Simulation and Modelling of Turbulence and Combustion

1. UNIVERSITY OF CAMBRIDGE DEPARTMENT OF ENGINEERING Simulation and Modellingof Turbulence and Combustion Stewart Cant Computational Fluid Dynamics Laboratory

2. People The CFD Lab combustion group: Carol Armitage, Gianluca Caretta, Nilan Chakraborty, Karen Hansen, Karl Jenkins, Yun Kang, Michela Oliviero, Andrew Parker, Stephen Tullis, Pankaj Vaishnavi, Saffron Wyse plus Daniele Baraldi, Paul Birkby, Kendal Bushe, Evatt Hawkes, Laurent Leboucher, John Ranasinghe and Bill Dawes, Mark Savill; Caleb Dhanasekeran, Will Kellar, Noel Rycroft Rob Prosser Jackie Chen, Chris Rutland

3. Acknowledgements • Financial support for the work has been provided by: • EPSRC • Alstom Gas Turbines Ltd • Shell Global Solutions Ltd • Rolls-Royce plc • with high-performance computing and support from: • EPSRC; through EPCC, CSAR and HPCx • Cambridge-Cranfield High-Performance Computing Facility • Daresbury Laboratory (Dr. David Emerson) • CTR Stanford/NASA Ames, Sandia National Labs

4. CFD-based Modelling Techniques • RANS • Average the governing equations - model all scales • Modelling generally well developed • Inexpensive (relatively!) - remains standard for industrial problems • LES • Filter the governing equations - modelling required at the sub-grid scale • Combustion physics and chemistry tends to happen on sub-grid scales • Now becoming applicable to industrial problems • DNS • Solve the governing equations directly - no modelling of the physics • Resolution of all scales required - high accuracy numerical methods • Computationally very expensive • Feeds modelling data to LES and RANS

5. RANS Approach -1 • Structured gridding: • - 2D Cartesian and axisymmetric • - non-uniform • - 3rd order QUICK scheme in space • - flux-limited to 2nd order using CCCT limiter • - 1st order Euler/2nd order Crank-Nicholson in time • - turbulence modelling: Reynolds stress or k-epsilon • - combustion modelling using Bray-Moss-Libby type • laminar flamelets + partially premixed extensions • CodeTARTAN

6. Reheat buzz combustion instability CFD (Tartan) vs. experiment

7. RANS Approach - 2 • Unstructured adaptive gridding: • - tetrahedral cells • - semi-automatic grid generation for arbitrary geometries • - 2nd order Jameson scheme in space • - 2nd order 4-step semi-implicit Runge-Kutta in time • - local grid refinement on any specified quantity • - standard turbulence modelling: k-epsilon • - combustion modelling using BML-type laminar flamelets • - parallel decomposition using standard tools • Code McNEWT

8. Flow with combustion past obstacles • Dynamic mesh adaption for uRANS and LES

9. Combustion in a vented channel • Static and dynamic mesh adaption

10. Oil industry case study - 1 • CAD import via 3Dgeo

11. Oil industry case study - 2 • Surface mesh

12. Oil industry case study - 3 • Volume mesh

13. Oil industry case study - 4 Flames developing from two separate ignition sources - test case for HPCx

15. Gas turbine combustion instability • Full 3D mesh • ca. 500 000 cells • Geometrical length scales from 0.7mm to 0.7m

16. Gas turbine combustion instability • Sector mesh • ca. 160 000 cells • Rising to ca. 700 000 cells with solution adaption

17. Gas turbine combustion instability • Mixture fraction & pressure vs.time Fuel injectors pressure time

18. The understanding… • CFD shows a self sustaining cycle mixture entering combustor is richer more heat release – pressure rises less fuel enters – and is pushed away from combustor mixture entering combustor is weaker less heat release – pressure falls more fuel enters – and is drawn into combustor

19. LES sub-grid reaction rate • Flame surface density (FSD or SDF) approach • Extension of flamelet formalism to LES sub-grid modelling - transport equation or algebraic closure • Further extension to partial premixing • Results are broadly in line with RANS experience • - but terms depend on filter size • Applications to gas turbine combustion instability

20. LES modelling test case • close-up view

21. Cambridge Buzz Rig: flameholder

23. DNS in support of modelling • DNS involves no modelling – must resolve all scales • DNS remains too expensive for application to industrial systems • Run canonical cases and extract statistical data • Develop and calibrate modelling for LES • Flame propagation; FSD and transport terms • Flame kernel configuration – spherical • Inflow-outflow configuration – planar • Grid sizes 643, 963, 1283, 1923, 3843, (5123) • Requires access to world class supercomputing - HPCx

24. Flame Kernel Surface grid size = 1283 c = 0.5

26. Flame wrinkling and thickening due to turbulence Reaction progress variable profile across the flame brush along with the progress variable profile of the initial laminar flame Contours of reaction progress variable with velocity vectors in x-z plane superposed

27. Mean behaviour of displacement speed Sd The variation of ρSd/ρ0SL, Sd/SL and (Sr+Sn)/SLacross the flame brush Variation of (1/ τ|grad c|SL) div u compared with ρSd/ρ0SL plotted across the flame brush

28. Behaviour of the terms affecting displacement speed Sd The variation of surface averaged SDF across the flame brush is shown by the red line. The scatter of SDF is shown by the blue dots. Reaction rate term, molecular diffusion term, normal component of molecular diffusion term, tangential diffusive term and reactive-diffusive imbalance across the flame brush

29. Budget of strain rate, curvature and propagation terms in the transport equation for flame surface density Budget of strain rate, curvature and propagation terms across the flame brush

30. Effect of tangential strain rate and curvature on SDF strain rate term Contours of joint pdf between SDF strain rate term and tangential strain rate Contours of joint pdf between SDF strain rate term and mean curvature

31. Statistics of flame normals and flame normal interactions Pdf of N1 on different c isosurfaces Pdf of N2 on different c isosurfaces Pdf of N3 on different c isosurfaces

32. Mutual interactions between flame normal components c = 0.7 c = 0.7 Scatter of N1 and N3 on c = 0.7 isosurface Scatter of N1 and N2 on c = 0.7 isosurface c = 0.7 Scatter of N2 and N3 on c = 0.7 isosurface

33. Future Work in Combustion DNS • Implementation of unsteady non-reflecting inlet boundary condition for viscous reacting flows Test case for non-reflecting inlet and outlet boundary conditions • Simulation for higher turbulent Reynolds number and grid size • Effect of filter size of FSD transport equation terms • Comparative study of algebraic models for FSD and wrinkling factor • Extension of FSD based modelling in thin reaction zone regime • Modelling of surface averaged Sd for LES combustion modelling

34. Conclusions • RANS combustion modelling is highly developed • - remains valuable for industrial applications • - offers a high level of geometrical flexibility • - requires desktop or PC cluster hardware • LES is the major CFD tool for the future • - techniques are under active development • - combustion requires high-level modelling • - requires PC clusters to supercomputers • DNS is an invaluable tool for the support of modelling • - requires top-end supercomputing • HPCx provides an excellent service for CFD