A coupled CFD and wake model simulation of helicopter rotor in hover

The helicopter rotor wake plays a dominant role since it affects the flow field structure. It is very difficult to predict accurately of the flow-field. The numerical dissipation is so excessive that it eliminates the vortex structure. A hybrid method of CFD and prescribed wake model was constructed by applying the prescribed wake model as much as possible. The wake vortices were described as a single blade tip vortex in this study. The coupling model is used to simulate the flow field. Both non-lifting and lifting cases have been calculated with subcritical and supercritical tip Mach numbers. Surface pressure distributions are presented and compared with experimental data. The calculated results agree well with the experimental data.


Introduction
The precise wake description is an important aspect in rotor aerodynamic predictions, because a flowfield induced by the wake changes The characteristic of the whole rotor. If the rotor wake can be accurately simulated, then aerodynamic characteristics of the rotor can be accurately obtained. Due to numerical dissipation the wake structure is difficult to distinguish.. And it cannot create induced velocity and the flow field. For this reason, some methods are developed to describe the wake flow field.
There are two commonly used methods to simulate the wake. One is wake capturing and another is wake coupling. The wake capturing methodology models the entire flowfield and attempt to Capture the structure of the solution as part of the solution. The wake capturing methodology has the advantage without any empiricism. However, it does suffer from Higher computational costs and numerical diffusion. In the wake coupling methodology, the geometry of the wake and circulation strength are Prescribed. Then the wake position obtained are embedded into the CFD analysis. The advantages of the wake coupling methodology are computational efficient and experimental support. meanwhile, It takes some experience to simulate the wake structure.
That is to say, The CFD solver provides the sectional aerodynamic loading to the wake solver, These are inputs to generate the wake model. the wake solver in turn gives the wake positions, their circulation strengths and vortex diffusion parameters to the CFD solver. Coupling analysis has been used to simulate the rotor aerodynamic and wake flowfield.

2.Governing Equations and Numerical Schemes
For hover cases, because of the periodicity of the flow in rotational coordinate system, the computational domain can be replaced by a domain around one blade. The periodicity boundary condition is used to consider the influence of other blades. Furthermore, the periodicity boundary condition can be used to reduce cost of computing. The government equation is given below Where w is the conserved variables. F and v F are the inviscid and viscous fluxes, respectively.
There is a source terms in the non-inertial frame of reference. It means the influence of the centripetal and the Coriolis force. For an hovering rotor rotating around the y-axis with the angular velocity Where q  is the grid velocity, it produce a grid flux. The finite volume discretization with central differencing for the flux approximation leads to 2 order scheme. The implicit Lower-Upper Symmetric Gauss Seidel operator(LUSGS) is used to obtain the update solution. Besides, the grid around the rotor is fixed.

3.Prescribed Wake Model
3.1Landgred wake model The prescribed wake model employs experimental data to to determine the wake location and structure. Because experimental data is applied, It's very fast to predict. This method can also be extended to the forward flight state. Some wake models have been developed such as the model introduced by Landgreb. For Landgreb wake model, the axial and radial coordinates of the tip vortex are given below Where dl is the differential element of prescribed wake geometry,  is the circulation and r is the vector connecting between the wake filament and grid. and h is the perpendicular distance of the evaluation point from the influencing vortex element. A Rankine vortex core model with a radius of one-tenth of the blade radius is used. The tip vortex strength is set to the maximum of bound circulation.

Hybrid method
The CFD gives the span load of the rotor in hover. This is used to give a vortex intensity. The trailing edge of the rotor according to starting position of the wake model. The wake is generated according to the wake model. and the induction flow field is generated. The induced velocity changes the effective angle of the rotor. The vortex age is shown in Fig 1. The left figure denotes the axial location. The right figure denotes the radial location. It's quite well comparing with the experiment data. So it is suitable to couple the wake model with CFD simulation.

Results and Discussion
An experimental study of a model helicopter in hover had been carried out by Caradonna  meter, and a chord length of 0.191m, according to the aspect ratio was 6. Fig 3 shows the grid topology.

Figure 3 : Grid topology
A summary of the simulation cases is given in Table 1. In the Caradonna-Tung experiment, the surface pressure distribution was measured at five rotor blade sections (0.50,0.68,0.80,0.89,0.96). The CFD coupled with prescribed wake model is simulated to get the aerodynamic of the rotor in hover. Five different sections of the blade were compared to the experimental data.

4.1Case-1 Subcritical Tip Mach Number Flow
The tip Mach number is 0.44. Fig 4 shows the computed results of the pressure distribution. There is much bigger difference without the wake model. And the simulation with wake model shows very good agreement for the radial stations between 0.5 to 0.95 stations. Also it also gives the coutour of pressure on the wall in the lower right corner of the figure.

4.2Case-2 Supercritical Tip Much Number Flow
The tip Mach number is 0.877. Fig 5 shows the results. In this condition there is a shockwave in the tip position. If without the wake model the difference can be seen clearly. The comparision between experiment data is quite very well with the wake model. The flowfield on the rotor is also given in the lower right corner of the figure.

5.Conclusions
Accurate simulation of rotor wake is very important. Comparing with wake capturing methodology, wake coupling methodology is efficient and it is also tested and verified. The accurate wake structure is given by the flow calculation parameter. The wake model induced the flowfield and changes the effective angle. Two pitch angles are calculated, one according to subcritical condition, and another according to supercritical condition. The CFD coupled with wake model agree well the experimental data.