Dynamic Mesh Theory

The dynamic mesh model in ANSYS Fluent can be used to model flows where the shape of the domain is changing with time due to motion on the domain boundaries. The dynamic mesh model can be applied to single or multiphase flows (and multi-species flows). The generic transport equation

(Equa-tion 3.1 (p. 35)) applies to all applicable model equa(Equa-tions, such as turbulence, energy, species, phases, ans so on. The dynamic mesh model can also be used for steady-state applications, when it is beneficial to move the mesh in the steady-state solver. The motion can be a prescribed motion (for example, you can specify the linear and angular velocities about the center of gravity of a solid body with time) or an unprescribed motion where the subsequent motion is determined based on the solution at the current time (for example, the linear and angular velocities are calculated from the force balance on a solid body, as is done by the six degree of freedom (6DOF) solver; see Using the Six DOF Solver in the User's Guide). The update of the volume mesh is handled automatically by ANSYS Fluent at each time step based on the new positions of the boundaries. To use the dynamic mesh model, you need to provide a starting volume mesh and the description of the motion of any moving zones in the model.

ANSYS Fluent allows you to describe the motion using either boundary profiles, user-defined functions (UDFs), or the six degree of freedom solver.

ANSYS Fluent expects the description of the motion to be specified on either face or cell zones. If the model contains moving and non-moving regions, you need to identify these regions by grouping them Flows Using Sliding and Dynamic Meshes

into their respective face or cell zones in the starting volume mesh that you generate. Furthermore, regions that are deforming due to motion on their adjacent regions must also be grouped into separate zones in the starting volume mesh. The boundary between the various regions need not be conformal.

You can use the non-conformal or sliding interface capability in ANSYS Fluent to connect the various zones in the final model.

Information about dynamic mesh theory is presented in the following sections:

3.2.1. Conservation Equations 3.2.2. Six DOF (6DOF) Solver Theory

3.2.1. Conservation Equations

With respect to dynamic meshes, the integral form of the conservation equation for a general scalar, , on an arbitrary control volume, , whose boundary is moving can be written as

(3.1)

where

is the fluid density

is the flow velocity vector

is the mesh velocity of the moving mesh is the diffusion coefficient

is the source term of

Here, is used to represent the boundary of the control volume, .

By using a first-order backward difference formula, the time derivative term in Equation 3.1 (p. 35) can be written as

(3.2)

where and denote the respective quantity at the current and next time level, respectively. The th time level volume, , is computed from

(3.3) where is the volume time derivative of the control volume. In order to satisfy the mesh conser-vation law, the volume time derivative of the control volume is computed from

(3.4)

where is the number of faces on the control volume and is the face area vector. The dot product on each control volume face is calculated from

(3.5)

where is the volume swept out by the control volume face over the time step .

Dynamic Mesh Theory

By using a second-order backward difference formula, the time derivative in Equation 3.1 (p. 35) can be written as

(3.6)

where , , and denote the respective quantities from successive time levels with denoting the current time level.

In the case of a second-order difference scheme the volume time derivative of the control volume is computed in the same manner as in the first-order scheme as shown in Equation 3.4 (p. 35). For the second-order differencing scheme, the dot product on each control volume face is calculated from

(3.7)

where and are the volumes swept out by control volume faces at the current and previous time levels over a time step.

3.2.2. Six DOF (6DOF) Solver Theory

The 6DOF solver in ANSYS Fluent uses the object’s forces and moments in order to compute the trans-lational and angular motion of the center of gravity of an object. The governing equation for the translational motion of the center of gravity is solved for in the inertial coordinate system:

(3.8)

where is the translational motion of the center of gravity, is the mass, and is the force vector due to gravity.

The angular motion of the object, , is more easily computed using body coordinates:

(3.9)

where is the inertia tensor, is the moment vector of the body, and is the rigid body angular velocity vector.

The moments are transformed from inertial to body coordinates using

(3.10) where, represents the following transformation matrix:

where, in generic terms, and . The angles , , and are Euler angles that rep-resent the following sequence of rotations:

Flows Using Sliding and Dynamic Meshes

• rotation about the Z axis (for example, yaw for airplanes)

• rotation about the Y axis (for example, pitch for airplanes)

• rotation about the X axis (for example, roll for airplanes)

After the angular and the translational accelerations are computed from Equation 3.8 (p. 36) and Equation 3.9 (p. 36), the rates are derived by numerical integration [439] (p. 783). The angular and translational velocities are used in the dynamic mesh calculations to update the rigid body position.