Aerodynamic characteristics simulation of helicopter rotor in hover using HeliX software

In order to predict hover performance of a new helicopter rotor, the aerodynamic performance and flow field of the rotor in hover is calculated by using HeliX software. The comparison between numerical results and wind tunnel test data of S-76 rotor as a validation case of CFD method demonstrate that HeliX software has the capability to consistently and reliably predict performance parameters for a helicopter rotor. The numerical results of the new rotor in hover suggest that the maximum hover efficiency of the new rotor is about 73% with collective pitch angle of 9.2°, while the shock induced separation and the reattachment phenomenon begin to appear on the upper surface near the blade tip. As the increase of collective pitch angle from 9.2° to 11.2°, hover efficiency decreases significantly due to the serious flow separation near the blade tip. The research in this paper can provide reference and guidance for aerodynamic optimization design of helicopter rotor.


Introduction
The flow field of helicopter rotor is different from that of fixed wing aircraft.The difference is shown in the following three aspects: first, the incoming flow velocity relative to rotor-blade changes along the span direction, and the rotor flow field includes both the incompressible flow zone of blade root and the subsonic and transonic flow zone of blade tip [1].Second, the rotor flow field is a typical unsteady flow.Because of the rotation of the rotor, even in the steady forward flight state, the incoming flow velocity and local attack angle of the rotor blade are also changing with the variation of the azimuth [2].Third, the rotor rotation produces strong blade tip vortex and wake vortex [3].These wake vortices around the rotor are easy to cause vortex-propeller interference, vortex-fuselage interference [4][5][6], and have negative impact on the rotorcraft aerodynamic performance.The complexity of rotor motion and flow brings difficulties in flow field simulation [7][8].For a long time, helicopter rotor design mainly depends on various simplified theories for aerodynamic performance analysis, and then continuously revised and improved according to ground or wind tunnel tests.
With the development of numerical methods and computer technology, modern computational fluid dynamics (CFD) methods have been widely used in the aerodynamic performance prediction of fixedwing aircraft and the establishment of aerodynamic databases.As an important branch of modern fluid dynamics, rotor computational fluid dynamics has developed rapidly in the past 40 years [9].According to the classification of control equations, the development of rotor CFD methods has mainly experienced four stages: small perturbation potential equation, full potential equation, Euler equation and Navier-Stokes equation.In the first two stages (potential equation), irrotational and isentropic assumptions are made for the flow, which is characterized by small amount of calculation.With the rapid development of high-performance computer technology, most CFD methods now use the method of solving Euler or RANS equations.The main advantage is that it can capture and transfer vorticity in the computational domain without making the assumption of irrotational, and make vorticity exist as a part of the solution.Due to the consideration of the viscosity of the gas, the Navier-Stokes equation can truly accurately describe the formation and transport of vortices.Under the framework of the Navier-Stokes equation, the flow field details can be studied in more depth, such as the study of some complex flow phenomena such as blade stall and wake vortex interference [1].
With the support of national numerical windtunnel (NNW) project [10], China Aerodynamics Research and Development Center has developed a numerical simulation software named HeliX with independent intellectual property rights for aerodynamic performance predictions of helicopter rotor.HeliX is the CFD software developed based on structured grid and block structured Cartesian grid.The software has the capabilities to simulate the flow field and calculate the aerodynamic performance of solo rotating parts such as helicopter rotor, propeller rotor, wind turbine rotor.In addition, HeliX has the capabilities to simulate the interference flow field of rotating parts, including helicopter rotorfuselage interference, propeller slipstream interference, wind turbine box-support interference.The software provides theoretical analysis tools for helicopter performance analysis and rotor optimization design, and has broad engineering application prospects and import academic value.
In order to meet the analysis requirements of hover performance of a new rotor, this paper uses HeliX software to numerically predict the aerodynamic performance of the rotor in hover, and analyze the corresponding flow details.

Numerical Method
In this paper, the flow control equations are compressible Navier-Stokes equations described by arbitrary Lagrangian-Eluer method, which allows arbitrary movement and deformation of the mesh.The integral forms in absolute coordinate system are expressed as (1) In formula (1),  represents the volume of the control body, S represents the area of the boundary interface of the control body,   V is the mesh velocity on the boundary interface, and  and e represent the density and total energy of the fluid respectively.,   u v and w represent momentum components of the fluid.
 I H is the convective flux on the boundary of the control body, and  V H is the viscous flux.The Roe flux difference dispersion scheme with second order upwind is used for the convection term, and the third order accuracy form of Vanalbada limiter is used for MUSCL interpolation.The LU-SGS implicit time marching method is used for the time discretion of the equations.It should be noted that the source term caused by solving the control equation in the rotating coordinate system needs to be implicit [11], so as to improve the robustness of the numerical method.The specific method of this paper is to put the Jacobian matrix of the source term in the U-scan operator which results in a small amount of additional calculation [12].The calculation assumes that the flow field is full turbulence.The turbulence model is k-ω SST two-equation model.In order to improve the convergence speed of the flow field, the multi-grid technology [13] is applied in this paper.

Calculation model and grid
A new helicopter rotor for aerodynamic performance predictions in this paper has three blades shown in figure 1.The rotor is a left-handed rotor with a rotation speed of 406rev/min and a radius (R) of 5 meters.Since the rotating coordinate system method is used to simulate the flow field of the rotor in hover in this paper, a computational grid is generated along 1/3 of the circumferential zone of the whole rotor.The computational grid is a structured overlap grid shown in figure 2 which consists of a background grid and a blade sub-grid.The background grid is the peripheral grid surrounding the blade sub-grid, which is a cylindrical three-dimensional structured grid with a circumferential angle of 120°.Both sides of the background grid are specified as periodic boundary conditions.The distance from the upper and lower boundary of the background grid to the blade disk plane is set to 8R, and the distance from the circumferential boundary to the blade tip is set to 5R.In order to reduce the numerical dissipation and capture the blade tip vortex accurately, the trajectory region of the blade tip vortex is meshed in the background grid and blade sub-grid.The sub-grid generated around the rotor-blade is shown in figure 3. It is considered that the blade tip vortex and blade root vortex have a significant impact on the aerodynamic performance of the blade during the rotor rotation [14].In order to ensure the high grid quality at the blade ends, the blade subgrid adopts C-O topology.The height of the first normal grid on the blade surface is about 0.005mm.

S-76 rotor validation case
In 2014, The AIAA Applied Aerodynamics Technical Committee put together a Rotorcraft Simulation Working Group to evaluate the capability of CFD softwares on rotor-in-hover performance predictions based on the same model rotor [15][16][17].The current research object of the working group is the S-76 rotor blade of 1/4.71 scale with a radius of about 2.85m (56.04 inch).This blade has been widely used and has a large number of wind tunnel test data, including test results of various blade tip geometries [18][19].Therefore, the S-76 rotor is selected as the standard case for validation of CFD method in this paper.The plane shape of the S-76 rotor is shown in figure 4. The computational grid of S-76 rotor is similar to that of the new rotor used in this study.The blade sub-grid of S-76 rotor is shown in figure 5.The working conditions of S-76 rotor are: the tip Mach number (M tip ) is 0.55, Reynolds number (Re) is 1.008×10 6 , and the variation range of collective pitch angle is 0° ~ 12°.The turbulence model is k-ω SST two-equation model.data are represented by discrete points.It can be seen that the CFD numerical results of aerodynamic performance of S-76 rotor are in good agreement with the wind tunnel test results, and the change trend of the numerical results is almost consistent with the experimental data in general.Under the same CT, the calculated value of hover efficiency is slightly lower than the test value, and its relative error is within 4%, which makes the rotor-in-hover performance predictions conservative.It can be further seen that the change trend of hover efficiency with CT is relatively flat when the CT is between 0.006 and 0.007.The calculated value of the maximum hover efficiency of S-76 rotor is about 70%.The above validation case shows that the numerical method and grid generation strategy used for rotor-in-hover performance prediction in this paper are reasonable and reliable, and HeliX software has the capability to consistently and reliably predict performance parameters for a helicopter rotor, and meets the needs of research work in this paper.It should be emphasized that the rigid blade assumption is adopted for the rotor in the calculation.Since the elastic deformation of the rotor is not taken into account, the calculated angle of attack of the airfoil at the blade tip is greater than the test angle of attack, which may be the reason for the difference between the calculation and the test.

Numerical results and analysis
In this paper, the aerodynamic performance of a new helicopter rotor in hover is numerically evaluated.The tip Mach number of the rotor is about 0.625, and the Reynolds number based on the blade tip speed and chord length is about 3.78×10 6 .The variation range of the collective pitch angle is -3° ~ 18°, and the taper angle of the rotor is 2°.

The aerodynamic performance of the rotor in hover
Figure 7 and figure 8 show the curves of thrust coefficient (C T ) and torque coefficient (C Q ) of the rotor with the collective pitch angle.It should be noted that the collective pitch angle of the rotor is defined at the 75% radial location of the blade, which is expressed by θ 0.75 in the figures.In this paper θ 0.75 varies from -2.8° to 17.2° with an interval of 2°.It can be observed that with the increase of θ 0.75 , the thrust coefficient C T increases monotonously, but the increasing trend is not absolutely linear.The torque coefficient C Q changes in a parabolic trend with the increase of θ 0.75 .The value of C Q is the smallest when θ 0.75 is almost 0°.With the increase of θ 0.75 from 1.2° to 17.2°, the torque coefficient C Q gradually increases.Figure 9 shows the relationship curve between hover efficiency and thrust coefficient of the new rotor.The hover efficiency of the new rotor is expressed by FM similar to that in S-76 rotor validation case.The calculation formula of FM is as follows High value of FM indicates good hover efficiency of the rotor.It can be observed from figure 9 that with the increase of CT, the hover efficiency of the new rotor first increases and then decreases.When CT is about 0.0055 at θ0.75=9.2°, the hover efficiency reaches the maximum value, which is about 73%.When CT increases from 0.0055 to 0.0065 (θ0.75=11.2°), the hover efficiency decreases significantly.FM is about 65% at θ0.75=11.2°.Obviously, the change trend of FM with CT around the maximum hover efficiency is different from that of S-76 rotor.Hover efficiency is an important parameter to measure the performance of helicopter rotor in hover, and is an aerodynamic performance index to be first considered in helicopter rotor design.Therefore, it is necessary for us to improve aerodynamic design of the new rotor by analysing the reasons for the decline of hover efficiency.

The flow details of the rotor in hover
Figure 10 shows the iso-surface of Q value at θ 0.75 =9.2°.Q>0 can be used to distinguish the threedimensional flow vortices of fluid [20][21], and indicates the magnitude of the flow field vorticity tensor exceeding the strain rate tensor.The value of Q is related to the velocity scale and length scale of the flow field calculation.It can be observed that the wake angle of the blade tip vortex calculated in this paper can be resolved is about 650°.When the blade pulls out the tip vortex, it also pulls out the root vortex and vortex sheet structure, and the layer of the vortex sheet reaches more than 2. Figure 10 reflects the characteristics of the blade tip vortex strength declining with height and the characteristics of the blade tip vortex developing inward, which are in line with the actual physical laws.This fully demonstrates that the numerical method adopted in this paper has a high accuracy in capturing the features of vortex and wake in hover, and can effectively simulate the complex flow field and its detailed characteristics of helicopter rotor in hover.In order to further analyse the reasons for the decline of hover efficiency, this paper presents the spatial flow image near the blade tip at θ0.75=11.2°,as shown in figure 12 which shows the flow field details such as blade surface pressure, Mach number contour on spatial section and spatial streamlines.It can be seen that shock-induced separation also occurs near the leading edge of the upper surface near the blade tip, and there is a large zone of backflow after the shock wave at the trailing edge of the upper surface near the blade tip.Obviously, this is the flow separation phenomenon that does not occur at the trailing edge of the upper surface near the blade tip at θ0.75=9.2°.It can be inferred that the shock wave also appears at the leading edge of the upper surface near the blade tip at θ0.75=11.2°and the shockinduced separation occurs in the corresponding region.Due to the large angle of attack of the local incoming flow and the increase of local shock wave intensity, the airflow decelerates and pressurizes through the local shock wave at the leading edge to form a larger reverse pressure gradient.Then the flow stall at the trailing edge of the blade appears and results in serious flow separation.This is the main reason for the significant decline in hover efficiency of the new rotor at θ0.75=11.2°.

Conclusion
In order to meet the analysis requirements of hover performance of a new rotor, in this paper we use HeliX software to numerically predict the aerodynamic performance of the rotor in hover, and analyze the corresponding flow details.The comparison between numerical results and wind tunnel test data of S-76 rotor as a validation case of CFD method shows that the numerical method and grid generation strategy adopted for predictions of aerodynamic performance of helicopter rotor in hover in this paper are reasonable and reliable.The numerical results of the new rotor in hover suggest that the maximum hover efficiency of the new rotor is about 73% with collective pitch angle of 9.2°, while the shock induced separation and the reattachment phenomenon begin to appear on the upper surface near the blade tip.As the increase of collective pitch angle from 9.2° to 11.2°, hover efficiency decreases significantly due to the serious flow separation near the blade tip.The HeliX software application results of S-76 model rotor and a new helicopter rotor demonstrate that HeliX software with independent intellectual property rights has the capability to consistently and reliably predict performance parameters for a helicopter rotor, has the capability to capture blade tip vortex and wake features, and can effectively simulate the complex flow field characteristics of helicopter rotor in hover.The research in this paper can provide reference and guidance for aerodynamic optimization design of helicopter rotor.

Figure 1 .
Figure 1.The new helicopter rotor model.

Figure 2 .
Figure 2. Structured overlap grid of the new rotor in hover.

Figure 3 .
Figure 3. Blade sub-grid of the new rotor in hover.

Figure 6
Figure 6 shows the comparison between the CFD results and experimental results of S-76 rotor about thrust coefficient (CT), torque coefficient (CQ) and hover efficiency (Figure of Merit, FM).In the figure 6, the curves of CFD numerical results are represented by solidlines, and the curves of wind tunnel test

Figure 6 .
Figure 6.Comparison between the CFD results and experimental results of S-76 rotor about thrust coefficient, torque coefficient and hover efficiency.

Figure 9 .
Figure 9. Curve of hover efficiency with thrust coefficient.

Figure 11
Figure 11 shows the surface streamlines near the blade tip and Mach number contour on spatial section at θ0.75=9.2°.It should be noted that the θc in the figure indicates the collective pitch angle without considering the geometric collective of the blade.According to the actual twist distribution of the blade, the blade itself has a twist angle of 5.2° (geometric collective) at 0.75R.So there is a relationship θ0.75=θc+5.2°.It can be clearly observed that the local flow separation phenomenon and the reattachment phenomenon after flow separation begin to appear on the upper surface of the leading edge near the blade tip at θ0.75=9.2°.It can be inferred from the Mach number contour on spatial section that the flow separation is induced by the shock wave near the leading edge.Although the incoming flow decelerates and pressurizes through the local shock wave at the leading edge to form a reverse pressure gradient, due to the weakness of the local shock wave intensity, the reattachment phenomenon after flow separation then occurs.So there is no obvious flow separation at the trailing edge of the upper surface of the blade at θ0.75=9.2°.