Regenerative Cooling of Liquid Rocket Engine Thrust Chambers

Regenerative cooling of liquid rocket engine thrust chambers Marco Pizzarelli ASI UNCLASSIFIED

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Regenerative cooling of LRE thrust chambers Outline: !

Thrust chamber environment (basics)

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Convective heat transfer (fundaments)

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Heat transfer characterization characterization:: hot-gas side coolant side wall conduction ! !

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Steady-state heat transfer

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Thermo-mechanicall characterizatio Thermo-mechanica characterization n

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Different thrust chamber designs

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Overview of advanced concepts

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Experimental characterization characterization of hot-gas side heat transfer

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Regenerative cooling of LRE thrust chambers Outline: !


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Heat transfer characterization characterization:: hot-gas side coolant side wall conduction ! !

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Thermo-mechanicall characterizatio Thermo-mechanica characterization n

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Experimental characterization characterization of hot-gas side heat transfer

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Regenerative cooling of LRE thrust chambers


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Thrust chamber environment (basics) A liquid rocket engine thrust chamber is the combustion device where the liquid propellants are injected, atomized, mixed, and burned to form hot gaseous reaction products, which in turn are accelerated and ejected at a high velocity to impart a thrust force A thrust chamber has three major parts: !

!

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an injector (that introduce the propellant into chamber) a combustion chamber (where propellants burn creating a hot gas)

the

a nozzle (where the hot gas is accelerated to supersonic velocities)

In large liquid-propellant rocket engines the thrust chamber is limited to the initial supersonic part of the nozzle (area ratio below 10). A nozzle extension is added to achieve the desired hot gas expansion ASI UNCLASSIFIED

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Vulcain thrust chamber

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Thrust chamber environment (basics) The increase of the combustion temperature improves the rocket engine specific impulse

$%&' (+)* where !

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-./: temperature of the combustion products 0: molecular mass of the combustion products

Combustion temperatures of rocket propellants are generally higher than the melting points of common metal alloys and refractory materials (up to K)

12))

From (2)

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!"#:

Thrust chamber environment (basics) The strength of most materials declines rapidly at high temperatures. For rocket engine applications, the temperature where a material loses to % of its room temperature strength is often selected as the maximum allowable wall temperature. This temperature is well below the material melting point

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Enough heat has to be absorbed to keep these walls at a sufficiently low temperature, so that the wall material is strong enough to withstand the stresses imposed by the fluid pressure, thermal gradients, and other loads Measurements of static stress to cause rupture after 100 hours (typically the “stress to density ratio” is the relevant variable) (1)

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&

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Combustion chamber pressure )* in rocket engines is “high” (up to bar) mainly because, for a given nozzle area ratio: when operating in the atmosphere the larger ./ the larger the specific impulse "# when operating in vacuum the larger ./ the smaller the engine !

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Higher )* is linked with higher combustion-gas mass flow rate per unit area of chamber cross section and therefore with higher heat transfer rate

Thrust coefficient

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9 : versus nozzle area ratio (note: $%&'9 :) (2) 7

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Thrust chamber environment (basics) Combustion chamber temperature and pressures are “high”

Necessity to: !

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cool the wall to a temperature considerably below its maximum allowable temperature (i.e., much below the combustion temperature) or to stop operation before the wall becomes too hot use high strength materials (the thickness, therefore the mass, of the thrust chamber wall depends strongly on the stresses it can support)

Rocket engine cooling is necessary for strength considerations. In fact, enough heat has to be absorbed to keep the walls at a sufficiently low temperature, so that the wall material is strong enough to withstand the stresses imposed by the fluid pressure, thermal gradients, and other loads. Consequently, the design of a thrust chamber is mainly a thermomechanical problem that requires a proper characterization of the heat transfer and the mechanical loads ASI UNCLASSIFIED

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Thrust chamber environment (basics) Regenerative cooling : the walls of large liquid-propellant rocket engines (that are always bi-propellant rockets) usually consist of an array of suitably shaped tubes machined or brazed together to form the thrust chamber. The fuel or the oxidizer is used as a coolant flowing in such tubes before it is injected in the combustion chamber. This method is called regenerative cooling because of the similarity to steam regenerators

RL-10 cutaway

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Thrust chamber environment (basics) Notes on regenerative cooling : This cooling technique mainly applies in mid-to-high thrust levels because the heat flux to the chamber walls increases as the hot-gas mass flow rate (and thus the thrust) increases !

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Large liquid propellant rocket engines are usually turbopump-fed engines; in this case a sufficiently large pressure drop is usually available for chamber cooling (w.r.t. pressure-fed engines). This availability permits the use of regenerative cooling, which requires sufficient pressure to force the coolant through the cooling passages. However there are examples of pressure-fed engines that are regeneratively cooled (e.g., Aestus uses mono-methyl-hydrazine as coolant)

Aestus thrust chamber

In regenerative cooling the heat absorbed by the coolant is not wasted; it augments the initial energy content of the propellant prior to injection, increasing the exhaust velocity slightly (0,1 to 1,5%) and most noticeably in small thrust chambers, where the wallsurface-to-chamber volume ratio is relatively large Generally the fuel is used as coolant because of the tube wall oxidization concern if oxidizer is used as coolant

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Thrust chamber environment (basics) From a thermal point of view, regenerative cooling consists of the steady flow of heat from a hot gas through a solid wall to a cool fluid. In fact, the heat from the combustion gases conducts through the walls –mainly in the radial direction- and is convected away by the fluid flowing in the cooling channels Such problem can be reduced to a one-dimensional cooling jacket model (ignoring the heat transfer through the walls that separate the coolant passages)

Typical configuration (1)

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One dimensional model (1)

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Convective heat transfer (fundaments) the most most rele releva vant nt heat heat tran transf sfer er mech mechan anis isms ms is the the forc forced ed conv convec ecti tion on In liquid rocket engines the Convection: conduction enhanced by motion of the fluid Forced Forced convec convectio tion n: the fluid motion is generated by an external device (e.g., a pump)

From (1)

;< or or => : wall heat transfer rate per unit area (or wall heat flux) [W/m ] 2

Velocity boundary layer (!): large velocity gradients Thermal boundary layer (!T ): large temperature gradients

@A B CDFE B G (hence WL~1) ~1)

! !T

HIJKILMNIOPQR ISMTIOUIV

In most situations: ! ~!T ASI UNCLASSIFIED

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Convective heat transfer (fundaments) The govern governing ing equati equations ons for steady steady,, two-di two-dimen mensio sional nal,, incomp incompres ressib sible le flo flow w with with consta constant nt properties and under the Prandtl’s hypothesis (thin boundary layer):

XY [X\ B 4 XZ X] cY XY XY _ a8 X Y XZ [ \X] B ^` aZ [ bX] c c cXd Xd a8 X XY `Y XZ [ `\X] B YaZ [ FX] c [ C X] where:

Z eTMLIUPMfOKQLQRRIRPfPgIhQRRHSIRfUMPiUfNKfOIOPYV ] eTMLIUPMfOOfLNQRPfPgIhQRRHSIRfUMPiUfNKfOIOP\V `! 8j- eTIOkMPijKLIkklLIQOTPINKILQPlLI dekKIUMmMUIOPgQRKinopqr C : dynamic viscosity [Pa s] b B Cp` : kinematic viscosity [m /s] F : thermal conductivity [W/(m K)] 2

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Convective heat transfer (fundaments) Simplifications of the energy equation:

c cXd Xd a8 X XY `Y XZ [ `\X] B YaZ [ FX] c [ C X] !

!

the viscous dissipation

d B DE-) and no axial pressure gradient (e.g., flat plate) cXXX Y XZ [ \X] B vX] c

in case of calorically perfect gas (i.e., it becomes:

where

!

C

st ccan be generally neglected (because of the low fluid velocity) su

v B Fp`DE is the thermal diffusivity [m /s] 2

ad B D T- [xw T8) it becomes: cXXX Y XZ [ \X] B vX] c

in case of an incompressible fluid (i.e.,

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Convective heat transfer (fundaments) In case of no axial pressure gradients (i.e., flat plate) the momentum and energy equations becomes:

cY XY XY X Y XZ [ \X] B bX] c cXXX Y XZ [ \X] B vX] c !

These equations are equal if: (most gases have

!

@A'_)

CD b @A B v B FE B _

Same solutions are possible introducing variables that have same boundary conditions:

Yy B zt QOT -y B {~{|{|{}} with Yyy B -yy B 4 at wall (i.e., ] B 4) Y B - B _ outside the boundary layer (i.e., ] • €)

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Convective heat transfer (fundaments) Same profiles of

!

!

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Yy and -y lead to:

Yy B -y • -H]V B -> [H{~z|{} V YH]V st wall shear stress: > B C su > wall heat flux:

=> B ^F sus{ > B ^F {}|{z ~

Combining the above relations:

=> B

‚ƒ} -> „z

st su >

^ -… .

In other terms:

†‡ B ˆ‰ (‡ ^ (… where ˆ‰ is the heat transfer coefficient and (‡ ^ (… is the driving potential ASI UNCLASSIFIED

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Convective heat transfer (fundaments) From the definition of

> and =>: > B C X]XY > Š C ‹ !

=> B ^F X]X- > Š F -> ^ -… !T

ŒIOUIe d B FC‹> Š F Š F H Š Mm @A Š _V !

!T

!

!T

Note that: !

the convective heat transfer coefficient does not depend on the wall temperature

!

where the boundary layer thickness is minimum, the heat transfer coefficient is maximum

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Convective heat transfer (fundaments) Relevant non-dimensional numbers: !

Skin friction coefficient

 Ž B _ > c 7 `‹

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Nusselt number

Y‘ B dF Z

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Reynolds number

’“‘ B `‹Z C

d B ‚ƒ„z} we obtain the Reynold’s analogy (flat plate): Y‘ B 7_Ž ’“‘ In case of @A ” _ and turbulent flow (Colburn’s analogy): Y‘ B 7_Ž ’“‘ @Awp Rearranging the relation

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Convective heat transfer (fundaments) In case of pipe (i.e., axial pressure gradients) the Colburn’s analogy for turbulent flow is still valid:

˜ –— B ™ 9 : š› œ˜p1 where: !

Reynolds number

< Ÿ ’“ B žŸ B C C¡ (Ÿ: pipe diameter; ¢: mass flux [kg/(s m )]; <: mass flow rate [kg/s]) 2

!

Nusselt number

!

Mass flux:

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Y B dFŸ ž B ¡_£` —¤¥ T¡ 20

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Convective heat transfer (fundaments) For a smooth pipe with turbulent flow having

§ ¤ _4¨ © ’“ © _4ª:

Ž B 4j’“4.j«3c This yields to:

–— B )j)™1 š›)j¬ œ)j11 This expression, often referred to as “ Dittus Boelter equation”, is useful in a fairly wide range of pressure gradients Surface roughness can have a large effect on the friction and heat transfer (that is, increasing of both  and )

Ž

Y

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Heat transfer characterization: hot-gas side ASI UNCLASSIFIED

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Heat transfer characterization: hot-gas side The hot gas flow is essentially a boundary layer flow

In the actual hot gases expansion within the thrust chamber, the boundary layer thickness at the throat does not strongly depend on the boundary layer “history” (in the injection region) Moreover, the boundary layer thickness may decrease in the flow direction (due to steep axial pressure gradients), reaching a minimum at the throat of the nozzle

expected maximum convective heat transfer ‚" rate at the throat ( /

d Š

!

From (1)

Note: Boundary layer is affected by wall curvature, axial pressure gradients, and normal pressure gradients; however the approach used for the flat plate and tubes is fairly valid (especially after the throat, that can be treated as a leading edge: ®¯°±²® )

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Heat transfer characterization: hot-gas side The turbulent convective hot-gas side heat transfer in the actual condition (i.e., high flow velocity and ) can be modeled as:

@A ” _

†* B ˆ* (‡³ ^ (‡ˆ where: / is the convective heat flux / is the heat transfer coefficient >´ >µ is the driving potential >´ is the adiabatic wall temperature >µ is the hot gas side wall temperature !

!

! !

!

= d - ^-

Note that: one dimensional isentropic flow modeling is assumed for the hot-gas flow !

!

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the hot-gas flow in a thrust chamber can be still assimilated to a boundary layer problem and thus * is only a weak function of the wall temperature

ˆ

in case of high velocity, the driving potential is not based on the free stream temperature but on the adiabatic wall temperature

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Heat transfer characterization: hot-gas side The adiabatic wall temperature is the temperature that would be attained at wall in case of adiabatic condition: / . Its deviation from the stagnation temperature of the free stream is evaluated by the recovery factor :

= B4

A

 B ((‡³)* ^^ ((** where !

!

!

-/ is the free stream temperature -./ is the free stream stagnation temperature the recovery factor is typically A'4j¶ and in case of turbulent flow with WA'_it is often approximated as: A B @Awp

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From (1)

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Heat transfer characterization: hot-gas side {·¸ B _[ ¹ º c (where ¹ B ¼|w, ½ B ¾, and À is the free stream Mach number): º » {¸ c ¿ - º ->´ B _ [ A¹»c >´ B _[A¹»c fL º º -/ -./ _ [ ¹»c º Note: for A B 4j¶ and Á B _j7 (¹ B 4j_): ->´ Š -./ if À © 4j5 ->´ B 4j¶§-./ if À B 6 Since

!

!

This highlights that: !

!

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the adiabatic wall temperature is essentially equal to the free stream stagnation temperature (i.e., the combustion temperature)

in case of adiabatic condition the flow at wall almost reaches the combustion temperature if the wall has a flow obstruction or a wall protrusion, then the kinetic gas energy is locally converted back into thermal energy essentially equal to the stagnation temperature and pressure of the combustion chamber. Since this would lead to local overheating and failure of the wall, rocket engine inner walls have to be smooth

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Heat transfer characterization: hot-gas side Many (although sometimes more complicated) correlations for the Nusselt number similar to .jÂ .j) are presented in the literature the Dittus Boelter equation (

Y B 4j47§ ’“ @A

Y' ’“

.jÂ and can be Almost all the proposed correlations are based on the assumption that the convective heat transfer applied to determine (at best) within about

Ã™)Ä

The fluid properties can be evaluated at local bulk temperature or at a given “film temperature” (e.g., the average value between the wall and the free stream temperature) The most known correlation is the one proposed by Bartz (1955):

d/Ÿ B 4j473 < Ÿ .jÂ CDE .j¨ `´Å C´Å .jc F. C. ¡ F . `Æ C. where: the subscript “ ” refers to properties evaluated at the combustion temperature the subscript “am” refers to properties evaluated at the average temperature between the wall and the free stream temperature is the free-stream value of the local gas density

4

! !

!

`Æ

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Heat transfer characterization: hot-gas side Since

SSME-MCC heat transfer coefficient (3)

–—' š›)j¬ where

< ’“'žŸ' Ÿ < B ž¡ ( is the hot gas mass flow rate, which is constant through the thrust chamber in case of steady state conditions) the hot gas side heat transfer coefficient is:

)j¬ < Ç ˆ*' È˜j¬

throat section

the maxi maximu mum m heat heat For a given mass flow rate, the trans ansfer coefficie icien nt occurs at the the throat of the thrust chamber (experimentally, the maximum observed ed slight slightly ly upstre upstream am becaus becausee of / is observ variable flow properties)

d

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Heat transfer characterization: hot-gas side chocked ked thrus thrustt cham chambe berr (i.e., The mass flow rate in a choc

À B _ at the throat) is:

& Ê )* <Ç B É š()*Ë where !

!

!

8./ is the stagnation pressure at the throat (it is assumed that the flow is isentropic and thus the stagnation pressure is constant all along the thrust chamber • 8./ is the chamber pressure) -./ is the stagnation temperature at the throat (it is assumed that the flow is adiabatic and thus the stagnation temperature is constant all along the thrust chamber • -./ is the chamber temperature) ÐÑÒ |Ó ÐÔÒ ÎÏw ¡Ì is the throat area, ’ is the hot gas constant, and Í B ½ c is a fluid constant ¾ weakly depending on ½ B  . For ½ B _Õ7 • Í Ö 4j36 ¿

Thus, the hot gas side heat transfer coefficient can be expressed as:

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.jÂ ¡Ì .j× 8 ./ d/' Ÿ.jc ¡

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Heat transfer characterization: hot-gas side The expression:

)j¬ Ê )jØ & )* ˆ*' È)j™ ÊË Ë highlights that: !

chamber pressu pressure re the cooling requirement increases increases rather rapidly with with increasing chamber

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the cooling requirement increases increases with decreasing thrust chamber chamber dimension

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the maximum maximum heat transfer coefficient coefficient occurs occurs at the throat of the thrust chamber

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scale scale laws laws can be used to characterize the hot gas side heat transfer

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Heat transfer characterization: hot-gas side Radiative heat transfer

The heat transfer rate to the thrust chamber walls can be augmented by the hot gas energy radiation Gases do not radiate over a continuous spectrum of wavelengths but rather over discrete “bands” (i.e., far from the “blackbody” emission spectrum). Moreover, gases absorb radiation as they radiate it. The most important radiating gases from common propellants are CO2 , H2O, CO, etc. (in general, polyatomic gases radiate more strongly than diatomic gases) The radiant power from hot gas to a “unit area” wall can be modeled as:

† B Ù* Ú (Û* where / is the gas emissivity (non-dimensional < 1); it is a complex function of the gas properties and / in the case of “blackbody” emission |Â c ¨) is the Stefan-Boltzmann constant ( 5,6697 / is the gas temperature !

!

!

Ü Ý -

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Ü B_

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ÝB

¤ _4 ÞpN q

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Heat transfer characterization: hot-gas side The wall is usually assumed to absorb all the incident radiation (like a “blackbody”) while reradiating negligible energy because >/ /

- ß-

Hence,

=à B Ü/ Ý -/¨ approximately represents the net radiant heat flux to the wall

In general, radiative heat flux increases with increasing temperature, pressure and chamber throat diameter If the gases contain solid or liquid particles, these may appreciably contribute to the emitted radiant energy. In this case, the particles radiate over a continuous spectrum of the wavelengths (i.e., luminous flames in contrast to the non-sooty flames that radiate very little in the visible region of the spectrum because the emitting bands of CO 2, H 2O, CO are all in the infrared region) Generally, radiative heat transfer in rocket thrust chamber is generally modest (especially in the absence of solid particles), from 5% to 35% of the total heat transfer

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Heat transfer characterization: coolant side ASI UNCLASSIFIED

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Heat transfer characterization: coolant side Assuming a one-dimensional cooling jacket model with low fluid velocity, the convective heat transfer rate to the coolant can be modeled as:

Cooling jacket schematic (cross section)

†á B ˆá (‡‰ ^ (á where: !

!

!

dâ : coolant heat transfer coefficient [W/(K m )] ->: coolant-side wall temperature -â: coolant free stream temperature 2

Detail of the one dimensional model

Note: in case of pipe flow (i.e., considering the coolant flowing in a number of tubes that constitute the thrust chamber) â represents the average coolant temperature (bulk temperature) instead the free-stream temperature. In this case, the fluid properties ( , , and E ) are evaluated at such average temperature. Finally, if the pipe cross section is not circular, the hydraulic diameter is used in the formulas

-

CF

D

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Heat transfer characterization: coolant side The bulk temperature of the coolant increases from the point of entry until it leaves the cooling passages, as a function of the heat absorbed and of the coolant flowrate, as imposed by the energy balance equation:

< < ãá B Çáäå á B Çá‰&á ä(á

where: ! !

!

!

!

æâ: wall heat transfer rate entering the coolant [W] <â: coolant mass flow rate [kg/s] äçâ: coolant bulk enthalpy increase in the cooling circuit [J/kg] ä-â: coolant bulk temperature increase in the cooling circuit [K] DEâ : coolant specific heat (assumed constant or a proper average value) [J/(kg K)]

Note that in the energy equation the assumption of low velocity has been made and thus the stagnation and the static conditions are equal None of the common propellants can absorb more than a few percentage of the heat of combustion (without vaporizing or decomposing and thus becoming unsuitable as coolants). The heat of combustion can be of the order of 100 MJ per kg of fuel while â can be of the order of 1 MJ/kg. This large difference is due to the fact that the combustion is a much more energetic phenomenon than convective heat transfer

äç

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Heat transfer characterization: coolant side Notes on coolant pressure drop

Provided that the coolant remains chemically stable, the cooling system should be designed so that the fluid absorbs all possible heat transferred from the hot-gas. Of course, the coolant pressure drop must be properly regulated because higher pressure drop allows a higher coolant velocity in the cooling channel (and thus a better cooling), but requires a heavier feed system, which increases the engine mass and thus also the total inert vehicle mass In order to limit the coolant pressure drop, abrupt change of flow direction and sudden expansion or contraction of flow areas should be avoided. Moreover, the inner surface of cooling passages should be smooth and clean

ä8

è

The pressure drop in a channel of length , diameter loss can be evaluated as follows:

c Gé ž ä8 B 7` ¤ Ÿ

where !

! !

Ÿ and without concentrated pressure

G: friction factor coefficient (it is mainly a function of ’“ and relative surface roughness) ž: coolant mass flux `: coolant density

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Heat transfer characterization: coolant side Typical rocket coolants operate in different thermodynamic regimes that can have a remarkable influence on the cooling performances Some examples and their typical state in the cooling circuit with respect to the critical point  and  : !

!

!

!

!

!

8 Water (liquid) 8 B 77_ bar and - B 3«5 K Hydrazine (liquid or sup. pres.) 8 B _«5 bar and - B 367 K Nitrogen tetroxide (liquid or sup. pres.) 8 B _4_ bar and - B «§_ K Methane (sup. pres.) 8 B «3 bar and - B _¶4 K Kerosene (sup. pres.) 8 B 74 bar and - B 35ê K Hydrogen (sup. pres.) 8 B _§ bar and - B §§ K

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Note: in most systems, particularly those fed from a turbopump, the coolant pressure is supercritical A

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Heat transfer characterization: coolant side Depending on the coolant thermodynamic (especially with respect to the critical pressure  and the boiling temperature ëì -defined only if  ) and flow conditions, different regimes in transferring heat can be recognized:

-

8©8 !

!

8

Forced convection (when  and > ëì or when single phase heat transfer

8©8

- ©-

8 í 8)

8

Nucleate boiling (when K)  and > ëì small vapor bubbles causes local turbulence increase and â greatly increases

8©8

- ^ - î 64

d

!

Film boiling (when K)  and > ëì a gaseous film insulates the wall, often causing its melting

8©8

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- ^ - ï 64

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From (2)

-> ^ -â A

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Heat transfer characterization: coolant side In case of subcritical pressure, to achieve a good heat-absorbing capacity of the coolant, the coolant flow velocity is selected so that boiling is permitted locally at wall but the bulk of the coolant does not reach this boiling condition. The maximum feasible heat transfer rate is referred to as Å´‘ . It mostly depends on the fluid pressure and velocity.

=

=ó²ô

Some examples: !

!

!

= B _6ð§4 ñò ÅÓ 8 B _«5 - B 367 K) ñò Nitrogen tetroxide: =Å´‘ B 3ð__ Ó Å #8 B _4_ bar and - B «§_ K) ñò Kerosene: =Å´‘ B 7 ð 3 Ó Å (8 B 74 bar and - B 35ê K) Hydrazine: Å´‘ (  bar and

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8

-> ^ -â A

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Heat transfer characterization: coolant side Many semiempirical relations have been found to determine the coolant heat transfer in round tubes and for liquids far from boiling and supercritical fluids sufficiently far the from critical point. These correlation are typically of the “Dittus Boelter”-type and have a typical uncertainty of 20÷30%:

–— B Ê š›)j¬ œ³

Modification terms are typically added to take into account for:

dâ)

!

entrance (increases

!

non-circular cross section

!

!

wall to coolant temperature difference (generally decreases â )

d

roughness (can greatly increases â )

d

!

(NASA)

curvature (either increases or decreases depending on the curvature orientation)

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(NASA)

dâ, A

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Heat transfer characterization: wall conduction ASI UNCLASSIFIED

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Heat transfer characterization: wall conduction Assuming a one-dimensional cooling jacket model, the heat transfer through the solid wall is modeled by:

†‡ B õ‡á H(‡ˆ ^ (‡‰V

Cooling jacket schematic (cross section)

where !

F>: thermal conductivity of the wall

material !

!

äé: wall thickness ->µ is the hot

gas side wall

temperature !

->: coolant-side wall temperature

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Detail of the one dimensional model A i S i l It li

Heat transfer characterization: wall conduction Realistic wall heat transfer

Heat transfer in an actual rocket engine thrust chamber is far more complicated than in a cooling jacket model because of the multidimensional heat transmission in the wall

coolant

hot combustion gas

Heat is transferred also through the walls that separate the coolant passages and thus also in the tangential direction The lateral walls may have the beneficial function of cooling fins (i.e., larger coolant-side heat transfer surface than hot-gas side heat transfer surface) Sketch of realistic heat transfer in a thrust chamber wall (2)

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Steady-state heat transfer For steady conditions and assuming a one-dimensional cooling jacket model, the heat transfer balance is:

=/ [ =à B => B =â

where !

!

!

!

=/ B d/ ->´ ^ ->µ =à => B ä‚}é ->µ ^ -> =â B dâ -> ^ -â

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: convective hot-gas side heat flux : radiative hot-gas side heat flux : conductive heat flux through the wall : convective coolant-side heat flux

A

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Steady-state heat transfer Combining the expressions of the heat fluxes: !

The heat flux in the wall is:

†‡ B å (‡³ ^ (á [ˆ†* ç

where is the overall heat transfer coefficient:

˜B˜[ á[˜ å ˆ* õ‡ ˆá !

The hot-gas side wall temperature is:

where:

( [ ö( † á ‡³ (‡ˆ B ˜ [ ö [ˆ* ö B ˆ* õ‡á [ˆ˜á

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Steady-state heat transfer The actual configuration is not one-dimensional because of the presence of an array of wjÂ, best cooling system consists of circular/rectangular cooling tubes. Note that since â many small-diameter tubes. In fact, large thrust chambers have hundreds of tubes with dimensions of the order of few mm (or even less)

d '_÷Ÿ

To take into account the actual configuration, the onedimensional model can be improved considering the “effective” areas through which the heat transfer passes:

=/ [ =à ¡/ B => ¡> B =â ¡â where: / : gas side area > : effective wall area â : effective coolant side area !

! !

¡ ¡ ¡

¡

Note that > and geometric areas

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¡â do not necessarily correspond to the 47

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=

-

The formulas of the conductive heat flux > and the hot gas side wall temperature >µ does not change, provided that the coolant heat transfer coefficient and the wall thermal conductivity are replaced by the “equivalent” values:

dây B dâ ¡¡/â F>y B F> ¡ ¡>/ Note that, since ¡â and ¡> are larger than ¡/ , the equivalent values ˆyá and õy‡ are larger than the original one ˆá and õ‡ Including this geometric effect implies a larger conductive heat flux => and a lower hot gas side wall temperature ->µ

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Steady-state heat transfer Typical heat flux in chemical rocket propulsion can vary from fractions of in the throat region of the Space Shuttle Main Engine)

ñò up to 160 ñò (as ÅÓ ÅÓ

The nozzle throat region has usually the highest heat-transfer intensity and is therefore the most difficult to cool. For this reason the cooling channels are often designed so that the coolant velocity is highest in this region by restricting the coolant passage cross section Note that the heat flux is practically independent of the wall temperature. This is because the inner wall temperature of a cooled thrust chamber must be kept so much lower than the than the combustion temperature that the differences in wall temperature cause only small differences in heat flux. In fact:

ä= ä/ =/ B d/ ->´ ^ ->µ ø =/ B ->´ ^>µ->µ Typical values can be ->´ '§644K and ->/ '544K (in the throat region). If ä->µ '744 K (e.g., wall temperature variation due to highly different cooling mass flow rate), it results that the heat flux Typical heat transfer rate distribution of a small thrust chamber (2) ASI UNCLASSIFIED 49

difference is only

äù¸ '5Ä. ù¸

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Steady-state heat transfer ·jû ¦ý .j× E ·¸ úMOUI d/' üý·jÓ ¦ and (in case of no radiation) =>'d/, the heat flux at the throat is: )j)*¬ & †‡Ë' È)j™ Ë Finally, because the thrust is ì/ Ìc and thus:

þ'8 Ÿ

þ B Žÿ8ì/ ¡Ì, comparing engines with equal thrust coefficient Žÿ gives )j)*Ø & †‡Ë' !)j˜

8

8

The peak heat flux (at the throat region) increases almost linearly with ./ because higher ./ is linked with higher combustion-gas mass flow rate per unit area of chamber cross section and therefore with higher heat transfer coefficient:

"# $ B ‰%%Ë

&%* &

'''

/Ë B ÊÇË* & * d/Ì & ¡Ì B Žÿ(8ì/ )* 
Moreover, increasing the engine thrust, the heat flux slightly reduces. This is due to the fact that larger engines have larger throat area and thus slightly smaller heat transfer coefficient:

"# &%* B ‰%%Ë

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.jÂ ž.jÂ < Ç & < ( ( % * * / ! &''' ¡Ì BŽÿ8ì/ &* < / BŽÿŽ+ &*/Ë B ÊË B 9+ B ‰%%Ë* d/Ì' ŸÌwjÂ B ¡Ì.jÌ w ) 50

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Steady-state heat transfer The relation !

!

)j)*Ø & ' implies that:

†‡Ë !)j˜

the maximum allowable heat flux limits the chamber pressure and thus the engine performances cooling is relatively easier in large-thrust engines

0gQSIMmmILIOP KLfKIRRQOPk TMmmILIOP gIQP PLQOkmIL LQPIke .j.4× K 12® B3 þ.jw

where the parameter depends on the adopted propellants.

3

Maximum heat flux versus chamber pressure and at different thrust levels of LOX/LH2 and LOX/RP-1 rocket engines (NASA)

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Steady-state heat transfer Effect of increasing the heat transfer parameters and temperature ‡ˆ :

(

ˆ* ˆá õ‡ p á

ˆ* , ˆá , and õ‡p á on the wall heat flux †‡

†‡

(‡ˆ

!

!

!

"

!

"

In fact: an increase of !

!

d/, or dâ, or F>päé leads to an increase of the overall heat transfer coefficient ç hgILI 5w B µw¸ [ä‚}é [µw6 and thus of => B ç ->´ ^ -â äé w { Ï8{ an increase of d/ implies an increase of 7 B d/ ‚ [µ QOT Pglk fm ->µ B 6 wÏ8}9 while an } 6 increase of dâ or F> päé implies a decrease of 7 (and thus of ->/ ) It is one of the major design goals to keep coefficient ˆ* “low” and the coefficient ˆá and á põ‡ “high” in order to reduce the hot gas side wall temperature (‡*

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Thermo-mechanical characterization

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Thermo-mechanical characterization Occurrence of both static and dynamic loads !

!

The walls of the thrust chambers are subjected to radial and axial loads from the chamber and coolant pressure, flight accelerations, vibration, and thermal stresses. They also have to withstand a momentary ignition pressure surge or shock, often due to excessive propellant accumulation in the chamber (this surge can exceed the nominal chamber pressure) The thermal stresses induced by the temperature difference across the wall are often the most severe stresses and a change in heat transfer or wall temperature distribution will affect the stresses in the wall. In particular, the most severe thermal stresses can occur during the start, when the hot gases cause thermal shock to the wall

Issues to be taken into consideration about the selection of the thrust chamber materials: !

!

!

The strength of the chamber wall against the thermal gradients and the high pressure in the cooling system (with respect to the hot-gas pressure) The chemical resistance of the material to the low-velocity coolant on one side and to the high-velocity hot-gas on the other The method of fabrication (metal forming and welding or machining, casting, etc.)

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Thermo-mechanical characterization Estimation of the wall stress (static loads)

Ignoring the walls that separate the coolant passages (i.e., assuming a one-dimensional cooling jacket model), the wall material undergoes a combination of a constant compressive stress E , caused by the pressure differential between the coolant and combustion gases, ì / , and the thermal stress Ì caused by the temperature gradient across the wall. The thermal stress induce compression on the hot-gas side and expansion on the coolant side. The maximum (compressive) stress occurs at the hot-gas side and can be evaluated as:

8 ^8

:

:B

:

8ì ^ 8./ A [ ?v=>äé äé 7 _ ^ b F > ìÅEà;<<=>;<Ìà;<< Ìµ;àÅ´@<Ìà;<<

where: : engine radius : wall thickness E: modulus of elasticity of the wall material : thermal expansion coefficient of wall material : Poisson’s ratio of the wall material > : thermal conductivity of the wall material !

! !

!

! !

A äé v b F

Note that, according to the cooling jacket method, wall temperature difference in wall material is: ASI UNCLASSIFIED

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= äé > ä- B

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Thermo-mechanical characterization At a given thrust level regenerative cooling is feasible only if the combustion pressure is Ç . These parameters are below a limiting value )*Ç and for a given wall thickness established by structural requirements to accommodate pressure and thermal stresses as well as by fabrication feasibility limits

&AB

äáAB

This limit arises because: !

the pressure differential stress proportional to:

:E B ECD|Eäâ·¸ à 'Eäâ·¸ 8ì ^ 8./ '8./ : Ì EF ù äâ :Ì Bc w|G} ‚} '=.j>×äé'8.jw./.j×äé =>'8./ p( (note that

!

:E

is

)

the thermal stress (note that

is proportional to: )

(NASA)

In other words: the thicker the wall the more it supports the pressure load. The request for thick wall is more pronounced with increasing chamber pressure !

!

the thinner the wall the more it supports the thermal load. The request for thin wall is more pronounced with increasing chamber pressure

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&AB

The limiting values of chamber pressure )*Ç and wall thickness cooling system configuration and material properties

äáABÇ are dependent on

(NASA)

With respect to stainless steels, copper alloys generally permit higher chamber pressure with wall thickness between 0,5 and 1mm (which is still feasible by means of milling technique because copper is a highly ductile material). For this reason, copper alloys are an excellent choice but for propellant combinations with corrosive or aggressive oxidizers (nitric acid or nitrogen tetroxide) stainless steel is often used as the inner wall material, because copper would chemically react. Maximum allowed temperature is about 850K for high-performance copper alloys (such as CuAgZr) and 900K for stainless steel. Thermal conductivity of copper alloys is 300-380 W/m K while of stainless steel is about 20 W/m K ASI UNCLASSIFIED

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F päé

Note that the copper alloys led to “high” value of > , which is beneficial for the heat transfer. In fact, considering typical values of the thermal conductivity and wall thickness of ª W/m2K whereas the hot gas and coolant side heat copper alloys structures, >  transfer coefficients are / â W/m2K. This leads to: higher wall heat flux > lower hot gas side wall temperature ‡ˆ lower temperature difference in the wall >µ > lower thermal stress Ë

F päé'_4H ðH_4 d jd '_4 ð _4 = (

!

!

I

!

!

- ^-

In fact:

MOULIQkMOJ ä‚}é lOTIL PgI giKfPgIkMk ä‚}é K d/jdâ then: w B w [äé [ w Š w [ w ) 5 µ¸ ‚} µ6 µ¸ µ6 => B ç -é>´ ^w-â µ & 7 B d/ {6‚äÏ}8{}[9µ6 Š µ¸6 ) ->µ B wÏ8 ) ->µ ^ -> B => ä‚}é B çä‚}é ->´ ^ -â ) :Ì BcEFw|ùG}äâ‚} BEFH{c }w|L|{G }CV ) !

!

!

!

!

!

!

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Different thrust chamber designs Different fabrication techniques: tubular-wall design

Tubular wall without outer shell (NASA)

Tubular wall with outer shell (2)

This type of cooling system is made of singularly formed tapered tubes (to reduce the tube area in the throat region) that are brazed together. Tube cross section can be circular or not. This construction technique generally imposes the use of stainless steel or nickel alloys –e.g. Inconel- (low thermal conductivity materials) with relative small thickness (even 0,2 mm can be realized because of the relative strength of these materials). Even if external bands of highstrength steel are generally added to contain the pressure loads, this design is limited to bar). The primary advantage of this design is its light relatively low heat flux (i.e., )* weight (because of the use of high strength materials) and the large gained experience in US (e.g., F-1, RL-10, J-2, RS-27)

& © ˜))

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Different thrust chamber designs Tubular-wall design used on relatively low chamber pressure thrust chambers or nozzle extensions

8 '64 é =M'

H-1: ./ bar (stainless steel 347; " Å 0,25mm)

8 '64 é =M'

J-2: ./ bar (stainless steel 347; " Å 0,25mm) ASI UNCLASSIFIED

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8 '54 bar éÅ=M '0,46mm)

F-1: ./ (Inconel X-750; "

8 '«4

LE-5A: ./ bar (nickel alloy)

8 '74ð«4 bar éÅ=M'0,25mm)

RL-10: ./ (stainless steel 347;

"

8 '744

SSME nozzle: ./ bar (stainless steel A-286) A

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Different thrust chamber designs Different fabrication techniques: channel-wall design

Channel wall with rectangular tubes (2)

This type of cooling system is realized by machining (typically milling) rectangular grooves of variable width and depth into the surface of a relatively thick contoured high-conductivity chamber and nozzle wall liner; an outer shell of nickel-alloy (high strength material) is added to enclose the coolant passages The advantage over the tubular-wall design is the possibility to use high-conductivity material for wall construction, such as copper alloys, and relatively small thickness (below 1mm). Consequently, this design can be used to extremely-high-heat-flux. This design, that is more recent in US than tubular-wall, is adopted in all relatively high pressure thrust chambers, that is, having )* bar (e.g., SSME-MCC, RS-68, Vulcain)

& í ˜))

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Different thrust chamber designs Channel-wall design generally used on relatively high chamber pressure thrust chambers

SSME-MCC:

Merlin 1C:

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8./'744 bar

8./'_44 bar 63

Vulcain:

8./'_44 bar

Aestus (note the liner made of steel instead of copper alloy): A

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8./'__ bar

Different thrust chamber designs Historical note on US thrust chambers First US thrust chambers (in the late 40s) were made using the welded, doublewall, sheet metal configuration (like in the V2) in steel or nickel alloys

When engines went to higher thrust levels, the sheet metal configuration reached a limit: walls thin enough to maintain heat transfer would buckle, whereas walls thick enough to resist buckling would have insufficient heat transfer. The answer in the United States was to go to a tubular configuration. Tubes were brazed to each other and to a metal shell or hat-bands for stiffening. The result was a light-weight yet flexible structure which is strong and had good heat transfer characteristics

(NASA)

When the Space Shuttle Main Engine (SSME) began development, it was apparent that the higher combustion chamber temperature and pressure required much stronger construction, as well as an extremely high heat transfer capability. This dictated a channel-wall construction along with a copper alloy hot wall for high thermal conductivity ASI UNCLASSIFIED

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Different thrust chamber designs Historical note on US thrust chambers

The advancement of the US thrust chamber design has permitted to improve the maximum allowable heat flux (at the throat) and thus the chamber pressure channel wall design up to 160 MW/m2 ( )* bar)

& B ™))

tubular wall design

disruptive improvement

up to 35 MW/m2 ( )* bar)

& B N)

up to 15 MW/m2 ( )* bar)

& B O)

sheet metal design

Rocket engines time evolution of the maximum throat heat flux (c)

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Different thrust chamber designs Focus on SSME-MCC

The Main Combustion Chamber of the Space Shuttle Main Engine is regeneratively cooled with hydrogen and has 390 coolant slots (430 in later versions) in the copper alloy ( NARloy-Z, a copper-silver-zirconium alloy with significantly greater strength than pure copper but with only slightly lower thermal conductivity) liner; the slots are closed out with a thin layer of electrodeposited copper (as a hydrogen barrier) and then electrodeposited nickel (for strength) The channel-wall design of the SSME-MCC has demonstrated ability to withstand chamber pressure of more than 200 bar and throat heat-flux levels up to 160 MW/m2. At a nozzle expansion ratio of 5, the chamber is attached to a tubular thin-wall nozzle composed of 1080 tubes, which is much more weight efficient than a channel-wall configuration at the lower heat flux ASI UNCLASSIFIED

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SSME-MCC sketch (NASA)

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Different thrust chamber designs Historical note on USSR thrust chambers In the Soviet Union, tubular-wall design has never been used and channel wall combustion chamber-nozzle configurations were used from the beginning. When the heat transfer rate is limited (e.g., the nozzle extension or small chamber pressure engine) they often used a variation of the channel wall design, namely the sandwich wall design: the inner liner is made of copper-alloy, a corrugated sheet metal is used as the divider and the outer shell can be made of steel, stainless steel or nickel-base alloy. The entire assembly is brazed and the corrugations provide flow passages for coolant circulation

Sketch of the RD-107 engine: channel-wall design for the thrust chamber and sandwich-wall design for the nozzle extension (NASA)

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RD-107 engine clearly showing the copper alloy inner liner

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Different thrust chamber designs Moon race rocket engines: F-1 (first stage of Saturn V, that brought 12 men on the moon)

Main characteristics: propellant: LOX /kerosene (RP-1) cycle: gas-generator (open cycle) chamber pressure: 70 bar thrust (sea level): 677 ton (still the highest for a flown engine) throttle range: N.A. Isp (seal level): 263 s exit to throat ratio: 16 dry weight : 8,4 ton thrust-to-weight ratio: 94 height: 5,8 m diameter: 3,7 m ! !

!

!

Bifurcation joint (from 178 to 356 Inconel X-750 tubes)

! !

!

! !

! !

Thrust chamber and nozzle extension: Up to Ì : tubular wall, double pass From : Ì to Ì bifurcated tubular wall, double pass From to : Ì Ì film cooling with turbine exhaust gas !

!

!

¡p¡ B § ¡p¡ B § ¡p¡ B _4 ¡p¡ B _4 ¡p¡ B _3

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Evident presence of soot coming from the film cooling at K

'¶44

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Different thrust chamber designs Moon race rocket engines: NK-33 (first stage of N1, that collected only 4 failures) Main characteristics: propellant: LOX /kerosene (Russian blend) cycle: staged combustion (close cycle) chamber pressure: 148 bar thrust (sea level): 154 ton throttle range: 50%-105% Isp (seal level): 297 s exit to throat ratio: 27 dry weight 1,2 ton thrust-to-weight ratio: 137 (one of the highest of all time) height: 3,7 m diameter: 2,0 m ! !

!

! !

! !

!

!

! !

Thrust chamber and nozzle extension: channel-wall design for the thrust chamber and sandwich-wall design for the nozzle extension Note the absence of visible soot in the copper alloy for the inner liner exhaust gas of the thrust chamber and stainless steel for the inner liner of the sandwich wall and the whole external jacket !

!

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Different thrust chamber designs Moon race rocket engines: F-1 vs NK-33

Š

thrust The images are in scale

With respect to the tubular-wall design of F-1 (not developed anymore), the thermo-mechanical superiority of the channel/sandwich-wall design (and other peculiarities) of NK-33 permits to have about the same thrust of one F-1 using 4 x NK-33 and: +110% chamber pressure +34 s (+13%) Isp -43% weight -25% volume Clearly, going to the moon is not just a matter of propulsion! !

! !

!

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Overview of advanced concepts: !

!

!

!

! !

!

!

!

! !

!

!

Chemical stability of coolants High aspect ratio cooling channels Hot-gas side wall surface roughness Hot-gas side wall oxidation Different heat transfer mechanism in the face plate region Hot gas side carbon deposition Combustion instabilities Thrust chamber life Influence of the thrust chamber dimension on the cooling requirements Methods of increasing the heat transfer parameters Additional methods to reduce the wall heat flux Heat transfer in nozzle extension Heat transfer in gas-generators/preburners

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Overview of advanced concepts Chemical stability of coolants

Several hydrocarbon fuels (such as RP-1) can form carbon deposits on the inside of cooling passages (coking ), impeding the heat transfer and raising wall temperatures. This carbon formation depends on fuel temperature in the cooling passages, the particular fuel, the heat transfer, and the chamber wall material. Kerosene coking occurs at temperatures larger than 450 K, while pure methane does not presents this problem when operated as rocket coolant

RP-1 carbon deposition characterization (NASA)

Hydrazine (N2H4) and its related compounds, mono-methyl-hydrazine (MMH) and unsymmetrical-di-methyl-hydrazine (UDMH), can exothermically decompose at temperatures as low as 370 K in case of N2H4 and 490 K in case of UDMH and under some conditions this decomposition can be a violent detonation. Hydrazine and its related components reacts with many materials: it is compatible with steels while copper alloys must be avoided Hydrogen is always supercritical in the channels and is an excellent coolant, has a high specific heat (low temperature gain in the cooling system), and is chemically stable (it leaves no residues)

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Overview of advanced concepts High aspect ratio cooling channels

Channel wall design permits the construction of high aspect ratio cooling channels (height to base ratio up to 10)

Cut of the Vulcain thrust chamber wall made of copper alloy liner and galvanic deposited Nickel outer shell (5)

This geometry leads to a larger number of channels and longer fins and both effects will increase the cooling heat transfer area.

(NASA)

The limits for the liner walls thickness are mainly given by the requirements of conventional milling tools. To date thicknesses of less than 0.5 mm are hardly achievable

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Effect on cooling channel aspect ratio on wall temperature (ASTRIUM) A

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Overview of advanced concepts Hot-gas side wall surface roughness

Surface roughness can have a large effect on the heat transfer coefficient and thus on the wall heat flux (which can be increased by a factor up to 2) and wall temperature. In addition, it is generally measured that hot-gas side surface roughness increases with chamber run-time. Major surface roughness on the hot-gas side may have dramatic consequences. In fact, if the nozzle inner wall has a flow obstruction or a wall protrusion, then the kinetic gas energy is locally converted back into thermal energy essentially equal to the stagnation temperature and pressure in the combustion chamber. Since this would lead to local overheating and failure of the wall, nozzle inner walls have to be smooth. Hot-gas side wall oxidation

Typical SSME-MCC heating evolution with test duration –up to 10% increase in 300 sec.- (NASA)

Typical SSME-MCC hot spots (NASA)

Since the rates of chemical oxidizing reactions between the hot gas and the wall material can increase dramatically with wall temperature, cooling also helps to reduce the oxidation of the wall material and the rate at which walls would be eaten away. The oxidation problem can be minimized not only by limiting the wall temperature, but also by burning the liquid propellants at a mixture ratio where the percentage of aggressive gases in the hot gas (such as oxygen) is very small, and by coating certain wall materials with an oxidation-resistant coating ASI UNCLASSIFIED

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Overview of advanced concepts Different heat transfer mechanism in the face plate region

Comparisons of analytical results with experimental heat transfer data obtained on rocket thrust chambers have often shown disagreement. Major deviations generally affect the face plate region because each injector configuration produces different combustion characteristics. This results in deviations from calculations based on the assumption of homogeneous product gases (as in the Bartz’s equations) In addition, assumption of purely radial heat flow has been made. In reality, circumferential variations are present, especially in the injector region. Peaks of heat flux result in longitudinal discolorations (streaks) of the inner surface of the chamber after a firing Evidence of multidimensional environment (and also wall oxidation) in a combustion chamber (NASA)

(NASA)

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Overview of advanced concepts Hot gas side carbon deposition

In the case of the LOX/RP-1, carbon solids are deposited on the chamber walls. After a firing, the carbon gives the interior of the thrust chamber the appearance of being freshly painted black. The carbon deposition has a low thermal conductivity, decreases with hot-gas velocity, and at chamber pressures larger than 140 bar carbon deposition is almost negligible

8 '54

The carbon deposit thermal resistance when ./ bar can be as high as 7000 cm2K/kW while the material thermal resistance > 2 can be as low as (in case of copper alloy structure) 10 cm K/kW. The equivalent material thermal resistance is practically the one of the carbon deposit ( > ù =10+7000 # 7000 cm2K/kW) and thus the hot-gas side wall temperature >/ greatly increases (although the carbon deposit withstands higher temperatures than metal alloys and thus may protect the metal liner)

(NASA)

äé pF

äé pF P;

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-

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Combustion instabilities

If combustion instabilities occur, they can very quickly cause excessive pressure vibration forces (which may break engine parts) or excessive heat transfer (which may melt thrust chamber parts). The high-frequency tangential modes appear to be the most damaging: heat transfer rates often increases 4 to 10 times and the pressure peaks are about twice as high as with stable operation.

Evidence of enhanced heat transfer and large shear stresses at the injector interface (AIAA-LPTC) ASI UNCLASSIFIED

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Overview of advanced concepts Thrust chamber life

The thermal gradients (both transient and stationary) cause severe thermal strain and thus local yield point excess (i.e., plastic deformations), such that the wall thins and the formation of progressive cracks after successive runs is possible. This limits the thrust chamber life and number of starts or temperature cycles of a thrust chamber

Throat section of SSME-MCC showing thinned hot-gas wall (NASA)

Vulcain thrust chamber liner with typical longitudinal failures (5)

(NASA)

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Overview of advanced concepts In particular, metal alloys are subjected by: !

reduction of the mechanical properties (i.e., yield and ultimate tensile strengths and elasticity modulus) with temperature

“NARloy Z” (CuAgZr) elasticity modulus ( NASA) !

!

“NARloy Z” (CuAgZr) yield and ultimate strengths ( NASA)

creep: plastic deformation under the influence of mechanical stresses (also below the yield strength of the material); creep is more severe in materials that are subjected to heat for long periods fatigue: the weakening and damaging caused by repeatedly applied loads. The nominal maximum stress values that cause such damage may be much less than the strength of the material (i.e., the ultimate tensile strength limit, or the yield strength limit)

No existing materials combine good creep and fatigue properties at elevated temperatures and thus the strength of materials decreases with increasing temperatures ASI UNCLASSIFIED

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Overview of advanced concepts Aside the discussed static pressure and thermal stresses, the thrust chamber material is exposed to additional loads which have an impact on the engine life: !

mechanical loads such as pressure fluctuations or mechanical vibrations of various sources

!

high temperature fatigue (particularly relevant for restartable engine)

!

high temperature creep (particularly relevant for long firing)

!

!

chemical attack at the surface by OH or other radicals or a simple oxidation through exposure to oxygen rich gases material weakening by hydrogen embrittlement

Example: the SSME have a expected design life of 55 missions (i.e., 7,5 hr operation). In reality, the average achieved life is 7,3 missions and after 3-4 missions the engine is replaced for heavy maintenance. The great difference between expected and achieved life is also due to the actual thermo-mechanical environment ASI UNCLASSIFIED

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( ASTRIUM)

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Overview of advanced concepts Influence of the thrust chamber dimension on the cooling requirements

For a small rocket engine, the integrated heat flux over the entire inner surface is below 2% of the heat of combustion. This percentage is smaller for larger rocket engines. In fact, for constant chamber pressure ./ , increasing the thrust chamber dimension (i.e., increasing the throat diameter Ì and thus the thrust ÿ ./ Ì ) implies that:

Ÿ

!

!

8

þ B Ž 8 ¡

æQ increases with ŸÌc 8 ¡ ./ æQ '< / B Ž+ Ì 'ŸÌc the heat transfer rate absorbed by the coolant æâ (i.e., the integrated wall heat flux) increases with ŸÌ.jÂ .jÂ 8 ./ æâ'éŸÌ =>Ì'éŸÌ Ÿ.jc 'ŸÌ.jÂ Ì (note that the chamber length è is considered constant because the time required for complete the heat of combustion

combustion does not appreciably change with chamber dimension)

This implies that: cooling is relatively easier in large-thrust engines the hypothesis of one dimensional adiabatic flow for the hot-gas is valid !

!

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Overview of advanced concepts Moreover, the heat of combustion be expressed as:

æQ and the heat transfer rate absorbed by the coolant æâ can æQ'< / QOT æQ'ŸÌc

æâ B <â ¤ äçâ' 
The coolant temperature gain is thus proportional to:

ä-â' Ÿwj_c Ì

That is, the larger the engine the smaller the temperature gain. This is important when the maximum permissive coolant temperature has to be limited (for kerosene carbon deposition at wall or for safety reasons with hydrazine). Moreover, this also suggests that expander cycle engines (where the larger the coolant temperature gain the larger the chamber pressure) are more efficient if the thrust is limited (small engines) ASI UNCLASSIFIED

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Overview of advanced concepts Note that thrust chamber dimensions are also subjected to other limitations, e.g.: Sufficient residence time in order to have adequate mixing, evaporation and complete combustion (that is, high efficiency) Low hot-gas pressure drop (that is, to limit the decrease of the stagnation pressure and thus to avoid specific impulse loss – this loss becomes appreciable when the combustion chamber area is less than 3 times the throat area) !

D+

!

Example: SSME-MCC (version Block IIA @ Nominal Power Level): !

!

8 B _¶5Õ6 Spþ B 3 çQ B _4j3 æQ B 
the heat of combustion of one kg of hot-gas products at chamber pressure ./ bar originating from liquid oxygen and hydrogen at the mixture ratio is MJ/kg (obtained under chemical equilibrium condition). The rate of the heat of combustion is:

the wall heat transfer rate entering the coolant (hydrogen) is:

V X X F F F æâ B <â ¤ äçâ B _§j_6 - ¤W«45¶j¶ FV ^ 35§j6 FV[ B ««jê »U ^^• æâ B 4j44êæQ ;‘HE=ÌY;M.ªÌµ´ë´à@Eu =M@;HEYÌ ;MÂ×Ìµ´ë´à@Eu {YHw ZV

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Overview of advanced concepts Methods of increasing the heat transfer parameters !

d/ (ˆ* & ' †‡ & and (‡ˆ &)

chamber pressure (NASA) wall roughness longitudinal ribs (in this case the increment is not necessarily of / , but of the gas side area / and thus of total heat transfer rate / à / ) Note: increasing the hot-gas side heat transfer coefficient may be useful for increasing the coolant enthalpy gain ( â / à / â ), e.g., in the expander-cycle engines. In this case, the total extracted heat can be augmented also with longer cylindrical part of the combustion chamber !

!

!

¡

d

H= [= V¡

äç B H= [= V¡ p<

!

dâ (ˆá & ' †‡ & and (‡ˆ &)

coolant velocity VINCI (ASTRIUM) wall roughness high-aspect-ratio-cooling-channels (that is, increasing the area ratio â / ) Note: increasing coolant heat transfer could result in an excessive coolant pressure drop !

!

¡ p¡

!

!

F>päé (õ‡p á & ' †‡ & and (‡ˆ &) !

!

high conductivity material thin structures

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(NASA)

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Overview of advanced concepts Additional methods to reduce the wall heat flux !

!

!

Liquid (generally the fuel) or gaseous (generally the fuel or a fuel-rich “warm”-gas) films on the inner surface supplied by continuous injection through either a porous wall or small orifices Propellant mixture ratio far from stoichiometric condition in the region near the wall, supplied by appropriately modified injector orifices (the heat flux is strongly sensitive to the injector design) Refractory insulating non-metallic liners or thermal barrier coating (thickness of the order of tens of in order to have “high” temperature in the refractory material and “low” temperature in the metallic liner). These materials (generally ceramics like silicon carbide –SiC-) are characterized by: low thermal conductivity low thermal expansion high melting or sublimation temperature high ultimate strength chemical resistance to oxidization

\

!

! !

!

From (5)

!

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Overview of advanced concepts Heat transfer in nozzle extension It is often advantageous to use a different cooling method for the downstream part of the diverging nozzle section, because its heat transfer rate per unit area is usually much lower than in the chamber or the converging nozzle section, particularly with nozzles of large area ratio. These methods are typically: radiation cooling (e.g, AJ10-190 in niobium alloy –Space Shuttle OMS-; RL-10B-2 in C-C – i.e., carbon fibers in a carbon matrix; Aestus in Haynes 25 –i.e., a Co/Ni/Cr/W metal alloy) ablative cooling (e.g., RS-68 in silica phenolic, LR87-AJ-5 and LR91-AJ-5 –Titan II engines-) film cooling with turbine discharge gas (e.g., F-1, J-2, Vulcain 2) dump cooling (e.g., Vulcain 2) !

! !

!

RS-68

Aestus

Radiative cooling (nozzle extension)

Regenerative cooling (thrust chamber) ASI UNCLASSIFIED

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->jÅ´‘' _«44 K

Regenerative cooling (thrust chamber) A

Ablative cooling (nozzle extension)

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Overview of advanced concepts Heat transfer in gas-generators/preburners

In a gas-generator or staged combustion rocket engine type the hot combustion gases that drive the turbine (with rotating speed up to 50000 rpm) are burned in a separate combustion chamber (referred to as gas generator or preburner, respectively). The higher the gas temperature at turbine inlet the lower the required turbine flow (of great relevancy for gas generator engine) State of the art turbine blade materials (such as single crystals which have been unidirectionally solidified) and special alloys can allow turbine inlet temperatures up to 1400-1600 K; however, reliability and cost considerations have kept actual turbine inlet temperatures at conservative values, such as 900 to 950 K, using lower cost steel alloy as the material. Such temperatures, which are obtained with mixture ratios far from stoichiometric (usually fuel rich), are sufficiently low, so that the combustion chamber and the hot turbine hardware (blades, nozzles, manifolds, or disks) still have sufficient strength without needing forced cooling ASI UNCLASSIFIED

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Measurements of static stress to cause rupture after 100 hours (typically the “stress to density ratio” is the relevant variable) (1)

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Experimental characterization of hotgas side heat transfer ASI UNCLASSIFIED

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Experimental characterization of hot-gas side heat transfer The most adopted apparatus to measure the hot-gas side heat transfer coefficient is the watercooled thrust chamber (also referred to as calorimetric thrust chamber). The hot-gas side part of the engine is equal to the practical one (eventually in scale). The test engine is divided into circular sections that are cooled by water

(DLR)

This apparatus permits to have reliable estimations of the convective heat transfer coefficient because it is a weak function of the wall temperature. That is, same hot-gas flows have same convective heat transfer coefficients even if the wall temperature is different due to the use of different cooling systems and fluids (e.g., water in the circular sections of the calorimetric chamber and one of the propellants in the regenerative cooling system of the actual thrust chamber) ASI UNCLASSIFIED

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Experimental characterization of hot-gas side heat transfer The procedure to characterize the hot-gas side heat transfer coefficient is: !

!

!

the average heat flux in the section temperature from inlet to outlet

=/

is measured from the increase in water

-

the adiabatic wall temperature >´ is estimated (e.g., using a one-dimensional model for the hot-gas expansion and a recovery factor)

-

the hot-gas side wall temperature >µ can be measured using thermocouples in the material (eventually more than one in the radial direction, also to evaluate the local / if the material thermal conductivity is known)

=

Then, the average heat transfer coefficient in the section is computed as:

= d/ B ->´ ^/ ->µ ASI UNCLASSIFIED

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Experimental characterization of hot-gas side heat transfer Hot-gas side convective heat transfer can be characterized using subscale rocket thrust chambers (i.e., making use of scaling techniques) !

!

!

!

Scaling is defined as the ability to design new combustion devices with predictable performance on the basis of test experience with specifically scaled hardware (mainly in terms of dimensions, flow rate, and pressure). This approach is the only way to evaluate novel and innovative designs by hot-fire test with considerably lower development cost

Particularly relevant in this context is the dimensional analysis, where variables that may influence the system are combined into non-dimensional groups. Scaling is obtained by keeping these groups constant between the subscale and the full-scale devices

Scaling of hot-gas side convective heat transfer (mainly the hot gas side heat transfer coefficient) can be achieved by means of subscale calorimetric thrust chambers

A beneficial effect of using subscale thrust chambers is that measurement accuracy of heat flux deteriorates with increasing thrust chamber dimension (i.e., larger thrust, pressure, vibrations, heat flux, temperature gradients, etc.)

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Experimental characterization of hot-gas side heat transfer Techniques to scale the hot-gas side heat transfer coefficient are illustrated considering the oxygen/hydrogen SSME main combustion chamber (MCC) liner development program (during the 1970s) as an example A subscale water-cooled calorimetric chamber was used to measure the heat flux at different sections. The nominal thrust level was 40 klbf (17.8 ton), that is approximately 1/10 scale, with respect to thrust, of the full-scale SSME. The throat diameter was 84 mm while full-scale SSME diameter is 262 mm. Injection elements are 600 and 61, respectively, but the geometry of the injection element was identical (NASA)

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Experimental characterization of hot-gas side heat transfer The water-cooled calorimeter chamber had 58 independent coolant circuits, each with separate temperature and pressure measurements The subscale chamber had the same combustion chamber length (injector face to throat) of 356 mm, throat convergence ramp angle, throat contour radius of curvature, combustor contraction ratio (combustion chamber to throat area) of 2,96, and nozzle expansion ratio (exit to throat area) of 5 as the full-scale MCC

Heat flux profiles have been acquired for chamber pressures between 86 and 114 bar. The maximum allowable chamber pressure for the calorimeter chamber was limited by the throat region burnout heat flux of 106,3 MW/m2

(NASA)

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Experimental characterization of hot-gas side heat transfer The average heat flux in each section from inlet to outlet

Heat flux profile ASI UNCLASSIFIED

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=/ is measured from the increase in water temperature

=/ for a test with K.4 B _4êÕ5 bar and Spþ B 3 (total heat load was 9079 kW) (3) A

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Experimental characterization of hot-gas side heat transfer The (average) hot gas heat transfer coefficient in each of the 58 circumferential cooling circuit was calculated as:

d/ B ->´ =^/ ->µ =

-

-

where / and >µ are experimentally measured while the >´ is calculated using a recovery factor and one-dimensional chemical equilibrium at the appropriate test chamber pressure and mixture ratio These data were used to predict the heat transfer coefficient in the same chamber at the maximum SSME chamber pressure condition. For each axial location, / was scaled from ./w bar (subscale condition) to ./c bar (full-scale conditions) by:

_4êj5

K B 74«j5

d

K B

.jÂ K ./c d/c B d/w K./w ASI UNCLASSIFIED

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Experimental characterization of hot-gas side heat transfer

d/ at 8./ B _4êj5 bar (subscale condition) and scaled profile of d/ at 8./ B 74«j5 bar (full-scale condition) ( 3)

experimental profile of

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8./ B 74«j5 bar: From the injector face to ~127 mm downstream, d/ was the same as the scaled value from 8./ B _4êj5 bar (subscale condition) to 8./ B 74«j5 bar (full-scale condition) because the

Full-scale SSME heat transfer coefficient at !

injector elements were the same and heat transfer rates near the injector were then primarily influenced by the distance from the injector !

Further downstream, where heat transfer rates are primarily convective (velocity driven), the full-scale / corresponded to axial locations where the hot gas Mach number was the same as in the calorimetric chamber

d

»

Note: this approach is different from using the scale law:

.jÂ ¡Ì .j× 8 ¡ ./ d/' Ÿ.jc ¡ hgILI ¡Ì B GH»V Ì In particular, the throat diameter effect is not taken into account (that is, the scaling due to absolute dimensions of the chambers is ignored and thus / could be over-predicted). In particular, for the throat diameter: mm for the subscale chamber Ì mm for the full-scale SSME chamber Ì

d

! !

Ÿ B ê«j_ Ÿ B 73_j56

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Estimated full-scale SSME profile of ASI UNCLASSIFIED

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d/ (3)

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Bibliography This presentation is mainly derived from: 1) Mechanics and Thermodynamics of Propulsion , Second Edition, Philip Hill and Carl Peterson, published by Pearson Education, Inc. 2) Rocket Propulsion Elements , Seventh Edition, by George P. Sutton and Oscar Biblarz, published by John Wiley & Sons 3) Scaling Techniques for Design, Development, and Test , C.E. Dexter et al., In Progress in Astronautics and Aeronautics Series, Vol. 200, published by AIAA 4) Many NASA technical reports from the 60s, 70s, and 80s and devoted to theoretical and experimental studies on rocket engine thrust chambers 5) Advanced Rocket Engines, Oskar J. Haidn, In Educational Notes RTO-EN-AVT150, Paper 6, published by NATO Cover illustration by NASA: Space Shuttle Main Engine – Main Combustion Chamber ASI UNCLASSIFIED

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Regenerative Cooling of Liquid Rocket Engine Thrust Chambers

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