Keywords

1 Introduction

As one of the dominant noise sources during the flight phases of taking-off and landing, high lift devices have always been a challenging problem to predict due to the complex and unsteady flow phenomena. During the past three decades, plenty of researches have been carried out to uncover the mechanisms of flow and consequent noise, especially on the slat noise.

However, most of current simulation studies are based on the full turbulence models, because the laminar–turbulent transition is not a major influence on the slat noise at low Reynolds numbers, which is the main focus [1]. Furthermore, the other studies, considering the transition effects, mainly focus on the flow but not the acoustic field.

In this study, a high lift configuration is numerically simulated and analyzed to compare the effects of the boundary layer transition. IDDES coupled with transition or turbulence models are occupied to predict the unsteady flow, and the FW-H equation is applied to obtain the far-field noise.

2 Numerical Method

In the present work, the open-source unstructured CFD solver Stanford University Unstructured (SU2) [2] is used. To accurately describe the unsteady turbulence, IDDES method is adopted with the shear-layer adapted length scale [3]. By combining the SST model [4] with the linear stability theory, the k-ω-γ model [5] introduces the intermittency factor γ into the modelled viscosity, thus adding transition effects while keeping the original SST equations unchanged. The combination method of IDDES-Tr has been published in the previous paper [6]. To achieve second-order accuracy in both space and time, Simple Low-dissipation AUSM (SLAU2) scheme with Monotone Upstream-Centered Schemes for Conservation Laws (MUSCL) approach and the backward Euler scheme with the dual-time stepping strategy are used.

The acoustic results are calculated by the in-house CFD solver [7], where the FW-H equation is solved with the most widely used Farassat 1A Formula. The integral surface could be either solid or penetrable, and the volume sources inside the penetrable surface are neglected.

3 Results and Discussion

In this study, the Reynolds number is 1.9 × 107 with C = 5 m. The freestream Mach number is 0.17 and the angle of attack is 5.5 deg. For both simulations, the time step is set to 0.0005 C/U∞, and the solution for the final 20 C/U∞ are statistically analyzed after the initial time of 10 C/U∞.

The near-field grid is shown in Fig. 1. The computational grid extends from the multi-element foil to 50 C in the x–y plane, and the permeable FW-H integral surface is along the mesh refinement region. The spanwise length is 0.3 C with 150 layers uniformly distributed in the spanwise direction and the overall mesh is 37 million.

Fig. 1
An area graph of Y versus X presents a mesh structure with a void in the shape, outer layer represents a permeable F W-H integral surface.

Near-field grid and the permeable FW-H integral surface

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Figure 2 presents the instantaneous flow structure with Q-criterion iso-surfaces. The resolution of the shear-layer instability and small-scale structures are very similar for both methods.

Fig. 2
6 heat maps of the instantaneous flow structures with Q-criterion is-surfaces. Top. I D D E S-T r presents very high intensity in the top corner and mild intensity in the middle. Bottom. I D D E S-F T presents very high intensity in the inner layer with low intensity in the middle.

Instantaneous flow structures with Q-criterion iso-surfaces

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Figure 3 presents the mean intermittency factor. γ grows from zero since the transition process starts and reaches one after the transition. Then the k-ω-γ model behaves as the SST model in the shear-layer, cove and separation regions.

Fig. 3
A heatmap of the mean intermittency factor presents a high intensity on the outer layer and a very low intensity outside.

Contour of mean intermittency factor

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The mean skin friction coefficients are shown in Fig. 4. For IDDES-Tr, pure laminar flows are shown on the lower slat surface and the lower flap surface. IDDES-Tr has smaller friction in the laminar region and larger friction after the transition. The flap boundary layer separation for IDDES-Tr is more downstream by about 1.5% C.

Fig. 4
3 multiline graph of C f versus X for I D D E S- T r and I D D E S-F T. A. It presents a steep straight rise and then a varying trend. B. It presents a straight rise and then a declining trend. C. It presents a steep straight rise and then a declining trend.

Mean skin friction coefficients (left: Slat; mid: main wing; right: flap)

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Figure 5 presents 2D streamlines and the distribution of mean Mach number. On the upper surface of each element, the maximum velocity is smaller for IDDES-FT than for IDDES-Tr, mainly due to the lower modelled viscosity in the laminar region. Thus, the separation region is smaller for IDDES-Tr in the streamwise and normal directions due to the difference in resistance to the negative pressure gradient.

Fig. 5
2 heatmaps of streamlining and the distribution. Top. I D D E S-T r presents high intensity in the outer layer with some very high intensity in the left corner. Bottom. I D D E S-F T presents a high intensity in the outer layer with a very high intensity in the left corner.

2D streamlines and the distribution of mean mach number

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Figure 6 presents the root-mean-square of the pressure coefficients (Cp,rms). IDDES-Tr has significantly lower pressure fluctuations in the attached flow regime. The relative difference decreases near the reattachment locations in the cove regions and after the separation location on the flap.

Fig. 6
3 multiline graphs of C p versus x for I D D E S-T r and I D D E S-F T. A. It presents a spike at minus 0.2 and rises to 0.3 then a declining trend. B. It presents a slow decline then a rising and a stable trend. C. It presents a steep rise up to 0.3 at 5 then a declining trend.

Root-mean-square of pressure coefficients (left: slat; mid: main wing; right: flap)

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Figure 7 presents the overall sound pressure level (OASPL) for different integral surfaces at r = 10 C. The Strouhal number range was set to [0.5, 1000]. The difference between the far-field noise from the solid wall and permeable surface is used to estimate the quadrupole noise [8]. The directivity for all integral surfaces has a dipole-like characteristic, while the quadrupole contribution has a monopole-like one. For the total noise from the permeable surface, IDDES-FT shows a noise increase at all angles compared to IDDES-Tr, and the maximum increase reaches 3.2 dB at θ = 300 deg. Among three elements, the main wing is the strongest noise source in most angles. The flap noise levels for IDDES-Tr and IDDES-FT are almost identical and differ slightly in the angles of the main peaks.

Fig. 7
2 polar plots of the far-field noise for different integral surfaces for O A S P L. Left. It presents an asymmetric circular pattern for all. Right. It presents a duel bend circular polarized trend.

Far-field noise for different integral surfaces

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4 Conclusion

Numerical simulations of a high lift configuration at Re = 1.9 × 107 are performed to assess the effects of the laminar–turbulent transition on the unsteady flow and noise. The flows are predicted by the IDDES method based on two models, and the acoustic results are obtained with the FW-H equation.

Regarding the transition effects, the following conclusions are summarized:

  1. 1.

    Both IDDES-FT and IDDES-Tr indicate similar flow mechanisms but different mean flow fields due to the transition effects. IDDES-Tr has lower Cf before the transition and larger outer-layer velocity. Therefore, a smaller flap separation region is calculated for IDDES-Tr. IDDES-Tr also has lower pressure fluctuations in the cove regions, which contribute to the far-field noise;

  2. 2.

    IDDES-FT indicates an increase in the OASPL at all angles up to 3.2 dB at θ = 300 deg. The same trend applies to the individual elements, except the slat. However, the slat has a small contribution, while the other two elements downstream are the dominant noise sources.