Laminar boundary layer in a flow past an aerofoil with a circular cavity

The paper describes a numerical study of a method of preventing the separation of a laminar boundary layer from the forward section of a symmetric aerofoil, the flow past which does not separate at zero angle of incidence. In order to increase the maximum angle of incidence at which the flow has still not separated, a circular cavity (vortex cell) located almost completely inside the aerofoil is introduced on the segment vulnerable to separation. The asymptotics of the corresponding flow at high Reynolds number are described using the Prandtl-Batchelor model. Krasnodar. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1998. The work was financially supported by the International Science Foundation (grants M4K000 and M4K300) and by the Russian Foundation for Fundamental Research (project No. 96-01-01290).     

Investigation of slat heel effect on the flow field over multi-element aerofoils

This paper presents results obtained from an experimental study of the flow field over a multi-element aerofoil which incorporates either a conventional or an advanced slat. Detailed measurements of the mean flow and turbulent quantities over a multi-element aerofoil model equipped with either type of slat have been made in a wind tunnel using stationary and flying hot-wire (FHW) probes. The perfomance of the two slats at two angles of attack, =10° and 20°, were investigated and compared with each other. The results showed a better performance for the advanced slat in terms of the mean velocity field and hence an increase in the lift performance. The advantage of the advanced slat was more pronounced for the multi-element aerofoil placed at the higher angle of attack, i.e., 20°. These findings were substantiated by the Reynolds stresses measured over the multi-element aerofoil, with the conventional slat exhibiting higher values compared with its advanced slat counterpart. Both the mean velocity and Reynolds stress results clearly demonstrated that the conventional slat had a lower stall margin than the advanced slat.     

Dynamic stall experiments on the NACA 23012 aerofoil

An experimental investigation was conducted to examine the dynamic stall characteristics of a NACA 23012 aerofoil section at a Reynolds number of 1.5 million. Time-dependent data were obtained from thirty miniature pressure transducers and three hot film gauges situated at the mid-span of the wing. The static stall mechanism of the NACA 23012 was determined to be via abrupt upstream movement of trailing edge separation. Under dynamic conditions, stall was found to occur via leading edge separation, followed by a strong suction wave that moved across the aerofoil. This suction wave is characteristic of a strong moving vortex disturbance. Evidence of strong secondary vortex shedding was also found to occur, and this appears symptomatic of dynamic stall only at low Mach numbers. Some evidence of flow reversals over the trailing edge of the aerofoil were indicated prior to the development of leading edge separation and dynamic stall.List of symbols c aerofoil chord - C _L sectional lift coefficient - C _M sectional pitching moment coefficient measured about the quarter-chord location - C _p pressure-coefficient - k reduced frequency, c/2V - M Mach number - P pressure - R _c Reynolds number based on chordc - t time - V free stream velocity - x distance along chord line - y distance along span - angle of attack - _a oscillation amplitude - _M Mean angle of oscillation - shear stress - circular frequency     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

A minimal model for flow control on an aerofoil using a poro-elastic coating

A minimal model is obtained for vortex-shedding from an aerofoil with a porous coating of flow-compliant feather-like actuators, in order to better understand this passive way to achieve flow control. This model is realized by linearly coupling a minimal-order model for vortex-shedding from the same aerofoil without any such coating with an equation for the poro-elastic coating, here modelled as a linear damped oscillator. The various coefficients in this model, derived using perturbation techniques, aid in our understanding of the physics of this fluid–structure interaction problem. The minimal model for a coated aerofoil indicates the presence of distinct regimes that are dependent on the flow and coating characteristics. The models and the parametric studies performed provide insight into the selection of optimal coating parameters, to enable flow control at low Reynolds numbers.     

AN IMPROVED NAVIER–STOKES PROCEDURE FOR ANALYSIS OF TWO-DIMENSIONAL AEROFOILS IN LAMINAR AND TURBULENT FLOWS

An accurate and robust Navier–Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier–Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k–ε turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, C_Lmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. © 1997 John Wiley & Sons, Ltd.     

Aerofoil section characteristics in shear flows

Summary The technique of Glauert's image method for a single source is applied to determine the image system of a single vortex in shear flows of arbitrary velocity profile. The aerofoil section characteristics are obtained analytically by the extension of the image system for a single vortex and for a single source to those for vortex and source distributions. Numerical calculations are made and the results show the effect on the aerofoil section characteristics of vorticity in flow fields which have been obtained by combining linear shear flows, by comparison with those obtained in uniform flow.

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Übersicht Das Glauertsche Bildverfahren für eine Einzelquelle wird verwendet, um das Bildsystem eines Einzelwirbels in einer Scherströmung von beliebigem Gesclwindigkeitsprofil zu ermitteln. Die Kennwerte für einen Tragflügelquerschnitt werden analytisch dadurch erhalten, daß das Bildsystem für einen Einzelwirbel und eine Einzelquelle zu einer Verteilung von Wirbeln und Quellen erweitert wird. Die Ergebnisse numerischer Lösungen zeigen die Abhängigkeit der Tragflügelkennwerte von der Verwirbelung in Strömungsfeldern mit linearen Scherströmungen und den Vergleich mit den entsprechenden, in gleichförmigen Strömungen erhaltenen Werten.

     

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°.     

Detection of flow separation and reattachment using shear-sensitive liquid crystals

Coatings of pure chiral nematic liquid crystals are known to change colour under different levels of surface shear stress. In this study, the liquid crystal was used to provide information about flow separation and reattachment on both a two-dimensional aerofoil and a delta wing. The tests were carried out at a free-stream velocity of 28 m/s and a number of incidence angles. The Reynolds numbers based on the central chord length of the models were 200,000 and 270,000 for the aerofoil and delta wing models, respectively. The study showed that locations of boundary layer separation and reattachment can be identified from spatial variations in the surface colour; the agreement between the results and those obtained using surface oil flow was good. Issues relating to interpretation of the crystal colour pattern and the limitation of this technique in detection of flow separation were also discussed.     

Effects of magnetic field on nanofluid forced convection in a partially heated microchannel

This paper numerically examines the laminar forced convection of a water–Al₂O₃ nanofluid flowing through a horizontal microchannel. The middle section of the microchannel is heated with a constant and uniform heat flux. The middle section is also influenced by a transverse magnetic field with a uniform strength. The effects of pertinent parameters such as the Reynolds number (0≤Re≤1000), the solid volume fraction (0≤?≤0.04) and the Hartmann number (0≤Ha≤100) on the flow and temperature fields and the heat transfer performance of the microchannel are examined against numerical predictions. The results show that the microchannel performs better heat transfers at higher values of the Reynolds and Hartmann numbers. For all values of the Reynolds and Hartmann numbers considered in this study, the average Nusselt number on the middle section surface of the microchannel increases as the solid volume fraction increases. The rate of this increase is considerably more at higher values of the Reynolds number and at lower values of the Hartmann number.     

Validation of turbulence models in a simulated air-conditioning unit

Details are given of a study to obtain experimental data in an idealized environment for the purpose of evaluating the corresponding computational predictions and which supplement parallel measurements made in actual packaged air-conditioning units. The system consisted of a purpose-built low-speed wind tunnel with a working section constructed to reproduce particular features of the real units. In the experiment, both the mean velocity profiles and turbulence properties of the flow are obtained from triple-hot-wire anemometry measurements. A numerical model, based on finite volume methodology, was used to obtain the solution of the Reynolds-averaged Navier–Stokes equations for incompressible isothermal flow. The Reynolds stress terms in the equations are calculated using the standard k–ϵ model and second-moment closure (Reynolds stress) models. The accuracy of the two models was evaluated against the experimental measurements made 10 mm downstream of a baffle. The results show that the standard k–ϵ model gave the better agreement except in regions of strong recirculation. © 1997 John Wiley & Sons, Ltd.     

Bluff body wakes with free, fixed, and discontinuous separation at low Reynolds numbers and low aspect ratio

Some comparative experimental results are presented of bluff body wakes with free, fixed, and discontinuous separation. The particular examples considered are a circular cylinder, a plain blunt trailing edge aerofoil and a segemented blunt trailing edge aerofoil. The evolution of the near wake and vortex shedding modes are compared and discussed.     

Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Computation of turbulent asymmetric wake

The development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two-dimensional Navier-Stokes equations along with the k-ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant C_u as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

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.     

Unsteady supersonic flow over an oscillatory aerofoil using a second-order TVD scheme

The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second-order space-accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0·0 and ± 1·0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co-ordinates for each time step. The calculations have been done for two angles of attack θ = 5·0° sin (ωt) and θ = 3·0° + 3·0° sin (ωt) for the free-stream Mach numbers 2·0 and 3·0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.     

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.     

Some new aspects of the slow flow of a viscous fluid through an axisymmetric duct expansion or contraction. II — Experimental part

The flow of a newtonian viscous fluid through a cylindrical duct in the vicinity of a section discontinuity is studied using a visualization technique. The evolution with the Reynolds number of the features of the stationary vortex cell is given, in particular the reversibility of the flow is verified for the very small Reynolds numbers. In the creeping regime a detailed analysis of the velocity and strain-rate fields is performed.