ANSYS FLUENT 12.0 Theory Guide

In sliding meshes, the relative motion of stationary and rotating components in a rotating machine will give rise to unsteady interactions. These interactions are illustrated in Figure 3.1.1, and generally classified as follows:

Where the multiple reference frame (MRF) and mixing plane (MP) models, discussed in Chapter 2, are models that are applied to steady-state cases, thus neglecting unsteady interactions, the sliding mesh model cannot neglect unsteady interactions. The sliding mesh model accounts for the relative motion of stationary and rotating components.

**Figure 3.1.1:** Illustration of Unsteady Interactions

The dynamic mesh model uses the ANSYS FLUENT solver to move boundaries and/or objects, and to adjust the mesh accordingly. The dynamic mesh model is used when boundaries move rigidly (linear or rotating) with respect to each other. For example

The dynamic mesh model can also be used when boundaries deform or deflect. For example

With respect to dynamic meshes, the integral form of the conservation equation for a general scalar, $\phi$ , on an arbitrary control volume,

, whose boundary is moving can be written as

${d\over dt}\int_V\rho\phi dV + \int_{\partial V}\rho\phi\lef... ...{\partial V}\Gamma\nabla\phi \cdot d\vec{A} + \int_V S_\phi dV$

(3.1-1)

where	$\rho$ is the fluid density
	$\vec{u}$ is the flow velocity vector
	$\vec{u}_g$ is the mesh velocity of the moving mesh
	$\Gamma$ is the diffusion coefficient
	$S_\phi$ is the source term of $\phi$

The time derivative term in Equation 3.1-1 can be written, using a first-order backward difference formula, as

${d\over{\sl dt}}\int_V\rho\phi dV = {\left(\rho\phi V\right)^{n+1} - \left(\rho\phi V\right)^{n} \over \Delta t}$

(3.1-2)

where

and

denote the respective quantity at the current and next time level. The

th time level volume $V^{n+1}$ is computed from

$V^{n+1} = V^{n} + {dV\over dt}\Delta t$

(3.1-3)

where

is the volume time derivative of the control volume. In order to satisfy the mesh conservation law, the volume time derivative of the control volume is computed from

${dV\over dt} = \int_{\partial V}\vec{u}_g\cdot d\vec{A} = \sum_j^{n_f} \vec{u}_{g,j}\cdot \vec{A}_j$

(3.1-4)

where

is the number of faces on the control volume and $\vec{A}_j$ is the

face area vector. The dot product $\vec{u}_{g,j}\cdot\vec{A}_j$ on each control volume face is calculated from

$\vec{u}_{g,j}\cdot\vec{A}_j = {\delta V_j\over\Delta t}$

(3.1-5)

where $\delta V_j$ is the volume swept out by the control volume face

over the time step $\Delta t$ .

In the case of the sliding mesh, the motion of moving zones is tracked relative to the stationary frame. Therefore, no moving reference frames are attached to the computational domain, simplifying the flux transfers across the interfaces. In the sliding mesh formulation, the control volume remains constant, therefore from Equation 3.1-3, ${dV\over dt} = 0$ and $V^{n+1} = V^n$ . Equation 3.1-2 can now be expressed as follows:

${d\over{\sl dt}}\int_V\rho\phi dV = {[\left(\rho\phi \right)^{n+1} - \left(\rho\phi \right)^{n}]V \over \Delta t}$

(3.1-6)