This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models

Choudhury, D.

Kim, S. E.

Missaghi, M.

Tselepidakis, D. P.

English

NASA Technical Reports Server

/ 99V' 
EXPERIENCE WITH TURBULENCE INTERACTION AND TURBULENCE-CHEMISTRY
MODELS AT FLUENT INC.
D. Choudhury, S.E. Kim, D.P. Tselepidakis,
and M. Missaghi
Fluent Inc.
Lebanon, New Hampshire
N95- 27893
Outline of Talk
* Part I: Turbulence Modeling
- Challenges in Turbulence Modeling
- Desirable Attributes of Turbulence Models
- Turbulence Models in FLUENT
- Examples using FLUENT
• Part II: Combustion Modeling
- Turbulence-Chemistry Interaction
- FLUENT Equilibrium Model
• Concluding Remarks
Part I:
Turbulence Modeling and Industrial
Flows
• Many industrial flows are turbulent; certainly in the markets
that two of our codes, FLUENTand RAMPANT, are focused in.
• Turbulence augments rates of mass, momentum and heat trans-
fer, often by orders of magnitude.
• Most combustion processes involve turbulence and often de-
pend on it.
• Choice of turbulence model dictates the accuracy of CFD pre-
dictions.
• There is still a large gap between the state-of-the-art and users'
expectations and needs.
131
https://ntrs.nasa.gov/search.jsp?R=19950021472 2020-06-16T08:03:44+00:00Z
Challenges in Turbulence Modeling
• Modeling the correlations: puluj_' and pu_¢
- Closures based on the "eddy-viscosity" concept (indus-
try's most popular choice)
- Closures based on transport equations (RSM)
• Modeling an additional transport equation for a scalar quantity
to fix the state of turbulence.
- Most popular choice: the kinetic energy dissipation rate,
g.
- However, this equation is derived by continuum mechanics-
based phenomenological considerations and intuition.
• Modeling of the viscosity-affected, near-wall laminar sublayer.
- Most popular choice: "Wall-functions" that bridge the
turbulent field to the solid wall.
- However, assumptions involved are not always right.
Desirable Attributes of Turbulence
Models in Commercial CFD Codes
• Accuracy and Universality
- The range of applicability should be as broad as possible.
- Applicable to complex geometries and unstructured meshes.
• Economy
- Mathematically simple.
- Memory. and CPU requirements should be moderate and
affordable (model formulation and grid distribution re-
quirements).
• Robustness
- Model should be able to solve a wide range of problems
with little or no convergence problems.
- Computationally efficient (fast execution speed and uses
memory, sparingly).
132
Turbulence Models in FLUENT
• k-¢ model adequate for simple flows with no significant strain
rages.
• lING k-e model for separated flows, flows with large streamline
curvature, swirling flows, or flows with significant strain rates.
• RSM recommended for swirling flows or highly anisotropic flows.
k-e Model: Some Comments
• \Yell-tested, used for over 20 years, limitations well understood.
• It forms a good compromise between universality and economy
of use for many engineering problems.
• Subject to the inherent limitations of the Boussinesq's hy-
pothesis, i.e., isotropic eddy-viscosity and Newtonian closure
(gradient-diffusion model).
• Many assumptions are introduced in deriving the modeled equa-
tions for the turbulent quantities, particularly the e-equation,
making their fidehty limited.
• The constants in the modeled equations are calibrated against
simple benchmark experiments.
• As a result, the k-E model performs poorly in flows with cur-
vature, swirl, rotation, separated flows, low-Reynolds number
flows, strongly anisotropic flows, etc.
133
Renormalization Group (I:tNG)
Based k-¢ Model
• Basic theory and derivation are described in Yakhot and Orszag
(1986). Further details and applications are in Yakhot, Orszag,
Thangam, Speziale, and Gatski (1992), Speziale and Thangam
(1992).
• Firstintroducedina commercialcode,FLUENT, in 1992.
• The R.bIGmethod isessentiallya scale-eliminationtechnique
that can be applicableto the Navier-Stokesand other scalar
transportequationsaswell.
• Removal ofsuccessivelyargescalesleadsto differentialtrans-
portequationmodelsand associatedformulaforquantitiesuch
asthe turbulentPrandtl/Schmidtnumber.
• The basicform oftheRNG-based k-eequationsremainslargely
the same with the standardk-¢ model. But, the constantsin
the model equationsarederivedexplicitlyfrom theo_,.
• The G-equation ends up with an additional source term, a
strain-dependent term.
• The RNG model can be integrated directly to a solid wall with-
out using ad hoc damping functions or damping terms used in
many near-wall models.
• High-Re form of the turbulence kinetic energy and dissipation
rate equations derived by RNG procedure axe:
N+cr_-_ = 1.42 P_-_.c_7+?-_ _ _ -R
where:
ak = a¢ = 0.7179
P;, = 2uTSijS_ i is the kinetic energy production
Sij -- ½kaxi + Oz;) is the mean rate of strain tensor
k 2
,.,T=C,, T
R c.,3(I-_) _l
-- l+fl_ J k
77= Sk/E, S = (2 S_jS_j)½
rl0 = 4.38, f_ = 0.015
134
RNG-Based k-e Model (Cont'd)
• In the low-Re RNG model, a differential relationship exists
between _Teand ve_ (Yakhot and Orszag, 1986).
• The turbulent Prandtl/Schmidt number is no longer a constant,
and computed from relationships relating the local value of the
number to the viscosity ratio (Yakhot and Omzag, 1986).
• In these relations, as £, _ 1,a _ s0 (the low-Re limit) and
as _ _ oo, a = a -1 _ 0.7179 (the high-Re limit). Here:
_' = ve_/uo, where v, ir = vo + VT
a = inverse turbulent Prandtl number (a -1)
c_0 = inverse molecular Prandtl number (a_ -1)
• In the low-Re regions, gk and a_ are obtained similarly from
the Prandtl number relationships, with a0 = 1.0.
• The relationships ensure that in the high-Re number part of
the flow where _ >> 1:
k 2
ve_ = _'T = 0.085 --
and the effective viscosity varies smoothly from the molecular
viscosity to the turbulent viscosity.
• The low-Re eddy-viscosity formula does not explicitly involve
any geometric length scale, i.e., the distance from a solid wall
used in the damping functions adopted by most low-Re near-
wall models, which is a very convenient feature for calculations
for complex three-dimensional geometries.
• In collaboration with the originators of the RNG model, Drs.
Yak_hot and Orszag, the model has been extended to account
for the effects of compressibility, swirl, rotation, and premixed
combustion.
• The RNG-based k-e model also wor "ks well with conventional
and enhanced (non-equilibrium) wall functions available in Flu-
ent Inc.codes.
135
The Reynolds-Stress Model in
FLUENT
• RSM solves transport equations for the Reynolds stresses: u_u_
(4 equations in 2D problems, 6 equations in 3D problems).
• RSM is the level of modeling that has a well established track
record of out-performing eddy-viscosity models in complex flows.
• It is computationally more expensive and more inclined to di-
vergence and stability problems.
• The simple and most widely tested form of the Launder, Reece
and Rodi (1975) form is used.
• The interpolation technique for co-located grids of Rhie and
Chow (1983) is used.
• It offers the best choice for highly anisotropic flows.
Example 1:
Circle-to-Rectangle Transition Duct
• Measured by Davis (1991).
• ReD = 3.9 x 102.
• Solution Domain.
- Upstream Inlet Boundary: x/D = -1.0
- Downstream Exit Boundary: x/D = 8.0
- A Quadrant of the duct modeled.
(y/o).+(z/b)' = 1
×
: STATION 6
STATION S
___. STATION 4
(__ STATION ,3
y STATION 2
STATION I
136
6.0
4.0q
&
2.0
Turbulent Flow in a Transition Duct
I , I I
 -oTo --o",
Calc. (RNG/k- e)
........ Calc. ( RSM / Soft. & Patel )
O Experiment ( David O. Davis )
{3 , , , I , , , I , t , I r , , Z t , ,0"0.00 0.20 0.40 0.60 0.80 1.00
s/s,g
f
tO"-"'-----"----
Exp.
Contours of computed streamwise velocity
(RNG-based k-e model)
137
Example 2:
Cyclone Sparator
, Measured by Qing (1983).
• RSM is used.
, Cylindrical 55 x 23 x 41 grid.
0.0
o_
E
_" -2.5
O
O
(D
-5.0
C_
X
-7.5
0.00
.... I .... I ' ' ' ' I ....
000
0 experiment
i r I rl i [ r I f l i I ] r I f , ,
0.25 0.50 0.75
R_ di_l Di.qt_ nc:._.: (R-r//R
.oo
138
Example 3:
180 ° Bend of Square-Cross Section
• Solution Domain
- Upstream Boundary: 5.0DH from the start of the bend
- Downstream Boundary: 5.0Dz{ from the end of the bend
- A symmetric half of the duct modeled.
• Mesh
- Orthogonal 101 x 47 x 27
- Distance from the wall _ 0.01DH
3.0
2.5
2.0
1.5
10
inside outside
' ' ' J .... i .... 12z/D=0"
/; ,' %oO 0.50
_ 0 O0 0"0"0" 0 00_D_Q
:F/ %0 o oo°-
"11
0.75
0.87:
/
0.25 0.50 0.75
90 ° _¢_ ;,_
0.50
......... k-£
0.50 RN(
........ RS_
ooo expt.
0.50
0.50
0.50
.00
139
3.0
2.5
2.0
1.5
1.0
0.5
0.00
inside outside
.... t I ' ' ' I ....
2zJD =0.
025 _
.. __.-..-.--- 0.50
., ooo-o;o-oo oooo-S..o.._oj ,
I°::'" ]i .-_ _- ...... . ......... k-e
............................. 0.50 RN(
• .-..-...-.- - - -- - ooo expt.
0.50
'//
./ 0.87_
_0.50
O-'I [
-c ,_.
"l
I 1 , 1 J I I 1 1 I I f t I I I I I I 0.50
0.25 0.50 0.75 .00
IS_° , ,5_,vt,,m
Part II:
Combustion Modeling
• With environmental awareness, legislations on combustion- gen-
erated pollutants such as NO::, SO= carbon monoxide, soot,
unburnt hydrocarbons, etc. have become increasingly tougher.
• Combustion simulation in industrial applications can help us to
design ¢ombustors with higher efficiencies and lower pollutant
emissions.
• The combustion process involves some of the most complex
phenomena such as chemistr3": multiphase flow, turbulence,
heat transfer and the interaction between these phenomena.
• Here we focus on gaseous combustion in which the reactants
may be mixed or non-mixed prior to flowing into the combustor.
140
Turbulence-Chemistry Interaction
• Accurate simulation of turbulent combustion requires a thor-
ough assessment of the way turbulence and chemistry interact.
The reaction rate and flame structure primarily depend on this
interaction.
. In turbulent flames, chemical rates can be significantly differ-
ent than those in laminar flames (sometimes several orders of
magnitude), and the mean chemical rate is not the same as the
rate calculated based on mean values of the various scalars:
 (01,02,...) # r(01,02,...)
• Turbulent-chemistry interaction is best characterized by the
Damkohler number which is the ratio of characteristic flow time
to chemical reaction time:
Da=_ _ t___
rr -- gl U'
• When Da < < 1 chemical reactions are orders of magnitude
slower than turbulent mixing and the influence of turbulence
on reaction can be neglected.
• When Da >> 1 chemical reactions are very fast and hence
combustion is controlled by turbulent mixing.
• At high Da we can exploit the laminar flame concept: turbu-
lent flame is comprised of an array of laminar flames (flamelets).
Hence chemical rate expressions can be those obtained in lam-
inar flames and the effect of turbulence can be characterized
through the probability density function (pdf).
• For turbulent diffusion flame, the pdf is usually expressed in
terms of a scalar which can best characterize mixing, e.g., the
mixture fraction. Since the rate of reaction is much higher
than the mixing rate, we can assume that the reaction system
is at equilibrium. The effect of turbulence is simply felt by the
fluctuations in the mixture fraction. The mean value of any
scalar in the flame is simply:
= I_ O(_)P(()d_
• For turbulent premixed flames the pdf is usually expressed
in terms of a scalar which can best characterize the reaction
progress, e.g., normalized temperature:
e=sdr(c)p(c)dc
141
FLUENT Equilibrium Model
• For turbulent diffusion flames we use a two-moment beta pdf
and equilibrium data to calculate various thermo-chemical scalars
in the flame.
• To obtain equilibrium data we use the popular CHEMKIN li_
brary of SANDIA, fully interfaced with our codes. CHEMKIN
contains data on all important gaseous fuels, combustion inter-
mediates and products as well as their properties.
• We obtain the mean mixture fraction and its variance from
their respective conservation equations:
8 _ o .,, o___+ 2,,,_ _-_ C_p_-7'_
• To save computational time we calculate the integrals before
the CFD calculations.
Concluding Remarks
• As of now, we provide our users with three turbulence models:
- the "conventional" k-6 model,
- the ReNormalization Group model,
- the Reynolds-Stress Model.
• The Renormalization group k-e model has broadened the range
of applicability of two-equation turbulence models.
• The Reynolds-stress model has proved useful for strongly anisotropic
flows such as those encountered in cyclones, swirlers and com-
bustors.
• Issues remain, such as near-wall closure, with all classes of mod-
els.
• Collaborative research with ICOMP will not only serve to fur-
ther quantify applicability of turbulence models but may bring
to market new ideas in the field of turbulence modeling for
industrial flows.
142


Experience with turbulence interaction and turbulence-chemistry models at Fluent Inc.

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