## CFD Modeling for Turbomachinery using Sliding Mesh Model

Mixing plane model:
A mixing-plane simulation is steady state simulation and only requires a rotor blade and a stator blade per stage. Between the rotating blade passage and the steady vane passage the flow properties are circumferentially averaged in a so-called mixing-plane interface. This removes all the transient rotor-stator interactions, though gives fairly representative results. The mixing plane model provides an alternative to the multiple reference frame and sliding mesh models for simulating flow through domains with one or more regions in relative motion. As discussed in the earlier blog CFD Modeling for Turbomachinery using MRF Model, the MRF model is applicable when the flow at the boundary between adjacent zones that move at different speeds is nearly uniform. If the flow at the boundary is not uniform, the MRF model may not provide a physically meaningful solution. The sliding mesh model may be appropriate for such cases (non-uniform boundary flows), but in many situations like in a multistage turbomachine, if the number of blades are different for each blade row, a large number of blade passages are required in order to maintain circumferential periodicity, wherein it is not practical to employ a sliding mesh.
In the mixing plane approach, each fluid zone is treated as a steady-state problem. Flow-field data from adjacent zones are passed as boundary conditions that are spatially averaged or mixed at the mixing plane interface. This mixing removes any unsteadiness that would arise due to circumferential variations in the passage-to-passage flow field (e.g., wakes, shock waves, separated flow), thus yielding a steady-state result. Despite the simplifications inherent in the mixing plane model, the resulting solutions can provide reasonable approximations of the time-averaged flow field.
Sliding mesh model:
The ﬂow problem in turbomachines is challenging to solve, not only because the ﬂow ﬁeld involved is characterized by three-dimensional highly unsteady complex phenomena, but also because the relative motion between the rotating geometry and the stationary conﬁguration makes it difﬁcult to compute with a single ﬁxed grid system. The analysis of turbomachinery often involves the examination of the unsteady effects due to flow interaction between the stationary components and the rotating blades. When a time-accurate solution for rotor-stator interaction rather than a time-averaged solution is desired, the sliding mesh model is best to compute the unsteady flow. The sliding mesh model is the most accurate method for simulating flows in multiple moving reference frames, but also the most computationally demanding. Most often, the unsteady solution that is sought in a sliding mesh simulation is time periodic. That is, the unsteady solution repeats with a period related to the speeds of the moving domains.
In the sliding mesh two or more cell zones are used. If the mesh in each zone is generated separately, then it needs to be merged before starting the simulation process. Each cell zone is bounded by at least one interface zone where it meets the opposing cell zone. The interface zones of adjacent cell zones are associated with
one another to form a grid interface. The two cell zones will move relative to each other along the grid interface.

A simple 2D case of a centrifugal blower is considered for simulation using sliding mesh approach. Blowers are one of the types of turbo machinery which are used to move air continuously with slight increase in static pressure. The centrifugal blower uses the centrifugal power generated from the rotation of impellers to increase the pressure of air/gases. When the impellers rotate, the gas near the impellers is thrown-off from the impellers due to the centrifugal force and then moves into the fan casing. As a result the gas pressure in the fan casing is increased. The gas is then guided to the exit via outlet ducts.

Blowers are widely used in industrial and commercial applications from shop ventilation to material handling, boiler applications to some of the vehicle cooling systems, power and energy source, environment, chemical engineering, etc.
The main aim of the analysis is to provide accurate enough transient flow field characteristics. To determine the flow pattern and pressure distribution.A 2-D model of the blower is used for simulation. The blower has 44 blades and it is running at 2500 RPM. The blower inlet total pressure is 200 Pa (gauge), and outlet pressure is at the ambient. The SMM simulation is run for several revolutions to reach a time-periodic solution for the blower. The geometry and all its specifications with the interface is shown below.

The working fluid used here is air.
Now in this problem the volute casing is not the surface of revolution, thus an interface is created between the stationary and rotating which is a surface of revolution.
Before performing the sliding mesh simulation, the MRF model can be set up for the blower in order to get a good initial condition and to help speed up convergence of the transient Sliding Mesh computation.
The pressure contour and velocity vector for the converged solution using MRF model is shown below
From the pressure contour it can be seen that the expected pressure jump across the blower blades. The pressure at both inlet and at the outlet is almost uniform.

From the velocity vector it can be seen that the initial flow field has been developed. The velocity at the inlet is small as indicated by the small vectors at the inlet, as it crosses the blades and progresses through the volute casing the velocity is increased. The flow is almost uniform at the exit, as there is sudden expansion at the exit there is flow separation as shown.

For most of the turbomachinery problems, we are interested in time periodic solution i.e., the cyclic behavior of unsteady solution after the initial start phase has passed, than startup transient behavior. Therefore we will pursue a time-periodic solution here for the blower. The time step size used here is 1.333e-4.

The time periodic variation of the pressure and velocity vector is shown in the video.
The time periodic solution can be achieved quickly with good initial conditions and this can be achieved by first converging the solution using MRF approach and using that as the initial condition for sliding mesh approach. Since this is a simple 2D case, the time periodic solution can be achieved easily by both the approaches, but for a complex 3D case it is better to go with the above approach.