Sonderforschungsbereich/Transregio 40 – Annual Report 2012
55
Transpiration Cooling Models applied to
Rocket Combustion Chambers
By M. Selzer, S. Schweikert†, J. von Wolfersdorf† A N D H. Hald
Institut für Bauweisen- und Konstruktionsforschung (BK), DLR Stuttgart
Pfaffenwaldring 37, 70569 Stuttgart, Germany
Transpiration cooling with porous high-temperature fiber ceramics promises many advantages over regenerative cooled combustion chambers. Longer durability due to low
thermal expansion coefficients, straightforward manufacturing processes promising decreased manufacturing costs, possible weight reductions and efficient coolant usage are
examples for these benefits while performance similar to those of regenerative cooled
combustion chambers can be achieved.
In the SFB/TRR 40 sub-project A5, the investigation of transpiration cooling is the set
goal. This report incipiently gives a summary of the validation experiments which served
as background to establish models, which potentially allow to assess the thermal efficiencies of this cooling technique. The analytical models, derived in the framework of
the SFB/TRR 40, are in good agreement with the validation experiments and therefore
enable to describe hot-gas wall and internal temperature distribution as well as pressure loss for transpiration cooled porous wall segments. Furthermore, a discussion concerning the application of these approaches in respect to realistic combustion chamber
situations is given. In doing so, the derived transpiration cooling models are adapted to
the geometrical and aero-thermal conditions of DLR’s C/C combustion chamber.
1. Introduction
The aim of the SFB/TRR 40 sub-project A5 is basic research on the cooling efficiency
of transpiration cooled rocket combustion chambers in development. For transpiration
cooling, the chamber wall is a porous and permeable material. Higher pressure levels on the outer side of the combustion chamber establish a coolant stream through
the porous material cooling the structure convectively. When entering the combustion
chamber, a coolant film is developed which decreases the heat loads onto the wall additionally. The combination of these mechanism makes transpiration cooling quite effective
and therefore an interesting cooling technique for perspective high performance combustion chambers. The utilization of its anisotropic character, which can be defined by
the manufacturing process, makes porous fiber reinforced ceramics an ideal candidate
for the application in combustion chamber walls. Our research is focused on transpiration cooling using C/C as reference material. Details concerning material characteristics
and manufacturing process are given for example in the SFB/TRR 40 annual report
2009 [1]. Within the SFB/TRR 40 framework extensive tests have been conducted using C/C wall segments, which are convectively heated up by a hot-gas cross flow. To
describe the aero-thermal situation of the porous segment, temperature, pressure and
† Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart
56
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
mass flux information have been continuously monitored for the hot-gas and the coolant
stream as well as for particular positions at the C/C wall and its supporting structure. The
data of these validation experiments serves as database to derive and validate analytical models describing transpiration cooling. These analytical approaches are published
and discussed in detail for example in [2, 3]. The validation experiments had been conducted at the ITLR hot-gas test facility. The facility as well as the instrumentation of the
setup are described in-depth in [2–5].
The emphasis of the latest research in sub-project A5 is the transcription of these analytical approaches to aero-thermal conditions like they are apparent in real combustion
chambers. In this regard DLR’s C/C combustion chamber tests serve as reference [6].
2. Heat transfer in porous media
In theory, a transpiration cooled wall is a two-domain problem with a solid and a fluid
domain, each with their own temperature field. The differential equations describing
these two domains are given in Eqn. 2.1 and 2.2.
d2 T s
dy 2
ṁ dTc
d2 T c
+ cp,c
hv (Ts − Tc ) = −kc
2
dy
Ac dy
hv (Ts − Tc ) = ks
Solid
(2.1)
Fluid
(2.2)
The indices s and c in the equations denote solid and coolant domain and Ac is the
coolant through flow area. The two differential equations are coupled via the volumetric
heat transfer coefficient hv , which is defined as
(2.3)
hv = Aspec h
with the volume specific inner surface area Aspec and the average areal heat transfer
coefficient in the pores h. Porous media here comprises different forms of inner structures, from regular structures like packed beds of spheres or tubes and densely packed
meshes, over different metallic or ceramic foams to materials with continous, but randomly distributed cracks. When looking at the literature concerning the heat transfer
from a porous medium to a coolant, many different correlations to evaluate hv depending on different parameters can be found. The most general ones suggest a dependance
of a Nusselt number as given in Eqn. 2.4.
(2.4)
N u = f (Re, P r, ǫ, lch /L)
Unfortunately, as a consequence of the different structures of the porous material, often
different definitions of the characteristic length lch , the Nusselt number and the Reynolds
number are used. When dealing with packed beds and foams, often the diameters of
the pebbles/tubes (dp ) or mean pore diameters (dm ) or a hydraulic diameter (dh ) are
used. Additionally, when dealing with unstructured porous media, a characteristic length
utilizing the Darcy coefficient kD (see Eqn. 3.7) can be found. The Nusselt number
in Eqn. 2.4 might correlate directly to hv , or might correlate to h. The corresponding
definitions are then
Nu =
h lch
kc
or
N uv =
2
hv lch
kc
(2.5)
Transpiration Cooling in Rocket Combustion Chambers
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TABLE 1. Different correlations for heat transfer in porous media.
From the above definitions, the relationship between these two definitions can be derived as
(2.6)
N uv = N u Aspec lch
The velocity in the Reynolds number is mostly given as a superficial velocity u or, by
dividing through the porosity, a mean velocity in the pores up ,
u=
ṁ
ρc Ac
up =
u
ǫ
(2.7)
Table 1 summarizes some of the correlations from literature for foams, packed beds
of spheres and decomposing glass filled polymer composites. The first column gives
the Nusselt correlation developed in the publication. The column marked uRe indicates
the velocity used in the publication for the Reynolds number and the column lch is the
used characteristic length. The correlations shown suggest a dependance of the Nusselt
number in the form of
N uv = C Ren P rm
(2.8)
with n ranging from 0.27 − 1. In [11] n is even a function of characteristic length and
sample thickness. In the correlations with a dependance on P r, this dependance was
not measured, but assumed from literature. So, m is either set to 0 or 0.33. C is either a
constant or a function of the ratio of characteristic length lch and sample thickness L.
58
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
3. Analytical transpiration cooling modeling
The following chapter summarizes so far derived models for transpiration cooling using CMC walls. These analytical approaches are published and discussed in detail for
example in [2–5]. This short summary should serve as background for the conversion to
real combustion chamber conditions.
3.1. Wall temperature and cooling efficiency
To predict the porous wall temperature and the cooling efficiency in non-adiabatic test
environments Langener et al. [4] developed a transpiration cooling model which incorporates the approach of Kays et al. [14] and is based upon the heat balance of the porous
wall segment. This heat balance on its part can be written as
hg (Tr,g − Tw ) = ρc cp,c vc (Tw − Tc ) + B (Tw − Tsink ) .
(3.1)
Beside the convective heat transfer from the hot gas flow onto the C/C segment and the
heat flux picked up by the internal cooling within the porous specimen, the third term of
Eqn. (3.1) describes the lateral heat losses between the C/C wall and the surrounding
channel parts (Fig. 1, upper left portion). In doing so, B accounts for the setup specific thermal resistance which can be quantified by evaluating the heat balance without
transpiration through flow. In this case the heat convected onto the C/C surface is only
laterally conducted between the wall segment and the channel parts. This parameter
is assumed to be constant for all blowing ratios. In the same term Tsink refers to the
temperature of the surrounding channel parts which completes the definition of the crucial temperature difference responsible for lateral heat fluxes. In addition, Langener et
al. showed in [2, 5] that a non-dimensional temperature ratio according to Eqn. (3.2)
has proven advantageous to compare experiments in non-adiabatic test environments.
This formulation is based on the wall temperature without cooling Tw,0 and therefore
separates non-adiabatic effects from the transpiration cooling effects.
Θ=
Tw,0 − Tw
Tw,0 − Tc
(3.2)
In case of no blowing Θ becomes 0 and if the wall temperature Tw equals the coolant
temperature Tc this parameter is 1 and a completely cooled wall is achived. Therefore,
this parameter can be interpreted as cooling efficiency.
3.2. Internal temperature distribution
To describe the internal thermal situation, Langener et al. [2] introduced a temperature distribution approach which is related to the position in the wall and derived from
the one-dimensional and steady state energy equation of the porous segment. Assuming thermal equilibrium of solid- and fluid-phase within the porous wall the two energy
equations collapse in one conservation equation. To consider lateral heat fluxes for the
internal temperature distribution approach as well, the energy equation of the wall segment is extended by a loss term, comparable to the one introduced for the heat balance
in Eqn. (3.1). The resulting energy equation is given in Eqn. (3.3). The coefficient B
accounts again for the setup specific thermal resistance and is assumed to be constant
Transpiration Cooling in Rocket Combustion Chambers
59
for all blowing ratios and positions in the C/C wall.
ks
dT (x)
d2 T (x)
− ρc cp,c vc
− B (T (x) − Tsink ) = 0
2
dx
dx
dT (x)
d2 T (x)
− C1
− C2 T (x) + C3 = 0
dx2
dx
(3.3)
This inhomogeneous linear differential equation of second order is solved by considering
boundary conditions for
x = 0 ∶ T = Tb
and
x = L ∶ T = Tw .
(3.4)
In doing so, the solution of this energy equation follows
T (x) = Th + Tp or respectively
(3.5)
T (x) = α1 eλ1 x + α2 eλ2 x + Tp .
The variable Tp accounts for the particular solution of the temperature profile T (x),
which can be determined by the variation of the constants. By these means a temperature distribution with exponential character is obtained. The constituent parts of this
solution for T (x) can be written as
α1 = T (x = 0) − Tp − α2 ,
α2 =
T (x = L) − Tp + eλ1 L (Tp − T (x = 0))
,
eλ 2 L − eλ 1 L
C3
C3
Tp =
−
and
λ2 (λ2 − λ1 ) λ1 (λ2 − λ1 )
¿
Á C 2
C1
Á 1
+ / − À( ) + C2 .
λ1/2 =
2
2
(3.6)
Langener et al. [2] used as boundary condition for the backside of the C/C wall a heat
transfer coefficient hc . Although this boundary condition is more general, it introduces
additional uncertainties concerning backside/coolant heat transfer. Therefore we decided to use measured backside temperatures Tb instead.
3.3. Pressure loss under heat load
To describe the pressure loss for porous materials, the Darcy-Forchheimer equation
(Eqn. (3.7)) is commonly used.The material intrinsic parameters kD and kF in Eqn. (3.7)
describe the permeability of the porous walls.
µ
ρ 2
dp
= −(
u+
u )
dx
kD
kF
with u =
ṁc
Ac ρ
and
ρ=
p
RT
(3.7)
This classical formulation of Darcy-Forchheimer describes pressure losses for through
flows where no reasonable heat transfer between material and gas is apparent. Langener considered in [3] temperature dependent properties of the coolant. A method
which is for example also applied in the high temperature and high pressure through
flow experiments by Gascoin [15]. Combining the temperature dependent coolant properties with an internal temperature profile of the porous wall leads to a more general
formulation of the Darcy-Forchheimer approach that is capable to describe the effect of
heat loads into the porous material and therefore aligns the predicted coolant pressure
60
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
1
.
m /A
F= m. c/Ac
g
g
Θ [−]
0.8
0.6
0.4
model
experiment, air
experiment, argon
experiment, helium
0.2
0
0
model
experiment
0.2%
g
T(x)/T [−]
0.9
0.3%
0.8
0.5%
0.7
1.0%
x 10
2.5
F=
0.0%
∆p/L [Pa/m]
1
3
0.2
0.4
0.6
F [%]
0.8
1
0.08
0.1
7
model (isotherm)
model (temp. corrected)
experiment
2
1.5
1
0.5
0.6
0
0.5
x/L [−]
1
0
0
0.02
0.04
0.06
u [m/s]
F IGURE 1. Thermal situation at the C/C wall segment (upper left) and examples for the application of the derived models in respect to the wall cooling efficiency (upper right), the internal
temperature distribution (lower left) and the pressure loss under heat load (lower right).
loss over the porous wall to the same level like the measured values (Fig. 1, lower right).
4. Transfer of transpiration cooling models to real application
The described models are validated with experiments conducted in the SFB/TRR 40
and therefore at loads well below the loads apparent in combustion chambers (see [2] for
SFB/TRR 40 loads). Therefore, in the following sections, the assumptions and limitations
of the models are assessed concerning their transfer to combustion chamber conditions.
4.1. Thermal boundary conditions
The thermal resistance B from Eqn. 3.1 is dependent on the specific surrounding of the
porous wall. As this is not known for a generic combustion chamber lateral heat flux is
neglected in the combustion chamber calculations. It is expected, that the heat fluxes
Transpiration Cooling in Rocket Combustion Chambers
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F IGURE 2. Pressure distribution over wall.
F IGURE 3. Temperature distribution over wall.
occuring between a real combustion chamber and the supporting structure are always
directed into the support structure, so this assumption is seen as conservative.
4.2. Geometry
The differential equations for temperature distribution Eqn. 3.3 to 3.6 and 3.7 for pressure distribution used in SFB/TRR 40 are valid for a flat plate and constant through flow
area. In a cylindrical combustion chamber wall, the through flow area Ac is a function of
the radius
Ac (r) = 2π r l
(4.1)
The impact of this varying through flow area is shown in the following.
4.2.1. Darcy-Forchheimer with varying through flow area
Inserting Eqn. 4.1 in 3.7 and solving yields the pressure function with variable through
flow area
p(r) =
η(pc , Tc ) ṁ 1
1
r
ṁ2
1 1
ln +
( − ) + p0
kD ρ(pc , Tc ) 2π l
r0 kF ρ(pc , Tc ) 4π l2 r0 r
(4.2)
Here, p0 is the chamber pressure and r0 is the inner radius. The coolant data is taken
from the real gas data base NIST [16] at the mean between inside and outside pressure,
which is believed to be reasonable for the investigated pressure differences. Fig. 2 compares the pressure distribution over the chamber wall for a flat plate and a cylinder wall
without a temperature gradient. If a constant inner chamber area is used, the pressure
drop is the highest. If the mean area between inner and outer chamber area is used, the
total pressure drop over the wall is, for the given flow condition, close to the pressure
drop for a varying through flow area. The pressure distribution over the chamber wall
differs slightly.
4.2.2. Temperature distribution in wall with varying through flow area
The differential equation describing the temperature distribution with a varying through
flow area and the assumption of local thermal equilibrium can be developed with the
62
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
heat balance depicted in Fig. 3 and is given in Eqn. 4.3.
ṁ cp,f 1 dT
d2 T
+ (1 +
)
=0
dr2
ks 2π l r dr
´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹¶
(4.3)
A
Introducing the dimensionless variables for temperature and radius
temperature: Θ =
T − Tc
Tw − Tc
radius: R =
r
ra
(4.4)
the differential equation can be written and solved to
d2 Θ A dΘ
R1−A
+
=0
⇒
Θ(R) = C0
+ C1
(4.5)
dR R dR
A−1
To evaluate the constants C0 and C1 , a fixed temperature boundary condition is used on
the hot wall side and a convective heat transfer with constant heat transfer coefficient
on the cold side is used, which yields the constants to
C0 = −
Bic
(1−A)
Bic ( RaA−1
−
Ri (1−A)
) + Ra1 A
A−1
,
C1 = 1 − C0
Ri (1−A)
A−1
(4.6)
Fig. 3 shows the difference between Eqn. 3.3 for a constant through flow area and Eqn.
4.5 for varying through flow area with an inner diameter of 50 mm and thermal resistance
B = 0 (see eqn 3.1). For the given conditions, the difference is very small.
4.3. Assumption of local thermal equilibrium
The assumption of local thermal equilibrium (LTE) is essential to the models described.
LTE requires a large enough Biot number in the pores (Bip ), so that the temperature
difference between solid and fluid is negligible. The experiments of SFB/TRR 40 indicate
LTE at the conditions tested. Next, a method will be shown to estimate a minimum
Bip that would satisfy this assumption and how this can be transferred to combustion
chamber conditions. Wang et al. developed a criterion [17], to determine whether the
assumption of LTE is valid for given conditions. They used an analytical solution for the
case of non local thermal equilibrium (NLTE) employing the dimensionless parameters
Bip , Biot number on the hot gas side (Big ) and dimensionless massflow (M).
Bip =
h v L2
ks
Big =
hL
ks
M=
ṁc cp,c L
ks
(4.7)
L in these equations is the thickness of the sample. With these solutions they were able
to show, that the assumption of LTE is independent of Big and depends only on Bip and
M. They developed the criterion given in Eqn. 4.8, where the error from the assumption
of LTE is smaller than 5%.
M ≤ 0.223 Bip 0.507
(4.8)
The case for equality in Eqn. 4.8 defines a lower limit for a Biot number and therefore a
minimum hv,min , where LTE can be assumed.
hv,min = Const (
ṁk 1.972 1.972
1
)
c pc
Ak
ks0.972 L0.028
(4.9)
If using the same material and the same through flow direction, thermal conductivity ks
remains constant and the specific mass flow can be adjusted accordingly. The influence
Transpiration Cooling in Rocket Combustion Chambers
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F IGURE 4. Calculated minimum hv needed for
local thermal equilibrium.
63
! " F IGURE 5. Ratio of hv,H2 and hv,N2 to hv,He
dependent on n and m.
of the thickness of the wall L is negligible. The only important factor left is the heat
capacity of the fluid, cp,c . In Fig. 4 the result of Eqn. 4.9 for the SFB/TRR 40 with Helium
as coolant is compared to the case of a H2 and a N2 cooled combustion chamber.
The curves in Fig. 4 define a lower limit of hv which still allows the assumption of LTE.
The hv distribution for helium is based on the experiments conducted in the framework
of SFB/TRR 40, where the existence of LTE is assumed. Chapter 1 showed, that hv
will change when changing the coolant properties. From literature, a correlation for the
volumetric Nusselt number in the form of
N uv = C Ren P rm
(4.10)
can be expected. Inserting the definitions in Eqn. 4.10 yields
hv = C̃ (
ṁc n m−n m−n m 1−m
) ρc
νc
cp,c kc
A
(4.11)
This equation can be used to determine the ratio of hv,1 /hv,2 , utilizing different coolants
1 and 2 at different conditions. This change is independent of C̃ and only depends
for a given specific mass flow on the fluid properties and n, m. Fig. 5 shows the ratio
for a H2 and for a N2 cooled chamber over Helium at a pressure of 5 bar and 300 K
dependent on the exponent n, m = 0 and m = 0.33 (values for n, m are typical values
from literature). It can be seen, that the ratio for both cases, a H2 and a N2 cooled
combustion chamber, is below the required ratio given by the analysis after Wang et al.
The minimum value of hv that can be derived from the experiments in the framework
of the SFB/TRR 40 is not high enough to allow for a transfer to combustion chamber
condition. Additionally, the experiments up to now were conducted with a through flow
perpendicular to the fibres in C/C, whereas in recent combustion chamber design, the
through flow is parallel. Experiments with parallel through flow direction are planned in
the future. Consequently, it is not possible at the moment to assess the assumption of
LTE in a combustion chamber.
4.4. Heat transfer correlation without cooling
The correlation to determine the heat transfer coefficient without cooling is crucial for
the described model. An equation often used is the correlation given by Bartz [18].
64
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
Froehlich gave a dimensionless correlation based on this equation [19] (see Eqn. 4.12),
which Serbest [20] compared to common heat transfer correlations. From all correlations
studied by Serbest, the modified Bartz correlation yields the highest Stantonnumber and
is therefore used as a conservative approach in this paper to estimate wall temperatures.
St0 = 0.0205 Re−0.18
Pr−0.18 (
d
Trec 0.35
)
Fg (x) F rRof
Tw
(4.12)
The parameters Fg (x) and FrRof are dependent on the combustion chamber and the
ratio of fuel. In the following both are set to 1.
5. Model results for combustion chambers/coolant requirements
The models described in the preceding sections are now applied on a sample case.
The hot gas and coolant properties are given in table 2. Particular attention is paid on
the scaling effects occuring when upping the chamber diameter and the influence of
the thermal conductivity of the material. Although the assumption of LTE could not be
verified at this point, the assumption is taken as valid for the following discussion.
5.1. Effect of thermal conductivity.
Fig. 6 illustrates the influence of increasing solid thermal conductivity on the temperatures in the chamber wall. The hot wall surface temperature is independent of thermal
conductivity. In contrast, the influence on temperature distribution in the wall is evident.
With the low thermal conductivities of C/C of around 13.5 mWK , most of the wall is cooled
to coolant temperatures with very steep temperature gradients at the hot side. When the
thermal conductivity is decreased even more (for example by using oxide ceramics instead of C/C) this effect is even more evident. When increasing thermal conductivity
(for example by employing C-fibers with higher thermal conductivity), the temperature
gradient is lower and heating of the fluid takes place in greater material depth. Fig. 7
shows the pressure distribution in the chamber wall corresponding to the temperature
distributions. In contrast to the measurements in the SFB/TRR 40, the influence of the
heat load on the pressure drop with comparable thermal conductivities between 1.35 to
13.5 mWK (perpendicular and parallel to the fibers) is rather small. This is attributed to
the temperature profile. Only a very small portion of the combustion chamber wall (and
therefore the fluid as well) is heated and therefore the influence is limited to a distance
of a few tenth of a millimeter. This effect increases when the thermal conductivity is increased, as can be seen in Fig. 7. From the figures it is also evident, that temperature
measurements in transpiration cooled combustion chamber walls should be placed as
close as possible to the hot side and, due to the large gradients, the precise placement
is very important.
5.2. Influence of transpiration cooling on specific impulse and design
Transpiration cooling introduces propellant over the length of the combustion chamber.
The fuel, which is used for cooling far downstream of the injector cannot efficiently contribute to the combustion. Therefore some performance loss occurs, when comparing
a transpiration cooled engine with a regeneratively cooled engine. This is discussed in
more detail in a recent publication by Herbertz et al. [21]. The specific impulse is reduced according to Eqn. 5.1, with τ the ratio of coolant mass flow to total mass flow and
an empiric transpiration cooling coefficient kT . Experimental data provides a transpiration cooling coefficient of kT = 0.31 for the current configuration of the ceramic thrust
Transpiration Cooling in Rocket Combustion Chambers
F IGURE 6. Temperature distribution in
chamber wall.
F IGURE 7. Pressure distribution in chamber
wall.
hot gas pressure
9.55 MPa
hot gas temperature
3571.8 K
hot gas viscosity
107.8 ⋅10−6 Pa s
hot gas density
4.3213 kg/m3
hot gas heat capacity
8745.1 J/kgK
coolant pressure
99.5-105 MPa
coolant entry temp.
62 K
coolant density
64.783 kg/m3
coolant viscosity
9.2794 ⋅10−6 Pa s
coolant heat capacity
12962 J/kgK
65
TABLE 2. Hot gas and coolant fluid properties.
F IGURE 8. Design diagram for a transpiration
cooled combustion chamber.
chamber [21].
I = I0 (1 − kT τ )
with: τ =
ṁc
ṁc
=
ṁc + ṁg ṁtot
(5.1)
With the models desribed in the preceding section, Fig. 8 is generated. For a given
allowed hot wall temperature and chamber diameter, the required τ can be determined.
τ is decreasing with increasing diameter, hence the losses due to transpiration cooling
decrease also. This is explained, because the required area specific coolant mass-flow
ṁc /Ac is constant with increasing chamber diameter. This results in a linear scaling of
the coolant mass flow with chamber diameter d. At the same time, the hot gas mass
flow with constant pressure and velocity is scaling with d2 . Together with Eqn. 5.1 the
loss in specific impulse compared to conventional cooled combustion chambers can be
evaluated.
66
M. Selzer, S. Schweikert, J. von Wolfersdorf & H. Hald
6. Conclusions
The models developed in the framework of the SFB/TRR 40 enable a preliminary
design of transpiration cooled combustion chambers. The models allow to determine,
dependent on coolant properties and coolant mass flow, the temperature distribution as
well as the pressure drop over the chamber wall in the cylindrical part of the chamber at
steady state conditions. A ratio of required coolant mass flow to total mass flow (τ ) can
be determined, which enables a first approach to compare the specific impulse of a transpiration cooled combustion chamber to a regeneratively cooled chamber. To achieve
this, at the moment, certain assumptions have to be made. The main concern in transfering the models to combustion chamber conditions lies in the assumption of LTE. The
assumption of LTE is firstly dependent on the material intrinsic characteristics. So experiments with fiber orientations similar to those of recent C/C chamber tests are planned
in the next phase of the SFB/TRR 40. Also, only a minimum hv can be derived from the
experiments. Transfering this hv dependent on the coolant properties in the SFB/TRR
40 to another condition shows, that this minimum hv is not enough to allow the transfer to combustion chamber conditions. So, a better determination of hv is necessary.
Transient tests planned for the next phase of the SFB/TRR 40 might allow for such a
better determination of hv . Additionally, these tests will show, whether the models can
be extended to describe transient behaviour. The next step is to validate the predictions
of these models with measurements in combustion chambers. The instrumentation of a
combustion chamber with sensors is much more difficult compared to the experiments
conducted in the SFB/TRR 40, where even in the small samples a multitude of sensors
was installed. The predictions from the models now allow to determine the best position
of the sensors in a combustion chamber. If thermocouples are installed in the chamber
wall, they should be installed as close as possible to the hot side. Also, the exact depth
is very important, as Fig. 6 shows a large temperature gradient. Ideally, the hot side wall
temperature would be measured by a pyrometer. This would also allow to determine the
best model for evaluating the heat transfer from the combustion gas to the chamber.
Acknowledgments
Financial support has been provided by the German Research Foundation (Deutsche
Forschungsgemeinschaft – DFG) in the framework of the Sonderforschungsbereich
Transregio 40.
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