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9.4.3 User Inputs for the Pressure-Based Solver

If you are using the pressure-based solver, in order to calculate a spatially periodic flow field with a specified mass flow rate or pressure derivative, you must first create a grid with translationally periodic boundaries that are parallel to each other and equal in size. You can specify translational periodicity in the Periodic panel, as described in Section  7.15. (If you need to create periodic boundaries, see Section  6.8.4.)

Once the grid has been read into FLUENT, you will complete the following inputs in the Periodic Conditions panel (Figure  9.4.3):

Define $\rightarrow$ Periodic Conditions...

Figure 9.4.3: The Periodic Conditions Panel

1.   Select either the specified mass flow rate ( Specify Mass Flow) option or the specified pressure gradient ( Specify Pressure Gradient) option. For most problems, the mass flow rate across the periodic boundary will be a known quantity; for others, the mass flow rate will be unknown, but the pressure gradient ( $\beta$ in Equation  9.4-3) will be a known quantity.

2.   Specify the mass flow rate and/or the pressure gradient ( $\beta$ in Equation  9.4-3):

  • If you selected the Specify Mass Flow option, enter the desired value for the Mass Flow Rate. You can also specify an initial guess for the Pressure Gradient, but this is not required.


    For axisymmetric problems, the mass flow rate is per $2\pi$ radians.

  • If you selected the Specify Pressure Gradient option, enter the desired value for Pressure Gradient.

3.   Define the flow direction by setting the X,Y,Z (or X,Y in 2D) point under Flow Direction. The flow will move in the direction of the vector pointing from the origin to the specified point. The direction vector must be parallel to the periodic translation direction or its opposite.

4.   If you chose in step 1 to specify the mass flow rate, set the parameters used for the calculation of $\beta$. These parameters are described in detail below.

After completing these inputs, you can solve the periodic velocity field to convergence.

Setting Parameters for the Calculation of $\beta$

If you choose to specify the mass flow rate, FLUENT will need to calculate the appropriate value of the pressure gradient $\beta$. You can control this calculation by specifying the Relaxation Factor and the Number of Iterations, and by supplying an initial guess for $\beta$. All of these inputs are entered in the Periodic Conditions panel.

The Number of Iterations sets the number of sub-iterations performed on the correction of $\beta$ in the pressure correction equation. Because the value of $\beta$ is not known a priori, it must be iterated on until the Mass Flow Rate that you have defined is achieved in the computational model. This correction of $\beta$ occurs in the pressure correction step of the SIMPLE, SIMPLEC, or PISO algorithm. A correction to the current value of $\beta$ is calculated based on the difference between the desired mass flow rate and the actual one. The sub-iterations referred to here are performed within the pressure correction step to improve the correction for $\beta$ before the pressure correction equation is solved for the resulting pressure (and velocity) correction values. The default value of 2 sub-iterations should suffice in most problems, but can be increased to help speed convergence. The Relaxation Factor is an under-relaxation factor that controls convergence of this iteration process.

You can also speed up convergence of the periodic calculation by supplying an initial guess for $\beta$ in the Pressure Gradient field. Note that the current value of $\beta$ will be displayed in this field if you have performed any calculations. To update the Pressure Gradient field with the current value at any time, click on the Update button.

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