Design of a two-element airfoil in a range of angles of attack

A numerical-analytical solution of an inverse boundary-value problem of aerohydrodynamics is obtained for a two-element airfoil in the full formulation, based on the velocity distribution defined on the sought airfoil contours in a range of angles of attack. It is demonstrated that flow separation does not occur in the entire range considered for a specified non-separated velocity distribution on the upper surfaces at the maximum angle of attack and on the lower surface at the minimum angle of attack. An example of constructing a sectional airfoil is given; verification of the results obtained is performed with the use of the Fluent software package. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 107–114, November–December, 2008.     

Flow past an airfoil at an angle of attack to an oncoming sonic stream

Guderley [1] proposed a theoretical example of sonic flow of gas past a symmetric airfoil at zero angle of attack to an oncoming stream. The linear distribution of the velocity over the airfoil surface was found from the solution describing this flow. It is of interest to generalize this example to the case of nonsymmetric sonic flow past an airfoil. In the present paper a study is made of sonic flow past a Guderley airfoil at an angle of attack and a study is made of the dependence of the velocity over the surface of the airfoil on the angle of attack. This dependence is obtained by means of the parabolic method of Spreiter and Alksne [2], which makes it possible to solve this problem directly in the plane of the flow. For comparison, flow past a parabolic airfoil at an angle of attack is considered, and an expression is obtained for the dependence of the distribution of the velocity over the surface on the angle of attack, this being a generalization of the formula of Zierep [3], who considered sonic flow past a parabolic airfoil at zero angle of attack.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–86, September–October, 1982.     

Extension of the problem of designing a wing airfoil with active flow controls to the case of systems involving a screen

The solution of the inverse boundary-value problem for a wing airfoil with slot air suction from the outer flow on its upper surface and control jet injection from its rear is generalized to include the case of the flow around such an airfoil in the presence of a screen. The complications due to the double connectivity of the flow region are overcome by means of introducing a fictitious flow beneath the screen. The solution is constructed using a numerical-analytical iteration procedure. Formulas for recalculating the aerodynamic characteristics and the velocity distribution over the airfoil surface to different flight regimes and suction-injection device operation regimes are derived. The effect of the injected jet energy, the airfoil-screen spacing, and the slope of the rectilinear airfoil undersurface on the aerodynamic and geometric characteristics of the airfoil, namely, the shape and the lift coefficient, is studied. The reliability of the results is confirmed by the results of calculations using the Fluent program.     

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 82–87, November–December, 2008.     

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.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

Time-resolved and volumetric PIV measurements of a transitional separation bubble on an SD7003 airfoil

To comprehensively understand the effects of Kelvin–Helmholtz instabilities on a transitional separation bubble on the suction side of an airfoil regarding as to flapping of the bubble and its impact on the airfoil performance, the temporal and spatial structure of the vortices occurring at the downstream end of the separation bubble is investigated. Since the bubble variation leads to a change of the pressure distribution, the investigation of the instantaneous velocity field is essential to understand the details of the overall airfoil performance. This vortex formation in the reattachment region on the upper surface of an SD7003 airfoil is analyzed in detail at different angles of attack. At a Reynolds number Re _c < 100,000 the laminar boundary layer separates at angles of attack >4°. Due to transition processes, turbulent reattachment of the separated shear layer occurs enclosing a locally confined recirculation region. To identify the location of the separation bubble and to describe the dynamics of the reattachment, a time-resolved PIV measurement in a single light-sheet is performed. To elucidate the spatial structure of the flow patterns in the reattachment region in time and space, a stereo scanning PIV set-up is applied. The flow field is recorded in at least ten successive light-sheet planes with two high-speed cameras enclosing a viewing angle of 65° to detect all three velocity components within a light-sheet leading to a time-resolved volumetric measurement due to a high scanning speed. The measurements evidence the development of quasi-periodic vortex structures. The temporal dynamics of the vortex roll-up, initialized by the Kelvin–Helmholtz (KH) instability, is shown as well as the spatial development of the vortex roll-up process. Based on these measurements a model for the evolving vortex structure consisting of the formation of c-shape vortices and their transformation into screwdriver vortices is introduced.     

Minimization of the Wing Airfoil Drag Coefficient Using the Optimal Control Method

The problem of designing a wing airfoil starting from the surface velocity (or pressure) distribution, given in multi-parameter form, is considered. In the diffuser region, the velocity decrease law is determined from the conditions of minimum drag and separationless flow for a given Reynolds number. The case of boundary layer suction for the purpose of improving the aerodynamic characteristics of the airfoil is studied. A solution is obtained using optimal control theory.     

A Model Problem of the Design and Aerodynamical Calculation of the Gliding Wing Airfoil of a Wing-in-Ground Vehicle

The problem of the design and aerodynamical calculation of a wing airfoil whose trailing edge glides over a plane horizontal surface is formulated and solved. The known airfoil undersurface is a rectilinear segment forming a given angle with the ground surface, while the upper surface is sought on the basis of a preassigned velocity distribution. This distribution is taken from a class of hydrodynamically advantageous distributions ensuring separationless flow around the airfoil within the framework of the mathematical flow model adopted. The problem is reduced to a mixed boundary value problem in a half-plane and solved analytically. For calculating the lift coefficient the assumption of a thin jetlet flowing between the horizontal region of the airfoil contour and the ground surface is introduced. The effect of the law of pressure decrease along the jetlet, from the stagnation to the exit value, on the lift coefficient is studied. On the basis of the calculations performed a conclusion is drawn concerning the influence of the rectilinear region slope on the airfoil shape; it is also shown how the slope and the value of the maximum velocity on the airfoil affect its shape and the lift coefficient.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at <Emphasis Type="Italic">Re</Emphasis> ≈ 10<Superscript>3</Superscript>

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 10⁴. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.     

EXPERIMENTAL INVESTIGATION ON LIFT INCREMENT OF A PLASMA CIRCULATION CONTROL AIRFOIL

利用等离子体激励器发展了新型的环量增升技术,并对二维NACA0012翼型绕流实施控制。由于NACA0012翼型为尖后缘构型,环量增升装置由2个非对称型介质阻挡放电等离子体激励器构成。一个等离子体激励器贴附于翼型吸力面靠近后缘处,其诱导的壁面射流沿来流方向指向下游;另一个等离子体激励器贴附于翼型压力面靠近后缘处,其诱导的壁面射流与来流方向相反指向上游。在风洞中通过时间解析二维PIV系统对翼型绕流流场进行了测量,基于翼型弦长的雷诺数Re=20 000。结果表明在等离子体激励器的控制下,翼型压力面靠近后缘处可以形成一个定常回流区,从而起到虚拟气动外形的作用,因此翼型吸力面的流场得到加速,压力面的流场得到减速,使得翼型压力面的吸力以及压力面的压力都得到增加,进而增加了翼型的环量。风洞天平测力实验进一步验证了该环量增升技术的有效性。在整个攻角范围内,施加控制的翼型的升力系数相比没有控制的工况有明显的提高。     

Measurement of parallel blade–vortex interaction at low Reynolds numbers

In this study parallel blade–vortex interaction for a Schmidt-propeller configuration has been examined using particle image velocimetry (PIV). This tandem configuration consists of a leading airfoil (forefoil), used to generate a vortical wake of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs) through a pitching or plunging motion, and a trailing airfoil (hindfoil), held fixed with a specified angle of attack and vertical spacing in its wake. The hindfoil incidence (loading) and not the vertical spacing to the incoming vortical wake has been found to dictate the nature of the interaction (inviscid vs. viscous). For cases where the vortex–blade offset is small and the hindfoil is loaded, vortex distortion and vortex-induced separations are observed. By tracking the circulation of the LEV and TEV, it has been found that the vortices are strengthened for the tandem arrangement and in certain cases dissipate quicker in the wake when interacting with the hindfoil. Time-averaged forces obtained using a standard control-volume analysis are then obtained and used to evaluate these vortex-interaction cases. A subsequent analysis of the varying pressure distribution over the suction side of the hindfoil is performed by integrating the Navier–Stokes equations through the velocity field. This allows for a direct comparison of the vortex-induced loading for the various configurations.     

Design of a thin airfoil in a channel with permeable walls

A general solution is obtained for the boundary value problem of designing a thin airfoil in a channel with permeable walls from the given pressure distribution. A suitable choice of permeability coefficients makes it possible to construct a thin airfoil in a channel with impermeable walls, in a jet, etc. The effect of the wall permeability on the shape of the airfoil is studied. Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–34, July–August, 1994.     

Active control of flow separation over an airfoil using synthetic jets

We perform large-eddy simulation of turbulent flow separation over an airfoil and evaluate the effectiveness of synthetic jets as a separation control technique. The flow configuration consists of flow over an NACA 0015 airfoil at Reynolds number of 896,000 based on the airfoil chord length and freestream velocity. A small slot across the entire span connected to a cavity inside the airfoil is employed to produce oscillatory synthetic jets. Detailed flow structures inside the synthetic-jet actuator and the synthetic-jet/cross-flow interaction are simulated using an unstructured-grid finite-volume large-eddy simulation solver. Simulation results are compared with the 2005 experimental data of Gilarranz et al., and qualitative and quantitative agreements are obtained for both uncontrolled and controlled cases. As in the experiment, the present large-eddy simulation confirms that synthetic-jet actuation effectively delays the onset of flow separation and causes a significant increase in the lift coefficient. Modification of the blade boundary layer due to oscillatory blowing and suction and its role in separation control is discussed.     

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. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Effect of asymmetric pulsed periodic energy supply on aerodynamic characteristics of airfoils

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of local pulsed periodic energy supply is considered. The numerical solution of two-dimensional unsteady equations of gas dynamics allowed determining the changes in the flow structure near a symmetric airfoil and its aerodynamic characteristics depending on the magnitude of energy in the case of its asymmetric (with respect to the airfoil) supply. The results obtained are compared with the calculated data for the flow around the airfoil at different angles of attack without energy supply. With the use of energy supply, a prescribed lift force can be obtained with a substantially lower wave drag of the airfoil, as compared with the flow around the airfoil at an angle of attack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 70–76, November–December, 2007.     

Friction and Heat Transfer in a Laminar Separated Flow behind a Rectangular Step with Porous Injection or Suction

Results of a numerical study of a laminar separated flow behind a rectangular step on a porous surface with uniform injection or suction are described. Two cases are considered: an unconfined flow past a step and flow evolution in a confined channel (duct). It is shown that mass transfer on the surface causes strong changes in the flow structure and substantially affects the position of the reattachment point, as well as friction and heat transfer. More intense injection leads first to an increase in the separation-zone length and then to its rapid vanishing due to boundary-layer displacement. Vice versa, suction at high Reynolds numbers Re _s > 100 reduces the separation-zone length. The duct flow has a complicated distribution of friction and heat-transfer coefficients along the porous surface owing to the coupled effect of the transverse flow of the substance and changes in the main flow velocity due to mass transfer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 18–28, January–February, 2006.     

Controlling the Turbulent Flow Past a Thick Airfoil by Means of Flow Enhancement in Vortex Cells Using Suction from Central Body Surfaces

On the basis of a numerical simulation of the turbulent steady-state flow past a thick airfoil with vortex cells built into the body contour, an unconventional technique for controlling flow separation by means of distributed suction from central bodies embedded in the cells is analyzed over a wide range of Reynolds numbers and suction velocities.     

Scanning PIV measurements of a laminar separation bubble

Scanning PIV is applied to a laminar separation bubble to investigate the spanwise structure and dynamics of the roll-up of vortices within the bubble. The laminar flow separation with turbulent reattachment is studied on the suction side of an airfoil SD7003 at Reynolds numbers of 20,000–60,000. The flow is recorded with a CMOS high-speed camera in successive light-sheet planes over a time span of 1–2 s to resolve the temporal evolution of the flow in the different planes. The results show the quasi-periodic development of large vortex-rolls at the downstream end of the separation bubble, which have a convex structure and an extension of 10–20% chord length in the spanwise direction. These vortices possess an irregular spanwise pattern. The evolution process of an exemplary vortex structure is shown in detail starting from small disturbances within the separation bubble transforming into a compact vortex at the downstream end of the separation bubble. As the vortex grows in size and strength it reaches a critical state that leads to an abrupt burst of the vortex with a large ejection of fluid into the mean flow.