RPA - Tool for Rocket Propulsion Analysis

Tool for Rocket
Propulsion
Analysis
Alexander Ponomarenko
contact@propulsion-analysis.com
www.propulsion-analysis.com
Cologne, Germany

RPA Overview
Tool for rocket propulsion analysis
RPA is a multiplatform computational package
intended for use in conceptual and preliminary
design of liquid-propellant rocket engines
RPA – Tool for Rocket Propulsion Analysis www.propulsion-analysis.com

RPA Overview
The motivation of RPA development was to...
● Provide modern tool for prediction of rocket engine
performance at the conceptual and preliminary
stages of design
● Capture impacts on engine performance due to
variation of design parameters
● Assess the parameters of main engine components
to provide better data for detailed analysis/design
● Assist in education of new generation of propulsion
engineers

RPA Overview
Features of the tool:
● Steady-state analysis
● Simplified physical models and wide usage of
semi-empirical relations
● Minimum of input parameters
● Rapid execution with accuracy sufficient for
conceptual and preliminary design studies

RPA Overview
Modules
Thermodynamics and
Thrust chamber performance analysis

RPA Overview
Modules
Thrust chamber sizing and
Nozzle contour design

RPA Overview
Modules
Thrust chamber thermal analysis

RPA Overview
Modules
Engine cycle analysis and
Dry mass estimation

Thermodynamics
Properties of reactants and reaction products
● Expandable thermodynamic data library based on
NASA Glenn thermodynamic database (also used by
CEA)
● Includes data for such propellant components as (but
not limited to):
– liquid hydrogen H2(L), liquid methane CH4(L), RP-1, RG-1,
synthine, MMH, UDMH, methyl alcohol
– liquid oxygen O2(L), nitrogen tetra-oxide N2O4, hydrogen
peroxide H2O2
● User may add own propellant components and
products of reaction

Thermodynamics
Used methods
Gibbs free energy minimization for problems p=const
● (p,T) = const
● (p,I) = const
● (p,S) = const
Helmholtz free energy minimization for problems V=const
● (V,T) = const
● (V,U) = const
● (V,S) = const

Performance Analysis
Assumptions:
● Ideal gas law is applied to all processes
● Adiabatic, isobaric, isenthalpic combustion in
combustion chamber at injector face
● Adiabatic, isentropic quasi-one-dimensional
nozzle flow for both shifting and frozen equilibrium
models

Infinite-area combustion chamber
pinj = pinlet
0
= pinlet
Iinj = Iinlet
Sinj = Sinlet = St
vinj = vinlet = 0
Subscripts:
inj = injector face
Inlet = nozzle inlet
t = nozzle throat
Finite-area combustion chamber
pinj > pinlet
0
> pinlet
Iinj > Iinlet
Sinj < Sinlet = St
vinj = 0 < vinlet

Ideal performance of thrust chamber
● Specific impulse in vacuum:
● Specific impulse at ambient pressure :
● Characteristic velocity:
● Thrust coefficient in vacuum:
● Thrust coefficient at ambient pressure :
Isp
vac
= ve +
pe
ve ρe
Isp
a
= Isp
vac
−
pa
ve ρe
Cf
vac
= Isp
vac
/c*
Cf
a
= Isp
a
/c*
c*
=
pc
0
vt ρt
pa
pa

Delivered performance of thrust chamber
● Specific impulse in vacuum:
● Specific impulse at ambient pressure :
● Characteristic velocity:
● Thrust coefficient in vacuum:
● Thrust coefficient at ambient pressure :
Correction factors are obtained from semi-empirical relations [1]
[1] For more details see: Ponomarenko, A. RPA: Tool for Rocket Propulsion Analysis. Assessment of
Delivered Performance of Thrust Chamber. March 2013.
(Isp
vac
)d = ζc ζn Isp
vac
(Isp
a
)d=(Isp
vac
)d−
pa
ve ρe
(Cf
vac
)d = ζn Cf
vac
(Cf
a
)d = ζn Cf
a
(c*
)d = ζc c*
pa
pa

Additional options:
● Analysis of nozzle performance with shifting and
frozen chemical equilibrium
● Optimization of propellant components mixture
ratio for max delivered
● Altitude performance analysis, over-expanded
nozzle performance analysis
● Throttled engine performance analysis
(Isp
vac
)d

Thrust Chamber Sizing
Supported options:
● Sizing for required thrust
level at a specific ambient
pressure
● Sizing for a specific
propellant mass flow rate
through the thrust chamber
● Sizing for a specific nozzle
throat diameter

Thrust Chamber Sizing
Parametric definition of chamber geometry
The size of combustion chamber and the shape of
nozzle inlet contour are defined parametrically by:
● mass flux at nozzle inlet or
chamber contraction area ratio
● chamber length or characteristic
length
● contraction half-angle
● relative parameters:
Ac / At
Lc
L*
R1/Rt
R2/ R2
max
Rn /Rt
b

Nozzle Contour Design
Supported options:
● Cone nozzle with a specified exit half-angle
● Parabolic nozzle contour with specified or
automatically assessed initial and/or exit half-angle
● Truncated ideal contour (TIC) with fixed expansion
area ratioand nozzle length (design method: axisymmetric
MOC)
● TIC with maximum thrust at fixed expansion area
ratio (design method: axisymmetric MOC)
● TIC with maximum thrust at fixed nozzle length (design
method: axisymmetric MOC)

Nozzle Contour Design
Direct optimization of nozzle contour
Cf = (Cf )2D (1−ζf ) → max
(Cf )2D = 2
Ae
At
∫
0
1
(1−
γ−1
γ+1
λ
2
)
1
γ−1
[1+λ
2 γ(2cos
2
β−1)+1
γ+1 ]̄r d̄r
To obtain the contour with the
maximum thrust coefficient at
specified conditions (area
ratio or nozzle length)
ζf = 1 −
2̄δe
**
1 +
1
γ Me
2
δ**
=
( 2
γ−1)
0.1
Rew0
0.2
(
0.015
̄Tw
0.5
)
0.8 (1+
γ−1
2
Mwe
2
)
γ+1
2(γ−1)
Mw
ν+1
̄S0.2
̄re
2
[∫
0
̄S
̄r1.25
M1+1.25ν
(1+
γ−1
2
Mw
2
)
1.36 γ−0.36
γ−1
d ̄S
]
0.8

Thrust Chamber Thermal Analysis
Supported methods to obtain gas-side heat flux:
● Radiation heat transfer:
● Convective heat transfer

Bartz method:

Ievlev method[1,2]
:
1. Lebedinsky E.V., Kalmykov G.P., et al. Working processes in liquid-propellant rocket engine and their simulation. Moscow,
Mashinostroenie, 2008
2. Vasiliev A.P., Kudryavtsev V.M. et al. Basics of theory and analysis of liquid-propellant rocket engines, vol.2. 4th Edition. Moscow,
Vyschaja Schkola, 1993
qr=εe σ(εr
T ∞
T∞
4
− εr
T w
Tw
4
)
εe=εw /[1−(1−εw)(1−εr
T w
)]
qw = αT (Taw−Tw) αT =
[0.026
Dt
0.2
(μ∞
0
)0.2
cp∞
0
(Pr∞
0
)
0.6 (pc
0
c
* )
0.8
(Dt
R )
0.1
] (At
A )
0.9
σ
σ=
[1
2
Tw
Tc
0 (1+
γ−1
2
M
2
)+
1
2]
−0.68
[1+
γ−1
2
M
2
]
−0.12
Taw=Tc
0
[1+Pr1/3
(γ−1
2 )M2
1+(γ−1
2 )M2
]
qw = αT ρx v∞(I∞
0
−Iw) αT =
( z
zT
)
0.089 Pr−0.56
(1−0.21
1−Pr
Pr
4/3
β
2
1− ̄Tw
)
0.9225
(307.8+54.8 log
2
( Pr
19.5))Pr
0.45
z
0.08
−650

Supported cooling methods: Heat transfer equations:
● Radiation cooling
● Regenerative cooling
 coaxial shells
 tubular-wall jacket
 channel-wall jacket
● Film cooling
● Thermal barrier coating
qw
Twg
+qr
T wg
=
λw
tw
(T wg−Twc) = εwc σ Twc
4
= qrc
T wc
qw
Twg
+qr
T wg
=
̄λw
tw
(T wg−Twc) = αc (Twc−̄Tc)
αc = ηf Nu
λc
de
(qw
T wg
+qr
Twg
)2 π̄r dx = ˙mc ̄cc d Tc
q
(1)
q
(2)
=
S
(1)
S
(2)
S =
(I∞
0
−Iw)T e
0.425
μ1000
0.15
R1500
0.425
(Te+Tw)
0.595
(3T e+T w)
0.15
qw
Twg
+qr
T wg
=
1
t1
λ1
+
t2
λ2
+...+
tN
λN
(Twg−T wc )

Regenerative cooling: coolant-side heat transfer
Nu = 0.021Rec
0.8
Prc
0.4
(0.64+0.36
T c
Twc
) for kerosene
[1]
for liquid hydrogen
[1]
for methane
[1]
for other coolants
[2]
Nu = 0.033Rec
0.8
Prc
0.4
(Tc
Twc
)
0.57
Nu = 0.0185 Rec
0.8
Prc
0.4
(Tc
T wc
)
0.1
Nu = 0.023Rec
0.8
Prc
0.4
1. Lebedinsky E.V., Kalmykov G.P., et al. Working processes in liquid-propellant rocket engine and their simulation. Moscow,
Mashinostroenie, 2008
2. Vasiliev A.P., Kudryavtsev V.M. et al. Basics of theory and analysis of liquid-propellant rocket engines, vol.2. 4th Edition. Moscow,
Vyschaja Schkola, 1993

Regenerative cooling: coolant-side heat transfer
Coefficient depends on geometric shape of the coolant passages
ηf
Coaxial-shell jacket: Channel- or tubular-wall jacket:
ηf =1.0 ηf =
a
a+δ
+
2b
a+δ
th ξ
ξ
ξ=
√2αc δ
λw
b
δ

Gaseous film cooling
BLC
Core (O/F)core
, Tcore
(O/F)f
, Tf[(O/F)b
, Tb
]1
mf
.
[(O/F)b
, Tb
]2
Wall
Combustion,Mixing
At each point downstream of
injection point, the mixing rate is
a function of distance from the
injection point and the relative
mass flow rate of the film.

Liquid film cooling
d T f =
2π r qw
T f
η ˙m f ̄cf
dx
d ˙mf =
2π r qw
T vap
Qvap
dx
Heating:
Vaporization:
.
Core
BLC
mf
Wall
Heating Vaporization,
Combustion,
Mixing
Combustion,
Mixing
Liquid
Gas
(gaseous film
cooling)

Engine Cycle Analysis
Supported options:
● Staged combustion cycle (SC)
● Full flow staged combustion (FFSC)
● Gas generator cycle (GG)
Allowed variations of the flow diagram:
● Number of combustion devices (gas generators or
preburners)
● Number of turbopumps
● Arrangement of turbines (serial or parallel)
● Availability of booster pumps
● Availability of kick pumps
● Availability of tap-off branches

Top-level input parameters:
● Type of combustion devices:
 oxidizer-rich
 fuel-rich
● Number of independent turbopumps,
● Number of gas generators/preburners
Component-specific input parameters:
● Efficiency of pumps and turbines
● Pressure drop in all components (valves, injectors, etc.)
● Temperature in combustion devices
● Turbines pressure ratios (for GG cycle)

Flow diagram decomposition (example)
Flow diagram Fuel feed Oxidizer feed Power
Oxidizer-rich SC cycle subsystem subsystem subsystem

Parameters of components
The pump shaft power:
The power developed by
gas turbine:
The power developed by
hydraulic turbine:
Np =
˙m
ηp
( pout− pin)
ρ
Nt = ˙mt ηt
γ
γ−1
R0
Tt in
0
[1−(1
δt
)
γ−1
γ
]
Nt = ˙mt ηt
( pout−pin)
ρ

Solving the analysis problem for
Gas-generator cycle:
for given thrust chamber pressure, find such a mass
flow rate through the turbines that the power of turbines
with specified pressure ratios is sufficient for developing
the required discharge pressure of pumps
Staged-combustion cycle:
for given thrust chamber pressure, find such a pressure
in preburners and turbine pressure ratios that for
specified temperature in preburners the power of
turbines is sufficient for developing the required
discharge pressure of pumps

Engine Dry Mass Estimation
● Based on the set of semi-empirical equations for
each major type of engines: gas generator, staged
combustion and expander cycles
● Initially developed at Moscow Aviation Institute
● RPA utilizes this method with slightly modified
coefficients to better fit the available data on
historic engines
● Results of chamber sizing and cycle analysis are
used as an input parameters of engine weight
estimation

Test cases
Thermodynamics
Comparison with NASA equilibrium code CEA has
been performed for a large number of test cases.
Few of them are presented here:

Test cases
Thermodynamics
A perfect agreement is obtained between the CEA
and PRA programs.

Test cases
Engine performance analysis
Comparison with available data on historic engines
has been performed.
An excellent agreement is obtained between the
actual and predicted performance.

Test cases
Comparison with available reference data has been
performed:
– SSME 40k [1]
– Aestus [2]
[1] Scaling Techniques for Design, Development, and Test.
Carol E. Dexter, Mark F. Fisher, James R. Hulka, Konstantin P. Denisov,
Alexander A. Shibanov, and Anatoliy F. Agarkov
[2] Simulation and Analysis of Thrust Chamber Flowﬁelds: Storable Propellant Rockets.
Dieter Preclik, Oliver Knab, Denis Estublier, and Dag Wennerberg

Test cases
SSME 40k

Test cases
Aestus

Test cases
● Obtained good agreement is sufficient for
conceptual and preliminary design studies.
● Quantitative and qualitative differences in results can
be explained by the following:
– RPA does not simulate fuel atomization and
dispersion, as well as droplets burning
– The hot gas properties for thermal analysis are
retrieved from quasi one-dimensional flow model
– The heat transfer is simulated in RPA using semi-
empirical relations

Test cases
Cycle analysis and weight estimation
Comparison with available data on historic engines
has been performed, including RD-170:
Obtained good agreement is sufficient for
conceptual and preliminary design studies.

Future development
Future development of RPA
● Design of thrust optimized nozzle contour (TOC),
● Improved options for thermal analysis (e.g., support
of jackets with bi-directional channels, support of BLC
formed by injector, designing the cooling jackets,
further validation including film cooling model),
● Improved options for modeling feed systems (e.g.
estimation of pressure drop in a hydraulic
components and efficiencies of the pumps and
turbines),
● Support of additional engine cycles (e.g. expander
cycle).

RPA - Tool for Rocket Propulsion Analysis
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RPA - Tool for Rocket Propulsion Analysis

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