Flow Past Airfoils Research Articles

Flows past airfoils for the low-Reynolds number conditions of flying in Martian atmosphere

Fixed-wing aircraft with potential for long-duration flight and efficient manoeuvrability is expected to be the next frontier of Mars surface exploration. However, the feasibility of such an aircraft demands for wing airfoil suitable for low Reynolds flight conditions. In this framework, the paper deals with the computational study of two wing sections specifically designed for Mars exploration aircraft. Two-dimensional steady Reynolds-averaged Navier–Stokes simulations, using the computational fluid dynamics tool SU2 with the γ−Reθ transition model and the XFoil panel flow solver, are performed to address airfoils’ aerodynamics. Computational tools are validated by simulating flow past the Eppler 387 airfoil at Re∞=60×103, and comparing the results with experimental data collected in wind tunnel experiments. Aerodynamic performances of optimal wing sections are investigated at Re∞=3.4×104 by considering pressure coefficients and skin friction coefficients. The application of a literature-based correlation, specifically tailored to identify transition and reattachment locations, is extended to separation point detection. Computational Fluid Dynamics analysis conducted on the studied airfoils revealed that separation occurs within the laminar regime. Additionally, examination of turbulent shear stresses highlighted the role of airfoil curvature in counterbalancing the suction defect produced by the laminar separation bubble. This curvature-induced effect was found to play a crucial role in optimizing airfoil efficiency.

Novel Approach to Improve Stability and Convergence of Flowfield Solution Processes: Mode Multigrid

In the field of computational fluid dynamics, stability and convergence problems are often encountered when solving the governing equation. This paper studies the effect of the mode multigrid on the stability and convergence of iterative algorithms. By further analyzing the mechanism for accelerating the convergence of mode multigrid, a new adaptive mode multigrid (AMMG) is proposed, and an adaptive selection criterion is formulated for the parameters of dynamic modal decomposition, which can accurately identify and filter out the unstable modes in the flowfield, thus efficiently obtaining the accurate steady solution. In the cases of laminar flow past circular cylinder and turbulent flow past airfoil, the AMMG significantly improves the stability of the iterative algorithm; in the case of transonic flow past airfoil, the AMMG solves the problem of shock wave shaking during the iteration, and the convergence is significantly improved. In summary, the AMMG method significantly enhances the stability and convergence of the iterative algorithm, and can be used as an effective convergence-preserving computation strategy.

Flow control using single dielectric barrier discharge plasma actuator for flow over airfoil

The single dielectric barrier discharge (SDBD) plasma actuator has been developed in the present work for high-accuracy, high-performance computing of flow control applications. The present physics-based SDBD model is a significant improvement over the one developed by Bagade et al., [“Frequency-dependent capacitance–based plasma model for direct simulation of Navier–Stokes equation,” AIAA J. 55, 180–194 (2017)], which was used for planar geometry using sequential computation. Based on the physics of SDBD operation, phase-averaged fully developed body force over an ac cycle is computed and stored, which is reused. Thus, the intensive body force computations are bypassed in the new model, and the body force due to the SDBD plasma actuator is incorporated in the compressible Navier–Stokes equation that is solved in a body-fitted curvilinear coordinates. Here, the modified SDBD model enables performing large-scale simulations for the aerodynamic flow control at low speed and transonic flow past airfoils used in unmanned aerial vehicles and executive jets. The flow control by SDBD plasma actuation is finally compared with other forms of flow control strategies.

A new accelerating technique for low speed flow: pseudo high speed method

This paper proposes a new accelerating technique for simulating low speed flows, termed as pSeudo High Speed method (SHS), which uses governing equations and numerical methods of compressible flows. SHS method has advantages of simple formula, easy manipulation, and only need to modify flux of Euler equations. It can directly employ the existing well-developed schemes of hyperbolic conservation laws. To verify the technique, several numerical experiments are performed, such as: flow past airfoils and flow past a cylinder. Analysis of SHS method and comparisons with some precondition methods are made numerically. All tests show that SHS method can greatly improve the efficiency of compressible method simulating low speed flow fields, which exhibits in accelerating the convergence rate and increasing the accuracy of the numerical results.

Flow criticality governs leading-edge-vortex initiation on finite wings in unsteady flow

Abstract

Turbulence closure for high Reynolds number airfoil flows by deep neural networks

The combination of turbulence big data with artificial intelligence is an active research topic for turbulence study. This work constructs black-box algebraic models to substitute the traditional turbulence model by the artificial neural networks (ANN), rather than correcting the existing turbulence models in most of current studies. We mainly focused on flows past airfoils at high Reynolds (Re) numbers. Our previous work has developed a turbulence model for flows at different Mach (Ma) number and angles of attack (AOA) with fixed Re number and achieved satisfying results. Nevertheless, for turbulence with variable Re numbers, the generalization ability of the model can not be enhanced effectively by simply increasing the train data. To model the nonlinearity of various turbulent effects at high Re number, prior knowledge about scaling analysis is integrated into the model design and deep neural networks (DNN) is adopted as the framework. Considering the different scaling characteristics, the flow field is divided into different regions and two individual ANN models are built separately. Besides, the combination of regularization, limiters, and stability training is adopted to enhance the robustness of the proposed model. The results of Spallart-Allmaras (SA) model are used as the datasets and reference to the modeling evaluation. The proposed model is trained by six flows around NACA0012 airfoil and applicative to different free stream conditions and airfoils. It is found that the results calculated by the proposed model, such as eddy viscosity, velocity profile, drag coefficient and so on, agree well with reference data, which validate the generalization ability of the model. This work shows the prospect of turbulence modeling by machine learning methods.

Accelerating the convergence of steady adjoint equations by dynamic mode decomposition

To improve the efficiency of adjoint-based optimization algorithms, dynamic mode decomposition (DMD) technology is used to accelerate the convergence of steady adjoint equations in this paper. During pseudo-time marching, adjoint fields are projected onto the modal space and modal analysis is carried out by DMD. When only first zero frequency mode is reserved, the convergence speed of adjoint equations is significantly enhanced. Through two examples of flow past airfoils in subsonic and transonic flows and a transonic optimization example, the validity of the proposed methodology is verified. Results indicate that the proposed methodology can improve optimization efficiency remarkably, and the iteration step number of adjoint equations is reduced by almost 60%.

FLOW PAST STATIONARY AND OSCILLATING AIRFOIL AT A LOW REYNOLDS NUMBER USING SHARP INTERFACE IMMERSED-BOUNDARY APPROACH

The present study reports on flow past airfoils (stationary and moving) using sharp interface immersed-boundary approach. Non-boundary conforming approach like immersed-boundary method offers a viable alternative over traditional boundary conforming approach by allowing us to model flow past arbitrarily complex shapes, by eliminating the need to re-grid the flow domain as the body exhibits motion. We present flow past a NACA 0012 airfoil at stationary conditions as well as exhibiting pitching motion. Evolution of vortex dynamics and wake structures are presented to show that the developed sharp interface immersed-boundary approach captures the flow physics of dynamic stall accurately. Moving body problems involving immersed-boundary approach usually encounter the issues of spurious oscillations and mass conservation. This is handled through a field extension strategy based on ghost cell approach, which allows for extrapolating the flow field value onto the ghost nodes, ensuring smooth temporal transition as the immersed surface moves through time. The results presented here show excellent agreement with the experimental results found in the literature.

Wall-modelled large-eddy simulation of turbulent flow past airfoils

We present large-eddy simulation (LES) of flow past different airfoils with $Re_{c}$, based on the free-stream velocity and airfoil chord length, ranging from $10^{4}$ to $2.1\times 10^{6}$. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. It is demonstrated that the wall model dynamically captures the instantaneous skin-friction vector field on arbitrary curved surfaces at the resolved scale. By combining the present wall model with the stretched-vortex subgrid-scale model, we apply the wall-modelled LES approach to three different airfoil cases, spanning different geometrical parameters, different attack angles and low to high $Re_{c}$. The numerical results are verified with direct numerical simulation (DNS) at low $Re_{c}$, and validated with experiment data at higher $Re_{c}$, including typical aerodynamic properties such as pressure coefficient distributions, velocity components and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results into aspects of flow physics that are not available from experiments. Two techniques to quantify hitherto unexplored physics of flows past airfoils are employed: one is the construction of the anisotropy invariant map, and the second is skin-friction portraits with emphasis on flow transition and unsteady separation along the airfoil surface. The anisotropy maps for all three $Re_{c}$ cases, show clearly that a portion of the flow field is aligned along the axisymmetric expansion line, corresponding to the turbulent boundary layer log-law behaviour and the appearance of turbulent transition. The instantaneous skin-friction portraits reveal a monotonic shrinking of the near wall structure scale. At $Re_{c}=10^{4}$, the interaction between the primary separation bubble and the secondary separation bubble contributes to turbulent transition, similar to the case of flow past a cylinder. At higher $Re_{c}=10^{5}$, the primary separation breaks into several small separation bubbles. At even higher $Re_{c}=2.1\times 10^{6}$, near the turbulent separation, the skin-friction lines show small-scale reversal flows that are similar to those observed in DNS of the flat plate turbulent separation. A notable feature of turbulent separation in flow past an airfoil is the appearance of turbulence structures and small-scale reversal flows in the spanwise direction due to the vortex shedding behaviour.

An a priori anisotropic goal-oriented error estimate for viscous compressible flow and application to mesh adaptation

We present a goal-oriented error analysis for the calculation of low Reynolds steady compressible flows with anisotropic mesh adaptation. The error analysis is of a priori type. Its central principle is to express the right-hand side of the error equation, often referred as the local error, as a function of the interpolation error of a collection of fields present in the nonlinear Partial Differential Equations. This goal-oriented error analysis is the extension of [39] done for inviscid flows to laminar viscous flows by adding viscous terms. The main benefits of this approach, in comparison to other error estimates in the literature, is that the optimal anisotropy of the mesh directly appears in the error analysis and is not obtained from an ad hoc variable nor a local analysis. As a consequence, an optimum is obtained and the convergence of the mesh adaptive process is very fast, i.e., generally the convergence is obtained after 5 to 10 mesh adaptation cycle. Then, using the continuous mesh framework, an optimal metric is analytically obtained from the error estimation. Applications to mesh adaptive calculations of flows past airfoils are presented.

Link-Wise Artificial Compressibility Method for attached and separated flows past airfoils

The performance of the recently developed Link-Wise Artificial Compressibility Method (LW-ACM) is evaluated for aerodynamic applications and then applied for both attached and separated flows. Numerical flow simulations are performed around NACA-0012 and TSAGI-12 shaped airfoils at low speed and high angle of attack. Results of aerodynamic characteristics of the airfoils were found in good agreements with previous investigations including LBM (PowerFLOW) and FVM (CFL3D). Results also showed that LW-ACM is efficient and rapidly convergent when used to solve both attached and separated flows.

Computational Investigation of Flow Separation over NACA 23024 Airfoil at 6 Million Free Stream Reynolds Number Using k-Epsilon Turbulence Model

Numerical simulation of flow past airfoils in the stalled region is a difficult problem due to some phenomena like strong vortex dynamics, boundary layer separation due to adverse pressure gradient etc. For accurate numerical prediction of separated flow, correct modelling of boundary layer is very much necessary to capture the details of the fluid flow. The following work is the CFD analysis of NACA 23024 airfoil. The analysis is carried out for a free stream Reynolds number of 6 million for which the wind tunnel results are available. The CFD analysis is carried out using Ansys Fluent Solver. The analysis is carried out using K-Epsilon turbulence model, Lift and drag coefficients measured in wind tunnel are compared with the CFD analysis results and the performance of the turbulence model is discussed

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics —such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil— and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil–fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

Evaluation and Analysis of Curvature-Corrected Filter-based Turbulent Model

AbstractPrediction of the characteristics of turbulent flow with streamline curvature is of great importance in engineering applications. In this paper, a curvature-corrected filter-based turbulent model is suggested by applying the Spalart-Shur correction term. This new version of the model (FBM-CC) has been tested and verified through two canonical benchmarks with strong streamline curvature: the flow in a two-dimensional U-duct and the free shear flow past NACA0012 airfoil with a round tip. Predictions of the FBM-CC model are compared with available experimental data and the corresponding results of the original FBM model. The numerical results show that the FBM-CC model significantly improves the sensitivity to the effect of streamline curvature and the numerical calculation accuracy, in relatively good agreement with the experimental data, which suggests that this proposed model may be employed to simulate the turbulent curved flow in engineering applications.

CFD Study of Solid Wind Tunnel Wall Effects on Wing Characteristics

Most of airplane structures include the components such as Fuselage, Wings, Empennage, Landing gear and Power plant etc. Wings are the important part of aircraft and these are airfoils attached to each side of the fuselage and are the main lifting surfaces that support the airplane in flight. SSD-2 airfoil, a modified version of NACA23015 airfoil is used to study the aerodynamic characteristics such as lift, drag, moment and wall effects with different wind tunnel blockage ratios. Generally, any new airfoil characteristics are derived from the extensive wind tunnel tests, however experiments are costly. Hence, to get the idea of aerodynamic characteristics and wall effects over airfoil with different wind tunnel blockage ratios, CFD tools are used such as ICEM CFD and ANSYS FLUENT. This paper presents the results of simulation of flow past SSD-2 airfoil. The study is carried out on a 2D airfoil section for free stream condition. Further the computations are made on 3D rectangular wing of solid wind tunnel simulation by varying wind tunnel height to get the different wind tunnel blockage ratios, keeping the other parameters constant. In solid wind tunnel simulation the lift and moment are less compared to free stream simulation results due to blockage effects. Finally, it is observed that increase in the wind tunnel blockage ratio, lift and moment decreases, drag increases with less difference in pressure; whereas decrease in wind tunnel blockage ratio, the lift and moment increases, drag decreases with more difference in pressure.

English

English

Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils

We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.

Hybrid Immersed Boundary Method for Airfoils with a Trailing-Edge Flap

In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing-edge flap is simulated using the immersed boundary method on a curvilinear mesh. An existing in-house-developed flow solver is employed to solve the incompressible Reynolds-Averaged Navier–Stokes equations together with the turbulence model. To achieve consistent wall boundary conditions at the immersed boundaries the turbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control using an adjustable trailing-edge flap is an efficient way to regulate the aerodynamic loading on airfoils.

Numerical study of flows past airfoils with wavy surfaces

The paper presents three-dimensional numerical studies on the aerodynamic characteristics of two different modified NACA0012 airfoils with different wavy surfaces using the large eddy simulations. Two types of wavy airfoils are investigated with wavy airfoil-A having a sinusoidal waviness on upper and lower surfaces with a constant chord length, while wavy airfoil-B having sinusoidal variation in both of the leading and trailing edges as well as on the upper and lower surfaces along the spanwise direction. The force characteristics and the flow structures are captured and compared with a corresponding standard NACA0012 airfoil with a Reynolds number of Re=1.6×105. The flow structures and surface pressure distributions on wavy airfoils were found to be significantly different from those on a conventional NACA0012 airfoil. For angles of attack less than the baseline stall angle of a NACA0012 airfoil, a slight decrease of lift coefficient was observed for both types of wavy airfoils, while the lift coefficient for the wavy airfoil-B increases up to 20% greater than that of a NACA0012 airfoil when the angle of attack is larger than the baseline stall angle of 13°. The flow over the leading edge of wavy airfoil-B remained attached at post stall angles of attack. In general, the wavy airfoil-A just exhibits a suppression the airfoil’s fluctuation force, while the wavy airfoil-B demonstrates an advantageous aerodynamic effect on the control of loss of lift in the post stall regime of a conventional NACA0012 airfoil.

Numerical Simulation of Turbulent Flow past Airfoils on OpenFOAM

The attached boundary turbulent flow around two different airfoils at low Mach number condition are numerically simulated using the v2-f and S-A RANS models, and the performance is evaluated. The numerical platform is an open source CFD code based on the Field Operation and Manipulation C++ class library for continuum mechanics (OpenFOAM).In the simulation, the pressure field is obtained with SIMPLE algorithm. The advective volume-face fluxes are approximated using second-order TVD scheme/ limited linear differencing. The velocity profile and the aerodynamic parameters of the conventional airfoil at 0° attack angle and the supercritical airfoil at 4° attack angle are simulated, and compared with the experiment data respectively. The result indicates that the solution of v2-f turbulence model is comparable with that of S-A model for conventional airfoil computation, but it is better for the supercritical airfoil computation, especially at the positions with strong pressure gradient and streamline curvatures.