Both approaches assume steady flow in the appropriate frame of reference for both the rotor and the stator.

The mixing plane approach performs a coupling between tangential averages on both sides of the interface between rotor and stator. Each of the rows sees a tangentially constant flow field at the coupling interface. Hence this approach is ment to capture the time-average interaction. Some additional modeling, the so-called deterministic stresses, can be added to take into account the average impact of unsteadiness, conceptually in the same way as Reynolds averaging is used to take into account the average impact of turbulence. In any case, you usually need spatially non-reflecting boundary conditions to avoid/minimise reflections of tangential non-uniformities on these tangentially constant boundary conditions.

The frozen rotor (or the multiple frame of reference) approach provides a local coupling, imposing the local flow conditions from one row to the other and vice versa. It is supposed to give a more accurate representation. However due to the absence of inertia however, this is physically inconsistent and leads to the generation of artificial wakes which then convect downstream of the coupling. To be avoided.

Both approaches assume steady flow in the appropriate frame of reference for both the rotor and the stator.

The mixing plane approach performs a coupling between tangential averages on both sides of the interface between rotor and stator. Each of the rows sees a tangentially constant flow field at the coupling interface. Hence this approach is ment to capture the time-average interaction. Some additional modeling, the so-called deterministic stresses, can be added to take into account the average impact of unsteadiness, conceptually in the same way as Reynolds averaging is used to take into account the average impact of turbulence. In any case, you usually need spatially non-reflecting boundary conditions to avoid/minimise reflections of tangential non-uniformities on these tangentially constant boundary conditions.

The frozen rotor (or the multiple frame of reference) approach provides a local coupling, imposing the local flow conditions from one row to the other and vice versa. It is supposed to give a more accurate representation. However due to the absence of inertia however, this is physically inconsistent and leads to the generation of artificial wakes which then convect downstream of the coupling. To be avoided.

MRF method is an approximation of the instantaneous (unsteady) flow solution when the rotor is in the position defined by the (fixed) mesh i.e. Meshes do not move with time. At the interfaces, appropriate transformations of the velocity vectors and velocity gradients are performed, and local fluxes of mass, momentum, energy, and other scalars are determined.

Limitations:-  It ignore the relative motions of the fluid zones with respect to each other, and thus do not account for fluid dynamic interaction at the interfaces.

 No account is taken for the relative motion of one domain with respect to the other.

 MRF in can only be used under equal periodic angle conditions.

 Limited up to steady-state numerical solutions.

As it's name suggests, the mixing plan model simply convert the interface boundary into Mixing plan. The mixing plane model uses a circumferential averaging technique which takes a general, non-uniform distribution of a flow variable on boundary and approximate through number of averaging points. As for multistage turbomachinery problems, we often know the stage boundary conditions (e.g. inlet total pressure and temperature and stage outlet static pressure) but not the inter-stage conditions. In addition, the blade counts will generally not be the same from one blade row to the next. The limitations of MRF model are overcome through the implementation of MPM model.

Limitations:-  Interpolation process can introduce errors in the mixing plane interface, if sufficient averaging points not considered.

 Wake effects, shock wave interactions will not be predicted.

 Errors in the mixing plane model increase as the interaction will be increased at the interface boundary i.e. decreasing the spacing between the consecutive stages.

 Note the following models may not be used with mixing planes:

– The LES turbulence model

– The models for species transport and combustion

– The VOF multiphase model.

– The discrete phase model for coupled flows.

I need some guidance regarding usage of Stage and Frozen rotor:

I have three domains:

Stationary: Guide vanes

Rotating: Turbine wheel

Stationary: Outlet diffusor

Is stage recommended between Turbine wheel and Outlet diffusor? Or should I use Frozen rotor in that interface?

Any explannation would be appreciated.

Thanks and Regards,

Juzer Rangwala

If you want to use periodic BC (1 guide vane blade and 1 rotor blade) to reduce computational demands then only mixing plane interface can be used. If you want to use full 360° guide vane row and turbine runner then both approaches are valid. Nevertheless according to limitations, advantages and disadvantages of both approaches the flow in the downstream diffusor will be different. For the steady stage RANS solution I would prefer the stage (mixing plane) approach ensuring the ensuring the more realistic (in terms of steady averaging) flow behavior. In order to predict e.g. efficiency with frozen rotor you would have to compute several runner positions according to guide vanes and then calculate average value. Similarly for torque. etc.