Mechanism of unconventional aerodynamic characteristics of an elliptic airfoil

Abstract The aerodynamic characteristics of elliptic airfoil are quite different from the case of conventional airfoil for Reynolds number varying from about 10~4to 10~6.In order to reveal the fundamental mechanism,the unsteady flow around a stationary two-dimensional elliptic airfoil with 16%relative thickness has been simulated using unsteady Reynolds-averaged Navier–Stokes equations and the γ-Reθt transition turbulence model at different angles of attack for flow Reynolds number of 5×10~5.The aerodynamic coefficients and the pressure distribution obtained by computation are in good agreement with experimental data,which indicates that the numerical method works well.Through this study,the mechanism of the unconventional aerodynamic characteristics of airfoil is analyzed and discussed based on the computational predictions coupled with the wind tunnel results.It is considered that the boundary layer transition at the leading edge and the unsteady flow separation vortices at the trailing edge are the causes of the case.Furthermore,a valuable insight into the physics of how the flow behavior affects the elliptic airfoil’s aerodynamics is provided.     

Double-stage Metamodel and Its Application in Aerodynamic Design Optimization

Constructing metamodel with global high-fidelity in design space is significant in engineering design. In this paper, a double-stage metamodel (DSM) which integrates advantages of both interpolation metamodel and regression metamodel is constructed. It takes regression model as the first stage to fit overall distribution of the original model, and then interpolation model of regression model approximation error is used as the second stage to improve accuracy. Under the same conditions and with the same samples, DSM expresses higher fidelity and represents physical characteristics of original model better. Besides, in order to validate DSM characteristics, three examples including Ackley function, airfoil aerodynamic analysis and wing aerody-namic analysis are investigated. In the end, airfoil and wing aerodynamic design optimizations using genetic algorithm are presented to verify the engineering applicability of DSM.     

Numerical analysis and optimization of boundary layer suction on airfoils

Numerical approach of hybrid laminar flow control(HLFC) is investigated for the suction hole with a width between 0.5 mm and 7 mm. The accuracy of Menter and Langtry’s transition model applied for simulating the flow with boundary layer suction is validated. The experiment data are compared with the computational results. The solutions show that this transition model can predict the transition position with suction control accurately. A well designed laminar airfoil is selected in the present research. For suction control with a single hole, the physical mechanism of suction control, including the impact of suction coefficient and the width and position of the suction hole on control results, is analyzed. The single hole simulation results indicate that it is favorable for transition delay and drag reduction to increase the suction coefficient and set the hole position closer to the trailing edge properly. The modified radial basis function(RBF) neural network and the modified differential evolution algorithm are used to optimize the design for suction control with three holes. The design variables are suction coefficient, hole width, hole position and hole spacing. The optimization target is to obtain the minimum drag coefficient. After optimization,the transition delay can be up to 17% and the aerodynamic drag coefficient can decrease by 12.1%.     

A new grid deformation technology with high quality and robustness based on quaternion

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation' is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation(TFI) technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation' improves the efficiency and quality of the basic quaternion deformation method significantly.     

CFD calculations on the unsteady aerodynamic characteristics of a tilt-rotor in a conversion mode

In order to calculate the unsteady aerodynamic characteristics of a tilt-rotor in a conversion mode, a virtual blade model(VBM) and an real blade model(RBM) are established respectively. A new multi-layer moving-embedded grid technique is proposed to reduce the numerical dissipation of the tilt-rotor wake in a conversion mode. In this method, a grid system generated abound the rotor accounts for rigid blade motions, and a new searching scheme named adaptive inverse map(AIM) is established to search corresponding donor elements in the present movingembedded grid system to translate information among the different computational zones. A dual-time method is employed to fulfill unsteady calculations on the flowfield of the tilt-rotor,and a second-order centered difference scheme considering artificial viscosity is used to calculate the flux. In order to improve the computing efficiency, the single program multiple data(SPMD)model parallel acceleration technology is adopted, according to the characteristic of the current grid system. The lift and drag coefficients of an NACA0012 airfoil, the dynamic pressure distributions below a typical rotor plane, and the sectional pressure distributions on a three-bladed Branum–Tung tilt-rotor in hover flight are calculated respectively, and the present VBM and RBM are validated by comparing the calculated results with available experimental data. Then, unsteady aerodynamic forces and flowfields of an XV-15 tilt-rotor in different modes, such as a fixed conversion mode at different tilt angles(15°, 30°, 60°) and a whole conversion mode which converses from 0° to90°, are numerically simulated by the VBM and RBM respectively. By analyses and comparisons on the simulated results of unsteady aerodynamic forces of the tilt-rotor in different modes, some meaningful conclusions about distorted blade-tip vortex distribution and unsteady aerodynamic force variation in a conversion mode are obtained, and these investigation results could provide a good foundation for tilt-rotor aircraft design in the future.     

Robust Navier-Stokes method for predicting unsteady flowfield and aerodynamic characteristics of helicopter rotor

A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes(RANS) equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method" and ‘‘minimum distance scheme of donor elements method" are established in this work. To improve the computational efficiency, Message Passing Interface(MPI) parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage(FAS) multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.     

Transition study of 3D aerodynamic configures using improved transport equations modeling

As boundary layer transition plays an important role in aerodynamic drag prediction,the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport(SST) eddy-viscosity model, a new method, the SST-N TS-N CF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the N TS equation proposed by Coder, which simulates Tollmien–Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2)A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERAM6 swept wing validate the predictive quality of the new SST-N_(TS)-N_(CF) model.     

Airfoil Aeroelastic Flutter Analysis Based on Modified Leishman-Beddoes Model at Low Mach Number

Based on modified Leishman-Beddoes (L-B) state space model at low Mach number (lower than 0.3), the airfoil aeroelastic system is presented in this paper. The main modifications for L-B model include a new dynamic stall criterion and revisions of normal force and pitching moment coefficient. The bifurcation diagrams, the limit cycle oscillation (LCO) phase plane plots and the time domain response figures are applied to investigating the stall flutter bifurcation behavior of airfoil aeroelastic systems with symmetry or asymmetry. It is shown that the symmetric periodical oscillation happens after subcritical bifurcation caused by dynamic stall, and the asymmetric periodical oscillation, which is caused by the interaction of dynamic stall and static divergence, only happens in the airfoil aeroelastic system with asymmetry. Validations of the modified L-B model and the airfoil aeroelastic system are presented with the experimental airload data of NACA0012 and OA207 and experimental stall flutter data of NACA0012 respectively. Results demonstrate that the airfoil aeroelastic system presented in this paper is effective and accurate, which can be applied to the investigation of airfoil stall flutter at low Mach number.     

Effects of relative thickness on aerodynamic characteristics of airfoil at a low Reynolds number

This study focuses on the characteristics of low Reynolds number flow around airfoil of high-altitude unmanned aerial vehicles(HAUAVs) cruising at low speed.Numerical simulation on the flows around several representative airfoils is carried out to investigate the low Reynolds number flow.The water tunnel model tests further validate the accuracy and effectiveness of the numerical method.Then the effects of the relative thickness of airfoil on aerodynamic performance are explored, using the above numerical method, by simulating flows around airfoils of different relative thicknesses(12%, 14%, 16%, 18%), as well as different locations of the maximum relative thickness(x/c = 22%, 26%, 30%, 34%), at a low Reynolds number of 5 · 105.Results show that performance of airfoils at low Reynolds number is mainly affected by the laminar separation bubble.On the premise of good stall characteristics, the value of maximum relative thickness should be as small as possible, and the location of the maximum relative thickness ought to be closer to the trailing edge to obtain fine airfoil performance.The numerical method is feasible for the simulation of low Reynolds number flow.The study can help to provide a basis for the design of low Reynolds number airfoil.     

Parametric analyses for synthetic jet control on separation and stall over rotor airfoil

Numerical simulations are performed to investigate the effects of synthetic jet control on separation and stall over rotor airfoils. The preconditioned and unsteady Reynolds-averaged Navier–Stokes equations coupled with a k x shear stream transport turbulence model are employed to accomplish the flowfield simulation of rotor airfoils under jet control. Additionally,a velocity boundary condition modeled by a sinusoidal function is developed to fulfill the perturbation effect of periodic jets. The validity of the present CFD procedure is evaluated by the simulated results of an isolated synthetic jet and the jet control case for airfoil NACA0015. Then, parametric analyses are conducted specifically for an OA213 rotor airfoil to investigate the effects of jet parameters(forcing frequency, jet location and momentum coefficient, jet direction, and distribution of jet arrays) on the control effect of the aerodynamic characteristics of a rotor airfoil. Preliminary results indicate that the efficiency of jet control can be improved with specific frequencies(the best lift-drag ratio at F+= 2.0) and jet angles(40 or 75) when the jets are located near the separation point of the rotor airfoil. Furthermore, as a result of a suitable combination of jet arrays, the lift coefficient of the airfoil can be improved by nearly 100%, and the corresponding drag coefficient decreased by26.5% in comparison with the single point control case.     

Conjugate heat transfer investigations of turbine vane based on transition models

The accurate simulation of boundary layer transition process plays a very important role in the prediction of turbine blade temperature field. Based on the Abu-Ghannam and Shaw (AGS) and c-Re h transition models, a 3D conjugate heat transfer solver is developed, where the fluid domain is discretized by multi-block structured grids, and the solid domain is discretized by unstructured grids. At the unmatched fluid/solid interface, the shape function interpolation method is adopted to ensure the conservation of the interfacial heat flux. Then the shear stress transport (SST) model, SST & AGS model and SST & c-Re h model are used to investigate the flow and heat transfer characteristics of Mark II turbine vane. The results indicate that compared with the full turbulence model (SST model), the transition models could improve the prediction accuracy of temperature and heat transfer coefficient at the laminar zone near the blade leading edge. Compared with the AGS transition model, the c-Re h model could predict the transition onset location induced by shock/boundary layer interaction more accurately, and the prediction accuracy of temperature field could be greatly improved.     

Aerodynamic design optimization of nacelle/pylon position on an aircraft

The arbitrary space-shape free form deformation (FFD) method developed in this paper is based on non-uniform rational B-splines (NURBS) basis function and used for the integral parameterization of nacelle-pylon geometry. The multi-block structured grid deformation technique is established by Delaunay graph mapping method. The optimization objects of aerodynamic characteristics are evaluated by solving NavierStokes equations on the basis of multi-block structured grid. The advanced particle swarm optimization (PSO) is utilized as search algorithm, which com-bines the Kriging model as surrogate model during optimization. The optimization system is used for optimizing the nacelle location of DLR-F6 wing-body-pylon-nacelle. The results indicate that the aerodynamic interference between the parts is significantly reduced. The optimization design system established in this paper has extensive applications and engineering value.     

Aerodynamic shape optimization for alleviating dynamic stall characteristics of helicopter rotor airfoil

In order to alleviate the dynamic stall effects in helicopter rotor, the sequential quadratic programming(SQP) method is employed to optimize the characteristics of airfoil under dynamic stall conditions based on the SC1095 airfoil. The geometry of airfoil is parameterized by the class-shape-transformation(CST) method, and the C-topology body-fitted mesh is then automatically generated around the airfoil by solving the Poisson equations. Based on the grid generation technology, the unsteady Reynolds-averaged Navier-Stokes(RANS) equations are chosen as the governing equations for predicting airfoil flow field and the highly-efficient implicit scheme of lower–upper symmetric Gauss–Seidel(LU-SGS) is adopted for temporal discretization. To capture the dynamic stall phenomenon of the rotor more accurately, the Spalart–Allmaras turbulence model is employed to close the RANS equations. The optimized airfoil with a larger leading edge radius and camber is obtained. The leading edge vortex and trailing edge separation of the optimized airfoil under unsteady conditions are obviously weakened, and the dynamic stall characteristics of optimized airfoil at different Mach numbers, reduced frequencies and angles of attack are also obviously improved compared with the baseline SC1095 airfoil. It is demonstrated that the optimized method is effective and the optimized airfoil is suitable as the helicopter rotor airfoil.     

Numerical study on flow fields and aerodynamics of tilt rotor aircraft in conversion mode based on embedded grid and actuator model

A method combining rotor actuator disk model and embedded grid technique is presented in this paper, aimed at predicting the flow fields and aerodynamic characteristics of tilt rotor aircraft in conversion mode more efficiently and effectively. In this method, rotor's influence is considered in terms of the momentum it impacts to the fluid around it; transformation matrixes among different coordinate systems are deduced to extend actuator method's utility to conversion mode flow fields' calculation. Meanwhile, an embedded grid system is designed, in which grids generated around fuselage and actuator disk are regarded as background grid and minor grid respectively, and a new method is presented for ‘donor searching' and ‘hole cutting' during grid assembling. Based on the above methods, flow fields of tilt rotor aircraft in conversion mode are simulated, with threedimensional Navier–Stokes equations discretized by a second-order upwind finite-volume scheme and an implicit lower–upper symmetric Gauss–Seidel(LU-SGS) time-stepping scheme. Numerical results demonstrate that the proposed CFD method is very effective in simulating the conversion mode flow fields of tilt rotor aircraft.     

Horn–Schunck optical flow applied to deformation measurement of a birdlike airfoil

Current deformation measurement techniques suffer from limited spatial resolution. In this work, a highly accurate and high-resolution Horn–Schunck optical flow method is developed and then applied to measuring the static deformation of a birdlike flexible airfoil at a series of angles of attack at Reynolds number 100,000 in a low speed, low noise wind tunnel. To allow relatively large displacements, a nonlinear Horn–Schunck model and a coarse-to-fine warping process are adopted. To preserve optical flow discontinuities, a nonquadratic penalization function, a multicue driven bilateral filtering and a principle component analysis of local image patterns are used.First, the accuracy and convergence of this Horn–Schunck technique are verified on a benchmark.Then, the maximum displacement that can be reliably calculated by this technique is studied on synthetic images. Both studies are compared with the performance of a Lucas–Kanade optical flow method. Finally, the Horn–Schunck technique is used to estimate the 3-D deformation of the birdlike airfoil through a stereoscopic camera setup. The results are compared with those computed by Lucas–Kanade optical flow, image correlation and numerical simulation.     

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.     

Numerical Simulation of Rotor-aerodynamic Surface Interaction in Hover Using Moving Chimera Grid

Three-dimensional unsteady Navier-Stokes equations are numerically solved to simulate the aerodynamic interaction of rotor, canard and horizontal tail in hover based on moving chimera grid. The variations of unsteady aerodynamic forces and moments of the canard and horizontal tail with respect to the rotor azimuth are analyzed with the deflection angle set at 0° and 50°, respectively. The pressure map of aerodynamic surfaces and velocity vector distribution of flow field are investigated to get better understanding of the unsteady aerodynamic interaction. The result shows that the canard and horizontal tail present different characteristics under the downwash of the rotor. The canard produces much vertical force loss with low amplitude fluctuation. Contrarily, the horizontal tail, which is within the flow field induced by the down wash of the rotor, produces only less vertical force loss, but the amplitudes of the lift and pitching moment are larger, implying that a potential deflection angle scheme in hover is 50° for the canard and 0° for the horizontal tail.     

Effects of yaw-roll coupling ratio on lateral-directional aerodynamic characteristics

Experimental investigation of large amplitude yaw-roll coupled oscillations was conducted in a low-speed wind tunnel using an aircraft configuration model. A special test rig was designed and constructed to provide different coupled motions from low to high angles of attack.A parameter ‘‘coupling ratio" was introduced to indicate the extent of yaw-roll coupling. At each pitch angle, seven coupling ratios were designed to study the yaw-roll coupling effects on the lateraldirectional aerodynamic characteristics systematically. At high angles of attack, the damping characteristics of yawing and rolling moments drastically varied with coupling ratios. In the coupled motions with the rotation taking place about the wind axis, the lateral-directional aerodynamic moments exhibited unsteady characteristics and were different from the ‘‘quasi-steady" results of the rotary balance tests. The calculated results of the traditional aerodynamic derivative method were also compared with the experimental data. At low and very high angles of attack, the aerodynamic derivative method was applicative. However, within a wide range of angles of attack, the calculated results of aerodynamic derivative method were inconsistent with the experimental data, due to the drastic changes of damping characteristics of lateral-directional aerodynamic moments with yaw-roll coupling ratios.     

Flow separation control on swept wing with nanosecond pulse driven DBD plasma actuators

A 15° swept wing with dielectric barrier discharge plasma actuator is designed.Experimental study of flow separation control with nanosecond pulsed plasma actuation is performed at flow velocity up to 40 m/s. The effects of the actuation frequency and voltage on the aerodynamic performance of the swept wing are evaluated by the balanced force and pressure measurements in the wind tunnel. At last, the performances on separation flow control of the three types of actuators with plane and saw-toothed exposed electrodes are compared. The optimal actuation frequency for the flow separation control on the swept wing is detected, namely the reduced frequency is 0.775, which is different from 2-D airfoil separation control. There exists a threshold voltage for the low swept wing flow control. Before the threshold voltage, as the actuation voltage increases, the control effects become better. The maximum lift is increased by 23.1% with the drag decreased by 22.4% at 14°, compared with the base line. However, the best effects are obtained on actuator with plane exposed electrode in the low-speed experiment and the abilities of saw-toothed actuators are expected to be verified under high-speed conditions.     

A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

It is of great significance to improve the accuracy of turbulence models in shock-wave/ boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent boundary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation(DNS). It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart–Allmaras(S–A) model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S–A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S–A model are obviously improved. Thus it can be concluded that the modification of S–A model with the pressure gradient can improve the predictive accuracy for simulating the shock-wave/turbulent boundary layer interaction.