RPA - Tool for Rocket Propulsion Analysis

Tool for Rocket Propulsion Analysis

Alexander Ponomarenkocontact@propulsion-analysis.comwww.propulsion-analysis.com Cologne, Germany

mailto:[email protected]

http://www.propulsion-analysis.com/

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 = pinlet0 = pinlet

I inj = I inlet

S inj = Sinlet = St

vinj = v inlet = 0Subscripts:

inj = injector face

Inlet = nozzle inlet

t = nozzle throat

Finite-area combustion chamberpinj > pinlet

0 > pinlet

I inj > I inlet

Sinj < S inlet = 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 :


I spvac = ve +

peveρe

I spa = I sp

vac−paveρe

C fvac = I sp

vac /c*

C fa = I sp

a /c*

c* =pc

0

vtρt

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.


(I spvac)d = ζ cζn I sp

vac

(I spa )d=(I sp

vac)d−paveρe

(C fvac)d = ζnC f

vac

(C fa)d = ζnC f

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


(I spvac)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:

A c / A t

LcL*

R1/R tR2/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


C f = (C f )2D (1−ζ f ) → max

(C f)2D = 2AeA t∫0

1

(1−γ−1γ+1

λ2)

1γ−1 [1+λ2 γ (2cos2

β−1)+1γ+1 ] r d r

To obtain the contour with the maximum thrust coefficient at specified conditions (area ratio or nozzle length)

ζ f = 1 −2 δe

**

1 +1

γM e2

δ** =( 2γ−1 )

0.1

Rew0

0.2 (0.015

T w0.5 )

0.8 (1+ γ−12

M we2 )

γ+12(γ−1)

M wν+1

S0.2

r e2 [∫0

Sr1.25M 1+1.25ν

(1+γ−12

M w2 )

1.36 γ−0.36γ−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=εeσ (εrT ∞T∞

4− εr

T wTw4 )

εe=εw /[1−(1−εw)(1−εrT w)]

qw = αT (T aw−Tw) αT=[ 0.026Dt

0.2

(μ∞0 )0.2c p∞

0

(Pr∞0)

0.6 ( pc0

c* )0.8

( Dt

R )0.1

] ( A t

A )0.9

σ

σ=[12 TwTc0 (1+γ−1

2M 2)+1

2 ]−0.68

[1+ γ−12

M 2]−0.12

T aw=Tc0 [1+Pr

1 /3( γ−12 )M 2

1+( γ−12 )M 2 ]

qw = αT ρx v∞(I∞0−I w) αT=

( zzT )0.089Pr−0.56

(1−0.211−Pr

Pr4 /3

β2

1− Tw )0.9225

(307.8+54.8 log2( Pr19.5 ))Pr0.45 z0.08−650


Supported cooling methods: Heat transfer equations:

● Radiation cooling

● Regenerative cooling

coaxial shells tubular-wall jacket channel-wall jacket

● Film cooling

● Thermal barrier coating


qwTwg+qr

T wg =λwtw

(T wg−Twc) = εwcσ Twc4 = qrc

T wc

qwTwg+qr

T wg =λwtw

(T wg−Twc) = αc (Twc−T c)

αc = ηf Nuλcd e

(qwT wg+qr

T wg)2π r dx = mc cc dT c

q (1)

q (2) =S(1)

S(2) S =(I∞

0−I w)T e

0.425μ1000

0.15

R15000.425

(T e+Tw)0.595

(3T e+T w)0.15

qwTwg+qr

T wg =1

t 1

λ1+t2λ2

+...+tNλN

(Twg−T wc)


Regenerative cooling: coolant-side heat transfer


Nu = 0.021Rec0.8Pr c

0.4(0.64+0.36T c

T wc) for kerosene[1]

for liquid hydrogen[1]

for methane [1]

for other coolants [2]

Nu = 0.033 Rec0.8 Prc

0.4( T c

T wc)

0.57

Nu = 0.0185 Rec0.8Prc

0.4 ( T c

T wc)

0.1

Nu = 0.023Rec0.8 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 transferCoefficient depends on geometric shape of the coolant passages


η f

Coaxial-shell jacket: Channel- or tubular-wall jacket:

ηf=1.0 ηf=aa+δ

+2ba+δ

th ξξ

ξ=√ 2αcδ

λw

bδ


Gaseous film cooling


BLC

Core (O/F)core

, Tcore

(O/F)f, T

f[(O/F)b, T

b]1

mf

.

[(O/F)b, T

b]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

ηm f c fdx

d m f =2π r qw

T vap

Qvap

dx

Heating:

Vaporization:

.

Core

BLC

mfWall

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:


N p =mηp

( pout− pin)ρ

N t = mtηtγ

γ−1R0T t in

0 [1−( 1δt )

γ−1γ ]

N t = 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

Thrust chamber thermal analysis ● 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

Thank you for your attention!


RPA - Tool for Rocket Propulsion Analysis

Science

rocket propulsion analysis

analysis of nozzle performance

rpa overview tool

altitude performance

products of reaction

nozzle contour design

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