Grid density effect for numerical simulation of civil aircraft in post stall

Stall will deteriorate flight safety and cause serious accidents for civil aircraft. RANS-LES hybrid approaches have become a compromise choice due to insufficient ability of RANS for large flow separation. In present work, Zonal Detached-eddy-simulation coupled with high-order spatial scheme were employed to investigated grid density effect in the numerical simulations. The calculations show that the grid density would affect the numerical simulation of the small-scale flow structure in the wake of region of the main wing, and further affect the disturbance of main wing to the horizontal tail. It is necessary to properly densify the grid downstream of the main wing in order to accurately predict the aircraft stall.


Introduction
The development of the civil aviation industry has increased the demand for future aircraft performance.Stall characteristic is an important part of overall safety performance index of civil aircraft.The aircraft will stall when the actual flight angle of attack reaches the critical range with flow separation on the wing, simultaneously the lift drops suddenly with increasing drag.Aircraft stall results in nonlinear aerodynamics characteristics and deteriorated maneuverability, then flight safety threaten seriously, which is one of the important causes of flight accidents.
Computational Fluid Dynamics (CFD) method is playing an increasingly important role in aircraft design [1].Aircraft stall is a typical instability flow phenomenon associated with large flow separations, however, accurate prediction of flow separation during aircraft stall posed a challenge to turbulence modeling.Reynolds-averaged Navier-Stokes Equations (RANS) can provide accurate predictions in linear part of the lift, which has insufficient ability for large flow separation in stall.Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) are not affordable due to excessive grid requirements caused by complex geometry of aircraft [2].Therefore, RANS-LES hybrid approaches have become a compromise choice for researchers in complex flow separation.
High-quality computing grid is the prerequisite for accurate numerical prediction.However, it is impossible to increase the grid density without limitation.After all, the original intention of RANS-LES hybrid approach is alleviate excessive computing resources.At present, there is still no unified standard for grid, although the guide to Detached-Eddy Simulation Grids has been proposed by Spalart [3] which is based on personal experience.In present work, the grid density effect was discussed for civil aircraft stall, thus providing reference for industrial application of RANS-LES hybrid method.

Zonal Detached-eddy-simulation Model
According to the reasons for triggering the flow separation, ZDES approach divides the flow separation into three types including triggered by geometry, pressure gradient and the dynamics of inflow boundary layer.Only the first two types flow separations appear in this work.
Original ZDES [4] was based on Spalart-Allmaras model, however, the ZDES approach in this study was constructed based on the Menter's two-equation SST model [5], which has been validated in the flow around a multi-element airfoil [6].
The hybrid length scale, l hyb , was introduced in the turbulent kinetic energy equation of original model.In the flow separation triggered by the geometry, l hyb can be defined as Where l SST is original SST approach.In the flow separation triggered by the pressure gradient on the curve surface, where l hyb can be defined as The detailed description of the model constant C DES, the grid scale Δ and delayed function f d can be found in reference [6].

Other Numerical Method
The cell-centered finite volume method was applied in this study to discrete the governing equations, and Roe's scheme has been used to discrete the inviscid flux with fifth-order WENO interpolation in order to reduce numerical dissipation of spatial schemes.Moreover, the implicit time marching scheme is LU-SGS method.

Test Case
The Common research model (CRM), as shown in Figure 1, was employed in this study, including main wing with supercritical aerofoil, fuselage and horizontal stabilizers.CRM was developed jointly by the Subsonic Fix Wing Aerodynamics Technical Working Group of NASA and the Drag Prediction Workshop Organizing Committee, which represents a modern commercial transport aircraft [7].The mean aerodynamic chord of CRM is 0.189m, and the experimental data European Transonic Wind tunnel (ETW) [8] was employed in this study was performed by European Transonic Wind tunnel (ETW).

The Grid System
The grid effect was studied based on multi-block structured grid in present work.a O-type was applied in the boundary layer for mesh refinement, and at least 50 grid points were distributed in the near-wall region, first cell normal scale of 1×10 -6 which satisfies y + =1.Then a H-type grid topology in the other region.The grid topology and the local grid was presented in the Figure 2.
The influence of aeroelastic deformation of main wing was considered in present work.Transfinite interpolation method was employed to grid deformation, which has been validated for CRM, the detailed description can be found in Reference [9].

Unsteady Time Step
Steady calculation was performed before unsteady calculation for an initial flowfield.The dimensionless time step was set to Δt * =0.01 in the unsteady calculations, which corresponds to a physic time step of Δt=8.8×10 -6 s, with 25 sub-iterations each time step to ensure that the residual is reduced by at least two orders.As a result, it takes 400 time steps to flow through one mean aerodynamic chord.The statistical average time lasts for at least 100 mean aerodynamic chord, which takes more 20000 CPU hours.

Zonal calculation
RANS mode was performed in the fuselage region and the lower surface region of the main wing where is the windward side.Zonal DES was performed in the upper surface region of main wing, empennage region and wake region, and the computational grid point density in these region has also been improved.Zonal DES region has been presented in Figure 3.

The Grid Density Effect
The grid refinement was performed in different region based on local flow.The region between nose and wing leading edge has less grid points than other region, where the flow is attached.And because of the complex flow separation, the grid was refined in the region between main wing and horizontal tail, where the wake from main wing would affect the horizontal tail.The key parameters of fine and medium grid was listed in Table 1.Both grids have the same grid topology and the first cell height for normal grids in the boundary layer.The fine grid firstly was generated, then the grid scale was increased in the wake region to form the medium grid.4.1.Aerodynamic coefficient ZDES was implemented with medium and fine grid.Calculation was carried out at freestream mach number of 0.25, and the angle of attack is 18° which correspond to deep stall state.Table 2 Gives the lift and drag coefficient with computation and experiment.The drag coefficient predicted by medium and fine grid are same and can be consistent with the test result.The difference in lift coefficient is significant, however, the computational result of fine grid is consistent with the test and medium grid gives lower lift coefficient than the test.4. The difference between calculations and experiment mainly occurs in the inner wing region (η=20.1%),where the fine grid gives a better consistency with experiment than medium grid.However, computational pressure distributions are gradually consistent with the test from the middle to outer wing region, and the grids give little difference in the pressure distributions.

Instantaneous Flow
Instantaneous density gradient at η=28.3% are presented in Figure 5, which can reflect the influence of the main wing wake on the horizontal tail.The fine grid presents abundant small-scale flow structure.By contrast, the medium grid Excessive grid dissipation causes the wake vortex structure to be rapidly reduced in the downstream region, the phenomenon is significant after the x/c=6 in streamwise.The interference of wake vortices on the horizontal tail will affect the lift of the horizontal tail, consequently, which can be interpreted the difference in lift coefficient between fine and medium grid.

Conclusion
The flow separation in stall of civil aircraft at stall was predicted using ZDES approach, and two grids, fine and medium grid, was employed in the numerical simulations for investigating the grid density effect.The calculations and experiment were compared in pressure distributions in wing span and aerodynamic coefficients, then the interference of main wing wake to horizontal tail was discussed.
The fine grid presented good consistency with test in the lift, drag and distribution in main wing.However, the medium grid provided difference with experiment in counterpart due to the grid density in the region of flow separation.Furthermore, the grid scale would affect the wake solution in calculation, then the disturbance of main wing to the horizontal tail.Therefore, it is necessary to properly densify the grid downstream of the main wing in order to accurately predict the aircraft stall.

Figure 1 .
Figure 1.The NASA Common research model.

Figure 2 .
Figure 2. Grid topology (left) and the grid details on the wing (right).

Figure 4 .
Figure 4. Pressure Distribution on main wing

Table 1 .
The grid information.

Table 2 .
The lift and drag coefficient.