## 9.5.5 Modeling Axisymmetric Flows with Swirl or Rotation

As discussed in Section  9.5.1, you can solve a 2D axisymmetric problem that includes the prediction of the circumferential or swirl velocity. The assumption of axisymmetry implies that there are no circumferential gradients in the flow, but that there may be non-zero circumferential velocities. Examples of axisymmetric flows involving swirl or rotation are depicted in Figures  9.5.3 and 9.5.4.

Problem Setup for Axisymmetric Swirling Flows

For axisymmetric problems, you will need to perform the following steps during the problem setup procedure. (Only those steps relevant specifically to the setup of axisymmetric swirl/rotation are listed here. You will need to set up the rest of the problem as usual.)

1.   Activate solution of the momentum equation in the circumferential direction by turning on the Axisymmetric Swirl option for Space in the Solver panel.

Define Models Solver...

2.   Define the rotational or swirling component of velocity, , at inlets or walls.

Define Boundary Conditions...

 Remember to use the axis boundary type for the axis of rotation.

The procedures for input of rotational velocities at inlets and at walls are described in detail in Sections  7.4.1 and  7.13.1.

Solution Strategies for Axisymmetric Swirling Flows

The difficulties associated with solving swirling and rotating flows are a result of the high degree of coupling between the momentum equations, which is introduced when the influence of the rotational terms is large. A high level of rotation introduces a large radial pressure gradient which drives the flow in the axial and radial directions. This, in turn, determines the distribution of the swirl or rotation in the field. This coupling may lead to instabilities in the solution process, and you may require special solution techniques in order to obtain a converged solution. Solution techniques that may be beneficial in swirling or rotating flow calculations include the following:

• (Pressure-based segregated solver only) Use the PRESTO! scheme (enabled in the Pressure list for Discretization in the Solution Controls panel), which is well-suited for the steep pressure gradients involved in swirling flows.

• Ensure that the mesh is sufficiently refined to resolve large gradients in pressure and swirl velocity.

• (Pressure-based solver only) Change the under-relaxation parameters on the velocities, perhaps to 0.3-0.5 for the radial and axial velocities and 0.8-1.0 for swirl.

• (Pressure-based solver only) Use a sequential or step-by-step solution procedure, in which some equations are temporarily left inactive (see below).

• If necessary, start the calculations using a low rotational speed or inlet swirl velocity, increasing the rotation or swirl gradually in order to reach the final desired operating condition (see below).

See Chapter  25 for details on the procedures used to make these changes to the solution parameters. More details on the step-by-step procedure and on the gradual increase of the rotational speed are provided below.

Step-By-Step Solution Procedures for Axisymmetric Swirling Flows

Often, flows with a high degree of swirl or rotation will be easier to solve if you use the following step-by-step solution procedure, in which only selected equations are left active in each step. This approach allows you to establish the field of angular momentum, then leave it fixed while you update the velocity field, and then finally to couple the two fields by solving all equations simultaneously.

 Since the density-based solvers solve all the flow equations simultaneously, the following procedure applies only to the pressure-based solver.

In this procedure, you will use the Equations list in the Solution Controls panel to turn individual transport equations on and off between calculations.

1.   If your problem involves inflow/outflow, begin by solving the flow without rotation or swirl effects. That is, enable the Axisymmetric option instead of the Axisymmetric Swirl option in the Solver panel, and do not set any rotating boundary conditions. The resulting flow-field data can be used as a starting guess for the full problem.

2.   Enable the Axisymmetric Swirl option and set all rotating/swirling boundary conditions.

3.   Begin the prediction of the rotating/swirling flow by solving only the momentum equation describing the circumferential velocity. This is the Swirl Velocity listed in the Equations list in the Solution Controls panel. Let the rotation "diffuse'' throughout the flow field, based on your boundary condition inputs. In a turbulent flow simulation, you may also want to leave the turbulence equations active during this step. This step will establish the field of rotation throughout the domain.

4.   Turn off the momentum equations describing the circumferential motion ( Swirl Velocity). Leaving the velocity in the circumferential direction fixed, solve the momentum and continuity (pressure) equations ( Flow in the Equations list in the Solution Controls panel) in the other coordinate directions. This step will establish the axial and radial flows that are a result of the rotation in the field. Again, if your problem involves turbulent flow, you should leave the turbulence equations active during this calculation.

5.   Turn on all of the equations simultaneously to obtain a fully coupled solution. Note the under-relaxation controls suggested above.

In addition to the steps above, you may want to simplify your calculation by solving isothermal flow before adding heat transfer or by solving laminar flow before adding a turbulence model. These two methods can be used for any of the solvers (i.e., pressure-based or density-based).

Improving Solution Stability by Gradually Increasing the Rotational or Swirl Speed

Because the rotation or swirl defined by the boundary conditions can lead to large complex forces in the flow, your FLUENT calculations will be less stable as the speed of rotation or degree of swirl increases. Hence, one of the most effective controls you can apply to the solution is to solve your rotating flow problem starting with a low rotational speed or swirl velocity and then slowly increase the magnitude up to the desired level. The procedure for accomplishing this is as follows:

1.   Set up the problem using a low rotational speed or swirl velocity in your inputs for boundary conditions. The rotation or swirl in this first attempt might be selected as 10% of the actual operating conditions.

2.   Solve the problem at these conditions, perhaps using the step-by-step solution strategy outlined above.

3.   Save this initial solution data.

4.   Modify your inputs (boundary conditions). Increase the speed of rotation, perhaps doubling it.

5.   Restart the calculation using the solution data saved in step 3 as the initial solution for the new calculation. Save the new data.

6.   Continue to increment the speed of rotation, following steps 4 and 5, until you reach the desired operating condition.

Postprocessing for Axisymmetric Swirling Flows

Reporting of results for axisymmetric swirling flows is the same as for other flows. The following additional variables are available for postprocessing when axisymmetric swirl is active:

• Swirl Velocity (in the Velocity... category)

• Swirl-Wall Shear Stress (in the Wall Fluxes... category)

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