a zooming approach to investigate heat transfer in liquid rocket engines with espss propulsion...

8/19/2019 A Zooming Approach to Investigate Heat Transfer in Liquid Rocket Engines with ESPSS Propulsion Simulation Tool

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O UTLINE

1. Objectives and Motivations

2. Software for system analysis2.1. EcosimPro

2.2. External Software

3. Test Case: Space Shuttle Main Engine

4. Space Shuttle Main Engine: Results

5. Conclusions

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A Zooming Approach to Investigate Heat Transfer in Liquid Rocket Engines with ESPSS Propulsion Simulation Tool


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Objective and Motivations

Main Frame• Liquid Rocket Engine system analysis

High delity modelling• High level of detail• Limited number of components• More difcult for transient analysis

Reduced order modelling• 0-D or 1-D, concentrated or

distributed parameters• A reasonable trade-off between

accuracy and computational costs• The whole system can be simulated

Final goal

Take advantage of a system modelling tool and zooming locally the level of detail,at component level

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EcosimPro: Software for System Analysis

• Object oriented software• Unsteady and Steady (design and

off design) analysis• Resistive-Capacitive philosophy:

• Resistive component :input → outputState → Fluxes

• Capacitive component :input → outputFluxes → State

• We will focus on a heat transferproblem between combustionchamber and cooling channels

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Transfer modelling in an expander cycle engine

Involved components: Combustion Chamber and Cooling Channels

Expander Cycle Modelling

Three congurations• TC1: Pure EcosimPro model• TC2: CFD combustion chamber +

EcosimPro cooling system with 1Dwall

• TC3: EcosimPro combustionchamber+ quasi-2D model forcooling system

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EcosimPro: Multi-species Reacting Combustion Chamber(EPCC)

• Finite volume quasi one dimensional formulation of the Euler equations, toretain lightweight philosophy of EcosimPro

• Non adiabatic component• Multi-species ow• Mixture of perfect gases•

Finite rate approach for the combustion terms• Detailed treatment of inviscid uxes: Roe and AUSM + up scheme

∂ u∂ t

+ ∂ f (u)

∂ x = S(u)

u = A

...ρ i...

ρuρE

f (u) = A

...ρiu

...ρu2 + p

ρuH

S(u) =

...ωi...

pAxq New Thrust Chamber Component

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EcosimPro: Multi-Phase Flow and Cooling System(EPCS)

• Quasi one-dimensional model for the uid• Homogeneous Equilibrium Model for the two phase ow

- Phases in thermodynamic equilibrium- Same pressure, temperature and velocity

• One dimensional or Three dimensional model for the walls• Only half channel is modelled thanks to symmetry considerations

Cooling channel with 1-D wall model

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CFD for Combustion Chamber (CFDCC)

CFD model• Two dimensional axisymmetric

simulation• Frozen ow assumption• Spalart-Allmaras one-equation

turbulence model•

Combustion products injection: fullinlet approach• Medium grid size 100 × 90 (axial ×

radial) nodes chosen among threegrid levels after a convergence study

Grid convergence verication

Grid renement Volumes (axial × radial) ∆ yminCoarse Grid 50 × 45 2 µmMedium Grid 100 × 90 1 µmFine Grid 200 × 180 0.5 µm

CFD grid convergence analysis: volumes and minimumvolume dimensions

p 0 , T 0

H 2

/ O 2

e q . c o m

b u s

t i o n

p r o d u c

t s

S u p e r s o n

i c O u

t l e

t

No-slip Wall

Symmetry

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Quasi-2D model for ow + Heat conduction (Q2DCS)

Coolant Flow• Steady state 1D mass and

momentum equations• Steady state 2D energy equation• Pressure varies axially• Stream-wise velocity and

temperature vary radially andaxially• Semi-empirical correlations for

friction, turbulent conductivity, heattransfer coefcient

Wall• 2D Heat conduction: wall

temperature varies both radially andaxially

Typical result from a quasi-2D computation

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Coupling EcosimPro and external software

Iterative ApproachThe loosed-coupling approach consists of four steps

1. The adiabatic wall temperature is retrieved. (i) In the CFD case a simulation for thecombustion chamber is performed with an adiabatic wall boundary condition .(ii) In theEcosimPro case the recovery factor is instead used in EcosimPro component to retrievestagnation wall enthalpy.

2. (i) In the CFD case a simulation with an isothermal wall boundary condition is performed,

the heat transfer coefcient is thus retrieved from the heat uxhc =

qT aw − T whg

(ii) In the EcosimPro case Bartz’s correlation used.

3. The hot gas side heat transfer coefcient and the adiabatic wall temperature are providedto the cooling system software to obtain a new wall temperature prole

4. The new temperature prole is imposed as boundary condition for the combustionchamber code and the process iterates from step 2.

Convergence is reached when two wall temperature proles differ less then a prescribedtolerance after two subsequent iterations (3-4 iterations)

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Space Shuttle Main Engine Test Case

Conguration• Hot gas side: SSME MCC at Full

Power Level (109% of rated thrust)• LOX/LH2• Chamber pressure

Pc = 225.87 bar• Mixture ratio O/ F = 6

• Regenerative cooling:• NARloy-Z copper alloy wall• 390 milled axial channels•

Mass ow rate:ṁ = 14.306 kg/ s• Inlet Conditions:

T in = 53.89K Pin = 445.47bar

Results are compared against• Wang and Luong approach:

• Hot gas ow: 2-D CFD• Heat conduction: 3-D• Coolant ow: 1-D

semi-empirical model• CFDCC + Q2DCS :

• Hot gas ow: 2-Daxis-symmetric CFD

• Heat conduction:quasi 2-D

• Coolant ow: quasi2-D

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SSME Heat Transfer Modelling: Results

• TC1: Pure EcosimPro•

TC2: CFD Comb.Chamber + EcosimPro Cool.channels• TC3: EcosimPro Comb.Chamber + quasi-2D Cool.channels

Wall heat ux

• An under-prediction of thewall heat ux wrt referencetest cases (black lines)

• Results obtained with Bartzshow a shifted peak and ahigher total ux

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Cooling channels side

• Total temperature increase is slightly over predicted when Bartz’s correlationis used

Total temperature increase

(a) x = 14.5 cm (b) x = 0 cm

(c) x = -20 cm (d) x = -35.6 cmComparison of hot gas side wall temperatures at

different axial stations

EcosimPro accuracy is comparable with the quasi2D model

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Cooling channels side• Total pressure losses are in good agreement with both reference methods,

highly dependent on roughness values

Total pressure losses

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Hot gas side• The hot gas side wall temperature is

higher than Wang and Luong(T max = 800K )

• Wall temperature computed in TC1and TC2 ( T max = 1009K ) iscomparable with “CFD+Q2DCS”

• Results obtained with Bartz show adifferent peak position andtemperature prole

Hot gas side wall temperature

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Conclusions

• EcosimPro exibility in being connected with external software has been proven

• Heat ux prole must be as accurate as possible: CFD input vs ad-hoccalibration

• Pure EcosimPro model is able to retrieve results that are in goodagreement with higher order models

• With the same hot gas side input (heat ux prole) EcosimPro coolingsystem is comparable with quasi2D models

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a zooming approach to investigate heat transfer in liquid rocket engines with espss propulsion...

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