N-S EQUATION CALCULATIONS ON MULTI-ELEMENT AIRFOILS WITH ZONAL PATCHED GRIDS

For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.

AERODYNAMIC FORCE AND FLOW STRUCTURES OF TWO AIRFOILS IN FLAPPING MOTIONS

Aerodynamic force and flow structures of two airfoils in a tandem configuration in flapping motions axe studied, by solving the Navier-Stokes equations in moving overset grids. Three typical phase differences between the fore- and aft-airfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertical force coefficient over the downstroke is 2.74, which is about 3 times as large as the maximum steady-state lift coefficient of a dragonfly wing; the time average of the horizontal force coefficient is 1.97, which is also large. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the 'pitching-up' motion near the end of the stroke. (2) In the cases of two-airfoils, the time-variations of the force and moment coefficients on each airfoil are broadly similar to that of the single airfoil in that the vertical force is mainly produced in downstroke and the horizontal force in upstroke, but very large differences exist due to the interaction. (3) For in-phase stroking, the major differences caused by the interaction are that the vertical force on FA in downstroke is increased and the horizontal force on FA in upstroke decreased. As a result, the magnitude of the resultant force is almost unchanged but it inclines less forward. (4) For counter stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased. As a result, the magnitude of the resultant force is decreased by about 20 percent but its direction is almost unchanged. (5) For 90 degrees -phase-difference stroking, the major differences axe that the vertical force on AA in downstroke and the horizontal force on FA in upstroke axe decreased greatly and the horizontal force on AA in upstroke increased. As a result, the magnitude of the resultant force is decreased by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also the largest resultant force); the 90 degrees -phase-difference flapping results in the largest horizontal force, but the smallest resultant force.

Effect of Cambering on the Aerodynamic Performance of Heaving Airfoils

In the present work,a parametric numerical study is conducted in order to assess the effect of airfoil cambering on the aerodynamic performance of rigid heaving airfoils.The incompressible Navier-Stokes equations are solved in their velocity-pressure formulation using a second-order accurate in space and time finite-difference scheme.To tackle the problem of moving boundaries,the governing equations are solved on overlapping structured grids.The numerical simulations are performed at a Reynolds number of Re=1100 and at different values of Strouhal number and reduced frequency.The results obtained show that the airfoil cambering geometric parameter has a strong influence on the average lift coefficient,while it has a smaller impact on the average thrust coefficient and propulsive efficiency of heaving airfoils.

Numerical analysis of the s1020 airfoils in tandem under different flapping configurations

The objective of this project is to improve the performance of the efficiency, thrust and lift of flapping wings in tandem arrangement. This research investigates the effect of the arrangement of the airfoils in tandem on the performance of the airfoils by varying the phase difference and distance between the airfoils. Three flapping configurations from an earlier phase of a research which gives high efficiency, thrust and lift are used in the tandem simulation. It is found all the different flapping configurations show improvement in the efficiency, thrust or lift when the distance between the two airfoils and the phase angle between the heaving positions of the two airfoils are optimal. The average thrust coefficient of the tandem arrangement managed to attain more than twice that of the single one （4.84 vs. 2.05）. On the other hand, the average lift coefficient of the tandem arrangement also increased to 4.59, as compared to the original single airfoil value of 3.04. All these results obtained will aid in the design of a better ornithopter with tandem wing arrangement.

Functional design of wind turbine airfoils based on roughness sensitivity characteristics

To improve aerodynamic performance of wind turbine airfoils,the shape profile characteristic of the airfoil is investigated.Application of conformal transformation,one functional and integrated expression of wind turbine airfoils is presented.Using the boundary layer theory,the aerodynamic model with roughness of wind turbine airfoils is introduced by studying flow separation around the airfoil.Based on the shape expression and aerodynamic performance of airfoils,the function design of wind turbine airfoils is carried out that the maximum lift-drag ratio and low roughness sensitivity are designed objects.Three wind turbines airfoils with different thickness are gained which are used at tip part of blades.As an example,the aerodynamic performance of one designed airfoil with relative thickness of 15%is simulated in different conditions of clean surface,rough surface,laminar flow and turbulent flow.The comparison of aerodynamic performance between the designed airfoil and one popular NACA airfoil is completed which can verify the better performance of the designed airfoil and reliability of the designed method.

Bi-objective path optimization of flapping airfoils based on a surrogate model

A bi-objective optimization problem for flapping airfoils is solved to maximize the time-averaged thrust coefficient and the propulsive efficiency. Design variables include the plunging amplitude, the pitching amplitude and the phase shift angle. A well defined Kriging model is used to substitute the time-consuming high fidelity model, and a multi-objective genetic algorithm is employed as the search algorithm. The optimization results show that the propulsive efficiency can be improved by reducing the plunging amplitude and the phase shift angle in a proper way. The results of global sensitivity analysis using the Sobol’s method show that both of the time-averaged thrust coefficient and the propulsive efficiency are most sensitive to the plunging amplitude, and second most sensitive to the pitching amplitude. It is also observed that the phase shift angle has an un-negligible influence on the propulsive efficiency, and has little effect on the time-averaged thrust coefficient.

INVESTIGATION OF UNSTEADY EXCITATION EFFECTS ON AERODYNAMIC PROPERTIES OF AIRFOILS

In this paper, the techniques to manage and control the flow over airfoils by using the external unsteady excitations are investigated. The mechanisms of these excitation effects are also explored. The principal goal of this study is to gain a better understanding and to find the possible ways for enhancing the aerodynamic efficients. The experimental investigations are carried out in two low-speed wind tunnels. The test models are two dimensional airfoils with different section geometries. Four means of excitations have been used in these experiments. (1) The pitch oscillation of the airfoil high-angle-of-attack situation. (2) The moving surface effects of the airfoil with a leading edge rotating cylinder. (3) Oscillating leading edge flaperon. (4) Small oscillating spoiler located near the leading edge of the airfoil. The lift, drag and pitch moment coefficients are measured in these experiments. But, we will put the emphasis only on the 'dynamic amplifying effects' on aerodynamic lift in this paper. Results obtained indicate that the beneficial aerodynamic effects of section lift increase can be obtained at the high angle of attack near stall regime, as long as the frequency and amplitute of the excitation are appropriately selected.

Multigrid fictitious boundary method for incompressible viscous flows around moving airfoils

In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NACA0012 airfoils. The calculations were carded on a fixed multigrid finite element mesh on which fluid equations were satisfied everywhere, and the airfoils were allowed to move freely through the mesh. The MFBM was employed to treat interactions between the fluid and the airfoils The motion of the airfoils was modeled by Newton-Euler equations. Numerical results of experiments verify that this method provides an efficient way to simulate incompressible viscous flows around moving airfoils.

TRANSIENT AERODYNAMIC BEHAVIOURS ASSOCIATED WITH STEPWISE INCIDENCE VARIATION OF AIRFOILS

Transient aerodynamic characteristics of airfoil are important for the safety of airplanes, the development of helicopter rotors and many other applications of unsteady aerodynamics. For a better understanding of these phenomena, it is necessary to investigate the simultaneous relation between the characteristics and the flow field. The purpose of the present study is to clarify experimentally the fundamentals of the aerodynamic behaviours associated with stepwise incidence variations from 0 to some certain values, including high angles of attack, of symmetric airfoils at low speeds, Reynolds number being of the order of 104. Temporal variations of surface pressure distribution, lift, drag and . pitching moment, and the observation of the flow field will be discussed.

NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS

Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.

Aerodynamic Performances of Wind Turbine Airfoils Using a Panel Method

One of the key features of Laplace＇s Equation is the property that allows the equation governing the flow field to be converted from a 3D problem throughout the field to a 2D problem for finding the potential on the surface. The solution is then found using this property by distributing ＂singularities＂ of unknown strength over discretized portions of the surface： panels. Hence the flow field solution is found by representing the surface by a number of panels, and solving a linear set of algebraic equations to determine the unknown strengths of the singularities. In this paper a Hess-Smith Panel Method is then used to examine the aerodynamics of NACA 4412 and NACA 23015 wind turbine airfoils. The lift coefficient and the pressure distribution are predicted and compared with experimental result for low Reynolds number. Results show a good agreement with experimental data.

Development of Airfoils Based on Their Aerodynamic Characteristics Using Artificial Neural Networks

One of the main concerns in Engineering nowadays is the development of aircrafts of low consumption and high performance. For this purpose, airfoils are studied and designed to have an elevated lift coefficient and a low drag coefficient, thus generating a highly efficient airfoil. The higher the efficiency value is, the lower the aircraft fuel consumption will be; thus improving its performance. In this sense, this work aims to develop a tool for airfoil creation from some desired characteristics, such as the lift and drag coefficients and maximum efficiency rate, using an algorithm based on an ANN （artificial neural network）. In order to do so, a database of aerodynamic characteristics with a total of 300 airfoils was initially collected from the XFoil software. Then, through a routine implemented in the MATLAB software, network architectures of one, two, three and four modules were trained, using the back propagation algorithm and momentum. The cross-validation technique was applied to analyze the results, evaluating which network possesses the lowest value in RMS （root-mean-square） error. In this case, the best result obtained was from the two-module architecture with two hidden neuron layers. The airfoils developed by this network, in the regions with the lowest RMS, were compared to the same airfoils imported to XFoil. The presented work offers as a contribution, in relation to other works involving ANN applied to fluid mechanics, the development of airfoils from their aerodynamic characteristics.

Analysis of non-symmetrical flapping airfoils

Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non- symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil＇s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interac- tions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter＇s wing.

A general model for trailing edge serrations simulation on wind turbine airfoils

Trailing edge serrations(TESs)are capable of noticeably suppressing the turbulent trailing edge noise induced by rotating wind turbine blades and become an integral part of a blade.However,the challenges involved in the dimensional design of serration height 2 h,wavelengthλand flap angleϕare yet to be dealt with in a satisfactory manner.To address the problem,a general model for simulating the effects of serrations on the hydrodynamic and aeroacoustic performance is proposed due to its ease of use and relatively low requirements for user input.The solid serrations are replicated by momentum sources calculated by its aerodynamic forces.Then,a case relevant to wind turbine airfoil is examined,a hybrid improved delay detached eddy simulation(IDDES)method coupled with FW-H integration is deployed to obtain the flow features and far-field sound pressure level.It is found that the modeling method could reproduce the flow field and noise as serrated airfoil.

Aerodynamic and Acoustic Optimization for Multi-element Airfoils

The paper is to integrate aerodynamic and aero-acoustic optimizatiom design of high lift devices,especially for two-element airfoils with slat.Aerodynamic analysis on flow field utilizes a high-order,high-resolution spatial differential method for large eddy simulation(LES),which can guarantee accuracy and efficiency.The aeroacoustic analysis for noise level is calculated with Ffowcs Williams-Hawkings(FW-H)integration formula.Fidelity of calculation is verified by standard models.Method of streamline-based Euler simulation(MSES)is used to obtain the aerodynamic characters.Based on the confirmation of numerical methods,detailed research has been conducted for the leading edge slat on multi-element airfoils.Various slot parameter influences on noise are analyzed.The results of the slot optimization parameters can be used in multi-element airfoil design.

Design optimization of unsteady airfoils with continuous adjoint method

In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method （FVM）. Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.

HYBRID CARTESIAN GRID/GRIDLESS METHOD FOR CALCULATING VISCOUS FLOWS OVER MULTI-ELEMENT AIRFOILS

A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.

Variable-Domain Variational Finite Element Solution of I_A Inverse Problem of 2-D Unsteady Compressible Flow around Oscillating Airfoils

In this paper, on the basis of the variational principles developed the finite element method (FEM) is employed for numerical solution of the inverse pro blem of 2 D unsteady compressible flow around oscillating airfoils by incorporating the non reflecting far field boundary conditions and a new unsteady Kutta condition. All unknown boundary (airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are determined via the functional variation with variable domain and artificial density concept. For the numerical realization of the variable domain variation, a special finite element with self adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.

Tests and numerical simulation of aerodynamic characteristics of airfoils for general aviation applications

This paper was to validate the effects of airfoil thickness ratio on the characteristics of a family of airfoils. Research was carried out in different ways. First,tests were conducted in the wind tunnel. And numerical simulation was performed on the basis of tests. Results from calculation were consistent with tests,indicating that numerical method could help evaluate characteristics of airfoils. Then the results were confirmed by compared with empirical data. The study also showed that the determining factor of lift is not only the thickness ratio,but the angle of attack,the relative camber and the camber line. The thickness ratio appears to have little effect on lift coefficient at zero angle of attack,since the angle of zero lift is largely determined by the airfoil camber. According to the research,numerical simulation can be used to determine the aerodynamic characteristics of airfoils in different environment such as in the dusty or humid air.

Numerical Investigation of the Effects of Wind Tunnel Model Vibrations on the Measured Aerodynamic Properties of Airfoils and Wings

This paper presents a numerical prediction of the unsteady flow field around oscillating airfoils at high angles of attack by solving unsteady Reynolds-averaged Navier-Stokes equations with SST turbulence model in order to simulate the effects of wind tunnel model vibrations on the aerodynamic properties of airfoils,especially high-aspect-ratio wings in a wind tunnel.The effects of the phase lagging between different modes of oscillations,i.e.,the airfoil plunging oscillation mode,the pitching oscillation mode,and the forward-backward oscillation mode,are also studied.It is shown that the vibrations (oscillations) of airfoils can cause the unsteady shedding of large-size separated vortex to precede the stationary stall incidence,hence lead to a stall onset at some earlier (lower) incidence than that in the steady sense.The different phase lagging has different effect on the flow field.When the pitching oscillation mode has small phase lagging behind the plunging oscillation mode,the effect of vibrations is large.Besides,if the amplitude of the oscillations is large enough,and the different modes of vibrations match or combine appropriately,the unsteady stall may occur 2° earlier in angle of attack than the case where airfoils keep stationary.