• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Effects of geometry variations on tandem airfoil interaction noise

    2020-08-08 02:46:28ZHANGChiSONGWenbin
    空氣動力學學報 2020年3期
    關鍵詞:接收點遠場聲壓級

    ZHANG Chi, SONG Wenbin

    (School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China)

    Abstract:Interaction noise of a tandem airfoil configuration is studied using high-order large eddy simulations (LES) methods on a multi-block structured grid. The sound could be generated from aerodynamic interactions between the two airfoils positioned one after the other. The flow field is first calculated, and spectral properties of pressure fluctuations at a few given observation points are analyzed. The far-field noise obtained using FW-H integration is presented for the base configuration. The interaction from the wake of the airfoil in the front could interact with the leading edge of the trailing airfoil for specific configuration settings. The geometric features of both airfoils are also varied simultaneously to study the combined effects on the noise. The impact of geometric characteristics of trailing-edge and leading-edge of the front and rear airfoil, respectively, is the focus of the research. A typical surrogate-based approach is deployed in this study to reduce computational costs. The results show that, by careful tuning of the geometry and configuration, aeroacoustic characteristics of the tandem airfoil configuration could be modified to achieve lower acoustic levels.

    Key words:aeroacoustics; high order scheme; tandem airfoil; interaction noise; FW-H method; response surface

    0 Introduction

    The noise standards for commercial aircraft operating in civil airspace surrounding airports are becoming increasingly stringent. The proposal from the Advisory Council for Aviation Research in Europe (ACARE) aims to achieve a 10 dB reduction by 2020[1]. Compared with the present Chapter 4 standard, the noise standard introduced by the International Civil Aviation Organization (ICAO) in February 2010 requires civil aircraft airworthiness noise emission to be reduced by 7 EPNdB[1]. The goal of N+3 generation NASA research aircraft wished to gain a 52 dB reduction in combined noise levels by 2025 compared to that of aircraft entering service in 2000[1]. Huge challenge is faced by engineers considering the gap between the state of the art and ambitious objectives set by the relevant organizations.

    Aircraft noise comes primarily from two sources, including airframe noise and engine noise. Both need to be reduced to a comparable level to achieve the overall objective of noise reduction. Aerodynamically generated noise is a major mechanism for aircraft noise. Two primary sources for aircraft noise are landing gear and high-lift devices. A number of different noise generation mechanisms have been identified in the literature. The interaction noise between two airfoils placed in tandem configuration has gained interest because it represents one of many typical configurations for aerodynamic noise generation. For example, high bypass ratio turbofan engine and contra-rotating open rotor (CROR) engine may lead to further reductions in fuel consumption, but will likely lead to higher noise levels compared to the current turbofan engines. The levels of noise generated from the interactions between rotor/stator in the turbofan engine and front/aft rotor in CROR can be higher than that of the self-noise of the rotor. In the take-off and landing configurations, the wake and vortex of the main wing would also interact with the horizontal tails. In these cases, interaction noise becomes one of the dominant sources. Such a configuration, though slightly different type, can also be found in typical landing gear configurations, in which, the wake shed from components in the upstream interacts with components in the downstream, generating a major source of noise for the take-off and landing configurations. The interactions of the wake from the front airfoil with the second airfoil are the primary research focus of the current paper.

    Changes in the geometry of leading-edge and trailing edge ofairfoils, rotors or stators and their relative position will alter the surrounding flow field, hence leading to changes in the noise generation as well as aerodynamic characteristics of the configuration. To accurately predict the noise level and study possible means for noise reduction, simplified configurations of two cylinders or rod and airfoil placed in tandem were studied widely in the literature. However, for tandem airfoil configurations, most related studies were focused on the aerodynamic performance. Studies on acoustic characteristics with numerical methods are relatively insufficient to the authors’ knowledge. There are several mechanisms of the sound generation of an airfoil in the flow field. Such noise can be divided into two categories: tonal noise and broadband noise. Broadband noise generated from the turbulence of flow is highly disordered. Therefore, the noise covers a broader spectrum of frequencies. The tonal noise is typically related to the flow feature with a certain stable periodic pattern. The noise sources of isolated airfoil include the following four items according to the paper by Migliore and Oerlemans[2]:

    a) Turbulent boundary layer-trailing edge noise.

    b) Laminar boundary layer-vortex shedding noise.

    c) Separation stall noise.

    d) Trailing-edge bluntness noise.

    The presence of the rear airfoil in the tandem configuration leads to interaction noise, and also self-noise of rear airfoil into the domain. The wake and the vortex shedding from the front airfoil will possibly impinge on the leading edge of the rear airfoil, hence generating interaction noise, which is affected by the geometry of both airfoils.

    This paper presents a computational study into the effects of changes in the geometry of the leading edge of the rear airfoil and trailing edge of the front airfoil could have on far-field noise. LES (Large Eddy Simulation) method from an in-house code is adopted in this paper to calculate the flow field. The far-field noise is obtained by FW-H method. The methodology used in the current paper is validated against benchmark cases to demonstrate its capability for noise prediction. NACA 0012-63 is chosen as the baseline airfoil in this paper. Mach number is kept constant as the takeoff and approach speed of aircraft is nearly 0.2 with a Reynolds number of 105. The combined effects of geometry variation from two airfoils are studied. The conclusions are drawn on the noise implications. This could be coupled with aerodynamic analysis in further studies.

    This paper is organized as follows: Section 1 presents the related work about the models and numerical methods. Section 2 introduces the methodology used for modeling the flow and calculating the sound. Validation is given by comparing results with benchmark cases. Section 3 presents the calculation result of the case using NACA 0012-63. Furthermore, a surrogate-based approach is used to study the geometry variations of the trailing edge of the front airfoil and the leading edge of the rear airfoil. Section 4 concludes the results obtained from the last section.

    1 Related work

    1.1 Typical models and configurations

    Tandem cylinder and rod-airfoil models have been investigated by many researchers using numerical and experimental methods. The widely mentioned tandem cylinder experiments were conducted in NASA Langley Research center at the Basic Aerodynamic Research Tunnel (BART) and Quiet Flow Facility (QFF). Experimental results revealed some flow features in this configuration with the two spaced at a diameter ratio of 1.435 and 3.7[3], respectively. Fifteen tandem cylinder solutions on the First Workshop on Benchmark problems for Airframe Noise Computations were summarized in the paper by Lockard[4]. There were also other studies related to the configuration, many of which are focused on flow control technology.

    Rod-airfoil interaction noise generated at low Mach number was investigated numerically by Casalino[5]with 2D URANS method. The spanwise effects were introduced into the time-domain formulation of the FW-H analogy by a statistical model. The results with spanwise correction compared very well to the accompanying experiment. Jacob conducted a low Mach number test on rod-airfoil in the large anechoic wind tunnel of the Ecole Centrale de Lyon, and a 2D URANS combined with a spanwise stochastic model was compared with the experiment[6]. Two CAA (Computational AeroAcoustics) methods were compared and validated with Jacob’s experiment by Schell[7]. A direct noise calculation with compressible DES (Detached Eddy Simulation) and a hybrid method with DES and Lighthill analogy were applied with StarCCM+. The calculations were three dimensional with a span of 0.3 m, which were the same as in the experiment. An incompressible LES coupled with Lighthill’s equation was used to predict the noise of rod-airfoil by Eltaweel[8]and again compared with Jacob’s[6]experiment. Most of these works identified that the leading edge is the dominant sound source.

    The effects of the geometry of isolate airfoil on the turbulent noise were studied numerically by Gill[9]. The dominant noise reduction mechanism was found to be related to the thickness and leading-edge radius of NACA series airfoil. The result was compared with an analytic flat plate that over-predict the noise by 3 dB at high frequencies. Paruchuri[10]extended Gill’s work to experiment with airfoil printed by 3D printer. Their work focused on the interactions of an isolated airfoil with the gust of a specific wavelength.

    As to the tandem airfoil configuration, most of the related studies were based on the background application in turbomachinery. McGlumphy[11]investigated the feasibility of using a tandem rotor in the rear stage of a core compressor. Laurent[12]studied the aerodynamic performance of tandem airfoil under a high angle of attacks. Shirsath[13]explored the effect of the angle of attack of the rear airfoil on unsteady aerodynamic quantities. It is to the author’s best knowledge that the aeroacoustics characteristics of two airfoils in a tandem configuration have not been sufficiently studied in the reported literature.

    It can be seen from the above that most of the researches focused on the flow condition and the geometry effects of an isolated airfoil. And the turbulence interaction is modeled with isotropic turbulence or generated by the wake of a rod. The wake of an airfoil and the geometry effect on interaction noise have not been studied numerically yet. In this paper, the background application the configuration corresponds to the take-off and approach flight conditions of aircraft. The flow conditions in the calculation stay unchanged while geometries of the two airfoils were varied.

    1.2 Numerical study

    In a typical CAA approach, three distinct phases are often used, including the calculation, extraction and characterization of the noise source, propagation calculation and analysis of noise levels at the receiving points. Accurate identification of noise sources using either numerical and experimental methods is a challenge. Numerical methods have a long term potential value as these can be integrated into the design process to study the effects of relevant factors such as geometry, configuration, and the effectiveness of noise reduction measures. It has become common practice to use RANS in aerodynamic design in industry settings on complex configurations; this has not been possible for noise calculations on realistic configurations due to the extremely high computational cost. Significant efforts are still required from the three areas of noise generation, propagation and characterization of observed noise. The current study focused on the problem of broadband noise generation for tandem airfoil configurations in order to further the state-of-the-art in the fields, development of hybrid approach appropriate for the simulation, improved understanding, characterization of noise generation mechanisms and more efficient numerical algorithms on massively parallel high-performance computing facilities.

    Jacob[5]also compared 2D URANS with 3D URANS and concluded that though 2D URANS over predicted the shedding frequency, the 3D URANS did not improve the shedding frequency significantly because of the intrinsic deficiency of the URANS formulation. Yi Jiang studied the rod-airfoil interaction noise with high order LES method[14]. The spacing between the rod and airfoil was studied as well. It was found that three modes of interaction exist for the variation of spacing.

    Liu[15]studied the trailing edge serration technology on the interaction noise of tandem airfoil without looking at other geometry variations. The chosen airfoil is the NACA-65 series, which was widely used in the propeller design. The aft airfoil is placed in the mirrored vertical direction. Chen[16]investigated the geometry optimization of a tandem airfoil at a low Mach number on aerodynamic performance. The geometry and relative positions are varied with 23 design variables in total.

    2 Numerical methods and validation

    2.1 Sound source and acoustic analogy model

    Far-field noise is obtained by the acoustic analogy method based on a two-step approach. First, the unsteady flow field around the sound source is simulated with CFD method; Second, the scattering of the sound wave is calculated by solving the wave equation. In this paper, the flow field for acoustic calculation is obtained from the result of LES method. Far-field noise is calculated with the sound analogy model FW-H.

    In the current work, LES is used to investigate the noise mechanism of tandemairfoil. A fifth-order weighted essentially non-oscillatory (WENO) scheme is used in the study. Roe method is used for the flux splitting. The temporal integration used is LU-SGS approach. The subgrid-scale (SGS) turbulence model used in this paper is the Smagorinsky-Lilly model. Far-field boundary condition is obtained with the method based on Riemann invariant from the 1-D inviscid flow. Side boundary is set as a symmetric boundary condition.

    2.2 Validation using turbulent rod configuration

    The experimental data fromBoudet for turbulent rod configuration is used to validate the numerical methods[17]. This configuration is a cylinder flow with an inflow speedU0=72 m/s, temperatureT=293 K andρ=1.2 kg/m3. Reynolds number based on rod diameter is 46000. A circular computational domain with a radius of 80D is used. The computation mesh used is a 181×181×31 sized structured grid. The first layer thickness is chosen as 0.05D(Dis the diameter of the rod andD=0.01m). A growth rate of 1.0359 is used.

    The first layer thickness in this paper is varied to investigate its effect on far-field noise. Three values were chosen for the first layer thickness, 0.05D, 0.013Dand 0.005D, which correspond toy+(yplus value) of 3.8, 1 and 0.38, respectively. Circumferential points at Case 2 is increased to study the effect ofx+(relative to the definition ofy+). The non-dimensional time step is set as Δt=0.002. The total flow time is chosen as 100,000 time steps. Acoustic data is sampled every time step, and the sampling frequency is 360 kHz. Table 1 shows the aerodynamic results of different first layer thickness. It can be seen that lowery+value gives a better shedding frequency. The drag coefficients and lift coefficients from these cases did not show much difference.

    Figure 1 shows the power spectra density (PSD) of pressure fluctuation in 70D. Seo[18]obtained the result from a two-dimensional LPCE (Linearized Perturbed Compressible Equations) computation with input from LES result. A sixth-order finite difference scheme was used. Strohal number is 0.19 in the experiment. It can be seen that controlling they+value at 1 can obtain better frequency result in comparison with the results obtained by others. For case 2, though the results slightly over predicted the peak frequency, the value agrees reasonably well with the aerodynamic result. It should be noted that only numerical results of pressure at location (0, 70D) was found in the published paper. Therefore, the overprediction at high frequency may result from that smaller scales flow structure was resolved by the finer grid.

    表1 不同網格的圓柱氣動結果Table 1 Aerodynamic results of rod using different grids

    圖1 點(0, 70D)處的壓力脈動自相關頻譜圖Fig.1 Pressure fluctuation auto-correlation spectra at a receiving point of (0,70D)

    Figure 3 depicts the span-wise coherence function of surface pressure at the given shedding frequencyf0. It can be seen that the harmonic frequency of shedding frequency decay more slowly than other frequencies. This means the span length is enough for capturing the flow scale apart from those corresponding shedding frequency. Therefore, corrections should be made on the final result. The correction method used here is introduced by Seo[18].

    圖2 點(0, 70D)處的壓力脈動自相關頻譜圖(放大)Fig.2 Enlarged auto-correlation spectra of pressure at receiving point of (0, 70D)

    (a) Spanwise coherence coefficient of surface pressure at Shedding frequency over the span (90°)

    (b) Two-point coherence function of surface pressure over the rod at 90° (z=0 and z=1.5D)

    Far-field noise calculated from the FW-H surface overlapped with the rod surface is shown in Figure 4. It can be seen that both the scale and frequency of the tonal noise are well predicted. The harmonics of the main tonal noise are also captured. The high fluctuation of the spectra is the common phenomenon that appears in the calculation of noise, which results from the relatively short length of the total sampling time.

    圖4 觀測點(0,1.85 m)處的聲壓級頻譜圖Fig.4 Sound pressure level at receiver point (0,1.85 m)

    2.3 Validation using rod-airfoil configuration

    The same rod airfoil configuration, as used by Jacob[6], is considered in this validation, as depicted in Figure 5. Freestream flow conditions are set asU0=72 m/s,T=293 K andρ=1.2 kg/m3. The reference chord length is chosen asc=100 mm, which results in a Reynolds number of 4.8×105.

    Three grids were compared to validate the meshused for the following studies.yplus values of the first layer in all three grids were kept at 1. The differences were the growth ratio in the normal direction and the number of points along the circumference direction. Table 2 shows the nodes number allocated on the surface of the rod and airfoil.

    Total computational domain is set as (-8c,8c) in vertical direction and (-10c,20c) in the horizontal direction. Computational methods are the same as the rod configuration but the non-dimensional time step is reduced toΔt=0.001. The sampling time for acoustic data was 20,000 time-steps and sampled every time step. Sampling frequency was then defined as 720 kHz. Results from RANS of 20,000 iterations were used as the initial values for LES calculation.

    The calculation results are shown in Figure 6. Results of three cases are compared with reference LES and experiment results. Turbulent intensity is obtained based on streamwise velocity fluctuations. Considering the rod was shifted 2 mm vertically in the experiment,the velocity profile at position A (x/c=-0.255) shows the greatest velocity deficit at the locationy/c>0. Apart from the result of grid No.2, all simulated cases exhibit a larger averaged velocity deficit compared to experimental results. And turbulent intensities are also larger along the middle line. Despite these differences, it is believed that the results obtained here are acceptable. These phenomena appear in nearly all the numerical simulations of rod airfoil configuration.

    圖5 圓柱機翼構型示意圖[6]Fig.5 Rod-airfoil configuration for validation[6]

    By comparing the calculated results of the two cases above, it can be seen that the method used in this paper is feasible in the current study on the geometry variation of tandem airfoil configurations.

    表2 三個圓柱機翼網格的細節(jié)參數(shù)Table 2 Mesh details of three cases

    (a) Averaged meanstreamwise velocity profile at x/c=-0.255

    (a) Averaged meanstreamwise velocity profile at x/c=0.25

    圖8 機翼前緣上方(0,1.85 m)處的遠場SPL頻譜圖Fig.8 Far-field SPL spectra at the location (0,1.85 m) above the airfoil leading edge

    3 Aerodynamic and aeroacoustics calculation of tandem airfoil

    3.1 Geometry and computational model

    The tandem airfoil model used here is a model used in the 1st International Workshop on High-Order CFD Methods[19], as shown in Figure 9. Thedoffis the distance of vertical displacement relative to the chordc.doffis set as 0.24 in this paper and the angle of attack of the front airfoil is set as 10°. Parameterdsepis the horizontal distance between the two airfoils. The airfoil used is NACA0012 and the methods used for generating the airfoil are described in the following.

    圖9 計算所選用的串聯(lián)機翼模型示意圖Fig.9 Tandem airfoil configuration chosen for computation

    Geometry variations are introduced for the leading edge radius and the maximum thickness of the aft airfoil. As for the front airfoil, maximum thickness and boat-tail angle are varied. Class/Shape Transformation method[20]is used to generate varied geometry. Leading-edge radius is related to the maximum thickness through the following expression:

    (1)

    wheretis the maximum thickness of airfoil, andIstands for non-dimensional parameter that controls the shape of leading edge. The standard NACA 4-series airfoil is defined withI=6.

    The model is shown as Figure 9. In this paper, the relative position of two airfoils did not changed, only geometries were varied. The chosen parameters are listed below in Table 3.

    表3 串聯(lián)機翼構型的外形參數(shù)Table 3 List of parameters for tandem airfoil configuration

    Two NACA0012 airfoils with the same chord ofc=100 mm were placed in tandem configuration with twice the chord length apart between the leading edge of the two airfoils. The front airfoil was rotated around point quarter-chord (0.25c, 0) to achieve an angle of attack of 10°.

    O-type blocks are used to discretize the computational domain.Each airfoil surface is meshed with 538 nodes along the circumferential direction. The normal direction growth ratio is set as less than 1.05 near the wall. Total nodes number is 128 in the normal direction near the wall.

    It should be notedthat the current noise result is calculated from the finite span 0.2c, as the length of span would directly influence the total noise results. Spanwise length correction has been made for the tandem airfoil cases.

    Q-criterion Iso-surfaces of tandem airfoil calculated using LES are shown in Figure 10. Periodic pressure fluctuations are generated from the leading edge shedding vortex on the upper face of the front airfoil. Thick low-speed zone occurs in the wake domain of the trailing edge. Then the vortices are pushed downward by the presence of the aft airfoil, impinging on the upper face of the aft airfoil. Finally, the vortices are mixed with the wake of aft airfoil downstream of the aft airfoil.

    圖10 Q準則等值面圖(速度云圖)Fig.10 Q-criterion iso-surfaces for velocity

    The turbulence flow is mainly developed at the upper face and trailing edge of the front airfoil, then the upper face of the rear airfoil. These areas are likely to be the primary regions for noise sources. The SPL (sound pressure levels) spectra are shown in Figure 11. Three FW-H integration surfaces comprised of the front airfoil and aft airfoil, and tandem airfoil were used to obtained the far-field results of the three lines, respectively. It can be seen that aft airfoil is the dominant noise source in the overall model. The maximum SPL frequency of aft airfoil in the tandem configuration is totally different from the isolated condition, which has a max SPL frequency of about 2700 Hz[21]. This is similar to the rod airfoil configuration. Therefore, the following work in this paper focused on the trailing edge of the front airfoil and the leading edge of aft airfoil.

    圖11 接收點(0,1.85 m)處的串聯(lián)機翼遠場聲壓級頻譜圖Fig.11 Sound pressure level of the tandem airfoil at the receiver (0, 1.85 m)

    3.2 Surrogate-based study of shape parameters

    This section adopted aresponse surface methodology to study the combined effects of variations in these geometric features on noise levels[22]. A Latin hypercube sampling method is used to generate a set of sample points. A series of Kriging based surrogate models were generated in order to find the best combinations of these geometry parameters regarding noise level reduction at the observation points. The response surface will demonstrate the combined effects of these geometry features and provide an insight into the design of future lower noise configurations.

    Four parameters were chosen in the study of the combined effect, including maximum thickness and boat-tail angle of the front airfoil, leading-edge radius and the maximum thickness of the aft airfoil. The ranges of these four parameters are listed in Table 4.

    表4 幾何外形參數(shù)變化范圍Table 4 Range of variations for geometry parameters

    A total of 30 sample points were obtained for the generation of the response surface. TheR2value is defined as the following to describe the accuracy of the model.

    (2)

    As Figure 12(a) shows, OASPL is increased with the maximum thickness when the boat-tail angle is low. Moreover, the two curves become closer when the maximum thickness is greater than 15% of the chord. That means that a low boat-tail angle has very few effects on OASPL when the maximum thickness is large. Judging from the different trend at low and high boat-tail angle, it is reasonable to presume that there is a certain range of ratios between maximum thickness and boat-tail angle that give the lowest sound emission. This ratio makes sure that there is a smooth transition from the maximum thickness point to the trailing edge. Figure 12(b) shows a similar trend as in Figure 12(a) apart from the fact that two curves are overlapped.

    (a) The effect of maximum thickness at different boat-tail angles

    (b) The effect of boat-tail angle

    (c) The effect of leading edge radius

    (d) The effect of maximum-thickness for different airfoils

    As to Figure 12(c), OASPL increases withI(leading edge radius) at small maximum thickness. Sharper leading edge can reduce the direct impingement of vortex on the surface of the aft airfoil, driving the vortex downstream more smoothly. While at larger maximum thickness, OASPL is smaller with largerI. In this case, the front of aft airfoil in inevitably large, leading to higher blockage at the leading edge. Sharper leading edge would make the pressure at the static zone higher. Whereas rounded leading-edge could relieve this phenomenon. Figure 12(d) shows a similar trend as Figure 12(c).

    The response surface is plotted with HAT (Hierarchical Axes Technology) graph. The effects of four parameters on OASPL are plotted. Variables in the outer axis are front airfoil maximum thickness in thexdirection and boat-tail angle in theydirection. In the inner coordinate, two variables are aft airfoil leading-edge radius in thexdirection and maximum thickness in theydirection.

    Far-field OASPL of the front airfoil is shown in Figure 13, wheretmaxmeans front airfoil thickness, andβmeans front airfoil boat-tail angle. It can be seen that front airfoil OASPL is less sensitive to the effect of aft airfoil geometry. The highest OASPL lies in the subplot (1,3) and (3,1). The counterpart front airfoil geometry is the combination of smalltmaxwith smallβ, and largetmaxwith largeβ. When an airfoil is featured with slim rear shape, namely low boat-tail angle, noise is decreased with the increase of maximum thickness. This conclusion is similar to that of James[9]. But the trend is reversed when the boat-tail angle is high. In this case, geometry has a blunt trailing edge. Because the scale of vortex shedding from the trailing edge is increased, making the airfoil thickness larger may worsen this phenomenon.

    圖13 接收點(0,1.85 m)接收到的前翼OASPL圖

    Figure 14 depicts the overall noise of the front airfoil and aft airfoil. It is obvious that tandem airfoil OASPL is more sensitive to the aft airfoil geometry. Two trendscan be observed from the HAT graph. The first one is that the trend is totally opposite in subplot (3,1) and (1,3). When front airfoiltmaxandβare small, tandem airfoil noise is larger if aft airfoiltmaxorIbecome larger. The second is that in the rest of the subplot, OASPL is lower when aft airfoil maximum thickness and leading-edge radii are either smaller or larger.

    The primary areas with low OASPL lie on the line between Figure 14 subplot (1,3) and (3,1). But the counterpart of this area in Figure 13 is the lowest noise areas of the front airfoil. It should be noted that aft airfoil takes the dominant position in tandem airfoil configuration. Figure 13 and Figure 14 show the opposite trend in subplot (3,1) and (1,3), since the response surfaces were generated from single front airfoil and tandem airfoil, respectively. The effect of the front airfoil is overwhelmed by aft airfoil.

    Figures 15 and 16 show the frequency obtained at max SPL. It is easy to find that the frequency has a very similar trend as max SPL. That means louder noise is accompanied at higher frequencies.

    圖15 接收點(0,1.85 m)接收到的前翼最大聲壓級對應的頻率圖Fig.15 Max SPL frequency of front airfoil at the receiver (0,1.85 m)

    圖16 接收點(0,1.85 m)接收到的串聯(lián)機翼最大聲壓級對應的頻率圖Fig.16 Max SPL frequency of tandem airfoil at the receiver (0,1.85 m)

    4 Conclusions

    Far-field noise characteristics of typical tandem airfoil configuration have been studied numerically with 3D LES combined with FW-H analogy. Geometric features of both airfoils are varied simultaneously to study the combined effects on noise. The results of four geometry parameters: front airfoil maximum thickness, front airfoil boat-tail angle, aft airfoil leading-edge radius and aft airfoil maximum thickness, have been investigated. The key findings are listed as follows:

    1) Geometries of both airfoils in tandem airfoil configuration should be considered for noise reduction. Since the reduction of noise from the front airfoil alone could worsen the overall noise level of the tandem airfoil configuration.

    2) The ratio between maximum thickness and boat-tail angle of front airfoil should bekept in a certain medium range. Too large or too small would worsen the aeroacoustics performance. This can avoid the sharp change in geometry that may induce vortex generation. Keeping the transition of flow from the maximum thickness point toward trailing edge could also avoid large trailing edge vortex.

    3) Sharp leading edge should only be used in a thin airfoil. Larger leading-edge radius should be used under the circumstance that maximum thickness islarge. Namely,Iandtmaxshould be both large or small at the same time in most cases.

    4) Noise frequency of max SPL has a similar trend as the max SPL. The frequency for the Max SPL should be carefully considered in order to avoid undesirable effects such as acoustic fatigue.

    The complex interactions between two airfoils in a tandem configuration make it necessary to consider the case using an integrated approach. The current study should be further extended to include spanwise effects for the same tandem configuration in the next steps of the research, along with comparative studies using an experimental approach. In reality, aerodynamic aspects should also be considered, which further complicates the problem.

    From the results, it is also suggested that configuration parameters such as the vertical and horizontal distance, and spanwise variations, should be included in the future, three-dimensional studies.

    猜你喜歡
    接收點遠場聲壓級
    機器噪聲平均聲壓級計算方法差異性實證研究
    電動工具(2024年1期)2024-02-29 01:40:24
    一種計算消聲室聲壓級的新方法
    計量學報(2020年2期)2020-04-11 04:33:22
    全新DXR mkll有源揚聲器
    演藝科技(2019年4期)2019-03-30 03:21:46
    基于仿真與實測的列車遠場氣動噪聲分析
    測控技術(2018年9期)2018-11-25 07:44:12
    更正
    動態(tài)網絡最短路徑射線追蹤算法中向后追蹤方法的改進*1
    某種陣列雷達發(fā)射通道遠場校準簡易方法
    淺海波導界面對點源振速方向的影響?
    應用聲學(2015年3期)2015-10-27 02:52:49
    Diodes1.9W D類音頻放大器提供高聲壓級水平并延長電池壽命
    戰(zhàn)斗部遠場水下爆炸對艦船沖擊損傷評估
    水蜜桃什么品种好| 欧美日本中文国产一区发布| 亚洲精品日韩在线中文字幕| 中文字幕色久视频| 午夜老司机福利剧场| 999精品在线视频| 亚洲人成网站在线观看播放| a级毛片在线看网站| 美女国产视频在线观看| 99九九在线精品视频| 一边摸一边做爽爽视频免费| 午夜福利一区二区在线看| 久久精品人人爽人人爽视色| 免费播放大片免费观看视频在线观看| 国产日韩一区二区三区精品不卡| 国产亚洲一区二区精品| 午夜福利一区二区在线看| 国产成人精品久久久久久| 精品久久久久久电影网| 亚洲国产最新在线播放| 三上悠亚av全集在线观看| 午夜福利,免费看| 高清黄色对白视频在线免费看| 国产麻豆69| 久久热在线av| 老汉色∧v一级毛片| 欧美老熟妇乱子伦牲交| 中文欧美无线码| 91久久精品国产一区二区三区| a级毛片黄视频| 午夜福利视频在线观看免费| 最近最新中文字幕大全免费视频 | 久久久久国产网址| 日韩伦理黄色片| 校园人妻丝袜中文字幕| 亚洲精品国产av蜜桃| 亚洲久久久国产精品| 男女下面插进去视频免费观看| 七月丁香在线播放| 欧美日韩国产mv在线观看视频| 久久久久久久国产电影| 亚洲人成77777在线视频| 日韩中字成人| 亚洲精品av麻豆狂野| 老汉色∧v一级毛片| 国产毛片在线视频| 欧美人与性动交α欧美精品济南到 | 亚洲精品国产av成人精品| 亚洲图色成人| 你懂的网址亚洲精品在线观看| 99热网站在线观看| 久久久久网色| 美女午夜性视频免费| 亚洲第一区二区三区不卡| 七月丁香在线播放| 久久久久精品性色| 久久亚洲国产成人精品v| 亚洲精品日韩在线中文字幕| 日本爱情动作片www.在线观看| 丰满饥渴人妻一区二区三| 国产精品国产av在线观看| 精品人妻偷拍中文字幕| 久久热在线av| 欧美成人午夜免费资源| 肉色欧美久久久久久久蜜桃| 日韩中文字幕视频在线看片| 女性被躁到高潮视频| 国产又爽黄色视频| 亚洲激情五月婷婷啪啪| 国产精品 欧美亚洲| 丝袜脚勾引网站| 精品一区二区三卡| 久久精品国产亚洲av高清一级| 精品久久蜜臀av无| 女性被躁到高潮视频| 久久狼人影院| av在线观看视频网站免费| 成人18禁高潮啪啪吃奶动态图| 久久人人爽人人片av| a级片在线免费高清观看视频| 超色免费av| 黑人欧美特级aaaaaa片| 久久精品久久久久久久性| 国产成人一区二区在线| 亚洲伊人久久精品综合| 丰满少妇做爰视频| 国产精品香港三级国产av潘金莲 | 久久精品人人爽人人爽视色| 在线观看三级黄色| 秋霞在线观看毛片| 日韩熟女老妇一区二区性免费视频| 国产欧美日韩综合在线一区二区| 热re99久久国产66热| 黑人巨大精品欧美一区二区蜜桃| 国产av精品麻豆| 久久这里只有精品19| 好男人视频免费观看在线| 亚洲国产精品国产精品| 中文天堂在线官网| 我的亚洲天堂| 国产乱人偷精品视频| 香蕉丝袜av| 在线观看三级黄色| 国产无遮挡羞羞视频在线观看| 日本黄色日本黄色录像| 搡女人真爽免费视频火全软件| 精品卡一卡二卡四卡免费| 亚洲国产精品国产精品| 日韩人妻精品一区2区三区| 丰满乱子伦码专区| 另类精品久久| 大陆偷拍与自拍| 在线观看三级黄色| 亚洲成人一二三区av| av有码第一页| 午夜激情久久久久久久| 亚洲av综合色区一区| 日韩,欧美,国产一区二区三区| 日韩伦理黄色片| 天天躁日日躁夜夜躁夜夜| 天天影视国产精品| 久久精品亚洲av国产电影网| 精品国产国语对白av| 少妇精品久久久久久久| 国产极品天堂在线| 亚洲婷婷狠狠爱综合网| 一级爰片在线观看| 如日韩欧美国产精品一区二区三区| 久久99热这里只频精品6学生| 尾随美女入室| 一级毛片 在线播放| 欧美国产精品va在线观看不卡| h视频一区二区三区| 亚洲av国产av综合av卡| 王馨瑶露胸无遮挡在线观看| 美女中出高潮动态图| 亚洲精品自拍成人| 精品国产国语对白av| 亚洲第一av免费看| 日本av免费视频播放| 美女福利国产在线| 考比视频在线观看| 亚洲美女视频黄频| 午夜激情av网站| 亚洲,欧美,日韩| 日本wwww免费看| 婷婷色综合www| 成年女人在线观看亚洲视频| 欧美日韩精品成人综合77777| 欧美日韩国产mv在线观看视频| 亚洲三级黄色毛片| 日韩伦理黄色片| 亚洲欧美清纯卡通| 亚洲在久久综合| 亚洲国产av新网站| 亚洲欧美精品综合一区二区三区 | 黑人猛操日本美女一级片| 国产亚洲一区二区精品| 性高湖久久久久久久久免费观看| 自拍欧美九色日韩亚洲蝌蚪91| 九色亚洲精品在线播放| 免费大片黄手机在线观看| 一级毛片 在线播放| 黄色视频在线播放观看不卡| 久久精品人人爽人人爽视色| 又粗又硬又长又爽又黄的视频| 99热全是精品| 肉色欧美久久久久久久蜜桃| 最近中文字幕高清免费大全6| 精品人妻一区二区三区麻豆| 成人手机av| 热re99久久国产66热| 精品国产一区二区三区四区第35| 美女主播在线视频| 亚洲国产精品成人久久小说| 90打野战视频偷拍视频| 97在线视频观看| 如何舔出高潮| 精品福利永久在线观看| 少妇猛男粗大的猛烈进出视频| 美女午夜性视频免费| 街头女战士在线观看网站| av卡一久久| 美女午夜性视频免费| 街头女战士在线观看网站| 丰满少妇做爰视频| 精品人妻熟女毛片av久久网站| 国产成人91sexporn| 午夜激情av网站| 国产欧美亚洲国产| 国产精品欧美亚洲77777| 如何舔出高潮| 亚洲精品日韩在线中文字幕| 国产精品久久久久成人av| 尾随美女入室| 免费久久久久久久精品成人欧美视频| 国产深夜福利视频在线观看| av在线观看视频网站免费| 精品国产国语对白av| 亚洲人成网站在线观看播放| 日日撸夜夜添| 国产精品久久久久久精品古装| 熟女电影av网| 丰满迷人的少妇在线观看| 亚洲精品一区蜜桃| 香蕉国产在线看| 亚洲成人手机| 午夜福利,免费看| 十分钟在线观看高清视频www| 人妻系列 视频| 波野结衣二区三区在线| 在线观看美女被高潮喷水网站| 女人高潮潮喷娇喘18禁视频| 亚洲天堂av无毛| 国产精品熟女久久久久浪| 深夜精品福利| 亚洲精品国产一区二区精华液| 国产成人欧美| 亚洲一区二区三区欧美精品| 亚洲欧美清纯卡通| 国产精品.久久久| 欧美另类一区| 精品亚洲成国产av| 日本午夜av视频| 国产精品嫩草影院av在线观看| 深夜精品福利| 欧美国产精品一级二级三级| 免费黄频网站在线观看国产| 国产极品粉嫩免费观看在线| 免费看av在线观看网站| 久久久亚洲精品成人影院| 男男h啪啪无遮挡| 成人午夜精彩视频在线观看| 99久久中文字幕三级久久日本| 国产精品国产三级国产专区5o| 日韩熟女老妇一区二区性免费视频| 97在线视频观看| 97在线人人人人妻| 欧美日韩一级在线毛片| 天堂俺去俺来也www色官网| 美女脱内裤让男人舔精品视频| 国产日韩一区二区三区精品不卡| 成年动漫av网址| 成人国产麻豆网| 亚洲精品第二区| 国产av码专区亚洲av| 国产综合精华液| 国产xxxxx性猛交| 国产国语露脸激情在线看| 久久久久国产精品人妻一区二区| 亚洲第一区二区三区不卡| 啦啦啦中文免费视频观看日本| 国产淫语在线视频| 国产精品亚洲av一区麻豆 | 亚洲国产日韩一区二区| 成人影院久久| 日韩电影二区| 一本色道久久久久久精品综合| 国产精品一二三区在线看| 99re6热这里在线精品视频| 亚洲综合色惰| 日韩制服丝袜自拍偷拍| 看非洲黑人一级黄片| 一二三四在线观看免费中文在| 国产高清不卡午夜福利| 日日爽夜夜爽网站| 熟女av电影| 久久久国产一区二区| 99久久人妻综合| 久久99精品国语久久久| 少妇人妻精品综合一区二区| 久久久久久久久久久久大奶| 成年人午夜在线观看视频| 性高湖久久久久久久久免费观看| 国产一区二区 视频在线| 青春草视频在线免费观看| 日韩制服骚丝袜av| 亚洲美女搞黄在线观看| 两性夫妻黄色片| 中文乱码字字幕精品一区二区三区| 女人久久www免费人成看片| 国产视频首页在线观看| 欧美变态另类bdsm刘玥| 有码 亚洲区| 日日啪夜夜爽| 亚洲av成人精品一二三区| 丰满饥渴人妻一区二区三| 成人毛片a级毛片在线播放| 亚洲国产欧美网| 人人妻人人爽人人添夜夜欢视频| 国产精品一区二区在线不卡| 亚洲国产av影院在线观看| 另类精品久久| 成人手机av| 最近2019中文字幕mv第一页| 男的添女的下面高潮视频| 一区二区三区乱码不卡18| 看免费成人av毛片| 久久热在线av| 国产伦理片在线播放av一区| 青春草亚洲视频在线观看| 巨乳人妻的诱惑在线观看| 国产麻豆69| 国产精品蜜桃在线观看| 国产精品国产三级专区第一集| av女优亚洲男人天堂| 国产av精品麻豆| 国精品久久久久久国模美| 久久av网站| 91久久精品国产一区二区三区| 精品国产一区二区三区四区第35| 日日撸夜夜添| 国产亚洲av片在线观看秒播厂| 少妇被粗大猛烈的视频| 美女视频免费永久观看网站| 日本色播在线视频| 国产精品久久久久久久久免| 午夜av观看不卡| 久久久久国产精品人妻一区二区| 亚洲激情五月婷婷啪啪| 免费黄色在线免费观看| 久久精品国产亚洲av高清一级| 午夜老司机福利剧场| 久久久国产精品麻豆| xxxhd国产人妻xxx| 亚洲精品美女久久久久99蜜臀 | 在线观看三级黄色| 免费少妇av软件| 日韩大片免费观看网站| 欧美av亚洲av综合av国产av | 中文字幕精品免费在线观看视频| 大陆偷拍与自拍| 精品少妇内射三级| 国产男女超爽视频在线观看| 亚洲国产最新在线播放| 香蕉丝袜av| 午夜91福利影院| 成年人免费黄色播放视频| 青青草视频在线视频观看| 18禁国产床啪视频网站| 国产高清国产精品国产三级| 免费看不卡的av| 亚洲内射少妇av| 精品国产一区二区三区四区第35| 免费久久久久久久精品成人欧美视频| 一区二区日韩欧美中文字幕| 亚洲精品国产色婷婷电影| 两个人免费观看高清视频| 久久久国产一区二区| 国产免费又黄又爽又色| 免费久久久久久久精品成人欧美视频| 精品国产一区二区三区四区第35| 欧美中文综合在线视频| 久热这里只有精品99| 啦啦啦在线观看免费高清www| 丁香六月天网| 18禁裸乳无遮挡动漫免费视频| 97在线人人人人妻| 少妇的丰满在线观看| av在线老鸭窝| 亚洲综合色惰| 国产精品久久久av美女十八| 大片电影免费在线观看免费| 日韩一区二区视频免费看| 中文精品一卡2卡3卡4更新| 久久久a久久爽久久v久久| 桃花免费在线播放| 国产成人精品一,二区| 爱豆传媒免费全集在线观看| 男人添女人高潮全过程视频| 一级毛片电影观看| 亚洲国产精品999| 国产精品一区二区在线不卡| 在线精品无人区一区二区三| 久久 成人 亚洲| 伦理电影大哥的女人| 卡戴珊不雅视频在线播放| 看十八女毛片水多多多| 精品久久久精品久久久| 久久99一区二区三区| 在现免费观看毛片| 一级,二级,三级黄色视频| 亚洲精品第二区| 亚洲精品久久久久久婷婷小说| 99热全是精品| 免费观看a级毛片全部| 亚洲精品中文字幕在线视频| 免费播放大片免费观看视频在线观看| 精品人妻一区二区三区麻豆| 欧美精品国产亚洲| 亚洲人成网站在线观看播放| 亚洲成国产人片在线观看| 三上悠亚av全集在线观看| 午夜日本视频在线| 国产免费一区二区三区四区乱码| 少妇精品久久久久久久| 黄片无遮挡物在线观看| 在现免费观看毛片| 亚洲欧美成人精品一区二区| 日韩制服骚丝袜av| 天堂俺去俺来也www色官网| 成年美女黄网站色视频大全免费| 国产精品女同一区二区软件| 巨乳人妻的诱惑在线观看| 免费播放大片免费观看视频在线观看| 少妇熟女欧美另类| 欧美日韩一区二区视频在线观看视频在线| 国产一区二区 视频在线| 国产xxxxx性猛交| 亚洲美女视频黄频| 日韩中文字幕欧美一区二区 | 99久久人妻综合| 街头女战士在线观看网站| 国产精品久久久久久精品电影小说| 成人亚洲精品一区在线观看| 欧美日韩视频高清一区二区三区二| 美女中出高潮动态图| 少妇人妻久久综合中文| 亚洲成人一二三区av| 国产精品无大码| 纯流量卡能插随身wifi吗| 精品一区二区免费观看| 天天影视国产精品| 国产亚洲最大av| 亚洲男人天堂网一区| av国产精品久久久久影院| 国产精品一区二区在线观看99| 婷婷色综合www| 成人毛片60女人毛片免费| 水蜜桃什么品种好| 亚洲色图 男人天堂 中文字幕| 18禁观看日本| 成年女人毛片免费观看观看9 | 国产乱来视频区| 一级,二级,三级黄色视频| 99久久精品国产国产毛片| 国产精品一区二区在线观看99| 日韩免费高清中文字幕av| 性高湖久久久久久久久免费观看| 最近中文字幕高清免费大全6| 亚洲国产日韩一区二区| 最近手机中文字幕大全| 男女边摸边吃奶| 蜜桃国产av成人99| 美女国产视频在线观看| 久久精品熟女亚洲av麻豆精品| 欧美另类一区| 久久久久国产网址| 高清欧美精品videossex| 美女大奶头黄色视频| 免费av中文字幕在线| 另类亚洲欧美激情| 国精品久久久久久国模美| 最近中文字幕2019免费版| 免费日韩欧美在线观看| 国产成人精品久久二区二区91 | www.自偷自拍.com| 亚洲综合色网址| 1024香蕉在线观看| 午夜福利视频精品| 男女下面插进去视频免费观看| 国产日韩欧美视频二区| 日韩伦理黄色片| tube8黄色片| 男女国产视频网站| 亚洲中文av在线| 超碰成人久久| 在线观看免费日韩欧美大片| 亚洲精品乱久久久久久| 一区二区日韩欧美中文字幕| 91在线精品国自产拍蜜月| 大陆偷拍与自拍| a 毛片基地| 制服诱惑二区| 老女人水多毛片| 男女国产视频网站| 女性生殖器流出的白浆| 男人爽女人下面视频在线观看| 免费人妻精品一区二区三区视频| 久久精品国产a三级三级三级| 欧美精品国产亚洲| 欧美人与善性xxx| 好男人视频免费观看在线| 成人毛片60女人毛片免费| 日韩中文字幕欧美一区二区 | 街头女战士在线观看网站| 乱人伦中国视频| 国产男人的电影天堂91| 亚洲久久久国产精品| 亚洲欧美一区二区三区久久| 久久免费观看电影| 午夜精品国产一区二区电影| 国产精品亚洲av一区麻豆 | 久久久亚洲精品成人影院| 999精品在线视频| 99久久中文字幕三级久久日本| 少妇的逼水好多| 日日摸夜夜添夜夜爱| 免费观看在线日韩| 热re99久久精品国产66热6| 日本vs欧美在线观看视频| 日韩欧美一区视频在线观看| 啦啦啦中文免费视频观看日本| 欧美日韩一区二区视频在线观看视频在线| 少妇熟女欧美另类| 少妇人妻久久综合中文| 少妇的逼水好多| 久久韩国三级中文字幕| 美女大奶头黄色视频| 黄色 视频免费看| 各种免费的搞黄视频| 亚洲,欧美精品.| 亚洲欧美一区二区三区久久| 18在线观看网站| 亚洲美女搞黄在线观看| 一级毛片电影观看| 久久女婷五月综合色啪小说| 亚洲欧美一区二区三区国产| 亚洲av成人精品一二三区| 一区福利在线观看| 高清不卡的av网站| 成人毛片a级毛片在线播放| 欧美成人精品欧美一级黄| 亚洲精品乱久久久久久| 欧美人与善性xxx| 亚洲精品国产av成人精品| 免费高清在线观看视频在线观看| 男女午夜视频在线观看| 久久ye,这里只有精品| 亚洲av电影在线进入| 水蜜桃什么品种好| 精品国产一区二区久久| 午夜免费观看性视频| 久久97久久精品| 边亲边吃奶的免费视频| 男人舔女人的私密视频| 一级毛片电影观看| 老司机影院毛片| 韩国av在线不卡| 亚洲av男天堂| a级片在线免费高清观看视频| 久久精品国产综合久久久| 麻豆av在线久日| 丝瓜视频免费看黄片| 欧美另类一区| 大陆偷拍与自拍| 建设人人有责人人尽责人人享有的| 精品一区二区免费观看| 亚洲第一青青草原| 99久久精品国产国产毛片| 如日韩欧美国产精品一区二区三区| 一级爰片在线观看| 亚洲色图综合在线观看| av网站免费在线观看视频| 亚洲美女搞黄在线观看| 欧美精品av麻豆av| 在线天堂最新版资源| 性色av一级| 在线观看三级黄色| 大香蕉久久网| 成年人午夜在线观看视频| 久久久久精品久久久久真实原创| 亚洲人成网站在线观看播放| 午夜老司机福利剧场| 91aial.com中文字幕在线观看| 久久国产精品男人的天堂亚洲| 91在线精品国自产拍蜜月| 欧美精品人与动牲交sv欧美| 99久久人妻综合| 成人漫画全彩无遮挡| 欧美xxⅹ黑人| 国产爽快片一区二区三区| 国产视频首页在线观看| 中文字幕人妻丝袜制服| 晚上一个人看的免费电影| √禁漫天堂资源中文www| 午夜福利在线免费观看网站| 国产精品一二三区在线看| 国产精品人妻久久久影院| 宅男免费午夜| 91精品国产国语对白视频| 熟女电影av网| 天天躁日日躁夜夜躁夜夜| 美女脱内裤让男人舔精品视频| 人妻人人澡人人爽人人| 欧美激情高清一区二区三区 | 亚洲精品在线美女| 少妇人妻 视频| 久久久久久久亚洲中文字幕| av一本久久久久| 日韩一本色道免费dvd| 亚洲国产色片| 免费高清在线观看视频在线观看| 国产精品久久久久久久久免| 精品一区二区免费观看| 青春草视频在线免费观看| 制服人妻中文乱码| 国产欧美亚洲国产| 亚洲欧美清纯卡通| 日韩av在线免费看完整版不卡| 香蕉精品网在线| 99热网站在线观看| 两个人免费观看高清视频| 久久99热这里只频精品6学生| 美女脱内裤让男人舔精品视频| 丝袜脚勾引网站| 亚洲天堂av无毛| 丁香六月天网| 国产片内射在线| 大香蕉久久网| 女性被躁到高潮视频| 如日韩欧美国产精品一区二区三区| 伊人久久国产一区二区| 男女边吃奶边做爰视频| 日韩,欧美,国产一区二区三区|