Transonic Airfoil Flow Research Articles

Numerical analysis of static and dynamic wind turbine airfoil characteristics in transonic flow

This study performed an aerodynamic characterization of the FFA-W3-211 wind turbine tip airfoil in transonic flow using Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations, for both steady and dynamic operational conditions. First, the boundary between subsonic and supersonic flow in static conditions was identified, depending on the angle of attack, the approach flow Mach number, and the Reynolds number. The analysis points out that higher Reynolds numbers promote the occurrence of local supersonic flow. Thereafter, to investigate the dynamic behavior in the transonic flow regime, a sinusoidal pitching motion with representative values was imposed. A hysteresis, similar to but distinct from dynamic stall, was observed for entering and leaving the supersonic and subsonic regions. Elevated reduced frequencies widened the hysteresis loop, resulting in increased normal forces on the airfoil. The study indicated that an increase in reduced frequency leads to an earlier onset of transonic flow. In conclusion, the risk of transonic flow occurring during normal operation of the next generation wind turbines predicted in earlier studies could be corroborated. Moreover, dynamic effects and Reynolds number dependencies can be significant.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

An improved neural network for modeling airfoil's unsteady aerodynamics in transonic flow

Understanding the aerodynamic hysteresis loop phenomenon is essential when assessing aerodynamic performance and designing aircraft control systems. This phenomenon is a result of time delay effects in unsteady flow. Traditional methods of predicting unsteady aerodynamic forces using computational fluid dynamics have drawbacks, such as long cycles and low efficiency. In this paper, we focus on predicting the aerodynamic hysteresis loop of the NACA (National Advisory Committee for Aeronautics) 0012 airfoil in transonic flow using a new model called LIDNN (Latin hypercube sample input deep neural network). This model integrates input signals and optimization methods to improve upon traditional neural network models. Based on the example validation, the LIDNN model is authenticated as an accurate and efficient method in predicting the unsteady aerodynamic hysteresis loop of the NACA 0012 airfoil in transonic flow, and another significant advantage of the proposed model is its ability to solve multivariable problems effectively, even under varying Mach numbers.

Numerical Study of the Effect of the Trailing-Edge Devices (Gurney Flap and Divergent Trailing-edge Flap) on the Aerodynamic Characteristics of an Airfoil in Transonic Flow for Drone Applications

Numerical Study of the Effect of the Trailing-Edge Devices (Gurney Flap and Divergent Trailing-edge Flap) on the Aerodynamic Characteristics of an Airfoil in Transonic Flow for Drone Applications

Multi-fidelity nonlinear unsteady aerodynamic modeling and uncertainty estimation based on Hierarchical Kriging

By fusing aerodynamic data from multiple sources, multi-fidelity methods can well balance model accuracy and computational cost. To extend multi-fidelity models for predicting unsteady aerodynamics with uncertainty estimation, an improved modelling framework based on the Hierarchical Kriging (HK) is proposed for nonlinear aerodynamic reduced-order modelling. This aerodynamic modelling framework is achieved by a two-stage modelling strategy. In the first stage, using the current and time-delayed low-fidelity aerodynamic load and pitching motion as input, a linear regression model is built to achieve preliminary aerodynamic prediction. In the second stage, the current and time-delayed preliminary prediction, as well as pitching motion history are used as the input of the Hierarchical Kriging model to predict the high-fidelity aerodynamic loads. The generalization capability of this improved modelling framework is firstly verified by several analytical examples. Furthermore, with three sets of training samples taken from harmonic pitching motions of an airfoil in transonic flow, the proposed model achieves accurate prediction on unsteady aerodynamics of other harmonic and random motions, and provides reliable uncertainty estimation of the predicted unsteady aerodynamics. In addition, the computational cost and prediction errors of multi-fidelity and the single-fidelity aerodynamic model are compared. Even with the same computational cost, the proposed multi-fidelity model still shows improved accuracy. Finally, using the uncertainty estimation of the proposed model, an active learning task is performed, which actively selects and incrementally adds the required training samples. With active learning, a good balance between model accuracy and cost of data acquisition is maintained, while avoiding over-fitting problems of the proposed model.

Characterization Of Shock Buffet On A Supercritical 2D Airfoil In Transonic Flow

The transonic flow over the supercritical OAT15A airfoil is investigated experimentally. Using time-resolved focusing schlieren sequences, we extracted the temporal evolution of the chordwise shock location for a wide range of combinations of Mach number and angle of attack. Based on this data, we identified the conditions of pre-buffet, buffet onset, fully-established buffet, and buffet-offset behavior. Key parameters characterizing most pronounced buffet behavior are presented and quantified in terms of the shock amplitude, its variation over multiple buffet cycles, and the associated frequency of the periodic shock oscillation. Fully-established buffet is identified at a Mach number of 0.72 and angle of attack of 5 deg. It is demonstrated that these operating conditions are characterized by a quasi-sinusoidal shock oscillation at a distinct frequency of 113 Hz, in good agreement with previous studies. This analysis reveals that the harmonic shock oscillation spanning a range of about 16.5% of the airfoil chord is accompanied by a coupled large-scale variation of the global flow topology. Both instantaneous and mean velocity components in the chordwise and vertical directions are discussed for representative phases of the buffet cycle. Instantaneous vector fields of both components provide insight into the flow organization throughout the buffet cycle and allow to identify the streamwise distance traveled by the shock wave within a full cycle. We can thus precisely capture the state of the shock wave and quantify the evolution of the shock-induced separation and the size of the turbulent wake. Severe variations of the flow topology are induced by the large-scale upstream and downstream shock displacement. The results show that incidents of massive flow separation are observed for shock positions being close to the upstream limit, and more general, that the wake influence is more pronounced when induced by an upstream traveling shock wave. Phase-averaged velocity profiles at significant locations along the airfoil suction side complement this analysis. Characteristic sets of velocity profiles are discussed in detail that allow to uniquely describe the development of the flow in each phase of the buffet cycle. Detailed contours and profiles of both velocity and Reynolds shear stress contributions across the wake region highlight the strong downstream influence the shock-induced turbulent wake. Phases of severe flow separation result in reverse flow persisting until the trailing edge which further substantiates the induced momentum deficit.

Flow control method by applying flexible shells procedure in transonic flow

PurposeIn the present research, the effect of the flexible shells method in unsteady viscous flow around airfoil has been studied. In the presented algorithm, due to the interaction of the aerodynamic forces and the structural stiffness (fluid-structural interaction), a geometrical deformation as the bump is created in the area where the shock occurs. This bump causes instead of compressive waves, a series of expansion waves that produce less drag and also improve the aerodynamic performance to be formed. The purpose of this paper is to reduce wave drag throughout the flight range. By using this method, we can be more effective than recent methods throughout the flight because if there is a shock, a bump will form in that area, and if the shock does not occur, the shape of the airfoil will not change.Design/methodology/approachIn this simulation pressure-based procedure to solve the Navier-Stokes equation with collocated finite volume formulation has been developed. For this purpose, a high-resolution scheme for fluid and structure simulation in transonic flows with an arbitrary Lagrangian-Eulerian method is considered. To simulate Navier-Stokes equations large eddy simulation model for compressible flow is used.FindingsA new concept has been defined to reduce the transonic flow drag. To reduce drag force and increase the performance of airfoil in transonic flow, the shell can be considered flexible in the area of shock on the airfoil surface. This method refers to the use of smart materials in the aircraft wing shell.Originality/valueThe value of the paper is to develop a new approach to improve the aerodynamic performance and reduce drag force and the efficiency of the method throughout the flight. It is noticeable that the new algorithm can detect the shock region automatically; this point was disregarded in the previous studies. It is hoped that this research will open a door to significantly enhance transonic airfoil performance.

Parametric Study of Separation and Reattachment in Transonic Airfoil Flows

Shock and boundary-layer interactions in transonic airfoils are investigated by means of wall-modeled large-eddy simulation. A distinctive flow model, organized and chaotic, occurs in this regime driven by the transition from laminar to turbulent flow, and therefore the appearance of coherent structures such as the Kelvin–Helmholtz instability. This phenomenon is crucial for designing transonic airfoils because it leads to a high rise in drag. Experimental observations show that the main variables of transonic airfoil flow are the freestream Mach number, the Reynolds number, and boundary-layer thickness. Simulations are performed to investigate the relation of various components of the shock/boundary-layer interaction, that is, the pressure rise to shock-induced separation, the length of the separation bubble, and the rear separation to the unit Reynolds number and the boundary-layer condition upstream of the shock. Flow around NACA0012 is investigated in a range of transonic Mach numbers at various unit Reynolds numbers. It is found that the bubble length on the airfoil changes rapidly with relatively small changes in the freestream Mach number. Simulation results show that the separation length decreases with increasing of the unit Reynolds number; however, increasing the boundary-layer thickness results in an increase in the bubble’s extent. Evaluation of the rear-separation region shows that, as the Reynolds number increases, the length of the rear separation declines at a given Mach number.

Leading Edge Shape Optimization of Whitcomb IL Airfoil in Transonic Flow Using a Multi-Objective Genetic Algorithm (MOGA)

Leading edge shape optimization of transonic airfoils requires creating an airfoil surface that reduces the drag divergence due to transonic shocks by either delaying them or reducing their strength at a given transonic cruise speed while maintaining the lift. Aircrafts like Boeing 757, Airbus A300, Boeing 777 and McDonnell Douglas AV-8B Harrier II use Whitcomb IL supercritical airfoil for efficient aerodynamic performance in transonic conditions. This study employs a multi-objective genetic algorithm for shape optimization of leading edge of the Whitcomb IL airfoil to achieve three objectives, namely dilation of shock, reduction in leading edge radius and increment of lift at a given transonic Mach number and at the given AoA. The commercially available software ICEM CFD and Fluent are employed for calculation of the flow field using the RANS (Reynolds-averaged Navier-Stokes equations) in conjunction with a two equation turbulence model. It is shown that the (MOGA) Multi-objective genetic algorithm can generate superior airfoil compared with Whitcomb IL airfoil by achieving three objectives. The optimized airfoil configuration is validated by wind tunnel testing facility.

A fourth-order entropy condition scheme for systems of hyperbolic conservation laws

Based on the analysis of the entropy condition scheme formulation, the accuracy order comes from initial value interpolation and flux reconstruction. Following the limiters of the traditional second-order Total Variation Diminishing scheme, higher accuracy order and non-oscillatory nature are retained with a newly proposed smoothness threshold method. Then, the scheme using the solution formula method in Dong et al. [(2002). High-order discontinuities decomposition entropy condition schemes for Euler equations. CFD Journal, 10(4), 563–568] is generalized to fully-discrete fourth-order accuracy, which retains the advantages of former schemes, i.e. it is a fully-discrete, one-step scheme with no need to perform with a Runge–Kutta process in time; an entropy condition is satisfied with no need of an entropy fix with artificial numerical viscosity; and an exact solution is achieved for linear cases if CFL→1. Numerical experiments are given with a 1D scalar equation for a shock-tube problem, a blast-wave problem, and Shu–Osher problem, a 2D Riemann problem, a double Mach reflection problem and a transonic airfoil flow problem for NACA0012. All tests are compared with a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme. Numerical experiments and efficiency comparisons show that the efficiency of the new fourth-order scheme is superior to the fifth-order WENO scheme.

Numerical Simulations on Unsteady Nonlinear Transonic Airfoil Flow

Large-amplitude excitations need to be considered for gust load analyses of transport aircraft in cruise flight conditions. Nonlinear amplitude effects in transonic flow are, however, only marginally taken into account. The present work aims at closing this gap by means of systematic unsteady Reynolds-averaged Navier-Stokes simulations. The RAE2822 airfoil is analyzed for a variety of sinusoidal gust excitations at different transonic Mach numbers. Responses are evaluated with respect to lift and moment coefficients, their derivatives and the unsteady shock motion. A strong dependency on inflow Mach number and excitation frequency is observed. Generally, amplitude effects decrease with lower Mach numbers or higher excitation frequencies. The unsteady nonlinear simulations predict lower maximum lift values and lower lift and moment derivatives compared to their linear counterparts for lower frequencies in combination with large-amplitude excitations. For the mid-frequency range, trends are not as clear. Additionally, it is shown that the variables of harmonic distortion and maximum shock motion might not be reasonable indicators to predict a nonlinear response.

Numerical Simulation of Harmonic Pitching Supercritical Airfoils Equipped with Movable Gurney Flaps

A two-dimensional numerical investigation was performed to determine the effect of an active Gurney flap on an oscillating supercritical RAE 2822 airfoil in transonic flow. The Navier-Stokes code Fluent was used to calculate the flow field around the airfoil using the Shear Stress Transport turbulence model. Dynamic simulations were based on a moving C-grid, whose harmonic pitching motion was managed using a compiled User Defined Function. Both effects of height and chordwise positioning were considered in this study. The heights of Gurney flaps ranged from 1% to 3% of airfoil chord lengths, while position ranged from the trailing edge to 10% upstream from the trailing edge. In comparison with the Baseline airfoil, the effect of the deployable Gurney flap is to enhance significantly the maximum lift and pitching-moment coefficients; however, an increment in the drag coefficient is also registered. The results indicate that the Gurney flap provides best performance close to the stall angle of attack.

Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks

In this paper, a fuzzy scalar radial basis function neural network is proposed, in order to overcome the limitation of traditional aerodynamic reduced-order models having difficulty in adapting to input variables with different orders of magnitude. This network is a combination of fuzzy rules and standard radial basis function neural network, and all the basis functions are defined as scalar basis functions. The use of scalar basis function will increase the flexibility of the model, thus enhancing the generalization capability on complex dynamic behaviors. Particle swarm optimization algorithm is used to find the optimal width of the scalar basis function. The constructed reduced-order models are used to model the unsteady aerodynamics of an airfoil in transonic flow. Results indicate that the proposed reduced-order models can capture the dynamic characteristics of lift coefficients at different reduced frequencies and amplitudes very accurately. Compared with the conventional reduced-order model based on recursive radial basis function neural network, the fuzzy scalar radial basis function neural network shows better generalization capability for different test cases with multiple normalization methods.

Pressure wave damping in transonic airfoil flow by means of micro vortex generators

In transonic airfoil flow, pressure waves are generated mainly at the trailing edge and in the case of a shock in the region of the shock/boundary layer interaction. Depending on the Mach number, these waves lead to oscillating shock waves and an unsteady pressure distribution. For a free steam Mach number of M=0.76 and a chord length based Reynolds number of Re=106, micro vortex generators (μVG) are applied to dampen pressure waves. This is studied experimentally in a shock tube and numerically by using a high-order finite difference scheme (under-resolved Direct Numerical Simulation). The agreement of the pressure distribution and Schlieren pictures between simulation and experiment is good. By means of numerical visualizations, instability waves are identified within the separated boundary layer above a marginal boundary layer separation bubble. The applicability of μVG for dampening the pressure waves and stabilizing the flow field is possible and is studied in this paper. By numerical Schlieren pictures and further visualizations, the flow around the VG is characterized. The spanwise oriented instability waves are partly disintegrated which is also confirmed by the analysis of the vorticity. Finally, the nonlinear wave propagation is investigated and an explanation for the typical 1 to 2 kHz pressure oscillation is given.

Physics-Based Low-Order Model for Transonic Flutter Prediction

This paper presents a physical low-order model for two-dimensional unsteady transonic airfoil flow, based on small unsteady disturbances about a known steady flow solution. This is in contrast to traditional small-disturbance theory, which assumes small disturbances about the freestream. The states of the low-order model are the flowfield’s lowest moments of vorticity and volume-source density perturbations, and their evolution equation coefficients are calibrated using off-line unsteady computational fluid dynamics simulations through dynamic mode decomposition. The resulting low-order unsteady flow model is coupled to a typical-section structural model, thus enabling prediction of transonic flutter onset for wings with moderate to high aspect ratios. The method is fast enough to permit incorporation of transonic flutter constraints in conceptual aircraft design calculations. The accuracy of this low-order model is demonstrated for forced pitching and heaving simulations of an airfoil in compressible flow. Finally, the model is used to describe the influence of compressibility on the flutter boundary, and its accuracy is demonstrated for the Isogai Case A classical flutter test case.

Natural laminar flow airfoil shape design at transonic regimes with multi-objective evolutionary algorithms

The natural laminar flow airfoil shape design at transonic regime is solved using multi-objective evolutionary algorithms in this paper. A shock wave control bump is used to reduce wave drag of natural laminar flow airfoil in transonic flow, and the eN transition prediction method based on the linear stability theory is used to predict the transition location. The multi-island parallel multi-objective evolutionary algorithms is implemented to optimize the airfoil shape equipped with shock wave control bump for obtaining a larger laminar flow region and a weaker wave drag simultaneously. Optimization experiment shows that it is easy to capture the Pareto front of wave drag minimization and laminar flow region maximization. Results demonstrate that both wave drag and friction drag performance of several chosen Pareto members are significantly improved via the optimal airfoil shape and shock wave control bump device compared to that of the baseline shape.

Rarefaction Effects for Transonic Airfoil Flows at Low Reynolds Numbers

The quantification of rarefaction effects for low-Reynolds-number () transonic () flows is essential for the aerodynamic design of vehicles moving in vacuum environments approaching the slip regime. Potential future applications include evacuated-tube high-speed ground transportation, high-altitude unmanned aerial vehicles, Martian aircraft, and rotorcraft. For the quantification of rarefaction effects, the NACA 0012 airfoil was analyzed using continuum Navier–Stokes equations in the low Reynolds transonic regime. The results were compared to the deterministic solution of the ellipsoidal statistical Bhatnagar–Gross–Krook model Boltzmann kinetic equation with the Runge–Kutta discontinuous Galerkin method. Numerical simulations using these methods were compared to the electron beam fluorescence experiments at a Reynolds number of 73 and a Mach number of 0.8. It was observed that the numerical solution of ellipsoidal statistical Bhatnagar–Gross–Krook model using the Runge–Kutta discontinuous Galerkin method with third-order accuracy is the most computationally efficient. It was also shown that, when the Reynolds number of the flow decreased from 10,000 to 1000, slip effects become dominant. The flow becomes fully rarefied at . Furthermore, rarefaction effects were quantified for the NACA 0007 and the NACA 2407 at 0 and 10 deg of angles of attack to investigate the effects of thickness, camber, and the angle of attack. It was observed that flow separation due to an increase in thickness resulted in higher rarefaction effects. It was concluded that thin airfoils with very smooth shape changes minimize the continuum breakdown and rarefaction effects.

The impact of unilateral vibrations on aerodynamic characteristics of airfoils in transonic flow

The work is devoted to the mathematical modeling of the influence of forced vibrations of a surface element on one side of the airfoil on the shock-wave structure of transonic flow around. The influence of parameters of oscillations on the airfoil wave drag and the lift force were qualitatively and quantitatively investigated for constant maximum velocity amplitude, which is close in magnitude to the sound velocity in the incoming flow, and for a wide range of frequencies. The arising of additional lift force is shown.

Experimental Aerodynamic Response for an Oscillating Airfoil in Buffeting Flow

In prior work, several authors including the present ones have noted the analogy between the fluid oscillations induced by a bluff body in cross flow (e.g., the classic von Kármán vortex street behind a cylinder) and the flow oscillations often called buffet that occur for flow around wings and airfoils in transonic flow at sufficiently large angles of attack. In the present study, an airfoil in low-speed flow is placed at very high angles of attack and buffet and/or a von Kármán vortex street is indeed found. Of interest is the fact that the required angles of attack at these low speeds are well beyond the angle of attack for the onset of stall. The dependence of the characteristic Strouhal or reduced frequency on angle of attack and flow velocity (Reynolds number) is also determined, as are the peak amplitudes of the oscillating flow. At the large static angles of attack where buffet occurs, the airfoil is oscillated at various frequencies near the buffet frequency and with several amplitudes. Lock-in is found for certain combinations of airfoil oscillation frequencies and amplitudes.

Flow-induced vibrations and the Landau equation

The initial and general transient temporal behaviours of flow induced vibrations were studied particularly with regard to the extent with which self-excited, flow-induced vibrations can be described by the Landau equation.Three different cases are studied experimentally, using bodies with generic shape. The first case represents a bluff body: resembling a simplified section of the Tacoma bridge, which has a single torsional degree of freedom. The second case is a two-dimensional airfoil in transonic flow having a heave and a torsional degree of freedom. The third case is an elastic half-wing model, also investigated in transonic flow.It is shown that in all three cases, beyond the critical point and at small initial amplitude the temporal development of the oscillations up to the limit cycle i.e. the envelope of the measured time functions, agrees with the corresponding curve, given by the solution of the Landau equation. For the Tacoma section and the airfoil the same agreement was demonstrated for initial amplitudes much larger than that of the limit cycle. In addition for both last cases the bifurcation behaviour was investigated and the Landau constants were determined. Finally an elementary physical explanation for the instability phenomenon was given.