This viewgraph presentation discusses the following: introduction to CFD Research Corporation; experiences with two-equation models - models used, numerical difficulties, validation and applications, and strengths and weaknesses; and answers to three questions posed by the workshop organizing committee - what are your customers telling you, what are you doing in-house, and how can NASA-CMOTT (Center for Modeling of Turbulence and Transition) help

Avva, Ram K.

Lai, Yong G.

Singhal, Ashok K.

English

NASA Technical Reports Server

EXPERIENCES WITH TWO-EQUATION TURBULENCE MODELS
Ashok K. Singhal, Yong G. Lai, and Ram K. Avva
CFD Research Corporation
Huntsville, Alabama
N95- 27894
OUTLINE
I
• Introduction to CFDRC
• Experiences with 2-Equation Models
Models Used
- Numerical Difficulties
- Validation and Applications
- Strengths & Weaknesses
Answers to Three Questions (Posed by Workshop
Organizing Committee)
1. What Are Your Customers Telling You?
2. What Are You Doing In-House?
3. How Can NASA-CMOTT Help?
INTRODUCTION TO CFDRC
• Young and Energetic (Turbulent) Organization, Dedicated to the
Continuous Process of Advancement and Effective Transfer of CFD
Technology
- PROJECTS
• TWO TYPES OF (_)_[P_I_I_[_T_[_' ACTIVITIES:
143
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INTRODUCTION TO CFDRC (Continued)
• Objective User of Turbulence Models
(0, 1, and 2 Equation Models, RSM and LES)
• Humble Developer, e.g. Monte Carlo Joint Scalar PDF
• Active Participant in Recent Small Eddies of Turbulence, e.g.
- Stanford Endeavor: "Collaborative Testing of
Turbulence Models" 1989-1993
- NationalWorkshops at: NASA MSFC, LeRC/CMOTT,
etc. 1987-1994
- ASME/Fluids Engineering Division, Biathlon, Lake
Tahoe, June 1994
TWO-EQUATION MODELS USED
• Standard k-_ Model (Launder & Spalding, 1974)
• Low-Re k-_ Model (Chien, 1982)
• Extended k-E Model (Chen& Kim, 1987)
• Multiscale k-E Model (Kim & Chen, 1988)
• RNG-Based k-E Model (Yakhot et. al. 1993)
• 2-Layer k-E Model (Rodi, 1991)
• k-_ ++ Models
• k-o) Model (Wilcox, 1991)
++ Models with Corrections for: Curvature, Rotation, Buoyancy,
Compressibility, etc.
]44
NUMERICAL DIFFICULTIES
• Positivity of k & _ (or co)Is Not Guar_Mtbdd in Iterative
Algorithms
• Strong Nonlinearity of Source Terms and Coupling Causes
Numerical Difficulties
• Inappropriate Specifications of _ (or co)at Boundaries or
in Initial Conditions May Also Cause Divergence
• Non-orthogonaitiy of Grids Adds to Difficulties
Non-smooth Change Over for Two-Layer Model Hinders
Convergence
VALIDATIONS PERFORMED
• Channel and Pipe Flows
• Backward-Facing Step
• Turnaround Duct
• Swirl-Flow Combustor
• Rotating Disk Cavities
• Boundary Layers
• Jets, Wakes, and Mixing Layers
• Periodic Wakes Behind Bluff Bodies
Examples of Successes and Failures
1) Flow Around a Square Cylinder; 2) 180 ° Square Duct; 3) S-Shaped
Annular Diffuser; 4) Dump Combustor; 5) Backward Facing Step
145
FLOW AROUND A SQUARE CYLINDER
Strouhal Number
Strouhal Number = fH
Uo
f = Frequency Of Vortex Shedding
H = Obstacle Height
U o = Freestream Velocity
Notes:
Time Strouhal
Model/Expt. Period Number
Expt.
Standard k-_
2-Layer k-E
RNG k-E
7.25
7.1
7.1
7.6
0.138
0.141
0.141
0.132
,
2.
Experiments By Durao, Heitor, and Pereira (1988)
Computations with CFD-ACE
Inlet: 78H Upstream; Outlet: 22H Downstream
Grid: 120 x 80
Time Steps: Over 70 Per Time Period
Ref.: Avva, R.K., Singhal, A.K., Lai, Y.G., "Numerical Simulation Of Periodic
and 3-Dimensional, Turbulent Flows With CFD-ACE," ASME Fluid Dynamics
Conference, Lake Tahoe, NV, June 19-23, 1994.
FLOW AROUND A SQUARE CYLINDER
Instantaneous Streamlines
Mid-Cycle
End of Cycle
146
FLOW IN A 180 ° SQUARE DUCT
i
Computational Domain
180 °
r +X/DH
90
"X/DH
°HIl
Oo
Z
• Experiment by Chang, Humphrey and Modavi (1983)
• Computations Done with CFD-ACE on a 40x40x20 Grid
Static Pressure Along Duct Walls
0.2 i : :
\
0.0 L_ +
°0.2
_j,L o0.4
o 0.1 i
-O.I o 0.3
o 0.S
+ 0.7
v O.O
-o.e __ Stdo k_
..... RNO
k..m
-I.0 i I i I
-II; -tO -6 O 6
o.
x/D.
v
o
'l
O
_t
I I I
10 15 20 5
Ref.: Awa, R.K., Singhal, A.K., Lat, Y.G., "Numerical Simulation Of Periodic
and 3-Dimensional, Turbulent Flows With CFD-ACE," ASME Fluid Dynamics
Conference, Lake Tahoe, NV, June 19-23, 1994.
FLOW IN A 180o SQUARE DUCT
Mean Axial Velocity at e = 3U
1.4 1.11
1+2
+
:3
,,. l.o
o.l
o+II
1.4
1.2
_° t. Q
o.8
o,I
z" +0.0
i i i i
0.2 0.4 ll.l o.l
R +
i I i i
0.2 0.4 0.I 0.1P
R"
[] Data
-- Std. k-¢
.... RNG
----- k-o)
R*-- r'rl
ro- r 1
Z
z=o./--_
1.2
_. 1.0
0.I
I.II
0
1.4
1.2
m
_ 1.0
0.|
Q.I
°o.-..
I l I I
o 2 o.4 o.l o.I
R"
t 1 i I
0.2 4.4 0.I O.ll
R"
147
S-SHAPED ANNULAR DIFFUSER
O :Da" cd'Stev_n & Fry(Ig't3)
: Reylolcb Strem Model
.... :K-£Mode[
UrUm..
_llon 2
0.0" Scat_a 3
o.o.
, _Stition 80.0
0.0 0.5 11 1.0
k-s Model and RNG Model Failed to Predict the Correct Location
of the Maximum Velocity Downstream
Computations with CFD-ACE; Publication Under Preparation
Confined Swirling Flow
for a Dump Combustor
_..J, ....--;I _"-"-"_ _ I
_ RI_'2 eem _="_ LL t !
XIH. 0.0 0.38 72.8
O ¢3 : Data ol Nejad et al.(1989)
: Reynolds Stress Model
20 ........... : K-¢ Model
- - - : RNG I_de¢
10- _lQ__ =/h=l.0
0
O'
O,
_ :ffh.lO.O
01
Ot .- I i i
0 1.0 2.0 rlh 3.0
K-_ model failed to preserve the vortex core strength
near center (see x/h=10 & 18)
* Computational results to be presented at
1994 ASME Winter Annual Meeting (Chicago)
148
BACKWARD-FACING STEP
Sensitivitv to Grid Refinement
,._ Pressure
c,
t.s_¢
"-9. "._ --
= - , .¢ i s
X/R
G.¢..40
4 .£-4_
Z.[-4D.
c,
_..£-O]
•'4 I-e_ _
•.--_ Skin Friction
I| ..........
• ..
, •
PS_ I .
.
J , i i i _ i
X/H
Low-Re Model Requires >30 Nodes in the Inter Layer
Ref. :
"Comparative Study of High and LowReynoldsNumber
Versions of k-e Models," R.K.Awa, C.E.Smith,A.K.
Singhal, AIAA-90-0246.
BACKWARD FACING STEP
2-Layer Model;
0¸003
0¸002
0001
0 000 P /'//'O
• [_O1) tO
-0®__ -;--
_-%-o_'; _ o
OOdles d_=
-- Std.kem
.... 2_W¢(I =1no<_ _ I_ _/tr)
-.- 2._m(1=, _ k _m =ue*eWr)
,'o ,; _, 2_ ;, =
X/H
o.15
O.10
O.O=3
0.00
-0.05
"O'IO-s o 5 I'0
0 0 0 0 0
/o oo_'s _=
-- $1d.lcem
_O_ - -- - 2_111 e¢¢10 I_ b_flor _ylp,)
0 :) -'-- 2 J_'fl_l I It n°dl In IIm IlUbllYl')
0
X/H
Computations with CFD-ACE; To Be Published
149
EXAMPLE APPLICATIONS
• Gas Turbine Combustors
• Liquid Rocket Engines
• Seals and Bearing Cavities
• Impellers, Inducers, and Fans
• ICEngines
• CFD Reactors
• External Aerodynamic Flows
• Plus Many More
STRENGTHS & WEAKNESSES
Strenqths of 2-Equation Models
• Numerically Economical
• Easy to Modify
• Reasonable Al_l_licability Within Engineering Accuracy
Weaknesses
• Use of Wall Functions Requires First Grid Outside the
Viscous Sublayer. This is Difficult to achieve, a Priori
• Low-Re Approach Does Not Offer Overall Advantage.
• Two-Layer Approach Needs More Work (e.g. Smoothing)
• Reynolds Analogy Inadequate for Heat-Transfer
Applications.
• Effect of Surface Roughness on Turbulence.
150
CMOTT/CP QUESTIONS
1. What Are Your Customers Telling You?
2. What Are You Doing In-House?
3. How Can NASA-CMOTT Help?
WHAT ARE CUSTOMERS TELLING?
• PLEASE Don't Confuse Us,
with Additional Models and False Hopes
Conclusions (Confusion) Over Last 15-Years
- Use k~E Model, with Wall Functions
Wall Functions, Oh No!, Never!!
Use Low-Re k~_.,.: Which One?, How?? (Good Questions)
k-_ Is No Gooey; Neglects Non-lsotropicity, etc., etc.
Jump on RSM Wagon, Now!
It Can Take You Anywhere, Eventually!!
Look How Great is this k~_ ++
When and How to Use it? (Good Questions)
Look How Accurate is this Scheme, No Numerical Diffusion.
Don't Contaminate the Solutions with Turbulence
151
WHAT IS CFDRC DOING?
• Using What is Available, in Best Possible Ways
• Listening to Both Sides (Model Developers and Users)
• Trying to Resist Peer Pressures
• Struggling to Find Resources for Mundane Goals Such as
Developing Guidelines for Correct Use of Turbulence
Models
HOW CAN CMOTT HELP?
CMOTT Has Been Providing Commendable Service in the
Very Difficult Subject: Turbulence
"Turbulence Subprogram" Should Help Further
Additional Effort is Needed in Many Areas, Such As:
Near Wall Treatment
Effect of Surface Roughness
Economical Heat Transfer Model
Documentation of Experiences in:
a) Model Robustness(In Addition to Accuracy)
b) Model Sensitivity to Grid Distribution and Boundary
Conditions
Transition Model (if Possible Suitable for k~_ Framework)
152
HOW CAN CMOTT HELP? (_Continued_)
NASA-CMOTT Is One of the Few Groups Sustaining
Momentum for Turbulence Modeling.
It Is In Unique (Privileged) Position for Embracing the
Challenge of Developing Specific Recommendations
(Guidelines) For:
a) Selection of Adequate Models for Different Class
of Problems
b) Correct Use of Each Model
• The Task Is Difficult But Practical
• Select Fewer Roads, Post Milestones, and Go Further
• Move An Inch Closer to Users
CMO'I'I"
I t t Y r I i t t t r 0
Oi ,,j,lllj, j
Developers Users
153



Experiences with two-equation turbulence models

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