UMassAmherst
First Dutch OpenFOAM Day
Nov 4th, 2010
Implementation of the OrientedEddy Collision Turbulence
Model in OpenFoam
Blair Perot
Mike Martell
Chris Zusi
Department of Mechanical and Industrial Engineering
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
UMassAmherst
Goal: Develop a New Turbulence Model
Navy Requirements
 Easy for others to test.
 Easy for others to adopt.
 Easy to test real world applications.
Our Requirements
 Solve coupled tensor PDE’s.
 Mixed BCs.
 Handle arbitrary numbers of equations.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
2
UMassAmherst
Why OpenFoam?
 Advantages over commercial code
• Free, open source, parallel
• Users can inspect, alter, expand on the source
code.
 Advantages over in house code development
• Many numerical methods, operators, utilities
already implemented and tested
 Large, user-driven support community
• Interact with other OpenFOAM users.
• Get help from CFD experts.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
3
UMassAmherst
Why OpenFoam?
 Advantages over commercial code
• Free, open source, parallel
• Users can inspect, alter, expand on the source
code.
 Advantages over in house code development
• Many numerical methods, operators, utilities
already implemented and tested
 Large, user-driven support community
• Interact with other OpenFOAM users.
• Get help from CFD experts.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
4
UMassAmherst
Why OpenFoam?
 Advantages over commercial code
• Free, open source, parallel
• Users can inspect, alter, expand on the source
code.
 Advantages over in house code development
• Many numerical methods, operators, utilities
already implemented and tested
 Large, user-driven support community
• Interact with other OpenFOAM users.
• Get help from CFD experts.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
5
UMassAmherst
Prior Experience:
In House Codes
 UNS3D: Moving unstructured staggered
mesh code for two-phase incompressible flows
 Stag++: Cartesian staggered mesh for
DNS/LES of incompressible turbulence.
Fluent
 User defined subroutines for RANS modeling.
OpenFoam
 Wind turbine blade simulation. Rotating
imbedded mesh.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
6
UMassAmherst
Wind Turbine Calculations with OpenFoam
Spin indicator
= second invariant of the strain tensor
 Runs on 8-16 CPUs
 No major issues
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
7
UMassAmherst
Eddy Collision Model Overview
Assumption:
Turbulent Flow = Flow of a Colloidal
suspension of disk-like spinning objects.
Pouring Spherical
objects results in
RANS eqns.
Pouring a concentrated
Disk suspension results
in OEC model
Mechanical and Industrial Engineering
8
Theoretical & Computational Fluid Dynamics Laboratory
UMassAmherst
Review of OEC Model Properties
 Cost roughly
about 10x k/e.
 Four model
constants.
 Realizable,
Material Frame
Indifferent,
Galilean
Invariant, Exact
in linear limit, etc.
LES
Log(Cost )
100
OEC
10
1
RANS
0.1
0.1
1
10
100
Log(Physics )
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
9
UMassAmherst
PDE Formulation
Dqi


 qk uk ,i  1   q 2  1  qi  ( Ai  Bi )  1 (  t )qi ,k ,k  Wi
3
R 
3
Dt
Eddy Size and
Orientation (vector)




q q

qq



 ui ,k   i 2 l   il  2ul*,k  Rkj  u j ,k   j 2 l   jl  2ul*,k  Rki    q 2  1  Rij
R 
Dt 

 q

 q




( K ), k ( K ), k
 Rij 
 Aij  M ij    t  Rij ,k  ,k  D   t    ( K ),k  E   t 
Rij  Wij
K
K
K
  ,k
DRij
Eddy
Velocity
Fluctuation
(tensor)
• Global Variables (sum many eddies – 20-50)
Rij  N1  Rij
T 
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory

1
2
Rii /  Rii q 2
2
10
UMassAmherst
Open Foam Formulation
Dqi


 qk uk ,i  1   q 2  1  qi  ( Ai  Bi )  1 (  t )qi ,k ,k  Wi
3
R 
3
Dt
fvm::ddt(qiINT)
- (1.0/3.0)*fvm::laplacian(dEff(), qiINT)
+ (1.0/3.0)*fvm::SuSp(((alpha*nu()*qsq + tauR)), qiINT)
==
- fvc::div(phi_, qiINT)
- ( qiINT & fvc::grad(U) )
- ( Ai + Bi )
Implicit terms on the left-hand side.
Explicit terms on the right-hand side.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
11
UMassAmherst
First Challenge: Multiple Eddies
 The Number of Eddies for
each physical location is
arbitrary.
 10 is minimal necessary.
 100 is usually very good.
6
23
37
1
49
55
102
108
2
998
256
16
Pointer lists
are employed
to keep track
of eddies
Rij_[eddy][cell].xx()
Pointer list with
an entry for
every eddy
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
Location in
mesh
9
Component
(11 in this
case)
12
UMassAmherst
Multiple Eddies: OpenFoam Solution
forAll(initOrientations_,i) {
...
solveqR(i, qi_[i], ...);
...
}
This system allows us to write
generalized functions which handle
any number of eddy vectors.
void OEC::solveqR(int i, volVectorField qiINT, ...) {
...
tmp<fvVectorMatrix> qEqn
The model can be implemented on
(
a per-eddy basis.
fvm::ddt(qiINT) = ...
Averaging all of the entities in a
);
...
given pointer list is also easy, which
solve(qEqn, mesh_.solver("q"));
is good because all we really care
...
about is the average R, K, etc.
}
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
13
UMassAmherst
Second Challenge: Tensors
 No gradient of a rank 2 (and higher) tensor
 Rij 
 D    t    ( K ),k
 K  ,k
Solution:
Break it
into vectors
forAll (mesh_.C(),
{
Rx[cell].x()
Rx[cell].y()
Rx[cell].z()
…
fvc::grad(R)
…
cell)
// internal cells
= Rtmp[cell].xx();
= Rtmp[cell].xy();
= Rtmp[cell].xz();
...
gradKgradR[cell].xx() = (
+
+
gradKgradR[cell].yy() = (
+
+
gradKgradR[cell].zz() = (
+
+
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
gradK[cell].x()*gradRx[cell].xx()
gradK[cell].y()*gradRx[cell].xy()
gradK[cell].z()*gradRx[cell].xz() );
gradK[cell].x()*gradRy[cell].yx()
gradK[cell].y()*gradRy[cell].yy()
gradK[cell].z()*gradRy[cell].yz() );
gradK[cell].x()*gradRz[cell].zx()
gradK[cell].y()*gradRz[cell].zy()
gradK[cell].z()*gradRz[cell].zz() );
14
UMassAmherst
Third Challenge: Boundary Conditions
 On wall, the boundary
conditions are mixed.
108
Y
23
1
6
49
wall
This is for an xz-wall.
We currently can not do
walls that are not
aligned with the tensor
coordinate directions.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
Rij
slip  wall
qi
wall
R13 
 R11

0
R

0
12
 y
y 



R22  0 R23  0 



R
33



y 
 q1  0 



q
2

 0
 y



q

0
 3

15
UMassAmherst
Last Challenge: Stable Time Marching
 Many source terms have no fvm:: (implicit)
implementation.
 Some explicit source terms can be unstable with
Explicit Euler time advancement.
Solution:
• Write a RK3 solver.
• Modify equations with explicit time derivative
• Use FOAM’s .storeOldTime() to save the old
time values.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
16
UMassAmherst
Last Challenge: Stable Time Marching
 Many source terms have no fvm:: (implicit)
implementation.
 Some explicit source terms can be unstable with
Explicit Euler time advancement.
Solution:
• Write a RK3 solver.
• Modify equations with explicit time derivative
• Use FOAM’s .storeOldTime() to save the old
time values.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
17
UMassAmherst
Last Observation:
 Gradient of a vector
 ax1
ai , j   a1
1
 x2
  a1,1

a2
a1,2

x2 

a2
x1
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
a2,1   g11


a2,2   g 21
g12 
 i a j

g22 
18
UMassAmherst
Summary:
 OEC is implemented in OpenFoam.
Mechanical and Industrial Engineering
Theoretical & Computational Fluid Dynamics Laboratory
19