Fluent 6.0 Staff Training Combustion and DPM

Fluent 6.0 Staff Training

Graham Goldin

October 25 2001

Company Confidential Copyright 2001 Fluent Inc. All rights reserved. 2

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 Enhancement of v5 models

Spray models

Multiple surface reactions


Laminar Flames

Chemistry invariably stiff Reaction time/length scales


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)

Laminar flames


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)

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


Sx

F

t

Q

i

n

i

tRQx

t

AJ


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 Q

where e3 = positivity rate (default = 0.2)

e2 = temp. redux (default = 0.25)


maxl

xCFLt

max

1

l

et

otherwise

TT

1

32 ees

Stiff solver


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



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



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.



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



Numerical methods

Segregated solver Fractional time stepping: over a time step t

Advance solution with no chemical source terms

(only convection and diffusion) for t

Then, advance chemistry in each cell for t 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


Sdt

dQ

ix

F

t

Q


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)



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 114:531-545, 1998

H2/O2/Ar 8 reacting species, 19 step mechanism

Moving mesh, segregated solver, fractional step stiff chemistry solver

Thanks to Dan Lee




Validation: comparison of adiabatic, constant volume

ignition delay (solid line) vs results from stand alone

CHEMKIN code Senkin (square symbols)


0.01

0.1

1

10

100

1000

850 900 950 1000 1050 1100 1150 1200

Temperature (K)

Ign

itio

n D

ela

y (

ms)

0.10

1.00

10.00

0.01 0.10 1.00 10.00

Pressure (MPa)

Ign

itio

n D

ela

y (

ms

)



Mesh


Temperature



Peak pressures


0

1

2

3

4

5

6

0 1 2 3 4 5 6

Experiment (MPa)

Flu

en

t (M

Pa

)

950

1000

1050

1100

950 1000 1050 1100

Experiment (K)F

lue

nt

(K)

Peak temperatures

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Experiment (ms)

Flu

en

t (m

s)

Ignition delay


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

Laminar flames


Strategy

Activate k-e model, but disable their solution

Initialize k to 10-10 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

Laminar flames: Non-premixed flames


Example : Mitchell flame

Laminar flames: Non-premixed 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

Laminar flames

Flame thickness = lF

sl

Intermediate specie

Temperature

preheat zone oxidation zone

inner

layer

Laminar flame speed = sl


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

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



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))

{


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);

}


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)

{

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;

}


Example: Deflagration

Stochiometric methane-air in an open pipe

VOF model with UDF

Laminar flames: Premixed


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

Laminar flames

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