1. Farhad Jaberi Department of Mechanical Engineering Michigan State University East Lansing, Michigan A High Fidelity Model for Numerical Simulations of Complex Combustion/Propulsion Systems

2. Objectives  Develop a high-fidelity numerical model for high-speed turbulent reacting flows  Study “laboratory combustors'' of interest to NASA for various flow and combustion parameters with the new model  Improve basic understanding of turbulent combustion in supersonic and hypersonic flows Technical Approach  LES/FMDF: A hybrid (Eulerian-Langranian) model, applicable to subsonic and supersonic turbulent combustion in complex configurations  DNS data are used together with experimental data for validation and improvement of LES/FMDF submodels Progress  New high-order numerical schemes are developed/validated for supersonic turbulent flows,  Compressible subgrid stress and energy flux models are implemented and tested,  Scalar FMDF model is extended and applied to compressible (supersonic) reacting flows,  LES/FMDF predictions are compared with experimental data,  DNS data for supersonic mixing-layer are generated. LES results are compared with the DNS data. Impact  Numerical Simulations of a scramjet combustor is now possible but reliability and accuracy of predictions are dependent on compressible models  Numerical experimental: A systematic and detailed study of various flow/reaction parameters on combustion stability and efficiency  Better understanding of supersonic combustion  Feedback to experimentalists and designers DNS of Supersonic Mixing Layer LES of Supersonic Co-Annular Jet Publications: (1) Z. Li, A. Banaeizadeh, F. Jaberi, Large Eddy Simulation of High Speed Turbulent Reacting Flows, International Symposium on Recent Advances in Combustion., 2008. (2) A. Banaeizadeh, F. Jaberi, LES of Supersonic Turbulent Flows with the Scalar FMDF, APS-DFD, 2009, (3) Li and F. Jaberi, Numerical Investigations of Shock-Turbulence Interactions in Planar Mixing Layer, AIAA Annual Meeting, 2010.

3.  Eulerian: Transport equations for the SGS moments - Deterministic simulations  Lagrangian: Transport equation for the FMDF - Monte Carlo simulations  Coupling of Eulerian & Lagrangian fields and a certain degree of “redundancy” LES/FMDF of Complex Turbulent Reacting Flows A Hybrid Eulerian-Lagrangian Mathematical/Computational Methodology

4. Filtered LES Equations -> Eulerian FMDF Equation -> Lagrangian Subgrid scalar FMDF: Reaction term Added to FMDF equation as a source/sink term For non-reacting flows: internal energy/enthalpy equation obtained from FMDF-MC is consistent with LES-FD equation For reacting flows: reaction terms are closed in FMDF Total derivative of pressure in enthalpy equation

5. LES of High Speed Turbulent Reacting Flows In LES, large-scale variables are correctly calculated when reliable and accurate numerical methods+BC, SGS models and chemical kinetics models are provided. For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order numerical schemes have been developed and tested. Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for supersonic and hypersonic flows are needed. Compressibility effects are included in the scalar FMDF for supersonic turbulent combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is established. Better mixing and SGS convection models for FMDF are desirable. DNS data for non-reacting supersonic mixing layer are generated and are being used for evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogen- air) mixing-layer are being generated. Comparison of LES results with experimental data for supersonic reacting flows is essential. Reliable and efficient reduced chemistry models and solver are needed. However, no serious problem is expected in the implementation of chemical reaction in LES/FMDF.

6. Rapid Compression Machine – LES/FMDF Predictions In-Cylinder piston Piston groove TemperatureContours piston piston Non-Reacting RCM Simulations Temperature Pressure FD: finite-difference (LES) MC: Monte Carlo (FMDF)

7. FD MC MC FD Temperature Contours Fuel Mass Fraction Contours Rapid Compression Machine - LES/FMDF Predictions Reacting Simulations - Consistency between finite-difference (LES-FD) and Monte Carlo (FMDF-MC) values of Temperature and Mass Fractions

8. 3D Shock Tube Problem– LES/FMDF Predictions 3D Shock Tube p 2 /p 1 =15 p1p1p1p1 p2p2p2p2 Two-Block Grid 5 MC per cell 20 MC per cell 50 MC per cell Compressibility effects are included in FMDF-MC. Without Compressible term FMDF-MC results are very erroneous. By varying the initial number of MC particles per cell, the filtered temperature does not noticeably change. By increasing the initial particle/cell number, MC particle number density becomes smoother and nearly the same as filtered density. Particle Number Density

9. 63.5 mm diam center jet Small-scale facility 10 mm diameter Center jet Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by NASA’s Hypersonic Program LES/FMDF of Co-Annular Jet Mixing and combustion Grid System for LES Cutler et al. 2007 Large-scale facility 3D LES Calculations with Compact Scheme Iso-Levels of Mach Number

10. Vorticity Magnitude LES/FMDF of Supersonic Co-Annular Jet Mixing Case – No Combustion Pressure Temperature

11. LES of Supersonic Co-Annular Jet Mixing Case – No Combustion Experiment Smagorinsky MKEV 0.02 MKEV 0.03

12. LES/FMDF of Supersonic Co-Annular Jet – Mixing Case Experiment Smagorinsky MKEV 0.02 MKEV 0.03 Instantaneous Scalar

13. LES-FD FMDF-MC Experiment Instantaneous ScalarMean Scalar LES - FD FMDF - MC LES/FMDF of Supersonic Co-Annular Jet – Consistency of FD and MC

14. DNS and LES of Supersonic Turbulent Mixing Layer DNS and LES of Supersonic Turbulent Mixing Layer DNS Without Incident Shock Wave Vorticity Contours M2=1.8 M1=4.2 Pressure Contours Vorticity Contours

15. Vorticity LES of Supersonic Turbulent Mixing-Layer - No Shock

16. Mean Scalar Mean Axial Velocity

17. Vorticity Contours DNS of Supersonic Turbulent Mixing-Layer with Shock DNS of Supersonic Turbulent Mixing-Layer with Shock No-Shock Shock-Angle 16 o Shock-Angle 18 o Shock-Angle 20 o Shock-Angle 22 o Imposed Shock

18. LES of Supersonic Turbulent Mixing-Layer with Shock LES of Supersonic Turbulent Mixing-Layer with Shock Pressure Scalar Mean Axial Velocity Mean Scalar

19. LES of High Speed Turbulent Reacting Flows In LES, large-scale variables are correctly calculated when reliable and accurate numerical methods+BC, SGS models and chemical kinetics models are provided. For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order numerical schemes have been developed and tested. Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for supersonic and hypersonic flows are needed. Compressibility effects are included in the scalar FMDF for supersonic turbulent combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is established. Better mixing and SGS convection models for FMDF are desirable. DNS data for non-reacting supersonic mixing layer are generated and are being used for evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogen- air) mixing-layer are being generated. Comparison of LES results with experimental data for supersonic reacting flows is essential. Reliable and efficient reduced chemistry models and solver are needed. However, no serious problem is expected in the implementation of chemical reaction in LES/FMDF.

20. Future Plans  Further improvement and validation of LES/FMDF: - DNS of supersonic turbulent reacting (H2) mixing layer - LES/FMDF of co-annular reacting (H2) jet - Improved SGS turbulence models for supersonic flows - Implementation/testing of reduced kinetics models  Reliable and accurate subgrid models for turbulence- shock-combustion interactions in strongly compressible reacting flows  ‘Correct ’ implementation of boundary/initial conditions  Efficient kinetics solver  Limited well-defined, detailed experimental data and DNS data for supersonic turbulent combustion Critical Challenges