Numerical Simulation of a Passive Control of the Flow Around an Aerofoil Using a Flexible,Self Adaptive Flaplet

Self-activated feathers are used by almost all birds to adapt their wing characteristics to delay stall or to moderate its adverse effects (e.g., during landing or sudden increase in angle of attack due to gusts). Some of the feathers are believed to pop up as a consequence of flow separation and to interact with the flow and produce beneficial modifications of the unsteady vorticity field. The use of self adaptive flaplets in aircrafts, inspired by birds feathers, requires the understanding of the physical mechanisms leading to the mentioned aerodynamic benefits and the determination of the characteristics of optimal flaps including their size, positioning and ideal fabrication material. In this framework, this numerical study is divided in two parts. Firstly, in a simplified scenario, we determine the main characteristics that render a flap mounted on an aerofoil at high angle of attack able to deliver increased lift and improved aerodynamic efficiency, by varying its length, position and its natural frequency. Later on, a detailed direct numerical simulation analysis is used to understand the origin of the aerodynamic benefits introduced by the flaplet movement induced by the interaction with the flow field. The parametric study that has been carried out, reveals that an optimal flap can deliver a mean lift increase of about 20% on a NACA0020 aerofoil at an incidence of 20 ^o degrees. The results obtained from the direct numerical simulation of the flow field around the aerofoil equipped with the optimal flap at a chord Reynolds number of 2 × 10⁴ shows that the flaplet movement is mainly induced by a cyclic passage of a large recirculation bubble on the aerofoil suction side. In turns, when the flap is pushed downward, the induced plane jet displaces the trailing edge vortices further downstream, away from the wing, moderating the downforce generated by those vortices and regularising the shedding cycle that appears to be much more organised when the optimal flaplet configuration is selected.     

An inviscid model of unsteady aerofoil flow with fixed upper surface separation

Presented in this paper is a new method for the prediction of unsteady, incompressible separated flow over a two-dimensional aerofoil. The algorithm was developed from an existing unsteady potential flow model¹ and makes use of an inviscid formulation for the flow field. The aerofoil is represented by vortex panels of linearly varying strength which are piecewise continuous at the corners. Discrete vortices with finite cores are used to model the separating shear layers. Following a brief summary of unsteady separation modelling, the theoretical framework is presented and the subsequent numerical implementation is discussed in detail. Results are given for flows which tend asymptotically to the steady state and conclusions are drawn regarding the usefulness of the method.     

Numerical analysis and modeling of plume meandering in passive scalar dispersion downstream of a wall-mounted cube

A DNS database is employed to examine the onset of plume meandering downstream of a wall-mounted cube and to address the impact of large-scale unsteadiness in modeling dispersion using the RANS equations. The cube is immersed in a uniform stream where the thin boundary-layer developing over the flat plate is responsible for the onset of vortex-shedding in the wake of the bluff-body. Spectra of velocity and concentration fluctuations exhibit a prominent peak in the energy content at the same frequency, showing that the plume meandering is established by the action of the vortex-shedding. The vortex-shedding and plume meandering display a low-frequency modulation where coherent fluctuations are suppressed at times with a quasi-regular period. The onset of the low-frequency modulation is indicated by a secondary peak in the energy spectrum and confirmed by the autocorrelation of velocity and scalar fluctuations. Unsteady RANS simulations performed with the v² − f model are able to detect the onset of the plume meandering and show remarkable improvement of the predicted decay rate and rate of spread of the scalar plume when compared to steady RANS solutions. By computing explicitly the periodic component of velocity and scalar fluctuations, the unsteady v² − f model is able to provide a representation of scalar flux components consistent with DNS statistics, where the counter-gradient transport mechanism that takes place in the streamwise component is also captured by URANS results. Nonetheless, the agreement with DNS statistics for the mean concentration and the plume width is limited by the onset of the low-frequency modulation in the vortex-shedding and plume meandering, giving a challenging modeling issue in the simulation of dispersion using the RANS equations.     

Computation of turbulent asymmetric wake

The development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two-dimensional Navier-Stokes equations along with the k-ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant C_u as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.     

A computational study on robust prediction of transition point over NACA0012 aerofoil surfaces from laminar to turbulent flows

Flowtransition from laminar toturbulent is prerequisite todecide whereabouts to apply surface flowcontrol techniques. This appears missing in a number of works in which thecontrol effects were merelyinvestigated without getting insight into alteration of transition position. The aim of this study is to capture the correctposition of transition overNACA0012 aerofoil at different angles of attack. Firstly, an implicit, time marching, highresolution total variation diminishing (TVD) scheme was developed to solve the governingNavier—Stokes equations forcompressible fluid flows around aerofoil sections to obtain velocity profiles around the aerofoilsurfaces. Secondly, the linear instability solver based on the Orr—Sommerfeld equations and the e^N methods were developed to calculate the onset of transition over the aerofoil surfaces. Forthe low subsonic Mach number of 0.16, the accuracy of the compressible solutions was assessed bysome available experimental results of low speed incompressible flows. In allcases, transition positionswere accurately predicted which shows applicability and superiority of the present work to beextended for higher Mach number compressible flows. Here, transition prediction methodology is described and the results of this analysiswithout active flow controlor separation are presented.     

On the simulation of the flow around a circular cylinder at Re=140,000

The flow around a circular cylinder at Reynolds number of 1.4 × 10⁵ is examined with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) methods. Such problem is in the upper limit of the flow regime where turbulent transition occurs in the free shear-layers and so the flow dynamics is dominated by the spatial development of vortex-shedding structure, and in particular by the Kelvin–Helmholtz rollers and turbulence onset. The objectives of this investigation are threefold: (i) determine the aptitude of distinct RANS and SRS models to simulate the correct flow regime; (ii) compare the predictions of selected methods with available experimental measurements; and (iii) examine key modelling and flow features that contribute to the observed results. The evaluated models range from RANS supplemented with linear, transition, and non-linear turbulent viscosity closures, to hybrid and bridging SRS methods. Bridging computations are conducted at various constant degrees of physical resolution (range of resolved scales). The results illustrate the complexity of predicting the present flow problem. It is shown that RANS and SRS formulations modelling turbulence in boundary-layers with the selected linear turbulent viscosity closures lead to a premature onset of turbulence which alters the flow regime of the simulations. Although the transition and non-linear RANS closures can predict the correct flow regime, the outcome of this study indicates that solely the bridging model at constant physical resolution is able to achieve an accurate and physics-based prediction of the flow dynamics. Nonetheless, the necessary degree of physical resolution makes the numerical requisites of such computations demanding.     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

Aspects of the transpiration model for aerofoil design

Transpiration is a technique in which extra non-physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co-ordinates are adjusted or to find shape corrections in inverse design methods. A first-order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.     

SUPERPOSITION TECHNIQUE FOR POTENTIAL FLOW AROUND AN AEROFOIL AND CONTROL OF THE CIRCULATION

In this paper the superposition technique for a potential flow around an aerofoil is investigated in the complex plane. The control of the circulation around the aerofoil by satisfying the Kutta condition at the flow field points is described.     

Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method

A complete first-order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non-circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body-fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.     

AN IMPROVED NAVIER–STOKES PROCEDURE FOR ANALYSIS OF TWO-DIMENSIONAL AEROFOILS IN LAMINAR AND TURBULENT FLOWS

An accurate and robust Navier–Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier–Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k–ε turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, C_Lmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. © 1997 John Wiley & Sons, Ltd.     

The influence of acceleration and deceleration on shock wave movement on and around aerofoils in transonic flight

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s² (106 g), starting at Mach 0.1, and decelerated at −1041m/s², starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.      

A computational study of the influence of viscoelasticity on the interfacial dynamics of dip coating flow

The effect of viscoelasticity on the interfacial dynamics of air displacing a viscoelastic fluid under the presence of gravity, i.e., the dip coating flows is examined. A stabilized finite element method coupled with a pseudo-solid domain mapping technique is used to carry out the computations. The fluid is modeled by the Finitely Extensible Non-linear Elastic Chilton–Ralison (FENE-CR) constitutive equation. Simulations at various Ca and Bo are performed in order to determine the limiting condition for dip coating where the flow characteristics become independent of Bo. For all values of Ca and Bo studied, the flow is characterized by recirculation near the interface. To this end the film thickness scaled with the capillary length, as a function of Wi, at low Ca and high Bo collapses onto a single curve, and agrees with the analytical expression for the film thickness in the low Wi limit. As the value of Ca is increased, the corresponding value of Bo that is required to collapse the results onto a single curve, i.e., the dip coating flow limit, is correspondingly higher. For a fixed Ca and Wi, increasing Bo results in a decrease in the film thickness, an increase in the size of the recirculation region and an increase in the strain rates subsequently leading to an increase in the normal stresses. We show that the interfacial dynamics in the dip coating flow are qualitatively similar to those observed in the Hele-Shaw flow. Specifically, at low Wi, film thinning occurs and as the value of Wi is increased, the formation of normal elastic stress boundary layers in the capillary transition region is observed. This is accompanied by a sharp increase in the film thickness and a compression of the air–liquid interface in the capillary transition region.     

附面层修正应用于无网格算法的研究

研究了无网格算法中的附面层修正方法,在一种布置点云方法的基础上,发展一种曲面拟合的重构方式构造流场物理量;找出了无网格算法与网格算法之间的联系,成功将AUSM＋-up格式移植到无网格算法当中,并应用于计算欧拉方程的数值通量;计算中采用了一种改进的隐式时间推进,并引入当地时间步长和残值光顺等加速收敛措施,成功的将附面层修...     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

A method for predicting unsteady potential flow about an aerofoil

A new model is presented for the calculation of the incompressible, inviscid flow around an arbitrary aerofoil undergoing unsteady motion. The technique was developed from the steady flow algorithm of Leishman and Galbraith¹ in which use was made of a linear distribution of panel vorticity. The procedure is in the same class as that of Basu and Hancock² but, because of the particular approach to the manner of specifying the shed vorticity, only a set of linear simultaneous equations needs be solved, unlike the method of Reference 2, complicated by the necessary solution of a quadratic. A brief history of unsteady flow modelling is given in the introduction, followed by the mathematical details of the current method. Results are presented and discussed for a number of cases which clearly illustrate relevant characteristics of unsteady flow.     

Experimental investigation to study flow and heat transfer characteristics over a NACA0018 aerofoil for different height ratios

Experiments are carried out to study flow and heat transfer characteristics over NACA0018 aerofoil when the body approaches the wall of a wind tunnel. Investigations have been done to study the effect of wall proximity due to flow separation around the body at Reynolds number 2.5 × 10⁵, different height ratios and various angles of attack. The static pressure distribution has been measured on upper and lower surfaces of the aerofoil. The results have been presented in the form of pressure coefficient, drag coefficient for different height ratios. Pressure coefficient values are decreased and then increased on the lower surface of the aerofoil and decreased on the upper surface of the aerofoil at all angles of attack. The negative pressure coefficient and drag coefficient decreases as the body approaches the upper wall of wind tunnel. The maximum value of drag coefficient has been observed at an angle of attack 30° for the aerofoil at all height ratios. The Heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficients are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. The variation of local as well as average Nusselt number has been shown with non dimensional distance for different angles of attack and for various height ratios. The local as well as average Nusselt number decreases as the height ratio decreases for all non-dimensional distance and angles of attack respectively. Maximum value of average Nusselt number has been observed at an angle of attack 40°.     

Unsteady supersonic flow over an oscillatory aerofoil using a second-order TVD scheme

The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second-order space-accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0·0 and ± 1·0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co-ordinates for each time step. The calculations have been done for two angles of attack θ = 5·0° sin (ωt) and θ = 3·0° + 3·0° sin (ωt) for the free-stream Mach numbers 2·0 and 3·0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.     

Investigation of slat heel effect on the flow field over multi-element aerofoils

This paper presents results obtained from an experimental study of the flow field over a multi-element aerofoil which incorporates either a conventional or an advanced slat. Detailed measurements of the mean flow and turbulent quantities over a multi-element aerofoil model equipped with either type of slat have been made in a wind tunnel using stationary and flying hot-wire (FHW) probes. The perfomance of the two slats at two angles of attack, =10° and 20°, were investigated and compared with each other. The results showed a better performance for the advanced slat in terms of the mean velocity field and hence an increase in the lift performance. The advantage of the advanced slat was more pronounced for the multi-element aerofoil placed at the higher angle of attack, i.e., 20°. These findings were substantiated by the Reynolds stresses measured over the multi-element aerofoil, with the conventional slat exhibiting higher values compared with its advanced slat counterpart. Both the mean velocity and Reynolds stress results clearly demonstrated that the conventional slat had a lower stall margin than the advanced slat.