1. Fluent 6.0 Staff Training Combustion and DPM Graham Goldin
October

2. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Summary
Laminar flames
General finite rate chemistry
Premixed laminar flames (flame sheet model)
Non-premixed laminar flames (equilibrium f model)
Turbulent flames
Enhancement of v5 models
Partially premixed model
EDC model
Discrete Phase Model
Spray models
Multiple surface reactions
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3. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar Flames
Chemistry invariably stiff
Reaction time/length scales << flow time/length scales
Special numerical methods required (stiff solvers)
Non-premixed (diffusion flames)
Fuel and oxidizer diffuse into the reaction zone, then burn
Premixed
Fuel and oxidizer mixed molecularly, then burn
Moving reaction front – usually thin and difficult to model
Deflagrations
Subsonic: very difficult to model since the flame speed depends on the chemistry as well as the molecular diffusion parameters, and the flame zone must be resolved.
Detonations
Supersonic: ignition due to heat release behind shock. Simpler to model than deflagrations since the shock is not resolved, and detailed molecular transport is not essential.
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4. General Finite-Rate Chemistry
Laminar flames
General Finite-Rate Chemistry
Fluent v6 can import a CHEMKIN II
detailed chemical mechanism file
File -> Import -> Chemkin…
Reactions
v5: Arrhenius with reversible reactions and third body efficiencies
v6: Pressure dependent reactions (Lindemann, Troe and SRI)
Low pressure and high pressure rates, with blending functions
Molecular transport
Critical in subsonic laminar flames since it determines mixing and flame speeds
Recommend using kinetic theory
Can get the Leonard-Jones parameters from the CHEMKIN transport database (TRAN.DB)
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Laminar flames: General Finite-Rate Chemistry
Numerical methods
Need special numerics since stiff reaction mechanism
Coupled solver
Advance species and temperature simultaneously over time step
v6: stiff solver option
Use Implicit for subsonic flames
Use Explicit for supersonic flames (detonations=explosions)
Segregated solver
Default steady, segregated algorithm will diverge
Can use unsteady, segregated algorithm, but time step must be near chemistry time-scale (typical 10-9s): not practical!
v6: has a fractional step scheme (hidden from the user)
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6. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Stiff solver
Coupled solver
Preconditioned NS:
G = preconditioning matrix
Q = [r, ui, T, Yi]
F = inviscid and viscous fluxes
S = source terms
Implicit spatial discretization:
J = Jacobian of S = d S/d Q
A = Jacobian of F = d F/d Q
Rn = Residual at previous time step = [d F/d xi – S]n
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7. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Stiff solver
Implicit stiff coupled solver
Default time step (stiff solver inactive)
where lmax is the maximum eigenvalue of the matrix G –1A
stiff solver active
where lmax is the maximum eigenvalue of the matrix G –1J,
and e1 is a the max time-step parameter (default = 0.9)
In addition, steady Implicit/Explicit stiff coupled solver
Limit updates when solution changing quickly
Qn+1 = Qn + s DQ
where e3 = positivity rate (default = 0.2)
e2 = temp. redux (default = 0.25)
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8. Example: Mitchell flame
Laminar flames: General Finite-Rate Chemistry
Example: Mitchell flame
Subsonic, methane-air, diffusion flame
Smooke mechanism
16 reactive species, 46 reaction steps
Molecular transport with kinetic theory
Axi-symmetric
Coupled, implicit solver
Thanks to Amish Thaker
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

9. Example: Mitchell flame
Laminar flames: General Finite-Rate Chemistry
Example: Mitchell flame
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

10. Example: Mitchell flame
Laminar flames: General Finite-Rate Chemistry
Example: Mitchell flame
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

11. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Convergence tricks
Stiff chemistry simulations are very difficult to converge
Start with a very coarse grid (~1000 cells)
Multiple adaptions after convergence to add resolution
I use region adaption to minimize cell volume changes
Start with a small CFL (~0.01) and ramp up (~100)
For premixed and partially premixed flames:
Patch unburnt ahead of stabilizer, burnt behind, or
Set premixed inlets to equilibrium (burnt) species and temperature
Disable reactions and solve for mixing.
Enable reactions – flame should propagate back to flame stabilizer.
For non-premixed flames:
For low temperature inlets and walls, an ignition source is required
Patch high temperature zone in mixing layer.
Or, temporarily set an inlet temperature above the ignition temperature
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12. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Detonation
Physics
Premixed fuel and oxidizer
Ignition (spark)
Slow (subsonic) deflagration transitions to detonation (supersonic)
Mixture ignited by heat increase behind shock
Front moves at Rankine-Hugoniot speed
Numerics
Spark details difficult to capture (small time/length scales)
Deflagration to detonation difficult to capture
Solution: Skip these and start simulation at detonation
Patch a high pressure in spark zone to initiate shock
Acceptable since spark kernel usually small, and simulation not sensitive to initial conditions
Explicit solver for shock capturing: not robust for stiff chemisty
Solution: 1 step chemistry with ‘tuned’ kinetics
Acceptable since detonation speed determined only by heat release.
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13. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Example: Detonation
Stochiometric methane-air in an open pipe
CH4 + 2O2 -> CO2 + 2H2O
R=Ae-E/RT [CH4][O2]2 A = 1013, E = 1.25*108
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14. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Numerical methods
Segregated solver
Fractional time stepping: over a time step Dt
Advance solution with no chemical source terms
(only convection and diffusion) for Dt
Then, advance chemistry in each cell for Dt as a
constant pressure reactor
where the chemical source term S = wk Wk / r, wk is the reaction rate, Wk is the molecular weight, and r is the density
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15. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: General Finite-Rate Chemistry
Numerical methods
Chemistry integrated with stiff ODE solver CVODE
Requires unsteady solution, even for steady state!
Final solution depends on time step!
Hence, only use for unsteady reacting flows
Fractional step scheme is first order accurate in time
Hidden from gui/tui: activate with scheme commands…
(rpsetvar ‘stiff-chem-seg? #t)
(models-changed)
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16. Example: Rapid Compression Machine
Laminar flames: General Finite-Rate Chemistry
Example: Rapid Compression Machine
Single, driven piston compresses hydrogen-oxygen-argon mixture which ignites due to heat of compression
Experiments by Lee, D., and Hochgreb, S., “Rapid Compression Machines: Heat Transfer and Suppression of Corner Vortex”, Combustion and Flame 114: , 1998
H2/O2/Ar 8 reacting species, 19 step mechanism
Moving mesh, segregated solver, fractional step stiff chemistry solver
Thanks to Dan Lee
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17. Example: Rapid Compression Machine
Laminar flames: General Finite-Rate Chemistry
Example: Rapid Compression Machine
Validation: comparison of adiabatic, constant volume ignition delay (solid line) vs results from stand alone CHEMKIN code Senkin (square symbols)
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18. Example: Rapid Compression Machine
Laminar flames: General Finite-Rate Chemistry
Example: Rapid Compression Machine
Mesh
Temperature
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19. Example: Rapid Compression Machine
Laminar flames: General Finite-Rate Chemistry
Example: Rapid Compression Machine
Peak pressures
Peak temperatures
Ignition delay
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20. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames
Non-premixed flames
Under the assumptions of
chemical equilibrium
constant diffusivities for all species and enthalpy (Le=1)
constant pressure
single, distinct fuel and oxidizer streams (diffusion flame)
the chemistry can be reduced to a single, conserved scalar, the mixture fraction, denoted f
In Fluent, the non-premixed model is only available for turbulent flows, so we have to trick the solver
Rapid solution
Minutes, compared to days for the finite rate solver
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

21. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Non-premixed flames
Strategy
Activate k-e model, but disable their solution
Initialize k to and e to 10+10
Turbulent diffusivity ~ 0
Activate Non-premixed model
Read in PDF file
Force variance to zero by zeroing production and dissipation constants via scheme…
(rpsetvar ‘cdvar 0)
(rpsetvar ‘cgvar 0)
Set appropriate (or tuned) molecular diffusivity
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

22. Example : Mitchell flame
Laminar flames: Non-premixed flames
Example : Mitchell flame
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.

23. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames
Premixed flames
Fuel and oxidizer mixed together at molecular level prior to burning (reactants)
Radicals and heat diffuse from burnt products into unburnt reactants and ignite
Flame moves as a front with laminar flame speed
Flame thickness = lF sl
Intermediate specie
Temperature
preheat zone
oxidation zone
inner layer
Laminar flame speed = sl
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24. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Premixed flames
Theory
Laminar flame speed, sl, determined by internal flame structure
balance between heat /radical production in inner layer and conduction/diffusion to preheat zone
Requires complex chemistry and transport properties
not feasible to resolve in industrial 3D simulations
Laminar flame thickness, lF ~ D / sl, ~ O(0.1mm)
D is the thermal diffusivity = l / r cp
Laminar flame speed is a function of reactant temperature, pressure and species composition
measured or computed from 1D complex chemistry simulations
determine flammability limits: typically between f=0.5 and f=1.5, where f is the equivalence ratio = (XF/XO) / (XF/XO)sto
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25. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Premixed flames
Strategy
Not feasible to resolve the small reaction zone,
as well as the detailed chemistry and molecular
transport properties
Model flame as a sheet propagating with a specified velocity, with heat release at the front
Use the VOF model, with UDFs for propagating speed and heat release
Thanks Boris Makarov and Andrey Troshko
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26. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Premixed flames
Flame sheet UDF (1)
#include "udf.h"
#include "sg.h"
#include "sg_mphase.h"
#include "flow.h"
#include "mem.h"
#define flame_speed 2.;
DEFINE_ADJUST(area_density, domain) {
Thread *t;
Thread **pt;
cell_t c;
Domain *pDomain = DOMAIN_SUB_DOMAIN(domain,P_PHASE);
real voidx, voidy, voidz=0;
Alloc_Storage_Vars(pDomain,SV_VOF_RG,SV_VOF_G,SV_NULL);
Scalar_Reconstruction(pDomain, SV_VOF,-1,SV_VOF_RG,NULL);
Scalar_Derivatives(pDomain,SV_VOF,-1,SV_VOF_G,SV_VOF_RG,Vof_Deriv_Accumulate);
mp_thread_loop_c (t,domain,pt)
if (FLUID_THREAD_P(t))
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27. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Premixed flames
Flame sheet UDF (2)
Thread *tp = pt[P_PHASE];
begin_c_loop (c,t) {
voidx = C_VOF_G(c,tp)[0];
voidy = C_VOF_G(c,tp)[1];
#if RP_3D
voidz = C_VOF_G(c,tp)[2];
#endif
/* calculation of the interfacial area density */
C_UDMI(c,t,0)= sqrt( SQR(voidx) + SQR(voidy) + SQR(voidz) ); }
end_c_loop (c,t)
Free_Storage_Vars(pDomain,SV_VOF_RG,SV_VOF_G,SV_NULL);
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28. Company Confidential Copyright 2001 Fluent Inc. All rights reserved.
Laminar flames: Premixed flames
Flame sheet UDF (3)
DEFINE_SOURCE(reactants, cell, thread, dS, eqn) {
real source;
Thread *tm = THREAD_SUPER_THREAD(thread);
Thread **pt = THREAD_SUB_THREADS(tm);
source = - C_UDMI(cell, tm, 0)*C_R(cell,pt[0]);
source *= flame_speed;
dS[eqn] = 0;
return source; }
DEFINE_SOURCE(product, cell, thread, dS, eqn)
source = C_UDMI(cell, tm, 0)*C_R(cell,pt[0]);
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29. Example: Deflagration
Laminar flames: Premixed
Example: Deflagration
Stochiometric methane-air in an open pipe
VOF model with UDF
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30. Competitors capabilities
Laminar flames
Competitors capabilities
CFX
Fractional step scheme (pressure based solver)
STAR
Offer a link to CHEMKIN
Fractional step scheme
GASP/FASTRAN
Equivalent coupled, density based solver
Company Confidential Copyright 2001 Fluent Inc. All rights reserved.