An Attempt to Evaluate the Cycloidal Rotor Fan Performance

In this work, the cycloidal rotor fan (CRF) performance was estimated by means of a numerical method based on Unsteady Reynolds Averaged Navier-Stokes equations (URANS). The fan with a cycloidal rotor belongs to the positive displacement machines of the rotary type. The numerical algorithm for simulation of the flow in the cycloidal rotor as well as postprocessing of the CFD results was prepared using Ansys CFX CEL. The methodology for the assessment of the CRF performance was proposed and verified. It was found out that the CRF performance strongly depends on the shape of the profile of the applied rotor blade. The NACA 0012 and CLARK Y profiles were tested for the same CRF structure and flow conditions. Also, the crucial importance for the CRF performance has the range of the blade pitch angle change.


Introduction
The application of the cycloidal rotor idea to the fans is not known so far. For the time, being the most widespread application of cycloidal rotors is for ship propulsion and control but the origin of the cycloidal rotor relates to the aeronautic domain [1] [2] [3]. Cycloidal rotor is an attractive propulsion system for a wide range of aircraft applications. This type of propulsion system has very good maneuverability for various flight conditions, including hovering, and is mainly dedicated to vertical take-off and landing (VTOL) aircrafts [1] [4]. It was experimentally proved that besides good aerodynamic performance the cycloidal rotor produces little aerodynamic noise, what may be promising in terms to use it for fans. So far several analytical models were developed [4] [5] [6] which to-gether with experimental investigations were helpful in design process of cycloidal rotors. However, currently, the Computational Fluid Dynamics (CFD) allows to take into account unsteady phenomena and it is willingly used in design and analysis of the operation of the cycloidal rotor of various configurations [7] [8] [9] [10].
The cycloidal rotor fan (CRF), like other cycloidal rotor applications, consists of several blades that describe the cycloidal path rotating about an axis perpendicular to the flow direction. The implementation of the cycloidal rotor for fans was numerically and experimentally investigated by authors in former works [7] [8]. The effectiveness of the elaborated CFD model was positively verified by experimental research using LDA measurements [8]. From the point of view of a positive displacement machine of the rotary type, the most effective design is the CRF with four blades. It presents a compromise between preserving a low oscillation of the flow stream, the complexity of the design and required rotational speed.
In the presented work the elaborated CFD algorithm for modelling the flow in the cycloidal rotor fan was used in order to estimate the performance characteristics of this type of machine. Also, it was investigated the influence of the blade profile shape on the CRF performance, the NACA 0012 and CLARK Y profiles were tested. Additionally, it was attempted to find the optimal blade pitch angle for the given rotational speed of the rotor.

Physical and Numerical Model
The cycloidal rotor fan (CRF), in contradiction to typical cross-flow fan, has no diffuser and its rotor generates the flow in any specified direction. It is possible by changing the blade pitch angle, α, of each blade individually during the rotor rotation with constant angular velocity, ω ( Figure 1). The change of the blade pitch angle from the positive value to the negative one during rotation makes possible to work each blade both as a puller or pusher, depending on the blade position angle, γ. For considered here cycloidal rotor, the top blade has initial position with a maximum value of blade pitch angle. During the anticlockwise rotation with 90˚, the blade pitch angle decreases to the zero value. After further 90˚, the blade pitch angle takes a negative value of maximal blade pitch angle. After the next 90˚, the blade pitch angle has again zero value and during the last quarter of rotation, the blade returns to the initial position. The flow direction in such fan can be easily changed by setting the arbitrary initial position of the blades pitch angles. The number of the blades in the proposed design is dependent on the ratio of the chord of the rotor blade, c, and rotor radius, R. In the presented design, the blade chord was 50 mm and the radius was 70 mm. For the value c/R in the range of ~0.25 -1.00, the maximum number of blades is four [11] (see Figure 1).
The volume flow rate of the cycloidal rotor fan (CRF) is affected by rotor swept area (i.e. rotor span and radius) and airflow velocity, which depends on the angular velocity (ω) and the range of change of the blade pitch angle (2α).
where n is the constant used for keeping the similar time step value for numerical simulations with various angular speed, ω.
An increment of the blade pitch angle in certain time step was calculated according to the relation [7]: It can be seen from relation (2)

Cycloidal Rotor Fan Performance Estimation
Let us assume that useful power (P u ) is the power transmitted by the machine (fan) to the working medium (air), and it may be calculated from the relation: where V  is a volume flow rate of the air and  Figure 3). On this surface, the flow velocity, as well as total pressure, were averaged. It has to be emphasized that such an assumption may lead to small inaccuracy in the power determination of the analysed herein cycloidal rotor fan. Therefore, it was decided to find another way for power calculation.
Another available method for determining fan power is to calculate its mechanical power (P m ) which results from the product of torque (M) and angular velocity (ω): The torque of the cycloidal rotor fan is calculated as a sum of the torques of Open Journal of Fluid Dynamics Because the available value of the torque in Ansys CFX CEL led to wrong results it was decided to write an own expression. As we know the torque is the cross product of a force and a length = × M F r (5) where, F is a force vector and r is a length vector, directed from the centre of rotation to the force point. According to the assumed Cartesian coordinate system, the considered fan rotates due to the positive torque acting in the z-direction:     is given to the fluid. Figure 6 presents the comparison of the useful and mechanical power ratio for CRF with NACA 0012 and CLARK Y blade profiles.
One has to bear in mind that the determination of the useful and mechanical power on the basis of CFD results is very sensitive to the many parameters, especially for transient simulation. It can be seen that the CRF with CLARK Y blade profile is much efficient than this with NACA 0012 blade profile, even though it generates less power.
Another possibility for estimation of the CRF performance is to apply the definition of the propulsive efficiency, which is defined as follows: where v out and v in are mean velocities at the outlet and inlet, respectively, calculated on the control surfaces ( Figure 3). The results of the calculated propulsive efficiency are included in Figure 7. One can conclude that also in this case the CRF with CLARK Y profile has higher efficiency for entire range of rotational speed and we may see that both characteristic curves are almost flat.
However, whereas the CRF was applied for the work mode in a duct, the propulsive efficiency rises rapidly. For the 4000 RPM for CRF with CLARK Y profile, this value rises to the 0.94, from 0.63 for the open rotor mode (Figure 7).
In Figure 8 the velocity field for the CRF built-up in the straight duct is presented. It can be easily concluded, that this type of fan is preferred rather to work as a puller than as a pusher. The velocity field at the CRF outlet is much less regular than in the inlet part. Application of the CRF to the ductwork is very promising, especially for the ducts of the "very" rectangular shape, where the transition from a rectangular to circular shape is very difficult to manufacture.
CRF performance also depends on the value of the maximal blade pitch angle, α max . It means that the air volume flow rate can be regulated by both rotational speed RPM and α max . Figure 9 shows the velocity field comparison for CRF with Open Journal of Fluid Dynamics   In Figure 10 the CRF with CLARK Y profile performance parameters for different values of maximal blade pitch angle was presented. We may see that by

Conclusions
The numerical analysis of the flow in cycloidal rotor fan (CRF) for two shapes of the blades, with NACA0012 and CLARK Y profiles, was performed by means of Ansys CFX CFD software. The transient analysis was made for four rotational speeds and values of maximal blade pitch angle in order to determine CRF performance characteristic. On the basis of the carried out CFD simulations, the following conclusion may be drawn: − By estimation of the torques and forces in Ansys CFX, the implementation of the own expressions is recommended. − It was extremely difficult to obtain quantitative information from CFD calculations of the flow in cycloidal rotor fan. − Definition of the useful and mechanical power ratio may be used for estimation of the CRF performance as well as the propulsive efficiency, and be an alternative for polytropic and isentropic efficiency. − The shape of the blade profile affects significantly the performance characteristic of a cycloidal rotor fan. The CRF with CLARK Y blade profile works more as a lift-type rotary positive displacement machine, which provides it with higher efficiency. − The useful power calculated for the CRF with open rotor and for CRF build-up in straight ducts differs from each other less than 3%, for the same working conditions. − The CRF may efficiently work as a puller fan for ducts of the rectangular shape of the cross-section. The proposed design of CRF is well scalable to arbitrary duct cross-section, especially for the cases of large ratio of width to height of the cross-section. − The higher value of the maximal blade pitch angle the higher power, but the choice of α max should take into account the maximum efficiency of CRF.
− For the cycloidal rotor fan (CRF), all three laws valid for dynamic fans are preserved, i.e.