Download - ANSYS Fluent V2F Turbulence Model Manual
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
1/20
ANSYS Fluent V2F Turbulence Model Manual
Release 15.0ANSYS, Inc.November 2013Southpointe
275 Technology DriveCanonsburg, PA 15317 ANSYS, Inc. is
certified to ISO9001:2008.
[email protected]://www.ansys.com(T ) 724-746-3304(F) 724-514-9494
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
2/20
Copyright and Trademark Information
2013 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited.
ANSYS, ANSYS Workbench, Ansoft, AUTODYN, EKM, Engineering Knowledge Manager, CFX, FLUENT, HFSS and anyand all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks ortrademarks of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark usedby ANSYS, Inc. under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, serviceand feature names or trademarks are the property of their respective owners.
Disclaimer Notice
THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFID-ENTIAL AND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS. The software productsand documentation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreementthat contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exportinglaws, warranties, disclaimers, limitations of liability, and remedies, and other provisions. The software productsand documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditionsof that software license agreement.
ANSYS, Inc. is certified to ISO 9001:2008.
U.S. Government Rights
For U.S. Government users, except as specifically granted by the ANSYS, Inc. software license agreement, the use,duplication, or disclosure by the United States Government is subject to restrictions stated in the ANSYS, Inc.software license agreement and FAR 12.212 (for non-DOD licenses).
Third-Party Software
See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary softwareand third-party software. If you are unable to access the Legal Notice, please contact ANSYS, Inc.
Published in the U.S.A.
http://ai_ginfo.pdf/http://ai_ginfo.pdf/ -
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
3/20
Table of Contents1. Introduction ..................................................................................................................................12. V2F Model Theory .........................................................................................................................3
2.1.Transport Equations for the V2F Model ........................................................................................32.2. Modeling the Turbulent Viscosity ...............................................................................................42.3. Model Constants ......................................................................................................................4
3. Problem Setup Using the V2F Model ...............................................................................................53.1. Enabling the V2F Model ............................................................................................................53.2. Defining V2F Boundary Conditions .............................................................................................73.3. Providing an Initial Guess for k, , and the Velocity Variance Scale ....................................................8
4. Solution Strategies for the V2F Model .............................................................................................115. Postprocessing for the V2F Model ..................................................................................................13Bibliography ......................................................................................................................................15
iiRelease 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
4/20
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.iv
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
5/20
Chapter 1: Introduction
Successful modeling of the separation of fluid from a curved surface (for example, the suction side of an airfoil) depends on the ability to correctly predict the stall angle. For such cases, eddy-viscosity tur-bulence models, such as the - models, are not satisfactory because they can sometimes overpredictthe turbulence kinetic energy and are not sensitive to the interaction between streamline curvatureand turbulence anisotropy. The Reynolds-stress model (RSM), on the other hand, accounts for severalturbulence features that are not well predicted by eddy-viscosity models, but is substantially morecomplex and sometimes is numerically unstable.
The model (V2F), based on Durbins - - model [2] (p. 15), is an alternative to eddy-viscositymodels and the RSM. The model is similar to the standard - model, but incorporates near-wallturbulence anisotropy and non-local pressure-strain effects. It is a general low-Reynolds-number turbu-lence model that is valid all the way up to solid walls, and therefore does not need to make use of wallfunctions. Although the model was originally developed for attached or mildly separated boundarylayers, it also accurately simulates flows dominated by separation.
This document describes the ANSYS Fluent model. V2F Model Theory (p. 3) provides theoreticalbackground information. Problem Setup Using the V2F Model (p. 5) describes how to set up a problem
using the model. Solution Strategies for the V2F Model (p. 11) describes the solution procedurefor problems involving the model, and Postprocessing for the V2F Model (p. 13) provides inform-ation about postprocessing options.
1Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
6/20
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.2
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
7/20
Chapter 2: V2F Model Theory
The model is a four-equation model based on transport equations for the turbulence kinetic energy( ), its dissipation rate ( ), a velocity variance scale ( ), and an elliptic relaxation function ( ).
The distinguishing feature of the model is its use of the velocity scale, , instead of the turbulentkinetic energy, , for evaluating the eddy viscosity. , which can be thought of as the velocity fluctuationnormal to the streamlines, has shown to provide the right scaling in representing the damping of tur-bulent transport close to the wall, a feature that does not provide.
The turbulence model theory is described in the following sections:2.1.Transport Equations for the V2F Model2.2. Modeling the Turbulent Viscosity2.3. Model Constants
2.1.Transport Equations for the V2F Model
The turbulence kinetic energy, , its rate of dissipation, , the velocity variance scale, , and the ellipticrelaxation function, , are obtained from the following transport equations:
(2.1
+
= +
+
+
(2.2 +
=
+ +
+
(2.3
+
= +
+
+
(2.4
=
+ + +
where
(2.5= =
+
The turbulent time scale and length scale are defined by
(2.6 =
3Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
8/20
(2.7)
=
(2.8)
=
(2.9)=
In the above equations, ,
,
,
,
,
,
,
, and
are constants.
and
are the turbulent
Prandtl numbers for and .
,
,
, and
are user-defined source terms and is the kinematic
viscosity ( ).
The variable is the solution to the elliptic relaxation equation ( Equation 2.4 (p. 3) ). Here, the
model uses an elliptic operator to compute a term analogous to the pressure-strain correlation of theRSM. Ellipticity is characterized by a modified Helmholtz operator, which introduces wall effects via alinear differential equation.
2.2. Modeling the Turbulent Viscosity
The turbulent (or eddy) viscosity,
, is defined as follows:
(2.10) =
2.3. Model Constants The model constants have the following default values [1] (p. 15), [3] (p. 15):
(2.11)= = = = = =
(2.12) = = = = = +
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.4
V2F Model Theory
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
9/20
Chapter 3: Problem Setup Using the V2F Model
To include the turbulence model in your ANSYS Fluent simulation, you need to activate themodel and options, and supply turbulent boundary conditions. These inputs are described in the followingsections:3.1. Enabling the V2F Model3.2. Defining V2F Boundary Conditions3.3. Providing an Initial Guess for k, , and the Velocity Variance Scale
3.1. Enabling the V2F Model
The following is a description of the procedure for setting up a problem.
Note
This procedure includes only the steps necessary for the turbulence model itself; youwill need to set up other models, boundary conditions, etc. as usual. See the ANSYSFluent User's Guide for details.
1. To enable the selection of the model, enter the following Scheme command in the main menuof the ANSYS Fluent console:
(allow-v2f-model)
2. To activate the model, select V2F under Model in the Viscous Model dialog box ( Figure 3.1: TheViscous Model Dialog Box with the V2F Option Available (p. 6) ).
Models Viscous Edit...
5Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
10/20
Figure 3.1: The Viscous Model Dialog Box with the V2F Option Available
3. Specify or confirm the Model Constants used in the transport equations.
Cmuis the constant
in Equation 2.7 (p. 4) , Equation 2.8 (p. 4) , and Equation 2.10 (p. 4) .
C1-Epsilonis the constant
.
C2-Epsilon
is the constant in Equation 2.2 (p. 3) .
C1is the constant
in Equation 2.4 (p. 3) .
C2is the constant
in Equation 2.4 (p. 3) .
Cetais the constant
in Equation 2.9 (p. 4) .
Cl is the constant
in Equation 2.9 (p. 4) .
Alphais the constant in Equation 2.7 (p. 4) .
TKE Prandtl Numberis the effective Prandtl number for transport of turbulence kinetic energy
. This effective Prandtlnumber defines the ratio of the momentum diffusivity to the diffusivity of turbulence kinetic energyvia turbulent transport.
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.6
Problem Setup Using the V2F Model
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
11/20
TDR Prandtl Numberis the effective Prandtl number for transport of turbulence dissipation rate
. This effective Prandtlnumber defines the ratio of the momentum diffusivity to the diffusivity of turbulence dissipation viaturbulent transport.
Important
After you have selected V2F and clicked OK, ANSYS Fluent will check to make sure thata license is available for this module. After the module has been enabled successfully,the item v2f will appear in the list of models in square brackets in the title bar of theANSYS Fluent console.
4. Specify the boundary conditions for the solution variables.
Boundary Conditions
See the section that follows ( Defining V2F Boundary Conditions (p. 7) ) and the ANSYS Fluent User's
Guide for details.5. Specify the initial guess for the solution variables.
Solution Initialization
See the ANSYS Fluent User's Guide for details.
3.2. Defining V2F Boundary Conditions
When you are modeling turbulent flows in ANSYS Fluent using the model, you must provide theboundary conditions for , , and in addition to other mean solution variables. The boundary con-
ditions for , , and at the walls are internally taken care of by ANSYS Fluent, which obviates the
need for your inputs. You must supply ANSYS Fluent with boundary condition inputs for , , and
at inlet boundaries (velocity inlet, pressure inlet, etc.). In many situations, it is important to specify corrector realistic boundary conditions at the inlets, because the inlet turbulence can significantly affect thedownstream flow.
To define inlet boundary conditions specific to the model, use the following procedure:
1. Open the appropriate boundary condition dialog box (e.g., Figure 3.2: Specifying Inlet Boundary Conditionfor the V2F Model (p. 8) ).
Boundary Conditions
7Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
Defining V2F Boundary Conditions
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
12/20
Figure 3.2: Specifying Inlet Boundary Conditions for the V2F Model
2. Make a selection from the Specification Method drop-down list in the Turbulence group box.
If you select K, Epsilon and V2 , specify values for the Turbulent Kinetic Energy , Turbulent DissipationRate , and Velocity Variance Scale , as appropriate.
If you select any of the other options (e.g., Intensity and Viscosity Ratio ), ANSYS Fluent will automat-
ically set the value of to
at the inlet.
Important
Note that ANSYS Fluent automatically assumes a zero-gradient boundary condition forthe variable at inlets. You can change the value of when you initialize a solution,but the default value of 1 is acceptable in most cases.
See Section 7.2.2 in the ANSYS Fluent User's Guide for more information about specifying the boundaryconditions for and at the inlets.
3.3. Providing an Initial Guess for k, , and the Velocity Variance Scale
For flows using the model, the converged solutions or (for unsteady calculations) the solutionsafter a sufficiently long time has elapsed should be independent of the initial values for , , and the
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.8
Problem Setup Using the V2F Model
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
13/20
velocity variance Scale . For better convergence, it is beneficial to use a reasonable initial guess for
, , and .
In general, it is recommended that you start from a fully-developed state of turbulence, using the fol-lowing guidelines.
If you were able to specify reasonable boundary conditions at the inlet, it may be a good idea to compute
the initial values for , , and in the whole domain from these boundary values. (See Section 26.15 inthe ANSYS Fluent User's Guide for details.)
For more complex flows (e.g., flows with multiple inlets with different conditions) it may be better tospecify the initial values in terms of turbulence intensity. 510% is enough to represent fully-developedturbulence. can then be computed from the turbulence intensity and the characteristic mean velocity
magnitude of your problem (
=
).
You should specify an initial guess for so that the resulting eddy viscosity (
) is sufficiently
large in comparison to the molecular viscosity. In fully-developed turbulence, the turbulent viscosityis roughly two orders of magnitude larger than the molecular viscosity. From this, you can compute
. Alternatively, you can use the approximation =
, or, if you have experimental measurements,
you can enter a profile for . (See Section 7.26 in the ANSYS Fluent User's Guide for details aboutboundary profiles.)
9Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
Providing an Initial Guess for k, , and the Velocity Variance Scale
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
14/20
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
15/20
Chapter 4: Solution Strategies for the V2F Model
For a simulation involving the model, you should use the following procedure to achieve fullconvergence:
1. Start by converging a flow simulation using one of the - models (for example, realizable - model).
2. In the Viscous Model dialog box, change the Model to V2F.
Models Viscous Edit...
3. Define a custom field function (for example, v2 ) as
, where is the turbulence kinetic energy. See
Section 11.13.1 in the ANSYS Fluent Users Guide for information about other custom field functions thatmay be useful for turbulence. For more general information about custom field functions, see Section30.5.
Define Custom Field Functions...
4. Patch a value for the velocity variance scale in all fluid zones using the field function created in theprevious step (for example, v2 ).
5. In the Solution Methods task page, make sure that the Velocity Variance Scale and the Elliptic Relax-ation Function have the same Spatial Discretization schemes as the Turbulent Kinetic Energy andTurbulent Dissipation Rate .
Solution Methods
6. Continue running the calculation using the model.
11Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
16/20
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.12
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
17/20
Chapter 5: Postprocessing for the V2F Model
ANSYS Fluent provides postprocessing options for displaying, plotting, and reporting various turbulencequantities, which include the main solution variables and other auxiliary quantities.
Turbulence quantities that can be reported for the model are:
Turbulent Kinetic Energy (k)
Turbulent Intensity
Turbulent Dissipation Rate (Epsilon)
Velocity Variance Scale (v2)
Elliptic Relaxation Function
Production of k
Turbulent Viscosity
Subgrid Turbulent Viscosity
Effective Viscosity
Turbulent Viscosity Ratio
Effective Thermal Conductivity
Effective Prandtl Number
Wall Ystar
Wall Yplus
13Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
18/20
Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.14
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
19/20
Bibliography[1] M. Behnia, S. Parneix, Y. Shabany, and P. A. Durbin. "Numerical Study of Turbulent Heat Transfer in
Confined and Unconfined Impinging Jets" . International Journal of Heat and Fluid Flow . 20. 1-9.1999.
[2] P. A.Durbin. "Separated Flow Computations with the k-epsilon-v2 Model" . AIAA Journal . 33(4). 659664.1995.
[3] S. Parneix, P. A. Durbin, and M. Behnia. "Computation of a 3D Turbulent Boundary Layer Using the V2F Model" . Flow Turbulence and Combustion . 10. 1946. 1998.
15Release 15.0 - SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.
-
8/10/2019 ANSYS Fluent V2F Turbulence Model Manual
20/20