Action of wind gusts and weak shocks on an airfoil in a transonic stream

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 20–27, May–June, 1993.     

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.     

Aerodynamic loading on a cylinder behind an airfoil

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re_d=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Re_c=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Re_c<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re_c>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding.     

Motion of an airfoil near a flat screen

Omsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 47–52, January–February, 1995.     

Dissolution of an ellipsoidal bubble in a slightly viscous liquid

The steady-state velocity, the degree of deformation, and the convective-diffusion-limited rate of quasisteady-state growth (or dissolution) are considered for gas bubbles having shapes close to those of spheres or disks. It is assumed that there are no surface-active substances in the liquid. A qualitative agreement is found between the calculated dissolution rate and the experimental data.Notation a radius of the sphere of equivalent volume - u bubble velocity with respect to the still liquid at infinity - kinematic viscosity of the liquid - liquid density - D gas diffusion coefficient in the liquid - surface tension - g gravitational acceleration - d [R=2au/]-Reynolds number - e [P=2au/D]-Peclet number - f [W=2au²/]-Weber number The author thanks V. G. Levich for a discussion of these results.     

Calculation of intense blowing on a blunt body and an airfoil

Various aspects of the problem of intense blowing through the surface of bodies have, been theoretically studied by a number of authors, within the framework of inviscid flow theory. A detailed bibliography on this topic is given, e.g., in [1, 2]. The well-known approaches to solution of this problem have a limited area of application. For example, asymptotic methods can be used for hypersonic flow regimes only at relatively low levels of the blown gas momentum ( = ² = _ov_o ²/ V ² 1). The same limitation applies to the numerical method of straight lines [2]. The forward Eulerian calculation schemes [3, 4] smear the contact discontinuity severely, and cannot handle the case where the blown gas and the gas in the incident flow have different thermodynamic properties (_o ). This paper presents results of a numerical investigation of supersonic flow over two-dimensional and axisymmetric bodies with intense blowing on the forward surface, performed using a time-dependent finite-difference method [5] with an explicit definition of the contact interface between the two cases. The calculations encompass a family of elliptic cylinders with semiaxis ratio 0.5 4, a flat-face cylinder, and a flat plate with rounding near the midsection, with variations in the blowing law, the incident flow Mach number M (3 M 10), the adiabatic indices, and the blowing parameter 0 0.5.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 117–124, January–February, 1977.In conclusion, the authors thank T. S. Novikov and I. D. Sandomirskii, who took part In the present calculations.     

Viscous flow past an airfoil

Incompressible viscous flow past an airfoil at low Reynolds numbers is investigated on the basis of a numerical solution of the complete Navier-Stokes equations. Steady flow regimes, with and without separation, are obtained and, moreover, periodic regimes with the formation of a vortex trail in the wake. The frequency of vortex formation is determined by the linear dimension of the projection of the airfoil on the normal to the freestream velocity. The relation between the Strouhal and Reynolds numbers, determined from this linear dimension, depends only slightly on the angle of attack and shape of the airfoil and is similar to the experimental dependence for circular cylinders.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 29–36, July–August, 1986.In conclusion the authors wish to express their warm thanks to G. I. Petrov for his interest in their work and valuable discussion of their results, and to V. P. Shkadova for discussing the formulation of the problem and the method of solution and for her constant readiness to advise on the organization of the calculations.     

Calculation of dynamic stall on an oscillating airfoil

A mathematical model of an unsteady separated flow around an oscillating airfoil is considered. This model is based on a viscid-inviscid approach. The points of separation and the intensity of vorticity displaced into the external flow are determined using boundary-layer equations in an integral form. Dynamic stall on an oscillating airfoil is studied. The mechanism and nature of antidamping are discovered. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 81–85, May–June, 2000.     

Laminar separation bubble on an Eppler 61 airfoil

Laminar separation bubble that occurs on the suction side of the Eppler 61 airfoil at Re=46000 is studied. The incompressible flow equations are solved using a stabilized finite element method. No turbulence model is used. The variation of the bubble length and its location, with the angle of attack (α), is studied in detail. An abrupt increase in the lift coefficient is observed at α∼4.5°. It is found to be related to a sudden decrease in the separation bubble length at the trailing edge of the airfoil. Significant differences are observed in the results from the 2D and 3D computations. Stall is observed in 3D simulations, but is found to be absent in 2D. The laminar bubble, which fails to reattach in 3D for α>14°, continues to reattach for α as large as 20° in the 2D computations. Reynolds stress calculations in both 2D and 3D indicate the extent to which the outer flow is affected by the presence of bubble. It is found that the Reynolds stress components ${\over{u{^\prime}}{v{^\prime}}}$ and ${\over{u{^\prime}}{w{^\prime}}}$ are of comparable order of magnitude indicating that spanwise fluctuations are significant. The effect of the time window used to compute the time‐averaged aerodynamic coefficients is studied. The time‐averaged and root mean square (rms) value of the aerodynamic coefficients are calculated for both 2D and 3D computations and compared with the previously published experimental results. The 3D computations show good agreement with the earlier data. The variation of the rms value of the aerodynamic coefficients with angle of attack shows certain peaks. The cause of their appearance is investigated. The effect of Reynolds number is studied. The increase in Re at α=10° is found to reduce the bubble length and cause it to move closer to the leading edge. Copyright © 2009 John Wiley & Sons, Ltd.     

Calculation of pressure on an airfoil contour in an unsteady separated flow

Simple formulas for calculating the pressure and the total hydrodynamic reactions acting on an arbitrarily moving airfoil are derived within the framework of the model of plane unsteady motion of an ideal incompressible fluid. Several vortex wakes may be shed from the airfoil owing to changes in velocity circulation around the airfoil contour. Cases with nonclosed and closed contours are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 109–113, May–June, 2008.     

Design of an airfoil with a given velocity distribution near an interface

Solutions for problems of profile design near a rigid wall or free surface are found as particular cases of the more general inverse problem of flow over an airfoil near an interface. The solution is based on a modification of the iteration method developed in [3, 4] for the direct problem of flow over a profile near an interface. In each step the apparatus of quasisolutions is employed. The calculations carried out demonstrate the efficiency of the method and reveal the effect of an interface, a rigid wall and a free surface on the geometric and aerodynamic characteristics of the profile.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 15–21, November–December, 1992.     

Cavitation flow past an arbitrarily-shaped airfoil

The problem of two-dimensional inviscid incompressible flow past an arbitrarily-shaped airfoil in the presence of developed cavitation is studied in an accurate nonlinear formulation.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–90, September–October, 1995.     

Efficiency of an auto-propelled flapping airfoil

The present study deals with an investigation of the flow aerodynamic characteristics and the propulsive velocity of a system equipped with a nature inspired propulsion system. In particular, the study is aimed at studying the effect of the flapping frequency on the flow behavior. We consider a NACA0014 airfoil undergoing a vertical sinusoidal flapping motion. In contrast to nearly all previous studies in the literature, the present work does not impose any velocity on the inlet flow. During each iteration the outer flow velocity is computed after having determined the forces exerted on the airfoil. Forward motion may only be produced by flapping motion of the airfoil. This is more consistent with the physical phenomenon. The non-stationary viscous flow around the flapping airfoil is simulated using Ansys-Fluent 12.0.7. The airfoil movement is achieved using the deformable mesh technique and an in-house developed User Define Function (UDF). Our results show the influence of flapping frequency and amplitude on both the airfoil velocity and the propulsive efficiency. The resulting motion is contrasts to the applied forces. In the present study, the frequency ranges from 0.1 to 20 Hz while the airfoil amplitude values considered are: 10%, 17.5%, 25% and 40%.     

Design of an airfoil with a flap of finite dimensions

A method of designing mechanized profiles is proposed. This method preserves the advantages of inverse boundary-value problems for simply connected domains and makes it possible to use quasi-solutions for satisfying the conditions of solvability. The problems of designing a profile with an infinitely thin flap of finite length and an airfoil with a flap of finite thickness are considered.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 173–180, January–February, 1995.     

Thrust generation by an airfoil in hover modes

A small airfoil is operated in combined harmonic plunging and pitching motions to generate thrust in a still air environment. By full utilization of dynamic stall vortices large thrust coefficients were attained. The vortical signature of thrust is a simple vortex street with the character of a jet stream.On sabbatical leave from the University of Colorado at Boulder.     

Force acting on a deformable contour moving in an arbitary fluid stream

A solution is given for the plane nonstationary motion of an arbitary deformable contour in the potential flow of an ideal incompressible fluid. The problem was solved by conformal mapping. A simple formula is obtained for the force acting on a small size contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 4–8, January–February, 1973.The author is grateful to L. I. Sedov and Yu. L. Yakimov for formulating the problem and supervising the research.     

Experimental and numerical study of the stability of a pre-separated flow on an airfoil

The problem of the origin and evolution of two-dimensional waves of unstable disturbances in the boundary layer on an airfoil in the region of adverse pressure gradient in the preseparation flow region is solved numerically. The stability of the experimental velocity profiles, including the inflected profiles, is studied. As a result of the calculations, the boundaries of the instability region and the parameters of the maximally unstable disturbances (frequency, growth rate, wavelength, and propagation velocity) are determined for each velocity profile. The characteristics obtained in the present work are in good agreement with the real experimental parameters of instability waves. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 126–132, January–February, 1999.     

Plunging wake analysis of an airfoil equipped with a Gurney flap

Experimental Techniques - Experimental measurements were conducted on a plunging Eppler 361 Gurney flapped airfoil to study wake structure and dynamic stall phenomenon in the wake. The heights of...