Transonic shock oscillations on NACA0012 aerofoil

The mechanism of the origin of shock oscillations on NACA0012 aerofoils is investigated using a moving grid thin layer Navier Stokes code. The method used to understand the mechanism is to initiate the shock oscillations on an aerofoil by moving the aerofoil from a regime of steady transonic flow into a regime of periodic flow by a change in airflow incidence. The results indicate that the shock induced bubble plays a leading role in the origin of shock oscillations and the trailing edge has an affect on its amplitude. Received 1 April 1997 / Accepted 1 December 1997     

Numerical investigation of dynamic stall of an oscillating aerofoil

The flow structure around an NACA 0012 aerofoil oscillating in pitch around the quarter-chord is numerically investigated by solving the two-dimensional compressible N–S equations using a special matrix-splitting scheme. This scheme is of second-order accuracy in time and space and is computationally more efficient than the conventional flux-splitting scheme. A ‘rigid’ C-grid with 149 × 51 points is used for the computation of unsteady flow. The freestream Mach number varies from 0.2 to 06 and the Reynolds number from 5000 to 20,000. The reduced frequency equals 0.25–0.5. The basic flow structure of dynamic stall is described and the Reynolds number effect on dynamic stall is briefly discussed. The influence of the compressibility on dynamic stall is analysed in detail. Numerical results show that there is a significant influence of the compressibility on the formation and convection of the dynamic stall vortex. There is a certain influence of the Reynolds number on the flow structure. The average convection velocity of the dynamic stall vortex is approximately 0.348 times the freestream velocity.     

Numerical study on flow separation control over NACA0015 aerofoil using electromagnetic fields

In this study, a flow solver was developed based on the governing RANS equations of compressible flows and was further extended to include the effects of electromagnetic forces namely Lorentz forces. Lorentz forces may be added as a source term in the governing fluid flow equations. Numerical studies were carried out for NACA0015 aerofoil at high angles of incidences from 15° to 30° and compared with some available cases of experimental and incompressible numerical solutions. The hydrodynamics performance was improved using a magnetic momentum coefficient of up to 0.048. The size of flow separation zone was decreased or completely eliminated by increasing this coefficient. The overall drag was not changed considerably, however the overall lift was increased up to 80 percent at stall angles.     

Direct numerical simulation of a NACA0012 in full stall

This work aims at investigating the mechanisms of separation and the transition to turbulence in the separated shear-layer of aerodynamic profiles, while at the same time to gain insight into coherent structures formed in the separated zone at low-to-moderate Reynolds numbers. To do this, direct numerical simulations of the flow past a NACA0012 airfoil at Reynolds numbers Re = 50,000 (based on the free-stream velocity and the airfoil chord) and angles of attack AOA = 9.25° and AOA = 12° have been carried out. At low-to-moderate Reynolds numbers, NACA0012 exhibits a combination of leading-edge/trailing-edge stall which causes the massive separation of the flow on the suction side of the airfoil. The initially laminar shear layer undergoes transition to turbulence and vortices formed are shed forming a von Kármán like vortex street in the airfoil wake. The main characteristics of this flow together with its main features, including power spectra of a set of selected monitoring probes at different positions on the suction side and in the wake of the airfoil are provided and discussed in detail.     

Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method

The unsteady, incompressible, viscous laminar flow over a NACA 0012 airfoil is simulated, and the effects of several parameters investigated. A vortex method is used to solve the two-dimensional Navier–Stokes equations in the vorticity/stream-function form. By applying an operator-splitting method, the “convection” and “diffusion” equations are solved sequentially at each time step. The convection equation is solved using the vortex-in-cell method, and the diffusion equation using a second-order ADI finite difference scheme. The airfoil profile is obtained by mapping a circle in the computational domain into the physical domain through a Joukowski transformation. The effects of several parameters are investigated, such as the reduced frequency, mean angle of attack, location of pitch axis, and the Reynolds number. It is observed that the reduced frequency has the most influence on the flow field.     

Thickness effect of NACA foils on hydrodynamic global parameters,boundary layer states and stall establishment

The present study experimentally investigates the hydrodynamic behaviour of 2-D NACA (15%, 25% and 35%) symmetric hydrofoils at Reynolds number 0.5×10⁶. Particular attention was paid to the hysteretic behaviour at the static stall angle, and a detailed cartography of the boundary layer structures (integral quantities and velocity profiles) is given to support the detachment mechanism and the onset of von Kármán instability for thick hydrofoils.     

Feedback control of laminar flow separation on NACA23012 airfoil by POD analysis and using perturbed Navier‐Stokes equations

The main purpose of this article is to develop a forced reduced‐order model based on the proper orthogonal decomposition (POD)/Galerkin projection (on isentropic Navier‐Stokes equations) and perturbation method on the compressible Navier‐Stokes equations. The resulting forced reduced‐order model will be used in optimal control of the separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 800, and high incidence angle of 24°. The main disadvantage of the POD/Galerkin projection method for control purposes is that controlling parameters do not show up explicitly in the resulting reduced‐order system. The perturbation method and POD/Galerkin projection on the isentropic Navier‐Stokes equations introduce a forced reduced‐order model that can predict the time varying influence of the controlling parameters and the Navier‐Stokes response to external excitations. An optimal control theory based on forced reduced‐order system is used to design a control law for a nonlinear reduced‐order system, which attempts to minimize the vorticity content in the flow field. The test bed is a laminar flow over NACA23012 airfoil actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. The results show that wall jet can significantly influence the flow field, remove separation bubbles, and increase the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate manner.     

A computational study on robust prediction of transition point over NACA0012 aerofoil surfaces from laminar to turbulent flows

Flowtransition from laminar toturbulent is prerequisite todecide whereabouts to apply surface flowcontrol techniques. This appears missing in a number of works in which thecontrol effects were merelyinvestigated without getting insight into alteration of transition position. The aim of this study is to capture the correctposition of transition overNACA0012 aerofoil at different angles of attack. Firstly, an implicit, time marching, highresolution total variation diminishing (TVD) scheme was developed to solve the governingNavier—Stokes equations forcompressible fluid flows around aerofoil sections to obtain velocity profiles around the aerofoilsurfaces. Secondly, the linear instability solver based on the Orr—Sommerfeld equations and the e^N methods were developed to calculate the onset of transition over the aerofoil surfaces. Forthe low subsonic Mach number of 0.16, the accuracy of the compressible solutions was assessed bysome available experimental results of low speed incompressible flows. In allcases, transition positionswere accurately predicted which shows applicability and superiority of the present work to beextended for higher Mach number compressible flows. Here, transition prediction methodology is described and the results of this analysiswithout active flow controlor separation are presented.     

Experimental investigation to study flow and heat transfer characteristics over a NACA0018 aerofoil for different height ratios

Experiments are carried out to study flow and heat transfer characteristics over NACA0018 aerofoil when the body approaches the wall of a wind tunnel. Investigations have been done to study the effect of wall proximity due to flow separation around the body at Reynolds number 2.5 × 10⁵, different height ratios and various angles of attack. The static pressure distribution has been measured on upper and lower surfaces of the aerofoil. The results have been presented in the form of pressure coefficient, drag coefficient for different height ratios. Pressure coefficient values are decreased and then increased on the lower surface of the aerofoil and decreased on the upper surface of the aerofoil at all angles of attack. The negative pressure coefficient and drag coefficient decreases as the body approaches the upper wall of wind tunnel. The maximum value of drag coefficient has been observed at an angle of attack 30° for the aerofoil at all height ratios. The Heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficients are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. The variation of local as well as average Nusselt number has been shown with non dimensional distance for different angles of attack and for various height ratios. The local as well as average Nusselt number decreases as the height ratio decreases for all non-dimensional distance and angles of attack respectively. Maximum value of average Nusselt number has been observed at an angle of attack 40°.     

Dynamic stall model for wind turbine airfoils

A model is presented for aerodynamic lift of wind turbine profiles under dynamic stall. The model combines memory delay effects under attached flow with reduced lift due to flow separation under dynamic stall conditions. The model is based on a backbone curve in the form of the static lift as a function of the angle of attack. The static lift is described by two parameters, the lift at fully attached flow and the degree of attachment. A relationship between these parameters and the static lift is available from a thin plate approximation. Assuming the parameters to be known during static conditions, nonstationary effects are included by three mechanisms: a delay of the lift coefficient of fully attached flow via a second-order filter, a delay of the development of separation represented via a first-order filter, and a lift contribution due to leading edge separation also represented via a first-order filter. The latter is likely to occur during active pitch control of vibrations. It is shown that all included effects can be important when considering wind turbine blades. The proposed model is validated against test data from two load cases, one at fully attached flow conditions and one during dynamic stall conditions. The proposed model is compared with five other dynamic stall models including, among others, the Beddoes–Leishman model and the ONERA model. It is demonstrated that the proposed model performs equally well or even better than more complicated models and that the included nonstationary effects are essential for obtaining satisfactory results. Finally, the influence of camber and thickness distribution on the backbone curve are analysed. It is shown that both of these effects are adequately accounted for via the static input data.     

Dynamic stall behavior from unsteady force measurements

A direct force measurement technique employing piezoelectric load cells is used to experimentally investigate a two-dimensional airfoil (NACA 0012) undergoing dynamic stall. The load cells are installed at each end of the airfoil and give the force response in two directions in the plane normal to the airfoil axis during oscillations. Experiments are carried out at a Reynolds number based on the airfoil chord equal to 7.7×10⁴, and at four reduced frequencies, k=0.005, 0.01, 0.02, and 0.04. Phase-averaged lift of the airfoil undergoing dynamic stall is presented. It is observed that hysteresis loops of the lift occur both when the airfoil is pitched to exceed its static stall limit and when it is still within its static stall limit, and they grow in size with increasing k at the same pitching mean angle of attack and pitching amplitude. Both the lift and the drag induced by the pitching motion are further analyzed using the methods of higher order correlation analysis and continuous wavelet transforms to undercover their nonlinear and nonstationary features, in addition to classical FFT-based spectral analysis. The results are quantitatively illustrated by an energy partition analysis. It is found that the unsteady lift and drag show opposite trends when the airfoil undergoes transition from the pre-stall regime to the full-stall regime. The degree of nonlinearity of the lift increases, and the lift show a nonstationary feature in the light-stall regime, while the nonlinearity of the drag decreases, and the drag shows nonstationary feature in both the light-stall and the full-stall regimes. Furthermore, the lift and the drag have significant nonlinear interactions as shown by the correlation analysis in the light-stall regime.     

High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall

In the present work, large eddy simulations of the flow field around a NACA-0012 aerofoil near stall conditions are performed at a Reynolds number of 5 × 10⁴, Mach number of 0.4, and at various angles of attack. The results show the following: at relatively low angles of attack, the bubble is present and intact; at moderate angles of attack, the laminar separation bubble bursts and generates a global low-frequency flow oscillation; and at relatively high angles of attack, the laminar separation bubble becomes an open bubble that leads the aerofoil into a full stall. Time histories of the aerodynamic coefficients showed that the low-frequency oscillation phenomenon and its associated physics are indeed captured in the simulations. The aerodynamic coefficients compared to previous and recent experimental data with acceptable accuracy. Spectral analysis identified a dominant low-frequency mode featuring the periodic separation and reattachment of the flow field. At angles of attack α ≤ 9.3°, the low-frequency mode featured bubble shedding rather than bubble bursting and reformation. The underlying mechanism behind the quasi-periodic self-sustained low-frequency flow oscillation is discussed in detail.     

Dynamic stall modelling on airfoils based on strong viscous–inviscid interaction coupling

The prediction of the aerodynamic performance of pitching airfoils in stall conditions is considered in the context of strong viscous–inviscid interaction modelling. The aim of the work is to demonstrate the capabilities of a low‐cost dynamic stall model well suited for engineering applications. The model is formulated on the basis of a standard panel method combined with a vortex blob approximation of the wake. The development of the boundary layer over the airfoil and the evolution of the shear layer in the wake are taken into account by means of strong viscous–inviscid interaction coupling. To this end a transpiration layer is added to the inviscid formulation which represents the displacement effect viscosity results in the flow while the non‐linear coupled equations are solved simultaneously. Separation is modelled by introducing a second wake originating from the separation point (‘double‐wake’ concept) which is provided as part of the boundary layer solution. The theoretical presentation of the model is supported with favourable comparisons to four sets of wind tunnel measurements. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of 2D/3D numerical modeling for deep dynamic stall experiments

The results of computational fluid dynamics (CFD) simulations in two and three spatial dimensions are compared to pressure measurements and particle image velocimetry (PIV) flow surveys to assess the suitability of numerical models for the simulation of deep dynamic stall experiments carried out on a pitching NACA 23012 airfoil. A sinusoidal pitching motion with a 10° amplitude and a reduced frequency of 0.1 is imposed around two different mean angles of attack of 10° and 15°. The comparison of the airloads curves and of the pressure distribution over the airfoil surface shows that a three-dimensional numerical model can better reproduce the flow structures and the airfoil performance for the deep dynamic stall regime. Also, the vortical structures observed by PIV in the flow field are better captured by the three-dimensional model. This feature highlighted the relevance of three-dimensional effects on the flow field in deep dynamic stall.     

Numerical simulation on the NACA0018 airfoil self-noise generation

Airfoil self-noise is a common phenomenon for many engineering applications. Aiming to study the underlying mechanism of airfoil self-noise at low Mach number and moderate Reynolds number flow, a numerical investigation is presented on noise generation by flow past NACA0018 airfoil. Based on a high-order accurate numerical method, both the near-field hydrodynamics and the far-field acoustics are computed simultaneously by performing direct numerical simulation. The mean flow properties agree well with the experimental measurements. The characteristics of aerodynamic noise are investigated at various angles of attack. The obtained results show that inclining the airfoil could enlarge turbulent intensity and produce larger scale of vortices. The sound radiation is mainly towards the upper and lower directions of the airfoil surface. At higher angle of attack, the tonal noise tends to disappear and the noise spectrum displays broad-band features.     

Lifting aerofoil calculation using the boundary element method

The bbundary integral formulation and boundary element method are extended to include lifting flow problems. This involves inclusion of a branch cut in the flow field and imposition of a Kutta condition to determine the circulation, Γ Additional boundary integral contributions arise from the cut surface. Techniques for calculating Γ are developed and we treat, in particular, a superposition procedure which permits very efficient computation. Numerical results are presented for an NACA0012 aerofoil at several angles of attack.     

On the birth of stall cells on airfoils

Critical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.     

Aspects of the transpiration model for aerofoil design

Transpiration is a technique in which extra non-physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co-ordinates are adjusted or to find shape corrections in inverse design methods. A first-order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.