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Haibin LI
25/05/09
Investigation of Gao-Yong turbulence model with OpenFOAM
04/08/2023 [email protected] 22
AbtractIn this talk, a relatively new turbulence model named Gao-Yong turbulence model is investigated using the open source software—OpenFOAM. A newly developed statistical partial average scheme is presented. As the ensemble average is taken on two groups of turbulent fluctuations separately, the partial average scheme able to capture the first-order statistical moment of the fluctuation field, providing valuable information in addition to what have been known in the past from the conventional Reynolds average. Without any empirical coefficients, the derived equations can be used to simulate statistical mean behaviours and coherent structures of various benchmark turbulent flows. The simulated results are in good agreement with experimental data.
04/08/2023 [email protected] 33
Content Turbulence model Gao-Yong turbulence model The deriving process of Gao-Yong turbulence
model Ensemble average Partial average
Open source software - OpenFOAM The simulated examples
04/08/2023 [email protected] 44
Turbulence Model
What – the conception Why – the significance How – the current methods
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Turbulence
Conception:Turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes.--wikipedia
No exact defination. Renolds Experiment
[email protected]/08/2023
Introduction
Open Source Software has many advantages
Vitality Never rise price, stop development or technical support due to
business problem
QualityBug track and fix by global members of open community Necessary for scientific computing software. Black box verification can not fully demonstrate the validity
especially for non-linear science software.
CreativityInnovative research might change the codes at any level.
[email protected]/08/2023
GAO-YONG TURBULENCE EUQTIONS
Based on partial average, modeling, rational deriving
No any adjustable empirical coefficients
Do not need wall function Some steady numerical examples
[email protected]/08/2023
GAO-YONG TURBULENCE EUQTIONS
x
x
dp
dpII
)(
)(
II
I M ~ IIII
II M ~
x
dpM II
)(
Define the partial average of the fluctuations as:
Where
x
x
dp
dpI
)(
)(
x
dpM I )(
[email protected]/08/2023
GAO-YONG TURBULENCE EUQTIONS
Applying the partial average to fluctuation equations we will get equations
)~~(~~
)~~
(~
IT
IITIII
II
III
MMp
UUUUt
U
)~
()~~(~)~
()~
(UUpUU
t
UTT
IIT
ITT
IT
IITIIIMM ~
2
1~2
1)()~~( Model
We also have continuity equation: 0)~
( U
[email protected]/08/2023
In coordinate system 123 constituted by ,
GAO-YONG TURBULENCE EUQTIONS
Suppose that the constitutive relationship still exists along the direction of mean flow velocity .
UUU~
,
ITTT 3
22
T
T ULCs~
TT
xyzT )123()(
Where
Where operator has the same meaning of “scale” in OpenFOAM
Where xyz global coordinate system, is coordinate transformation tensor.
Suppose is orthotropic and is the principal material axesT U
[email protected]/08/2023
GAO-YONG TURBULENCE EUQTIONSenergy dissipation due to eddy viscosity is the work done by fluctuation force over L
also
considering the phenomenon of turbulence energy inversion,
item should be subtracted from the right-hand side
of the second equation , therefore
)~
(!
~
1
Un
ULtU
t
ULFe
n
n
LUUpe TT ))~
()~~(~(
LDt
UD)(
))(
)~
()~~(~(
)~
(!1
Dt
UDUUpL
Un
UL
TT
n
n
[email protected]/08/2023
IMPLEMENTATIONDevelopment from scratch
Bad generality, readability Repeated work one year for one example
Based on secondary development of closed source software. Limited the innovation, procedure has to be changed. Debug is difficult. Failed
Based on OpenFOAM Rapidly development Quick investigation, one month for one example
[email protected]/08/2023
NUMERICAL EXAMPLESLid-driven cavity flow is selected
because of simple and the data at handReynolds number =10,00080X80X1 Grid is employedGao-Yong model and K-Epsilon model is
seperately usedTransient simulation is finishedInitial flow field is stationary
[email protected]/08/2023
Comparison of U-velocity profiles along a vertical line passing through the geometry centre of the cavity
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U-velocity profiles along a vertical line passing through the geometry centre of the cavity from t=0s to t=6s, Gao-Yong turbulence model
[email protected]/08/2023
U-velocity profiles along a vertical line passing through the geometry centre of the cavity from t=7s to t=80s, Gao-Yong turbulence model
[email protected]/08/2023
Comparison of StreamlinesRe=10,000Grid 80X80X1, t=80s, Gao-Yong modelby Erturk
[email protected]/08/2023
Comparison of StreamlinesRe=10,000Grid 80X80X1, t=80s, K-Epsilon modelby Erturk
[email protected]/08/2023
Streamlines from t=0s to t=6s, Gao-Yong modelt=1s t=2s t=3s
t=4s t=5s t=6s
[email protected]/08/2023
Streamlines t=6s, DNS & Gao-Yong model
DNS, Mesh 256X256 by Liu Hong Gao-Yong, Mesh 80X80
[email protected]/08/2023
Comparison of Vorticity Contour
The Stream Function Vorticity Method by Erturk
Gao-Yong turbulence model t=80s
Re=10,000 Grid 80X80X1, t=80s
[email protected]/08/2023
Comparison of Vorticity Contour
The Stream Function Vorticity Method by Erturk
K-Epsilon Turbulence model t=80s
Re=10,000 Grid 80X80X1, t=80s
[email protected]/08/2023
Conclusion An innovative CFD method Gao-Yong turbulence model is
able to be investigated quickly thanks to the open source software OpenFOAM
Gao-Yong turbulence model is able to gain real viscosity field in complex flow under coarse grid and unsteady condition.
The existing closed source software has limitations to the users, and therefore fail in the research, especially in the innovation research.
There is an improvement space for OpenFOAM in some aspects, such as: Function of open community. Open project management. Open source code management. Effective bug track system. User interface.
