1. AMS 599 Special Topics in Applied Mathematics Lecture 4 James Glimm Department of Applied Mathematics and Statistics, Stony Brook University Brookhaven National Laboratory

2. Turbulent mixing for a jet in crossflow and plans for turbulent combustion simulations

3. The Team/Collaborators Stony Brook University –James Glimm –Xiaolin Li –Xiangmin Jiao –Yan Yu –Ryan Kaufman –Ying Xu –Vinay Mahadeo –Hao Zhang –Hyunkyung Lim College of St. Elizabeth –Srabasti Dutta Los Alamos National Laboratory –David H. Sharp –John Grove –Bradley Plohr –Wurigen Bo –Baolian Cheng

4. Scramjet Project –Collaborated Work including Stanford PSAAP Center, Stony Brook University and University of Michigan

5. Schematics of the transverse injection of an under- expanded jet into a supersonic crossflow Structures expected: bow shock, counter-rotating vortex pair, recirculation zones, large scale structures on the jet surface

6. Outline of Presentation Problem specification and dimensional analysis –Experimental configuration –HyShot II configuration Plans for combustion simulations –Fine scale simulations for V&V purposes –HyShot II simulation plans Preliminary simulation results for mixing

7. Main Objective Compare to the Stanford code development effort. Chemistry to be computed without a model (beyond dynamic turbulence model). Hereby we can offer a UQ assessment of the accuracy of the Stanford code. If the comparison is satisfactory and the two codes agree, the UQ analysis of the Stanford code (in this aspect) will be complete. –Applications to the UQ program

8. Problem Specification and Dimensional Analysis Simulation Parameters: Experimental ConfigurationSimulation Parameters: Experimental Configuration –Fine grid: approximately 60 micron grid Mesh = 1500 x 350 x 350 = 183 M cellsMesh = 1500 x 350 x 350 = 183 M cells –If necessary, we can simulate only a fraction of the experimental domain –If necessary, a few levels of AMR can be used –Current simulations = 120 microns, about 10 M cells HyShot II configurationHyShot II configuration –Resolution problem is similar 3/4 volume after symmetry reduction compared to experiment3/4 volume after symmetry reduction compared to experiment –Full (symmetry reduced) domain needed to model unstart –Resolved chemistry should be feasible –Wall heating an important issue

9. Flow and Chemistry Regime Turbulence scale << chemistry scaleTurbulence scale << chemistry scale –Broken reaction zone Autoignition flow regimeAutoignition flow regime –T c << T –Makes flame stable against extinction from turbulent fluctuations within flame structure Unusual regime for turbulent combustionUnusual regime for turbulent combustion –Broken reaction zone autoignition distributed flame regime –Query to Stanford team: literature on this flow regime? Knudsen and Pitsch Comb and Flame 2009Knudsen and Pitsch Comb and Flame 2009 Modification to FlameMaster for this regime?Modification to FlameMaster for this regime? –Opportunity to develop validated combustion models for this regime, for use in other applications Some applications of DOE interestSome applications of DOE interest

10. Flow, Simulation and Chemistry Scales; Experimental Regime Turbulence scale << grid scale << chemistry scaleTurbulence scale << grid scale << chemistry scale Turbulence scale = 10 micronsTurbulence scale = 10 microns << grid scale = 60 microns<< grid scale = 60 microns << chemistry scale 200 microns<< chemistry scale 200 microns Resolved chemistry, but not resolved turbulenceResolved chemistry, but not resolved turbulence Need for dynamic SGS models for turbulenceNeed for dynamic SGS models for turbulence Transport in chemistry simulations must depend on turbulent + laminar fluid transport, not on laminar transport aloneTransport in chemistry simulations must depend on turbulent + laminar fluid transport, not on laminar transport alone

11. Simulation Plans: HyShot II Regime Compare to laboratory experimental regime and resolved chemistry simulations (V&V)Compare to laboratory experimental regime and resolved chemistry simulations (V&V) Simulate in representative flow regimes defined by the large scale MC reduced order model, both for failure conditions (unstart) and for successful conditions.Simulate in representative flow regimes defined by the large scale MC reduced order model, both for failure conditions (unstart) and for successful conditions. Provide improved combustion modeling to the MC low order model, for the next iteration of an MC full system search.Provide improved combustion modeling to the MC low order model, for the next iteration of an MC full system search. Investigate “gates” which serve to couple system components into full systemInvestigate “gates” which serve to couple system components into full system –For combustion chamber: fuel nozzle, inlet flow and exit nozzle Exactly how can the “gate” be defined to achieve the decoupling?Exactly how can the “gate” be defined to achieve the decoupling? –Essential step for relating UQ of components to UQ of full system

12. Preliminary Simulation Results: Mixing Only 3D simulation. 67% H 2 mass concentration isosurface plot compared to experimental OH-PLIF image (courtesy of Mirko Gamba). The grid is 120 microns, 2 times coarser than the Intended fine grid mesh size.

13. Preliminary Simulation Results: Mixing Only Black dots are the flame front extracted from the experimental OH-PLIF image.

14. Preliminary Simulation Results: Mixing Only Velocity divergence plotted at the midline plane. Bow shock, boundary layer separation, barrel shock and Mach disk are visible from the plot.

15. Preliminary Simulation Results: Mixing Only H 2 H 2 mass fraction contour plotted at the midline plane

16. Preliminary Simulation Results: Mixing Only Stream-wise velocity Stream-wise velocity contour plotted at the midline plane

17. Preliminary Simulation Results: Mixing Only H 2 H 2 mass fraction contour plotted at x/d=2.4

18. Preliminary Simulation Results: Mixing Only Stream-wise velocity Stream-wise velocity contour plotted x/d=2.4

19. Preliminary Simulation Results: Mixing Only Comparison between Smagorinsky model (left) and dynamic model (right) Mass fraction plot, using 240 micron grid Mass fraction plot, using 240 micron grid

20. Preliminary Simulation Results: Mixing Only Comparison between 240 micron grid (left) and 120 micron grid (right) with dynamic model, mass fraction plot with dynamic model, mass fraction plot

21. Future Work Improve code capability –Add missing physics –Add Chemistry Validation Study (comparison with existing experiments, such as HyShot II ground experiments, and Stanford Mungal jet-in- crossflow experiments) UQ/QMU analysis