ORIGINAL PAPER

c�-Efficiency evaluation of transpiration cooled ceramiccombustion chambers

Armin Herbertz • Markus Ortelt • Ilja Muller •

Hermann Hald

Received: 3 December 2013 / Revised: 14 February 2014 / Accepted: 18 March 2014 / Published online: 29 April 2014

� CEAS 2014

Abstract Achievable benefits of the transpiration cooled

ceramic thrust chamber are the reduction of weight and

manufacturing cost, as well as an increased reliability and

higher lifetime due to thermal cycle stability. The tran-

spiration cooling principle however reduces the engine

performance. In order to evaluate the performance losses a

c�-analysis is performed. Due to the transpiration cooling

the characteristic velocity decreases with increasing cool-

ant ratio. The goal of the chamber development is therefore

to minimize the required coolant mass flow. The paper

discusses the test specimen set up for the ceramic thrust

chamber tests. Chamber operating parameters are listed.

The paper discusses the impact of transpiration cooling on

the calculated c� efficiency. The evaluation is based on test

results with the ceramic combustion chamber conducted in

four separate test campaigns between 2008 and 2012.

Keywords Ceramic combustion chamber � Transpiration

cooling � Characteristic velocity

List of symbols

a Sonic velocity, m/s

A Cross section area, m2

c� Characteristic velocity, m/s

CF Thrust coefficient

d Diameter, m

F Thrust force, N

g0 Gravitational acceleration, m=s2

I Specific impulse, m/s

kT Transpiration cooling coefficient

l (Chamber) length, m

l� Characteristic chamber length, m

_m Mass flow, kg/s

p Pressure, Pa

R Mass mixture ratio (oxidizer to fuel)

V Volume, m3

g Efficiency

q Density, kg/m3

s Coolant ratio

Subscripts

0 Initial, injection

c Chamber

e Exit (nozzle)

fu Fuel

id Ideal

k Coolant

ox Oxidizer

t Throat (nozzle)

vac Vacuum

1 Introduction

The transpiration cooling principle, while slightly reducing

the specific impulse, highly increases chamber wall life-

time. Furthermore, depending on the ceramic materials

used in thrust chamber construction, it is possible to sub-

stantially reduce the engine’s mass and manufacturing cost,

compared to that of metallic engines. A small fraction of

propellant is routed to the wall cooling channels. The

coolant passes through the porous wall and exchanges heat

This paper is based on a presentation at the 4th CEAS European Air &

Space Conference, September 16–19, 2013, Linkoping, Sweden.

A. Herbertz (&) � M. Ortelt � I. Muller � H. Hald

DLR, Stuttgart, Germany

e-mail: armin.herbertz@dlr.de

123

CEAS Space J (2014) 6:99–105

DOI 10.1007/s12567-014-0062-0

with the wall. A film layer on the inner side of the chamber

wall is created by the transpiration flow, further protecting

the wall from the hot gases.

The Deutsches Zentrum fur Luft- und Raumfahrt—

German Aerospace Center (DLR) concept of a transpira-

tion cooled ceramic thrust chamber consists of an outer

load-carrying carbon fibre reinforced plastic (CFRP) shell

and an inner porous and permeable ceramic matrix com-

posites (CMC) liner, which is actively cooled. The concept

leads to a functional split between outer shell and liner. The

outer CFRP structure carries most of the mechanical loads

created by inner chamber pressure and longitudinal com-

pression and bending moments induced by nozzle move-

ments and thrust. The permeable liner provides the cooling

functionality and acts as an interface to the combustion

area. The use of CFRP for the outer jacket avoids or

reduces problems created by materials with high thermal

expansion coefficients or mismatches, as are present in case

of combined application of CMC and metal. The coolant

mass flow is provided by a tap-off valve. The pressure

difference between the coolant distribution reservoir and

the chamber adjusts itself, according to the material prop-

erties, during operation. Figure 1 shows the functional

principle of the ceramic rocket engine thrust chamber. As

indicated there are two free parameters in the design

influencing the local pressure difference. The depth of the

cooling reservoir can be varied axially and thereby the

local radial length of passage of the coolant, which corre-

sponds to the pressure loss occurring during wall transition,

can be tailored. The manufacturing is performed by axial

stacking of fiber ceramics layers. It is possible to stack

material of different porosity and permeability according to

the local coolant requirements (as indicated by the different

hatchings in Fig. 1). The manufacturing process, the

ceramic materials and the chamber assembly process are

described in more detail in previous publications [4, 6].

Based on test results scaling analyses have been per-

formed in the past, indicating that for large diameter and

high pressure applications it is possible to build ceramic

chambers operating with coolant ratios of \1 % of the

chamber mass flow [8]. This paper discusses the expected

impact on chamber performance in relation to the applied

coolant ratio.

2 DLR test campaigns with ceramic thrust chambers

Experiments with porous CMC materials for rocket engine

chamber walls have been conducted at the DLR since the

end of the 1990 s at various testbenches under a wide

variety of test conditions. Table 1 lists the test campaigns

of DLR’s ceramic thrust chambers. The test cases used for

the analysis described in the following section were part of

the DLR projects Keramische Schubkammer—Ceramic

Fig. 1 Functional principle of a transpiration cooled ceramic thrust

chamber

Fig. 2 MT5-A thrust chamber at the P6.1 test bench in Lampolds-

hausen (March 2012)

Table 1 DLR ceramic thrust chamber test campaigns

KSK-KT KSK-ST5 MT5-A WS1

Year 2008 2010 2012 2012

Test bench P8 P8 P6.1 P6.1

Propellant

combination

LOX/LH2 LOX/LH2 LOX/GH2 LOX/GH2

Injection

temperature

(fuel)

�55 K �55 K �135 K �150 K

Injection

temperature

(oxidizer)

�155 K �155 K �125 K �140 K

Coolant H2 H2 H2 H2

Wall material C/C Al2O3 and

C/C

Al2O3 and

C/C

various

Nozzle material Copper C/C C/C C/C

Injector API API TRIK TRIK

Chamber

diameter (dc)

50 mm 50 mm 50 mm 50 mm

Throat diameter

(dt)

31.6 mm 32.5 mm 20 mm 20 mm

Characteristic

chamber

length (l�)

0.86 m 0.68 m 1.75 m 1.83 m

100 A. Herbertz et al.

123

Thrustchamber (KSK) and Keramische Bauweisen fur

Experimentelle Raketenantriebe von Oberstufen—ceramic

design of experimental rocket engines for upper stages

(KERBEROS). Project (KSK) was conducted from 2007 to

2010. Project (KERBEROS) started in 2012 and is ongo-

ing. The injectors used in those campaigns were DLR’s

Advanced Porous Injector (API) and Transpira-

tionsgekuhlter Referenz-Injektor in Koaxialbauweise—

transpiration cooled coaxial referencing injector (TRIK).

Figure 2 shows test operation of a ceramic thrust chamber

during the test campaign MT5-A. The test campaigns and

the specimen thrust chambers are described in more detail

in a previous publication [7].

3 Analysis of test data

This section discusses the performance impact of transpi-

ration cooling based on available test results. In all cam-

paigns a substantial amount of hydrogen was used for

chamber wall cooling. This resulted in very cold wall

temperatures. The transpiration coolant flow rate is defined

in this paper as the ratio of coolant mass flow to total mass

flow:

s ¼ _mk

_mk þ _mfu0þ _mox0

ð1Þ

As can be noted (cf. Table 2 on page 11) the amount of

coolant was in those sub-scale campaigns of the same order

as the hydrogen used for combustion in the injector. In

order to operate the chamber of a full-size rocket engine

efficiently, much lower coolant ratios are required [5].

However due to favorable scaling effects, the cooling of

large diameter and/or high pressure combustion chambers

requires much lower coolant fractions. This is further dis-

cussed in previous publications [6, 8].

No direct measurement of thrust degradation due to

transpiration cooling has been performed in the DLR test

campaigns. The thrust can be expressed as a function of the

thrust coefficient (cf. Eq. 3).

I ¼ F

_m g0ð2Þ

F ¼ CF At pc ð3Þ

The characteristic velocity (c�) is defined as:

c� ¼ At pc

_mð4Þ

Along with the definition of c� (cf. Eq. 4) this leads to the

relation of the specific impulse and the characteristic

velocity.

I ¼ c� CF

g0

ð5Þ

For a fixed nozzle (i.e. constant value for CF) the specific

impulse is therefore in theory proportional to the charac-

teristic velocity. Experimental studies performed in the

1990s however indicate that the impact of transpiration

cooling on the specific impulse is lower than on the char-

acteristic velocity [3]. The c�-efficiency is therefore a

conservative estimation for the Ivac-efficiency.

The characteristic velocity is an indicator for chamber

performance. It is mainly influenced by the quality of the

injector and the characteristic chamber length.

The characteristic chamber length (l�), defined as the

ratio of chamber volume to throat area ratio, is related to

the retention time of the propellants in the combustion

chamber. For the propellant combination LOX/LH2 a

choice of l� ¼ 1 m is a conservative value, while a choice

of l� ¼ 0:75 m represents an aggressive value [9].

l� ¼ Vc

At

ð6Þ

3.1 c� Efficiency

The characteristic velocity (c�) is independent of nozzle char-

acteristics and therefore commonly used as a figure of merit for

comparison of combustion chamber designs [11]. In order to

evaluate the thrust chambers performance the characteristic

velocity is compared with the ideal characteristic velocity.

gc� ¼c�

c�id¼ At pc

ð _mk þ _mfu0þ _mox0

Þ c�idð7Þ

Here the ideal characteristic velocity is determined for each

test case according to Eq. (8) based on measured chamber

pressure. The chamber pressure was usually measured near

the injector [10]. Additionally the stagnation pressure was

measured in the igniter chamber. In cases where pressure

measurement in the main chamber failed, the measurement

from the igniter chamber was used for calculation of c�.Those cases are marked in Table 2.

c�id ¼pcid

qtidatid

ð8Þ

Typical values for the efficiency gc� range from 92 to 99.5 %

[11]. The density and velocity required to calculate the ideal

characteristic velocity, according to Eq. (8), are obtained by

use of the NASA code chemical equilibrium with applica-

tions (CEA) [1]. In this study thermal transport properties for

shifting equilibrium (eql) are used in all calculations.

The ideal c� is determined according to the current total

mixture ratio. For a fixed injection mixture ratio R0, an

increasing coolant ratio s (coolant mass flow per total

chamber mass flow) reduces the total chamber mixture

c�-Efficiency evaluation of transpiration cooled ceramic combustion chambers 101

123

ratio Re. Figure 3 shows the resulting chamber mixture

ratio and inherent increase in c� for a variation of the

coolant ratio. For an initial mixture ratio of R0 ¼ 5:5 the

ideal characteristic velocity reaches a maximum value at a

total mixture ratio of R ¼ 2:7. This corresponds to a

coolant ratio of s ¼ 13:75 %. The calculations presented in

this paper therefore do not normalize the characteristic

velocity with a theoretic value for the injection conditions.

Instead for each dataset the ideal characteristic velocity is

calculated separately, taking into account variations in

injection temperatures and total mixture ratio.

The total or final mixture ratio is calculated according to

Eq. (9).

Re ¼_mox0

ð _mfu0þ _mfuk

Þ ¼R0 ð1� sÞ1þ s R0

ð9Þ

3.2 Available test data

In order to obtain suitable data for the performed analysis,

the test data was processed. A simple moving average

(SMA) of 101st degree, representing a time interval of 0.1–1

s, was used to average the test data. The averaged signals at

steady state operation were taken as a basis for calculation.

Figure 4 shows an example of original signal, the averaging

and the selection of the test data. The reference time for the

steady state data is arbitrarily selected immediately before

the initiation of the shutdown sequence. Table 2 lists test

runs used for the c�-evaluation presented in this paper.

4 Resulting dependencies of c�

Relating the characteristic velocities to the ideal charac-

teristic velocity leads to the efficiency calculated according

to Eq. (7). Figure 5 shows the calculated efficiencies of the

characteristic velocity.

4.1 Transpiration cooling coefficient

By applying linear regression to the data, for extrapolation

of the impact of the transpiration cooling on c�, an off-set

for the characteristic velocity can be determined. For a

coolant ratio of s ¼ 0 % (i.e. no transpiration cooling), the

efficiency is extrapolated from test data. It is assumed that

the impact on the characteristic velocity can be assessed by

use of Eq. (10). The worst conceivable case is a loss in

performance equivalent to the applied coolant ratio

(kT = 1). This would mean that the coolant does not con-

tribute anything to the thrust, therefore reducing the per-

formance according to the applied mass ratio. The ideal

case on the other hand would be kT = 0, when the coolant is

fully accelerated, as if it were entirely injected through the

faceplate.

The proposed linear approach fits the test data best. A

nonlinear approach, which somehow represents the geom-

etry, may be better suited. Currently no test data for

chambers of larger or smaller diameter than 50 mm is

available to develop and validate such an approach.

gc� ¼ ð1� kT sÞ ð10Þ

For campaigns with few performed tests (e.g. KSK-ST5),

the regression analysis may provide incorrect values with

extrapolated initial efficiencies above 100 %. In such cases

the regression analysis is performed with a fixed value of

gc�0¼ 100 %. Calculated values for the derived cooling

coefficients and initial efficiencies are shown in Table 3.

Based on the test data extrapolation, the averaged tran-

spiration cooling coefficient for all DLR ceramic thrust

chamber campaigns is kT ¼ 0:6:

Fig. 3 Ideal characteristic velocity as a function of the coolant ratio,

for an initial mixture ratio of R0 = 5.5

Fig. 4 Signal averaging and selection of steady state test data

102 A. Herbertz et al.

123

4.2 Error discussion

Several uncertainties remain with this approach and leave

room for further investigation. The exact value of the

transpiration cooling coefficient kT will likely depend on

the chamber design and its interaction with the injector.

Modeling and analysis of each chamber therefore requires

the use of unique coefficients.

During the short test durations on the experimental test

benches complete steady state concerning the ceramic wall

temperature was never reached. In order to avoid errors due

to transient behavior as much as possible, data was pro-

cessed at a time shortly before shutdown. While the hot gas

side and wall side is nearly steady state at that time, there

always remain some transient conditions, which can not be

fully avoided. The temperature of the injected propellants

changes constantly during test operation. This is due to the

continuous depletion of the tanks. The liquid volume in the

tank decreases and the fluid temperature increases during

test operation.

Concerning the uncertainties in the measurement it has

to be noted that the evaluation of gc� depends on several

measured quantities, as described by Eqs. (7) and (8). The

Table 2 Selected reference

chamber conditions during the

test campaigns of DLR’s

ceramic thrust chamber

a Chamber pressure

measurement in igniter

campaign Test # Ref.

time (s)

Chamber

pressure (MPa)

Injection

mixture

Coolant

ratio (%)

Total mass

flow (kg/s)

Char. velocity

(m/s)

KSK-KT 081208 25 9.1a 5.5 8.71 3.148 2269.4

KSK-KT 081212a 25 9.11a 5.5 9.13 3.157 2267.2

KSK-KT 081212b 28 9a 5.5 9.14 3.159 2238.2

KSK-ST5 100629a 6 5.34 6.68 17.63 2.069 2139.3

KSK-ST5 100629b 15 5.7 5.78 16.08 2.049 2306.5

KSK-ST5 100702a 60 5.54 5.45 15.15 2.066 2224.6

MT5-A 120222a 16 4.73 6.27 14.51 0.649 2287.5

MT5-A 120223b 14 5.87 6.23 14.23 0.804 2294

MT5-A 120224b 14 5.68 6.22 9.89 0.765 2330.7

MT5-A 120227b 15 5.79 5.6 9.82 0.777 2340.7

MT5-A 120301 15 5.71 5.59 8.45 0.766 2342.1

WS1a 121031a 14 5.8 5.33 9.38 0.761 2395

WS1a 121031b 15 5.67 5.66 8.41 0.75 2375.6

WS1a 121107 15 5.55a 5.5 7.05 0.74 2357.9

WS1b 121120a 16 5.68a 5.67 8.94 0.755 2364.6

WS1b 121120c 20 4.52 2.05 4.32 0.577 2457.7

WS1b 121122 22 4.4 2.05 2.7 0.566 2440.6

WS1b 121126a 8 4.34a 1.91 2.56 0.563 2423.9

WS1b 121126b 8 4.36a 1.9 2.64 0.568 2409.2

WS1b 121127 8 4.37a 2.08 2.69 0.563 2439.9

Fig. 5 Efficiency gc� as a function of the coolant ratio s for different

test campaigns

Table 3 Transpiration cooling coefficient for the ceramic thrust

chamber

Campaign Initial gc� (%) Coefficient kT

KSK-KT gc�0¼ 100 kT ¼ 0:94

KSK-ST5 gc�0¼ 100 kT ¼ 0:59

MT5-A gc�0¼ 97:5 kT ¼ 0:38

WS1 gc�0¼ 100 kT ¼ 0:50

c�-Efficiency evaluation of transpiration cooled ceramic combustion chambers 103

123

characteristic velocity directly depends on the accuracy of

the measurement of chamber pressure and mass flow. The

calculated ideal characteristic velocity also depends on

the injection temperatures. Table 4 lists the instrumenta-

tion measurement accuracy, as specified by the

manufacturers.

While the measurement error specified by the supplier of

the pressure sensors is negligible, the data used for aver-

aging, as discussed in Sect. 3.2, oscillates by approximately

�1 %. This increased error margin results from the mea-

surement chain implemented at the test bench. Due to the

chosen installation of the pressure measurement, there are

further uncertainties with respect to the calculated char-

acteristic velocity, concerning the position of the chamber

pressure measurement. Taking everything together indi-

vidual errors of calculation of up to 3 % are expected. The

regression analysis however provides a good basis for

performance evaluation.

4.3 Comparison with metallic transpiration cooled

chambers

In the frame of the German–Russian research program

Technologien fur Hochleistungs-Raketenmotoren—tech-

nologies for high-performance rocket engines (TEHORA)

several tests with transpiration cooled metallic combus-

tion chambers were conducted between 1995 and 1998 [2,

3]. Obviously the configuration in those test was sub-

stantially different from that used in ceramic thrust

chamber tests. The resulting linear regression (applying

the same normalizing process as described in Sect. 4.1)

leads to similar cooling coefficients as those listed in

Table 3.

In the frame of the (TEHORA) program thrust mea-

surement of the test chamber was performed. The degra-

dation of the specific impulse was therefore measured

independently of the c� performance. Losses in the specific

impulse efficiency were observed to be only about half as

large as those of the characteristic velocity efficiency [3].

5 Conclusion and outlook

Test data generated between 2008 and 2012 in DLR’s

ceramic thrust chamber development projects has been

analyzed concerning c�-efficiency. The test campaigns

were performed with different mixture ratios, different

components and different geometries. Each configuration

therefore exhibits a different relation between coolant ratio

and performance loss. In general however it can be con-

cluded that for coolant ratios below 1 % of the total mass

flow, the expected reduction of the characteristic velocity is

\0.6 %.

The associated reduction of the specific impulse was not

measured in DLR’s test campaigns. According to results of

past experimental studies it is significantly lower than the

loss in the characteristic velocity. Consequently based on

available test data the losses in specific impulse can be

expected to be 0.3–0.6 of the transpiration coolant mass

flow rate. Scaling analysis of the transpiration cooled

ceramic thrust chamber has shown that for large scale and

high pressure applications coolant ratios below 1 % are

well feasible. Expected losses in the specific impulse for

high performance cryogenic rocket engines will therefore

range in the order of 1.5 s.

This loss in performance is the price to pay for the

introduction of a new technology that will reduce the

manufacturing effort and increase chamber life time.

Whether this is economical worthwhile is subject of

further investigation, taking into account a detailed ana-

lysis of expected manufacturing costs, as well as the

impact on the payload mass of selected space transpor-

tation systems.

References

1. Gordon, S., McBride, B.J.: Computer Program for Calculation of

Complex Chemical Equilibrium Compositions and Applications,

Vol. II: Users Manual and Program Description. NASA Lewis

Research Center. NASA RP-1311 (1996)

2. Gorgen, J., Knab, O., Haeseler, D., Wennerberg, D.: Impact of

intentional and unintentional combustion chamber porosity on

rocket engine characteristics. In: Fourth international symposium

on liquid space propulsion (2000)

3. Haeseler, D., Mading, C., Rubinskiy, V., Gorokhov, V., Khri-

sanfov, S.: Experimental investigation of transpiration cooled

hydrogen-oxygen subscale chambers. In: 34th joint propulsion

conference. AIAA 98–3364 (1998)

4. Hald, H., Herbertz, A., Kuhn, M., Ortelt, M.: Technological

aspects of transpiration cooled composite structures for thrust

chamber applications. In: 16th AIAA/DLR/DGLR international

space planes and hypersonic systems and technologies confer-

ence. Bremen (2009)

5. Herbertz, A.: Systemanalytische untersuchung einer brennkam-

mer in faserkeramischer bauweise von raketenantrieben. Ph.D.

thesis, RWTH Aachen (2008)

Table 4 Instrumentation accuracy as specified by manufacturer

Position Sensor

type

Supplier Range Accuracy

Injection

temperature

Type K,

class 3

TC-direct 73–233

K

�2.5 K

Chamber

pressure

P900

strain

gauge

Measurement

specialties

(Europe)

Up to

20

MPa

�2 kPa

Mass flow Coriolis

Elite

series

Emerson Var. �0.03 %

104 A. Herbertz et al.

123

6. Herbertz, A., Ortelt, M., Muller, I., Hald, H.: Potential applica-

tions of the ceramic thrust chamber technology for future tran-

spiration cooled rocket engines. Trans Jpn Soc Aeronaut Space

Sci Aerospace Technol Jpn. 10(ists28) (2012). https://www.

jstage.jst.go.jp/result?favorite=&type=100%2C200&language=en

&item1=2&word1=Potential?applications?of?the?ceramic?

thrust?chamber?technology?for?future?transpiration?cooled?

rocket?engines.?&cond1=2&item2=8&word2=herbertz&cond2

=2&translate=0&category=070000%2C070100%2C072100%2C

073100%2C074100%2C075100&searchlocale=en&fromid=AF13

S010

7. Herbertz, A., Ortelt, M., Muller, I., Hald, H.: Transpiration-

cooled ceramic thrust chamber applicability for high-thrust rocket

engines. In: 48th joint propulsion conference, Atlanta, Georgia.

AIAA-2012-3990 (2012)

8. Herbertz, A., Selzer, M.: Analysis of coolant mass flow

requirements for transpiration cooled ceramic thrust chambers.

In: 29th international symposium on space technology and sci-

ence. Nagoja (2013)

9. Humble, R., Henry, G., Larson, W.: Space Propulsion Analysis

and Design. McGraw-Hill, New York (1995)

10. Ortelt, M., Hald, H., Elsaßer, H., Herbertz, A., Muller, I.:

Structural investigations on cryogenically operated and transpi-

ration cooled fiber reinforced rocket thrust chambers. In: 48th

joint propulsion conference, Atlanta, Georgia. AIAA-2012-4010

(2012)

11. Sutton, G.P., Biblarz, O.: Rocket Propulsion Elements, 7th edn.

Wiley, New York (2001)

c�-Efficiency evaluation of transpiration cooled ceramic combustion chambers 105

123