Modeling laminar partially premixed flames with complex diffusion in OpenFOAM R

Transcription

1 Modeling laminar partially premixed flames with complex diffusion in OpenFOAM R Danny Messig, Jens Keller, Bernd Meyer, Christian Hasse Institute of Energy Process Engineering and Chemical Engineering Freiberg, Germany Sixth OpenFOAM Workshop Pennstate

2 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 2

3 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 3

4 Introduction Scope: Numerical simulation of a laminar flame with complex diffusion What is diffusion? Transport phenomenon caused by concentration and temperature gradients What is flamelet? Subgrid model, representing chemistry, kinetics and transport Physical representation of interaction between chemical reactions and transport Why flamelet? Solving detailed chemistry conventional computational expensive FLUT s (Flamelet Look Up Table) enormous speed up 4

5 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 5

6 Theoretical background Governing equations: ρ t + (ρv) = 0 (ρv) + (ρvv) = p + τ + ρg t Dp (ρh) + (ρvh) = q + t Dt + Q Radiation t (ρy i) + (ρvy i ) = j i + R i OpenFOAM standard: ( ) λ (ρh) + (ρvh) = h + Dp t c p Dt t (ρy i) + (ρvy i ) = (µ Y i ) + R i 6

7 Theoretical background Radiation model based on RADCAL [1]: Q Radiation = 4σp N i=1 Laminar heatflux q and species fluxes j i : q = N h i j i i=1 }{{} Inter-diffusion λ T }{{} Fourier s law ( X i a i T 4 T 4 ) N RT D T,i X i M i=1 i X i }{{} Dufour effect j i = ρu i Y i, (u i diffusion velocity) 7

8 Theoretical background Diffusion velocities u i : u i = u D,i + u T,i + u C u D,i = 1 λ 1 X i, Le i ρc p X i λ Le i =, c p ρd m,i u T,i = D T,i ρy i 1 T T, u C = Fickian diffusion Lewis number Soret effect n (u D,i + u T,i ) Y i, correction to ensure i=1 Different modelling approaches for Le i, respectively mixture-average diffusion coefficient D m,i N j i = 0 i=1 8

9 Theoretical background Flamelet: Mixture fraction Z: ρ Z + (ρvz) = (ρd Z Z) t Combustion in a diffusion flame takes place in the close vicinity of the surface of stoichiometric mixture Z st 9

10 Theoretical background Flamelet: Changes are mainly in orthogonal direction on iso-mixture fraction surfaces Changes of temperature and composition are expressed as a function of the orthogonal coordinate 10

11 Theoretical background Flamelet: Coordinate transformation and assumption leads to simplified 1D flamelet equations: ρ Y i t = ρχ 2Le i 2 Y i Z 2 + R i Mixture fraction Z is now the independant coordinate Full 1D flamelet equations can be found in [2] 11

12 Theoretical background new solver: lamreactingfoam: Full transport equations for mixture-average diffusion implemented! Different diffusion models available Added radiation [1] Neglecting Dp/Dt for open laminar flames Implemented in OpenFoam-1.5.x using alternatechemistrymodel [3] 12

13 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 13

14 Validation Validation against: 1 Fluent calculations 2 Experimental data 14

15 Validation against Fluent Case setup: Laminar, diffusion dominated gas flow species properties from same database R i = Q Radiation = 0 Domain with L = 0.25 m Inlet Y O2 Y H2 O Y CH4 Y H2 Y CO2 Y N2 T u x [ ] [ ] [ ] [ ] [ ] [ ] [K] [m/s] boundary conditions 15

16 Validation against Fluent Results: CO 2 -profile along outlet 16

17 Validation against experimental data Flame characterisation: premixed, partially premixed and non-premixed flame (f.l.t.r) ( ) Vprim. Air Primary equivalence ratio: Φ = V prim. Air st 17

18 Validation against experimental data Case setup: Geometry data from [4] Extruded domain (z < 0 cm) Fully developed velocity profile at inlets non-uniform volume cells 3D structured 2 wedge mesh Inlet 1 Inlet 2 Domain L = 20 cm Φ VCH4 Vprim. Air Vsec. Air [ ] [cm 3 /min] [cm 3 /min] [cm 3 /min] Bennett-flame [4] configuration 18

19 Validation against experimental data Numerical setup: Diffusion models: Full transport: Full transport equations for mixture-average diffusion with Le i const. Le and radiation Le = 1: Full transport equations with Le i = Le = 1 and radiation Original: alternatereactingfoam with Sc = ν/d m,i = 1, no Soret/Dufour effects and no radiation Chemical Mechanism: GRI-Mech

20 Validation against experimental data Results: Temperature profiles on centerline 20

21 Validation against experimental data Results: OH mole fraction profiles on centerline 21

22 Validation against experimental data Comparison of maximum centerline temperature T max,c, flame height H T, flame height H OH : Source T max,c H T H OH [K] [cm] [cm] Φ = Experimental by Bennett et. al. [4] CFD by Bennett et. al. [4] CFD by Claramunt et. al. [5] lamreactingfoam Φ = Experimental by Bennett et. al. [4] CFD by Bennett et. al. [4] CFD by Claramunt et. al. [5] lamreactingfoam

23 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 23

24 Flamelet results Scope: Compare different radial profiles of CFD-calculation of lamreactingfoam with results produced by an inhouse flamelet code Verification for using the flamelet model in OpenFOAM R More details of the coupling between FLUT s and OpenFOAM R is given in talk A CFD-Flamelet model based time scale analysis of multi-feed stream in a high pressure gasifier in the next session [6] 24

25 Flamelet results Set up: Bennett-flame configuration [4] Diffusion models: Unity Lewis-Number Le i = Le = 1 Non-unity constant Lewis-Number Le i = const. Le Flamelet calculations: Full flam.: Full set of flamelet equations Simple flam.: Simplified set of flamelet equations Analytical approach for profiles of scalar dissipation rate χ CFD: lamreactingfoam Chemical mechanism: GRI-Mech 1.2 No radiation 25

26 Flamelet results Unity Lewis-Number Le i = Le = 1 CO 2 mass fraction and temperature T as functions of Z 26

27 Flamelet results Non-unity constant Lewis-Number Le i = const. Le CO 2 mass fraction and temperature T as functions of Z 27

28 Contents 1 Introduction 2 Theoretical background 3 Validation 4 Flamelet results 5 Conclusions 28

29 Conclusions Full laminar diffusion transport equations in OpenFOAM 1.5 successfully implemented Verification of corresponding diffusion methods in OpenFOAM 1.5 with Fluent 12.0 and Cantera 1.8 CFD improvement compared to published num. results for Bennett-flame [4] Flamelet results in good agreement with full transport solutions 29

30 Acknowledgement The results described above were obtained in the research project HotVeGas. The project was supported with public funding by the German Federal Ministry of Economics and Technology (Project ID B) This research has been also funded by the German Federal Ministry of Education and Research in the framework of Virtuhcon (Project ID ) 30

31 Literatur I [1] W. L. Grosshandler. RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment. Technical report, NIST technical note 1402, [2] J. Keller. Influence of molecular diffusion flux modeling on the structure of non-premixed and partially premixed flames. Master s thesis, TU Bergakademie, [3] Gschaider B., Rehm M., Seifert P., Meyer B. Implementation of an alternative chemistry library into openfoam. In Open Source CFD International Conference 2008, Berlin,

32 Literatur II [4] B. A. V. Bennett, C.S. McEnally, L. D. Pfefferle, M.D. Smooke. Computational and Experimental Study of Axisymmetric Coflow Partially Premixed Methane/Air Flames. Combustion and Flame, 123: , [5] K. Claramunt, R. Consul, C. D. Pérez-Segarra and A. Oliva. Multidimensional mathematical modeling and numerical investigation of co-flow partially premixed methane/air laminar flames. Combustion and Flame, 137: , [6] Vegendla P., Weise S., Messig D., Hasse C. A CFD-Flamelet model based time scale analysis of multi-feed stream in a high pressure gasifier. In 6th OpenFOAM Workshop,