Time‐dependent turbulent cavitating flow computations with interfacial transport and filter‐based models

Turbulent cavitating flow computations need to address both cavitation and turbulence modelling issues. A recently developed interfacial dynamics‐based cavitation model (IDCM) incorporates the interfacial transport into the computational modelling of cavitation dynamics. For time‐dependent flows, it is known that the engineering turbulence closure such as the original k–ε model often over‐predicts the eddy viscosity values reducing the unsteadiness. A recently proposed filter‐based modification has shown that it can effectively modulate the eddy viscosity, rendering better simulation capabilities for time‐dependent flow computations in term of the unsteady characteristics. In the present study, the IDCM along with the filter‐based k–ε turbulence model is adopted to simulate 2‐D cavitating flows over the Clark‐Y airfoil. The chord Reynolds number is Re=7.0 × 10⁵. Two angles‐of‐attack of 5 and 8° associated with several cavitation numbers covering different flow regimes are conducted. The simulation results are assessed with the experimental data including lift, drag and velocity profiles. The interplay between cavitation and turbulence models reveals substantial differences in time‐dependent flow results even though the time‐averaged characteristics are similar. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of leading edge cut on the aerodynamics of ram‐air parachutes

The effect of the configuration of leading edge cut on the aerodynamic performance of ram‐air parachutes is studied via two‐dimensional flow simulations. The incompressible Reynolds‐averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite‐element formulation. The Baldwin–Lomax model is employed for turbulence closure. Flow past an LS(1) 0417 airfoil is investigated for various configurations of the leading edge cut and results are compared with those from a Clark‐Y airfoil section. It is found that the configuration of the leading edge cut affects the lift‐to‐drag ratio (L/D) of the parachute very significantly. The L/D value has strong implications on the flight performance of the parachute. One particular configuration results in a L/D value that is in excess of 25 at 7.5° angle of attack. Results are presented for other angles of attack for this configuration. Copyright © 2004 John Wiley & Sons, Ltd.     

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

Numerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

Computation of two‐dimensional flows past ram‐air parachutes

Computational results for flow past a two‐dimensional model of a ram‐air parachute with leading edge cut are presented. Both laminar (Re=10⁴) and turbulent (Re=10⁶) flows are computed. A well‐proven stabilized finite element method (FEM), which has been applied to various flow problems earlier, is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Baldwin–Lomax model is employed for turbulence closure. Turbulent flow computations past a Clarck‐Y airfoil without a leading edge cut, for α=7.5°, result in an attached flow. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift‐to‐drag ratio obtained with the present computations is in good agreement with those reported in the literature. The effect of the size and location of the leading edge cut is studied. It is found that the flow on the upper surface of the parafoil is fairly insensitive to the configuration of the cut. However, the flow quality on the lower surface improves as the leading edge cut becomes smaller. The lift‐to‐drag ratio for various configurations of the leading edge cut varies between 3.4 and 5.8. It is observed that even though the time histories of the aerodynamic coefficients from the laminar and turbulent flow computations are quite different, their time‐averaged values are quite similar. Copyright © 2001 John Wiley & Sons, Ltd.     

Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at α < 15°, forming a small separation bubble, and full separation occurs at α ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at α ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.     

Adjoint‐based airfoil optimization with discretization error control

In this article, we develop a new airfoil shape optimization algorithm based on higher‐order adaptive DG methods with control of the discretization error. Each flow solution in the optimization loop is computed on a sequence of goal‐oriented h‐refined or hp‐refined meshes until the error estimation of the discretization error in a flow‐related target quantity (including the drag and lift coefficients) is below a prescribed tolerance. Discrete adjoint solutions are computed and employed for the multi‐target error estimation and adaptive mesh refinement. Furthermore, discrete adjoint solutions are employed for evaluating the gradients of the objective function used in the CGs optimization algorithm. Furthermore, an extension of the adjoint‐based gradient evaluation to the case of target lift flow computations is employed. The proposed algorithm is demonstrated on an inviscid transonic flow around the RAE2822, where the shape is optimized to minimize the drag at a given constant lift and airfoil thickness. The effect of the accuracy of the underlying flow solutions on the quality of the optimized airfoil shapes is investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

The drag of three-dimensional rectangular cavities

Cavities and other surface cut-outs are present on aircraft in numerous forms, from cargo bays and landing gear housing to rivet depressions and panel handles. Although these surface imperfections make a significant contribution to the overall drag on an aircraft, relatively little is known about the flow mechanisms associated with cavities, particularly those which have a strongly three-dimensional geometry. The present work is a wind tunnel investigation of the drag forces and flow regimes associated with cavities having a 2:1 rectangular planform geometry. The effects of both the cavity depth and the flow incidence angle have been examined in terms of the overall cavity drag increment and the mean surface pressure distributions. The drag forces have been determined from both integrated pressures and direct force balance measurements. For the model normal to the flow direction the flow within the cavity was remarkably symmetrical in all the configurations examined. In most cases the cavity flow is dominated by a single large eddy. However, for cavities yawed to other incidence angles there is considerable flow asymmetry, with strong vorticity shedding and high drag in some cases, notably with depth/narrowest width ratio of 0.4–0.5 at 45–60° incidence. The present data correspond well with established results and extend the scope of information available for design purposes and for the development of numerical models.Nomenclature A _p planform area of model - C _D pressure drag coefficient (F _D /(A _p · q)) - C _D drag coefficient increase due to cavity (C _D – c_f) - c _f local skin friction coefficient - C _L pressure lift coefficient (F _L /(A _p · q)) - C _p mean surface pressure coefficient (P – P _s )/q) - F _D drag force - F _L lift force - h depth - L longest planform dimension of model - P surface pressure on model - P _s freestream static pressure - P _t freestream total pressure - q freestream dynamic pressure (P _t – P_s) - Re Reynolds number (U _R · W/v) - U _R freestream velocity - W narrowest planform dimension of model - Z vertical cartesian coordinate - incidence angle - kinematic viscosity     

平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

Forced‐convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

This paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non‐staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of $30°~90°$. The Reynolds number ranges from 1000 to 50 000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within $30°~45°$under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.     

不同交通流状态下桥梁气动导数的风洞试验研究

为了考虑实际运营车辆对桥梁气动导数的影响,根据车辆密度模拟了三种交通流状态,基于强迫振动装置,分别对每个交通流和无车状态下的桥梁气动导数进行风洞试验研究,讨论了不同攻角下不同车流的车辆对桥梁气动导数的影响,探究了车辆对气动导数影响的百分比以及气动导数变化量的变化规律。研究结果表明:不同攻角下不同车流的车辆均对直接导数A*2、H*4和交叉导数A*4、H*2影响显著,A*2、A*3变化量随着折减风速有一定的变化规律。虽然不同攻角下不同车流的车辆对气动导数的影响程度及影响规律不同,并且车流的繁忙程度对大多数气动导数的影响规律不明显,但是车辆对桥梁气动导数的影响不容忽略。     

Optimal airfoil shapes for low Reynolds number flows

Flow over NACA 0012 airfoil is studied at α = 4^° and 12^° for Re?500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non‐uniform rational B‐splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non‐monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd.     

Aerodynamic behaviour of prismatic bodies with sharp and rounded edges

The aerodynamic behaviour of prismatic bodies in a wide range of angles of attack is addressed in the present work. In particular, we focus on bodies with a basically rectangular shape, either sharp or cylindrical edges and different thicknesses. In general, the thinnest bodies exhibit the largest lift-to-drag ratio at moderate angles of attack, which is further enhanced with rounded edges. At larger angles of attack, bodies with rounded edges exhibit smaller drag than bodies with sharp edges. Roughness was found to enhance the lift-to-drag ratio significantly at small angles, and drag is reduced at larger angles.List of symbols A Cross-sectional area - b Span width - c_D Drag coefficient - c_D,r Recalculated drag coefficient applying a different reference area - c_L Lift coefficient - c_L,r Recalculated lift coefficient applying a different reference area - c_M Pitching moment coefficient - D Drag area - F_D Drag force - F_L Lift force - H Height - L Lift area - l Reference length - M Pitching moment - q Dynamic pressure - Re Reynolds number - Re_Cx Critical Reynolds numbers - T Thickness - t Time - v Velocity - W Width - Angle of attack - , , Angles characterising posture and position of ski jumpers - Fluid density - Aspect ratio - kinematic viscosity     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of flow regime change from subsonic to transonic on the air loads of an oscillating airfoil

In this research, the effect of flow regime change from subsonic to transonic on the air loads of a pitching NACA0012 airfoil is investigated. To do this, the effect of change in flow regime on the lift and pitching moment coefficients hysteresis cycles is studied. The harmonic balance approach is utilized for numerical calculation due to its low computational time. Verifications are also made with previous works and good agreements are observed. The assessment of flow regime change on the aforementioned hysteresis cycles is accomplished in the Mach number range of M=0.65–0.755. The reduced frequency and pitch amplitude also vary from k=0.03 to 0.1 and α₀=1–2.51°, respectively. Results show that the effect of increase in Mach number is to increase and decrease the lift coefficient during downstroke and upstroke, respectively, whereas at low reduced frequencies, the effect of increase in Mach number may lead to a reverse manner when airfoil moves toward its extremum angle of attack. Results also reveal that as the pitch amplitude varies, the shape of lift coefficient hysteresis cycle depends more on the pitch amplitude than on the appearance of shock. It is shown that as the Mach number increases, the incidence angles correspond to the extremum pitching moment, and depending on the reduced frequency, lie between zero and extremum angle of attack. These incidence angles shift toward the extremum angle of attack as the reduced frequency decreases. Results also show that the increase in pitch amplitude at low Mach number, in such a way that leads to the formation of shock around the extremum angle of attack, causes the extremum pitching moment to appear around these angles and at high Mach number, depending on the reduced frequency, the extremum pitching moment incidence angles would be between zero and extremum incidence angle.     

Effect of magnetic Reynolds number on the two‐dimensional hydromagnetic flow around a cylinder

Numerical experiments have been conducted to study the effect of magnetic Reynolds number on the steady, two‐dimensional, viscous, incompressible and electrically conducting flow around a circular cylinder. Besides usual Reynolds number Re, the flow is governed by the magnetic Reynolds number R_m and Alfvén number β. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The pressure Poisson equation is solved to find the pressure fields in the entire flow region. The effects of the magnetic field and electrical conductivity on the recirculation bubble, drag coefficient, standing vortex and pressure are presented and discussed. For low interaction parameter (N<1), the suppression of the flow‐separation is nearly independent of the conductivity of the fluid, whereas for large interaction parameters, the conductivity of the fluid strongly influences the control of flow‐separation. Copyright © 2008 John Wiley & Sons, Ltd.     

垂向双蝠鲼变攻角滑翔水动力性能研究

为了探究垂向间距和攻角对双蝠鲼在沿垂向分布集群滑翔时的水动力性能影响,根据蝠鲼的实际外形建立了蝠鲼计算模型,设置了4种间距排布即0.25, 0.5, 0.75, 1倍体厚排布以及9种攻角状态即-8°～8°,随后借助Fluent软件进行了双蝠鲼变攻角、变垂向间距的集群滑翔数值模拟,结合流场压力云图以及速度云图对集群系统平均升/阻力以及集群中各单体的升/阻力进行了分析.数值计算结果表明:双蝠鲼沿垂向分布在攻角范围为-8°～8°进行集群滑翔时系统平均阻力均高于单体滑翔时所受阻力.单体在集群滑翔过程中获得减阻收益,当双蝠鲼以负攻角集群滑翔时,下方蝠鲼阻力减小,且垂向间距越小,减阻效果越明显;当以正攻角集群滑翔时,上方蝠鲼获得减阻收益.当双蝠鲼以负攻角滑翔时,系统平均升力大于单体滑翔时所受升力;当双蝠鲼以负攻角滑翔时,系统平均升力小于单体滑翔时所受升力,系统平均升力几乎不受垂向间距影响.下方蝠鲼升力始终大于上方蝠鲼升力,但随着垂向间距的增大,升力差距逐渐减小.     

Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier–Stokes equations using the Petrov–Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number Re_N and that based on the total velocity is defined as the total Reynolds number Re_T. Simulations are conducted for two Reynolds numbers of Re_N=500 and Re_T=500, two flow attack angles of α=0° and 45° and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0° and 45°. For a constant normal Reynolds number of Re_N=500, the mean drag and lift coefficients at α=0° are very close to those at α=45°. The difference between the root mean square (RMS) lift coefficient at α=0° and that at α=45° is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0° and 45° are similar to each other. The present simulations show that the agreement in the force coefficients between the 0° and 45° flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for Re_N=100–600, α=0° and 45° and G/D=1. Flow for G/D=1 is found to be two-dimensional at Re_N=100 and weak three-dimensional at Re_N=200. While well defined biased flow can be identified for Re_N=300–600, the gap flow for Re_N=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.     

Experimental study of the aerodynamic characteristics of a low-aspect-ratio flat plate array in a configuration of interest for a tidal energy converter

Wind tunnel experiments were conducted for the flow around a single flat plate and through an array of three parallel flat plates at different angles of incidence to compare their lift and drag coefficients for several values of the Reynolds number around 10⁵ and for three aspect ratio values. The selected cascade configuration is of interest for a particular type of tidal hydrokinetic energy converter. The main differences in the lift and drag forces are discussed, finding that for a plate in a cascade the maximum lift coefficient takes place at a quite different angle of attack, depending on the aspect ratio. The optimal conditions for extracting power from a tidal current are analyzed.