Simulation and Modelling of Turbulence and Combustion

Stewart Cant Computational Fluid Dynamics Laboratory UNIVERSITY OF CAMBRIDGE DEPARTMENT OF ENGINEERING

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

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

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

RANS Approach -1

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

Reheat buzz combustion instability CFD (Tartan) vs. experiment

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

Flow with combustion past obstacles

· Dynamic mesh adaption for uRANS and LES

Combustion in a vented channel

· Static and dynamic mesh adaption

· CAD import

Oil industry case study - 1

via 3Dgeo

· Surface mesh

Oil industry case study - 2

· Volume mesh

Oil industry case study - 3

Oil industry case study - 4

Flames developing from two separate ignition sources - test case for HPCx

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

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

Gas turbine combustion instability · Mixture fraction & pressure vs.time

pressure Fuel injectors time

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

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

· close-up view

LES modelling test case

Cambridge Buzz Rig: flameholder

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 64 3 , 96 3 , 128 3 , 192 3 , 384 3 , (512 3 ) Requires access to world class supercomputing HPCx

Flame Kernel Surface grid size = 128 3 c = 0.5

Flame wrinkling and thickening due to turbulence

Contours of reaction progress variable with velocity vectors in x-z plane superposed Reaction progress variable profile across the flame brush along with the progress variable profile of the initial laminar flame

Mean behaviour of displacement speed S

d The variation of ρS

d /ρ 0 S L , S d /S L

and (S

r +S n

)/S

L

across the flame brush Variation of (1/ τ|grad c|S

L

) div u compared with ρS

d /ρ 0 S L

plotted across the flame brush

Behaviour of the terms affecting displacement speed S d Reaction rate term, molecular diffusion term, normal component of molecular diffusion term, tangential diffusive term and reactive-diffusive imbalance across the flame brush 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.

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

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

Statistics of flame normals and flame normal interactions Pdf of N 1 on different c isosurfaces Pdf of N 2 on different c isosurfaces Pdf of N 3 on different c isosurfaces

Mutual interactions between flame normal components

c

= 0.7

c

= 0.7

Scatter of N 1 and N 2 on c = 0.7 isosurface

c

= 0.7

Scatter of N 1 and N 3 on c = 0.7 isosurface Scatter of N 2 and N 3 on c = 0.7 isosurface

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 S d for LES combustion modelling

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