CFD Simulation of high pressure real gas flows

CFD Simulation of high pressure real gas flows on the progress form art to physics :o) Maria Magdalena Poschner Prof. Dr. rer. nat. Pfitzner UNIVERSITÄT DER BUNDESWEHR MÜNCHEN Fakultät für Luft und Raumfahrt Institut für Thermodynamik LRT 10

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 2

Motivation Modern high pressure rocket combustion engine (Vulcain II Ariane 5) Injector head consisting out of 566 single coaxial injectors. Single coaxial injector investigated at the Mascotte test rig 3

Mascotte V03 Chamber: Cross section: 50 mm 50 mm Length: 458 mm Injector: Coaxial injector LOx diameter: 5 mm GH2 diameter: 10 mm Mascotte high pressure (60 bar) operating points and CFD inlet boundary conditions: Oxygen Hydrogen m [g/s] 100 70 T [K] 85 287 4

Comparison with experimental data Comparison of OH distribution of the flame resulting from CFD with chemiluminescence measurements of the OH concentration [ S. Candel et. al., 1998] 5

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 6

Governing Equations Favre averaged governing equations Continuity: Momentum: Species: Enthalpy: Terms have to be modelled + Equation of State T, p / p p T, 7

Equations of state ρ Oxygen Hydrogen Tc [K] 154.581 33.25 Pc [bar] 50.43 12.97 436.129 31.014 c [kg/m^3] Hydrogen P = 60 bar Equations of State: Ideal: pvm nrmt Oxygen Redlich Kwong: Peng Robinson: p RmT a Vm b TVm (Vm b) p RT a (T ) 2 Vm b Vm 2bVm b 2 a and b are calculated from the critical properties Tc and pc using empirical expressions 8

Modeling of Enthalpy / Entropy / Cp All thermodynamic properties are calculated as the sum of an ideal reference value and a departure function: Enthalpy Entropy Spec. heat capacity at const. pressure 9

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 10

Changes in OpenFOAM Starting point: reactingfoam Modifications: (up to now) Calculation of density, enthalpy, entropy and cp in thermophysicalproperties class Modifications: (in future) Development of a real gas LES version of reactingfoam Application of a flamelet combustion model by transporting mixture fraction, variance of mixture fraction and scalar dissipation rate 11

Flat Plate 60 bar T 60 bar 12

Qube with temperature distribution t =60 0.0bar s t = 0.0123 s 60 bar, 80 K 280 K 13

Qube with temperature distribution t =60 0.0bar s t = 0.0123 s 60 bar, 80 K 280 K 14

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 15

Project proposition Development of an ideal gas LES version of reactingfoam Find reason for pressure oscillations Improve temperature calculation 16

State of work Pressure oscillations minimized Improvement of compressibility formulation Addition of a correction term in pressure equation Improvement of calculation sequence in pressure equation and thermophysicalproperties Temperature calculation no problem when pressure and density calculation consistent Development of Real Gas LES Version of reactingfoam 17

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 18

paraview 19

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts In rememberence of the first day at Summer School IV. Project proposition for the OF Summer School 2009 V. OpenFOAM and physics That's just the way it flows VI. Future work and Conclusion 20

Future work and Conclusion Conclusion Goals for Summer School accomplished Future work Accelerate solver Improve pressure equation Improve SGS modelling Implementation of Flamelet combustion model 21

Thank you for your attention 22

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Real Behaviour of Fluid Mixture Critical temperature and pressure of heptane nitrogen mixture vs. heptane mass fraction Critical temperature and pressure of heptane nitrogen mixture vs. heptane mass fraction [Okong o, Bellan 2002] [Okong o, Bellan 2002] 24

Phase Equilibrium Chamber pressure is supercritical for pure components. BUT Critical pressure of mixture may be much higher than critical pressures of pure components. => Subcritical conditions for mixture! ρ Oxygen Hydrogen Tc [K] 154.581 33.25 Pc [bar] 50.43 12.97 436.129 31.014 c [kg/m^3] Phase equilibrium for H2/O2 mixtures at different pressures 25

Cubic EOS + pressure based solver More than one solution possible when solving cubic EOS for density! Choose solution by minimizing Gibbs free enthalpy! N g T, Vm g 0 T RT xk ln xk k p k 1 26

Real mixing temperature 27

Comparison of mixture density 28

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers I. Boundary conditions & modelling in CFX I. Results and Discussion (RCM 3 2nd IWRCM) II. Status quo in OpenFOAM III. Future work 29

Operating Points and Boundary Conditions GH2 Mascotte high pressure (60 bar) operating points and CFD inlet boundary conditions: Oxygen &[g/s] 100 m T [K] 85 Hydrogen LOx Wall & Outlet Boundary Conditions: 70 Wall: Smooth and adiabatic 287 Outlet: Static Pressure = 60 bar 30

T 60 bar, 80 K 280 K 31

Comparison Density / Enthalpy / Cp CFX / OF 32

Outline I. Experimental setup for validation II. Real gas thermodynamics with pressure based solvers III. OpenFOAM and the fine Arts A memorial of the first day at Summer School I. Project proposition for the OF Summer School 2009 II. OpenFOAM and physics That's just the way it flows I. Conclusion 33