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					A High Fidelity Model for Numerical
     Simulations of Complex
 Combustion/Propulsion Systems

                 Farhad Jaberi
     Department of Mechanical Engineering
           Michigan State University
            East Lansing, Michigan
                        Objectives                                         Technical Approach
 q    Develop a high-fidelity numerical model for            q    LES/FMDF: A hybrid (Eulerian-Langranian)
      high-speed turbulent reacting flows                         model, applicable to subsonic and supersonic
 q    Study “laboratory combustors'' of interest to               turbulent combustion in complex configurations
      NASA for various flow and combustion
                                                             q    DNS data are used together with experimental
      parameters with the new model
                                                                  data for validation and improvement of
 q    Improve basic understanding of turbulent
                                                                  LES/FMDF submodels
      combustion in supersonic and hypersonic flows

                         Progress                                                  Impact
 q    New high-order numerical schemes are                    q   Numerical Simulations of a scramjet combustor
      developed/validated for supersonic turbulent                is now possible but reliability and accuracy of
      flows,                                                      predictions are dependent on compressible
 q    Compressible subgrid stress and energy flux                 models
      models are implemented and tested,                      q   Numerical experimental: A systematic and
 q    Scalar FMDF model is extended and applied to                detailed study of various flow/reaction
      compressible (supersonic) reacting flows,                   parameters on combustion stability and
 q    LES/FMDF predictions are compared with                      efficiency
      experimental data,
                                                              q   Better understanding of supersonic combustion
 q    DNS data for supersonic mixing-layer are
      generated. LES results are compared with the            q   Feedback to experimentalists and designers
      DNS data.

Publications: (1) Z. Li, A. Banaeizadeh, F. Jaberi, Large
     Eddy Simulation of High Speed Turbulent Reacting
     Flows, International Symposium on Recent Advances in    LES of Supersonic
     Combustion., 2008. (2) A. Banaeizadeh, F. Jaberi, LES    Co-Annular Jet
     of Supersonic Turbulent Flows with the Scalar FMDF,                            DNS of Supersonic Mixing Layer
     APS-DFD, 2009, (3) Li and F. Jaberi, Numerical
     Investigations of Shock-Turbulence Interactions in
     Planar Mixing Layer, AIAA Annual Meeting, 2010.
LES/FMDF of Complex Turbulent Reacting Flows
    A Hybrid Eulerian-Lagrangian Mathematical/Computational Methodology




q   Eulerian: Transport equations for the SGS
    moments
     - Deterministic simulations

q   Lagrangian: Transport equation for the FMDF
     - Monte Carlo simulations

q   Coupling of Eulerian & Lagrangian fields and
    a certain degree of “redundancy”
 Filtered LES Equations -> Eulerian           Total derivative of pressure
                                                 in enthalpy equation



                                                  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
                             Reaction term


FMDF Equation        Subgrid scalar
                         FMDF:
-> Lagrangian                                                   Reaction term




                                              Added to FMDF
                                               equation as a
                                             source/sink term
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.
Rapid Compression Machine – LES/FMDF Predictions




                     Piston groove
In-Cylinder
                                     piston
                              Non-Reacting RCM Simulations
    FD: finite-difference (LES)
    MC: Monte Carlo (FMDF)

                                                           Temperature



                                              piston
                                              piston
                                                                   piston
                                      Temperature      Pressure
                                       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



    FD                 MC



       Temperature Contours




  FD               MC



 Fuel Mass Fraction Contours
3D Shock Tube Problem– LES/FMDF Predictions
                                           3D Shock Tube
                                                                   p2

                                      p1                           Two-Block Grid

                                            p2/p1=15

                  • 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.
  5 MC per cell      20 MC per cell                     50 MC per cell


Particle Number
    Density         Particle Number                     Particle Number
                        Density                             Density
Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by
                      NASA’s Hypersonic Program




                                                                               63.5 mm diam
                         Small-scale facility           Large-scale facility
       10 mm diameter




                                                                                   center jet
           Center jet




                           Cutler et al. 2007            Cutler et al. 2007


                       3D LES                                             LES/FMDF of
                  Calculations with
                  Compact Scheme                                         Co-Annular Jet
                                                                         Mixing and combustion




                                                Iso-Levels of
                                                Mach Number

                                                                              Iso-Levels of
Grid System for LES
                                                                              Mach Number
LES/FMDF of Supersonic Co-Annular Jet
          Mixing Case – No Combustion

                Vorticity Magnitude




   Pressure                     Temperature
 Experiment
Smagorinsky   LES of Supersonic Co-Annular Jet
 MKEV 0.02       Mixing Case – No Combustion
 MKEV 0.03
LES/FMDF of Supersonic Co-Annular Jet – Mixing Case




       Instantaneous Scalar     Instantaneous Scalar
              Experiment
             Smagorinsky
              MKEV 0.02
              MKEV 0.03
LES/FMDF of Supersonic Co-Annular Jet – Consistency of FD and MC
                                                       LES - FD
    Instantaneous Scalar            Mean Scalar
                                                       FMDF - MC




                                                    Experiment

                                                          LES-FD

                                                         FMDF-MC
  DNS and
                  Pressure Contours
   LES of
 Supersonic
                M1=4.2
 Turbulent        Vorticity Contours
Mixing Layer    M2=1.8

               DNS Without Incident Shock
                        Wave




                                   Vorticity Contours
LES of Supersonic Turbulent Mixing-Layer - No Shock




                                   Vorticity
LES of Supersonic Turbulent Mixing-Layer - No Shock
 Mean Axial Velocity




                             Mean Scalar
DNS of Supersonic Turbulent Mixing-Layer with Shock




                       Imposed Shock

      No-Shock
   Shock-Angle 16o
   Shock-Angle 18o
   Shock-Angle 20o
   Shock-Angle 22o




                             Vorticity Contours
LES of Supersonic Turbulent Mixing-Layer with Shock




    Pressure                    Scalar
          Mean Axial Velocity




                                         Mean Scalar
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.
                 Critical Challenges
q Reliable and accurate subgrid models for turbulence-
shock-combustion interactions in strongly compressible
reacting flows
q ‘Correct’ implementation of boundary/initial conditions
q Efficient kinetics solver
q Limited well-defined, detailed experimental data and
DNS data for supersonic turbulent combustion



                      Future Plans
q 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

				
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posted:10/10/2013
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