A novel hybrid method for aerodynamic noise prediction of high-lift devices

Jun TAO, Gang SUN

a Department of Aeronautics & Astronautics, Fudan University, Shanghai 200433, China

b Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, China

KEYWORDS

Abstract Aerodynamic noise of High-Lift Devices (HLDs) is one of the main sources of airframe noise, and has immediate impacts on the airworthiness certification, environmental protection and security of commercial aircraft.In this study, a novel hybrid method is proposed for the aerodynamic noise prediction of HLD.A negative Spalart-Allmaras (S-A) turbulence model based Improved Delayed Detached Eddy Simulation (IDDES) method coupling with AFT-2017b transition model is developed, in order to elaborately simulate the complex flow field around the HLD and thus obtain the information of acoustic sources.A Farassat-Kirchhoff hybrid method is developed to filter the spurious noise sources caused by the vortex motions in solving the Ffowcs Williams-Hawkings (FW-H) equation with permeable integral surfaces, and accurately predict the far-field noise radiation of the HLD.The results of the 30P30N HLD indicate that,the computational Sound Pressure Levels(SPLs)obtained by the Farassat-Kirchhoff hybrid method conform well with the experimental ones in the spectrum for the given observation point,and are more accurate than those obtained by the Farassat 1A method.Based on the hybrid method, the acoustic directivity of the HLD of a commercial aircraft is obtained, and the variation of the SPLs in the spectrum with the deflection angle of the slat is analyzed.

1.Introduction

Airframe noise has become a prominent source of the aircraft noise as the engine noise has been reduced greatly due to the development of high-bypass-ratio turbofan engine and the application of the technologies such as acoustic liner.During takeoff and landing phases, airframe noise has even been of the same order of magnitude as engine noise.Aerodynamic noise of HLDs is one of the main sources of airframe noise,and has attracted increased interest from scholars around the world.Physically, aerodynamic noise of HLD results from multi-scale, unsteady and complex flow phenomena, such as laminar-turbulent boundary layer transition and separation,shear layer mixing and transition, shock wave-boundary layer interaction, wake-boundary layer mixing, shear layer-wall interaction, etc.Furthermore, aerodynamic noises are essentially the weak pressure fluctuations varying with temporal and spatial distributions.For HLD, the aerodynamic noise is far less in the level of energy than the pressure fluctuations inside the flow field, and the spatial scale of the aerodynamic noise differs from the characteristic scale of the physical model significantly.All these make it more difficult to study the aerodynamic noise of HLD.

Scholars and research institutions from all over the world have carried out a large number of numerical studies on the important noise sources of HLD associated with the complex flow phenomena.Khorrami,1Choudhari,2–3and Lockard4et al.conducted numerical studies on the aerodynamic noise of HLD via Unsteady Reynolds-Averaged Navier-Stokes(URANS)methods,and analyzed the effects of flow structures on the aerodynamic noise, such as the shear layer around the slat cusp and the vortex shedding from the trailing edge of the slat.Zhang et al.5analyzed the acoustic characteristics of the 30P30N HLD via a Wall-Modeled Large Eddy Simulation(WMLES) method.Their results showed that the slat was the primary noise source, the main element contributing most to the low-frequency noise, and the flap was the smallest noise source.Huang et al.6simulated the near-field noise of an HLD configuration using Large Eddy Simulation (LES)method, and analyzed the generation mechanisms of the slat screech tones.Nebenfu¨hr et al.7performed numerical simulations for a three-element HLD configuration through an S-A turbulence model-based Detached Eddy Simulation (DES)method, and analyzed the effect of the turbulence structures in the slat cove on the aerodynamic noise.Terracol et al.8conducted numerical simulations for the 30P30N HLD via Delayed Detached Eddy Simulation (DDES) and Zonal Detached Eddy Simulation (ZDES) method respectively, and compared the results of the noise sources by the two RANS/LES methods with the experimental results.Sakai et al.9carried out numerical studies on the DLR-F16 HLD model through DES methods with five different sub-grid scales.By comparing with the experimental results, they analyzed the simulation accuracy and the spectrum characteristics of the aerodynamic noise via different DDES methods.Ashton et al.10conducted numerical simulations for the 30P30N HLD using structured and unstructured meshes respectively.By comparing with the experimental results, they analyzed the capability of the IDDES method to capture the detailed information of the noise sources in the flow.Abalakin et al.11performed numerical simulations for the 30P30N HLD using IDDES method, and analyzed the association of the noise sources with the noise spectral characteristics by comparing with the experimental results.

On the basis of the simulations for the near-field noise sources, various studies have been conducted for the far-field noise predictions of HLD.Ewert et al.12–15from German Aerospace Center (Deutsches Zentrum fu¨r Luft und Raumfahrt,DLR)developed Stochastic Noise Generation and Radiation (SNGR) method and Random Particle Mesh (RPM)method to obtain the mean flow field, and conducted a series of studies on the broadband characteristics of the aerodynamic noise of HLD by solving the acoustic perturbation equation.Dierke et al.16studied the noise interaction between the HLD and the engine by solving the linearized Euler equation based on the mean flow field.Zhang et al.17–19developed a series of far-field noise radiation prediction methods, and performed multiple simulations to predict the radiated airframe noise including the aerodynamic noise of HLD.Liu et al.20obtained the noise sources of the mean flow field via the SNGR method, and the far-field aerodynamic noise of an HLD configuration by solving the linearized Euler equation through the high-precision discontinuous finite element method.Li et al.21–23developed a series of engineering algorithms for predicting far-field aerodynamic noise,and successfully applied them to the aerodynamic noise prediction of HLD.Ko¨nig et al.24solved the acoustic perturbation equation and the FW-H equation respectively to predict the far-field aerodynamic noise and directivity of an HLD configuration on the basis of the near-field noise sources simulated via LES method, and pointed out that the slat noise is the dominant noise source of the HLD configuration.Kanjere et al.25predicted the far-field aerodynamic noise of an HLD configuration by solving the FW-H equation,and analyzed the effects of the spoiler on the spectral characteristics of the aerodynamic noise.Ma and Zhang26predicted and analyzed the aerodynamic noise characteristics of a leading-edge slatted HLD model by obtaining the aerodynamic noise sources via LES method and the far-field noise radiation through solving the FW-H equation.Khorrami and Mineck27conducted numerical simulations via the FUN3D codes combined with the FW-H method to obtain the noise characteristics of an 18%-scale, semi-span Gulfstream aircraft model, and validated the reliability of the employed method by comparing the computational results with the experimental ones.Salas and Moreau28analyzed the aerodynamic characteristics of an HLD configuration by combining the LES method with the FW-H method,and investigated the effects of the wind tunnel installation on the aerodynamic noise.Wang et al.29obtained the near-field noise source information of the 30P30N HLD via DDES method, analyzed the far-field aerodynamic noise characteristics by solving the FW-H equation, and studied the influences of the slat parameters on the aerodynamic noise.

From the existing studies,the hybrid method combining the CFD method with the acoustic analogy method (solving the FW-H equation) has become the most effective and feasible way for the aerodynamic noise prediction of HLD.Accurate CFD simulations lay the foundation for the aerodynamic noise prediction.However,in most of the current studies,CFD simulations for the aerodynamic noise prediction of HLD are conducted based on fully turbulent computations, and the laminar-turbulent transition is rarely considered.Furthermore,the most widely used method for solving the FW-H equation is the Farassat 1A Formula.Nevertheless,it has been shown that the Farassat 1A Formula cannot filter the spurious noise sources caused by the vortex motions when there are vortical flows through the permeable integral surfaces.30–33

Given the above,a novel hybrid method is proposed for the aerodynamic noise prediction of HLD.In order to simulate the noise sources of HLD,a negative S-A turbulence model based IDDES method coupling with AFT-2017b transition model is developed.Besides, a Farassat-Kirchhoff hybrid method is developed to filter the spurious noise sources caused by the vortex motions across the permeable integral surfaces in solving the FW-H equation.Finally, numerical simulations are performed to the 30P30N HLD and the HLD configuration of a commercial aircraft based on the proposed method, and the aerodynamic noise results are obtained.

The remainder of this paper is organized as follows.In Section 2,the numerical methods and validations for flow field are performed.In Section 3, the prediction method for the aerodynamic noise is introduced.In Section 4, two computational cases are presented and analyzed based on the proposed method.In Section 5, some conclusions are drawn according to the previous results and analyses.

2.Numerical methods and validation for flow field

2.1.Numerical methods for flow field

In this study, a negative S-A turbulence model based IDDES method coupling with AFT-2017b transition model is developed, in order to simulate the flow field around the HLD and thus obtain the information of acoustic sources.

In order to suppress the non-physical solutions caused by the source term of the S-A turbulence model, the source term is modified and the following negative S-A turbulence model34is adopted.

For the purpose of incorporating boundary layer transition of HLD and capturing more flow details,the AFT-2017b transition model is employed.The AFT-2017b transition model35is defined by the following two equations:

The AFT-2017b transition model is coupled with the negative S-A turbulence model through the following equation,and the model determines the onset of transition when the amplification factor n～reaches a critical value Ncrit.

By combining DDES method and WMLES method, an IDDES method is developed on the basis of the negative SA turbulence model and AFT-2017b transition model.In the IDDES method, the length scale of DDES branch is given by

where lRANSis the length scale of RANS, fdis the delay function,CDESis a constant,and ψ is the coefficient function of the grid scale Δ.

The length scale of WMLES branch is given by

where fBis the hybrid function, and feis the evaluation function.

Then the length scale of IDDES branch is expressed as

As for the spatial discretization, the ROE scheme36is adopted for the inviscid flux terms where the 5th order WENO-Z scheme37is adopted for the high order reconstruction, and the 4th order centered difference scheme38is employed for the viscous flux terms.An implicit dual time stepping method39with a pseudo time sub-iteration is used for time discretization where the LU-SGS scheme is employed in the sub-iteration.

2.2.Validation of numerical methods

2.2.1.Validation of negative S-A turbulence model

Numerical simulations based on RANS method are performed for the NACA0012 airfoil using the original S-A turbulence model and the negative S-A turbulence model, respectively,and the results are compared with the experimental ones.

Fig.1 shows the computational grid of the NACA0012 airfoil, and the grid number of the entire computational domain is about 2.5 × 105.The computation conditions are set as:Ma = 0.3, Re = 6 × 106.

Fig.240shows the comparison of the pressure coefficients between the computational results and the experimental ones for the NACA0012 airfoil under the Angle of Attack (AOA)of 9.86°.It can be seen from the comparison that the pressure coefficient distributions obtained by the negative S-A turbulence model are slightly closer to the experimental ones than those obtained by the original S-A turbulence model.

Fig.341shows the comparisons of the computational lift coefficient curves with the experimental curve for the NACA0012 airfoil.As shown in the figure, when the AOA is small, the results obtained by the original S-A turbulence model are almost the same as those obtained by the negative S-A turbulence model.When the AOA is larger than 10°, the results obtained by the negative S-A turbulence model are slightly smaller than those obtained by the original S-A turbulence model.Comparing the two computational lift coefficient curves with the experimental results, we can see that the lift coefficients obtained by the negative S-A turbulence model are closer to the experimental ones than those obtained by the original S-A turbulence model.

Fig.441shows the computational drag coefficient curves compared with the experimental curve for the NACA0012 air-

Fig.1 Computational grid of NACA0012 airfoil.

Fig.2 Comparison of pressure coefficients between computational results and experimental ones for NACA0012 airfoil(AOA = 9.86°).

Fig.3 Comparisons of lift coefficient curves for NACA0012 airfoil.

From the above comparison results for the NACA0012 airfoil, it can be concluded that the results obtained by the negative S-A turbulence model agree very well with the experimental ones in general,which thus verifies the reliability of the negative S-A turbulence model.

2.2.2.Validation of AFT-2017b transition model

In order to validate the AFT-2017b transition model, numerical simulations based on RANS method are conducted to the NLF (1)-0416 airfoil, and the computational results are compared with the experimental ones.

Fig.5 shows the computational grid of the NLF (1)-0416 airfoil, and the grid number if the entire computational domain is about 2.5 × 105.The computational conditions are set as: Ma = 0.1, Re = 2 × 106.

Fig.642shows the computational lift-to-drag polar curve of the NLF (1)-0416 airfoil compared with the experimental results.As shown in the figure, the computational lift-todrag polar curve conforms well with the experimental one.

Fig.742shows the computational transition positions of the NLF(1)-0416 airfoil compared with the experimental ones.It is worth mentioning that the experimental results do not provide the exact transition positions, but the transition regions instead.As can be seen from the figure, the computational transition positions of the NLF(1)-0416 airfoil are all located within the transition regions of the experimental results for both the upper and lower surfaces.

From the comparisons above, it can be seen that the computational lift coefficients, drag coefficients, and transition positions of the NLF(1)-0416 airfoil are in good agreement with the experimental results, which indicates that the numerical method coupling the AFT-2017b transition model with the negative S-A model is highly reliable.

The validation of the negative S-A turbulence model based IDDES method coupling with the AFT-2017b transition model is illustrated in Section 4.

3.Prediction method for aerodynamic noise

Fig.4 Comparisons of drag coefficient curves for NACA0012 airfoil.

foil.As can be seen, the lift coefficients obtained by the negative S-A turbulence model are basically the same as those obtained by the original S-A turbulence model, and conform well with the experimental ones.

In this study,the FW-H equation with permeable integral surfaces is solved to predict the aerodynamic noise in far field based on the acoustic sources obtained by the numerical simulations of flow field.In general, the following Farassat 1A Formula43is widely used for solving the FW-H equation with permeable integral surfaces.

Fig.5 Computational grid of NLF (1)-0416 airfoil.

Fig.6 Computational lift-to-drag polar curve of NLF(1)-0416 airfoil compared with experimental results.

Fig.7 Computational transition positions of NLF(1)-0416 airfoil compared with experimental results.

However, during the derivation of the Farassat 1A Formula, the spatial derivative is converted into the temporal derivative,so the Farassat 1A Formula fails to filter the spurious noise sources caused by the vortex motions through the permeable surfaces.33In order to avoid or suppress the spurious noise sources,various methods based on some approximations and assumptions have been developed,such as equivalent source method,30,44spatial averaging technique,45–48and frozen turbulence.32,49–50In this study, the three-dimensional Kirchhoff frequency domain formula shown as follows is employed to filter the spurious noise sources because no spatial derivative is converted into temporal derivative.

As for solving the FW-H equation with permeable integral surfaces, although the Kirchhoff formula is able to filter the spurious noise sources, its solution process is extremely complicated, which costs a large amount of computation.However, Farassat 1A Formula is more efficient than the Kirchhoff formula due to no operation of the spatial derivative.Therefore, a Farassat-Kirchhoff hybrid method is employed in this study in solving the FW-H equation with permeable integral surfaces in order to balance the accuracy and efficiency of the aerodynamic noise prediction.Taking the aerodynamic noise prediction of HLD as an example, the three-dimensional Kirchhoff frequency domain formula is used on the integral surface in the wake region where the vortex motions are vigorous, while the Farassat 1A Formula is used on the other integral surfaces where the vortex motions are gentle.

4.Computational cases of aerodynamic noise

4.1.30P30N HLD

The 30P30N HLD is the configuration studied by AIAA BANC-II (The Second Benchmark Problems for Airframe Noise Computations) Workshop.Fig.8 shows the geometry of the 30P30N HLD, where the geometric chord length is 0.4572 m.The chord lengths of the slat and flap are 0.15 and 0.3 times that of the whole airfoil,respectively, and the deflection angles of the slat and flap are both 30°.

The negative S-A turbulence model based IDDES method coupling with AFT-2017b transition model is employed to perform the numerical simulations of flow field for the 30P30N HLD.Fig.9 shows the grid schematic of the 30P30N HLD,the span length of the computational model is set to 1/9 of the chord length according to the recommendations of the AIAA BANC-II Workshop,and the grid number of the entire computational domain is about 2.9 × 107.

In order to validate the accuracy and reliability of the method for predicting the aerodynamic performance of the 30P30N HLD, the chord length of the computational model is set to 0.5588 m with reference to Ref.51, and the computational conditions are set as:Ma=0.2,Re=5×106,Δt = 2.5 × 10-5s.

Fig.8 Geometry of 30P30N HLD.

Fig.9 Grid schematic of 30P30N high-lift devices.

Fig.10.51shows the comparison of the computational lift coefficients with the experimental ones for the 30P30N HLD.As shown in the figure, the lift coefficients obtained by the IDDES method agree well with the experimental ones.Meanwhile, the computational maximum lift coefficient and stall angle are basically the same as the experimental ones.

In order to validate the accuracy and reliability of the method for predicting the pressure coefficient distributions and aerodynamic noise of the 30P30N HLD, the chord length of the computational model is set to 0.4572 m with reference to Ref.52, and the computational conditions are set as:AOA=10°,Ma=0.17,Re=1.71×106,Δt=2.5×10-5s.

Fig.11.52shows the computational pressure coefficient distributions compared with the experimental ones for the 30P30N HLD.As can be seen, the computational pressure coefficients conform well with the experimental ones, with slight differences on the slat.

Moreover, in order to validate the accuracy and reliability of the method for predicting the boundary layer transition of the 30P30N HLD, the chord length of the computational model is set to 0.5588 m with reference to Ref.53, and the computational conditions are set as: AOA = 8°, Ma = 0.2,Re = 9 × 106, Δt = 2.5 × 10-5s.

Table 153shows the computational transition locations compared with the experimental ones (x/c) for the 30P30N HLD.It is worth mentioning that the experiment only provided the transition locations on the upper main surface, and the lower the main surface, the upper the flap surface.As can be seen from Table 153,the computational transition locations are in good accordance with the experimental ones.

Fig.10 Computational lift coefficients compared with experimental ones for 30P30N HLD.

Fig.11 Computational pressure coefficients of 30P30N HLD compared with experimental ones.

Table 1 Computational transition locations compared with experimental ones.

Fig.12 Schematic of permeable surfaces for 30P30N HLD.

In order to predict the aerodynamic noise, the permeable surfaces shown in Fig.12 are used for solving the FW-H equation.On the basis of the permeable surfaces, the Farassat 1A method and the Farassat-Kirchhoff hybrid method are employed respectively to predict the far-field aerodynamic noise of the 30P30N HLD.As for the Farassat-Kirchhoff hybrid method, the Farassat 1A Formula is implemented on Surface 1, and the three-dimensional Kirchhoff frequency domain formula is implemented on Surface 2.As for the Farassat 1A method,the Farassat 1A Formula is implemented on both Surfaces 1 and 2.

Figs.13 and 14 show the computational spanwise vorticity magnitude of the whole 30P30N HLD and that near the slat region.As can be seen,high vorticity magnitudes are observed in the slat cove, the flap cove, the shedding region at the trailing edge of the slat,and the shedding region at the trailing edge of the flap, which contribute significantly to the overall noise.

Fig.15 shows the Q criteria of the 30P30N HLD colored by the velocity in x direction.As shown in the figure, there are obvious vortex structures at the slat cove, the flap cove, the trailing edge of the slat,and the upper surface and trailing edge of the flap.These vortex structures are significant sources of the aerodynamic noise.

With reference to the location of the microphone set in the wind tunnel test in Ref.48, an observation point located 1 m below the 30P30N HLD is given for the prediction of the far-field aerodynamic noise.Fig.1648gives the computational spectral SPL results at the observation point compared with the experimental results for the 30P30N HLD.From the comparison in Fig.16, the computational SPLs obtained by the Farassat-Kirchhoff hybrid method agree well with the experimental results.In addition, the computational SPLs obtained by the Farassat-Kirchhoff hybrid method are very close to those obtained by the Farassat 1A method in the low frequency range, and are relatively smaller than those obtained by the Farassat 1A method in the high frequency range (especially over 10000 Hz).By employing the Farassat-Kirchhoff hybrid method, the spurious noise sources caused by the vortex motions in the wake region are filtered.Since the aerodynamic noise in the high frequency range is closely related to the vortex motions in the wake region, the computational SPLs obtained by the Farassat-Kirchhoff hybrid method in the high frequency range are smaller than those obtained by the Farassat 1A method.

Table 248shows the computational Overall Sound Pressure Levels (OASPLs) obtained by both the Farassat-Kirchhoff hybrid method and the Farassat 1A method compared with the experimental OASPL.As can be seen, the computational OASPL obtained by the Farassat-Kirchhoff hybrid method is very close to the experimental one, and is smaller than that obtained by the Farassat 1A method due to the filtration of the spurious noise sources.

Therefore, it can be concluded that the Farassat-Kirchhoff hybrid method filters the spurious noise sources caused by the vortex motions and obtains more accurate aerodynamic noise prediction results compared with the Farassat 1A method,which validates the accuracy and reliability of the Farassat-Kirchhoff hybrid method developed in this study.

Fig.13 Spanwise vorticity magnitude of 30P30N HLD.

Fig.14 Spanwise vorticity magnitude near the slat of 30P30N HLD.

Fig.16 Computational spectral SPL results at observation point compared with experimental results for 30P30N HLD.

Table 2 Comparison of OASPLs for 30P30N HLD.

4.2.HLD of a commercial aircraft

On the basis of the Farassat-Kirchhoff hybrid method,further simulations are conducted to the HLD of a commercial aircraft and the aerodynamic noise characteristics of the HLD are analyzed.

Fig.17 shows the cross section of the HLD extracted from a commercial aircraft and the three-dimensional computational model of the HLD.The chord length of the HLD configuration is 3.52 m.

Numerical simulation for flow field is performed via the developed IDDES method to obtain the information of the acoustic sources.Similarly, the span length of the computational model is also set to 1/9 of the chord length following the suggestion of the AIAA BANC-II Workshop.Fig.18 shows the 2D view of the computational grid, and the grid number of the entire computational domain is about 2.9 × 107.The computational conditions are set as:AOA = 8°, Ma = 0.2, Re = 6 × 106, Δt = 2.5 × 10-5s.

Fig.19 shows the permeable surfaces of the HLD configuration for solving the FW-H equation.In the same way, the Farassat-Kirchhoff hybrid method is implemented through using the Farassat 1A Formula on Surface 1 and using the three-dimensional Kirchhoff frequency domain formula on Surface 2.

Fig.20 shows the computational spanwise vorticity magnitude of the HLD configuration.As can be seen,there are high vorticity magnitude regions in the slat cove, the flap cove, the trailing edge of the slat,and the trailing edge of the flap,which contribute greatly to the overall noise.

Fig.21 shows the Q criteria of the HLD configuration colored by the velocity in x direction.As can be seen, obvious vortex structures are distributed in the regions of the slat cove,the flap cove,the trailing edge of the slat,and the upper surface and trailing edge of the flap, which are significant sources of the aerodynamic noise.

In order to investigate the acoustic directivity of the HLD configuration, as shown in Fig.22,36observation points are positioned uniformly, at the circle of which the center is the trailing edge of the slat and the radius is 12 m.

Fig.23 shows the computational acoustic directivity results of the HLD configuration.As can be seen, the radiated noise mainly influences the first, the third and the fourth quadrants.The highest SPL is observed at the directivity of θ=290°,and the second highest SPL is observed at θ = 300°.

Fig.24 shows the spectral SPL results at the observation point directly beneath the HLD configuration (θ = 270°).As can be seen, the low-frequency noise is more obvious than the high-frequency noise.The single-frequency peak of the noise is 74.2 dB, which occurs at the frequency of about 902 Hz.

Fig.17 Cross section and computational model of the HLD of commercial aircraft.

Fig.18 Computational grid of HLD configuration (2D view).

Fig.19 Schematic of permeable surfaces for HLD configuration of commercial aircraft.

Fig.21 Q criteria of HLD configuration of commercial aircraft,colored by the velocity in x direction.

Furthermore, in order to investigate the impact of the deflection angle of the slat on the aerodynamic noise, numerical simulations are performed for two HLD configurations with different deflection angles of the slat.Compared with the baseline configuration,the slats of the two HLD configurations are deflected downward by 4° (δ = -4°) and 8° (δ =-8°), respectively.Fig.25 shows the spectral SPL results of the two HLD configurations with different deflection angles of the slat at the observation point (θ = 270°) compared with those of the baseline configuration.As can be observed, the aerodynamic noise tends to increase as the deflection angle of the slat becomes bigger.

Fig.22 Observation circle around HLD configuration.

Fig.23 Computational acoustic directivity results of HLD configuration.

Fig.24 Spectral SPL results at observation point directly beneath HLD configuration (θ = 270°).

Fig.25 Spectral SPL results of two HLD configurations with different deflection angles of slat at observation point (θ = 270°)compared with those of baseline configuration.

5.Conclusions

In this study,a novel hybrid method is proposed for the aerodynamic noise prediction of HLD.

In order to elaborately simulate the complex flow field around the HLD and thus obtain the information of acoustic sources,an IDDES method is developed based on the negative S-A turbulence model coupling with the AFT-2017b transition model.Numerical simulations for the NACA0012 airfoil validate the accuracy and reliability of the negative S-A turbulence model, while numerical simulations for the NLF (1)-0416 airfoil validate the accuracy and reliability of the AFT-2017b transition model.Then, CFD simulations are conducted to the 30P30N HLD, and by comparing with the experimental results, it is indicated that the developed IDDES method is reliable for the flow field simulation of HLD.

As for far-field aerodynamic noise prediction, the FW-H equation with permeable integral surfaces is solved.For the purpose of filtering the spurious sound sources caused by the vortex motion across the permeable integral surfaces, a Farassat-Kirchhoff hybrid method is developed to solve the FW-H equation.The results of the 30P30N HLD indicate that the computational spectral SPLs obtained by the Farassat-Kirchhoff hybrid method agree well with the experimental ones for the given observation point, and are more accurate than those obtained by the Farassat 1A method.

Finally, based on the hybrid method, numerical simulation is performed for the HLD of a commercial aircraft.The acoustic directivity of the HLD configuration is obtained, and the variation of the spectral SPLs with the deflection angle of the slat is analyzed.Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was co-supported by the Shanghai Pujiang Program,China(No.20PJ1402000),the Open Project of Key Laboratory of Aerodynamic Noise Control, China (No.ANCL20200302) and Shanghai Key Laboratory of Aircraft Engine Digital Twin, China (No.HT-6FTX 0021-2021).