Hydrodynamic interaction of cascades of plates during their relative motion

The problem of the hydrodynamic interaction taking place between the profiled plates of a (turbine) cascade is considered. This problem has hitherto been little studied — existing papers [1, 2] consider the model of effectively steady-state flow, the flow of the liquid at any instant of time being regarded as free from eddies, while time plays the part of a parameter; however, under practical conditions the field of velocities around moving cascades changes rapidly with time, so casting doubt on the validity of the steady-flow mode. The model proposed in this paper allows for high-frequency pulsations in the flow. The approximate solution here derived determines the interference between the profiles on the basis of a limiting solution with infinitely large Strouhal numbers. A typical calculation is presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 49–54, January–February, 1974.     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

UNSTEADY LIFT FORCE ON A TOWED SPHERE

An experimental effort to characterize the broadband flow-induced lift forces on a spherical body that is towed underwater is described. The body itself is the transducer which is comprised of a small geophone encased in a near-neutrally-buoyant sphere, 7·62 cm in diameter. The research described in this paper quantifies the flow-induced unsteady lift force signal as a function of the sphere diameter Reynolds number (7620<Re<34 290) and the Strouhal number (1·5<St<30). It is found that the broadband flow-induced unsteady lift forces are proportional to the product of an area and the dynamic pressure of the flow, as expected. These data are compared to similar data measured previously on a finite-length, right-circular cylinder in cross flow. This comparison indicates that the cylindrical body creates more unsteady side force than does the spherical one, particularly at the lower end of the Strouhal number range.     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

Stability of self-similar pipe flow with suction

The stability of self-similar flows with various boundary conditions at the wall is investigated. In the region of nonexistence of self-similar solutions an oscillatory regime is detected. The problem of stability with respect to disturbances of general form is studied. The dependence of the critical values of the axial Reynolds number and the Strouhal number on Re is calculated for various suction rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 18–25, September–October, 1991.     

Acoustic effect on the root part of a turbulent jet

Results are presented of experimental investigations of the effect of low-frequency acoustic perturbations of different frequency and constant intensity on the root part of a nonisothermal subsonic turbulent jet escaping from a direct-jet injector with a conical diffusor in the 0.031–0.054 range of Strouhal numbers. Experimental dependences of the mean velocity and the longitudinal intensity of the turbulence are presented as a function of different parameters for both the unperturbed flow and for the flow in the acoustic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 182–186, July–August, 1970.The authors are grateful to A. S. Ginevskii, I. M. Koshelev, and A. S. Modnov for discussing the results of this research.     

垂直向上气液两相流中两相斯托拉赫数的研究

试验研究了三角形、T形两种形状4种规格的物体,在垂直上升气液两相流中,发生气液两相涡街时,气液两相斯托拉赫数的变化规律,在测得大量数据的基础上,得出了发生气液两相涡街时,气液两相斯托拉赫数的通用关系式,研究表明,气液两相斯托拉赫数在两相工况下为一变数,其值与来流截面含气率、涡街发生体形状和特征尺寸、来流方向等因素有关,应用此关系式,根据测得的两相涡街频率可将涡街发生体作为测量两相流流量与组分的测量元件。     

A SERIES IN 1/√Re TO REPRESENT THE STROUHAL–REYNOLDS NUMBER RELATIONSHIP OF THE CYLINDER WAKE

In this Brief Note, we show that shedding frequency data is well collapsed, over a large range of Re from 50 up to at least 140,000, by using a Strouhal number that depends upon an effective wake width, which includes not only the physical body diameter, but also a characteristic width of the separating shear layers. The use of this effective wake width also leads to a new formulation for the relationship between Strouhal number (S) versus Reynolds number (Re) for the cylinder wake, which may be expressed as an expansion in powers of (1/√Re): EquationTruncated two-term or three-term series have much less error-of-fit when compared with the traditional S–Re relationships commonly in use. A good test of any S–Re functional relationship is now made possible by comparison with Henderson's numerical data for two-dimensional laminar shedding, over a much larger range of Re (up to Re=1000) than is possible to obtain experimentally. It seems significant that even a two-term fit, given by S=0·2698 −1·0271/√Re has one order of magnitude less error than the traditional three-term fit. By using such √Re-formulae in both the laminar and 3-D wake turbulent regimes, we may accurately represent S–Re data over a large range of Re, although the validity of these representations at these higher Re needs further support. In summary, this Brief Note not only provides physical support for the use of such S–Re relationships as shown above, but also demonstrates that these formulations fit the data closer than traditional S–Re expressions.     

Influence of transverse slits on the hydrodynamic coefficients of a wing of finite span in stationary and nonstationary motion near a wall

The method of matched asymptotic expansions is used to construct an approximate solution to the problem of the influence of narrow transverse slits on the hydrodynamic coefficients of a thin rectangular wing moving near a wall. The flow in the neighborhood of a slit is described by a local asymptotic solution satisfying the condition of continuity of the pressure on the leading edge of the slit and matched to the main solution. Results of the calculations illustrate the influence of the slits on the hydrodynamic characteristics of the wing at different Strouhal numbers and aspect ratios.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 122–128, November–December, 1980.     

Rotating cylinder in a flowing viscous incompressible fluid

New results are obtained in the problem of flow of a viscous fluid past a rotating cylinder by numerical solution of the Navier—Stokes equations for Reynolds numbers 10 Re 100. The drag and lift have been calculated. The oscillatory flow regime in the wake behind a fixed cylinder is investigated for Re = 80. The Strouhal number for auto-oscillations is 0.16.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–21, January–February, 1982.I am grateful to G. I. Petrov and V. Ya. Shkadov for constant interest in the work and helpful discussions.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

Flapping flight produced by high-frequency forced vibrations of a wing

Forced vibrations of an elastic wing are investigated. The main attention is devoted to the solution of the problem for Strouhal number k 1. It is shown that an elastic wing makes it possible to obtain high efficiencies and high thrust coefficients in a wide range variation of the Strouhal number. The maximum of the thrust is usually achieved near resonance, while the maximum of the efficiency is achieved in a different regime, which is determined by the parameters of the vibrating system.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–158, March–April, 1984.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Optimization of body shape at small reynolds numbers

The problem of the optimization of the shape of a body in a stream of viscous liquid or gas was treated in [1–5]. The necessary conditions for a body to offer minimum resistance to the flow of a viscous gas past it were derived in [1], The necessary optimality conditions when the motion of the fluid is described by the approximate Stokes equations were derived in [2], The shape of a body of minimum resistance was found numerically in [3] in the Stokes approximation. The optimality conditions when the motion of the fluid is described by the Navier—Stokes equations were derived in [4, 5], and in [4] these conditions were extended to the case of a fluid whose motion is described in the boundary-layer approximation. The necessary optimality conditions when the motion of the fluid is described by the approximate Oseen equations were derived in [5] and an asymptotic analysis of the behavior of the optimum shape near the critical points was performed for arbitrary Reynolds numbers.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp, 87–93, January–February, 1978.     

Transition flow of a fibrous suspension in a pipe as the flow of an anisotropic fluid

The transition flow is considered of a fibrous suspension in a pipe. The flow region consists of two subregions: at the center of the flow a plug formed by interwoven fibers and fluid moves as a rigid body; between the solid wall and the plug is a boundary layer in which the suspension is a mixture of the liquid phase and fibers separated from the plug [1–3]. In the boundary region the suspension is simulated as an anisotropic Ericksen—Leslie fluid [4, 5] which satisfies certain additional conditions. Equations are obtained for the velocity profile and drag coefficient of the pipe, which are both qualitatively and quantitatively in good agreement with the experimental results [6–8]. Within the framework of the model, a mechanism is found for reducing the drag in the flow of a fibrous suspension as compared to the drag of its liquid phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–98, September–October, 1985.     

Body shape with minimum total radiant energy flux toward its surface

During a space vehicle's entry into a planet's atmosphere at hypersonic speed one of the important problems is the aerodynamical surface heating due to convective and radiant heat fluxes from the gas after passing through a strong shock wave. Due to the high destructive action of this heating, an important problem is the selection of the aerodynamic shape allowing the minimum heat influx to its surface. The problem of determining the shapes of an axisymmetric body from the condition of minimum total convective heat flux along the lateral face of the body was considered under various assumptions in [1–7]. There are a number of entry conditions (for example, into the earth's atmosphere with a speed of 11 km/ sec at an altitude of about 60 km [12]) during which the radiative component becomes dominant in the total heat flux toward the body. A numerical solution of the problem of hypersonic flow of a nonviscous, non-heat-conducting radiating gas around a body is obtained at this time only for a limited class of bodies and primarily for certain entry conditions (for example, [8–12]). On the basis of these calculations it is impossible to make general conclusions concerning arbitrary body shapes. Therefore, approximate methods were proposed which permit the distribution of radiant heat flux to be obtained for an arbitrary axisymmetric body in a wide range of flight conditions [13–15]. In the present work an expression is derived for the total radiant heat flux over the entire body surface and similarity criteria are found. A variational problem is formulated to determine the shape of an axisymmetric body from the condition of minimum total radiant-heat flux over the entire body surface. It is solved analytically for the class of thin bodies and in the case of a strongly radiating gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 84–89, July–August, 1976.     

Wave processes in semi-open tubes

A numerical method based on the solution of the complete problem of integration of a system of nonstationary nonlinear Euler equations for an ideal and perfect gas is developed. A special form of the dimensionless equations is obtained and the concept of the asymmetry of the pressure peak at the closed end of the tube is introduced, making it possible, using Godunov's scheme, to obtain a physically explicable solution even on grids with a small number of points. The frequency characteristics of the semi-open tube are obtained on the Strouhal number interval from 0.05 to 1.25. It is shown that at the linear resonance frequencies the conditions are favorable for the formation and amplification of shock waves leading to heating of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 169–171, September–October, 1990.     

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.     

Fluid-dynamic forces and wake frequencies on a tilted rectangular cylinder near a solid wall

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder with two different values of the aspect ratio (l/s=3 and 4). We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number when the cylinder is placed at various distances from a bottom wall and different values of attack angle. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 5 times the thickness of the cylinder. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.     

Vortex shedding and surface pressures on a square cylinder at incidence to a uniform air stream

This article describes results of experiments on vortex-shedding frequencies and surface pressures of a square cylinder at non-zero angle of incidence. The range of Reynolds numbers was 2000–21 000, but the lower range was emphasized. For Reynolds numbers greater than 5300, the Strouhal number shows a similar trend with changing angle of incidence; that is, a rapid rise in Strouhal number occurs at an angle of around 13°. The occurrence of such a jump in Strouhal number was found to be associated with onset of the flow reattachment, bringing in a strong pressure recovery on the lower side face of the cylinder. For lower Reynolds numbers Re=2000–3300, the maximum Strouhal number occurs at a relatively higher angle of 17°. Around this angle, the pressure measurements exhibit a rather weak pressure recovery, suggesting a less firm shear-layer reattachment to the side face of the cylinder. The nature of the reattaching flow was further examined by spectral analysis of the fluctuating pressure coefficients measured on the lower side face of the cylinder.