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

A Zooming Approach to Investigate Heat Transfer in Liquid Rocket Engines with ESPSS Propulsion Simulation Tool M. Leonardi, F. Di Matteo, J. Steelant, B. Betti, M. Pizzarelli, F. Nasuti, M. Onofri 8th European Symposium on Aerothermodynamics for Space Vehicles Lisbon, Portugal, 2/6 March 2015 Sapienza Activity in ISP-1 Program 15/01/10 Pagina 1

OUTLINE 1. Objectives and Motivations 2. Software for system analysis 2.1. EcosimPro 2.2. External Software 3. Test Case: Space Shuttle Main Engine 4. Space Shuttle Main Engine: Results 5. Conclusions M.Leonardi 2 / 16

Objective and Motivations Main Frame Liquid Rocket Engine system analysis High fidelity modelling High level of detail Limited number of components More difficult 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 M.Leonardi 3 / 16

EcosimPro: Software for System Analysis Object oriented software Unsteady and Steady (design and off design) analysis Resistive-Capacitive philosophy: Resistive component : input output State Fluxes Capacitive component : input output Fluxes State We will focus on a heat transfer problem between combustion chamber and cooling channels M.Leonardi 4 / 16

Transfer modelling in an expander cycle engine Involved components: Combustion Chamber and Cooling Channels Three configurations TC1: Pure EcosimPro model TC2: CFD combustion chamber + EcosimPro cooling system with 1D wall TC3: EcosimPro combustion chamber+ quasi-2d model for cooling system Expander Cycle Modelling M.Leonardi 5 / 16

EcosimPro: Multi-species Reacting Combustion Chamber (EPCC) Finite volume quasi one dimensional formulation of the Euler equations, to retain lightweight philosophy of EcosimPro Non adiabatic component Multi-species flow Mixture of perfect gases Finite rate approach for the combustion terms Detailed treatment of inviscid fluxes: Roe and AUSM + up scheme u t + f(u) = S(u) x. ρi u = A. ρu ρe f(u) = A. ρiu. ρu 2 + p ρuh S(u) =. ωi. pax q New Thrust Chamber Component M.Leonardi 6 / 16

EcosimPro: Multi-Phase Flow and Cooling System (EPCS) Quasi one-dimensional model for the fluid Homogeneous Equilibrium Model for the two phase flow - 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 M.Leonardi 7 / 16

CFD for Combustion Chamber (CFDCC) CFD model Two dimensional axisymmetric simulation Frozen flow assumption Spalart-Allmaras one-equation turbulence model Combustion products injection: full inlet approach Medium grid size 100 90 (axial radial) nodes chosen among three grid levels after a convergence study Grid convergence verification Grid refinement Volumes (axial radial) y min Coarse Grid 50 45 2 µm Medium Grid 100 90 1 µm Fine Grid 200 180 0.5 µm CFD grid convergence analysis: volumes and minimum volume dimensions p 0, T 0 H 2 /O 2 eq. combustion products Symmetry No slip Wall Supersonic Outlet M.Leonardi 8 / 16

Quasi-2D model for flow + Heat conduction (Q2DCS) Coolant Flow Wall Steady state 1D mass and momentum equations Steady state 2D energy equation Pressure varies axially Stream-wise velocity and temperature vary radially and axially Semi-empirical correlations for friction, turbulent conductivity, heat transfer coefficient 2D Heat conduction: wall temperature varies both radially and axially width = 1.016 mm width = 0.546 mm Typical result from a quasi-2d computation height = 2.892 mm M.Leonardi 9 / 16

Coupling EcosimPro and external software Iterative Approach The loosed-coupling approach consists of four steps 1. The adiabatic wall temperature is retrieved. (i) In the CFD case a simulation for the combustion chamber is performed with an adiabatic wall boundary condition.(ii) In the EcosimPro case the recovery factor is instead used in EcosimPro component to retrieve stagnation wall enthalpy. 2. (i) In the CFD case a simulation with an isothermal wall boundary condition is performed, the heat transfer coefficient is thus retrieved from the heat flux q h c = T aw T whg (ii) In the EcosimPro case Bartz s correlation used. 3. The hot gas side heat transfer coefficient and the adiabatic wall temperature are provided to the cooling system software to obtain a new wall temperature profile 4. The new temperature profile is imposed as boundary condition for the combustion chamber code and the process iterates from step 2. Convergence is reached when two wall temperature profiles differ less then a prescribed tolerance after two subsequent iterations (3-4 iterations) M.Leonardi 10 / 16

Space Shuttle Main Engine Test Case Configuration Hot gas side: SSME MCC at Full Power Level (109% of rated thrust) LOX/LH2 Chamber pressure P c = 225.87 bar Mixture ratio O/F = 6 Regenerative cooling: NARloy-Z copper alloy wall 390 milled axial channels Mass flow rate: ṁ = 14.306 kg/s Inlet Conditions: T in = 53.89K P in = 445.47bar Results are compared against Wang and Luong approach: Hot gas flow: 2-D CFD Heat conduction: 3-D Coolant flow: 1-D semi-empirical model CFDCC + Q2DCS : Hot gas flow: 2-D axis-symmetric CFD Heat conduction: quasi 2-D Coolant flow: quasi 2-D M.Leonardi 11 / 16

SSME Heat Transfer Modelling: Results TC1: Pure EcosimPro TC2: CFD Comb.Chamber + EcosimPro Cool.channels TC3: EcosimPro Comb.Chamber + quasi-2d Cool.channels An under-prediction of the wall heat flux wrt reference test cases (black lines) Results obtained with Bartz show a shifted peak and a higher total flux Wall heat flux M.Leonardi 12 / 16

width = 1.574 mm width = 1.567 mm width = 1.015 mm width = 0.918 mm width = 1.574 mm width = 1.016 mm width = 1.027 mm width = 0.546 mm SSME Heat Transfer Modelling: Results Cooling channels side Total temperature increase is slightly over predicted when Bartz s correlation is used height = 2.892 mm height = 5.658 mm (a) x = 14.5 cm (b) x = 0 cm height = 2.464 mm height = 2.466 mm (c) x = -20 cm (d) x = -35.6 cm Comparison of hot gas side wall temperatures at different axial stations Total temperature increase EcosimPro accuracy is comparable with the quasi2d model M.Leonardi 13 / 16

SSME Heat Transfer Modelling: Results Cooling channels side Total pressure losses are in good agreement with both reference methods, highly dependent on roughness values Total pressure losses M.Leonardi 14 / 16

SSME Heat Transfer Modelling: Results Hot gas side The hot gas side wall temperature is higher than Wang and Luong (T max = 800K) Wall temperature computed in TC1 and TC2 (T max = 1009K) is comparable with CFD+Q2DCS Results obtained with Bartz show a different peak position and temperature profile Hot gas side wall temperature M.Leonardi 15 / 16

Conclusions EcosimPro flexibility in being connected with external software has been proven Heat flux profile must be as accurate as possible: CFD input vs ad-hoc calibration Pure EcosimPro model is able to retrieve results that are in good agreement with higher order models With the same hot gas side input (heat flux profile) EcosimPro cooling system is comparable with quasi2d models M.Leonardi 16 / 16