.311 0.00 0.118

'5 . 1 <. 377 ^.311 0.01 0.122

P(ATM) = l.u8

0(W/CM2) = 0.029

G(li/S-CM2) = '.2

XINLET = -0.01

L/0 TW TB X H

(K) (K) (W/CM2

2.8 <. ^+05 '.266 -0.01 0.209

7.5 '.368 ^.291 -0.00 Q. 379

12.2 *. '16 '.307 0.00 0. 267

16.9 U. '27 '.3C7 0.01 0.2^^3

21 . 6 «. 393 ^.307 0. 02 0. 337

26.3 '. ''3 ^.307 0.02 0.21^

31 . 0 '.'86 '.307 0.03 0. 162

35. 7 <. ''1 '.3C7 0. OU 0.216

'0 . h !. 'Sh '.307 0. 0<f 0. 197

'5 . 1 '.'61 '.307 0. 05 0.186

69
P(ATM) = 1.07 G(G/S

Q(W/CM2) = G,062 XINLE

L/0 tw

(K)

2.{i k»kk2

7.5 U.392

12.2 k,kZ9

16.9

21.6 '.'08

26.3 ^.513

31.0 w.sm

35.7 U.^73

<. '90

^5.1 '.5C9

CM2) = U.3

= -0.01

TB X H

(K) (W/CM2

'. 276 -0.01 0. 375

'•302 0. 01 0.69'i

'.302 0.02 0. <«5'^ '.302 0.03 0.'+31

!. 302 0.05 0. 569

'.302 0.06 P. 295

'.302 0.07 0. 261

'.302 0.09 0,365

'.302 0. 10 0.350

'.302 a. 11 0.301

= 1.10 &(G/S- CM2) = '. 7 2) = 0.117 XISLET = -0. 02

L/0 TW TB X H

(K) (K) (W/CM2

2 . 8 '. 50'^ i*. 290 -0.01 0. 5'^7

7.5 '. '3'^ '.323 0.02 1.056

12 . 2 '+. '9'+ '.323 0 . QU 0. 686

16 . 9 '.509 '.323 0. 06 0. 632

21 . 6 k, i+71 '.323 0.09 0. 790

26.3 *. 5b3 '.323 0.11 C. 4^79

31.0 '+. 563 '.323 0.13 0. '89

35 . 7 '.537 '.323 0.16 0. 5'^8

'O . k 558 '.323 0.18 0. '98

^5 . 1 580 '.323 G . 21 C.'^56

P(aTM) = 1.08 &(G/S

C(W/CH2) = 0.180 XINLE

L/0 TW

(K)

2.8 '.'9 3

7.5 '.'21

12.2 '.'90

16.9 '.512

21.6 '.'70

26.3 '•551

31.0 '.5'^5

35.7 '.52'+

'O.'^ '.563

'5.1 '•581

CM2) = '.3

= -C. 02

TB X H

(K) (W/CM2

'.306 0 . 01 0. 971

'•308 0. 05 1.59'+

'.308 0.09 0.969

'.306 0. 12 0.88'f

'.308 0. 16 1.109

'•308 0. 2C 0. 7'^1

'.306 0. 2'+ 0. 761

'•308 0. 26 0.633

'.306 0. 32 0. 706

'•306 0^ 36 0^ 660

70
P(ATM) = l.Qi

G(H/CM2) = 0.143

5{&/S-CM2) = I*,

5

XI^JLET = -0.C2

L/0 T W T8 X H

( K) ( K

)

( W/CM2

2.3 '.503 i+.30'+ C. 01 0. 90^+

7.5 '.'36 '.30'+ 0. Oi^ 1. 365

12.2 i^. '82 '.3Ct* 0.08 1.012

16.9 '96 t*. 30U 0. 12 P. 937

21 . 6 '.'72 30'+ 0.16 1.070

26. 3 «. 5'42 '•30'^ 0. 20 0. 756

31.0 !. Sifl i^. 30'^ 0. 23 0. 761

35 . 7 '.527 '+.30'^ 0. 27 0.808

'O . k '. 565- '.30'^ 0 . 31 0. 690

kb . 1 '.587 ^.30'+ 0. 35 0,636

P(aTM) = 1.13 &(S/S-CM?) = 10.7

0(W/CM2) = 0.003 XINLET = -0.01

L/D TW IB X H (K) (K) (W/CM2

? . 3 '.322 '.275 -0.01 0.157

7 . 5 i*. 321^ '•277 -0.01 0.159

12.2 *. 333 '.260 -0.01 0. I'^O

16.

y

'.339 ^.283 -0. CI 0. 132

21 . 6 336 '.286 -0.01

26.3 i^. 3'^0 '.288 -0.01

31 . J k, ZkZ '.291 -0.01 0. l'+3

35 . 7 '.29'4 -0. CI C. 137

'0 . ' '.361 '.297 -0.01- 0.115

'5 . 1

i*. 360 '.299 -0.01 0.123

= 1.07 G (G/S- CM?) = 11.0

G(W/CM2) = 0.056 XISLET = -0.01

L/0 TW TB X H

(K) (K) (W/CM2

2.3 '. i+e^ '•280 -0.01 0. 320

7.5 '.'63 '•300 0^00 0^391

12.2 <. ^78 '.300 0.01 0. 369

16,9 t^. '86 ' . 3 C 0 0.01 C. 353

21 . 6 '. '88 '.300 0. 02 0. 350

26.3 506 '•300 0. 02 318

31 . a !. 526 '.300 0.03 0. 286

35.7 <• 50 1 '.3C0 0.03 C. 327

'O . ' '.516 '.300 0. 0'^ 0. 30't

'5 . 1 '.529 '•300 0.05 0.287

71
P(ATM) = 1.07

Q(W/CM2) = 0.113

G(G/S-CM2) = 10.5

XINLET = -0,01

L /D TW TB X H

(K) (K) (W/CM2

2 . a 513 <4.298 0.00 0. 527

7.5 ^. W85 <».298 0.01 0. 60^4

12.2 ^.298 0.02 0. 576

16.9 501 ^4.298 0.03 0.557

21 . tj itSd <4.298 0. ou 0. 56'4

26.3 ^4. 532 '4.298 0. 05 C. i48'4 31 . 0 5t43 <4.298 0.06 0. '61

35.7 521 ^4.298 0.07 0.507

kQ . < I*, 5k3 ^.298 0.08 0. 4461

145.1 ^4. 562 ^.298 0.09 0.^428

= 1.07 G (G/S- CM2) = ic.u

Q(W/CM2) = 0.180 XINLET = -0.01

L/0 TW TB X H

(K) (K) (W/CH2

2 . d ^4. 523 14.300 0.00 0.811

7.5 U. ^493 <4.300 0.02 0.9 36

12.2 t4. 505 ^4.300 G. QI4 0. 879

16.9 '4. 51^4 U.300 Q. 05 0. 8I42

21.6 t4. 508 ^4.300 0.07 0. 867

26 . 3 <4, 53^4 ^•300 0.08 0. 771

31.0 t4. 536 ^4.300 0. 10 0.763

3 5.7 U. 526 14.300 0. 12 0.798

uo.u '4.56 6 14.300 0.13 0. 679

^45 . 1 '4.576 <4.3 00 0.15 0.653

P(ATM) = 1.07 G (G/S- CM2) - IC. I4 Q(H/CM2) = 0.177 XINLET s -0.00

L/0 TW TB X H

(K) (K) (W/CM2

2.3 I4. 516 14.295 0,01 0. 797

7.5 l4.1»8i 14,295 0,02 0.936

12.2 I4. I482 I4.295 0,0l4 0,9ii5

16.9 I4. I473 I4.295 0.05 0.993

21.6 I4.I475 14.295 0. 07 0.977

26.3 i4. 530 I4.295 0.09 0.750

31.0 I4. 533 14,295 0.10 0, 7i»l

35 . 7 i4. 518 I4.295 0.12 0. 792

I4O .14 14.527 14.295 0,13 0. 761

l45. 1 I4. 566 14,295 0,15 0,651

72
P (ATM) = 1.0 7 G (G/S- CM2) = 1 0 . d

Q (W/C M2 ) = 0.113 X iMLL r = - 0

.

CI

L /D T W TB X H

( K) (K ) ( W/CM2

2 . 8 *+ . 't7

2

k,292 - 0

.

00 0 • 62 8 7.5 296 c

.

01 0. 762

12.2 ^.296 0. 02 0. 767

16.9 k , ^32 i*.296 0 . 03 0.835

21 . 6 ^4. i+29 14.296 0. 0'+ 26.3 i*. 511 1*. 296 G . 05 n. 527

31.0 it. 536 '.296 0. 06 0. 1^72

35 . 7 ^4. '85 '.296 0. 07 0.600

^0 .

i4 k, '.296 0. 08 0. 663

£5 . 1 '.525 '.296 0. C9 0.1+95

P(ATM) = 1.07 G (G/S- CM 2) = 10.6

0(W/CM2) = 0,Qbk XIMLET = - C. 01

1 / L / U X 1 1 T W TB . X H

( <) (K ) (W/CM2

2.8 4+. '19 !. 282 -0.00 0. '63

7.5 k,kQ5 '.3C0 0. oc 0.599

12.2 k, 1*25 '.300 0.01 0.507

16.9 '.397 '.300 0.01 0.652

21 . 6 39 j '.300 0.02 0. 700

26 . 3 !. ''5 '.3G0 02 0. '3 7

31 . J !. 500 ^.300 0.03 0. 316

35. 7 !. 1+28 '.300 0.03 Q,i*3k

kQ .k k. kl 7 '.300 0. 0'+ Q»5k2

i+5 . 1 U, 1*57 '.3C0 0.0 5 0. '03

P(ATM) = I.IQ G (G/S- CM2) = 11.0

0(W/CM2) = 0.007 KINLCT = -0. 02

I/O TW TB X H

(<) (<) (W/CM2'

2.8 '.317 '.263 -0.02 0.131

7.5 k. 321 '.267 -0.02 0.130

12.2 '.326 '.270 -0.02 0. 126

16.9 i*. 331* k.27t* -0.01 0.116

21.6 U, 331 I*. 277 -0.01 0. 131

26.3 k, 339 '.260 -0.01 0.120

31. 0 '.339 '.2e'4 -0.01 0. 128

35.7 338 '.287 -0.01 C. lifO

'C . k ^.291 -0. 01 0. l<fl

k5 . 1 3ki '.29'f -0.01 0.130

73
P(ATM) = 1.13

Q(M/CM2) = 0.008

G(G/S-CM2) = 27.5

XIMLET s -0.01

L/D TW TB X H

(K) (K) (W/CM2

2.6 ^4. 315 ^.275 -0.01 0. 193

7.5 316 ^•277 -0.01 0.19<«

12.2 319 U.279 -0.01 0.190

16.9 k. 321 it,280 -0.01 0. 191

21.6 322 <».2e2 -0.01 0. 196

26.3 '.322 <t.26<* -0.01 0.202

31.0 323 <».286 -3.01 0.209

35.7 k, 323 '.288 -0.01 0.218

^0 . U U. 327 '.290 -0.01 0. 206

'5.1 U. 327 '.292 -0.01 0.219

P(ATM) = 1.07 G(G/S-CM?) = 27.0

Q(W/CM2) s 0.066 XINLET s -0.00

L/D TW TB X H

CK) (K) (W/CM2

2 , 8 (. <f80 '.286 -0.00 0. 3'^6

7.5 «. '75 '.297 -0.00 0.372

12 . 2 <. '78 '.298 0.00 0.367

16.9 «. '82 '.298 0.00 0. 360

21 . 6 *. '76 '.298 0.01 0.370

26.3 '.'30 '.298 0.01 0. 362

31.3 '. '83 '.298 0.01 0.358

35. 7 *. '76 '.298 0.01 0. 372

IfO . ! '.'*96 '.298 0.02 0. 333

'5 . 1 ^.'97 '.298 0.02 0. 332

F(ATM) = 1.06 G(G/S- CM2) s 27.

k

C(W/CM2) = 0.177 XINLET « -0. 00

L/D TM TB X H

(K) (K) (W/CM2

2.8 •.507 '.289 0.00 0^61'*

7,5 '.'»98 '•269 0.01 0^691

12.2 '.'86 '•269 0.01 0^893

16.9 *. '95 '•289 0. 02 0^862

21. 6 '•'91 '.269 0.03 0.876

26.3 U.521 <».289 0.03 0.76<*

31. 0 526 0.7'»7

35.7 (».508 <».289 O.OV 0.606

'0 . k 5'*0 '•.269 0.05 0.707

'5.1 <. 561 «».269 0^06 0.652

74
P(ATM) = 1.07

G(W/CM2) = 0.262

GfS/S-CM?) = 26.7

XINLET = -0.00

L/C TW TR X H

In) K

)

2.d U. 515 '.299 0.00 1.216

f »o i».299 0.01 A 7 n 1 • o'+O 12. 2 '.2 99 0.02 1. 32'+

H . 5 u i '.299 0.03 9 C 1 21 . 6 '.506 '.299 0. 0'+ 1. 272

H . V C U '.299 0.05 i. • i. O 7

-J X . u aH .. 17 ?c. ?c. ^.299 0. 06 1 . 1 7 f^ O . r i*H . *1 1 1 . X X '.299 G.C7 X . C H X

iiH nU . 4 L . '^ 7 7 '.299 0.08 U . 7 o C

ii H n '.299 0. 09 U a 7 .} 5

DfATMl — 1 17 Ij I J ^ o CM2) = 27.6

57 U V T u 1 r T

^ 1 !l L L 1 r - n . nn

L/D TW 1 Y H

IK) K

)

2 . 9 '+. 511 U 5 Q ft n n n u . u u 1.287

7.5 H . '9 2

Ll 7 Q a U . U 1 1. ' 1 2

12.2 '92 '+.298 0.02 1. '16

1 b . y H . :> U • '.298 C. 03 4 7 7 7

1 . SM

21 . 6 '.502 '.298 0.0'+ 1. 3'+7

(1 b • o * • p 1 ^ '.298 0.05 7 C. 7

o 1 . U H . D 1 P '.298 0. 06 7 n 1 . c b U

7 r, 7 H . ^ L D ^.298 0.07 7 9 P 1 . o <i L

n i» H U . H

c; c, Q H . 5 D 0 ^.298 0.08 1 Die: X . U 1 7

. O C IL '.298 0.09 nU . M0

/iH cD

P(ATM) - 1 17 CM2) = 28.3

Uln/onci — u. 1 7 a ^ i IN L C 1 = -0.00

L / U T U1 w TP X un

(K) (K) (W/CM2-' K)

2.8 <. '95 *. 292 0.00 0. 883

7.5 *. '66 '.292 0.01 1,028

12 . 2 'sg '.292 0.01 1.073

16.9 *. '62 '.292 0.02 1.052

21 . 6 i^. '6'+ '.292 0.03 1. 0'+3

26 . 3 <. 519 '.292 0.03 0. 787

31 . 0 «. 527 '.292 0. Oi^ 0. 762

35.7 '.506 ^.292 G.0<+ 0.837

<40 . '.508 ^.292 0.05 0. 826

'5.1 I*, 555 '.292 0.06 0.681

75
P(ATM) = 1.07

Q(W/CM2) = 0,063

G(G/S-CM2) = 27,9

XINLtT = -0,00

L /O TW

(K)

2.8 '.397

7,5 £»,385

12.2 i*,385

16.9 k,ZS'*

21.6 '.378

26.3 k,ki^b

31.0 '.''I

35.7 '.'01

i^Q , k 'O'^

kS,l ^.'28

P (ATM) = 1.10 G (G/S

G (W/C'^2 ) = 0 . 00 8 KIHLL

TB X H

(K) (W/CM2

'.291 -Q. 00 0. 599

<».297 G. OC C. 726

'.297 0.00 0. 721

'.297 3.00 0.730

'.297 0.01 0.781

'.297 0.01 0.581

'.297 0.01 0. ''l

'.297 0.01 0.613

^.297 0.02 0 .596

'.297 0. C2 0. '6'4

CM2) = 27.3

» -0.01

L/0 TW TB X H

(K) (K) (H/CH2

2 . 8 '. 32'^ k, 2bU -0.01 0, 195

7.5 32 3 '.286 -0,01 C, 2C5

12.2 ^. 327 '.288 -0.01 0, 194^

16 . 9 k, 332 ^.290 -0.01 0.183

21.6 331 '.292 -C. 01 0. 198

26 . 3 1^, 332 '.29'+ -0.01 0.202

31.0 !, 330 '.296 -0.01 0. 22'^

35.7 k, 332 '.298 -0.01 0.223

^0 . k '+. 3k3 '.300 -3.01 0.177

'5. 1 U, Zk2 '.3C2 -0, CI C, 189

P(ATf1) = 1.93 S(G/S

Q(W/CM2) = Q.119 XINLE

L /D TW

(K)

2 . d <. 99^^

7.5 '.967

12.2 5. 010

16,9 5.0t^0

21.6 '.998

26.3 5,C3G

31,0 5,026

35.7 5.025

i+C^ 5.097

'5.1 5,099

CH2) = 13.1

= -0.C3

TP X H

(K ) (W/CM2

5.022 -0. 02

5.03C -COO

5.032 0.01

5.0 32 0.03 15. '6'*

5.0 32 0. 0'^ »•»

5.032 0.06 ««««««

5.032 0.07

5.032 0.09

5.0 32 0.10 1.830

5.032 0. 12 1. 78U

76
P(ftTH) = 1.96 G(G/S-CM2) = 13.1

Q(W/CM2) = 0.123 XINLET = -0.03

L/D TW T8 X H

(K) (K) ( W/CM2-K)

2.9 U. 995 5. 02'4 -0.02

7.5 '+.969 5.0 3U -0.00

12.2 5. Oil 5.036 0.01

16.9 5. 0*4l 5.0 36 0. 05 27. i465

26

21.6

. 3 5.

5.001

03'4

5.036

5.0 36 0.06

0. 0^4 »******

31.0 5.030 5. G 36 0.08 ******

35 . 7 5.027 5.0 36 0. C9 ****** 5.102 5.0 36 0. 11 1. gt+a

'45 , 1 5. lOi* 5,0 36 0.13 1. 991

F(ATM) = 1.99 G (G/S- CM2) = 13 . 1 0(W/CM2) = 0.13^4 XINLET = -0.0^

L/C TW TB X H

(K) (K) (W/CM2- K)

2 . 8 5.010 5.025 -C. 03 ******

7.5 <4. 990 5. 03^4 -0.02 ******

12 . 2 5.015 5.GU3 0.00 ****** 16.9 5. 039 5.0*43 0.02 ******

21 . 6 5. 013 5.0^3 0. 0*4 ******

26 . 3 5.032 0. 05 « 31 . u 5. 029 5.0*43 0.07 ****** 35.7 5.028 5.0*43 0. 09 ******

^40. ^4 5.103 5.0*43 0.11 2. 252

^45 . 1 5.106 ' 5.0*43 0. 12 2. 122

P(ATM) = 2.01 G (G/S- CM2) = 28 • 1 Q(W/CM2) = 0.193 XINLET = -0.1*4

L/D TW TB X H

(K) (K) (W/CM2- K)

2.8 5.00 5 *4.959 -0. 1*4 309

7.5 '4.995 *4,967 -0.12 7.06*4

12.2 5. 007 *4.97l4 -0. 11 6. 037

16.9 5. 028 *4.981 -0. 10 *4. 23*4

21.6 5. 006 *4.989 -0. 09 11. 268

26 . 3 5. 019 *4.9S6 -0. 07 8.596

31.0 5. 017 5.003 -0. 06 1*4. 691

35.7 5. 012 5.C11 -0.05

^40. <4 5. 089 5.018 -0. 0*4 2. 807

t45 . 1 5.091 5.025 -0.02 3.000

77
P(ATn) ~ 2»01 5 (G/S- C M £: ) = 2 7,7

X IN LcT = - 0 • Ih

-

u / u

T U 1 V Lin

\ \ 1 f u / r M 5

P R V • 'J c H La Q C ft u . m 5 n c c <i • U t> p

7 c; 7 • SJ 1 c — U . 1 O

I ^ • c o t U ck — n -ID 16.9 5. Ot+6 ^.975 -0.11 1.895

21 . 6 5.025 1+.960 -0. 10 3.026

2b . 3 5. 020 <*.985 -G. 10 3.961

31.0 5.017 '.ggi -0. 09 5.187

35 . 7 5. Old -0.08 6. 272

i+0 .i+ 5.096 5.002 -0.07 1. i^og

i*5 . 1 5. 09d 5.007 -C. 06 1. '97

P(ATM) = 2.02 G(G/S

Q(W/CM2) = J.37i+ XISlE

. . .. L / D T W(K)

2.6 '.939

' 7.5 '.912

12.2 '.929

16.9 U,9o3

21.6 ..; '.9^2

26 . 3

• !. 96 0 31.0 i+.gbS

35.7 '•953

,k 5.056

'5.1 5.071

PCATM) = 1.99 G(G/S

0(H/CM2) = 0.125 XINLE

CME) = '5.3

= -0.3'^

T3 X H

(K) (W/CM2

'.736 -0.33 1. 8'^2

'.753 -0.32 2. 353

'.770 -0. 30 2. 3'^5

'.786 -0. 29 2.119

'+.803 -0.27 2. 696

'•8 20 -0. 26 2,67'+

'.837 -0. 2'^ 2. 927

'.85'^ -0.23 3. 759

'.871 -0. 21 1. 913

'•888 -0.20 2.0'^1

CM?) = 13.3

= - 0. 0'^

L/U TW TB X H

(K) (K) {W/CM2-K)

2.8 '.966 5. 021 -0.03 »»

7.5 '.930 5.030 -0,02

12 . 2 5.002 5.0 39 -0.00

16.9 5. 0'+3 5.0 39 0.02 32. 981

21 . 6 '. 976 5.0 39 0.03

26 . 3 5.033 5.0 39 0.05

31 . 0 5. 029 5. 0 39 0. 06

35 • 7 5. 03G 5.C 39 G. C8 ««««««

'o . ; 5.107 5.0 39 0. 10 1. 825

f+S . 1 5.105 5.039 0.11 1.905

78
P (ATM ) = 2.0 1 G (G/S- CM2) = 27 • 7

Q (H/CM2) = 0.135 XIMLET = - 0 . l'*

L / U

T U1 w T1 uvX n

i 1^ \ \ <\l \ \ I / u / r" M 9 — V \

Iv J o o c » 0

1. Q C fl 4 . y tp 0 *" U . IH 2 . U t> P

-J r- t? . Jit: H . y bu ~ 0 • 1 .3 11 • f y b

12.2 5. 02i* ^+.969 -0. 12 2. i+SS

1 b .

"3 c n c»

t' » U H b H . y f t» — U . 1

1

A A Q C 1 • tjy 3

21 . 6 5. 025 U.960 -0.10 3. 026

c n o n

t> • u 2 U U.985 -0 . 10 o § y b 1 31.0 5.017 ^.991 -0. 09 5.187

t> . U 1 0 '+.996 -0.08 £L 5 7 5 b . c r 2

5.096 5.0 02 -0.07 1. i+og

^5.1 5 • ogd 5.007 -C. 06 1 . ny 7

P(ATn) = 2.02 G ( G / S- CM2) - k5,3

Q (W/C M2 ) = J . 37i+ XISl ET - -O.Si*

L / D T W T3 X H

( K) (K) ( W/Cn2- K)

2.6 . 93

9

U.736 -0. 33 1 . 8h2

7.5 U . 91

2

t».753 -0. 32 2.353

12 . 2 t». 929 ^.770 -0. 30 2. 3'»5

16.9 H . 9o 3 if .786 -0.29 2. 119

21 . & 9^2 ^+.803 -0. 27 2. 696

•DC 7 2 6.3 H . 3 b U ^4.8 20 -0.26 2 . b f H

31 . 0 965 ^.837 -0. 2U 2. 927

6b m f H • 95 J U.85W -0.23 1 7 C Q

5. 066 ^.871 -0. 21 1.913

• 1 5.071 <*.888 -0.20 2 • 0 Hi

P(ATn) - 1.93 CM2) = 13.3

Q (H/CM^ ) = 0 • 12? V T u I r T X IN L h 1 = -0. O^i

L /U T W TB X H

I K) (K) ( W/Cn2- K)

2.6 966 5. 021 -0.03 M M ! M M M

7 , 5 '.93 0 5.030 -0.02

12.2 5.002 5.039 -0.00

16.9 5. 0'»3 5.0 39 0.02 32. 981

21.6 976 5.039 0. 03

26.3 5. 033 5.0 39 0.05

31 . 0 5. 029 5.0 39 0.06

35.7 5. 03C 5.C 39 0. C6

i*Q . (4 5. 107 5.0 39 0. 10 1. 825

»*5 . 1 5. 105 5.0 39 C.ll 1.905

79
P(ftTM) = 1.9d S(G/S-CM2) = 13.

W

Q{W/:m2) = 0.113 XISLET = -0.03

1 / n L / u T U TD1 aVA n

I Is

;

1 1\ 1 2 . 8 981 5. 019 -0.02

7.5 950 5.027 -0.01

12.2

16 .9

5.

5.039

OOh

5.0

5.032

32

0.01

0.02

»

21 . 6 k, 98d 5.0 32 0 . 0^+ 26.3 5.032 5.0 32 C. 05 ******

31.0 • 5. 029 5.032 0.07 ****** 35.7 5.027 5.0 32 0. 06 ****** 5.103 5.G 32 0.10 1. bSk

5,105 5.0 32 0. 11 1. 63^+

DfATMl r\ftlH^ — 1 - 1* •3 1 G (G /S- CM2) = 13.4*

U • u o H XINLET — — u • U H

L / U TW TQ VA n (K) ( w / L n d

c • 0 5.021 c. n n Q !? • U U \7 — U . U H

c 7 n c t? . J U o

7 n 1 • O 5.002 P . U 1 H - U . u o ******

1 C . C 5. 025 p . u ly - U • U Q o 7 n y . £. 0 U 16.9 5. 0'47 5.C23 -0.01 2.701

21 . 6 5. 022 5.028 -0.01

2 6.3 5. 3«+G 5.0 32 0. oc 7. 665

31.0 5.035 5.032 0.01 20. 693

35.7 5.037 5.0 32 0.02 10. 776

i+O . ^4 5. 09d 5 .C 32 0.03 0.966

^5 . 1 5.093 5.0 32 0.03 C.956

P(AT^1) = 2. 0 0

• G (G /s- CM2) = k7 .3

Q(W/CM2) = 0 . 023 XINLET - -0.32

L/D TW TP X H

(K) (K) (W/CM2'

2 . 6 i+. 726 ^.716 -0. 32 2. 697

7.5 k, 721 ^.717 -0. 32 6. 221

12 . 2 '.739 i*. 718 -0. 32 1. 3^45

16.9 i+. 751 ^+.71^ -0. 32 0. 876

21 .6 ^4. 7'+2 U.720 -0. 32 1. 261

26 . 3 750 i4.72C -C. 32 C. 966

31.0 k, 7£t9 ^+.721 -0. 32 1.021

35.7 U. 753 ^4.722 -0. 32 0. 917

^0 . ^4 79l ^4.723 -Q. 32 C. 1423

^5 . 1 ^4. 79^4 14.7214 -0. 31 0. 14O8

80
P(ATM) = 2,00 J ( /S- CM2) = ^6 . 6

Q(W/CM2) = 0.113 XINLET = -0, 32

L /n TB

• X H (K) (K) ( W/CM2

2 . d i+. 82 7 '.719 -0,32 1.095

7,5 '.826 i^, 72^* -0.32 1.158

12.2 '.655 ^.729 -0 . 31 0. 9'+3

16.9 8d3 ^.735 - G , 31 0.796

21 , 6 7i+0 -Q. 3C 0. 9'+

7

2 6,3 ti, 980 -0.30 0 . fl?6

31 . Q tf,891 ^.750 -0.29 C, 838

35.7 k, 992 i+. 755 -0.29 0, 862

kQ ,k i+. 96G 760 -0, 29 0,591

, 1 ^.765 -0. 28 0. 586

P(ATM) = 2.0J G (5 /S- CM?) = ^6, k

Q(W/CM2) = 0.183 XINLET = - 0. 31

L/0

2.8

7,5

12,2

16.9

21 . 6

26 . 3 31 . Q 35 , 7

kC . k

k5 . 1

TW

(K)

t^. 906

'. 90 3

'.930

t^. 959

'.936

U. 958

959

*. 959

5. 01*2

5. 0«+5

TR

(K)

',7'^G

v. 748

'.756

i^, 76i^

4,771

4. 779

4.767

4. 795

4. 802

4.810

•0. 31

•G . 30

•0. 29

•0. 29

•0. 28

•0. 27

0.27

0. 26

0.25

0. 25

(W/CH2-K)

1.106

1. 180

1. 049

0. 934

1.100

1.023

1. C65

1.113

0.763

0. 777

P(ATM) = 2.0]

&(W/CM2) = 0.250

G(5/S-CMZ) = 46.6

XINLET = - C. 31

L/D TW IP X H

(K) (K) (W/CM2

2.3 4. 931 4.742 -0. 31 1. 317

7.5 4. 911 4.753 -0.30 1.575

12.2 4. 936 4.764 -0.29 1. 453

16 . 9 4. 965 4.775 -0.28 i. 314

21 . 6 4.941 4.786 -0.27 1.612

26. 3 4. 961 4.797 -0.26 1.527

31 . u 4. 962 4,8C8 -0.25 1.628

35.7 4. 956 4,819 -0.24 1. 837

40 .4 5,050 4.831 -0.23 1. 140

45. 1 5.054 4.84? -0. 22 1.179

81
P(ATn) = 2. 0 Q G (5/ S- CM2) = '7.i^

G ( W/C M2 ) = u • 37 3 X INL tr - - 0 .

L /D T W T B X H

( <) Its J ( W/CM2

2 • tt 'f. 919 1. 7 0 H » f do - U . o 1 1.953

' • 5

1 Q r*! a H • O Jo _- n 7 r

U . 51, 2 . ' 3 8

1 2 • 2 H . 92 1 '•763 -0.29 2.35 3

16.9 '.956 - U . c f 2. 123

2 1 • 6

i O O "7 '.92 3 '.797 -0. 26 2.966

26.3 9t^8 '.815 -0. 25 2.801

31.0 H . 95 1 '.832 -0, 23 3.123

3 5.7 *. st+g -0. 22 '.122

5, 063 '.867 -C. 21 1. 899

'5.1 5. 070 '.88'^ -0. 19 2.008

P(ATM) - 1. 50 G (3/S- CM2) = 62.9

Q(W/CM2) = 0 . 029 XINLET = - 0 . C 5

L/0 TW TB X H

( K) (K) (W/CM2

2.8 '.602 '.56'^ -0.05 C. 773

7.5 566 '.566 -0.05

12.2 '.603 '.567 -0. 05 0. dii^

16.9 '. 627 '.568 -0.05 0. 501

21 . 6 £.603 '.570 -J. 05 0 . 86'^

26 . 3 607 '.571 -0.05 0. 816

31 . 0 '.597 '.573 -0. 05 1. 196

35.7 U. 597 '.57'f -0.05 1. 238

,k '.621 '.575 -0.05 . 0.635

^5. 1 '.653 '.577 -0.05 0. 381

P(AT1) = 1.35 G(S/S-CM2) = 6'^. 6

0(W/CM2) = 0.171 XINLET = 0.00

L/0 TW T9 X H

(K) (K) (W/CM2

2 . 8 '.668 '. 557 0.00 1. 537

7.5 '.651 '.557 0.00 1.610

12.2 '.657 '.557 0.01 1.556

16.9 '.691 '.557 0.01 1. 276

21.6 U,661 '.557 0.01 1.6'40

26. 3 '.666 '.557 0 . 02 1. 326

31. C U. 687 (.557 0. C2 1. 311

35 .7 (.680 '.557 0. 02 1. 390

'+0 . « '. 732 '.557 0.02 0.976

'5 . 1 (. 738 (.557 0.03 0.9'^2

82
F(ATM) = 1,37 G(3/S-CM2) = 61.2

0(W/CM2) = C.305 XINLET = G.CC

L/0 TW T8 X H

(K) (K) (W/CM2- <)

2 . 8 k, 669 '+.575 0. oc 3. 252

7 . 5 65U '.575 0.01 3, 868

12.2 U. 66b '.575 0.31 3. 361

16 . 9 k, 695 '.575 0.02 2. 552

21 . & 687 '4.575 D. 02 2.729

26.3 702 '.575 0.03 2. i+ll

31 . U 't. 706 ^,575 0.03 2. 330

35 . 7 721 '+.575 J. 0'+ 2. 067

i+ , 8 0 4 '.575 0. 0'+ 1.335

h5 . 1 k, 339 '.575 0.05 1. 156

F{ATM) = 1.36 G (S/S- CMZ) = 61. 2 Q(W/CM2) = G.lUl XIMLET = COG

I/O TW T3 X H

(<) (K) (W/CM2- K)

2 , a 693 '+.57C 0. JC 1. 156

7.5 '.671 '.570 0. OC 1. i+lO

12 . 2 '.677 '.570 0.01 1.326

16 . 9 682 '.570 0.01 1. 263

21 . 6 i*. 677 '.570 0. CI 1.318

26.3 k, 706 ',570 0.01 1. 0'+5

31 . 0 U. 702 1+.5 70 0.02 1.076

35.7 693 '.570 3.02 1,152

kL .

i+ ^+. 732 ^.570 C. 02 0,371

k5, 1 t*. 737 '.570 0.02 0. 8'+7

P(ATM) = 1,06 G (S/S- CM2) = 33. 5

0(W/CM2) = 0,075 XINLET = 0. rc

L/D TW TB X H

I K

I

1 1\ 1 \ W / o n c" K I 2 . 8 t»6«t '.283 0 .00 Ckik

7.5 i+. i+61 '.283 0.00 0, '20

12.2 '.283 0.01 0. 368

16. 9 '.'87 '.283 0.01 0. 367

21 , 6 '56 '.283 0.01 0, '33

26.3 '.283 0.01 0. 393

31 , 0 U, '78 '.283 0. 01 0. 38'+

35 . 7 «. '71 '.283 0.02 0. 397

. k <• 500 '.283 0. 02 C. 3'+'+ k5 ,

1

'. '98 '.263 0.02 0. 3'+8

83
P(ATM) = 1.06 5(G/S-CM2) = 28,5

C(W/CM2) = J.2'»3 XINLET = 0.00

L/D TW T3 X H

<K) (K) (W/CM2

2. d ^4.^79 '.285 0.00 1.251

7.5 4*52 u.2e5 0.01 1. '51

12.2 k, k73 '.285 0.02 1.296

16 .9 ^.265 0.03 1. 168

21 . 6 ^.285 0. 0<^ 1.357

26 . 3 512 ii.285 1. 072

31 . C U.515 it. 285 0.05 1. 055

35.7 tt. 503 U.265 0. 06 1. 116

559 ^.285 0. 07 0.886

'5. 1 it. 570 ^.285 0.08 0. 65<^

= 1.9d G (G/S- CM2) = 13.7

0(W/CM2) = 0.008 XINLET = 0.11

L/D TW IB X H

(K) (K) (W/CM2

2.8 5. 050 5.035 0.11 0.'+96

7.5 5. 052 5.035 0.11 0. '36

12.2 5. 050 5.C35 C.li p.i^ei

16.9 5.050 5.035 0.11 0.501

21 . 6 5. 0'»9 5.035 0.11 0.5<^5

26.3 5. 050 5.035 0. 11

31.0 5.050 5.035 0.11 0. '8't

35.7 5. 050 5.035 0.11 0.(^80

'O . ' 5. 0'+9 5.035 0.12 Q*5kQ

5. 0'»6 5.035 0. 12 0. 655

P(ATM) = 1.93 G(G/S- CM2) - ik. 0 &(W/CM2) = 0.023 XISLET - 0. 09

L/D

2,6

7.5

12.2

16.9

21.6

26. 3

31. Q

35. 7 'O.'^

kS . 1

TW

(K)

5. Oi»5

5. 039

5. 0«»2

5. Ot^'+ 5. 0«+3

5. 0't6

5. 0'»7

5. Oi^6

5.052

5. 052

7B

(K)

5.036

5.0 36

5.036

5.036

5.036

5.036

5.036

5.036

5.0 36

5.0 36

0.09

0.10

0. 10

0. 10

0.11

0. 11

0.11

0.12

0.12

0. 12

H

(W/CM2-K)

7. 5't5 <. 3i^8

3.380

'•115

2.852

2.580

2.7'^'^

1.705

1.712

84
P(ATH) = 1.9'9

G(W/CM2) = O.C6it

3(3/S-CM2) = 13.2

XIMLET = 0.13

L/C TW T9 X H

(K) (K) (W/CM2- K)

2.8 5. 5.039 0.13 12. 902

7,5 5. 03^+ 5.039 0. 1(4 12. 2 5. om 5.039 0. 15 23. 070

16 . 9 5. 0't5 5.0 39 0. 16 9. 590

21.6 5. 0<iO 5.C 39 0.17 ^'.'10

26.3 5.039 0.17 11.505

31 . 0 5. Ot*6 5.0 39 0. 16 8.689

35 . 7 5. 5.0 39 0. 19 11. '65

5. 058 5.0 39 0. 20 3. 378

kS . 1 5. 058 5.039 0. 21 3. 32'*

P(ATM) = 1.9b G (S/S- CM2) = 30. 8

C{W/CM2) = 0.065 XINLET = C. C3

L/U TW T9 X H

(K) (K) (W/3M2- K)

2.8 5. 016 5.020 0.03

7.5 5. C2U 5.020 0.01*

12. 2 5. Oil 5.020 0 . 0^

16.9 5, 009 5.C2C 0. 01* 21.6 5. Oli* 5.020 0.05

26.3 5. 015 5.020 0.05

31 . G 5. 015 5.020 0.05

35 . 7 5. Oil 5. 020 G . 06

5. 022 5.020 0.06 27.620

k5,l 5. 02'+ 5.020 0.06 15. 796

P(ATM) = 1.93 G (Ci/S- CM2) = 31.

0(M/CM2) = 0.007 XIMLET = 0. 00

L/D TW T3 X H

(K) (K) (W/CM2- K)

2.9 5. 012 S.QDk 0.00 0. 880

7.5 5. 013 5.00<t 0.00 0. 790

12.2 5. Oil 0.00 1.013

16.9 5. 01

J

5.C0'» 0.00 1. 121

21.6 5. Ol't 5.0GW 0.00 0. 710

26.3 5. 013 5.Q0U 0.00 0.807

31.0 5. 012 5.00'* 0. 00 0. 887

35.7 5. Oil 5.0 G<* 0.00 1. 103

. ^ 5.010 5.00U 0.00 1.199

'5.1 5.012 5.00^ 0.00 0.965

85
F(ATf1) = 1.95

Q(W/CM2) = 0.023

G(G/S-CM2) = 30.7

XINLET = 0.00

L/0 TW X H

(<) (K) (W/CM2

2 . d 5.035 5. 016 0.00 1. i+sg

7.5 5.033 5.C16 0. OC 1.671

12.2 5. 031 5.016 0.00 1.370

16 . -3 5. 033 5.016 0.01 1. 658

21.6 5.030 5.016 G. 01 1. 978

2 6.3 5.031 5.016 0.01 1.881

31.0 5.03 3 5.016 0.01 1.678

35.7 5.031 5.016 0.01 1. 956

5.037 5. 0 16 0.01 1. 338

kB . 1

' 5.039 5,016 0. Gl 1.239

F(ATM) = 1.95

G(W/CM2) = 0.06'+

G(G/S-CM2) = 31.6

XINLET = O.CO

L/D TW TB X H

(<) (K) (W/CM2

2 . 8

' 5.023 5. 012 0.00 5. 880

7.5 5.020 5.012 0. CI 8.085

12.2 5.018 5,012 0.01 10. 628

16.9 5.025 5.0 12 0.01 715

21.6 5. 022 5.0 12 0.01 6. 108

26.3 5.022 5.C 12 G.02 6. t4kO

31.0 5.025 5.012 0.02 5. 0i»3

3 5.7 5,021 5.012 0.02 6.817

C . 5.031 5.012 0.03 3. 380

^5 . 1 ^ 5.036 5. 012 0.03 2. 708

P(ATM) = 1.0 4 G(G/S- CM2) = 56.

0(W/CM2) = 0.033 XISLET = 0. 00

L/D TW TB X H

(K) (K) (W/CM2

2. 8 i*. 958 '.96'+ 0.00 ******

7.5 U.965 '.96<^ 0.00 2.596

12.2 '.990 U.96V 0.00 0.105

16.9 U. 962 '.96U 0.00 ******

21 . 6 990 0.00 0.106

26.3 U.973 '.96<» 0. 00 0. 298

31 . 0 '.96<^ 0.00 0. 286

35.7 '.965 '.96«^ 0.00 6.33^

<«0 • <t *. 960 '.96<» 0. 00 *^***** 'S.l '.976 '•96<» 0.00

86
P(ATM) = 1.90

Q(W/CM2) = J.CQ7

G(G/S-CM2) = k2,2

XlNLtT = COG

L /D TW TB X H

2.8 5. 00 7 ceo 0.00 0.275

7 a f • J/. '3 Q 1 H • ^ 0 U U . U U r c 7 U . b 0 0

12.2 98'+ '.980 0 .00 1.770

16.9 987 ^.980 C . 0 c 1.096

21 . 6 98 5 . 9 8 0 0. 00 1. 653

26 . 3 t*. 998 ^.980 0.00 0. '19

31 . 0 ^.989 '.980 0.00 0.805

35 . 7 ^.995 '.960 0. cc 0.506

kC ,k 933 '.980 0.00 2. 199

k5 . 1 '.996 '.980 0. GO 0. '62

= 1. 90 G (G/S- CM2) = '2. 1 0(W/CM2) = 0.029 XINLET = O.OC

L/D TW 19 X H

(K) (K) (W/CM2

2.8 5. 02>:> '.980 0.00 0. 59'+

7.5 5.013 '.980 0.00 0,875

12.2 5.010 '.980 0. 00 0. 968

16.9 5. 025 '.980 0. CO 0. 651

21 . 6 5.011 £.980 0.00 0. 952

26. 3 5.017 '•980 0.01 0.799

31 . 0 5.006 '.980 0.01 1.123

35.7 5.013 '.980 0.01 C. 876

^0 . 5. 01'+ '.980 0.01 0.873

k5 . 1 5.023 '.980 0.01 0.672

= 2.03 G (G/S- CM2) = 1+5.3

0(W/CM2) = 0.06'+ XI^^LET = -0.10

L/D TW TB X H

(K) (K) {W/CM2

2.3 5.021 1+.982 -0. 10 1. 655

7 . 5 5. 003 '.983 -0.10 3. 172

12.2 5.000 i+.98'+ -0.10 3. 895

16.9 5. 016 '.98'+ -0.C9 2. 029

21 . 6 5. 00^* '.985 -0. 09 3. 328

26.3 5.013 '.986 -0. 09 2. 313

31 . 0 5. 013 <+.986 -0.09 2. 367

35.7 5.007 <+.987 -0. 08 3.229

<+C . < 5.017 <+.986 -0. 08 2,15k

kS . 1 5. 02'+ '.989 -0.08 1.80 3

87
P(ATM) = 2.00 3(G/S-CM2) = k7,8

Q(ii/CH2) - 0.117 XINLET = -0.11

L/0 TW TB X H

(K) (K) (W/CM2

2. 8 5. 007 975 -0. 11 3. 681

7.5 99'» U.976 -C. IC 6. 30'^

12 . 2 '.996 '.977 -0. 10 5. '61

16.9 5. 015 '.977 -0.10 3.129

21 . 6 5.00 3 '.978 -0.09 '. 699

2 6.3 5. COG '.9 79 -0.C9 5.62'^

31 . 0 5.00 3 '.960 -0.08 5.110

35 . 7 ^4.990 '.981 -0. 06 6.872

£0 . k 5. 019 '.981 -0.07 3. 093

'5 . 1 5.020 '.982 -C.C7 3. 086

= 1.93 G (G/S- CM2) « (1.6

0(W/CM2) = 0.266 XINLET e O.CO

L/D TW TB X M

(K) (K) (H/CM2

? . 8 k, 992 5. 000 0.01

7.5 '.988 5.0C0 0.02

12.2 5.009 5.000 0.03 27. 31i^

16.3 5. 059 5.000 0. Oif '.'87

21 . 6 5.055 5.000 0.05 '. 789

2 6.3 5. 106 5.0C0 0.06 2. '90

31.0 5.097 5.000 0.07 2.728

35. 7 5. 11+8 5.000 0. 08 1.789

i+O . k 5. 217 5.000 0.09 1.219

^5 . 1 5. 25G 5.000 0.10 1. 059

P(ATM) = 1.97 G(G/S-CH2) « 11.9

C(W/CM2) = 0.123 XIvJLET » C.02

L/D TW TB X H

(K) (K) (H/CM2-K)

2 . 8 5.015 5. C26 0.03

7.5 '.970 5.026 0.05

12 . 2 5.008 5.026 0.07

16.9 5.029 5.026 0.06 '3.'^97

21 . 6 5.001 5.026 0.10

26 . 3 5. 022 5.026 0.12

31 . 0 5.022 5.026 0.13

35 . 7 5. 02'^ 5.026 0.15

'G . k 5.081 5.026 Q.17 2. 26'^

'5.1 5.11'^ 5.026 0. 19 1. '03

88
P(ATM) - C {W/CM2)

1.53

= u . 008

S(G/S-CM2) - 15,8

XINLET - -0.21

L / 0

Til T W 7B X H

(K) (K) (W/CM2

2.8 £.073 £.026 -0, 21 0.175

7.5 £.071 £.0 29 -0.21 0. 19£*

12.2 083 £.0 32 -0.21 0. 160

16.9 090 £.0 35 -0, 21 C. 151

21 . 6 U. 089 £+.0 38 -0.21 0.161

26.3 £. 095 £. 0£+l -0. 21 0.153

31. 0 £+.096 0 £+£ -0. 21 0.155

35 . 7 £.10 1 £. 0 £+7 -0. 21 C. 153

I4G . k £.108 £.051 -0. 21 0. l£+2

^5 , 1 £+. Ill £+,05£+ -0, 21 0. l£+£t

P(ATM) = 1.5 3 G (3/S- CM?) = 15. £

12) = 0.03!+ XINLET = -0. 21

L /D TW T9 X H

( K) (K) (W/CM2

2 . 8 £.220 £.032 -0. 21 0. 182

7.5 £. 223 £+.0£i£4 -0.21 0. 191

12 . 2 £+. 26£+ £.055 -0. 20 0. 16£i

16.9 £. 288 £.067 -0. 20 0.155

21.6 £.237 £.079 -0. 20 0. 165

26 . 3 305 £•091 -0.20 0.160

31 . 0 £. 31£* £.102 -0.19 0.162

35 . 7 £. 329 £+.ll£+ -0. 19 0.160

£0 . £4 £.357 £.126 -0.19 0. l£+8

£5 . 1 £.365 £•137 -0.19 0.151

P(AH) = 1.5J &(G/S-CM2) = 16.

C

0(W/CM2) = 0.065 XISLET = -0.21

L/0 TW TB X H

(K) (K) (W/CM2

2.6 £.39 0 £.037 -0.21 0.185

7,5 £. £+02 £.059 -0.20 0. 191

12 . 2 £. £f66 £.061 -0.20 0. 170

16.9 £.503 £.103 -0. 19 0.163

21 . 6 £.505 £+.12£+ -0. 19 0. 172

26.3 £. 53'+ £+.l£+6 -0.19 0. 168

31 . 0 £. 551 £.167 -0.18 0. 171

35.7 £. 575 £.189 -0. 18 0. 169

£0 . £ £.626 £.211 -0.17 0.158

£5.1 £.636 £.233 -0.17 0.162

89
f(aTM) = G (W/CM2)

1.53

= 0.115

G(G/S-CM2) = 15.9

XINLFT = -C.21

I/O

2 . 8 7.5

12 . 2

16.9

21 . 6

26. 3 31.0

35. 7 ^40.^

'5 . 1

P(ATM) = 1.50 G(5/S-CM2) = 16.2

0(W/CM2) = 0 . 253 XINJLET = -0.21

L / D TW TB X H

(K) (K) (W/CM2

2. 3 U. 726 067 -0. 20 0. 3e'«

7.5 6'»7 U.13C -0. 18 0. '90

12.2 £.710 -0.16 0. 'go

16. 7'-*5 -0.15 0.518

21 . b 707 '.320 -0.13 0. 65'*

26.3 738 '.383 -0.11 0. 715

31 . 0 U. 736 -0.09 €.87'*

35 . 7 i*. 733 ',510 -C.Ob 1.13'4

^0 . k 818 '.573 -0.06 1.036

k5 . 1 '.319 '.637 -0. Ot^ 1. 385

TW TB X H

(K) (K) (W/CM2

k. 652 k, Zkh -0. 21 0. 190

'.653 '.082 -0.20 0.201

'.721 '.117 -0. 19 0.190

752 '.152 -0.18 0. 191

k, 725 '.188 -0. 17 0. 213

U. 752 '.223 -0.17 C. 217

'. 75C '.258 -0. 16 0.233

756 '.29'^ -0. 15 0. 2'+8

'.813 '.329 -0. 1'^ 0. 237

'.813 '.365 -0.13 0. 255

P{ATM) = 1.50 G (G/S- CM2) = 33.9

Q(W/CM2) = 0.0o3 xislet = -0. 21

L/0 TW TB X H

(<) (K) (H/CM2

2 . 8 k, 205 k, C29 -0. 21 0. 360

7.5 '.212 '.0 39 -0.21 0. 365

12.2 k, Zkl '.050 -0.21 0. 329

16.9 '.261 '.060 -0.20 0. 31<»

21 . 6 '. 261 £.070 -0. 20 0. 329

26.3 '.280 '.080 -0.2C C. 316

31 . 0 '.287 '.090 -0.20 0. 321

35 . 7 '. 29o '•100 -0.20 0. 323

'0 . k '. 329 '.110 -0. 19 0. 269

k5 . 1 338 -.121 -C.19 0.290

90
P(ATrt) = 1. 50 G (G/S- CM2) = 33.6

Q(W/CM2) = 0. 113 XINLET = -0.21

L/0 TW

• TB X H

(K) (K) (W/CM2

2.8 k, 3!+0 it. 033 -0. 21 0. 367

7.5 k, 352 ^4. 050 -0 . 21 0. 37'+

12.2 '.oea -0.20 0. 336

16.9 '.0 86 -0. 20 0. 323

21.6 k,k3Z h,lQk -0.19 0. 3'+3

26. 3 '.121 -0.19 0. 327

31 . 0 k, k77 '.139 -0.19 0. 33'+

35.7 '.157 -0.18 0. 3'40

. k, 5W9 '+.175 -0.19 0.303

^4. 563 '.192 -0.18 0.305

P(ATM) = 1. 50 G (G/S- CME) = 33.9

0(W/CM2) = 0.251 XINLET = -C.21

L/0 TW TB X H

(K) (K) (W/CM2

2.8 '.677 -0. 21 0. 397

7.5 '.651 '.080 -0.20 O.'^'^O

12.2 i^. 695 '.117 -0.19 0. '35

16 . 9 '.723 '.153 -?. 18 0. ''1

21 . 6 '.699 '.190 -0.17 0. '93

26 . 3 '•720 '.226 -0.17 0.509

31 . Q '. 715 '.262 -0. 16 0.552

35 . 7 '. 715 '.299 -0. 15 0. 60'+

'0 . ^ '.799 '.336 -0.1'4 0. 5'^2

^5.1 '.802 '.372 -0.13 0. 58'4

P(ATM) = 1.50 G (G/S- CM2) = 3'^. 0 C(k//CM2) = 0.512 XINLET = -0. 21

L/0

2.8

7.5

12.2

16.9

21.6

26.3

31 . a 35 . 7 'O . < '5.1

TW

(K)

*. 678

'.611

'+. 657

'.697

'. 659

'.689

*. 69'»

k, 678

t*. SZi*

U, 83d

TP

(K)

'.062

k,iZ3

'.3C6

'.367

'.'26

'.'89

'.550

'.611

0.20

0. 16

0.17

0.15

0.13

0.12

0. 10

0. 06

0. 07

0.05

H

(W/CM2-K)

0. 833

1. 051

1. 08'*

1.133

1. '51

1.592

1. 931

2. 715

1. 673

2. 261

91
P(AT«) - 1.50

Q(W/CM2) = 0.112

G(G/S-CM2) = i+S.O

XINLPT = -0.17

1 / n L / UT U T VA

11n (K) (K) (W/CM2

2 . 8 383 £13 -0. 16 0. 661

7.5 U. 391 ^.222 -0. 16 C. 663

12.2 'le '.231 -0. 16 0. 599

16.9 U. i+36 i+.2*»0 -0.16 0.573

21 . 6 i+. i+37 ^.2^9 -0.15 0. 595

26 . 6 '.258 -0. 15 0. 587

31 . 0 ^. t»58 '.267 -0. 15 0.587

35 . 7 i*. ''9 ^.276 -0.lt* 0. 6U7

i+C . ^ U. t+95 ^.285 -0.11+ 0. 53tf

^5. 1 U. 506 <+.29'* -0. IW C. 529

P(ATM) = 1.53

Q(W/CM2) = 0.212

3(&/S-CM2) = '5.6

XIvJLtT = -C.17

L / 0 TW TB X H

CO (K) ( W/CM2

2 . 8 '.219 -0. 16 0. 651

7.5 k. 559 '.236 -0.16 n. 655

12.2 '.601 '.253 -0.15 0. 609

16 . 9 '.628 '.270 -0.15 0.591

21 . 6 !. 626 it. 2 8 7 -0. 1'^ 0. 625

26.3 <. &'' '.3C'+ -O.l'^ 0. 623

31 . 0 <. e5k '.321 -0.13 0.636

35.7 <. 6'+3 '.338 -0.13 0.693

^0 . k k. 721 '.355 -0.12 0.579

^5.1 '.732 '.372 -0.12 C. 588

P(ATM) = 1.50 G(G/S- CK2) = '5.5

C(W/CM2) = O.t^lS XINlET = -0. 16

I/O TW TB X H

(K) (K) ;W/CM2

2.8 k. 652 '. 235 -0. 16 0. 999

7.5 '.613 '.266 -0. 15 1. 18'^

12.2 <. 6t^0 '.297 -0. 1'^ 1.21'^

16.9 '.673 '.329 -0. 13 1.209

21 . 6 k, bkQ '.360 -0. 12 1. ''' 26.3 '.663 U,391 -0. 11 1.530

31 . 0 '.668 '.'22 -0.10 1.692

35.7 k,(ik6 '•'53 -0.09 2.137

'O . < k, 763 '.'a'^ -0.08 1. '90

'5.1 '.758 k,5l5 -0. 07 1. 6'+7

. 92
F(ATM) = 1.50

C(W/CM2) = 0.557

G (G/S-CM2) = kk,i^

XlU^zT = -C.16

L/D TW TB X H (K) (K) (W/CM2

2.8 U , 638 250 -0.15

7.5 595 -0.lt* 1. 793

12 . 2 619 ^+.319 -0.12 1.858

16,9 k, 659 '.35'* -0.11 1. 828

21 . 6 63U t+.386 -0.10 2.270

26. 3 't. 652 ^.^23 -0.08 2. ^+28

31.0 t*. 658 -0.07 2. 775

35 . 7 U, 633 ^92 -0.05 3. 95^+

i+O . H i*. 785 U.527 -0 . 0i» 2. 162

'5.1 U. 796 U.561 -0.03 2. 379

P(ATM) = 1.36 &(G/S

C(H/CM2) = 0.113 ><INlE

L/D TW

(K)

2.8 t+.675

7.5 '.656

12.2 it. 678

16.9 U.65 6

21.6 it. 665

26.3 '.655

31.0 i+.657

35.7 k.okS

kQ,k it. 675

k5 .1 682

CM2) = 57.7

= 0. 00

TB X H

(K) (W/CM2

566 0.00 1.033

^.566 0.00 1. 131

'+.566 0.01 1.006

^.566 0. CI i. 225

'.566 0.01 1. li+S

'.566 0.01 1.269

'.566 0. 01 1. 2'+5

'+.566 0.02 1. 368

'.566 0.02 1. 031+

'+.566 0.02 0.975

P(ATM) = 1,36 G(G/S

Q(H/CM2) = 0.395 XINLE

L/0 TW

(K)

2.8 '.660

7.5 ',6'»0

12.2 '.657

16.9 i*.662

21.6 '.652

26.3 ',711

31.0 '.711

35.7 '.709

kU,t* '.860

'5.1 '.897

CM2) - 57,3

= C, 00

TB X H

(K) (W/CM2

',565 0,00 U. 070

'.565 0.01 5.171

'.565 0.02 '.209

k,5S5 0.03 3.971

'.565 0.03 I*. '38

'.565 0.01+ 2.6'+ < '.565 0.05 2. 630

',565 0.05 2.681

',565 0.06 1.307

'.565 0.07 1. 160

93
P(4TM) = 1,1*1*

Ci(W/CM2) = O.im

G(G/S-CM2) = 37.0

XIMLET = 0.00

L /O TW TB X H

( <) (K) (W/CM2

2 . 8 7(+0 ^.632 G. 00 1. 056

7.5 h, 730 ^.632 0.01 1. 163

12.2 735 ^.632 0.01 1.105

16.9 '.739 '.632 0.01 1. 062

21 . 6 '.632 0.02 1. 059

26.3 7i»u '.632 0. 02 1.053

31.0 7W0 '.632 0.02 1.057

35.7 '.632 0.03 1.052

UO . k k, 759 '.632 J. 03 0. 696

^5.1 763 '.632 0.03 0.865

P(ATM) = l.'^3 G(G/S- CM2) = 23. ' 0{W/CM2) = 0.11'^ » 0. 13

L/0 TW TB X H

(K) (K) (W/CM2

2.8 *. 726 '.628 0. 13 1. 155

7.5 k, 720 '.628 Q*lk 1. 231

12.2 '. 726 '.628 0.1'^ 1. 160

16.9 '.735 '.628 0.15 1.063

..21.6 '. 731 '.628 0. 15 1. 101

2 6.3 '.738 '.628 0. 16 1. 03'^

31,0 t*, 736 '.628 0. 16 1.057

35.7 '. 735 '•628 0.17 1.066

k. 756 '.628 0.17 0. 687

'5.1 '. 759 '.628 C. 18 0.868

P(ATM) = 1.10 G(G/S- CM2) = 36.9

Q(W/CM2) = 0.028 XINLET * - 0

.

07

L/0 TW TB X H

(K) (K) (H/CM2

2 . d '. Ill '.027 -0. 07 0. 3<^0

7.5 116 *.: 32 -0.07 0. 338

12.2 '. 127 '.037 -0. 07 0. 315

16.9 '. 13'« '.0'^2 -0.07 0. 310

21 . 6 '.139 '. 0'^7 -0.07 0. 306

26. 3 *• 151 '.C52 -0.07 P. 285

31 . 0 *. 151 '.057 -0. 07 0.300

35.7 '.152 '•062 -0.07 0. 31'^

'0 . k <. 170 '.066 -0.07 Q.Z7W

'5 . 1 '.173 '.071 -0. 06 0.260

94
P(ATM) = l,i*k

&(W/CM2) = 0.11'+

G(G/S-CM2) = 37,0

XIMLET = 0,00

L/0 TW TB X H

(<) (K) (W/CM2

2 . 3 k, 7ki if .632 0. 00 1. 056

7,5 k, 730 if ,632 0,01 1. 163

12.2 if. 735 if .632 0,01 1,105

16.9 if, 739 if .632 0,01 1. 062

21 . 6 if. 7'fU if . 632 0.02 1. 059

26,3 if,7ifu if .632 0, 02 1,053

31. 0 if . 7ifa if .632 0.02 1,057

35.7 if. 7if

a

if ,632 0,03 1.052

»k if. 759 if .632 J. 0 3 0. 696

hb . 1 if . 76 3 if .632 0.03 0. 865

P(ATM) = l.if3 G (G/S- CM2) = 23. if 0(W/CM2) = O.llif XINLET = 0. 13

L/D TW TB X H

(<) (K) (W/CM2

2 . 8 if. 726 if .628 0.13 1. 155

7.5 if , 720 if ,628 a . lif 1,231

12,2 if , 726 if, 628 0, lif 1, 160

16.9 if , 735 if ,628 0.15 1.063

21.6 if. 731 if .628 0, 15 1. 101

26,3 if , 738 if. 628 0, 16 1, 03if

31,0 if, 736 if .628 0, 16 1.057

35,7 if, 735 if ,628 0,17 1.066

ifO.if if. 756 if. 628 0.17 0. 887

if, 759 if .628 C. 18 0, 866

P(ATM) - I.IQ G(G/5-CM2) = 36.9

Q(W/CM2) = 0,023 XI^^LET = -0.07

L/D TW TB X H

(K) (K) (W/CM2

2 . 8 if. Ill if. 027 -0.07 0. 3ifO

7.5 if, 116 if .C 32 -0,07 G. 338

12.2 if, 127 if .037 -0. 07 0. 315

16.9 if , 13i4 if.0if2 -0.07 0. 310

21 . 6 if. 139 if . Oif7 -0.07 0. 306

26,3 k, 151 if,C52 -0,07 C.285

31 . 0 if , 151 if. 057 -0.07 0. 300

35.7 if , 152 if .062 -0.07 0. 3i<f

ifO . if if. 170 if. 066 -0.07 0, 27<»

if5.1 if . 173 if. 071 -G. 06 0. 280

95
C / A T M ) - 1 1 — Unci —

\m \ n f \^ n 1 • u • X X c A X ^ U C 1 CP

-

L / 0 TM TR1 \J Y n

( K) ( K) ( W/CM2

' 2.3 km D29 0 . 3 i* 9

7.5 . 37

0

U . C i»7 0 7 U • J *t vJ 12.7 U* .. U*^ 3u rtu n 7 u • o c o 16 .>J -0. 07 0. 323

21.6 u. 'sg ^.103 -0. 06 0. 332

26 . 3 t*56 ^.121 -0. 06 0. 33^+

31 . 0 (+67 If. 1^0 -0. 06 0. 3U1

35.7 U .^476 U.159 _ f> — u . 05 C. 3^+9

i+0 . ^* 522 ^.177 -0. 05 0. 323

^5 . 1 i*. 532 '.196 -0. 05 0.332

P(ATM) = 1,10

0(W/CM2) = 0.175

G(G/S-CM2) - 32.8

XINLET = -0.07

L/D TW TP X H

(K) ( K) (W/CM2

2.8 *, ^76 '.037 -0.07 0. 399

7,5 U , kbb '.061 -C. 06 0.'+35

12.2 k. k76 '.066 -0.06 0. ''6

16.9 *. '92 '.111 -0.05 0. '61

21 .6 <, '86 '.136 -0.05 0. 501

26.3 U,50k '.161 0.511

31.0 i*. 51<+ '.186 -0,0'+ 0. 53'+

35.7 '.517 ',211 -0, C3 0. 572

kQ . k U . 553 ',235 -0.03 0. 536

'5.1 '.561 '.260 -0.02 0. 58<+

P(ATH) = 1,05 G (G/S- CM2) = 31.7

Q(W/CM2) = 0,3t+0 XINLET r -0. 06

L/0

2.8

7.5

12.2

16.9

21 .6

26 , 3

31 . 0 35.7

'0 . k

'5 . 1

TW

(K)

*. '97

'. '66

k. '83

I*, 506

<. '90

'.501

502

'.'96

'.587

'.592

TR

(K)

'.o'+e

'.135

'.179

'.223

'.267

'.276

k,Z7b

'.276

'.276

0. 05

'0.0'+

0.03

0. 02

0.01

0.00

0.01

0.02

0.03

0.0<^

H

(W/CM2-K)

0. 758

0.909

0. 960

1. O'+O

1. 27'+

l.'*51

1. 506

1.550

1. 092

1.077

96
P(ATM) = 1.26

Q(W/CM2) = 0.113

G(G/S-CMZ) = 30.

XINLFT = -0.12

L /D TW TB X H

(K) (K) (W/CM2

2 . 8 U. 270 '4. 0142 -0.12 0. '495

7 . 5 '.291 '4.055 -0.11 0. '431

12.2 '4.313 ^4.068 -0.11 0. '465

16 .<:) k, 33'i '4.082 -0.10 0. '450

21.6 '• 3t*k '4,C 95 -0.10 0. '457

26 . J i*. 356 '4.109 -C. 10 0. '459

31 . 0 ^4. 371 '4.122 -0. 09 0. '456

35 . 7 ^4. 377 44. 135 -0.09 0. '470

'G . k '.'426 '4.1^49 -0. 09 0. '4C9

1*5 . 1 1*37 '4.162 -o.de 0. '413

P(4TM) = 1.13 G(G/S-CM2) = 13,5

C(W/CM2) = 0.C65 XIMLET = -C.C7

L/Q TW 18 X H

(K) (K) (W/CM2

2.6 '4. '420 '4.0 5'4 -C.C7 0. 167

7 . 5 '4. '457 '4.057 -0.07 0.161

12.2 '4. '48'4 '4.080 -0. 06 0.160

16 . 9 '4. '499 '4.102 -0.06 0. 162

21 . 6 '4.500 '4.125 -0.05 0. 172

26 . 3 <4.511 '4.1'48 -0. 05 0.177

31 . 0 '4.519 '4.170 -0.0'4 0.185

35 . 7 '4. 516 '4.193 -9 3 014 0. 199

l*C . '4 '4. 550 '4.216 -C. 03 0.193

'45 . 1 I*, 553 '4.238 -0.03 0.205

P(ATM) - l.O-i G(G/S-CM2) = 13.9

0(W/CM2) = 0.116 XINLET = -0.C7

L/D TW TB X H

(K) (K) (W/CM2

2,8 «4. 523 '4.0<4l -0.06 0. 2'4l

7.5 «4,509 '4.075 -0. 05 0.268

12.2 '4. 515 '4.108 -0. 05 0.286

16.9 '4.528 '4.1'42 -0. 0'4 0. 301

21 . 6 t4.523 '4.176 -0.03 0.335

26.3 «4. Skk '4.210 -0.02 0. 3(48

31 . 0 '4.2'4<4 -0.01 0. 386

35 . 7 t*,5kl '4.2 78 -0. 01 0. ''1

.(* <4.5dO '4.307 0.00 0.'^27

'5.1 '4.580 '.307 0.01 0.<^26

97
P{ATM) = l.Od G(G/S-CM2) * 13.7

Q(W/CH2) = 0.175 XIMLET = -0.07

L/D TW TP X H

(<) (K) {W/CM2

2.6 k,5i<i '.051 -0. 06 0.37'.

7.5 <t.503 <*.103 -0. 05 0. '38

12.2 '.511 -O.OV 0.'»93

16.9 k, 527 (.207 -0.02 0«5'^e

21 .6 '.520 '.259 -0. 01 0.670

26.3 '•539 '.306 0.00 0. 753

31.0 ^. 537 '•306 0.01 0.761

35 . 7 k» 531* '.306 0.03 0. 770

<*0 . k '.590 '.306 0,0k 0. 618

'5.1 <».590 (.306 0.05 0.618

= 1.10 CM2) » 1'^.5

Q(«/CM2) = 0.063 XINLET = -0.07

L/D TW TO X H

(K) (K) (W/CM2

2.6 '•'06 (•037 -0.07 0.172

7.5 k. 'la -0.07 0. 177

12.2 '•'17 (.081 -0. 06 0^189

16.9 '.'09 '.lO'^ -0. 06 0^207

21.6 '•'06 '•126 -0.05 0. 225

26.3 <. ''3 (.l'^9 -0.05 0^215

31.0 <. '5'* '.171 -0.0'^ 0^ 223

35.7 '. 'SI '.igs -0. 0'^ 0^2'^5

'0 •< '.'55 '•215 -O.Oi^ 0^26'^

'5 .

1

'. '73 (.238 -0.03 0^269

P{ATM) = 1.95 G(&/S- CM2) = 7.2

Q(W/CM2) = 0.160 XINLET = -O.l'^

L/0 TW TB X

(K) (K)

2.3 '•966 '•909 -0.12

7.5 <. 986 '.9'^0 -0.08

12.2 '.983 (.972 -0. 0'^ 16.9 '.988 5.003 -0.01

21 . 6 '.986 5.011 0.03

26.3 '.991 5.011 0. 06

31.0 '•969 5.011 0. 10

35^7 5^78'^ 5.011 0.13

'0 .< 7. 56'^ 5.C11 0. 17

'5.1 7.869 5^011 0.20

H

(W/CM2-K)

2.070

3. 377

l'^.'»99

0.207

0.063

0. 056

98
P(ATM) = 1.97 G (G/S- CH2) = 7. 2

0(W/CM2) = 0.155 XlfJLCT = -0.16

L/0 TW TR X H (K) (K) { W/CH2

2. i 5.012 -0. lit 1.695

7.5 5. om -0.10 2. i+Ul

12.2 5,008 '.978 -3.06 5. i+8C

16.9 5. Oli* 5.010 -0.03 38. 991

21 . 6 5.013 5.031 0.01

26.3 5. 021 5. 0 31 0.05 ******

31 . 0 6. 762 5.0 31 0. 09 0.095

35 . 7 7. 676 5.031 0.13 0.063

^0 . k 6. 093 5.0 31 0.17 0, 05k

kS . 1 e. 113 5.031 0. 20 0. 05i+

F(ATM) = 1.15 G (G/S- CM2) = 9. 5

G(W/CM2) = 0.256 XINLET = -0. 05

L/0

2.

a

7. 5 12.2

16.9

21 . 6

26. 3 31 . C 35 . 7

^0 . k

k5. 1

TW

(<)

^.505

k,52k

529

i*. 589

7.810

13. 30 3

TO

(K ) ^•222

^.322^

^.372

U.3 72

^.372

i+. 372

U.372

^.372

it. 372

i*.372

O.OU

0. 01

0.01

0. 0<4 0. 06

0.09

0. 12

0.1<4

0. 17

0. 19

H

(W/CM2-K)

0. 897

1.977

2. 2C0

1. 691

1»652

1. 628

1, 396

1. 18<*

0.075

0.029

P(ATM) = 1.50

0(W/CM2) = 0.253

G(G/S-CM?) = 7.1

XINLET - -0. 08

L /D

2 . 8

7.5

12.2

16 . 9

21.6

26. 3

31.0

35 . 7

1

TW

(<)

i*. 720

U. 708

h,73k

i*. 759

i». 733

k. 7bk

7. 556

12. bkO

16. 331

18. 559

TP

(K)

if. €67

'.687

if. 687

'.687

687

'.667

if.ee?

if.eer

•0.05

0.01

0. C3

0.07

0. 11

C. !<

0. 18

0. 22

0.26

0. 30

H

(W/CM2-K)

1.566

<. 655

5. 'ifi^ 3.5t^9

5.51i^

3. 312

P. 086

0. 032

0.021

0.018

99
P(ATM) = l,tt7

Q(W/CM2) * 0.273

G(S/S-CM£) r lit.l

XINLET = -C.C7

L/0 TW T8 X H

(K) (K) (W/Cf^2

2 . 8 <i.632 ^.533 -0.05 1.822

7 . 5 i*.585 -0.03 3. '58

12.2 t*. 7i.k <*.637 -0.01 3.511

16.9 U.729 ^.663 0.01 091

21.6 666 <4.663 0.03

26.5 k, 799 <i. 663 0.05 1. 981

31.0 U. 759 ^.663 0. 07 2. 822

35.7 if. 876 **.663 0. 09 1. 268

<iO . k 900 ^.663 0.12 1. 1'tl

k5,l 5.905 663 0. lU 0.218

P(ATM) = l.i»8 G (G/S- CM2) = Ik,

5

Q{W/CH2) = 0.28'+ XINLET = -0. 07

L / 0 TW 7B X H

(K) (K) (W/CM2

2.8

' 728 '.528 -0.06 l.'^21

7.5 k, 725 '.582 -O.O'^ 1.982

12.2 k. in '.635 -0.02 3. 089

16.9 k. Ikk '.672 O.Cl 3.990

21.6 '.736 '.672 0.03 '.'67

26. 3 7t»2 '.672 0. 05 k,09k

31.0 k* 7k7 '.672 0.07 3. 81'^

35.7 k. 7^k ^.672 0. 09 2. 33'f

5. 769 '.672 0. 11 0. 259

W5.1 8. 253 '.672 0.1'^ 0.079

P(ATM) = 1.^5 G (G/S- CM2) = 1'^. < G(W/CM2) - 0.308 XINLET = -0. 07

L/D TW TB X H

(K) (K) (W/CM2

2.8 '.722 '.533 -0.06 1.623

7.5 '.718 k.SSi -0.03 2. '09

12.2 *. 721 k.bk'i -0. 01 '.279

16.9 ^.739 '.671 0.01 '.569

21.6 '.730 '.671 0. 0'^ 5. 210

26.3 '.739 '.671 0.06 '.579

31.0 '. 91'^ '.671 0.09 1.265

35.7 6. 755 '.671 0.11 0. i<*a

kO ,k 11. 103 '.671 0.13 0. 0'^8

kS»l 13.196 '.671 0.16 0.036

100
P(ATM) = I, 3k G(G/S-CM2) = 56.3

Q(W/CM2) = Q,ki^b XINLET = -O.Cl

I/O TW TB X H

(K) (K) (W/CM2

2 . 6 U. 637 -0.00 *. 936

7,5 k» 637 ^.551 0.01 5. 191

12.2 '.633 ^.551 0.01 5. '67

16.9 '.653 '.551 0.02 U. 380

21 . 6 k. 65^ '.551 0.03 k. 356

26.3 i^. 690 '.551 C. 0*^ 3.219

31 . 0 k, 766 '.551 0.05 2.077

35.7 '.96 9 '.551 0. 05 1. 068

(C . k 5. 331 '.551 0. 06 0. 573

i+5 . 1 5. 561 '.551 0.07 0. ''2

P(ATM) = 1.31 5(G/S

0(W/CM2) = 0 . 530 XINLt;

L/0 TW

(K)

2 . •) k. 616

7.5 '.615

12.2 '.627

16.9 '.803

21.6 5.522

26.3 6.507

31.0 7.287

35 . 7 7. 9'^5

. k 8. '52

'5.1 6. '28

CM2) = 61.2

= -0. 00

T8 X H

(K) (W/CM2

'.528 0.00 6. 053

'.528 0.01 6. 139

'.528 0.02 5. '02

'.528 0. 03 1.933

'.528 0. O^^ 0. 533

'.528 0.05 0. 268

'.528 0.06 0.192

'.528 0.06 0.155

'.528 0.07 0.135

'.528 G. 08 C. 136

P(ATM) = i.Oa G(G/S

Q(W/CM2) = 0.212 XI>iLL

L/0 TW

(K)

2.8 '.'86

7.5 '.'17

12.2 '.'36

16.9 '.509

21.6 '.'66

26.3 '.5'#1

31.0 '.535

35.7 '.518

'0.'* i*»5&k

'5.1 8.135

CM2) = '.6

= -0. C2

TB X H

(K) (W/CM2

<. 30't 0.01 1. 163

^.30i+ 0. 05 1. 877

'.30'+ 0. 10 1. 152

'.30'* 0. 1<4 1.031

'. 30'^ 0. 16 1.307

'.30<f 0.23 C.893

^.30^ 0. 27 0. 915

0.31 0.989

'.30'+ 0. 36 0. 756

'.3C'* 0. 055

101
PfATM) = 1. 1 1 G (G/ S- CM? J = <. . 5

w • w L V X -0.03

L / n TU TB

• Y un

( K) (K

)

? . ft • "T W V 1.672

• X w ^ • ^ w u 0-05 U.*t . QU ?C 1X * • *J O w X1 .. AO 1V ^o 16.9 '.501 <«.360 0. l<f 1.612

21.6 k, kbb (i.360 0. 19 2. 100

26.3 4. 535 <*.360 0. 2U 1.297

31 . 0

t*. 531 <i.360 0. 29 1. 331

35.7 <».522 <4.360 0. 31* l.'»07

^0 . W 6.370 ti.360 0. 36 0.057

^5.1 13. 961 i«.36Q 0.(*3 0. 02<»

P(ATM) = 1. 0 7 G(G/S- CM2) = «.&

Q(W/CM2) = 0 . 20 9 XINLET « -C.02

L/0 TW TB X H

(K) (K) (W/CM2

2.8 '93 '.302 0.01 1. 093

7,5 '. '27 '.302 0.05 1.660

12.2 (. 'S'^ '.302 0. 09 1. 1'^5

16.9 502 '.3C2 0.1'^ 1. OtfO

21 . 6 '. '73 '.302 0. 16 1.222

26. 3 '.530 (•SOZ 0.22 0.883

31.0 ^* 53'^ '.302 0. 27 0. 698

35.7 '. 521 '.302 0. 31 C.952

'O . <* '.578 '.302 0. 35 0. 756

'5 . 1 6. 791 '.302 O.'^O 0. 08'i

P(ATM) = i. u 7 G(3/S- CM?) = 10.5

G(W/CM2) = 0 . 2'*7 XINLET = -COO

L/D

2.<1

7 . 5

12.2

16 . 9

21 . 6

26.3

31 . a 35 . 7 (0 . " ^5 . 1

TW

(K)

'. 515

'. '35

'. 502

'. 507

'. 506

£. 52'^

*. 526

«. 51'*

'.59'^

6. 233

TB

(K)

'.299

'.299

'.299

'.299

'.299

'•299

'.299

'.299

'.299

'.299

0.01

0.03

0.05

0. 07

0. 10

0.12

0. 1'^ 0.16

0.19

0. 21

(W/CM2-K)

1. l'+7

1. 336

1. 22'^

1. 192

1. 196

1. 101

1. 092

1.151

0. S'^O

0.128

102
P(ATM) = 1.07

G(W/CM2) = 0.257

G(G/S-CM2) = 9.8

XINLET - -0,00

I/O TW TB X H

(<) (K) (W/CM2

2 . 8 k. 522 '.296 G. 01 1.137

7.5 '+.'83 '.296 0.0'+ 1. 373

12.2 '.296 C . 06 1.300

16.9 '.511 '.296 0.08 1. 195

21 . 6 k, '98 '.296 0. 11 1. 276

26.3 '.519 '.296 C. 13 1. 15'+

31.0 'i. 520 '.296 0.16 1.151

35 . 7 '.505 '.296 0. le 1.229

^0 . H k. 853 '.296 0. 21 0. '62

'5.1 10. oi: '.296 C . 23 0. 0'+5

F(ATM) = 1,07

Q(W/CM2) = 0.2'+5

S(G/S-CM2) = 10.3

XINLET = -0. 00

I/O

2 . d

7.5

12.2

16. 9

21 . 6

26.3

31.0

35 . 7

'O . ' (5.1

TW

(K)

k. 517

'89

500

512

502

'.527

U, 529

'.633

'.571

5. '01

T9

(K)

'.301

'.301

'.3C1

'.301

'.301

* . 3 C

1

'.301

'.301

'.301

'.301

0.01

0.03

0.05

0. 08

0. 10

0. 12

0.1<+

0.17

0. 19

0. 21

H

(W/CM2-K)

1. 139

1.306

1.232

1. 162

1. 218

1.085

1.077

0. 7'+0

0. 907

0. 223

P(ATM) = 1.07

Q(W/CM2) = 0.297

G(G/S-CME) = 27.1

XIML£T = - C. 00

L/0 TW TB X H

(K) (K) (W/CM2

2. 8 «. 509 '.296 0.00 1. 397

7,5 '.'86 '.296 0.01 1. 5'+'+ 12.2 «. '9 2 '.296 0.03 1. 519

16.9 '.505 '.296 0.0'+ i.'+ia

21 . 6 '. 502 '.296 0.05 1. ''3

26.3 '.513 '.296 0.06 1. 369

31. 0 '.51'^ '.296 0.07 1. 359

35. 7 '. 502 '•296 0.06 l.'^'fO

kC . ' '. 866 '.296 0. 09 0. 520

'5.1 8. 666 '.296 C. IC D. 068

103
P(ATM) = 1.9d

Q(H/CM2) = 0.163

G(G/S-CM2) = 13.1

XINLET = -C.C3

L/D TW T3 X H

{ K) (K) (W/CM2-K)

2 . 9 U. 990 5.025 -0.02

7.5 '.963 5.C35 0.00

12 . 2 5. OO** 5.0 35 0.02

21

16.9

. 6

5.036

k, 995

5.035

5.035 0.

0,Qk

07

»******

26 . 3 5. 0£*2 5.035 0. 09 2'*.878

31 . 0 5. '59 5.035 0. 11 0. 383

35.7 5. 596 5.035 0.13 0. 289

kQ . k 6. 21+6 5.0 35 0.15 0. 13^^

45.1 6. 305 5.035 0. 17 0.128

= 1.99 CH2) = 13.3

Q(W/CM2) = 0.172 XIMLET = -0.05

L/0 TW TB X H

(K) (K) (W/CM2-K)

2.8 <. 991 5.020 -0. Qt* ******

7.5 '.967 5.0 33 -0.02

12.2 5.005 5.0<+'* 0.00 ****** 16.9 5. 035 0.03 ******

21 . 6 5.021 5,Qkk 0.05 ******

26. 3 5. '33 0.07 0.<*(*2

31 . 0 5. 918 0.09 0. 197

35 . 7 6. 296 5. cut* G . 12 0. 138

1*0 . <* 6. 508 0. 1'^ 0.116

'5.1 6. '91 0. 16 0.119

P(ATf1) = 1.93 G(G/S-CM2) = 27.8

Q(W/CM2) = 0.250 XINLET = -0.11

L/C TW TB X H

(K) (K) (W/CM2

2.8 5.019 '.957 -0. 10 k, 056

7.5 5.012 '.968 -0.09 5.688

12.2 5. 016 '.979 -0.07 6. 7'»8

16.9 5. 03i^ '.990 -0. 06 5.677

21.6 5. 010 5.001 -0.0'* 26.575

26. 3 5.028 5.012 -0.03 15. 356

31 . Q 5. 0'*7 5.023 -0. 01 10. 358

35.7 5.085 0. OC <».837

(0 .< 5. 186 5.03<* 0. 02 1. 6<*'» k5 .

1

5. ''d 5.03U 0.U3 0.603

104
F(ATM) = 1.97

0(W/CM2) = 0.281

3(ii/S-CM?) = 27,

U

XINLET - -0.10

L /O

2 . 3 7.5

12.2

16 . 9

21 . 6

26.3

31.0

35 . 7 hO • 14 '5 . 1

TW

(K)

5. 00^+

'.992

5.002

5. 03'+

5. 211

5. 622

5. 703

5. 536

5.971

5.971

TB

(K)

k,377

t+.989

5.0 01

5. 0 li+ 5.G26

5.030

5.030

5.030

5,030

0.09

•0.07

0,06

Q,Qk

Q. 02

0. 01

0.01

0.03

0.0 5

0.06

H

(W/CM2-K)

7. 075

18. 82d

20. 9'»7

8.532

1. '20

0, '72

0. '18

0. 3'*9

0. 299

0. 299

P(ATM) = 1.9 a 0(W/CM2) = 0.276G(ii/S-CM2) = 28.0

XIMlET = -0.12

I/O TW T9 X H (<) (K) (W/CM2

2 . B 5.059 '.956 -0. 11 2. 687

7.5 5. 067 ',968 -0,09 2, 799

12.2 5, 02t+ ',960 -0,07 6. 21'+

16.9 5,070 '.992 -0. 06 3.5 32

21.6 5. 202 5. 00'^ -0 . 0'^ 1. 398

26.3 5.113 5.016 -0.02 2.850

31 . 0 5,317 5.028 -0.01 0. 957

35 . 7 5, 382 0.01 0. 795

'O . * 5.857 5.0 3'^ 0.03 0. 336

k5, 1 5. 927 5. 03'+ 0.309

P(ATM) = 1.9 6 & (G/S- CM2) = 27. 1 0(W/CM2) = O.Zf+o XINLET = -0. 09

I/O TW TB X H

(K) (K) (W/CM2

2 .8 5.008 '.966 -0.08 5. 888

7.5 '.992 '.977 -0. 06 16. C08

12.2 5.00 3 '.988 -0. 05 15.689

16 , 9 5.031 '.999 -0.03 7.535

21 . 6 5.011 5.009 -0.02

26.3

31 . 0 5.030

5. 010 5.020

5.02'4

-0.

0.01

CO

»

38. 789

35.7 '.989 5,02'+ 0.02 ******

'O . < 5. 312 5.02'^ 0. O'f Q. 853

'5 . 1 5. 297 5. 02'* C. 05 0.901

105
P(ATf1) = 2.01

Q(W/CM2) = Q,k55

G(G/S-CM2) = 1*5,3

XINLET = -0.33

L/0 TW TB X H

(<) (K) (W/CM2- K)

2.8 '.921 -0. 32 2.538

7.5 '.899 '.762 -0. 30 3. 320

12 . 2 k. 919 '. 781 -0.26 3. 311

16.9 '.956 i+.eci -0. 26 2. 931

21 . 5 '.927 '.821 -0. 25 k, 276

26 . 3 i^. 951 '.S'^l -0.23 !. 11^2

31 . 0 1** 956 '.861 -0. 21 I*, 691

35 . 7 1*. 960 '.880 -0. 19 5.711

kO . ^ 5.200 '.goo -0.18 1.517

k5 . 1 5. 275 '.920 -0. 16 1. 281

F(ATM) = 1.98 G Ci/S- CM2) = 13. !

Q(W/CM2) = 0.171 XINlET = -0.

L/0 TW TR X H

(K) (K) (W/CM2- K)

2.8

7.5 14.925

'.961

5.029

5. 016

-0.01

-0.03 »

12.2 I*, 991^ 5.0 3t4 0.01

16.9 5.037 5.0 3i4 0.03 71. 2i^8

26.

21 . 6

3 5.

'.976

060

5.03t»

5,0Zk

0.06

0.06

»

6. 723

31.0 5. 300 5. 0 3'^ 0. 10 0. 6'^i4 35.7 5. 9'^9 5.03'^ C.12 0.187

'40.'* 6. kkZ 5.03'^ 0. II4 0.122

• '5.1 5.03i^ 0. 16 0.123

P(ATM) = 2.00 G (G/S- CM2) = I47 • 0 Q(W/CM2) = 0.'+71 XI^^LET = -0. 31

L/0 TW IB X H

(K) (K) (W/CM2- K)

2.8 '.907 '.7i^9 -0. 30 2.967

7.5 I*, 832 '.768 -0.28 '.12'^

12 . 2 1*. 908 I*. 767 -C. 27 3. 907

16.9 !. 9'49 '.807 -3.25 3. 312

21 . 6 1*. 921 '.826 -0. 23 <. 9614

26. 3 !. 960 '•8'+6 -0,21 1+.119

31.0 !. 992 ! . 8 65 -0.20 3. 706

35 . 7 5.000 14.885 -0. 18 1^. G6i4

1*0 .

i* 5. 230 14.901^ -0. 16 1.1* <*2 1*5,1 5,t*05 i^.92i^ -O.IU 0.978

106
P(ATM) = 2.00

G(W/CM2) = 0.578

G(G/S-CM2) = it6.9

KIMLET = -0.31

L/D TW TB X H

(K) (K) (W/CM2

2 . 8 895 'i. 755 -0. 29 '.125

7.5 ^.897 ^.775 -G. 27

12.2 5. 060 ^.796 -0. 25 2. 193

16 . y 5.589 ^.817 -0.23 0. 74+8

21 . 6 6. 037 '.838 -0. 21 C. '82

26 . 3 6. 32 8 '+.8 58 -C.19 0. 393

31.0 6.205 '.879 -0.17 0. '36

35 . 7 6. i*06 '.goo -0. 15 0. 38'+

^0 . k 6. 70*4 '.921 -0. 12 0. 32'+

k5 .

1

6. 695 '.9'+l -0. 10 C. 329

P(ATM) = 1.36 G(G/S

0(W/CM2) = 0.363 XlNue

L / fJ T W (K)

2.8 '.651

7.5 '.632

12.2 '.656

16.9 4+. 689

21.6 '.658

26.3 '.711 " 31.0 '.73'+

35.7 '.87H

'0.'+ 5.055

'5.1 5.326

CM2) =61.3

= 0.00

TO X H

(K) {W/CH2

<. 567 G. 00 '. 32'+

'.567 0.01 5. 611

'.567 0.02 '• 08'^

'.567 0.02 2.963

'.567 0. G7 3. 981

'.567 0.03 2.515

'.567 0.0'+ 2.171

'.567 0.05 1. 180

'.567 0.05 0. 7i42

'.567 0. 06 0. '76

P(ATM) = 1.06 G(G/S-CM?) = 31.5

Q(W/CM2) = 0.298 XINLET = 0.00

L/0 TW T9 X H

(K) (K) (W/CM2

2.8 <. '69 '.285 0.01 1.617

7.5 *. ''6 '.285 0.01 i.6'»2

12.2 i^. '76 '.285 0. 02 1.555

16 . 9 <. 50 J '.285 0.03 1. 38U

21 . 6 '.285 0. Qif 1. 677

^6.3 '.502 '.285 0.05 1. 369

31 . 0 '.506 '.285 0. 06 1,3'»7

35.7 <. '93 ^.285 0.07 1. '28

<«0 •'« 5. ''0 U.2e5 3. 08 0.258

1*5 . 1 9.505 '.285 0.06 0.057

107
P(ATM) = 1.06

C(W/CM2) = 0.313

G(G/S-CM2) » 30.

C

XINLET = 0.00

L /D TW TP X H

(K) (K) (W/CM2

2.6 if . i*6 3 '.285 0.01 1. 763

7.5 '.285 0.02 2.057

12.2 1*. t»69 U.285 0.03 1.698

16.9 U. '96 '.285 0. Qt* 1. '86

21.6 1*56 '.285 0. 0'^ 1.805

26. 3 i*. 498 '.285 0. 05 1. '68

31.0 '.503 '.285 0.06 1. '3'^

35 . 7 '.375 '.285 0.07 0.530

<40 . k 9.357 '.285 0. 08 0. 062

k5 , 1 11. 579 '.285 0.09 0. 0<*3

= 1. Oo G (G/S- CM2) = 29.'+

0(W/CM2> = 0.331 XI>JLET = 0.00

L /D TW TB X H

(K) (K) (W/CM2

2.8 '.286 0.01 1.903

7.5 k. k'65 '.286 0.02 2. 221

12.2 k,k7Q '.286 C.03 1.801

16.9 <. '98 '.286 Q,QU 1.560

21 . 6 '.'58 '•286 0.05 1.926

26. 3 *. '97 4.286 0. 06 1. 570

31.0 '.586 4.286 0.07 1. 102

35 . 7 8. 969 '.286 0.08 0. 071

'O . ' 12. 56i^ (•286 0. 09 O.QtfO

'5 . 1 13. 5'^3 '.286 0.10 0. 036

P(ATM) = 1.06 G(G/S-CM2) = 29.0

G(M/CM2) = 0.3'*3 XIMLET = 0.00

L/0 TW TP X H

(K) (K) (W/CM2

2.8 (•288 0.01 2^072

7.5 !. '31 (.286 0. 02 2. 395

12.2 (. '65 (.288 C.03 1.9(*0

16.9 (.288 1,667

21.6 '.'53 (•288 0.05

26.3 «. '92 (.288 0.06 1. 665

31.0 5. '51 (.288 0.07 0.295

35. 7 10.928 (•286 0. 06 0.052

lU. 151 (•286 0^10 0^035

(5.1 It*, 7'*5 (.288 0. 11 0. 033

108
P(ATrt) = 1. 06 3 (G/S-CM2) = 28.7

G(W/CM2) = 0.350 XINLET = C.CO

L /D T W T3 X H

(K) (K) (W/CM2

2.8 t*. '57 U.291 0.01 2. 104

7.5 i*,291 0.02 2.455

12 . 2 '.291 0.03 1.963

16 . 9 U.291 0.04 1.683

21.6 456 ^.291 0.05 2.116

26 . 3 '4.503 ^.291 0. 06 1. 648

31 . 0 7.if93 '.291 0. 06 0.109

35 . 7 12. 179 i*. 291 0.09 0. 044

. ^ 15. 36W 4.291 0.10 0.032

^5 . 1 15. 636 4.291 0.11 0.031

P(ATM) = 1.9 3 G (G/S- CM2) = 12.3

C(W/CM2) = 0.113 XIMLET = 0. 18

L/0 TW TB X H

( K) (K) (W/CM2-K

2.8 5. 036 5. 043 0. 19

7.5 5. :26 5.043 0. 20

12 . 2 5. 034 5. 043 0. 22

16 ,9 5.043 5.043 0. 24

21 .b 5. 041 5.043 G.25 ******

26 . 3 5. 167 5.043 0. 27 0.915

31.0 5. 220 5.043 0.26 0.643

35 . 7 5. 3S3 5.0 43 0. 30 0. 354

4C . 4 5. 583 5.043 0. 32 G. 210

45.1 5.616 5.043 0. 33 0. 198

F(ATf1) = 1.96

C(M/CM2) = 0.193

&(G/S-CM2) = 29.8

XINLET = 0.01

L/Q TW TB X H

(K) (K) (W/Crt2

2.8 5.012 5.018 0.02 ******

7.5 5.004 5.016 0. 03 ******

12.2 5.021 5.018 0. 04 73.916

16.9 5. 050 5.018 0.05 5. 980

21 .6 5.111 5.C18 0.06 2. 075

26. 3 5. 179 5.018 0.07 1.201

31.0 5.134 5.018 0.08 1,166

35. 7 5. 241 5.018 0.09 0. 865

4C .4 5.39C 5.018 G.IO 0.519

45. 1 5.437 5.018 0. 11 0.461

109
P(ATM) = CM?) r 18.7

A X W ^ 1

L / n TR

•

X un

( K

)

\ ~ # w n ^

c • o U * 7 Q ri '.136 -0.17 n . 7?

7

12.2 '.688 U . i !7 C. 73i^

£iH .. 7?f C Q3 ^.270 -0.13 n 7 7 li U . f f * 21.6 68b L 7 17 — nU • inX u 1. 01<^

c c • o ••HUH u • y o

11.117 1 1 Q

•3 1 . U U 7 9 7 '.'71 -0.06 1 . mu 35.7 '.718 '.538 -0. 0^4 1.977

<4. 883 -0. 02 1. 258

^5.1 6. 950 '.669 0.00 0.156

P(ATM) s l.i»7 G(5/S- CM?) = li^. 5

C(W/CM2) = 0.350 XIMLET r -0.20

L/0 TW Te X H

(K) (K) (H/CM2

2.8 1*. 706 <. 067 -0. 19 0.5(^8

7.5 '.636 '.152 -0.16 0. 721+

12.2 U. 639 '.238 -0.13 0. 776

16.9 <. 726 '.323 -0. 11 0. 868

21.6 ^.689 '.'09 -0.08 1.250

.26,3 713 '•'9<^ -0.05 1.567

31.0 k. 718 '.580 -0.03 2. 536

3 5.7 U. 711 14.665 0.00 7.526

'O . ^4 827 '.665 0.03 2.15'^

'5 .

1

5. 032 '.665 0.05 0.952

P(ATM) = 1. ^8 G {5/S- CM2) = ik. 6

C(W/CM2) = 0 . 366 XINLET - -C.20

L/D

2.8

7.5

12.2

16.9

21 . 6

26.3

31. 0 35.7

'0 . <4 '5. 1

TW

( K)

'. 708

l4. 6'4l

k» 69C

'.727

'.692

'.716

'. 719

<. 725

5. 189

12. 238

TB

(K)

'.073

'.161

'.250

(.'26

'.515

'.6C3

'.670

'.670

'•670

-0. 19

>0.16

0. 13

-0. IC

0. 08

-0.05

-0. 02

0.01

0.03

0. 06

H

(W/CM2-K)

0. 576

0* 763

0. 831

0. 9'4l

1. 377

1.79'»

3. 152

6. 591

0.705

0.0'^A

110
F(ATM) = 1.1*7

Q(rt/CM2) = O.I43I

G(&/S-CM2) = Ik,

5

XINLET = -0.20

L/D TW IP X H

(K) (K) (W/CM2

2.3 k, 69b -0.18 0.703

7.5 '.629 '.leg -0.15 0. 981

12.2 '+.679 '.29'+ -0.11 1. 121

16.9 W. 718 '.'CO -9.08 1. 352

21 . 6 £.687 k,5tiS -0.05 2.363

26 . 3 5. 333 '.610 -0.02 0. 596

31.0 15,3143 k. 662 0. 02 0. O'+O 35.7 2G. 195 '.662 0.05 0.028

i+G . k 27. 673 '+.662 0. 08 0.019

'45 . 1 26. 33U '.662 0.11 0. 020

P(ATM) = 1.50

0(W/CM2) = 0.559

G(G/S-CM2) = 33.9

XINLET = -C.21

L/D TW TB X H

(K) (K) (W/GM2

2.8 '.668 '.065 -0. 20 0.925

7.5 '.603 '.126 -0. 16 1.170

12 . 2 k. bkd '.186 -0.16 1.209

16.9 U. 690 '.21+7 -0. 1*+ 1. 261

21 . 6 «. 6'*9 '.307 -0.13 1. 63'*

26.3 '.681 '•366 -G. 11 1.78'+

31 . 0 1*. 686 '.'29 -0.09 2. 167

35 . 7 '.676 '.'89 -0.07 2.978

i+O . < 5. 50'+ '.550 -0. 05 0, 585

'5 . 1 11. 555 £•610 -0.03 0.080

= l.'*5 G (G/S- CM2) = 33.8

Q(H/CM2) = 0.703 XIMLET = -0.18

L/D

2.8

7.5

12 . 2

16.9

21 .6

26.3

31.0

35.7

<iO . 't kS , 1

TW

(K)

'. 6'+5

'.581

'.62 5

'. 7u5

13. 009

18. '70

21. 038

23. 051

28. 122

2'+. '20

TR

(K)

'.078

'.153

'.227

'.301

'.375

'.'50

'.5 2'+ '.598

'.629

111

0.17

-0.1^

0. 12

•9. 10

-0. 06

•0.05

0.03

0.01

0.01

0.0<»

H

(W/CM2-K)

1.2'+2

1. 766

1. 7'*2

0. 062

0. 050

0. 0'*3

0. 038

D.030

0.035
P(ATM) = 1.50 CM2) = 5

0(W/CM2) = 0. 62 0 XINLET » -0.16

, I/O TW TB X H

(K) (K) {W/CM2

2.8 k, 629 <. 25'* -0. 15 1. 655

7.5 '.590 '.288 -0.13 2.053

12.2 <**609 '.322 -0. 12 2.157

16.9 U. 65 0 '.356 -0.10 2.108

21.6 '.623 '.390 -0.09 2. 662

26.3 (*• bkZ -C. C7 2.8'^3

31.0 '.651 '•'58 -0. 06 3.210

35.7 t4. 62'* '.'92 -O.O'^ '•688

k. dl<f '.526 -0.02 2. 150

^5.1 5.W09 '.560 -0.01 0. 730

P(ATH) = 1.36 G (G/S- CM2) = k2,0

C(W/CM2) = 0. 675 XINLET = -O.IG

L/0 TW TB X H

(K) (K) (W/CM2

2.8 '. 288 -0.09 2.010

7.5 ^.576 '.3'^0 -0.07 2.860

12.2 '.600 '.391 -0.06 3.231

16.9 '• 6<i<^ '.''3 -0. 0'^ 3.372

21 . 6 <. 616 '.'95 -C. 02 5. 567

26.3 '.638 '.5'^7 -0.01 7. '13

31.0 766 '.570 0.01 3.'^39

35.7 6. 550 '.570 0.03 0.3<^1

'O . k 10. 737 '.570 0. 0'^ 0. 110

'S.l 11.912 *. 570 0.06 0.092

P(ATM) = 1.36 6(G/S-CM2) = ''.3

0(W/CM2) = 0.712 XINLET = -0.10

L/D TW TB X H

(K) (K) (W/CM2-K)

2.8 '.611 '.266 -0. 09 2. 065

7.5 '.569 '.320 -0. 08 2.857

12.2 '.587 '.373 -0.06 3.338

16.9 '.635 '•'27 -O.O'^ 3. '32

21.6 '.60'^ '.'81 -0. 03 5. 799

26.3 '.682 '.535 -0.01 '.82'^

31. 0 6. 261 '.566 0.01 0.'»20

35.7 10. 570 '•566 0.Q2 0.119

'O.'^ 13.101 '.566 O.O'^ 0.08t>

'5.1 13.985 *».566 0.06 0.076

112
P(ATM) = 1.36

Q(W/CM2) = 0.625

G(iS/S-CM2) = <43.6

XINLET = -O.IC

L/0 rw ^ B X H

(K) (K) (W/CM2

2. a 606 ^.290 -0.09 2.616

7 . 5 U. 562 '4,353 -0.07 3. 9'+9

12 . 2 k. 580 '4.4+15 -0. 05 5.016

16 .'rJ 5. 6dO -0. C3 0.686

21 . 6 12. 571 k,5i*0 -0.01 0. 103

26. 3 15. 571 4+. 570 0.01 0.075

31 . 0 17. 252 i4.570 0. 03 0.065

35 . 7 19. IQh '4.570 0.05 C. 057

kQ . it 22, 73k '.570 0.07 0.04+5

^5. 1 lb* a?

a

'4.570 0. 09 0.058

P<ATM) = 1.3o

0(W/CM2) = O.'45o

G(3/S-CM2) = 59.5

XI^^uET = 0.00

L/D

2. d 7.5

12 . 2 16.9

21 . 6

26 . 3 31 . 0 35. 7

^40 . k k5 .

1

TW

(K)

44. 651

44. 625

4+. 6'42

44. 761

t+. 919

5. 1445

5. 232

5. 4+09

5. 785

6,037

TB

(K)

44 . 5 64+

4+, 5644

44 . 5 64+

44 . 564+

. 564+

• 5 64+

. 564+

. 5 64+ .564+

.564+

0.00

0,01

0.02

0, C3

0, 04+ 0. 04+ 0.05

0. 06

0.07

0,06

(W/CM2-K)

5. 295

7,559

5. 909

2. 318

1,287

0. 786

0. 684+

0. 54+C

0. 374+

0,310

F(ATM) = C(W/CM2) = 0.277

&{S/S-CM2) = 23.8

XINLET = C.13

L/D

2 . 8

7.5

12.2

16.9

21 . 6

26.3

31 . C 35 . 7

4+0 . ^

445 . 1

TW

(K)

4*. 705

44. 669

44. 70 1

4+. 717

44. 719

5.000

44. 9^46

5. 197

5. 589

5. 892

7B

(K)

4+.627

4+,627

4+. 627

4+.627

44 . 6 27

44. 627

44. 627

44. 627

44. 627

4+,627

0, 13

0. 15

0. 16

C. 17

0.18

0.20

U. 21

0.22

0.23

0. 25

H

(W/CM2-K)

3,536

*4«4+56

3.708

3. 079

2,998

0,74+3

0,868

0,4+66

0,288

0, 219

113
P(ATM) = 1.05 G(G/S-CM2) = 31.1

Q(H/Cf^2) = Q,kQk XI^LET = -0.06

L/D TW TB X H

(K) (K) (W/CM2

2 . 8 <4. <»8^ 053 -0.05 0. 937

7.5 k57 '.1C6 -0. O** 1. 152

12.2 '.159 -0.03 1.295

16.9 U96 <*.212 -0.01 l.t*21

21 . 6 '76 '.265 -0.00 1. 915

26.3 <*. W88 ^.277 0.01 1.915

31. 0 <«. U90 '.277 0.02 1.896

35.7 u.uai k,277 0.03 1.979

<tO . k 6. 22'* *».277 0.05 0.207

kS.i 12.975 '.277 0. G6 0. 0(t6

= 1.03 & (G/S- CM2) = 13.2

Q(W/CM2) = 0.283 XISLET = -0.07

L/0 TW TB X H

(K) (K) (W/CM2

2 . 8 i+. 506 '.072 -0.05 0.653

7.5 U. i+87 '4.159 -0.03 0. 56'4

12.2 U. '96 '.2*46 -0.01 1.131

16.9 14.517 '.307 0.01 1. 3'+8

21 . 6 512 14.307 0.03 1. 378

26.3 '.307 0.05 1. 313

31 . 0 521 '.307 0.07 1. 322

35.7 U. 513 '.307 0.09 1.373

<t0 . ^4 '.307 0. 11 0. 987

'5.1 5.091 '.307 0. 13 0. 361

PCATM) = 1.03 &(G/S

Q(W/CM2) = 0.302 XINLL

L/D TW

(K)

2 . 8 <. 501^

7.5 <• 'S'^

12.2 1^9^

16.9 '4,515

21.6 '4. 510

26.3 '4. 519

31.0 '4.518

35 . 7 '4.510

'O . ! 5. ^471

'5.1 11. 871

CM2) = 13.3

= -0. 07

TB X H

(K) (H/CH2

'. C75 -0. 05 0. 70'^

'•167 -0.03 0.952

'.258 -0.01 1.285

'.306 0.01 l.'^l47

14.306 0.03 1. 1487

14.306 0.05

'4.3Q6 0.07 1. 1»26

14.3 06 0.10 1.'486

14. 306 0. 12 0.260

'.306 O.li^ 0. 01^0

114
F(ATM) = 1.10

C(W/CM2) = 3.365

G(G/S-CM2) = 12.5

XINLET - -0.07

L/C TW TB X H

(K) ( K) (W/CM2

2 . d W. '95 it. C91 -0.06 0. 902

7.5 U,k7b <i.2C8 -0.03 1. 360

12.2 U86 ^4. 32U -0.00 2. 255

16.9 if. 510 ^.327 G . C 3 1.995

21 . 6 t*. 506 U.327 0.05 2.038

26. 3 5. 12U ^.327 0.0^ 0.U59

31 . G 15. 776 k.327 G. 11 0. 032

35.7 21. 1*03 W.ZZ7 0.11+ 0.021

27. 20h '.327 0. 16 0. 016

k5, 1 2^+. 5it'4 ^.327 0. 19 0.018

P(ATf1) = l.lj G(G/S-CM2) = 12.6

C(H/CM2) = 0.33o XiNiLFT = -0.07

L/C TW TB X H

(K) (K) {W/CM2-K)

2.6 i+.t+ag '. 086 -0. 06 0. 81't

7.5 '.'79 '.193 -0. 03 1. 178

12.2 '.'35 '.301 -0.01 1.812

16.9 '.505 '.32'^ 3. 02 1. 829

21.6 '.SOg '.32'+ 0. 05 1. 822

26.3 '.51'^ '.32'^ 0. 07 1.775

31.0 '. 788 k.Z2k 0. 10 0. 726

35.7 12.70'+ '.32'+ 3.12 O.O'tO

'0.'+ 20 . 931 '.32'+ 0. 15 0. 020

'5.1 2'+. 0 33 '.32'+ 0.17 0.017

P(ATM) = 1.07 G(G/S-CM2) = 13.5

Q(W/CM2) = 0.263 XINlET = -0.06

L/D TW TP X H

(K) (K) (W/CM2-K)

2.d '. 365 '. 072 -0. 05 0. 918

7.5 '.32d '.152 -0. 03 1. 531

12.2 '.392 '.233 -0. 02 1. 682

16.9 '.'05 '.3C0 O.GO Z,^5W

21, b k,3b7 '.300 0. 02 '.010

26.3 '.'90 '.3 00 O.O'^ l,ki5

31.0 '.'56 '. 300 0. 06 1. 719

35.7 '.5'+2 '.300 0. 08 1. 107

'0.'+ 5.189 '.300 0. 10 0. 302

'5.1 6.185 ',300 0. 12 O.lkZ . 115
P (ATM ) = 1.98 G (G/S- CM2) = 13.1

C(W/CM2) = 0.180 XISLCT = -0.0'+

L /D TW TB X H

(<) (K) (W/CM2- K)

2 . 8 993 5.023 -0.02

7 . 5 5.0 36 0. OC

12 . 2 5.007 5.036 0.02

16.9 5.039 5.0 36 0,05 57. ''2

21 . 6 5. 31i+ 5.0 36 0.07 0. 6'+7

26 . 3 5. 892 5.0 36 C . 09 0.210

31.0 6. 39^+ 5.0 36 0.12 0.132

35 . 7 6. '82 5.0 36 0. It^ 0. 12'»

kQ » k 6. 631 5.0 36 0 . 16 0.113

^5 • 1 6.582 5.0 36 0. 18 0.116

P (ATM ) = 2.0 0 G (G/S- CM2) = 13.2

C(W/CH2) = 0.209 XISLET = -0. 05

I/O TW TB X H

( <) (K) ( W/CM2- K)

2 . a 5.301 5. 028 -0.03

7 . 5 5.082 5.0UU -0.01 5.501

12.2 6. 527 5.0'*7 0.02 0. I'll

16.9 6 . g'tS 5.0U7 0.05 0.110

21.6 6. 986 0.08 0. 108

26.3 6. 985 S,Qk7 0. IC 0. 108

31 . 0 6.907 0. 13 0.112

35 . 7 6. 892 5.0U7 0. 16 0.113

kii 7.320 5»Qk7 G. 19 0.106

'5.1 6.926 5.0U7 0.21 0.111

P(ATM) = 1.97 G (G/S- CM2) = 27.5

C(W/CM2) = 0.30'+ XISLlT = -0. 10

L / 0 TW TB X

( K) (K) ( W/CM2- K)

2 . 8 5.00 9 if .96<+ -0.09 6. 70 3

7 . 5 5.033 '.977 -0.07 5. '35

12.2 5 t 2^Q '.990 -0.05 1.215

16 . 9 5.535 5.0 0'+ -0. 0'+ 0.571

21 . 6 5. 935 5.017 -0. 02 0. 331

26 . 3 5. 992 5.030 0. 00 0.316

31.0 5 . 919 5. 0 30 0.02 0. 3'+2

35 . 7 5. 996 5.030 0. 0'+ 0.315

6. 129 5. 0 30 0.06 0. 276

k5, 1 6. 109 5.030 0.07 0. 28.1

116
P(ATM) = 1.97

Q(H/CM2) = 0.328

G(G/S-CM2) = 27.6

XINLET = -0.10

L /D TW TB X H

(K) (K) (W/CM2

2.8 5. 0«»7 -0.09 3.957

7.5 5. 292 ^.978 -0.07 1.080

12.2 5. 996 992 -0.05 0. 327

16.9 6. 137 5.CC7 -0. 03 C. 290

21.6 6. 1«*2 5.021 -0.01 0. 293

26,3 6. 167 5.0 29 0.01 0.288

31.0 - 6. 072 5.029 0.03 0.315

35.7 6. 151 5.C29 0.05 0.292

6. 282 5.029 0.07 0. 262

6. 236 5.029 0.09 0.272

P(ATM) = 2.01 G(G/S- CM2) = 5C •3

C(W/CM2) = 0.601 XINLET = -0.32

L/0 TW TB X H

(K) (K) (W/CM2

2.8 '.9'*2 '.7t»8 -0. 31 3.105

7.5 5.179 ^.771 -0.29

12.2 6. 375 tf.79*» -0.27 0. 380

16.9 6. 596 i*.817 -0.25 0.338

21.6 6. 636 t».8'*0 *0.23 0.33<*

26. 3 6. 6(*6 ^•863 -0.21 0.337

31 . 0 6. 568 ^.886 -0.19 0.357

35.7 6. 33<» <f.9C9 -0.16 G.^07

(»0 •<» 6.956 <».932 -0.1<* 0.297

6.66<f <».955 -0.12 0.315

P(ATM) = 1.97 G(G/S-CM2) * 13.3

Q(M/CM2) = 0.207 XINLET - -0.03

L/D TW TB X H

(K) (K) {W/CM2

2.8 955 5.019 •0.02

7.5 '.911 5.030 0.01

12.2 5.160 5.030 0.03 1.586

16.9 6. <»65 5.030 0.06 0.1W<»

21.6 6. 850 5.030 0.08 O.ll'*

26.3 6. 958 5.030 0.11 0.108

31.0 6.89(» 5.030 O.ik 0.111

35. 7 6.933 5.030 0.16 0.109

kQ*k 7.097 5.030 0.19 0.100

«»5.1 6.995 5.030 0.21 0. 105

117
P(ATM) = 1,36

G(W/CM2) = a.U9n

G (G/S-CMZ) =61,3

XIMLET = O.QO

L/Q T W TB X H

( <) (K

)

( W/CM2

2 . fi 567 0.01 8. 711

7.5 . 6 1 6 ^* . 5 67 0 . J

1

1 C . 198

12.2 't. 7^6 U.567 0.02 2.157

16.9 5.191 ^•567 0.03 0.798

21.6 5. 98 6 ^+.567 0 . Oi+ 0. 351

2 6.3 7.086 i*. 567 0 . C5 C . 198

- 31.0 7. 3146 ^.567 0.06 0.179

35.7 7. 776 ^4,567 0.06 0.155

kC » 6.159 ^.567 0 . Q 7 0.139

kb , i 8 . 3 6 6 t*. 567 C.Ob C . li+2

P(ATM) = 1. 36 G (G/S- CM2) = 62.8

Q(W/CM2) = 0 . 60 2 XINLZT = 0. 00

L / D TW TB X H

(<) (K ) ( W/CM2

2 . « U. 60 0 if. 570 0.01 19. ^*7k

7.5 i+. 868 '.570 0 . 02

12.2 6. d5i* '.570 0.03 0.263

16.9 e. 758 '.570 Q,Qk 0.1'+'+

21 . 6 9.177 '.570 0.05 0. 131

- 26.3 9. 582 '.57C 0. C6 0. 120

31 . 0 9. 536 '.570 0.07 0.121

35 . 7 9. 851 '.570 0.06 0.11'+

kQ .k '.57C 0.09 0. 100

k5.1 IC. 290 '.570 0. IC 0. 105

P(ATM) = 1.07 G(G/S-CM2) = 28.5

C(W/CM2) = 0.395 XINLET = 0.00

L/0 TW Ta X H

(<) (K) (W/CM2

2 . 8 '. '55 '+.293 0. 01 2. '37

7.5 '.293 0. 02 2.805

12.2 '.'+71 '.293 0. 03 2. 226

16 . 9 U.502 '.293 0. 05 1.888

21 . 6 I*. 816 '+.293 c. 06 0. 752

26 . 3 12. 366 '.293 0. G7 0. C+S

31 . 0 16. 318 '.293 3. 09 0.033

35 . 7 17. 137 '.293 0. 10 0. 031

kQ . <+ 19. 313 '.293 0. 11 0. 026

t*5.1 17. d'+'+ '.293 c • 12 0. 029

118
P(ATM) = 1.06 3(3/S-CM?) = 33.3

C{W/CM2) = Q,mi XINLET = G.CO

L/0 TW X H

(K) (K) (W/CM2-K)

2 . 6 Ui+O i». 291 G. 01 2. 382

7.5 U. i+2C if. 291 0.02 3. 331

12 . 2 i+. 1+53 ^.291 0.03 2. 577

16.9 k, 52A '.291 1. 821

21 . 6 13. 095 '.291 0.06 0. Of+g

26.3 18. 372 '.291 C. 07 0.031

31 . 0 lb. 266 '..291 0. 06 C. 031

35 . 7 16. 20 3 '.291 a. 09 0. C31

kO . k 20 . ^475 '.291 0. 10 0.027

k5 . 1 18. 107 '.291 0.12 0. 031

P(ATM) = 1.06

Q(W/CM2) = 0.502

5(G/S-CM2) = 3C.5

XINLET = 0.00

L/0 TO X H

(K) (K) (W/CM2

2 . 6 '.266 0.01 3.185

7.5 '.'IC '.286 0.02 '• 01+5

12.2 k. '62 '.286 0. 0'^ 2. 851

16.9 IS. '57 '.266 0. G6 0.035

21 . 6 21. 05't '.266 0.07 0.030

26.3 20. '52 '.266 0. 09 0. 031

51 . J 19. 665 '.266 0. 10 0. 033

35 .7 19. 092 ^.286 G. 12 0.03'*

'C . k 20 . 659 '.286 0.13 0. 031

k5, 1 17. 990 '.266 0. 15 0.037

P(ATM) = 1.06

G(W/CM2) = 0.686

S(5/S-CM2) = 31.9

XINLET = 0.00

L/0

2.6

7.5

12.2

16.9

21 . 6

26.3

31 . 0 35.7

'C . k

'5 . 1

TW

( K)

'.^03

17. 286

2'4. 192

21^. 158

22. 611

21. 288

19. 750

19. 053

20. 891

19. 015

TB

(K)

'.269

'.269

'.289

'.289

'.289

'.289

'.2e9

'.289

^.289

<t.269

0.01

0 .03

0.05

0.07

0. 09

0.11

0. 13

C. 15

0.17

0. 19

H

(W/CM2-K)

6. 018

0.053

0. 03<*

0. 03<t

0. 037

0. O'^O

G. O'^'^ 0. 01^7

0. Qttl

0. 0<t7

119
P(ATM) = 1.07

Q(W/CM2) = 0.703

S(G/S-CM?) = 31.9

XIVJLET = O.OU

L /O TW TB

t <

)

2 . 3 ^+.293

7 . 5 CO. o u > 1 12.2 2U. 292 '+.293

16.9 L ? Q7

21.6 22. 713 **.293

26.3 c i . J J i U ? Q 7 31 . 0

•1 G A 7 ii 1^3 . 0 J H U 9 Q 7 35. 7 1^ . 1 D C

/i 9 Q 7 'C . c911 . IDA 1 U D L. 9 Q 7 k5 . 1 1t7 . C O H

9 Q 7

' = 1.07 bib/

12) = 0 . iil 9 X i ^J L t I

L /D TW

I ^ \ \ N

1

\ Is 1 2 . H i*. '79 ^4.295

7 . 5 H . H > o

t. 9 Q C H . C ^ 9

12 . 2 i+.t»75 '.295

16.9 H . 5 (j U u 9 Q c; 21 . 6 10. 381

26 . 3 17 1 Q ii i. f . i y H UH . c9 QR3 9

31 . 0 9 Q c; H • C " 9

35 . 7

1 ft iT 1 9 U 9 Q

^0 . on i. 7 n ii 9 Q t; k5, 1

1 A 9 U Q £i 9 Q c;

= 1.98 M 9 1 —

12) = 0 . 19 3 X i N L L 1 —- Ti 1 U . i

L/0 T W T B (K) (K ) 2 . 6 5.019 5. 03'+

7 . 5 5. 9«*9 5.0

12 . 2 6. '23 5. a 3U

16.9 5. 0 34

21 . 6 6. %57 5.0 3t+ 26. 3 6. ^410 5.03U

31 . 0 6. 326 5.03'^

35 . 7 6. 316 5.03'^

<4Q . ^ 6. 393 5.03«^

k5 . 1 6. 329 5.034

0.01

0 .03

0.05

0 .07

G .10

0. 12

0. 14

0. 16

0. 18

0. 20

0.01

0. 02

0.03

0.05

0. 06

0.07

G. 06

0. 10

0.11

0.12

0.06

0.10

0. 12

3. 15

0.17

0.19

0. 21

G. 23

0.26

0. 26

H

(W/CM2-K)

4. 483

C. 044

0. 035

0. 0 35

C. 0 38

0.041

0.045

0.047

C. C42

0. 047

H

(W/CM2-K)

2. 272

2. 353

2. 314

2. 040

0. 069

0.033

0.0 30

0.030

0.026

0. 030

H

( W/CM2-K)

0.211

0. 139

0.133

0. 136

0. 140

0. 149

0.150

0. 142

a. 149

120
P(ATM) = 1.91

C(W/CM2) = 0.20a

G(G/S-CM2) = 35.2

XIMLET = 0.00

L/0 TW TB X H

(K) (K) (W/Crt2

2 . 8 97*4 '.968 0.01

7.5 5. J33 ^.988 0.01 2. 199

12.2 5.205 '.988 0.02 0. 960

16.9 5. 358 '.988 0.03 0. 563

21 . 6 5. '53 '.988 3. O^^ 0. ''7

26.3 5. 507 0.05 C. i+Ol

31 . 0 5. ^+32 U.988 0.06 0. '69

35 . 7 5. '37 '.968 0.07 0.'^17

5. 552 ^.988 0. 08 0. 369

k5 . 1 5. 534 ^.988 0. 09 0. 381

P(ATM) = 1.96 5 (G/S- CM2) = 30. 7 G(W/CM2) = 0.2'tH XINLET = 0. 00

L/D TW TB X H

(<) (K) (W/CM2-

2

7.5

. 6 5.

5.110

012

5.023

5. 023 0.01

0.02

»

2.813

12.2 5. '22 5.023 0.03 0. 612

16 . 9 5. 63d 5.023 0.05 0. 397

21 . 6 5. 66S 5.023 0. 06 0.378

26.3 5. 669 5.023 0.07 0.378

31 . 0 5. 596 5.023 0. 09 0.ii26

35 . 7 5. 6'*3 5,023 0. 10 0. 390

kO . ^+ 5. 722 5.023 0.11 0. 3k<i

5.701 5.023 0.12 0. 360

P(ATM) = 1.95 G(G/S- CM2) = 30.5

0(W/CM2) = 0.301 XINLET = 0. 00

L/D TW TB X H

(K) (K) (W/CM2-

2. fl 5.073 5. 016 0.01 5. 298

7.5 5.818 5.016 0.03 0. 375

12.2 5,3k6 5.016 0. o^^ 0. 323

16.3 5. 995 5.016 0.06 0.308

21 . o 5. 969 5.016 0.06 0. 316

2 6.3 5.957 5.016 0.09 0. 320

31 . 0 5. 866 5.016 0. 11 0. 35^^

35.7 5. 897 5.016 0.12

'O . k 5. 982 5.016 0. 1^+ 0. 312

1*5,

i

5.9<»6 5,016 0.15 0. 32if

121
A 1 N L tl 1 -* rt • nnuu

L / U T U TQ V n

{ 1

» Nl \ In 1

{ U / CtAO \ fi / Kjn C cat) H . b a f

li C C. 7 H . D b J U . U 1 7 7 a

f • t> H . H U • LI ^

1 C • C

/. C c, 7 H . 5 b >3 n n 7 'J . U on ft 7 7 16,9 6. 156 4,563 0.03 C. 346

21.6 7. 513 4.563 0. 04 0.187

26.3 7.924 4.563 0.05 0.164

31.0 7. 716 4.563 0.06 0. 175

35.7 7.835 4.563 0.07 0.168

40 • 4 8. 084 4.563 0. 08 0.157

45.1 b. 076 4.563 0.09 0.157

P(ATM) = 1.43

G(W/CM2) = 0.323

G(G/S-CM2) = 42.2

XISLET = -0.00

L/0 TW T8 X H

(K) (K) (W/CM2

2 . e 4. 696 4.626 0.00 4.616

7.5 4.681 4.626 0.01 5.875

12 . 2 4. 698 4.626 0.02 4. 527

16.9 4.840 4.626 0.03 1.512

21.6 5.037 4.626 0. 04 0. 786

26. 3 5.751 4.626 0.04 0.287

31.0 6. 405 4. 626 0. 09 0. 182

3 5.7 6.916 4.626 0.06 0.141

40 . 4 7.215 4.626 0.07 0.125

45.1 7.275 4.626 0.Q8 0.122

P(ATM) = 1. 44 G(G/S- CM2) = 34.4

Q(W/CM2) = 0.467 = 0. 03

L/D TH T9 X H

(K) (K) (W/CM2

2.8 4. 675 4.632 0. 04 10.959

7.5 5.294 4.632 0.06 0.705

12.2 8. 380 4.632 0.07 0.124

16.9 9.716 4.632 0.08 0.092

21.6 10.296 4.632 0.10 0.062

26. 3 10. 663 4.632 0.11 0.077

31 . 0 10.902 4.632 0.13 0. 074

35 . 7 11. 177 4.632 0.14 0.071

-f O .4 12.165 4.632 0.16 0.062

45 . i 12. 083 4.632 0.17 0.063

122
F(ATM) = 1.05

Q(W/CM2) = 0.529

5(G/S-CM2) = 30,i*

XIMLET = -0.06

L/D

2 . 9 7.5

12 . 2 16 . 9

21 . 6

26 . S 31.0

35 . 7 kQ . k

h5 . 1

TW

(K)

^i. ''1

k, k5Z

6. ^+66

19. 5W5

20 . 259

20.501

23.396

2C. 592

T9

(K)

k. 06'+

U.135

^.206

'.276

tt.276

'.276

k,27S

k,27b

'.276

^.276

•0.05

• 0 . C 3

•0.02

0.00

0.02

0.03

0.05

0.07

0. 08

0.10

H

(W/CM2-K)

1. 309

1. 726

2. lUU

2.530

0. 2'+l

0.035

0.033

0.033

0.026

C. 032

P(ATM) = 1.99

0(W/CM2) = 0.26'3

G(G/S-CM?) = 13.2

XIMLET = -CC^

L/D TW TB X H

(K) (K) (W/CM2'

2 . 6 6. 632 5.029 -0.02 0. l'+'+ 7.5 7. 990 5.038 0.02 0.088

12.2 6. m3 5.0 38 0.05 0.08'+

16.9 8. 277 5.0 38 0.08 0.080

21 . 6 8. 238 5.0 38 0.12 0.081

26 . 3 8. 153 5.038 0.15 0.083

31 . 0 6.027 5.038 0.18 0. 087

35 . 7 7. 955 5.038 0.22 0. 089

. k 6.110 5.038 0. 25 C. 085

k5 . 1 7. 963 5.038 0. 28 0.089

P(ATM) = 1.97

0(W/CM2) = 3.39i+

G(G/S-CM2) = 27.5

XINLET - -0. 10

L/D

2.8

7 . 5

12.2

16.9

21 . 6

26.3

31 . 0 35. 7

i+C . k

TW

(K)

5.839

6. 520

6. 622

6. 738

6. 723

6. 703

6.57U

6. 606

6. 751

6. 67'*

TB

(K)

'.969

^.986

5.003

5.020

5.029

5.029

5.029

5.029

5.C29

5.0 29

•0.08

0.06

•O.OU

•0.01

C. 01

0. 0<+ 0. 06

0. 06

O.li

0.13

H

(W/CM2-K)

P. '53

0.257

0. 2'+3

0.229

0. 232

0. 235

0.256

0.250

0. 229

0. 239

123 I
F(ATM) = 2.00 G(G/S-CM2) = 'e.S

Q(W/CM2) = 0.755 XISLET = -0.30

L/0 T W TH X H

(K) (K) (W/CM2

2.

a

5.959 k. 760 -0.29 0.630

7. 5 6. 922 ^.781 -0. 26 C. 353

12.2 7. 219 '.802 -a. 23 C. 313

16.9 7,520 <*.823 -0. 20 0.280

21 . 6 7. 533 -0. 17 0.281

26 . 3 7. 596 -0. 15 0. 277

31 . 0 7.329 U.8e5 -0.12 0. 3C9

35 . 7 '.906 -0.09 0. 292

^0 . k 7,6k7 U.926 -0. 06 0. 259

kS. 1 7. 755 i*.3k7 -0.03 0. 269

P(ATM) = 1.86 G (G/S- CM2) s '3 . 7 0(k^/CM2) = 1. C13 XINLEf = -0.15

L/D TW X H (K) (K) (W/CM2

2.8 8.227 789 -0.13 0. 295

7.5 9. 226 U.831 -0. 10 0. 231

12.2 9. 576 '.873 -C. 07 0.215

16.9 9. 935 -0.03 0.202

21.6 9. 863 k,355 0.00 0.207

26.3 9. 798 ^.955 0.03 0.209

31.0 9. 366 ^.955 0.07 P. 230

35.7 9.510 ^.955 0.10 0.222

10. 0'+g ^.955 0.13 0.199

i»5.1 9. 911 '.955 0. 17 0. 20^^

P(ATM) = 1.37 &(G/S-CM2) = 62.8

Q(W/CM2) = 0.985 XISLET = 0.00

L/D TW TB X H

(K) (K) (W/CM2

2.8 lO.llU k» 57b 0.01 0. 178

7.5 lt^.9D2 I*. 57b 0.03 0.095

12.2 16. 673 I*, 57b 9. C. 081

16.9 16. 693 '.576 0.06 0. 070

21.6 19. 203 '.576 0. 08 0. 067

26.3 18. 626 '.576 0. C9 0. 070

31.0 17. '87 '.576 G. 11 0. 076

35.7 16. 719 '.576 0. 13 0.081

'O . < 17. 538 '.576 0.1<^ 0. 076

'5 . 1 15. 053 '.576 0.16 0. 09<^

124
P(ATM) = 1.06

C(W/CM2) = a. 853

G(G/S-CM2) = 37.6

XINLET = COD

L/0 TW T8 X H

(<) (K) (W/CM2

2.8 2C. lOG 1+.290 0.01 0. 055

7.5 26. 927 t*.290 0.03 0.0 38

12 . 2 25, 153 ^.290 3.06 0. OUl

16.9 2/+. 908 '.290 0.0 8 0. 0'»2

21.6 ^.290 0.10 0. 0W5

26.3 22. 663 t*.290 0.12 0. 0^*7

31 . 0 21. 366 ^.290 0. It* 0.051

35 . 7 21. 310 ^.290 0. 16 0.052

. 23. ^kA it. 290 0.18 0 . Oi+t+ k5 .

1

21.910 ^.290 0. 21 0. 0'*9

P(ATM) = i.9»i G(G/S-CM?) = 0(W/CM2) = 0.2'+i+ XINLET = G.C8

L/0 TW T? X H

(K) (K) (W/CM2

2 . 8 6. 520 5.035 0.10 0. 165

7.5 7. 150 5.0 35 0.12 C. 115

12.2 7. 181 5.035 0. 15

16.9 7.212 5.0 35 0.18 0.112

21.6 7, Ittu 5. C 35 0.21 C. 116

26.3 7. 06U 5.0 35 0.2** 0.121

31.0 6. g^^d 5.0 35 0. 27 0.128

35 . 7 6. 927 5.0 35 0. 29 0. 129

^0 .

t» 7 . C 3 : 5.035 32 0.122

k5 .

1

6. 9'*3 5.035 0. 35 0. 128

125
4. Notation

Symbol

D

C

P

He

G

h

It

m

Q

q

Tb

T8 INLET

B OUTLET

Ttc

$

Denotes

Inside tube diameter

Specific heat at const, pressure

Enthalpy at Tg ,nlet . P

Enthalpy at Ttc. P

Mass velocity

Heat transfer coefficient

Thermal conductivity

Length along test section

Pressure

Mass flow rate

Total heat added to fluid

Heat flux

Bulk fluid temperature

Fluid temperature at test section

inlet

Fluid temperature at test section

outlet

Transposed critical temperature

Inside wall temperature

4zq

D[{iTc- iiN)GT

Viscosity

Units

cm

J/g-K

J/g

J/g

g/s -cm®

W/cm^-K

W/cm-K

cm

atm

g/s

W

W/cm®

K

K

K

K

K

g/cm- s

126
5. REFERENCES

Study of development of an inductive energy storage system, Technical

Report AFAPL-TR-69-102; Aero Propulsion Laboratory,

Wright-Patterson AFB, Ohio,

Lucas, E. J. , Thome, R, J. , and Stekly, Z. J. J. , Superconductivity

in steady state and pulsed applications for flight vehicles, Avco

Research Report presented at NATO Advisory Group for Aerospace

Research and Development, U. S. Air Force Academy (1972),

Brechna, H. , and Green, M, A. , Pulsed superconducting magnets,

Applied Superconductivity Conference, Annapolis, Maryland (1972)

(to be published).

Lucas, E. J, , Punchard, W. F, B. , Thome, R, J. , Verga, R. L. , and

Turner, J, M. , Model coil test results for a pulsed superconducting

magnet energy storage system, presented at the 1972 Applied

Superconductivity Conference, Annapolis, Maryland (to be published),

McConnell, P. M, , Liquid helium pumps, Nat, Bur. Stand, (U. S. ), Interagency Report 73-316 (1973).

Dahl, P. F, , Morgan, G. H, , and Sampson, W. B. , Loss measurements on twisted multifilament superconducting wires, J. Appl, Phys.

40, 2083 (1969).

Morgan, G. H. , Theoretical behavior of twisted multicore superconducting wire in a time-varying uniform magnetic field, J. Appl. Phys.

41, 3673 (1970).

Jackson, J. , Transient heat transfer and stability of superconducting

composites. Cryogenics 9^, 103 (1969).

Gardner, G. C. , Unsteady state heat generation and heat transfer in

superconducting composites. Int. J. of Heat and Mass Transfer 1

0

, 1055 (1967).

127
Giarratano, P. J, , Hess, R. C. , and Jones, M. C. , Forced convection

heat transfer to subcritical helium I. Nat, Bur. Stand, (U. S, ), Interagency Report 73-322 (1973).

Baylis, J. A., Unpublished (1972).

Morgan, G. H, , Unpublished (1972).

Forsythe, E, B. , Underground power transmission by superconducting

cable, Brookhaven National Laboratory report 50325 (1972).

Giarratano, P, J. , Arp, V. D, , and Smith, R. V. , Forced convection

heat transfer to supercritical helium, Cryogenics 11, 385 (1971).

Johannes, C. , Studies of forced convection heat transfer to helium I, Advances in Cryogenic Engineering, 1

7

, 352 (Plenum Press, 1972).

Ogata, H. , and Sato, S. , Measurements of forced convection heat

transfer to supercritical helium. International Cryogenic Engineering

Conference, Proceedings 4th, Eindhoven Netherlands, May 24-26, 1972,

IPC Science and Tech. Press, Ltd., Guildford, England, 291 (1972).

Tanaka, H, , Nishiwaku, N. , and Hirata, M. , Turbulent heat transfer

to supercritical carbon dioxide, JSME Semi -International Symposium

127 (1967).

Shiralkar, B. S, , and Griffith, Peter, Deterioration in heat transfer

to fluids at supercritical pressure and high heat fluxes, J. Heat

Transfer, 91,, 27 (1969).

Shitsman, M, E. , Impairment of the heat transmission at supercritical

pressures, Teplofizika Vgsokikh Temperator, J^, 267 (1963),

Powell, W, B. , Heat transfer to fluids in the region of the critical

temperature, Jet Propulsion, 27 , 776 (1957).

Giarratano, P. J. , Hess, R. C. , and Jones, M, C. , Forced convection

heat transfer to subcritical helium I, Paper D3, Cryogenic Engineering Conference, Atlanta, Georgia, August 8-10, 1973 (to be published

in Advances in Cryogenic Engineering, Vol 19).

128
Goldmann, K. , Heat transfer to supercritical water at 5 000 psi flowing

at high mass flow rates through round tubes, International Developments

in Heat Transfer , American Society of Mechanical Engineers, New York

(1961).

Sixsmith, H, , and Giarratano, P. J, , A miniature centrifugal pump,

Rev, Sci. Inst. 41_, 1570 (1967).

Giarratano, P. J, , Arp, V. D, , and Smith, R. V, , Forced convection

heat transfer to supercritical helium, Cryogenics 11, 385 (1971).

Kutateladze, S, S, , Heat transfer in condensation and boiling. State

Sci, and Tech, Pub, of Lit. on Machinery, Moscow (AEC translation

3770, Tech, Info. Service, Oak Ridge, Tenn. ). Brentari, E, G. , Giarratano, P, J. , and Smith, R. V, , Boiling heat

transfer for oxygen, nitrogen, hydrogen, and helium. National Bureau

of Standards Tech. Note No, 317, Sept, 1965,

Johannes, C. , and Mollard, J, , Nucleate boiling of helium I in channels

simulating the cooling channels of large superconducting magnets,

Adv. Cry, Eng. 333 (Plenum Press, 1972).

Daniel, Cuthbert, and Wood, Fred S. , Fitting Equations to Data

(Wiley-Interscience, N. Y. , 1971).

McCarty, R. D, , Thermophysical properties of helium-4 from 2 to

1500 K with pressures to 1000 atmospheres. National Bureau of

Standards Tech. Note No. 631, Nov., 1972.

Jergel, M. , and Stevenson, R, , Heat transfer to liquid helium in

narrow channels with laminar and turbulent flow, Appl. Phys. Letters

17_, No. 3, 125, Aug. 1970,

Keilin, V. E. , Klimenko, E. D. , and Kovalev, I. A. , Apparatus for

measuring hydraulic resistance and heat transfer in the two-phase

flow of helium, RTS 5062, National Lending Library for Science and

Technology, Boston Spa, Yorkshire (1968).

129
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA TvirjCTo ia -xl-i SHEET NBSIR 74-363

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Heat Transfer in Pulsed Superconducting Magnets

5. Publication Date January 1974

6. Performing Otganixation Code

/ . AU 1 iiOR(.S^ V. Arp, p. J. Giarratano, R. C. Hess, and M. C. Jones9» jtrcilvr«uuu j{ ^plM

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS , Boulder Labs

DEPARTMENT OF COMMERCE

Boulder, Colorado ovJiU^i

10. Project/Task/ Work Unit No. 2750459

11. Contract/Grant No. FY14557300411

12. Sponsoring Organization Name and Address

Air Force Aero Propulsion LaboratoryWright Patterson AFB, Ohio 45433

13. Type of Report & Period

Covered

Interim Report

14. %>onsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The first section of this report summarizes design problems for the

development of advanced superconducting pulse magnets, leading to recommendations for future work, primarily in (1) evaluation of eddy-current,

hysteresis, and frictional losses, and (2) transient heat transfer between

the superconductor and the helium. Two subsequent sections report

measurements of forced convection heat transfer respectively to subcooled

liquid helium and to supercritical helium just above the critical pressure.

7. KEY WORDS (Alphabetical order, separated by semicolons) Forced COnvection heat transfer;

pulsed power systems; pulsed superconducting magnets; superconductor losses;

supercritical helium; transient heat transfer.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

E UNLIMITED.

UNCL ASSIFIED

1 1 FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-DC 66244-P71

USCOMM - ERI-