Swirling and Rotating Flows

Many important engineering flows involve swirl or rotation and ANSYS Fluent is well-equipped to model such flows. Swirling flows are common in combustion, with swirl introduced in burners and combustors in order to increase residence time and stabilize the flow pattern. Rotating flows are also encountered in turbomachinery, mixing tanks, and a variety of other applications.

When you begin the analysis of a rotating or swirling flow, it is essential that you classify your problem into one of the following five categories of flow:

• axisymmetric flows with swirl or rotation

• fully three-dimensional swirling or rotating flows

• flows requiring a moving reference frame

• flows requiring multiple moving reference frames or mixing planes

• flows requiring sliding meshes

Modeling and solution procedures for the first two categories are presented in this section. The remaining three, which all involve “moving zones”, are discussed in Flows with Moving Reference Frames (p. 17).

Information about rotating and swirling flows is provided in the following subsections:

1.5.1. Overview of Swirling and Rotating Flows 1.5.2. Physics of Swirling and Rotating Flows

For more information about setting up swirling and rotating flows in ANSYS Fluent, see Swirling and Rotating Flows in the Fluent User's Guide.

Basic Fluid Flow

1.5.1. Overview of Swirling and Rotating Flows 1.5.1.1. Axisymmetric Flows with Swirl or Rotation

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 nonzero circumferential velocities. Examples of axisymmetric flows involving swirl or rotation are depicted in Figure 1.3: Rotating Flow in a Cavity (p. 9) and Figure 1.4: Swirling Flow in a Gas Burner (p. 9).

Figure 1.3: Rotating Flow in a Cavity

Figure 1.4: Swirling Flow in a Gas Burner

Your problem may be axisymmetric with respect to geometry and flow conditions but still include swirl or rotation. In this case, you can model the flow in 2D (that is, solve the axisymmetric problem) and include the prediction of the circumferential (or swirl) velocity. It is important to note that while the

Swirling and Rotating Flows

assumption of axisymmetry implies that there are no circumferential gradients in the flow, there may still be nonzero swirl velocities.

1.5.1.1.1. Momentum Conservation Equation for Swirl Velocity

The tangential momentum equation for 2D swirling flows may be written as

(1.23)

where is the axial coordinate, is the radial coordinate, is the axial velocity, is the radial velocity, and is the swirl velocity.

1.5.1.2. Three-Dimensional Swirling Flows

When there are geometric changes and/or flow gradients in the circumferential direction, your swirling flow prediction requires a three-dimensional model. If you are planning a 3D ANSYS Fluent model that includes swirl or rotation, you should be aware of the setup constraints (Coordinate System Restrictions in the Fluent User's Guide). In addition, you may want to consider simplifications to the problem which might reduce it to an equivalent axisymmetric problem, especially for your initial modeling effort. Because of the complexity of swirling flows, an initial 2D study, in which you can quickly determine the effects of various modeling and design choices, can be very beneficial.

Important

For 3D problems involving swirl or rotation, there are no special inputs required during the problem setup and no special solution procedures. Note, however, that you may want to use the cylindrical coordinate system for defining velocity-inlet boundary condition inputs, as described in Defining the Velocity in the User's Guide. Also, you may find the gradual in-crease of the rotational speed (set as a wall or inlet boundary condition) helpful during the solution process. For more information, see Improving Solution Stability by Gradually Increas-ing the Rotational or Swirl Speed in the User's Guide.

1.5.1.3. Flows Requiring a Moving Reference Frame

If your flow involves a rotating boundary that moves through the fluid (for example, an impeller blade or a grooved or notched surface), you will need to use a moving reference frame to model the problem.

Such applications are described in detail in Flow in a Moving Reference Frame (p. 18). If you have more than one rotating boundary (for example, several impellers in a row), you can use multiple reference frames (described in The Multiple Reference Frame Model (p. 22)) or mixing planes (described in The Mixing Plane Model (p. 25)).

1.5.2. Physics of Swirling and Rotating Flows

In swirling flows, conservation of angular momentum ( or = constant) tends to create a free vortex flow, in which the circumferential velocity, , increases sharply as the radius, , decreases (with

finally decaying to zero near as viscous forces begin to dominate). A tornado is one example of a free vortex.Figure 1.5: Typical Radial Distribution of Circumferential Velocity in a Free Vortex (p. 11) depicts the radial distribution of in a typical free vortex.

Basic Fluid Flow

Figure 1.5: Typical Radial Distribution of Circumferential Velocity in a Free Vortex

It can be shown that for an ideal free vortex flow, the centrifugal forces created by the circumferential motion are in equilibrium with the radial pressure gradient:

(1.24) As the distribution of angular momentum in a non-ideal vortex evolves, the form of this radial pressure gradient also changes, driving radial and axial flows in response to the highly non-uniform pressures that result. Thus, as you compute the distribution of swirl in your ANSYS Fluent model, you will also notice changes in the static pressure distribution and corresponding changes in the axial and radial flow velocities. It is this high degree of coupling between the swirl and the pressure field that makes the modeling of swirling flows complex.

In flows that are driven by wall rotation, the motion of the wall tends to impart a forced vortex motion to the fluid, wherein or is constant. An important characteristic of such flows is the tendency of fluid with high angular momentum (for example, the flow near the wall) to be flung radially outward (see Figure 1.6: Stream Function Contours for Rotating Flow in a Cavity (p. 11) using the geometry of Figure 1.3: Rotating Flow in a Cavity (p. 9)). This is often referred to as “radial pumping”, since the ro-tating wall is pumping the fluid radially outward.

Figure 1.6: Stream Function Contours for Rotating Flow in a Cavity