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information on creating and using user-defined function, see the separate UDF Manual.
If you are modeling axisymmetric swirling flows, you can specify an additional direction component for the viscous and/or inertial resistance coefficients. This direction component is always tangential to the other two specified directions. This option is available for both density-based and pressure-based solvers.
In 3D, it is also possible to define the coefficients using a conical (or cylindrical) coordinate system, as described below.
Note that the viscous and inertial resistance coefficients are generally based on the superficial velocity of the fluid in the
porous media.
The procedure for defining resistance coefficients is as follows: 1. Define the direction vectors.
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To use a Cartesian coordinate system, simply specify the Direction-1 Vector and, for 3D, the Direction-2 Vector. The unspecified direction will be determined as described above. These direction vectors correspond to the principle axes of the porous media. For some problems in which the principal axes of the porous medium are not aligned with the coordinate axes of the domain, you may not know a priori the direction vectors of the porous medium. In such cases, the plane tool in 3D (or the line tool in 2D) can help you to determine these direction vectors.
(a) \porous region. (Follow the instructions in
Section 27.6.1 or 27.5.1 for initializing the tool to a position on an existing surface.)
(b) Rotate the axes of the tool appropriately until they are aligned with the porous medium.
(c) Once the axes are aligned, click on the Update From Plane Tool or Update From Line Tool button in
the Fluid panel. FLUENT will automatically set theDirection-1 Vector to the direction of the red arrow of the tool, and (in 3D) the Direction-2 Vector to the direction of the green arrow.
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To use a conical coordinate system (e.g., for an annular, conical filter element), follow the steps below. This option is available only in 3D cases.
(a) Turn on the Conical option.
(b) Specify the Cone Axis Vector and Point on Cone Axis. The cone axis is specified as being in the direction of the Cone Axis Vector (unit vector), and passing through the Point on Cone Axis. The cone axis may or may not pass through the origin of the coordinate system.
(c) Set the Cone Half Angle (the angle between the cone's axis and its surface, shown in Figure 7.19.2). To use a cylindrical coordinate system, set theCone Half Angle to 0.
Figure 7.19.2: Cone Half Angle
For some problems in which the axis of the conical filter element is not aligned with the coordinate axes of the domain, you may not know a priori the direction vector of the cone axis and coordinates of a point on the cone axis. In such cases, the plane tool can help you to determine the cone axis vector and point coordinates. One method is as follows:
(a) Select a boundary zone of the conical filter element that is
normal to the cone axis vector in the drop-down list next to the Snap to Zone button.
(b) Click on the Snap to Zone button. FLUENT will automatically \Cone Axis Vector and thePoint on Cone Axis. (Note that you will still have to set the Cone Half Angle yourself.) An alternate method is as follows:
(a) \(Follow the instructions in Section 27.6.1 for initializing the tool to a position on an existing surface.)
(b) Rotate and translate the axes of the tool appropriately until the red arrow of the tool is pointing in the direction of the cone axis vector and the origin of the tool is on the cone axis.
(c) Once the axes and origin of the tool are aligned, click on the Update From Plane Tool button in
the Fluid panel. FLUENT will automatically set the Cone Axis Vector and the Point on Cone Axis. (Note that you will still have to set the Cone Half Angle yourself.)
2. Under Viscous Resistance, specify the viscous resistance coefficient
in each direction.
Under Inertial Resistance, specify the inertial resistance coefficient in each direction. (You will need to scroll down with the scroll bar to view these inputs.)
For porous media cases containing highly anisotropic inertial resistances, enable Alternative Formulation under Inertial Resistance.
The Alternative Formulation option provides better stability to the calculation when your porous medium is anisotropic. The pressure loss through the medium depends on the magnitude of the velocity vector of the ith component in the medium. Using the formulation of Equation 7.19-6 yields the expression below:
(7.19-10)
Whether or not you use the Alternative Formulation option depends on how well you can fit your experimentally determined pressure drop data to the FLUENT model. For example, if the flow through the medium is aligned with the grid in your FLUENT model, then it will not make a difference whether or not you use the formulation.
For more infomation about simulations involving highly anisotropic porous media, see Section 7.19.8.
Note that the alternative formulation is compatible only with the pressure-based solver.
If you are using the Conical specification method, Direction-1 is the cone axis direction, Direction-2 is the normal to the cone surface (radial ( )
direction for a cylinder), and Direction-3 is the circumferential ( ) direction.
In 3D there are three possible categories of coefficients, and in 2D there are two:
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In the isotropic case, the resistance coefficients in all directions are the same (e.g., a sponge). For an isotropic case, you must explicitly set the resistance coefficients in each direction to the same value. When (in 3D) the coefficients in two directions are the same and those in the third direction are different or (in 2D) the coefficients in the two directions are different, you must be careful to specify the coefficients properly for each direction. For example, if you had a porous region consisting of cylindrical straws with small holes in them positioned parallel to the flow direction, the flow would pass easily through the straws, but the flow in the other two directions (through the small holes) would be very little. If you had a plane of flat plates perpendicular to the flow direction, the flow would not pass through them at all; it would instead move in the other two directions.
In 3D the third possible case is one in which all three coefficients are different. For example, if the porous region consisted of a plane of irregularly-spaced objects (e.g., pins), the movement of flow between the blockages would be different in each direction. You would therefore need to specify different coefficients in each direction.
Methods for deriving viscous and inertial loss coefficients are described in the sections that follow.
Deriving Porous Media Inputs Based on Superficial Velocity, Using a Known Pressure Loss
When you use the porous media model, you must keep in mind that the porous cells in FLUENT are 100% open, and that the values that you specify for and/or must be based on this assumption. Suppose, however, that you know how the pressure drop varies with the velocity through the actual device, which is only partially open to flow. The following exercise is designed to show you how to compute a value for
which is appropriate for the FLUENT model.