A numerical study of the unsteady leading edge separation bubble on an oscillating airfoil

A preliminary study of unsteady leading edge separation bubbles on a NACA 0012 airfoil is undertaken using a finite difference procedure. In this preliminary study the interaction between the viscous and inviscid flow field is neglected. Prior to applying the procedure to the study of the leading edge bubble several calculations are performed, to assess the accuracy of the numerical procedure. These test cases include stagnation point flow, flow about a circular cylinder, and flow over an oscillating flat plate. Calculations are then carried out for flow over the leading edge of a NACA 0012 airfoil oscillating in pitch between 9° and 21° incidence at chord Reynolds numbers of 1.0 × 10⁶ and 2.5 × 10⁶. The results show that for the flow conditions considered, a small leading edge separation bubble is present throughout the entire motion cycle. The bubbles are predicted to move forward and decrease in size as the incidence increases. The results also indicate that the viscous flow in the leading edge region is quasi-steady and that the bubble height is inversely proportional to the Reynolds number. Even with the neglect of interaction, the predicted leading edge bubble behavior is in qualitative agreement with experimental data, indicating that the approach taken should be a feasible method of studying leading edge bubble dynamics and dynamic stall provided that the procedure is extended to include interaction effects.     

DNS for flow separation control around an airfoil by pulsed jets

Direct numerical simulation (DNS) for flow separation and transition around a NACA-0012 airfoil with an attack angle of 4° and Reynolds number of 100,000 has been reported in our previous paper. The details of flow separation, formation of the detached shear layer, Kelvin-Helmholtz instability (inviscid shear layer instability) and vortex shedding, interaction of nonlinear waves, breakdown, and re-attachment are obtained and analyzed. The power spectral density of pressure shows the low frequency of vortex shedding caused by the Kelvin-Helmholtz instability still dominates from the leading edge to trailing edge. Based on our understanding on the flow separation mechanism, we try to reveal the mechanism of the flow separation control using blowing jets and then optimize the jets. DNS simulations for flow separation control by blowing jets (pulsed and pitched and skewed jets) are reported and analyzed. The effects of different unsteady blowing jets on the surface at the location just before the separation points are studied. The length of separation bubble is significantly reduced (almost removed) after unsteady blowing technology is applied. The mechanism of early transition caused by the blowing jets was found. A blowing jet with K-H frequency, sharp shape function (very small mass blowing), pitching and skewing obtained the best efficiency based on the increase of the ratio of lift over drag and decrease of blowing mass flow. In this work, a DNS code with high-order accuracy and high-resolution developed by the computational fluid dynamics group at University of Texas at Arlington is applied.     

Optimization of the motion of a flapping airfoil using sensitivity functions

The motion of a flapping NACA0012 airfoil is optimized by means of numerical simulations for a Reynolds number equal to 1100. The control parameters are the amplitudes and the phase angles of the flapping motion in addition to the mean angle of attack. Sensitivity functions are used to compute the gradient of a cost functional related to the propulsive efficiency of the airfoil and a quasi-Newton method is adopted to drive the control parameters towards their optimal values. The ability of a flapping airfoil to produce sufficient lift and thrust forces for appropriate kinematics is demonstrated. Furthermore, a linear dependence between heaving and pitching amplitudes is found for optimal configurations leading to a constant value of the maximum effective angle of attack roughly equal to 11°. This value corresponds to the angle yielding the maximal lift-to-drag ratio for this Reynolds number when the NACA0012 airfoil does not flap. Previous results such as the high propulsive efficiency when a 90° phase angle exists between heaving and pitching, or the reversal of the von Karman street for a Strouhal number close to 0.2, are confirmed here with a new methodology. Finally, optimal kinematics for various types of missions are given and the corresponding flows are described.     

One- and two-equation turbulence models for the prediction of complex cascade flows using unstructured grids

One- and two-equation, low-Reynolds eddy-viscosity turbulence models are employed in the context of a primitive variable, finite volume, Navier-Stokes solver for unstructured grids. Through the study of the complex flow in a controlled-diffusion compressor cascade at off-design conditions, the ability of the models under consideration to predict the laminar separation bubble close to the leading edge and the boundary layer development is investigated. In order to control the unphysical growth of turbulent kinetic energy near the leading edge stagnation point, appropriate modifications to the conventional models are employed and tested. All of them improve the leading edge flow patterns and significantly affect the size of the predicted laminar separation bubble. The use of an adequately refined mesh around the airfoil, that is formed by triangles placed in a quasi-structured way, allows for the generation of grid elements of moderate aspect ratios. This helps to readily overcome any relevant problems of accuracy; a second-order upwind scheme without flux limiters or least squares approximations is successfully employed for the gradients. The test case includes quasi-3D effects by considering the streamtube thickness variation in the governing equations.     

Direct numerical simulation of flow separation around a NACA 0012 airfoil

Direct numerical simulation (DNS) for the flow separation and transition around a NACA 0012 airfoil with an attack angle of 4° and Reynolds number of 10⁵ based on free-stream velocity and chord length is presented. The details of the flow separation, detached shear layer, vortex shedding, breakdown to turbulence, and re-attachment of the boundary layer are captured in the simulation. Though no external disturbances are introduced, the self-excited vortex shedding and self-sustained turbulent flow may be related to the backward effect of the disturbed flow on the separation region. The vortex shedding from the separated free shear layer is attributed to the Kelvin-Helmholtz instability.     

Bluntness impact on performance of waverider

Waverider serves as a good candidate for hypersonic vehicles, especially for high lift-to-drag ratio aircraft. Restricted by aerodynamic heat and manufacture techniques, the sharp leading edge of waverider needs to be blunted. In order to study the blunt leading edge’s influences on the waverider, computational fluid dynamics tools are used to study the aerodynamic and aero-thermodynamic property of waverider with different blunt radii. The numerical methods are validated by test case and empirical formula. Numerical simulations show that blunting the leading edge could reduce the maximum heat flux effectively, but it also degrades the aerodynamic performances. When the blunt radius increases, the aerodynamic performance degrades significantly, while the heat flux wears off. With a fixed blunt radius, the aerodynamic performance mainly depends on the angle of attack; while the heat flux is less affected by the angle of attack. When designing waverider, the influence of bluntness on aerodynamic force and heat flux should be considered synthetically and the optimal balance point needs to be determined.     

Three-dimensional effects in multi-element high lift computations

In an effort to discover the causes for disagreement between previous two-dimensional (2-D) computations and nominally 2-D experiment for flow over the three-element McDonnell Douglas 30P-30N airfoil configuration at high lift, a combined experimental/CFD investigation is described. The experiment explores several different side-wall boundary layer control venting patterns, documents venting mass flow rates, and looks at corner surface flow patterns. The experimental angle of attack at maximum lift is found to be sensitive to the side-wall venting pattern: a particular pattern increases the angle of attack at maximum lift by at least 2°. A significant amount of spanwise pressure variation is present at angles of attack near maximum lift. A CFD study using three-dimensional (3-D) structured-grid computations, which includes the modeling of side-wall venting, is employed to investigate 3-D effects on the flow. Side-wall suction strength is found to affect the angle at which maximum lift is predicted. Maximum lift in the CFD is shown to be limited by the growth of an off-body corner flow vortex and consequent increase in spanwise pressure variation and decrease in circulation. The 3-D computations with and without wall venting predict similar trends to experiment at low angles of attack, but either stall too early or else overpredict lift levels near maximum lift by as much as 5%. Unstructured-grid computations demonstrate that mounting brackets lower the lift levels near maximum lift conditions.     

Numerical study of passive and active flow separation control over a NACA0012 airfoil

This paper is focused on numerical investigation of subsonic flow separation over a NACA0012 airfoil with a 6° angle of attack and flow separation control with vortex generators. The numerical simulations of three cases including an uncontrolled baseline case, a controlled case with passive vortex generator, and a controlled case with active vortex generator were carried out. The numerical simulation solves the three-dimensional Navier-Stokes equations for compressible flow using a fully implicit LU-SGS method. A fourth-order finite difference scheme is used to compute the spatial derivatives. The immersed-boundary method is used to model both the passive and active vortex generators. The characteristic frequency that dominates the flow is the natural frequency of separation in the baseline case. The introduction of the passive vortex generator does not alter the frequency of separation. In the case with active control, the frequency of the sinusoidal forcing was chosen close to the natural frequency of separation. The time- and spanwise-averaged results were used to examine the mean flow field for all three cases. The passive vortex generators can partially eliminate the separation by reattaching the separated shear layer to the airfoil over a significant extent. The size of the averaged separation zone has been reduced by more than 80%. The flow control with active vortex generator is more effective and the separation zone is not visible in the averaged results. The three-dimensional structures of the flow field have also been studied.     

Separated supersonic flow past a trailing edge at incidence

Supersonic laminar flow past a thin trailing edge at incidence is considered theoretically from the standpoint of triple-deck viscous-inviscid interactions, for large Reynolds numbers. At sufficient angles of incidence one-sided regular separation appears, leading to the possibility of a catastrophic stall. A numerical scheme based on coupling a shooting technique with windward differencing to account for flow reversals is described, along with a comparison with another method of treating reversed flow. The results obtained point to stall-free separated flow occurring, as predicted in some more recent studies. An abrupt reattachment is found to take place just prior to the trailing edge, followed by a strong downwash in the near-wake, and this forces the aavoidance of aatastrophic stall. The general features agree qualitatively with experimental observations.     

Instability of the flow in the vicinity of trailing edge of a class of thin aerofoils

A numerical study has been undertaken to investigate the notion of absolute/convective instability in laminar incompressible trailing edge flows past wedge-like shapes with curved boundaries of the form y=α(−x)^m. The effects of various trailing edge shapes m and relative thickness α on the flow separation and the development of instabilities in the vicinity of trailing edge are investigated. The nonlinear viscous-inviscid interaction equations, which have been derived by means of the asymptotic theory of flow separation, are solved first numerically to construct genuine mean velocity profiles representing the correct flow in the vicinity of the trailing edge. The absolute/convective nature of the asymptotically formed velocity profiles via a composite expansion is then ascertained by using a spatio-temporal analysis based on the Briggs-Bers pinching criterion. Although no absolute growth is encountered upstream of the trailing edge of the airfoil shapes considered, in particular the wake region behind the trailing edge of Joukowski type profiles is found to be persistently susceptible to absolute instability. It is found that separation is enhanced as the relative thickness of the airfoil gets bigger. This, in turn, is shown to lead to an additional enhancement of the absolute instability character by both increasing the absolute growth rate as well as the extent of the unstable region. Shedding frequency of the Karman vortex street is also determined behind the trailing edge shapes considered.     

收集口形状和角度对汽车风洞试验段轴向静压因数的影响

为研究风洞收集口形状和角度对试验段轴向静压因数的影响,通过数值仿真和试验验证研究翼型收集口在多种角度下轴向静压因数的变化,并与平板型收集口对比.结果表明:收集口形状对轴向静压因数变化规律没有影响,轴向静压因数总是随开口角度的增大而减小;对于同一形状收集口,只在上方张开某一角度比在两侧张开相同角度的轴向静压因数略低.收集口角度变化对轴向静压因数会产生规律性影响:随收集口角度增大,从剪切层外部特别是上方进入到射流核心区的流量增加,导致核心区流速增加,从而导致轴向静压因数降低.     

Bifurcations and buffet of transonic flow past flattened surfaces

Turbulent transonic flow past flattened aerodynamic surfaces is investigated numerically using the RANS equations. The study is focused on: (★) a buffet onset caused by instability of the shock wave/boundary layer interaction, (★★) instability of the entire flow structure and related flow bifurcations.For a symmetric airfoil at zero angle of attack, computations reveal both bifurcations and buffet in a range of the freestream Mach number M_∞. At nonzero angles of attack, α=±1°, there are two ranges of M_∞ in which the buffet onset takes place. For a Whitcomb type airfoil, computations demonstrate instability of the flow structure only at negative α. Axisymmetric flow past axisymmetric bodies is also considered, and instability of the flow structure at certain freestream Mach numbers is shown.     

Numerical simulation of thrust generating flow past a pitching airfoil

Earlier analytical and experimental studies predict that pitching motions at high frequency can generate thrust on the airfoil. The present work is an effort towards a systematic understanding of the influence of various parameters on thrust generation from a harmonically pitching airfoil. Quantitative instantaneous force computations have been discussed together with qualitative vortex patterns using a 2-D discrete vortex simulation of incompressible viscous flow. In general, thrust force increases with the oscillation frequency. The trend is very similar to the inviscid theory prediction. Further, the thrust force is seen to decrease with the increase in mean angle of attack. However, in a clear deviation from inviscid theory trends, pitching at high amplitudes about high mean angle of attack, only drag is observed for high values of reduced frequency considered. The effect of location of the pitching axis is also found to be significant on the propulsive characteristics of the airfoil.     

A gPC-based approach to uncertain transonic aerodynamics

The present paper focus on the stochastic response of a two-dimensional transonic airfoil to parametric uncertainties. Both the freestream Mach number and the angle of attack are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. The results allow for a better understanding of the flow sensitivity to such uncertainties and underline the coupling process between the stochastic parameters. Two kinds of non-linearities are critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement characteristic of the supercritical profile and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. The sensitivity analysis, thanks to the Sobol’ decomposition, shows that a strong non-linear coupling exists between the uncertain parameters. Comparisons with the one-dimensional cases demonstrate that the multi-dimensional parametric study is required to get the correct shape and magnitude of the standard deviation distributions of the flow quantities such as pressure and skin-friction.     

Comparison of uniform perturbation and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to impelement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.     

Optimization of a synthetic jet actuator for aerodynamic stall control

The numerical simulation of aerodynamic stall control using a synthetic jet actuator is presented and the automatic optimization of the control parameters is investigated. Unsteady Reynolds-averaged Navier-Stokes equations are solved on unstructured grids using a near-wall low-Reynolds number turbulence closure to simulate the effects of a synthetic jet, located at 12% of the chord from the leading edge of a NACA 0015 airfoil, for a Reynolds number Re = 8.96 × 10⁵ and incidences between 12° and 24°. Then, an automatic optimization procedure coupled with the flow solver is employed to optimize the parameters of the actuator (momentum coefficient, frequency, angle with respect to the wall) at each incidence in order to increase the time-averaged lift. A significant increase of the maximum lift is obtained (+52% with respect to the baseline airfoil) and the stall delayed from 16° to 22° for optimal parameters. The flow characteristics and the influence of the respective control parameters are analysed.     

Computational simulation and analysis of double-swept blade in BVI noise reduction

The TURNS computational fluid dynamics (CFD) code with the Beddoes prescribed wake and the WOPWOP computational acoustics code is used to study blade-sweep blade–vortex interaction (BVI) noise reduction design. The CFD three-dimensional unsteady solutions of blade surface pressure distributions are used as the input to WOPWOP acoustics computational code to produce the overall sound pressure level (OASPL) on a 3-rotor radiation observer hemisphere around the helicopter rotor. To study the effects of blade sweep on BVI noise reduction, computations are performed on a baseline rectangular blade and a corresponding double-swept blade to better understand the impact of blade sweep on BVI noise reduction in relation to the interaction angle between blade leading edge and the shed tip-vortex. The present study indicates that tip-region blade forward sweep produces favorable BVI angles for dominate BVIs to reduce the maximum BVI noise level on the advancing side, while increasing noise level on the retreating side. Increasing in the noise level on the retreating side as a trade-off for decreasing in the maximum noise level on the advancing side results favorably in the reduction of the overall maximum noise level and in changing the ‘hot’ noise spots into a more desirable ‘less hot’ noise region.     

基于模型模拟的植被NDVI与观测天顶角和LAI的关系

利用PROSPECT和SAIL模型模拟了不同叶绿素含量、不同LAI和不同观测天顶角下的植被冠层反射率,分析了NDVI随LAI、观测天顶角和叶绿素含量的变化规律。结果表明:叶绿素影响冠层反射率主要在可见光波段,冠层反射率随叶绿素含量的增加而下降;冠层反射率随观测天顶角的增加而增加,而LAI较高时,其受观测天顶角的影响较小。观测天顶角相同时,随叶绿素含量的增加NDVI呈上升趋势;叶绿素含量一定时,NDVI随LAI的增加而增加。LAI为1时,在不同叶绿素含量下,随观测天顶角的增加,NDVI呈先下降后上升的趋势,拐点在观测天顶角65°或70°处,而LAI为3、5和7时,NDVI呈现下降趋势。叶绿素含量较高时,NDVI受观测天顶角的影响较小。当LAI较大和叶绿素含量较低时,NDVI随观测天顶角的增加(>70°)下降较快。     

Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies

In this article, we present numerical solutions for flow over an airfoil and a square obstacle using Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved solid boundary treatment approach, referred to as the Multiple Boundary Tangents (MBT) method. It was shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Lennard-Jones Potential (LJP) in the advection equation to repair particle fractures occurring in the SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Numerical results suggest that the improved ISPH method which is consisting of the MBT method, artificial particle displacement and the corrective SPH discretization scheme enables one to obtain very stable and robust SPH simulations. The square obstacle and NACA airfoil geometry with the angle of attacks between 0° and 15° were simulated in a laminar flow field with relatively high Reynolds numbers. We illustrated that the improved ISPH method is able to capture the complex physics of bluff-body flows naturally such as the flow separation, wake formation at the trailing edge, and the vortex shedding. The SPH results are validated with a mesh-dependent Finite Element Method (FEM) and excellent agreements among the results were observed.     

一种飞翼布局飞行平台FADS系统应用方案研究

对于一些高性能飞行器(如飞翼布局飞行器),仅采用安装在机头表面的测压孔的FADS系统方案.某些情况下不一定能够给出较为准确的飞行姿态数据;针对飞翼布局飞行平台对高精度迎角、侧滑角的依赖性.给出了一种采用安装于机头表面的测压孔和机翼前缘的测压孔相结合的FADS系统方案,推导了其空气动力学模型,并用BP神经网络拟合出了迎角和侧滑角的修正曲线,结果表明该方案能够满足系统精度的要求。