Theory for the Mixing Plane Feature
The Mixing Plane boundary condition is typically applied to interior boundaries at the intersection of rotating and nonrotating domains. The boundary condition intends to obtain a steady-state solution by taking into consideration all possible spatial configurations corresponding to different relative positionings of the rotating and nonrotating domains. While the word “plane” in “mixing plane” refers to the interior boundary on which the condition is applied, the word “mixing” refers to the averaging operation performed on dependent variables in the plane.
The solution thus obtained from the Mixing Plane condition is independent of the relative positioning of the rotating and nonrotating domains. It alleviates the need to perform time-averaging operation on solution steps from computationally expensive time dependent studies. Moreover, it allows users to take advantage of symmetry planes in the geometry of the problem.
The Mixing Plane duplicates the degrees of freedom at the boundary, thus allowing for discontinuous solution values on either sides of the boundary. Consequently, flow, turbulence and wall distance quantities may be defined on the up and down sides, which are denoted by subscripts “u” and “d”, respectively. Also, the normals are defined as nd = n and nu = −n.
Using the framework described in the previous paragraph, mixing is introduced as follows. In the case of subsonic flows, modeled using one of the Single Phase Flow interfaces, the Nitsche’s method is utilized to apply the following Dirichlet conditions at the mixing plane boundary:
.
Here, the ordered subscript, d|u, should be read as “down side or up side” and the operator “mix(·)” performs averaging on the mixing plane boundary. When expanded, the above equation is equivalent to:
, .
The mixing of u is performed by averaging the components along the normal and tangential directions of the plane.
When the Nonisothermal Flow multiphysics coupling feature is active, similar conditions on the temperature apply. They are given by
.
For high-speed flows in the transonic and supersonic flow regimes, using one of the High-Mach Number Flow interfaces, one must take averaged values of dependent variables into consideration when computing the characteristic variables. In other words, we replace p, T, and u with mix(p), mix(T), and mix(u) respectively, in Equation 5-11 and Equation 5-12 in the CFD Module User’s Guide. Mixed values of derived variables, such as density and speed of sound, are obtain using mixed values of dependent variables. The primitive variables (denoted by subscript “face”), obtained from transformation of the these characteristic variables using Equation 5-13 in the CFD Module User’s Guide, are used to apply appropriate conditions at the “up” and “down” sides of the mixing plane boundaries, that is
, , .
The conditions on the turbulence variables, for the k-ε model, low Reynolds number k-ε model, and Realizable k-ε model are
, .
The conditions on the turbulence variables, for the k-ω model and SST model are
, .
If transition modeling is included in the SST model, then
.
The conditions on the turbulence variable, for the Spalart–Allmaras model are
.
The conditions on the turbulence variables, for the v2-f model are
, , , .
If wall distance variable is solved for, then
.
See Mixing Plane for the feature node details.