Embed Size (px)
Citation preview
31 March 1966 RSIC-535
TRANSPIRATION AND FILM COOLING
OF LIQUID ROCKET NOZZLES
John E. Terry"Gus J. Caras
DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED
Best Available Copy
Research Branch
Redstone Scientific Information Center
Research and Development Directorate..
U. S. Army Missile Command
Redstone Arsenal, Alabama 35809
ABSTRACT
This report presents a summary of current theoretical andexperimental work conducted on transpiration and film coolingof rocket nozzles. An effort was made to assess the presenttechnology to bring the reader abieast of the general statu:3 ofthese cooling techniques. Major probiem which exist in devel -
oping transpiration and film cooling are presented in the con-
clusions.
The discussion of various aspects of transpiration and filmcooling is not meant to be exhaustive. Its purpose is to provide
a background for the reader who is interested in further pursuingthese cooling techni 1 ues.
iiI
FOREWORD
This report presents a summary of the pertinent literature pub-lished primarily since 1960 on transpiration and film cooling. Theoryand analytical procedures which have been developed and experimentaleffort which has been devoted to the rocket iozzle cooling techniquesare reviewed and, where possible, compared. Those theoreticalapproaches which are best substantiated by experiment and useful forpropulsion application are pointed out where sufficient information is
available to make this decision. An effort has been made to determinethe status of the technology, pointing out critical gaps, if any, whichstill exist.
The following sources of information available at the RedstoneScientific Information Center were searched primarily for the periodfrom 1960 to the present.
1) Redstone Scientific Information Center holdings (books, reports,and journals).
2) NASA (a computer tape search of NASA tapes which containreferences fr- -' the Scientific and Technical Aerospace Reports
and the Internattiý:al Aerospace Abstracts).3) Defense Documentation Center (pertinent references and
documents furnished by Defense Documentation Center).
iii
CONTENTS
Page
ABSTRACT ........... ..................................... .
Section I. INTRODUCTION ............... ...... 1..
Section II. TRANSPIRATION COOLING ................. 3
1. Status of Transpiration Cooling ... .............. 3 _ _-2. Theoretical and Experimental Investigations ............ 53. Self-Cooling ....... ........................ . 26
4. List of Symbols for Transpiration Cooling .............. 31
Section III. FILM COOLING ................................ 34
1. Status of Film Cooling ........ ....................... 342. Theoretical and Experimental Investigations ............ 38
3. List of Symbols for Film Cooling ...................... 60
Section IV. CONCLUSIONS ........ ......................... 63
LITERATURE CITED ............. ........................ .. 65
V
ILLUSTRATIONS
Table Page
I Advantages and Disadvantages of Various Wall
Materials .............. ........................ 8II Properties of Some Refractory Materials ........... 9
III "Rigimesh" Specimen with Nitrogen Coolant .......... 25IV "Rigimesh" Specimen with Water Coolant ........... 25
V Test Results for Three-Dimensional FilmCooled Nozzle ........ ..................... ... 59
Figure
I Comparison of Cooling Techniques for Nozzles -02 /H2 Fuel and H2 Coolant ....... .............. 2
2 Transpiration Cooling ........... ................. 33 Self-Cooling of Rocket Nozzle ........ ............. 44 Cracked Outer Layer Caused by Differential
Sintering Shrinkage .......... ................... 65 Strength-to-Weight Ratios of Some Refractory
Metals ............... ......................... 106 Heat Absorption Capabilities of Some
Transpiration Coolants ..... ................. ... 117 Coolant Weight Requirements Versus Wall
Temperature ............. ...................... 138 Sketch of Element of Wall Used in Setting Up
Heat Balance for Transpiration Cooling ..... ........ 149 Comparison of Transpiration Cooling with
Convection Cooling .......... ................... 1610 Comparison of Heat Transfer Results ..... ......... 1811 Predicted and Measured Skin Friction for Air
Injection into a Turbulent Boundary Layer ........... 1812 Turbulent Mass Transfer Parameter Versus
Molecular Weight of Coolant Gas ... ........... .... 1913 Two-Phase Coolant System (Coolant Exits at
a Quality) ............. ........................ 2014 Two-Phase Coolant System (Coolant Exits
Superheated) ....... ....................... ... 2315 Flow of Hot Gas Through a Rocket Nozzle with a
Liner at the Throat ....................... 2716 Model After the Liquid/Vapor Interface Has
Formed ............... ......................... 27
vi
Figure Page
17 Comparison of Computed Interface RecessionDistance with Grosh Solution: Zinc, P = 0. 3.. .... 29
18 Interface Recession for Various Infiltrants .... ...... 3019 Film Cooled Combustion Chamber ....... .......... 3520 Rocket Engine Performance Variation with
Coolant Film Thickness ...... ................ ... 3721 Agreement Between Equation (44) and the
Data of Various References ..... .............. ... 4022 Multislot, Film Cooled Pyrolytic Graphite Nozzle 4323 Gaseous Film Cooling for Standard N6zzle
with Multislot Cooling ........ ............. . 4424 Variation of Analytical and Experimental Nozzle
Temperatures with Flow Rate - Radiation/HydrogenFilm Cooling ......... ...................... ... 45
25 Variation of Analytical and Experimental NozzleTemperatures with Flow Rate - Radiation/HeliumFilm Cooling ......... ...................... ... 46
26 Variation of Specific Impulse Efficiency with FilmCoolant Flow Rate for Helium, Hydrogen, andMethane ................ ........................ 47
27 Variation of Average Test Section Temperaturewith Film Coolant Flow Rate for Different FilmCoolants ............ ........................ .. 49
28 Variation of Film-Cooled Length with FilmCoolant Flow Rate for Different Film Coolants .... 50
29 Variation of Film-Cooled Length with FilmCoolant Flow Rate for Different CombustionPressures - HZO Film Coolant .... ............ ... 51
30 Variation f Film-Cooled Length with FilmCoo ,nt Flow Rate for Different CombustionTemperatures - H.O Film Coolant ........... 52
31 Variation of Film-Cooled Length with FilmCoolant Flow Rate for Different Main StreamReynolds Numbers - H.O Film Coolant ......... ... 53
32 Temperature Ratio Parameter as a Function ofthe Le.igth Parameter for Ammonia Film Coolant-Gas Stream Reynolds Number = 0.55 (10') ........... 56
33 Temperature Ratio Parameter as a Function ofthe Length Parameter for Water Film Coolant -Gas Stream Reynolds Number = 0. 55 (10s) ........... 57
vii
Section I. INTRODUCTION
Recent advances in rocket motor devclopment have intensified theproblem of effectively cooling the nozzle operating under conditions ofhigh, local heat flux. Motor development advances have proceeded at
a faster rate than material technology to the point wl. re uncooled mate-rials cannot withstand the environment now capable of being generated.For this reason, cooled nozzle designs become necessary, even thoughcooling systems usually add weight to the rocket and sometimes penal-
ize the performanLc.
Regenerative (convection) cooling has been used successfully onSATURN, TITAN, ATLAS, etc., but this method provides for a maxi-mum heat dissipation on the order of 5000 Btu/ft -sec, which can beeasily exceeded in a rocket nozzle. I Dump cooling is limited becauseits maximum heat dissipation is about 1500 Btu/ft -sec. Z Ablationcooling is quite attractive, particularly for engines which can be throt-tled, but controlling the fabrication process and obtaining reproducibleproperties for the char and virgin material have proved to be difficult. z
Further, the maximum heat dissipation currently provided by ablationcooling is about 500 Btu/ft _-sec. Heat sink cooling is simple anc7 inex-pensive, but this cooling method is limited to a firing duration of onlya few seconds at high heat flux conditions.
From the many studies that have been made on rocket nozzle cooling,it is generaliy agreed that film and transpiration type cooling will benecessary for the increasingly more severe nozzle environments beingconsidered. These studies have indicated that on the basis of equal
coolant flow rates, transpiration cooling provides the most effectiveperformance under severe operating conditions. This is shown inFigure 1. Despite the fact that extensive investigations have been devotedto film and transpiration cooling, practical application of these methodsto high performance rocket engines is meeting with some development
difficulties. In transpiration cooling, the major problem in applicationis to achieve very small, closely spaced passages through which thecoolant will flow.J In liquid film cooling, additional work is requiredin film stability anti in determining the most feasible velocity ratio of
4injected coolant to free stream gas .
Desig- :Qquirements for future combustion chambers will likely
dictate thi ':e of a combination of two or more cooling methods. Somecool: .g combinations which are promising are film/heat sink, transpi-rationiheat sink, film /rad&ation, transpiration/radiation, film/ablation,transpiration/ablation, film/regenerative. transpiration/'regenerative,
6000 - - - - - 11 5.- 1.o25 in, PI100, p ia, T,.521ý-°
Mulliulot (9 Slots)o (0.5 in, Spacing)
; 40ooI I-.- Ix,
2000--L
IpronpIrali• Sino* Slot t5.38 1
0 -t !ý -t- 11 1 II 'r0 0.0003 0.001 0,01 0.10 1.0
Coolant/Propellant Flow Ratio
Figure 1. Comparison of Cooling Techniques for Nozzles-
02 /H 2 Fuel and H, Coolant 5
transpiration/ film, and radiation/heat sink. Combinations of regen-
erative-film cooling and ablative-film cooling have been used success-6fully on several engines, but no production engines utilizing only filmor transpiration cooling for the nozzle operating at high temperaturesare known to exist.
This report is concerned with a summary of the currenttheoretical and experimental studies on transpiration and film cooling.No attempt has been made to discuss in detail all the extensive work
that has been devoted to these cooling techniques but only the highlightsof some of the most notable work that is currently being used in develop-ment. Also, an effort has been made to define the major problemswhich still exist in developing these cooling techniques. Transpirationor film cooling combined with other cooling techniques has not been
evaluated because most of these combinations deserve separate, exten-sive surveys. As nidy be expected, comnbining cooling methods corn-pounds the complexity (.f analytical analyses.
Since self-cooling is in essence a type of transpiration cooling, adiscussion on this cooling method is included in Section II o- transpi-ration cooling. The literature indicates that developn-wnt in self-ccoolinghas been for solid roc kets using high-energy metalliz,-'d propel'ats,
and ro indication was found that it is to be appl!,,,' to liquid rocket cooling.ttowever, there is no knotwn reason why self-cooling cannot be appliedto cooling of liquid a: well as solid rockt t nozzles.
Section II. TRANSPIRATION COOLING
1. Status of Transpiration Cooling
Transpiration is commonly defined as that process whereby a
fluid transpires through a porous medium. When transpiration is used
as a means of cooling, there are at least two principal heat reducing
mechanisms at work r'irst, heat is absorbed by the cooling fluid asit travels against the direction of heat flow from some reservoir to a
surface of higher temperature and consequently lowers the wall tem-perature; an.d, second, as the fluid emerges from the surface of the
wall, it forms an insulating layer between the surface of the wall andthe hot gas
Figure 2 shows one of the methods of achieving transpiration cool-ing. In this metl-od, the wall is manufactured from a porous materialand the coolant is bloNT, throuoh the pores. The coolant film on the ihot-gas side is, therefore, continuously renewed and the cooling effect-
iv~ness can be made to stay constant along the surface. When a liquidis used as a coolant, a liquid film is Treated on the hot-gas side which
is evaporated on its surface, and the heat absorbed by the evaporationprocess increases the cooling effectiveness. This process is frequently
referred to in the literature as evaporative-transpiration cooling. 7
Hot gas
..
Coolant iFigure 2. Transpiration Cooling
Another type of transpiration cooling consists of a porous refractorymatrix which is filled with a material that vaporizes in service to pro-
vide protective heat sink and/or gaseous therrial barrier (Figure 3).Although this type of cooling has been investigated specifically for solid
rocket nozzle applications, it could be used for az '.- nozzle application
where high-heat flux and long-firing duration preclude the use of an
uncooled or a regeneratively cooled nozzle. 4 Tbe inatri\ is usually madeout of a high temperature melting material such as tungsten in which alow melting material (such as copper, silver, zinc, etc.) is infiltrated.
II
Self-cooled nozzle insert
Figure 3. Self-Cooling of Rocket Nozzle
This type of cooling is frequently referred to in the literature as self-
cooling or autotranspiration to distinguish from the type where the entire
chaniber or nozzle wall is made out of a porous material through which
the coolant transpires.
Although in theory transpiration cooling provides the greatest
cooling effectiveness as compared to other cooling methods, it has not
been applied for cooling rocket engine nozzles. Most of the published
literature deals with theoretical rather than experimental investigations.
Some of the difficulties associated with the application of this cooling
method are the fabrication of porous shapes with uniform porosity and
the inherent weakness of large porous surfaces as compared to solid
sections. To take advantage of the transpiration cooling, and also to
alleviate structural problems, it is desirable to make use of a partially
porous surface, since it is not necessary for all areas of an engine to
be cooled. Thus, the forward surfaces, with the largest heat transfer
rates, can be transpiration cooled while the rearward areas, where
heating is not so severe, can be protected by the coolant film introduced
into the boundary layer. 8
Recent technological innovations include the development of sintered
metals and ceramics of controlled porosity and the development of multi-
layer, fine wire-mesh screens. TI'ese new techniques offer the most
promising approach to achieving transpiration cooling in rocket nozzle
systems.
In general, the state of development of transpiration cooling is not
as advanced as that of film cooling. There are no liquid rocket nozzlestoca-a; that arc cooled by transpiration cooling alone or in combination
with sore., other cooling technique. A review of the literature suggeststhat cons'derable experimental work is rcquired not only in the area of
4
fabrication of porous materials and the selection of proper coolantsbut also in understanding the mechanisms of transpiration cooling andverifying theory. Most of the experimental work, for example, has
been centered around flat surfaces and one-phase coolil.g which areeasier to treat analytically.
2. Theoretical and Experimental Investigations
a. Wall Materials
Fabrication of porous shapes by sintering is a modernapplication of clay pottery technology. Practically any metal which canbe reduced to a fine powder can be used. Fabrication of the porousshape is accomplished by either one of two basic processes. In the
first method, suggested by Meyer-Hartwig,7 the metal powder is mixedwith a binder, formed in a mold to the desired shape and sintered in afurnace after the mold is removed. In the second technique, developedby Duwez and Martin,9 the powdered metal is mixed with a gas-evolving
compound such as ammonium bicarbonate. The mixture is then pressed
into the desired shape and the pressure maintained on the material whileit is sintered in a reducing (hydrogen) atmosphere. A comparison ofthese two methods shows the Meyer-Hartwig process permits the fabri-cation of an almost unlimited variation in artidle shape although shrink-
age during sintering may cause cracking (Figure 4) or make porositycontrol rather difficult.
1 0
The second fundamental method of fatricating a porous metal mate-rial is to use wire-mesh screens. This method can be used with any
metal sufficiently ductile to be drawn into wire. The wire is woven intoa cloth or gauze to the desired contour and then sintered. The porosityof the material is determined by the wire spacing.
A more recent method is based on a combination of felting techniques
and powder metallurgy and appears to combine the advantages of boththe powdered-metal and wire-winding techniques. In this method, metalfibers mixed with a viscous fluid are beaten into a slurry, which is then
charged to a porous felting mold. Vacuum drying removes the liquid,
leaving the fibe;:s deposited on the inner mold surface, and the resultingfelt is sintered. Porous metal products can be fabricated in the formof continuous sheets or in intricate shapes.
A nove, concept for fabrication of wall materials for transpirationcooling was advanced by Aerojet-General Corporation." This methodconsists of stacking together very thin washers which have been previously
5
S.... I
Figure 4. Cracked Outer Layer Caused by Differential
Sintering Shrinkage'2
6
grooved to extremely high tolerances by photoetching or chemicalmilling processes. After feasibility demonstration, Aerojet-General
Corporation plans to design a flight-weight chamber using this concept.
Of the methods used for fabricating porous media, the wire-windingand felting techniques have the best stre-ngth qualities. Magnusson,Misra, and Thompsonl0 give a more detailed review of these methods.Table I summarizes the most important advantages and disadvantages
for the several types of wall materials.
In general, a material for fabrication of the porous wall must meet
the following requirements:
1) It must have the necessary properties at the operating temper-ature to maintain its structural and dimensional integrity.
2) It must be corrosion and erosion resistant to the propellant
and the coolant at operating tempE ratures.3) It must be resistant to thermal shock.
Since the first criterion of any potential material in a high temperatureenvironment is a high melting point (m. p. ), the materials consideredare tungsten, tantalum, molybdenum, and columbiu-n. Most of theother refractory materials were not considered because of scarcity orbecause they did not offer significant advantages over the materialsnamed above. The use of non-metallic materials presents problemsin design, fabrication, and frequently incompatibility with the coolantat high temperatures.
Table II presents the pertinent properties of the refractory metalsfor service above 3000°F. All of these metals possess adequate cor-rosion and erosion resistance, are resistant to thermal shock, and,have sufficient strength and ductility at elevated temperatures.
The strength-to-weight ratios plotted in Figure 5 are an indicationof the relative weights of nozzles fabricated from various materials.The strength-to-weight ratios were obtained by dividing the ultimatetensile strength (UTS) by the density. These values are approximate,since the UTS can vary appreciably depending upon the method of fabri-cation, heat treatment, and testing techniques. In addition to the puremetals, there are many alloys of these refractory metals that could be
used.
7
grooved to extremely high tolerances by photoetching or chemical
milling processes. After feasibility demonstration, Aerojet-GeneralCorporation plans to design a flight-weight chamber using this concept.
Of the methods used for fabricating porous media, the wire-windingand felting techniques have the best strength qualities. Magnusson,Misra, and Thompsonl0 give a more detailed review of these methods.Table I summarizes the most important advantages and disadvantages
for the several types of wall materials.
In general, a material for fabrication of the porous wall must meetthe following requirements:
1) It must have the necessary properties at the operating te-nper-
ature to maintain its structural and dimenhional integrity.2) It must be corrosion and erosion resistant to tLe propellant
and the coolant at operating temperatures.3) It must be resistant to thermal -hock.
Since the first criterion of any potential material in a high temperatureenvironment is a high melting point (m. p. ), the materials considered
are tungsten, tantalum, molybdenum, and columbium. Most of theother refractory materials were not considered because of scarcity orbecause they did not offer significant advantages over the materialsnamed above. The use of non-metallic materials presents problemsin design, fabrication, and frequently incompatibility with the coolant
at high temperatures.
Table II presents the pertinent properties of the refractory metalsfor service above 3000*F. All of these metals possess adequate cor-rosion and erosion resistance, are resistant to thermal shock, and,
have sufficient strength and ductility at elevated temperatures.
The strength-to-weight ratios plotted in Figure 5 are an indicationof the relative weights of nozzles fabricated from various materials.The strength-to-weight ratios were obtained by dividing the ultimate
tensile strength (UTS) by the density. These values are approximate,since the UTS can vary appreciably depending upon the method of fabri-cation, heat treatment, and testing techniques. In addition to the puremetals, there are many alloys of these refractory metals that could be
us 2d.
7
Id g 04)
.04) - 4) ~ .2 4 )
0.0 (4 '40 - 40 to k4 0
Ci) 0 T E4o '0 0 0
(d' 0 >)1 0 > 0) >
it 'd .0 0 r Ic0 0 44
9 - N 0 ~ 0 0 0) 0 u 0
as -0 4) U)>
r) P4 4-' '4 !,.0)>) $4 > >
Do) .0 )(d~ to0
0-' .1 0> k. N '.40)
0- 00 k 0 '
4) k44)0 0 > o 4
'0 . 4 0 "' 0o 0 '4 c'-L ) .0 ) .l.. ( 4, 4
0 Ef4)
Q)
4F.4
.00
> 4)
0. 0
rd ~~~C U) x ,o0ý Ln Lo000
00 0 00 0 0 0NN -- -0
044J0000 0
LAAL0 o 0 0 X L
0 .n C' '00
u 00 r'-: 11 1LA N
0
00 0
1 0 0 0 'm~ LA c) '
0- r N *n NLALA0 100 0l r n nL0; 0i' ~ v 0- 'D ALmANa ,
10 i0'-H-
on 0It 00 0 0n a '0 o nL
0 ~ '0CD A
'0 0
Sa, 0 0nID '0 N n 0 00C; a, CD -n 0') C. 00D 0 0 a,
0 o '0 0' 00 0' N0 t 0 1 0 -I Lo LA
0 r.
-4 U
C). '0"" C)'0
Hd ( 1cn H
0 E 00 09
Soo -
800 Q___
700 ,. Tungten (m.p.,6152 0F)
__600
S500
I.-
•, Z• •/-' • lColunmbium, (m.p. 4379°F) !
200
1; 00 _ _ _
Montlybeum (m.p.5425*F)
Temberaure (mO.439F)
b.oo\ Coont0 400 800 1200 1600 2000 2400 2800 3200
Figure 5. Strength-to-Weight Ratios of Some Refractory Metals 8
b. Coolantsi
To date, most of the interest in transpiration coolants hasbeen centered around low molecular-weight gases and liquid metals.Gases exhibit a large heat transfer reduction in both turbulert and lam-inar boundary layers which is a desirable property.' One disadvantagein using gases, however, is the corresponding decrease in matrix ther-mal conductivity that results from the characteristically 1,w conductivityof the gaseous fluid. Liquid inetals offer the greatest conluctivity ofcooling fluids. Coolants other than gases and liquid metals have notreceived a great deal of attention because of the complexity of in-jectionthrough the porous matrix, chemical incompatibility with the matrix,etc. 14
10
Figure 6 gives the heat absorption capabilities of several transpi-ration coolants at 34 atmospheres of pressure. In each case, except
cryogenic hydrogen, the initial temperature has been taken at 77"F.In the absence of phase change and chemical reaction, each of these
curves would be nearly a straight line with a slope equal to the heatcapacity of the vapor in question. Phase changes introduce the verticaljumps shown in this figure, and dissociation (2NH 3--•NZ + 3Hz) accountsfor the strong upward curvature displayed by ammonia. 1 5
3.2- 1.8� p: 34 otm.
2-8 1.6S Cryogenic
'a~ 1.4 H2 H2 NH 30° 2.4- 1.2
S2.01.0
* t S• 16 0
ao ~ Q8H 2 0c 12 0.- 0 0.6
0.4 HF
S0.4 0.2 0
X z N2H41 4H
200 400 600 800 lOGO 1200
Temperature (OK)
0 400 800 1200 100
Temperature (OF)
Figure 6. Heat Absorption Capabilities of SomeTranspiration Coolants
The ultimate criterion for evaluating coolants is minimization of
the system weight required to maintain the nozzle wall at the desired
temperature. In addition, tl-e following characteristics are desirable
in coolants:'3
1) A low mn. p. and high boiling point for liquid coolants.2) Thermal stability and compatibility with the wall material so
that no reactions occur which may impair the integrity of the
nozzle or interfere with the flow of the coolant.3) Use of the coolant should not entail any complex storage,
handling, or inherent safety hazards since these tend to com-plicate logistics and increase system weights. These consid-
erations refer to such things as the necessity for cryogenic orpressurized storage facilities, preheating systems, and safety
ha2zards which arise from the explosiveness or toxic nature of
the coolant.
11
r _ _ j ,, , ,=,, -- .: _
4) High storage density is desirable in order to minimize storagetank volume and weight.
5) A low molecular weight is desirable since the coolant is injectedinto the exhaust gas stream.
6) Knowledge of the physical properties of the fluid is necessary
for proper evaluation of coolants and design of the coolingsystem.
Figure 7 gives the coolant weights required to maintain the wall
at specified temperatures for some coolants.13 These weights wereobtained from a steady-state heat balance without consideration to the
actual heat transfer mechanism, and are based on the following assump-tions:
1) The heat flux to the wall remained constant at 10 Btu/sec-in.2
2) The coolant was heated from the liquid at the m. p. (or gasat the boiling point for H2 , He,andN2.) to the indicated walltemperature.
3) The liquids were vaporized at an assumed nozzle pressure of
500 psia (i. e. , when the coolant temperature reached the
saturation temperature at 500 psia it boiled, absorbing itslatent heat).
The comparative standing of the coolants depends upon the allowable
wall temperature. At temperatures of about 2700*to 3500°'. lithium is
the best coolant because of its high specific heat and latent heat ofvaporization. Hydrogen follows closely at these high temperatures andis superior to all of the coolants, including lithium, at wall temperatures
below about 2700°F. Water ranks second to hydrogen at wall temper-atures below 1500-F.
C. Single-Phase Transpiration Cooling
Most of the analytical and experimental investigations on
transpiration cooling have been concerned with the laminar boundarylayer. This is primarily a result of the laminar flow problem beingmore amenable to analytical treatment than the turbulent flow. Unfor-tunately, transpiration cooling is more likely to be used where turbulentflow and consequently higher heating rates are involved. Even if theflow is laminar initially, the disturbance resulting frornthe injection
of the coolant tends to cause transition to turbulent flow. 16
The basic mechanism of heat transfer in transpiration cooling canbest be understoor' hy referring to Figure 8. The element considered
has a plane s'irface 1 coinciding with the outside wall si:rface, and a
12
0.1
Nitrogen'-•
1Water Sdu
Jl Lithium .. ,-- Ntoe
i i , , $sium
0.0,1 Helium -r0
a0
SI ~Sodium "
•€• Hydrogeo •
Fiue7 oln egtRqite t Hessealiuemerur
t13
ZHydrogen
0.0010 :,z
Lithium "
0.0001 ..Soo I000 1500 2000 2500 3000
Wall Temperature (OF)
Figure 7. Coolasit Weight Requirements Versus Wall Temperature
13
Tgl
Boundary Layer--CpPaVaTa dA
To
Figure 8. Sketch of Element of Wall Used in
Setting Up Heat Balance for Transpiration
Cooling
plane surface ®ý apart from the inside surface of the wall by such a
distance that it is situated outside the boundary layer present on this
side. Heat is carried by convection with the coolant through surfaces
0D and® . it is assumed that the coolant has attained the wall surfacetemiperature T when it leaves the wall. Heat will also be transferred
wby conduction through the fluid layers immediately adjacent to the out-
/aTo
side wall surface in the amount of -k dA. Fusthermore, heat
w RY rw
may be transferred to the outside wall by radiation q dA. In addition,
heat may also flow into the element by conduction in the porous mater-
Jal or by transverse flow of the coolant within the bouniary layer; the
sum of these flows is designaded q dAc i The heao balance may then beqcd
wr itten:
ka(v) dA + cirdA + q thedA' cpplav 1Tv- Ta)d (l
For constant wall temperature and negaigible heat flow alone the houndary
layer, qcd 0. If the heat transferred to the outer surface by both con-duction through the fluid layers and radiation iswritten in terms of heat
transfer coefficients, Equation (1) reduces to:
T -ýT a
T T Ta cPa~ /' a 2g +_
Ih h
\'g,cv hg' cj)
14
The values of the heat transfer coefficients to be used in Equation (2)d-epend upon whether the boundary layer is laminar or turbulent. Theaverage heat transfer coefficient may be written:
g,t = Cppg g g,t (3)
The final equations for the temperature ratio, or cooling effective-ness, are given below. (Derivation of these equations is given inReport No. NACA TR 1182.17)
1) Laminar flow without radiation (h 0):
* Ta 1Tg- T aVa f RegPr 2/3 (4)* a 1 aa g,cv g/
P9gVg 9Tg, t 0.664
2) Lan ,;.,ar flow with radiation:
T w T 1 (5)
aa _r_ _/_ _11+ gpgV 0.664 --g9--- +hg' t .• r
hg, cv gcv
3) Turbulent flow without radiation:
T T 1w a _
S + 2.11
where
r . Re 9 Pr 2/3 Pavag g0. 037 pgV
4) Ttirbulent flow with radiation:
Tw W Ta I
T - Ta P v Re 0 2 Pr '2/ 1 (7)
g) V 0. 037 rh g, cv ei
15
A comparison of transpiration cooling with convection cooling forboth laminar and turbulent flow for a Prandtl number of 0. 7 is shownin Figure 9. Low values of the temperature difference ratio indicategood cooling effectiveness. 17
77477 TI - - Effectiveness0 0
-C0.4to 0.4 - Cneto
* I ' -- Tranpiration - .- Transpiration
:L I-T-FI-C 0002 0004 0006 0008 0.010 0.012 C 0.002 0.004 0 06 0,008 0,010 0.012
Coelant- Flow Ratio (PovIPgVI) roolant- Flow Ratio (Pay a /PvgV )
(a) Laminar flow without radiation (b) Laminar flow with radiation
Reynolds number 14Reynolds number = 04
S0.8 .?C18 -Convection - -Co ctnI.. -- Transpiration 1ý
Sr 0 a:
FrTheraalEfetvns
0002 0004 000 0.06 010 0t~ .002 0.00 0.06 008 010 .0T
ColntFo Thermal~.V)Coln-la aio(aa/t 6
(c) Trulent fow withutEraditiones (dt TubletflwwthrditoReynlds umbe 10~Reynlds umbe
Fiur . om'7sn fTrnpato Coln.ih ovcin oln
16 1Fiemn.
A number of experimental results are reported for air injectioninto a turbulent boundary layer on zero pressure gradient
surfaces. Figur.e 10 compares the available heat trans-fer results in the form of Stanton numbers with several analyses. Thethree analyses do not differ markedly, although Dorrance and Dore 24
are somewhat lower. The experimental data, covering a range of Machnumbers from 0 to 2. 7 show considerable scatter, but the trend iscorrectly predicted by all three analyses. Similar results for skinfriction are shown in Figure 11, and the bulk of the data tends to agree
with the prediction of Rubesin and van Driest. The onl r conflictingevidence is the experimental data of Mickley and Davis which showskin-friction values much lower than the other investigators -- evenlower than those predicted by the film theory. Since the majority ofthe experimental data favors Rubesin and van Driest, it appears that
this represents the more realistic and certainly the more conservative
estimate of skin friction and heat transfer in the presence of air injection.
To determine the influence of molecular weight of the coolant gas
on the heat transfer and skin friction, '.he rmass transfer parameter wasplotted against the molecular weight at a constant value of the reduced
parameter, Cf/Cf and CH/CH of 0.5. The results are shown in-1 0 0
Figure 12 where it is seen that the molecular weight plays a moresignificant role for the light gases, while the heavier gases do notappear to be so sensitive to this property. 25
Librizzi and Cresci1 investigated experimentally the downstreaminfluence of mass injection on the heat transfer to the surface of an
axisymmetric nozzle in turbulent flow. Helium and nitrogen were usedas coolants and were injected through a porous region upstream of thenozzle throat at various rates. The results of the experiments showeda decrease in heat transfer with increasing mass injection, helium being
more effective for the same mass flow rate than nitrogen. This decreasein heat transfer became less prominent as the distance downstream ofthe porous region increased.
Bernicker8 studied transpiration cooling of a two-dimensionalnozzle with relatively lov test pressures resulting in a laminar boundarylayer. Two test nozzles were used, each having the porous region ata different position with respect to the nozzle throat. Helium and airwere used as coolants. The results showed an appreciable decrease inthe equilibrium surface temperature over the zero injection case, withthe decrease due to helium injection persisting for a greater distancedownstream of the injection area.
17
1.0 I IExperimental Result. (1M,-,20)
0.8 r7 Analysis of Rubosin (26)0.8 ~-"~' Svan Driest (27)
Analysis of Dorrance a Dore (24)
CHCHO
04 ___ ___
0.2
00 0.4 0.8 12 1.6 2.0 2.4 2.8 3.2
Figure 10. Comparison of Heat Transfer Results
1.0 :~
Q. ExerimntalMeasurement (22)
-- Experimental Measurement ofMickley SDavis (23)
0.6
Cf
0.4
0.2
ZDorrance D ore (24)
0 0.4 0.8 1.2 1.6 20 2.4 2.8 3.2
Pw Vw 24 P* U& Cf0
Figure 11. Predicted and Measured Skin Friction for Air Injection intoa Turbulent Boundary Layer
18
0.0
00
10 00 10
00
-j 0
00.00
4- 0
0. 0 0
0 0 0
0 -44
0-
.a O&I 0-IDD
0
00
0 0 0 0
W-,~ ~ ~ Wd 07-f-AJ&4*WDJ~~~d *OSUJ SON U-.q
19)
d. Two-Phase Transpiration Cooling8
A review of the literature reveals that very little experi-mental work has been done in two-phase transpiration cooling. Thereare several advantages which two-phase transpiration cooling provides.As with evaporative film cooling, full use is made of the coolant'slatent heat of vaporization. In addition, when vaporization of the coolanttakes place within the wall structure, the heat capacity of the super-heated vapor also contributes to the cooling effect.
A sketch of the model portraying the two-phase process is shownin Figure 13. The liquid is heated to saturation temperature in RegionII, and in Region III boiling occurs at constant temperature. The
SSolid Tem p. (TS) Ho t Ga s F lo w,
Coolant Flow
Fluid Temp. (1) I.
0 xI L
Figure 13. Two-Phase Coolant System (Coolant Exits at aQuality) !3
assumption was made that inside the wall T s5 t and dts/dx_0. Sinceboiling occurs at constant temperature in Region III:
(d_) = 0 (8)
If it is also true that at x L, Ts = t and x_•L, Ts>t and dTs/dx>_ 0,the following statement must also be true:
( -dT- =0 (9)
The combination of Equations (8) and (9) represents a zero heat fluxin Region III. There are two solutions possible.
20
(1) L-x . In this case-the liquid is actually exitingfrom the pores at saturation temperature and is boiling at the boundaryx = L. It is then possible to have a finite solid temperature gradientX= T,.
(2) T5 * t at x = L. It is then possible for:
( sdTs > 0. (10)d dx ]x =L i
The fluid in the first solution can be treated as a single phase through-out. The temperature distribution in the wall can be obtained fromthe analysis of single-phase flow. The possibility of boiling occurringat the boundary is, of course, dependent on the heat transfer in the
boundary layer.
The second solution can be handled analytically, since boundarycondition can be found to replace Ts = t at x = L. The mathematicaldescription of Region II is the same as that given in the single-phasecase with the suitable substitution of the system properties.
3 enXs 0 +F, knCn e (11)
Region II3 Xnx
t = CC +E Cne (12)n=1
In Region III, the heat balance for the solid is characterized by:
(1 - d) =: ha (Ts - ts) (13)ha2
Equation (13), when integrated, becomes:
6x -6x --Ts = tstB1 e + B. e (14)
Since the boiling temperature is assumed constant, the energy
balance for the fluid phase involves the enthalpy: -
dHG•-dH ha(Ts - ts) (15)
21
Substituting Equation (14) into Equation (15) and integrating yields theenthalpy distribution in the boiling region:
6 x 6 - xH =.B 0 1+-BI e 2 -B. e (16)
Equations (11), (12), (14), and (16) represent the solution to the tem-
perature profile in the porous wall. The boundary conditions needed
to evaluate the seven constants of integration and the location of x are:
Atx=L
1) H=H2
2) (1 - CpL (t- tR) + (H,- H,)j
At x = xi
3) H = Hi
4) TsII = TsIII
5) tII =ts
6) (1 kw /T + -kL d II
7) ddc•tI = .0
At x = o
8) (dT- =0\ d~x ]_II=
Figure 14 shows a model where the coolant is heated to boilingtemperature in Region II and boils at constant temperature in Region III,
and the vapor is superheated in Region IV. In Regions II and IV, the
general solution to the temperature profiles is similar to that given in
the single-phase analysis.
3
Ts = E0 +, LnEnevnX (17)n=1
Region II3
t = E0 +'-, En (18)n=2
22i
Coolant Flow
SolidTempTS) 00*1Hot Gas FlowI IFluid~= Tmp t
0 Xl x2L
Figure 14. Two-Phase Coolant System (Coolant Exits Superheated) 1
"T s =oi Tem B - 5X (19)
Region III H= B e 6 B e 6X (20)
0 6 1 62
3 n
Ts = F0 + B, PnFn e (21)
nii
Region IV
i 3 Xnx !
ts= F0 +, FFne (22)
n=i
The boundary conditions needed to evaluate the 11 constants of inte-
gration and the location of the boiling region are:
At x =L
) ttL
23
dTs dt2) (1- (e) kw -* -- + Ekv- G jCpL(ts - tR) (H2 - 1 i) + CpL(tL ts)]
At x = x
3) H= HZ
4) tiv = ts
5) TsIII = TsIV
/dt\ =
7) (1- ) k r]IwýdT s IIIL tx = G CpL(ts- tR)+ (HZ H1 )
At x = x
8) H =H 1
9) tII =ts
10) Ts 11 = TslII
11) [ 0
12)+ 1kL =-p(' - tR)12) I -• ),•,• -----xx ]i II
At x |o
1 dTs - 0
dx
The United Nuclear Corp( ration conducted some experimental
work 1 3 on two-phase ,ranspiration cooling. The experiment was not
intended to simulate rocket nozzle conditions, but was simply designated
to demonstrate this method of cooling and compare transpiration cooling
with w-iter and nitroo en.
Inithai experinments wt- -e performed with the low density, woven,
type 304 stainless "Rigimesh" specimen made by Aircraft Porous Media,
Incorporated. The specimen was 2 inches by 2 inches by 1/8 inch thick.
)'4
The temperature on both faces of the specimen was measured by thermo-couples. Both nitrogen and water, as coolants, were passed in thespecimens, v,1,i le the hot gas temperature was in excess of 20010"F.With no coolant, the hot-gas side reached 1400'F. Outside wall tern-peratu-es of 400°to 800°F were measured with nitrogen flows of 0. 6to 2. 4 ft /min, and 220'F with a water flow of about 5. 6 X 10- ft 3 /min.The results of this cxperirnent are summarized in Th.bles III and IV.
Double wall specimens consisting of two 1/, -inch thick sections ofgrade "X" sintered stainleF,€ steel made by Aircraft Porous Media, Incor-porated were also used. These specimens becarne partially plugged withimpurities from the water. A filter with pores smaller than those inthe specimen should be used. Nevertheless, two-phase flow in a porouswall was demonsstrated.
Table III. 'Rigimesh" Specimen with Nitrogen CooLant
" O It.iiAl II1• Nit rogen
,' 4A II%,1,l huot Ga SlFIow hIft.t Fluxk i- I l F , I i p F F ,. T p .ll ' f tC ' l nr in 1 1t. i /S c , - I n
o n• $4, .2000 1 . 84 0. -11
2 [Ol}-• "-20U0 2.•1) O. 21
A jO -(l 4 2 0 0 2. 4 0. 21
4t 1 13- 7Is U 201 0 0.071
)415 2s•5 t22 J >_______ 0.0 0.075
Table IV. "Rigirnesh'' S- m cinmn witi Xater Coolant
Inside
Wdll Hot G •s Water b!,.,w,Run £enlp. F rilp. F ft III II (mm'M Iler• tz
1 22 :-2100 7.4 x I" Fxcess water,At b,,ttowm of
-Ii.-t wAI.
% setted t,, ymid-
i plan,
4 ' .0 0 0. intire \&all
ýU~t wctird
-.a tA r.
wit: n e,/5
3. Self-Cool ing
The self-cooling process (Figure 3) can be described in thefollowing manner: after ignition, the temperature of the surface rises
rapidly until the coolant melts and then flows through the matrix underthe action of pressure forces; all fluid emerging from the hot surfaceis vaporized resulting in a gaseous-licuid coolant interface that recedeswith time; the rate of recession of the interface and, consequently, the
gascous coolant mass flow rate are fanctions of the temperature dis-tribution within the composite and of the pressure drop through the
porous structure caused by viscous and inertial effects on the coolantmass flow; the vaporization of the coolant and interface recession will
continue until firing is terminated or the coolant is exhausted. The
following cocling mechanisms are possible in the process:
1) Heat absorption at the gaseous-liquid interface where thecoolant vaporizes.
2) Convective codling as the gaseous coolant flows through
the porous structure.3) Reduction of the convective heat transfer coefficient by
mass additio,. into the boundary layer (transpiration
cooling effect).4) Heat absorption within the composite if the gaseous
coolant dissociates internally.5) Heat absorption at the surface if an endothermic reaction
takes place between the gaseous coolant and hot gas.
In addition to these mechanisms, cher ical reactions may occurthat are unfavorable from the standpoirt of heat transfer. It is possiblethat dissociated products may recombine in the vicinity of the surface tocause severe heating. Exotlermic chemical reactions between the
coolant and the hot gas would also have an u:ffavorable effect on heattransfer 28
Despite the interest in -he self-cooling concept, very few th-eore-
tical analyses have been deveioped. The analysis which appears to bethe most prevalent is that of Gessner et al. These investigators con-
sidered the flow of hot gas through a rocket nozzle having a throat insertconsisting of a porous refractory mairix, which is filled with an infil-
trant (Figure 15). If the thickness of the inscrt is small compared tothe nozzle-throat radius, the insert can be considered to be an infiniteplate of finite thickness. The plate is considered to be a turgaten-infiltrant cormpos;itc of constant porositvy with a single infiltrant thatvaporizes below the melting point of the refractory matrix. After thesurface is heated and the infiltrant boiling point is r-ached, a
26
inLiner
,--Hot I
Gas
Figure 15. Flow of Hot Gas Through a
Rocket Nozzle with a Liner at the Throat 29
liquid/vapor interface begins to recede and infiltrant vapor starts toflow through the porous structure. A schematic diagram of the modelafter heating has begun and the liquid/vapor interface has formed isshown in Figure 16. Recession of the liquid/vapor interface continuesuntil heating is ended or until the infiltrant is exhausted. To simplifythe analysis, the following conditions were prescribed:
1) One-dimensional, unsteady-state heat transfer.2) Temperature-constant thermcphysical properties.3) Equal matrix and infiltrant vapor temperatures at a given
depth in the porous structure.4) Heat of fusion of infiltrant combined with heat of vaporization.5) Negligible heat conducted through infiltrant in gaseous phase
as compared to heat conducted through the porous matrix.6) Negligible radiation between hot gas and heated surface as
compared to convective heating.7) No diffusion or chemical reactions between infiltrant vapor
and hot gas.8) Negligible radiation within porous structure.
Hot Gas--D. -"-'• OD
Region I IX_-Infiltrant Vapor FIl.- Interfac
Region 1 , L
Insulated
Figure 16. Model After the Liquid/VaporInterface Has Formed 28
17
After heating has begun, but before vaporization of the infiltrantoccurs, a heat balance of any internal volume element can be written:
a~ 'r3TIkm (1 P) + kcPIjr C cp 3T (23)-8T = [m .In - P) + P:cCP CIO
where
T = T(x, 0)
The corresponding initial condition and boundary conditions are written:
T(x, 0) TO (24)
0=
(o < 0 < 0o)
a(1 = 0 (0 < 0 < 0o) (26)
After vaporization occurs and a liquid/vapor interface forms, two
regions exist for which heat balances must be written. The first region
is between the heated surface and the interface, and the second is!,eutween the interface and the insulated surface. The heat balances andc-:.rresponcting initial and boundary conditions can be written:
Region 1 = between heated surface and Hiquid/vapor interface:
km(l - P) Cc g - PmCm(1 - -T (27)
with
kI p)() h - (28)T
0 0 0max'
-km(l - P) (a) X(Gc) - -k(l P) + kP1(-3Tý (29)\a - 9g~ 5 \x 18+
(0 1- 0 e Omax)
Region 2 = between liquid/vapor interface and insulated surface:
6 <x 5L
Ikm(l - P) + kcP1 a T IpmCrn(l - P) + PcCcPI1 (0
with Equation (29) applicable at the interface with
aT = 0 (0 n 0 _Omax) (31)axh
When heating begins, but before vaporization of the infiltrant occurs(1< 0 < 01 ), the temperature distributions can be determined readily
ir closed form by Equation (23) by the separation of variables technique.iv the instant the infiltrant vaporizes, however, a set of two partialiifferential equations [Equation's (27) and (30)1_must be solved whichare coupled by the interface equation Equation (29) .
Based upon the foregoing model and theory, a one-dimensionalnumerical solution was programmed for the IBM 7094 computer byGessner et al. To check the accuracy of the computer solution, a com-parison was made to the theoretical solution of Grosh. and the agree-ment was excellent, as may be seen in Figure 17, which is a typicalcase of porous tungsten infiltrated with zinc. In this figure,the inter-face recession is plotted against time.
.2.02 .o Computer Program Solution
0.1 I 0
Tit", 9 490c
Figure 17. Comparison of Computed InterfaceRecession Distance with Grosh Solution:
Zinc, P = 0. 329
In Figure 18, the interface recession for various infiltrants isplotted against time. An explanation of this figure is as follows:
a. Teflon (Case 7)
The very, low dissociation temperature (1400°F) and low ther-mal diffusivity of Teflon causes almost immediate recession (0, = 0. 25sec). Exhaustion of the infiltrant occurred in only about 30 seconds.
b. -Zinc (Case 3)
The low boiling point of zinc (2313°F) results almost in imme-
diate interface recession also (0t = 1.3 seconds). The zinc coolant wasexhausted in about 72 seconds. Zinc was markedly superior to silveruntil the zinc was exhausted.
c. Silver (Case 1)
The beginning of recession 01 does not occur until 47.9 seconds
because of silver's high boiling point and, to a lesser extent, the highthermal diffusivity of the composite. The high volumetric latent heatof silver results in slow interface recession.
d. Silver (Case 14)
All of the cases previously discussed were for a matrix porosityof 20 percent. Case 14 is for an 80 percent porous matrix. Recessionfor this case commences at about the same time as for Case 1.Increased porosity was found to reduce significantly the composite
thickness requirement.
2,0
1.0
(CueJ ?) Ji0-(
CI 0
OOC
01 P0 00 200
r'...e& (am')
Figure 18. Interface Recession
for Various Infiltrants
30
The general conditions under which the above experiments were
conducted were typical of those encountered in a solid rocket enginewith a two-inch thick insert:
Hot gas temperature = 6200°F
Reynolds number = 190,000
Hot gas specific heat = 0.446 Btu/lb-°F
Hot gas mass velocity = 1, 233, 000 lb/hr-ft2
Hot gas pressure = 226 psia
Stanton number = 0. 00237
Convective heat-transfercoefficient 1303 Btu/hr-ft2 ° F
Initial composite tem-perature 70°F
The above cases are, only a sample of the experimental work per-
formed on self-cooling. Additional data and results on other infiltrants,including ammonium chloride and lithium chloride, are available. z8
No references to the literature could be found on any analytical or
experimental work which was conducted in connection with this type ofcooling to liquid rocket nozzles. Although several coolants were inves-tigated, no definite recommendation of certain coolants over otherswas made. This, of course, can be easily understood since the selectionof a particular coolant would depend greatly on the intended application
and the particular environment such as temperature, firing time, etc.
against which the nozzle is to be protected.
4. List of Symbols for Transpiration Cooling
a = Specific area per unit volume of porous wall.
A = Surface area.
A' = Surface area separating element under consideration.
c = Specific heat.
cp, Cp = Specific heat at constant pressure.
Cf = Local skin friction ' ,fficient with mass transfer.
CH = Lccal heat transfer Stanton number in presence of masstransfer.
31
CRo = Local heat transfer Stanton number in presence of masstransfer referring to solid wall subject to the same free
stream conditions and held at same temperature as theactual wall.
e = Refers to conditions at outer edge of boundary layer.
G = Flow rate per unit area.
h = Film coefficient.
ho = Convective heat-transfer coefficient with no transpiration.
h = Local heat transfer coefficient,
H = Enthalpy of fluid.
k = Thermal conductivity.
P = Interconnected porosity.
Pr = Prandtl number.
q = Heat flow.
Re = Reynolds number.
t = Local Stanton number.
t = Fluid temperature.
T = Temperature.
Ts = Solid temperature.
TP = Boiling.
u, v = Velocities, parallel Lnd normal to surfacez respectively.
x, y = Distance.
6 = Root of differential equation.
= Porosity.
0 = Time.
O8 = Time at which interface recession begins.
kn = Root of differential equation.
Vn = Root.
p = Density.
Pava = Average mass velocity of coolant.
32
PgVg = Average mass velocity of main flow.
= CpPava/hg, cv
= hTpa/G.
Subscripts
a = Coolant.
c = Infiltrant.
cd = Conduction.
cv = Convection.
g = Combustion gas or gas side.
L = Liquid.
m = Matrix material.
r = Radiation.
R = Reservoir.
s = Boiling point.
t = Transpiration.
= Wall.
33
Section Ill. FILM COOLING
1. Status of Film Cooling
The film cooling technique, permitting simple thrust-chamberwall construction, was used in many early rockets, notably the GermanV-2 nozzle. Either liquid or gaseous coolant is injected along the gasside wall surface by means of tangential or nearly tangential coolantholes, slots, or louvers. The coolant alters the temperature profilethrough the thermal boundary later, and decreases the heat flux to thenozzle wall. Where a combustion chamber of short length is used,
injection can be provided at the injector face, and the film-cooling
effect will persist to the throat region. In a fully film-cooled design,injection points are located at incremental distances along the wa]llength as shown in Figure 19 for liquid film cooling. In liquid film
cooling, the vaporized film coolant does not diffuse rapidly into themain gas stream but persists as a protective mass of vapor adjacentto the wall for an appreciable distance downstream from the terminus
of the liquid film. Thus the length of the hot gas flow passage pro-tected by film cooling is significantly longer than that of the liquid film.3
With liquid film cooling, heat is transferred principally by meansof evaporation. With gaseous film cooling, heat transfer occurs bymeans of sensible heat exchange. Liquid film cooling has an advantage
over gaseous film cooling in that the density storage requirements areless, and the utilization of the latent heat of vaporization of a liquidsignificantly improves the cooling technique? 2 Generally, liquids havehigher specific heats than gases although hydrogen and helium areexceptions.
Judicious spacing of injection locations can provide optimum wall-temperature distribution. Inefficient cooling resi,)t9 from overcooling
of the wall in the injector region. Also, the large variation in walltemperature can result in severe thermal stresses. Injection velocity
and injection manifold design are important because proper matchingof film coolant to mainstream gas velocity can contribute to a reductionin coolant flow as a result of improved efficiency. 2
Film cooling may be~sed effectively to protect the combustionchamber and nozzle walls several ways as follows:3 3
1) Reduction of the "adiabatic" wall temperature to a value belowthe material limiting value.
34
LL'
11uo .0
:2>- 40
o c0'9a
I 35
2) Reduction in the heat flux to a wall which is also cooled byradiation, convection,or a heat sink.
3) Maintaining a non-oxidizing gas adjacent to refractory surfacesotherwise capable of withstanding full combustion gas tempera-
ture, such as uncooled tungsten, tantalum, or various carbides.
With film cooling, there are no inherent limitations on cooling
capacity (as found with regenerative cooling), time (as with ablativecooling), or chamber pressure (as with radiation cooling). However,a disadvantage to film-cooled design is where one of the propellante,(usually the fuel) or an inert fluid is used as a coolant at the nozzlethroat, there is a performance penalty (specific impulse loss) due to
gas and temperature stratification. 33 The stratification loss is avariable depending upon the effective film temperature, and is inde-pendent of the effective chemical combustion efficiency. The magnitudeof this effect on specific impulse is presented for various film tempera-tures and film thicknes3 in Figure 20. An additional specific impt iseloss may be incurred due to the operation at propellant mixture ratiosother than optimum in order to insure sufficient propellant as film
coolant. Film coolants such as hydrogen, helium and ammorn` showpromise because low molecular weight will contribute to a high ratioof temperature to molecular weight without coolant combustion, and,2hence, no appreciable performance degradation will occur. 2
If the performance loss element is taken into consideration, themost likely film-cooling applications would be either in supplementationor in large-thrust designs where only a small percentage of the totalpropellant flow would be required. 2
Gaseous film cooling has been found to be an effective coolingmethod both analytically and experimentally, and the feasibility of thismethod has been established. Special attention will have to be given tothe velocity ratio of coolant to free stream at the point of injection 4
before liquid film cooling can be demonstrated with complete success.
Also, surface film stability under high turbulance, phase changes alongthe cooled length, and end..'hermic or exothermic decompositions areproblems which require further study in liquid film cooling. Although
considerable analytical and experimental work has been devoted to thecomplex phenomenon of film instability, the results are subject to controversy an 1 inadequately verified analytical solutions. A thorough
analysis of film instability background is available. 34 Work is beingdevotei to developing an analytical model and applying it to experimentaldata on the problem of thn boundary layer in liquid fi in cooling of rocket
noi.zles.I
36 1
(ids ,/dg I) olD Ss~ndwi *IJps66S
90 6 0
0
-0000
0 0
0 0 0
S 0 4)
0- C -: 0 00
/20) 0MLihy j4j
0 07
2. Theoretico! und Experimental Investigatior.s
a. Gaseous Film Cooling
(1) Theoretical Investigat ons. Several correlations ofredicted adiabatic wall temperatur with film cooling are available.1 ' 4 ',36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 In many cases, analyses were empiri-
cally derived and employed to correlb.te experimental data obtained at
relatively iow temperature differences between the gas stream and the
injected coolant.
!he boundary-layer model of a film cooled surface has been used
by many authors to deriv~e an analytical expression, for fi'm cooling
effectiveness r, in terms of the Reynolds number of the cooling fluid at
the slot exit Vcyc/v, the ratio of coolant velocity to mainstream velocityVc!Vg, and the ratio of downstream distar.ce to slot width x/yc, in the
forni43 , 45
i = constant (V)c--c 8 (32)iL
where
Tad - Tad'Tad _Tc
In early work, the following expressions were deduced by Wiegardt"
(assuming that the boundary-layer thickness equals 0. 37 x (Vxv'
IVgx \ 0 . 8 (V 2ycýU-z (33)
Tribits arnd Kleiii 1
T-4.6 2 1 gX_ (0c.c)O0 (3.t)
Hartnett et a:(7
S= 3.3 \v•-c Yc) j-
38•i I
38 5I% JC
46In later work, the following expressions were deduced by Stollery:
l~ /0.8 v )0.2T 3. 09(. ! (36)
Seban and Back:4 5
T= 11. 2( c (37)
Kutateladze and Leont'ev:
'1 = 3. 44. 16 + ý(•-v-c) 0--- ] (38)
Librizzi and Cresci:'j ' \080. -1= 3.0 3.0 + (-cYC____] (39)
Stollery and E1-Ehwany 44 made a simplified derivation whichequated the film cooling effectiveness in terms of enthalpy. Thisexpression, which obtained go9d correlation to experimental data, is:
'= 3.091 Vgx c (40)
where
}l, ad - H (41)
Recently, Spaulding43 presented a comparison of the theories ofmost of the authors mentioned above in predicting the adiabatic walltemperature in film cooling systems. To emphasize the similaritiesin the theories, he restricted his discussion to two-dimensional,uniform-property flows. As a result of comparing the theories andcomparing experimental data from several different sources, an arti-ficially contrived equation was proposed that would reasonably fit allthe experimental data corresponding to velocity ratios of coolant tomainstream, Vc!Vg, for values ranging from nearly 0 up to about 14,and data taken from difrerent shapes of geometrical arrangements atthe slot. The results can be expressed, for uniform properties, asfollows:
39
for X < 7: ii 1 (42)
7for X 7: Ti = X (43)
where
X 0.-91 + 1.41 O-(1 + 1.4-1 -(44)
Although this theory is not exact, Spaulding has shown that it canbe used over a broad range of geometrical slot arrangements and Vc/Vgwith fair correlation to experimental data. Figure 2 1 sliows the cor-relation obtained with this theory.
004
t0o 10 100
Figure 21. Agrecment Betweea Equation (44)and the Data of Various R, ierences43
Perhaps the closest simulation and the most flexible theory wasdeveloped by liatch and Papell. LEater ,nvestigat ors S, 4 haveuseu this s imulation to correlate thi-eir test results withi reas onablygood -sults. In contrast to most other theoretical models, the 1-atchand Papell model begins by assulming that the coolant film Cxists as a(tiscrete layer (no mixing). Two empirical modifications are then madeto take care of the ni ix ng phenomenon. This model provides a goodbasis for correlating experimental data taken reasonably close to thecoolant slot (0 < x/S < 150).:I
The HIatch and Papell film cooling correlating equation, developedfor relatively high oas stream temperatures, was used (n a simplified
theo)retical heat-transfer model and qualified by empirically determinedc (nstants and parameters. Altlion gh this e(juation was developed by
'- 0
using data covering a wide range ol coolant gas properties and valuesof basic parameters, it was, however, limited to tangential injection of
the coolant parallel to an adiabatic wall. Subsequently, Papell 50 pre-sented further semiempirical corrections to be applied to the equationto correct data obtained with coolant injection through angled slots andnormal holes. Data were obtained for coolant injection through slots
at angles up to and including 99 degrees relative to the adiabatic walland also through rows of normal holes. These data were restrictedto subsonic flow with no pressure gradient in the flow direction. TheHatch -Papell equation for gaseous film cooling of angled slots is asfollows:
Tad Tad E •CLc S cIfc+v'STad') K) f(g)8 In cos n . 8 Peff
(45)
where
f = 1 + 0.4 tan- (Yg- for Vg >i.0 (46)\Vc/ \Vc V c
=Vc 1 5 V- 1) for V c_ 1. 0 (47)Vg Vg"
where
Sin P 48Peff tan-' \Cos (48)Cos P + (Vc
and where all angles are in radians. With only convective heat transfer,K=0. 04. The equation assumes that there is no heat addition to the cooledwall, that is, Tad' is the adiabatic value of wall temperature reachedwith film cooling. The heat transfer coefficient, hg, is measured at theslot location without cooling, the velocities are computed at the slotlocation, and all the coolant properties are computed at the temperatureand pressure of the coolant as it emerges from the slot.
The correlating equation developed for slot injection of the coolant
[Equation (45)] contained a discrete value of slot height as a basic para-meter and, therefore, could not be applied to the hole configuration data.A modification was made by defining an effective slot height S' as thetotal coolant flow area divided by the width of the first row of holes,S' = Ac/Y. Further, for values of velocity ratio greater than unity, it
was found that a corrective term for the modified slot correlatingequation equal to -0. 08 (Vg/Vc) generalized the data. The resulting
41
correlating equation for normal hole injection of the coolant is:
51Cp) A)S f(X.9 +lncos 0 . 8IPeff -0. 08(I.\& >
Sellers has shown that Equation (45) can be used for multiple-
slot correlation as well as single-slot. The adiabatic wall temperaturewith gaseous film cooling, Tadi, is determined from Equation (45).Now, assume that a new slot is introduced downstream. Again, theadiabatic wall temperature is determined from Equation (45), but notethat the adiabatic wall temperature without film cooling, Tad , is afunction of the distance downstream of the slot, x, and is actually theTad' curve from the original slot. The procedure is repeated if addi-tional slots are added, noting that Tad is different for each slot and eachtime is equal to the Tad, results from the preceding slot. Sellers usedthe foregoing concept to show rather good agreement between the experi-mental and calculated wall temperatures using 2, 3, 4, and 5 slots of-various dimensions. In correlating his data, Sellers used K = 0 ratherthan K = 0. 04 as shown in Equation (45) since, he indicates, there issome evidence from rocket engine film-cooling experiments that avalue of K = 0. 04 may be too large.
(2) Experimental Investigations. Most experimental dataobtained for gaseous film cooling have been for cylindrical combustionchamber sections. The literature shows few experimental studies ongaseous film cooling of nozzles at high free stream temperatures.,s' 52
Some experimental data have been obtained at relatively low nozzletemperatures. 2,48,49,
The Marquardt Corporation made film cooling calculations usingthe Hatch-Papell equation for several coolants and nozzle configurationsto provide a comparison of conventional film cooling analysis with theirexperimental results. The analytical and experimental studies includeda two-row hole pattern, a tangential slot, and multislots.
When multislot cooling was used, the analysis procedure was modi-fied to account for the effect of upstream film cooling by using an adia-batic wall temperature at any location which was the same as the wall( i. e. , recovery) temperature which would have been predicted at thatlocation fromnthe upstream cooling alone. This is the modificationwhich was discussed by Sellers as mentioned previously. The multi-slot nozzles tested were designed as shown in Figure 22. The hydrogencooling requirements for various values of maximum wall temperatureare shown in Figure 23. Although four test runs were made on this
42
4t
ChamberI
Coolant Supply/ Coolan Manifold
Slot No, I I0
7I
Slotted Pyrolyticj
Graphite Disks 0- Ring
Belleville Spring
Figure 22. Multislot, Film Cooled Pyrolytic Graphite Nozzle 5
43
H2 Coolont, 0 2 /H 2 , Po0 lOOPsi0
0.0016
0.0014
0.0012
CL
* 0.0010
0
" 0.0005_o
0.00065
0.00040.0 4 -Slot No. 6
0.00020 3000 4000
Maximum Wall Temperature (OF)
Figure 23. Gaseous Film Cooling for Standard Nozzle with Multislot
Cooling5
44
nozzle configuration, using hyd rogen, methane, and carbon monoxide
as coolants, a comparison of the)retical and experimental results wasnot repo rted upon. (Thc end result (of the test was to determine throat
erosion--methane and hydrogen induced none and carbon monoxide
induced a slight amount. ) 11 owever, it was c(mcluded that mu Iltislotcooling is a most promising means ()f cooling when high energy pro-
pellants are used.
The variation of analytical and experimental nozzle temperaturewith coolant flow rate for single slot injecticfn is shown in Figure 24for hydrogen cooling and in Figure 25 for helium cooling. The liinited
data indicate that helium is about as good as hydrogen as a film coolanton an equal weight flow basis, rather than being inferior by a 3:1 weightflow ratio as was predicted analytically.
0.10 __ _
0.08 -
"Theofetical, Exit
Sv•( (Adiabatic Wall)
or
U.
Z 0.04 - -o Maximum Throat r0 (Pyrometer, Molyb-U -~denum Nozzle)
002
0 a \
1000 1500 2000 25C0 3000 3500 4000
Wall Temperature (OF)
','igure 24. Variation of Analytical and Fxperimental
Nozzle Temperatures with Flow Pate-Radiation/Hy-drogen Film Cooling5
The effcct on tl,rust (of film cooling wit" ihydroggen, helium, and
methane is shown in F'igure 2(6. The data show that ,rethane cooling
may incur a large loss in perfrlorm'ance, wh*..reas small amounts ofhelium c-an be used with no l()ss 4f performance. Indleed, some (if the
data for hel i.im show an increase a ()Xve the performance without c ouling.
The one available point for hlydr,)i.en cooling s.ih)ws a surprisin,, resul"
in that no loss ii specific impulse was indicated.
4S
020 1 I
Max imum ThroatTemperature
0 15 r ' '
Theoretical, EWit(Adiabatic Wqlt)
005 .Zvra* F',i' t , • . .Tomporc two """
Avwrage Thmooft ,., -.Temperature - " .. "' " -
0 1 1100 ,500 2000 2500 3000 3500 4000
Wall Temperature (OF)
Figure 25. Variation of Analytical and Experimen-
tal Nozzle Temperatures with Flow Rate - Radia -
tion/Ilelium Film Coolings
b. Liquid Film Cooling
The mechanism of liquid film cooling has been well docu-
mented and a 3ummarization of the results of many of the investigationsis available. 4 As with gaseous film cooling, most of the experimentalistshave studied ,ooling of cylindrical sections and little work has been
done on nozzles. Even in cylindrical flow, the various investigatorsdo not agree, primarily on the effective heat transfer coefficient.54 Theinvestigators of gaseous film cooling have introduced empirical para-
meters involving dimensions of injection sl(,•s, velocity of injectedcoolant, and other paranieters which cannot be easily applied to the
vapor phase o" lquid film cooling. Therefore, most of the theoreticalwork on gaseouis film cooling cannot be applied directly to the theoryof liquid film cooling. As mentioned before, the effect on film stability
of adverse pr,,ssure gradients has not been satisfactorily determined.
(1) Theoretical and Experimental Study by Emmons31 .
One notable experimental investigation and analytical study on liquidfilm cooling was carried out by Emmons who obtained informationregarding the effect of the gas streanm temperature, pressure, Reynolds
number, and physical properties of the film coolant upwn the convectiveheat transfer coefficient between the hot gas stream and the surface ofthe liquid film, and obtained information concerning the insulation effect
46
I w
c f- 0
S.SI' S 0 f-4
c Uo
to , ;i.0 .c
V E U 0
I E
I 0
00•
>
- _ _ __- _;,,_
(po
47
___ _ _ __ ___U o
pr(,vided by the film coolant vapor for the area downstreanm from the
liquid film. These studies were made on a horizontal 3-inch-insided;ameter film cooled combustion chamber which was placed between
Lwo convectively cooled chambers. Hydrogen-air combustion gas wasused at pressures from 250 to 750 psia and temperatures from 2600°to 4100°R with a gas stream Reynolds number of 0.55 (10 ) to 1.83 (10').
Water, anhycirous ammonia, ethyl alcohol, and Freon 113 liquid filmcoolants were introduced tangentially. The film cooled combustionchamber was instrumented to determine the wall temperature.
Figure 27 is typical of the data obtained, which shows how the walltemperature varies with coolant flow rate. Figure 28 shows the linear
dependence of the cooled length (which is dafined as the chamber length,which is below the boiling point oi the coolant ) on coolant flow. Figure29 presents the experimentally determined values of the film-cooled
length as a function of the film coolant flow rate. The curve wasobtained by the method of least squares. The results indicate that thecombustion pressure, within the range 250 to 750 psia, has an insignif-
icant influence upon the flow rate of the film coolant required forcooling a given film-cooled length. Figure 30 presents the experi-mentally determined film-cooled length as a function of the requiredcoolant flow rate when the combustion pressure and Reynolds numberare held constant, Figure 31 shows the film-cooled length as functionof film coolant flow rate when the combustion temperature and pressurewere maintained constant.
(a) Liquid Phase - The analytical analysis made byEmmons fcr the liquid cooling is derived for the case of turbulentincompressible flow of the hot gas stream. The flow model employedconsisted of a turbulent stream of hot gas ilowing over a stable liquidfilm having a uniform temperature equal to the 1, Iing point of theliquid. The coolant is assumed to evaporate fro , .a liquid film sur-
face at a uniform rate and diffuse into the hot gas z eam within a sub-layer region adjacent to the liquid surface withi a velocity equal to thefilm coolant flow rate per unit surface area Q divided by the specificweight of the coolant yc. The velocity profile within the sublayer isbased upon a diffusivity variation relationship which takes into accountthe vapor injection velocity at the wall.
The expression relating the heat transfer coefficient hf betweenthe liqiid film surface azrd the hot gas stream and the film coolant
derived by Emmnns is as follows:
k%-o WO i. (9)f 9. byc
I 48O
0 ý0
4-)
9'It
E:4.4
9- c* .0
* ~0-
2 t
0 0 'u
o
.0 §~ En
CL >
04
0n
- 0j
9.0 --
8.0 .. . .
7.0
S6,0 6 Coolant Jo
5 (Btu/Ib)
CP
Water -11700/Ammonia - 515
oo Alcohol - 4860 Freon - 85_E
rr 4.0
3.0 Freon-113
2.0
1.0 -• ,A
0 0044.- 0.06 0.12 0.16 0.211 0.24
S• Film Coolant Flow Rate (lb/ec)
Figure 28. Variation of Film-Cooled Length with Film Coolant
Flow Rate for Different Film Coolants
50
ILO
Combustion Temp. 4100 OR10.0 Reynolds No. 0.955(10)5
Combustion Press. .250 pla
o Combustion Press. 500 psia
) CombustionPress. 75C psia
9.0
8.0
7, .0 •2 Ic
0_C
U•. 6.0E
5.0
4.0
30
0.02 0.03 0.04 OD5 0.06 0.07 0.08
Film Coolant Flow Rate (lb/sec)
Figure 29. Variation of Film-Cooled Length with Film CoolantFlow Rate for Different Combustion Pressures - H 20 Film Coolant~l
51
11.0
10.0 Combustion Press.= 500 psia
Reynolds No. s 0.955 (10)5
SCombustion Temp. 2600 OR
9.0 Combustion "emp. 3200 OR
0 Combustion 7emp, 4100 OR
-. 31.0
e-
• 7.0
00
E
6.0
5.0 A
4.0
3.00.01 0.02 0.03 0.04 0.05 0.06 0.07
Film Coolant Flow Rote (tb/sec)
FigurL 30. Variation of Film-Cooled Length with Film Coolant
Flow Rate for Different Combustion Temperatures - H2O Film
Coolant 31
"a2
10.0Combustion Temp. a 4100oRCombustion Press. = 500 psia
, Reynolds No. z 0.55 (10)5
9.0 Reynolds No. = 0.955 (10)5
9.0 ) Reynolds No. M 1.83 (10)5
8.0
-II
7.0
E
4.0
3.0
3.0
2.00 0.04 0.08 0.12 0.16 0.20
Film Coolant Flow Rate (lb/sac)
Figure 31. Variation of Film-Cooled Length with Film Coolant
Flow Rate for Different Main Stream Reynolds Numbers -
HZO Film Coolant 31
Ss53
in which hf is defined in terms of the gas stream temperature Tg, theliquid film surface temperature Tv, and the rate of heat transfer q bythe expression:
q z hf (Tg - Tv) (51)
The relationship between 00 and hf is given by:
hf = Tg - T (52)
Emmons used Equation (52) to calculate the heat transfer coefficientfor the liquid film by employing various values of film coolant flowrate Q.
An expression was derived for the ratio of film coolant flow rateQ to the mass velocity of the gas stream G in terms of the pertinentphysical properties of the gas and coolant as follows:
Q= Vmkv (Tg - T( ZY9 Oov _ 13.89 YgVmkv(T- T(53)G-. -o b Yc~ (53)
where the average calculated value of the empirical parameter b is0.110.
Since the Nusselt number is defined by:
Nu hfD (54)Kg9
an expression was derived for the Nusselt number applicable for liquidfilm cooling by subst~ituting Equations (52), (53), and (54), rearranging
and simplifying.
Nu -- F0 Re V 89. 3NFO-kg(Tg, - \T (55)2 (Vm kv vs YcOovs
(b) Vapor Phase - Data obtained from the convectivelycooled combustion chamber downstream of the film cooled unit indicatedthat a cooling effect occurred even though no liquid was present. Appar-ently, the cold vapor blanketed the wall from the hot gas stream forsome distance.
54
k
For the vapor phase, Emmons emplo-yed a flow model similar tothat employed by Hatch and Papell, with the exception that the restrictionof an adiabati- wall was removed. The final result of the analysis was
the development of the following equation relating the heat flux and walltemperature distribution to the film coolant flow rate:
T T 2qw
In il = In g wh 2rDhgx (56)Tg + Tw - 2Tv vfcCpc
To correlate with experimental data, Equation (56) was modifiedto account for the flow conditions of the hot gas stream. An empiricalfunction, in terms of the flow rate ratio, was determined that bestcorrelated the experimental data for vapor film cooling. The finalequation for correlating the data is:
n 1rDhvx fd /--- (57);Tf cC p c \Vc!
where
d 1 + 0.25 tan- (15 - Wg) (58)\W~fc ) =W7 fc I
and where the angle in the empirical function (Equation 58) is expressedin radians.
Figure 32 presents the results of plotting the semitheoreticalEquation (57) with experimental data. Using the empirical function(Equation 58) in conjunction with Equation 57 corrects the experimentaldata with reasonable accuracy for ammonia. Since the data for water(Figure 33) exhibited a greater degree of scatter, Emmons concludedthat the empirical function f(wg/ýfc) does not correlate the data withthe desired degree of accuracy at larger values of the flow rate para-meter. He hypothesized that much of the data scatter was caused byturbulent mixing between the gas stream and the film coolant. (Tur-
bulent mixing was neglected in the analysis. )
(2) Theory Used by Marquardt CorporationS4. Forliquid film cooling in the nozzle section, Marquardt Corporation usedthe Stanton number for smooth flow and applied the following equationto be integrated over the section of interest:
dwc 2 Sti Cp(TgS- Tdx CFPi)
__ .(rT 1 dx (59)
Wg (A )- AHc
55
0.9 __ ,,Symbol W
0.8 • Wfc
0.7 El A e,.0 5.55
0.6 -
0.5
0.4
t11 I%
0.÷ 0.3Is
0.2
0.1 -
0 0.2 0.4 0.6 0.3 1.0 1.2 1.4 1.6 1.6 2.0
r 2" dXWtc Cpv Wtc
Figure 32. Temperature Ratio Parameter as F'•nction of the Length
Parameter for Ammonia Film Coolant - Gas Stream Reynolds
Number 0. 55 (105)
56
I.00.9 ______
Symbol Wg
0.0 to0 25.9A 17.9
0.67 E 9.64
0. 6
0 5
0.4 E
"A1+____' I 0.3
I-I 0"I'•0 o
0.2
0 1t0 2.0 3.0 4.0 5.0
2vdh, x1 wI)
LWqc C j'wt
Figure 33. Temperature Ratio Parameter as a Function of the Length
P.trarneter for Water Film Coolant - Gas Stream Reynolds
Number = 0.55 (10s)
57
Equation (59) represents a conservative approach since the coolingability of the vapor downstream from the liquid was neglected. Thecooling effect of the vapor might be quite large when considering acoolant which has a low heat of vaporization and a high specific heat.However, at the time Marquardt Corporation made their analysis, andsubsequent to that time, the literature did not show a good correlatingequation to predict the effect of vapor cooling downstream from theliquid.
(3) Experimental Study by Marquardt Corporation ".Marquardt Corporation made a study on the behavior of a liquid filmin a typical nozzle throat. The study .,cluded the spreading of thefilm introduced at discrete points, the stability of the film, and thecooling effect of the film. The three-dimensional test nozzle was theconvergent-divergent type having a 12. 8-degree inlet half angle, a3.4-degree exit half angle, and a 1.3-inch throat diameter. Thenozzle was comprised of three copper segments, one comprising theinlet m)n to the throat and two making up the exit Between the segmentswere brass coolant injection rings, through whici, water coolant wasinjected independently by each segment. Water coolant was injectedat the nozzle inlet plane, at the throat, and between the throat andeyit plane. The coolant exit velocity component was tangent to thenozzle wall and perpendicular to the gas stream.
Table V lists the test results obtained with the three-dimensionalnozzle, along with theoretically required coolant flow rates calculatedon the basis of a Stanton number of 0.003, calculated coolant manifoldgas stream pressure differentials, and the coolant head pressuresacross the injection rings.
The test on the three-dimensional noz...le verified the resultsobtained from prior tests on two-dimensional nozzles. The followingconclusions were drawn:
I) The lccation of liquid injection is an important factor toachieve best film cooling performance. In general, the coolantshould be injected at locations where it is least subject to thegeneration of instabilities by the gas stream.
2) Injecting the liquid in a straight converging section and at thethroat provides the best liquid film cooling performance.
3) Inefficiency in film cooling is caused by film instabilityresulting in liquid lose ,o the gas stream prior to evaporation.
58
�, 0C
� C a�
2
�n �n 0 -� �j I-� -, I
cl
-� C- C
N0z
I -
0 I�- Io JE I� K � -� r
K- �- -H ____ __ _____
I C - 0
.1
K
-t
_____________________________________ I
'�2 -?H IC 0 0 r- -I�J. '1* C'0 C 0
C
L. I
H
I C
I -� C- I-N a.
I
4) Film instability is caused by interaction of the gas stream onthe liquid film. Thick film and film flow maldistribution aidinstability.
5) Direct correlation of the instability behavior in the tests was
not possible due to the complexity of thin film instability.
6) Satisfactory film distribution at injection can be achieved bydesigning the injector to have a pressure differential of atleast ten times greater than other forces affecting coolantdistribution, such as gravity head in a hoi zontally mounted
nozzle.
(4) Computer Program Development. Aerojet-General
Corporation 11 is developing a computer program (8083) to evaluate the
effectiveness of film cooling and regenerative cooling at very highthrust chamber pressures for a liquid rocket thrust chamber cooledby a combination of film and regenerative cooling. This program is
similar to an existing program, but incorporates several improvementswhich give results more closely approximating actual test data. Themethod used to calculate the temperature of the film in film cooling isbasically that described by Hatch and Papell. The method of calculatingthe film cooling effectiveness and the manner in which it is used has
been modified to conform to hot-firing data. Incorporated into thecomputer program are the physical properties of N.04 and AeroZINE50 which will allow the option of film cooling or regenerative coolingwith either fluid.
3. List of Symbols for Film Cooling
A = Gas flow area.
b = Empirical parameter.
CF = Rocket nozzle thrust coefficient.
Cp = Specific heat at constant pressure.
d = Differential of a function.
D = Inside diameter of the rocket motor chamber.
D1 = Hydraulic diameter.
f = Function.
F = Fanning friction coefficient.
60
G = Gas mass velocity.
h = Convective heat-transfer coefficient 0. 02 6 5 kf(Re)f' (Pr)i",
for gaseous film coolingi.
H = Enthalpy.
AHv = Heat of vaporization of the liquid film coolant.
k = Coefficient of thermal conductivity.
K = Constant; 0. 04 with only convective heat transfer.
L = Width of adiabatic wall.
Nu = Nusselt number.
P = Pressure.
Pr = Prandtl number.
Q Film coolant flow rate per unit surface area.
q Heat transfer rate per unit area.
Re =.te•. Ids number.
S = Cocla-, slot height.
J' =Etfectiv,' coolant slot height, At/y.
St = Stant ) number.
t =- Stic temperature.
T 7 Stagnation temperature.
Tad Adiabatic wall temperature without film cooling.
fad' Adiabatic wall temperature with film cooling.
Tc= Temperature of ccolant at exit slot.
V Velocity.
"wv = Flow rate.
x = Distance along wall.
X = Dimensionless distance.
y z Width of first row of holes.
Yc Width of slot in directlion normal to wall.
a Thermal diffusivity, k/pCp.
Coolant injection angle relative to adiebatic wall.
~eff Effective coolant injection angle.
SI III . ... .
y = Specific weight.
S= Cooling effectiveness.
0o= AHv + Cpl (Tv - To).
p. = Dynamic viscosity.
v = Kinematic viscosity.
s= Kinematic viscosity of gas evaluated at Tv,
p = Mass density.
- = Shear stress.
Subscripts
ad = Adiabatic wall.
c Coolant slot exit for gaseous film cooling and coolant forliquid film cooling.
tg + tcf Properties evaluated at----,-ior gaseous film cooling
and liquid film for liquid film cooling.
g = Main body of gas.
1 = Liquid.
m = Average conoitio-s i- the gs stream.
o = Dry wall.
w = Wall.
v = Vapor.
ch - Ccmbust" 7n (ha-nbe-.
i = TTliti.l or base cod-iiiun.
62
A'
Section IV. CONCLUSIONS
Although transpiration cooling i:. Lheory provides the greatest cool-
ing effectiveness as compared to other cooling rncthýds. this ixiethod
has not been applied to the cooling of rocket engine nozzlcs. The pro-
blem of fabrication of porous shapes with uniform porosity as well as
the necessary structural properties has not been completely solved.
Most analytical and experimental studies on transpiration cooling
have been conducted by making several simplifying assumptions. These
assumptions include flat plates ratier than curved shapes, gaseous
coolants, laminar flow, and temperature environments considerably
lower than those encountered in high temperature liquid rocket nozzles.
Before this form of cooling can be successfully applied, it is necessary
to conduct extensive research under conditions that approximate closely
those encountered in actual service.
Self-cooling has received considerabie attention as a method of
cooling solid propellant rocket nozzles and several tests proving its
feasibility have been conducted. It appears that this form of cooling
has not been considered at all for liquid rocket nozzles; however, based
on the literature reviewed, there is no apparent reason why it cannot
be used.
In gaseous film cooling, there is adequate analytical work, cor-
related with experimenLal data, to design a rocket nozzle cooling system
and to predict the effectiveness of the coolant. Multislot cooling is
very promising when high energy propellants are used. Gases with
low molecular weight are more attractive as coolants because with their
use there is less loss in specific impulse.
Although liquid film cooling has been combined successfully with
other cooling techniques, there are presently no adequate analytical
solutions verified by experimental data to predict the effectiveness of
the cooling mechanisms when operating at high mainstream temperatures.
Additional analytical and experimental research is necessary to
understand surface film stability mnder high turbulence and to predict
the effectiveness of the vapor coolant downstream from the liquid.
Additional work in liquid film cooling is necessary in determining the
most feasible velocity ratio of coolant to mainstream gas since film
thickn•e.- -nd flow maldistribution aid instability.
63
LITERATURE CITED
1. Polytechnic Institute of Brooklyn, Brooklyn, New York, TRAN-SPIRATION COOLING OF A TURBULENT BOUNDARY LAYER INAN AXISYMMETRICAL NOZZLE by Joseph Librizzi and RobertJ. Cresci, February 1963, PIBAL Report No. 772, (AIAA Journal,Vol. 2, No. 4, April 1964, pp. 617-624) (Unclassified Report).
2. George P. Sutton, William R. Wagner, and J. D. Seader,ADVANCED COOLING TECHNIQUES FOR ROCKET ENGINES,Astronautics and Aeronautics, January 1966, pp. 60-71.
3. The Marquardt Corporatinn, Van Nuys, California, TRANSPIRATION-FILM COOLING STUDY USING SPIRAL-WOUND-RIBBON NOZZLES,February 1965, First Quarterly Progress Report, Report No.25, 156, Contract No. AF 04(611)-10387 (Unclassified Report).
4. S. E. Colucci, COOLING METHODS FOR SOLID ROCKETNOZZLES, Chemical Engineering Techniques in Aerospace, Editedby D. J. Simkin, Chemical Engineering Progress, Vol. 60,Symposium Series, No. 52, 1964, pp. 116-129.
5. The Marquardt Corporation, Van Nuys, California, SPACECRAFTENGINE THRUST CHAMBER COOLING - FINAL REPORT, 22 July1964, Report No. 6069, N64-29196 (Unclassified Report).
6. Chemical Propellant Information Agency, John S. Hopkins University,Silver Springs, Maryland, LIQUID PROPELLANT ENGINEMANUAL (U), 5 November 1965, CPIA/M5 (Confidential Report).
7. F. Meyer - Hartwig, COOLING OF THERMALLY HIGH STRESSEDSURFACES BY A COOLANT INTRODUCED THROUGH PORES INTHE MATERIAL (TRANSPIRATION CONSTRUCTION MATERIAL)(Kiihlung hochhitzbeanspruchter Oberfliiaichen mit einem durch Porenim Werkstoff zugefUhrten Kkihlmittel (Schwi tzbaUstoffe)) Translatedinto English from the German by the Air Materiel Command,Renort No. FB1470, 1 December 1940, Translation No.F- 9-2067-RE, ATI No. 22204 (Unclassified Report).
8. Massachusetts Institute of Technology, Naval Supersonic Laboratory,AN EXPERIMENT WITH A TRANSPIRATIO'T1-COOLED NOZZLEby Richard P. BcA,.icker, July 1960, AFOSR TN 60-1484, AD-254 260(Unclassified Report).
65
t I I
9. Jet Propulsion Laboratory, PREPARATION AND PHYSICALPROPERTIES OF POROUS METALS FOR SWEAT COOLINGby P. Duwe% and H. F. Martin, August 1947, Progress Report3-14 (Unclassified Report).
10. Aerojet-General Corporation, Azusa, California, TRANSPIRATIONCOOLING AND FLOW-SEPARATION CON f ROL BY GASEOUSINJECTION IN A POROUS NOZZLE (Supplement II to Final Report)by A. W. Magnusson, B. Misra, and W. R. Thompson, June 1961,AFFTC-TR-61-53, AD-263 458, AF 33(616)-5552 (UnclassifiedReport).
11. Aerojet-General Corporation, Sacramento, California, ADVANCEDROCKET ENGINE-STORABLE (U), Quarterly Technical Reportfor period July-September 1965, 15 October 1965, Report No.AFRPL-TR-65-189, AGC Report No. 10830-Q-1, Contract No.AF 04(611)- 10830 (Confidential Report).
12. Air Force Materials Laboratory, Research and TechnologyDivision, Air Force Systems Command, SELF-COOLED ROCKETNOZZLES by P. Schwarzkopf and E. D. Weisert, August 1965,Report No. RTD-TDR-63-4046, Vol. III, AD-473 691 (UnclassifiedReport).
13. United Nuclear Corporation, TRANSPIRATION AND FILM COOLINGFOR SOLID PROPELLANT ROCKET NOZZLE3 Iv S. Hyman et al,7 February 1961, Report No. NDA 2150-1,AD-273 333, Contract No.DA-30-069-ORD-3094 (Unclassified Report).
14. U. S. Naval Ordnance Test Station, China Lake, California,TRANSPIRATION COOLING WITH LIQUID METALS, PART 2:THEORETICAL DETERMINATION OF OPTIMUM COOLING PARA-METERS NEAR STAGNATION REGIONS by W. H. Thielbahr,August 1965, NAVWEPS Report No. 8732, NOTS TP3791 (Unclas-sifieA Report).
15. D. E. Rosner, TRANSPIRATION COOLING WITH CHEMICALREACTIONS, Pyrodynamics, Vol. 2, May 1965, pp. 221-247.
16. Air Force Flight Dynamics Laboratory, Research and TechnologyDivision, Air Force Systems Command, Wright-Patterson AirForce Base, Ohio, HYPERSONIC TURBULENT TRANSPIRATIONCOOLING INCLUDING DOWNSTREAM EFFECTS by L. W. Woodruffand G. C. Lorenz, June 1965, Technical Report No.AFFDL- TR-65- 11 (Unclassified Report).
66
I, i
17. National Advisory Committee for Aeronautics, Wa3hington, D. C. ,COMPARISON OF THE EFFECTIVENESS OF CONVECTION,TRANSPIRATION AND FILM COOLING METHODS WITH AIR ASCOOLANT by E. R. G. Eckert and J. N. B. Livingood, 1954,Re-pert No. NACA TR 1182 (Uaclassified Report).
•8. Massachusetts Institute of Technology, Cambridge, Massachusetts,HEAT, MASS, AND MOMENTUM TRANSFER FOR FLOW OVERA FLAT PLATE WITH BLOWING OR SUCTION by H. S. Mickleyet al, September 1962 (Unclassified Report).
19. Rosemount Aeronautical Laboratories, University of Minnesota,MEASUREMENT OF RECOVERY FACTORS AND HEAT TRANS-FER COEFFICIENTS WITH TRANSPIRATION COOLING IN ATURBULENT BOUNDARY LAYER AT M = 3 USING AIR ANDHELIUM AS COOLANTS by B. M. Leadon and C. J. Scott,February 1956, Technical Report No. 126 (Unclassified Report).
20. National Advisory Committee for Aeronautics, Washington, D. C. ,THE EFFECT OF FLUID INJECTION ON THE COMPRESSIBLETURBULENT BOUNDARY LAYER - PRELIMINARY TESTS ONTRANSPIRATION COOLING OF A FLAT PLATE AT M = Z. 7WITH AIR AS THE INJECTED GAS by Morris W. Rubesin ,Constantine C. Pappas, and Arthur F. Okuno, 21 December 1955,NACA Research Memorandum A55119 (Unclassified Report).
21. National Advisory Committee for Aeronautics, Washington, D. C.,THE INFLUENCE OF SURFACE INJECTION ON HEAT TRANSFERAND SKIN FRICTION ASSOCIATED WITH THE HIGH-SPEEDTURBULENT BOUNDARY LAYER by Morris W. Rubesin, 1955,NACA Research Memorandum A55L13 (Unclassified Report).
22. National Advisory Committee for Aeronautics, Washington, D. C.THE EFFECT OF FLUID INJECTION ON THE COMPRESSIBT .;TURBULENT BOUNDARY LAYER - THE EFFECT OF SKIN•RICTION OF AIR INJECTED INTO THE BOUNDARY LAYER
O•k A CONE AT M = 2.7 by Thorval Tendeland and Arthur F. Okwi,,June 1956, NACA Research Memorandum A56D05 (UnclassifiedReport).
23. National Advisory Committee for Aeronautics, MOMENTUMTRANSFER FOR FLOW OVER A FLAT PLATE WITH BLOWINGby H. S. Micklcy and R. S. Davis, November 1957, NACATechnical Note 4017 (Unclassified Report).
67
24. W. H. Dorrance and F. J. Dore, THE EFFECTS OF MASS
TRANSFER ON COMPRESSIBLE TTHR"_JIJENT BOUNDARY-
LAYER SKIN-FRICTION AND HEA i.-NSFE•, Journal of the
Aerospace Sciences, Vol. 21, No. 6, June 1954, pp. 404-410.
25. J. P. Hartnett, D. J. Masson, J. F. Gross, and C. Gazley, Jr.,
MASS TRANSFER COOLING IN A TURBULENT BOUNDARY
LAYER, IAS National Summer Meeting, Los Angeles, California,
28 June - 1 July 1960, ISA Paper No. 60-66.
26. National Advisory Committee for Aeronautics, AN ANALYTICAL
ESTIMATION OF THE EFFECT OF TRANSPIRATION COOLING
ON THE HEAT TRANSFER AND SKIN-FRICTION CHARACTER-
ISTICS OF A COMPRESSIBLE, TURBULENT BOUNDARY LAYER
by M. W. Rubesin, 1954, NACA Technical Note 3341 (Unclassified
Report).
27. Rand Corporation, Santa Monica, California, ON MASS TRANSFER
NEAR THE STAGNATION POINT by E. R. van Driest, Rand
Symposium on Mass-Transfer Cooling for Hypersonic Flight,
1957 (Unclassified Proceedings).
28. Research and Technology Division, Wright-Patterson Air Force
Base, Ohio, SUMMARY REPORT, SELF-COCLED ROCKET
NOZZLES by F. B. Gessner, R. J. Ingram, and J. D. Scader,
March 1964, Report No. RTD-TDR-63-4046, AD-601 574
(Unclassified Report).
29. F. B. Gessner, J. D. Seader, R. J. Ingram, and T. A. Coutlas,
ANALYSIS OF SELF-COOLING WITH INFILTRATED POROUS
TUNGSTEN COMPOSITES, Journal of Spacecraft and Rockets,
Vol. 1, No. 6, November-December 1964, pp. 643-648.
30. Wright Air Development Division, Wright-Patterson Air Force
Base, Ohio, TRANSIENT TEMPERATURE CHANGE IN SEMI-
INFINITE POROUS SOLID WITH PHASE CHANGE AND TRANSPI-
RATION EFFECTS by R. J. Grosh, January 1960, TR 60-105
(Unclassified Report).
31. Purdue University, Jet Propulsion Center, Lafayette, Indiana,
EFFECTS OF SELECTED GAS STREAM PARAMETERS AND
COOLANT PHYSICAL PROPERTIES ON FILM COOLING OF
ROCKET MOTORS by D. L. Emmons, August 1962, Report No.
TM-62-5, Contract No. Nonr 1100(21) (AMSE Transactions-
Journal of Heat Transfer, Vol 86, No. 2, May 1964, pp. 271-278)
(Unclassified Report).
68
32. Air Force Institute of Technology, School of Engineering, Wright-Patterson Air Force Base, Ohio, AN EXPERD.IENTAL INVESTI-GATION OF NOZZLE COOLING FOR A SMALL ROCKET ENGINEby Donald J. Alser, August 1963, Master's Thesis (UnclassifiedThesis).
33. Clifford D. Coulbert, SELECTING A THRUST CHAMBER COOLINGTECHNIQUE FOR SPACECRAFT ROCKET ENGINES, AmericanInstitute of Aeronautics and Astronautics Summer Meeting, LosAngeles, California, 17-20 June 1963, AIAA Paper No. 63-241(Unclassified Paper).
34. S. Ostrach and A. Koestel, FILM INSTABILITIES IN TWO-PHASE FLOWS, The Sixth National Heat Transfer Conference,Boston, Massachusetts, 11-14 April 1963 (Unclassified Proceeding).
35. Purdue University, Jet Propulsion Center, Lafayette, Indiana,ANALYTICAL AND EXPERIMENTAL INVESTIGATION OF FILMCOOLING IN ROCKET NOZZLES by D. L. Crabtree, R. A. Gater,and C. F. Warner, 1964, N65-20353, Contract No. Nonr 1100(21)(ITS 1964 Review of Research, pp. 21-41).
36. S. S. Kutateladze and A. I. Leont'ev, FILM COOLING WITH ATURBULENT GASEOUS BOUNDARY LAYER, Thermal PhysicsHigh Temperature, January 1963, pp. 281-290.
37. J. P. Hartnett et al, VELOCITY DISTRIBUTIONS, TEMPERATUREDISTRIBUTIONS FOR AIR INJECTED THROUGH A TANGENTIALSLOT INTO A TURBULENT BOUNDARY LAYER, ASME Trans-actions - Journal of Heat Transfer, Series C, Vol. 83, January1961, pp. 293-306.
38. K. Wieghardt, HOT AIR DISCHARGE FOR DE-ICING (Foreigntitle not available) Translated into English from the German bythe American Astronautical Federation, Translation F-TS-919-RE,December 1946 (Unclassified Report).
39. R. A. Seban, HEAT TRANSFER AND EFFECTIVENESS FOR ATURBULENT BOUNDARY LAYER WITH TANGENTIAL FLUIDINJECTION, ASME Transactions - Journal of Heat Transfer,Series C, Vol. -`3, 1961, pp. 293-306.
40. J. Chin et al, ADIABATIC WALL TEMPERATURE DOWNSTREAMOF A SINGLE INJECTION SLOT, ASME Paper No. 58-A-104,1958 (Unclassified Paper).
69
41. J. Klein and M. Tribus, FORCED CONVECTION FROM NON-ISOTHERMAL SURFACES, University of Michigan Press, AnnArbor, Michigan, 1953 (Heat Transfer Symposium).
42. Lewis Research Center, NASA, Cleveland, Ohio, USE OF ATHEORETICAL FLOW MODEL TO CORRELATE DATA FOR FILMCOOLING OR HEATING AN ADIABATIC WALL BY TANGENTIAL
INJECTION OF GASES AT DIFFERENT FLUID PROPERTIES byJames E. Hatch and S. Stephen Papell, 1959, Report No. NASA
TN D-130 (Unclassified Report).
43. D. B. Spalding, PREDICTION OF ADIABATIC WALL TEMPER-ATURES IN FILM-COOLING SYSTEMS, AIAA Journal, Vol. 3,No. 5, May 1965, pp. 965-967.
44. J. L. Stollery and A. A. M. El-Eiwany, A NOTE ON THE USE OFA BOUNDARY-LAYER MODEL FOR CORRELATING FILM-
COOLING DATA, International Journal of Heat Mass Transfer,Vol. 8, January i965, pp. 55-56.
45. R. A. Seban and I. H. Back, VELOCITY AND TEMPERATUREPROFILES IN TURBULENT BOUNDARY LAYERS WIlf> TANGEN-TIAL INJECTION, ASME Transactions - Journal of Heat Transfer,Series C, Vol. 84, 1962, pp. 45-54.
46. Aeronautics Department, Imperial College, England, UnpublishedWork of J. Stollery, 1962.
47. Lewis Research Center, NASA, Cleveland, Ohio, AN EXPERI-MENTAL INVESTIGATION OF GASEOUS-FILM COOLING OF A
ROCKET MOTOR by James G. Lucas and Richard L. Golladay,October 1963, NASA TN D-1988, N63-21895 (Unclassified Report).
48. Naval Ordnance Laboratory, White Oak, Maryland, AIR-FILMCOOLING OF A SUPERSONIC NOZZLE by Bing H. Lien, August
1964, Aerodyna'iic Research Report No. 224, NOLTR 64-65,N64-31672, AD-448 477 (Unclassified Report).
49. S. E. Colucci, L. Kurylko, and C. George, SOLID ROCKETCOOLING (U), Proceedings of the Fifth U. S. Navy Symposiumon Aeroballistics, Vol. I, October 1961, (Confidential Proceedings).
50. Lewis Research Center, NASA, Cleveland, Ohio, EFFECT OFGASEOUS FILM COOLING OF COOLANT INJECTION THROUGHANGLED SLOTS AND NORMAL HOLES by S. Stephen Papell,
September 1960, NASA TN D-299 (Unclassified Report).
70
51. John P. Sellers, Jr., GASEOUS FILM COOLING WITH MULTIPLE
INJECTION STATIONS, AIAA Journal, Vol. 1, No. 9, September
1963, pp. 2154-2156.
52. Allison Division, General Motors Corporation, Indianapolis,Indiana, DEVELOPMENT OF COOLING SYSTEM FOR SOLID
ROCKET NOZZLES - FINAL TECHNICAL REPORT (U), 15November 1962, Engineering Department, Report No. 2994,Contract No. AF 04(611)-56. (Confidential Report).
53. Aerojet-General Corporation, Sacramento, California, HIGHCHAMBER PRESSURE ROCKETRY PROGRAM (U), 22 February1965, Quarterly Progress Report 8191-Q-lI, Contract No.
AF 04(611)-8191 (Confidential Report).
54. The Marquardt Corporation, Van Nuys, California, THRUSTCHAMBER COOLING TECHNIQUES FOR SPACECRAFT ENGINES-FINAL REPORT, 15 July 1963, NASA CR-50959, N63-21074,Contract No. NAS-7-103, (Unclassified Report).
55. The Marquarut Corporation, Van Nuys, California, RAMJETSTRUCTURAL ELEMENTS AND NONREGENERATIVELY COOLEDCOMBUSTION CHAMBERS AND NOZZLES (U), August 1964,Report No. X64-17794, AD-351421, Contract No. AF 33(657)-12146,
(Vol. 9 of "Final Summary Technical Report on the Calendar Year1963 Ramjet Technology Program" (U) (Confidential Report).
"71
_UNCLASSIFJIDSecurity Classification
DOCUMENT CONTROL DATA- R&D(Soweuriy classiflcation of riII). body of abaImct and tdnrxng annotatf Wn Suatl z. hntgra. When dut op..ll report It cla...tod)
1.?R|HINATING C•TIVITY (C.iormlt authOr) 20. REPORT S1ECURITY C L:.S41,FICATION'estone cientific Information CenterResearch and Development Directorate UnclassifiedU. S. Army Missile Command 11 Gmovp
Redstone Arsenal, Alabama 35809 J N/.AJ. REPORT TITLE
TRANSPIRATION AND FILM COOLING OF LIQUID ROCKET NOZZLES
"4. O-DSCRIPTIVE NOTES (Type of report and Inclusie date*)
NoneS. AUTHOR(S) (Lsf name. how, namo. Initial)
Terry, J. E. and Caras, G. J.
1. 5 " jRT DATE 7I TOTAL NO. OP PAGES ?b. NO. Or RewS
31 March 1966 _74 55O.. CONTYRACT OR GRANT NO. N/A OF OMIGINATOR' RMEPORT HlUMOIE'l)
SPROJECT ,o. N/A F.SIC-535
Sb. OTHER R&PORT 4NO(S) (Any oeh., nurumh., 'hat way be **s..edro.le pcr•)
d. AD.f
10. AVA ILAGILITY/LIMITATION NOTICES
Distribution of this document is unlimited.
11. SUPPLEMENTARY NOTES 12 SPONSORING MWITArAY ACTIVITY
None Same as No. 1
I. ASTRACT
This report presents a summary of current theoretical and experimentalwork conducted or. transpiration and film cooling of rocket nozzles. An effortwas made to assess the present technology to bring the reader abreast of thegeneral status of tht~se cooling techniques. Major problems which exist indeveloping transpiration and film cooling are presented in the conclusions.
The discussion of various aspects of transpiration and film cooling is not
meant to be exhaustive. Its purpose is to provide a backg-ound for the readerwho is interested in further pursuing these cooling techniques.
DD ."'.1. 1473 UNCLASSIFIEDSecurity Classification 75
UNCLASSIFIEDSecurity Classificiation
LINK A LINK B LINK CKEY WORDS ROLE WT ROLE WT ROLE TT
Transpiration Cooling
Film Cooling
Self Cooling
Engine Nozzle Cooling
INSTRUCTIONS
I. ORIGINATING ACTIVITY: Enter the name and address 10. AVAILLABILITY/LIMITATION NOTICE&: Enter any lia-of the contractor, subco.tracti, grantee, Department of De- itationa on fw'thsr dissemination of the report, other than thosefense activity or other organization (corporate author) issuing imposed by security classification, using standard statementsthe report. such as:2a. REPORT SECURITY CLASSIFICATION: Enter the over. (1) "Qualified requesters may obtain copies of thisall secur.t a28slaication of the report. Indicate whether ( p) from yb c s t"Restricted uats" it included. Marking is to be in accord- report from DDC."ance with appropriate security regulations. (2) "Foreign announcement and disaiemination of this
21. GROUP: Automatic downgrading is specified in DoD Di- report by DDC is not authorized."rective 5200. !0 and Armed Forces Industrial Manual. Enter (3) "U. S. Government agencies may obtain copie.; ofthe irc.up number. Also, when applicable, show that optional this report directly from DDC. Other qualified DDC
I markings have been used for Group 3 and Group 4 as author- users shall request through| ized. ,11
3. RFPORT TITLE: Enter the complete report title in all (4) "U. S. military agencies may obtain copies of thiscapital letters. Titles in all cases should be unclassified, report directly from DDC. Other qualified usersIf a meaningful title cannot be selected without classifica- shall request throughtion, show title classification in all capitals in parenthesis ,,immediately following the title.
4. DESCRIPTIVE NOTES: If appropriate, enter th,! type of (5) "All distribution of this report is controlled. Qual-;eport, e.g., interim, progress, summary, annual, or final. ified DDC users shall request throughGive the inclusive dates when a specific reporting period iscovered.
If the report has been furnished to the Office of Technical5. AUTHOR(S): Enter the name(s) of author(s) as shown on Services, Department of Comr-ierce, for sale to the public, indi-or in the report. Entet last name, first name, middle initial. cate this fact and enter the price, if known.If military, show rank and branch of service. The nam. ofthe principal author is an absolute minimum requirement. IL SUPPLE3ENTARY NOTES: Use for additional explana-
6. REPORT DATE: Enter the date of the report as day, tory notes.
month, year; or month, year. If more than one date appears 12. SPONSORING MILITARY ACTIVITY: Etter the name ofo.: the report, ure d-te of publication, the departmental project office or laboratory sponsoring (pay-
7a. TOiAL NUMBER OF PAGES: The total page count ing for) the research and development. nclude ad&'ss.
should follow normal pagination procedures, i.e., enter the 13. ABSTRACT: Enter an abstract giving a brief and factualnumbe, of pages containing information. summary of the document indicative of the report, even though
it may also appear elsewhere in the bo, of the technical re-7b. NUMBER OF REFERENCES Enter thy total number of port. If additional space is required, a continuation sheetrtere.'eer cited % the report. shall be attached.
go. CONTRACT OR GRANT NUMBER: If appropriate, enter It is highly desirable that the abstract of classif•ed re-the applicable number of the contract or grant under which ports be unclassified. Each paragraph vf the abstract shallthe report vas written, end with an indication of the military tecurity claasdiication
8b, Sc, & S .. PROJECT NUMBER: Enter the appropriate of the information in the paragraph, represented es (TS), (.S.
military department identification, such as project number. (C), or (U).subproject number, system numbers, task number, etc. There is no limitation on the length of the abstract. How-
9a. ORIGINATOR'S REPORT NUMBER(S): Enter the offi- ever, the suggested length is from 150 to 225 words.
cial report number by which the document will be identified 14. KEY WORDS: Key woras are technic:,Ily meaningful termsand controlled by the originating activity. This number must or short phrases that characterize a report and may be used asbe unique to this report. index entries for cataloging the report. Key words must ".e
9b. OTHER REPORT NUMBER(S): li the report has been selected so ihat no security classification is required. aden-assigned any other raport numbers (aither by the originator fierr. such as equipment model designation. trade name. "sili-
or by the aponsor), also enter this number(s). tary project code name. geolgraphic location. may be u%,d askey words but will be followed by an indicatLon nf technical
context. The assignment of links, rules, and weights is
_UNoptional. CLASSIFIED
76 Security Class i -ft nili0Wn
![SELF-CONTAINED AIR CONDITIONERS - Thermal Zone...5. Calculate net cooling capacities. Net total cooling = 67,500 – 2355 = 65,145 BTUH [19.09 kW] Net sensible cooling = 52,304 –](https://img.pdfslide.net/doc/110x75/5eb92028c1f63272796e97f4/self-contained-air-conditioners-thermal-5-calculate-net-cooling-capacities.jpg)
![Preliminary Work for DNS of Rocket-Nozzle Film-Cooling · 2017. 10. 20. · pressures and temperatures for a short testing time in the order of 5-7 ms [16]. The axisymmetric nozzle](https://img.pdfslide.net/doc/110x75/61444cb0aa0cd638b460c464/preliminary-work-for-dns-of-rocket-nozzle-film-cooling-2017-10-20-pressures.jpg)
