Flow Past Airfoils Research Articles

Investigation of two dimensional flow past multi element airfoils for general transport aircraft

PurposeAir connectivity network is an important part of the overall connectivity network of any country. This becomes even more crucial for the interior regions, which have no access to sea routes and have inadequate road and rail connectivity. In India there is uniform distribution of airports throughout the country but only a few of them are currently used because of poor infrastructure availability at these airports. Any aircraft operating from these airports, having minimal infrastructure, need to have efficient high‐lift systems for short takeoff and landing ability as one of the key requirements. The purpose of this paper is look at the performance of a new high‐lift airfoil configuration for application to a general transport aircraft.Design/methodology/approachThe present study deals with two‐dimensional analyses of a high‐lift system for general transport aircraft. The JUMBO2D, a multi‐block structured viscous code has been used to make preliminary analysis of the proposed high‐lift system. The configuration consists of three elements, namely, the main airfoil with nose droop, a vane and a flap.FindingsIn the present work the code has been revalidated by computing for NLF (1) 0416 airfoil (clean) and NACA 1410 airfoil with double‐slotted flap. The computed results compare very well with the experimental data. The proposed high‐lift configuration of general transport aircraft has then been analyzed in detail for both takeoff and landing conditions with and without nose droop. The effect of gap between main element and vane on the aerodynamic performance has also been investigated.Originality/valueThis computational study looks at the performance of a new high‐lift airfoil configuration for application to a general transport aircraft.

Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil

The preconditioning technique can address the stiffness of a low Mach number flow, while its stability is poor. Based on the conventional preconditioning method of Roe's scheme, a low-diffusion scheme is proposed. An adjustable parameter is introduced to control numerical dissipation, especially over the dissipation in the boundary layer and extremely in a low speed region. Numerical simulations of the low Mach number and low Reynolds number flows past a cylinder and the low Mach number and high Reynolds number flows past NACA0012 and S809 airfoils are performed to validate the new scheme. Results of the three tests well agree with experimental data, showing the applicability of the proposed scheme to low Mach number flow simulations.

Analysis of flows past airfoils at very low Reynolds numbers

This article presents the special features of airfoil flows at very low Reynolds numbers, which are of interest for unmanned micro-air-vehicles. Airfoil flow solutions at low Reynolds numbers are obtained with an efficient numerical analysis based on a pseudo-time integration method using artificial compressibility for solving accurately the Navier—Stokes equations. The flow problem is solved in a rectangular computational domain obtained by a coordinate transformation from the physical flow domain around the airfoil at incidence. This method uses a second-order central differencing approach on a stretched staggered grid. A special decoupling procedure using the continuity equation reduces the problem to the solution of scalar tridiagonal systems of equations, which enhances substantially the computational efficiency of the method. The pressure distribution, lift, and drag coefficients are presented for several NACA airfoils at various incidences and low Reynolds numbers between 400 and 6000. Streamline contours for the flow with separations past several airfoils at low Reynolds numbers have also been generated and compared. For a better understanding of the complex flow separation phenomena in the viscous flows past airfoils at very low Reynolds numbers, the onset of separation and reattachment locations have been calculated, and a detailed study is presented on the influence of the Reynolds number, angle of attack, relative thickness and camber, and the maximum camber position along the chord.

Resonant interaction of periodic pulsed energy source with shock-wave structure in transonic flow past airfoil

The interaction of a periodic pulsed energy source with a closing shock wave that arises near an airfoil in transonic flight regimes has been studied. The evolution of the shock-wave structure near a symmetric airfoil is analyzed based on a numerical solution of two-dimensional nonstationary equations of gasdynamics. A resonance interaction mechanism is established that leads to a significant (by an order of magnitude) decrease in the wave drag of the airfoil.

Bifurcations of transonic flow past simple airfoils with elliptic and wedge-shaped noses

A turbulent transonic flow past two symmetric airfoils with flat midparts is studied numerically. Using the Reynolds-averaged Navier-Stokes equations, we analyze the flow past a 9% thick airfoil with an elliptic nose. A range of the free-stream Mach number M∞, in which flow bifurcations occur, is determined. Values of M∞that give rise to significant changes in the lift coefficient with variations of the angle of attack are specified. Flow bifurcations are also revealed for a thin double wedge, i.e., a sort of a hexagon.

Self-sustained oscillations and bifurcations of transonic flow past simple airfoils

A turbulent flow past two symmetric airfoils, whose bow and aft portions are circular arcs, whereas midparts are flat, is studies numerically. The amplitude of lift coefficient oscillations versus the free-stream Mach number M∞ is analyzed at zero angle of attack. Ranges of M∞ in which there exist flow bifurcations are determined.

Direct numerical simulations of tonal noise generated by laminar flow past airfoils

A numerical investigation is presented of noise generated by flow past symmetric NACA airfoils with different thickness and at various angles of attack at M = 0.4 and a Reynolds number based on chord of Re = 50 , 000 . Direct numerical simulations (DNS) are employed to directly compute both the near-field hydrodynamics and the far-field sound. The DNS data are then used to investigate whether the approach of determining tonal noise radiation based on the surface pressure difference, as done in the classical trailing-edge theory of Amiet, yields satisfactory results for finite thickness airfoils subject to mean loading effects. In addition, the accuracy of Amiet's surface pressure jump function is evaluated. Overall, the modified theory of Amiet appears to be suitable for finite thickness airfoils up to moderate incidence. However, when increasing the airfoil thickness to 12% chord, which corresponds to a trailing-edge angle of 16 . 8 ∘ , an unexpected phase change between the incident and scattered pressure is found at the frequency of the forced instability waves. This phase change is attributed to the flow oscillating around the trailing edge at a separate wake frequency. For the largest incidence investigated, Amiet's response function does not predict the total surface pressure difference as accurately as for zero or small incidence at the vortex shedding frequency, resulting in a poor prediction of the directivity and amplitude of the acoustic pressure. Moreover, predicting the airfoil self-noise based on the surface pressure difference appears not to be generally applicable at higher angles of attack because the radiated sound is only partly due to classical trailing-edge noise mechanisms. In these cases, it appears as if volume sources in the flow cannot be neglected.

Finite element computation of turbulent flow past a multi-element airfoil

Flow past multi-element airfoil is studied via two-dimensional numerical simulations. The incompressible Reynolds averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite element formulation. The Spalart–Allmaras and Baldwin–Lomax models are employed for turbulence closure. The implementation of the Spalart–Allmaras model is verified by computing flow over a flat plate with a specified trip location. Good agreement is seen between the results obtained with the two models for flow past a NACA 0012 airfoil at 5° angle of attack. Results for the multi-element airfoil, with the two turbulence models, are compared with experiments for various angles of attack. In general, the pressure distribution, from both the models matches quite well with the experimental results. However, at larger angles of attack, the computational results overpredict the suction peak on the slat. The velocity profiles from the Baldwin–Lomax model are, in general, more diffused compared to those from the Spalart–Allmaras model. The agreement between the computed and experimental results is not too good in the flap region for large angles of attack. Both the models are unable to predict the stall; the flow remains attached even for relatively large angles of attack. Consequently, the lift coefficient is over predicted at large α by the computations. Overall, compared to the Baldwin–Lomax model, the predictions from the Spalart–Allmaras model are closer to experimental measurements.

Flow past airfoil moving reciprocally in a channel by vortex method

The velocity and pressure fields of a ship’s propulsion mechanism of the Weis-Fogh type, in which a airfoil moves reciprocally in a channel, are studied in this paper using the advanced vortex method. The airfoil and the channel are approximated by a finite number of source and vortex panels, and the free vortices are introduced from the body surfaces. The viscous diffusion of fluid is represented using the core-spreading model to the discrete vortices. The velocity is calculated on the basis of the generalized Biot-Savart law and the pressure field is calculated from integrating the equation given by the instantaneous velocity and vorticity fields. Two-dimensional unsteady viscose flows of this propulsion mechanism are numerically clarified, and the calculated results agree well with the experimental ones.

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments.

Efficient second-order analytical solutions for airfoils in subsonic flows

This paper presents simple and efficient analytical solutions for the velocity and pressure distributions on airfoils of arbitrary shapes, which are obtained considering the rigorous boundary conditions, without the use of the small perturbation assumption. A second-order accurate method using special singularities in the expression of the fluid velocity is first developed for airfoils in inviscid incompressible flows, by simultaneously solving the symmetric and anti-symmetric flow components defined by coupled boundary conditions. Accurate analytical solutions in closed form are thus derived and then successfully validated by comparison with the exact solutions for special airfoils obtained by conformal transformation and with numerical inviscid results. The method is then extended to model the main viscous effects on the velocity and pressure distributions, by considering the real velocity behavior at the airfoil trailing edge in viscous flow and the displacement thickness of the boundary layer developed on the airfoil and the wake. The resulting analytical solutions including viscous effects, derived for attached flows past airfoils at moderate angles of attack, were found in good agreement with experimental and numerical viscous results for various incidences, Reynolds and Mach numbers (Karman–Tsien compressibility correction was used to extend the solutions to compressible subsonic flows). In all cases studied (symmetric and cambered thick airfoils of arbitrary shapes, with rounded or pointed leading edges), these analytical solutions in closed form were found to be very efficient and accurate.

Calculation of impulsively started incompressible viscous flows

AbstractThe paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.

다중 격자 Navier-Stokes 해석을 위한 수렴 특성 연구 : II. 내재적 예조건자

본 연구는 다중 격자 Navier-Stokes 방정식 해석의 수렴성 향상을 그 목적으로 한다. 다중 격자 기법의 성능 향상을 위해 최근 많이 사용되고 있는 예조건화된 다단계 시간 전진 기법의 효율성 향상을 위한 연구를 수행하였다. 압축성 유동장 해석시 자주 이용되는 ADI 예조건자와 DDADI 예조건자의 수렴 특성 비교 연구를 수행하였다. 2차원 압축성 난류 유동장 해석에 적용함으로써 DDADI 예조건자가 ADI 예조건자에 비해 우수한 수렴특성을 가짐을 확인하였고, 이를 통하여 Fourier 해석을 통한 예조건화 특성 연구와 일치하는 수렴 특성을 확인하였다. Spalart-Allmaras(S-A) 난류 모델과 Baldwin-Lomax (B-L) 난류 모델의 적용을 통해 난류 모델에 따른 수렴성 비교를 수행하였다. The objective of this study is convergence acceleration of multigrid Navier-Stokes solvers. This study has been performed to enhance the performance of preconditioned multi-stage time stepping method which is a popular smoother for the multigrid Navier-Stokes solvers. Comparative study on the convergence characteristics of the ADI and DDADI preconditioners has been conducted. It is shown that the DDADI preconditioner has better performance than the ADI by numerical tests on the 2-D compressible turbulent flows past airfoils. The Spalart-Allmaras turbulent model and the Baldwin-Lomax turbulent model have been compared with the multigrid calculations.

Fast preconditioned multigrid solution of the Euler and Navier–Stokes equations for steady, compressible flows

AbstractNew versions of implicit algorithms are developed for the efficient solution of the Euler and Navier–Stokes equations of compressible flow. The methods are based on a preconditioned, lower‐upper (LU) implementation of a non‐linear, symmetric Gauss‐Seidel (SGS) algorithm for use as a smoothing algorithm in a multigrid method. Previously, this method had been implemented for flows in quasi‐one‐dimensional ducts and for two‐dimensional flows past airfoils on boundary‐conforming ‘O’‐type grids for a variety of symmetric limited positive (SLIP) spatial approximations, including the scalar dissipation and convective upwind split pressure (CUSP) schemes. Here results are presented for both inviscid and viscous (laminar) flows past airfoils on boundary‐conforming ‘C’‐type grids. The method is significantly faster than earlier explicit or implicit methods for inviscid problems, allowing solution of these problems to the level of truncation error in three to five multigrid cycles. Viscous solutions still require as many as twenty multigrid cycles. Copyright © 2003 John Wiley & Sons, Ltd.

Unsteady vorticity–streamfunction algorithm for external flows

A non-inertial vorticity–streamfunction algorithm of the Reynolds-averaged Navier–Stokes equations is developed for studying unsteady and turbulent flows past airfoils. The equations are solved on a non-orthogonal C-grid using a combined finite-difference/finite-volume technique. Comparative computations are carried out employing three different turbulence models. These are the algebraic zero-equation model of Baldwin and Lomax [1], and the one-equation models of Baldwin and Barth [2] and Spalart and Allmaras [3]. The performance of the models is evaluated against experiments of the Aérospatiale-A airfoil at incidences up to 40° and against two cases of an oscillating NACA 0015 airfoil experiencing light and deep stall. The computations demonstrate that the vorticity–streamfunction formulation combined with standard eddy-viscosity turbulence models is capable of predicting accurately unsteady and turbulent flows past airfoils.

Computational study into the flow field developed around a cascade of NACA 0012 airfoils

Numerical simulation of flow past airfoils is important in the aerodynamic design of aircraft wings and turbomachinery components. These lifting devices often attain optimum performance at the condition of onset of separation. Therefore, separation phenomena must be included if the analysis is aimed at practical applications. Consequently, in the present study, numerical simulation of steady flow in a linear cascade of NACA 0012 airfoils is accomplished with control volume approach. The flow field is determined by solving two-dimensional incompressible Navier-Stokes equations while the effects of turbulence are accounted for by the k- ϵ model. Boundary layer developed at the suction and the pressure surfaces of the airfoil is investigated together with relevant pressure contours for different angles of attack and solidity. Separation point at the airfoil surface is predicted at high angles of attack. Pressure, lift and drag coefficients are computed and the results are compared with the predictions of isolated single NACA 0012 airfoil as well as the data available in the literature. However, the leading edge rotation is also introduced to determine the effect of leading edge rotation on stall inception of isolated airfoil. It is found that increase in solidity increases the angle of attack at which separation occurs and pressure, lift and drag coefficients are highly influenced by the angle of attack and the solidity. The results of leading edge rotation indicates that the drag coefficient reduces considerably while the lift coefficient increases.

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.

Surface vorticity modeling of flow around airfoils

A surface vorticity method based on the new Kutta condition has been developed for solving the steady flow around an airfoil and unsteady separated flow past airfoil with a spoiler. In a discussion of the Kutta condition, it is argued that the appropriate Kutta condition is required to obtain a satisfactory solution. In this paper, two new methods of satisfying the Kutta condition incorporated in the surface vorticity method are described. The first method, which is based on results from flow visualization, is to introduce an additional control point at a short distance downstream of the trailing edge. In order to account for the fact that the velocity above the trailing edge is different from that below as in the real flow, the second method is to add a finite segment of vortex sheet downstream of the trailing edge. The present Kutta conditions are incorporated into the surface vorticity method and extend to solve unsteady flow around an airfoil with a spoiler. The computational results are in reasonable agreement with other computation as well as experiments.

Finite element computation of unsteady viscous transonic flows past stationary airfoils

Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations. The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique. Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10∘ angle of attack compare well with numerical and experimental results from other researchers

Viscous-Inviscid Interaction Using the Navier-Stokes Equations

A numerical model for the calculation of incompressible viscous flows past airfoils and wings has been developed. The approach is based on a strong viscous-inviscid coupling of a boundary element method with the Navier-Stokes equations in vorticity-stream function formulation. A semiadaptive or fully adaptive grid is used. The interaction is achleved by iterative updating of the boundary conditions, through the wall transpiration concept. The Navier-Stokes equations are discretized on a semistaggered grid. Space-marching integration is performed starting from the stagnation streamline on two independent blocks. Results are presented for two different airfoils.