## 3 Methods for Modeling and Simulating Rotational Motion  
There are several approaches to modeling rotating motion in CFD, for example, mixing plane, frozen rotor, sliding mesh, morphing mesh, or the overset mesh method. Each method has its own advantages and disadvantages. In this current paper, we used mixing plane, frozen rotor, and sliding mesh approaches, which shall be introduced briefly in the following paragraphs. The mixing plane interface is also known as stage or averaged rotating local region in some CFD software [20]. With the mixing plane method, the interaction between two regions can be simulated, in which one of them is a stator, or a nonrotating region, while the other one is a rotor, which carries out the actual rotation. This method can model and simulate steady and unsteady flows. When this approach is used in the rotating region, the governing equation is solved in a rotating coordinate system, while in the stationery region, the equations are solved in a stationary coordinate system. Within the rotating region, the flow field is averaged circumferentially; thus, the exiting flow has some rotary motion depending on the geometry and a modeled rotational speed. There are several advantages of the mixing plane method. It calculates a uniform circumferential velocity, pressure, and turbulence variables distribution due to the averaging; therefore, torque, power, and other quantities can be examined as well. In addition, it provides a single value that represents the average value for a complete rotation. The disadvantage of the mixing plane approach is that wake and vortex shedding cannot be examined, not even in a transient simulation, due to the averaging [21; 22; 23; 24]. For the simulations, a 1.1512675 \(\times\) 10\({}^{-4}\) time step with second-order temporal discretization was used based on the following consideration: the tip speed ratio (\(\lambda\)) was 4; therefore, the rotational speed was 1447.75 RPM. A 1447.75 RPM equals 24.12791667 RPS; therefore, the time requirement for one rotation was 0.041445766 s. Accordingly, the time requirement for one degree of rotation is 0.000115127129132344 s, which was rounded to 1.15127 \(\times\) 10\({}^{-4}\) s.  
The frozen rotor approach, similar to the mixing plane method, requires two domains, in which one domain is stationary while the other one is rotating. The frozen rotor interface is often referred to as a moving reference frame (MRF). The frozen rotor approach is easily understandable if we simplify the whole mathematical approach for this technique into a rotating wall boundary condition. In this case, the solid body is rotating around its axis of rotation, while the velocity, near the wall, has an \(\omega\times r\) component, where \(\omega\) is the angular velocity and \(r\) is the distance from the axis of rotation. This method does not average the fluid quantities; thus, it provides nonuniform circumferential velocity, pressure, and turbulent quantities on the domain's exiting face. In addition, the frozen rotor approach can be used during steady and unsteady simulations to simulate wake and vortex shedding. The advantages of the frozen rotor interface are the following. The wake and the vortex shedding can be examined near the edges and near the blade tips. The disadvantage is that the relative position of the moving component is fixed; consequently, motion is modeled by adding the Coriolis and centrifugal forces to the momentum equation [21; 22; 23; 24]. It is important to note that if performance such as quantities, such as torque, power, etc., are to be obtained, then the simulation must be repeated in different angular positions to eliminate the value dependency of each position [20; 22]. The sliding mesh approach is a rotating motion interface, where there are also two domains: a stationary and a rotational one, similar to the previous methods. However, in this case, the rotational domain actually rotates. This approach can only be used in transient simulations due to the motion of the mesh.