Interpolation formulas for maxwell viscosity of certain metals as a function of shear-strain intensity and temperature

The purpose of this study is the construction of interpolation formulas for the dependence of Maxwell viscosity, a quantity which is the reciprocal of shear-strain relaxation time , on shear-strain intensity and temperature for several metals: iron, aluminum, copper, and lead. This function was interpolated in various temperature and deformation velocity ranges in accordance with available experimental data for iron (0 10⁷ sec^–1, 200 ° T 1500 °); aluminum (0 10⁷ sec^–1, 300 ° T 900 °); copper (0 10⁵ sec^–1, 300 ° T 1300 °); lead (0 10⁶ sec^–1, 90 ° T 400 °); temperatures in °K.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 114–118, July–August, 1974.     

Effect of suspended particles on the stability of plane poiseuille flow

The behavior of the neutral stability curves is investigated for various values of the particle relaxation time and mass concentration 0 100 and 0 f 0.1. It is shown that as increases from zero the flow is at first destabilized and then at >6 becomes stable, while at >40 the stabilizing effect of the dispersed phase grows weaker. It is found that there is a certain interval 10< <40 on which the flow is most stable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 46–53, January–February, 1986.     

Spectral and correlation characteristics of the turbulent boundary layer on an extended flexible cylinder

In marine geophysical seismological prospecting extensive use is made of towed receiving systems consisting of extended flexible cylinders containing acoustic sensors over which the water flows in the longitudinal direction. The boundary layer pressure fluctuations on the cylinder surface are picked up by the sensors as hydrodynamic noise. This paper is concerned with the study of the energy and spacetime characteristics of the pressure fluctuations in the turbulent boundary layer on an extended flexible cylinder in a longitudinal flow. The pressure fluctuations on the cylinder surface have been investigated experimentally for Re_X=(2–4)·10⁷, a dimensionless diameter of the pressure fluctuation sensors d _p ⁺ =d_pu^*/=500, where d_p is the sensor diameter, u^* the dynamic viscosity, and the viscosity coefficient, and frequencies 0.02311.259 (=^*/U). The spectral and correlation characteristics of the pressure fluctuations on the surface of the flexible cylinder are found to differ from the corresponding characteristics for a rigid cylinder [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i aza, No, 5, pp. 49–54, September–October, 1989.     

On the approximate solution of elastic contact problems for a circular annulus

Paper concerns the Boussinesq and Reissner-Sagoci contact problems for a rigid punch in contact with the plane face of an isotropic elastic half-space over a circular annulusbra. It is shown that a simple combination of the interior and exterior Dirichlet and Neumann solutions for a circle, when expressed in terms of oblate spheriodal coordinates, yields extremely accurate approximate solutions provided that 0b/a0.8.     

Hypersonic flow past blunt-edged delta wings

A method is proposed for calculating hypersonic ideal-gas flow past blunt-edged delta wings with aspect ratios = 100–200. Systematic wing flow calculations are carried out on the intervals 6 M 20, 0 20, 60 80; the results are analyzed in terms of hypersonic similarity parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–179, September–October, 1990.     

The irrotational waves and the convergence of Levi-Civita's series

Summary The paper shows that the existence of irrotational surface waves established by an investigation of Levi-Civita may be extended till the breaking, but that it is valid when is 0,84 p 1 (and when p₁=np with n whole number). No solution is known till to day when is p<0,84 (and when is 1,00<p₁<<1,68).

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Sommario La nota estende la dimostrazione dell'esistenza di onde superficiali irrotazionali, data dal Levi Civita per una ampiezza finita ma sufficientemente piccola dimostrando l'esistenza di queste onde fino al frangimento. Tanto questa dimostrazione che quella originaria di Levi Civita sono valide finchè sia 0,84 p 1 (e quando sia p₁=np con n intero). Nessuna soluzione è nota fino ad oggi quando sia p<0,84 (e quando sia 1 p₁ 1,68).

     

Study of initial segment of turbulent jets of various gases in a parallel air stream

Results are presented of a study of the gasdynamic parameters and the geometric characteristics of the mixing zone of axisymmetric jets of gases of differing density (Freon-12, air, and helium) propagating in a parallel air stream, within the limits of the initial segment (0x/R3–30). Experimental data are presented on the effect of different densities (0. 27 n8.2) and velocities (0m1.7) of the gas jet and the parallel stream on the mixing process.     

Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

For many solid materials the stress relaxation process obeys the universal relationF = – (d/d lnt)_max = (0.1 ± 0.01) ( ₀ — _i ), regardless of the structure of the material. Here denotes the stress,t the time, ₀ the initial stress of the experiment and _i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storageE () and lossE () moduli. Useful numerical approximations ofE () andE () are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence ofE (). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.     

Internal waves generated by the turbulent wake of a sphere

Internal waves generated by the turbulent wake of a sphere travelling horizontally through a linearly stratified fluid were studied using shadowgraph and particle-streak photography. The Reynolds and internal Froude number ranges considered were 2,000 Re 12,900 and 2.0 Fi 28.0, respectively. Two quite distinct flow regimes based on the structure of the turbulent wake were identified. In one, the wake is characterized by large-scale coherent structures. In the other, the wake, as viewed on a side-view shadowgraph, grows in a roughly symmetric fashion to a maximum height and then collapses slowly; such flows are termed the smallscale structures regime.Wave lengths and maximum wave heights of the internal waves were measured as functions of Nt and Fi, where N is the Brunt-Väisälä frequency and t the time. It was found that the wave lengths scale well with the streamwise dimension of the spiralling coherent structures. The maximum amplitude of the internal waves were found to scale with the vertical dimension of the turbulent wake, upon varying the internal Froude number.     

A decomposition depended on directions for nonsingular linear transformation

ＡＤＥＣＯＭＰＯＳＩＴＩＯＮＤＥＰＥＮＤＥＤＯＮＤＩＲＥＣＴＩＯＮＳＦＯＲＮＯＮＳＩＮＧＵＬＡＲＬＩＮＥＡＲＴＲＡＮＳＦＯＲＭＡＴＩＯＮＺｈａｎｇＳｈｅｎｘｕｅ（张慎学）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ...     

Calculation of transverse flow of a stream of rarefied gas past a plate

We give the results of a calculation by the Monte Carlo method of the coefficient of resistance and the field of flow past a plate placed perpendicular to a stream of rarefied gas at Mach numbers M = 2–20 and Reynolds numbers Re₀27. The calculations were carried out for two forms of the law governing the variation of the coefficient of viscosity as a function of temperature (T, T). The results are compared with available calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1976.     

Interaction between a distributed source and the free surface of a viscous fluid

A self-similar solution of the Navier-Stokes equations describing steady-state axisymmetric viscous incompressible fluid flow in a half-space is investigated. The motion is induced by sources or sinks distributed over a vertical axis with a constant density. The horizontal plane bounding the fluid is a free surface. It is found that in the presence of sources a solution of the above type exists and is unique for any value of the Reynolds numberR > 0, but in the case of sinks only on the interval –2 R < 0. The results of calculating the self-similar solutions are presented. The asymptotics of the solutions are found asR 0 andR .Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–65, March–April, 1996.     

On flow and stability of a Newtonian fluid past a rotating plane

An exact solution is given for the steady flow of a Newtonian fluid occupying the halfspace past the plane z=0 uniformly rotating about a fixed normal axis (Oz). This solution is obtained in a velocity field of the form considered by Berker [2] and can be deduced as a limiting case, as h+, of the solution to the problem relative to the strip 0zh imposing at z=h either the adherence boundary conditions or the free surface conditions. Furthermore, the stability of this flow, subject to periodic disturbances of finite amplitude, is studied using the energy method and the result is compared with those corresponding to stability of flows in the strip 0zh.

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Sommario In questa nota si mostra che-oltre alla calssica soluzione di von Karman [1] — esiste, per opportuni valori del gradiente di pressione all'infinito, una soluzione esatta per il moto stazionario di un fluido Newtoniano posto nel semispazio limitato dal piano z=0 uniformemente rotante attorno ad un asse ad esso perpendicolare (Oz). Tale soluzione, ottenuta sulla scia del lavoro di Berker [2], si può dedurre anche come limite, per h+, della soluzione del problema relativo alla striscia 0zh quando sul piano z=h si assegnano o le condizioni di aderenza o le condizioni di frontiera libera. Si studia poi la stabilità di tale moto rispetto a perturbazioni spazialmente periodiche di ampiezza finita col metodo dell'energia e si confronta il risultato ottenuto con quelli relativi alla stabilità dei moti nella striscia 0zh.

     

Possibility of impulsive gas transport through a capillary at high initial pressure in the system (P 0≥100 MPa)

The possibility of impulsive (using a chemical explosive) gas transport at high initial pressure from a secondary into a primary vessel in times 100t175sec has been experimentally demonstrated. In the first 90sec the proposed device is insensitive to the high internal gas pressure. Whent90sec the strength properties of its elements must be taken into account. By this time the amount of gas in the primary vessel has increased by approximately 43% relative to the initial amount. The use of lightweight pistons (titanium, aluminum or magnesium instead of steel) makes it possible to bring the piston travel time within the range insensitive to the strength properties.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–9, September–October, 1993.     

Distinctive Features of the Flow past a Flight Vehicle Integrated with an Air-Breathing Engine at High Supersonic Velocities

The aerodynamic characteristics and distinctive features of the flow past hypersonic integral-layout flight vehicles with air-breathing engines intended for cruising atmospheric flight are experimentally investigated. The experiments were conducted on a simplified model designed with regard for the general principles of integration for vehicles of the class considered. The tests were run in a high-speed supersonic wind tunnel over the Mach and Reynolds number ranges 4 M 9 and 10⁵ Re₀ 10⁶.Balance testing was conducted, the pressure distributions over the vehicle surface were measured, the flowfield parameters were determined using a moving total-pressure tube, and flow shadowgraphs were obtained. The measured data are compared with the results of the calculations for three-dimensional inviscid flows. The effects of mounting a nacelle and contouring the internal duct are considered. The effect of the corrections on the duct flow in the absence of jet modeling is estimated.     

Heat transfer process in turbulent flows

A system of differential equations is proposed to describe turbulent flows of incompressible fluid boundary layer type with constant thermophysical characteristics A turbulent temperature conductivity is introduced which is expressed in terms of the energy and scale of turbulence, the dimensionless gradients of the mean velocity and turbulence energy, and the dimensionless distance, to the surface being streamlined. This system is integrated on an electronc computer by the mesh method for the flow in a flat-plate boundary layer with different Prandtl numbers (0.2P100) For air (P=0.71) the system is integrated for nonzero values of the transverse mean velocity component on the streamlined surface (0v_W/U0.0045).Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 18–24, July–August, 1972.     

Calculation of the pressure on the side surface of bodies consisting of a spherical segment joined to an inverted cone in a supersonic stream

The results of investigations of inviscid flow over inverted cones with nose consisting of a spherical segment were published for the first time in Soviet literature in [1–4]. In the present paper, a numerical solution to this problem is obtained using the improved algorithms of [5, 6], which have proved themselves well in problems of exterior flow over surfaces with positive angles of inclination to the oncoming flow. It is shown that the Mach number 2 M , equilibrium and nonequilibrium physicochemical transformations in air (H = 60 km, V = 7.4 km/sec, R₀ = 1 m), and the angle of attack 0 40° influence the investigated pressure distributions. A comparison of the results of the calculations with drainage experiments for M = 6, = 0-25° confirms the extended region of applicability of the developed numerical methods. Also proposed is a simple correlation of the dependence on the Mach number in the range 1.5 M of the shape of the shock wave near a sphere in a stream of ideal gas with adiabatic exponent = 1.4.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 178–183, January–February, 1981.     

Numerical solution of the Navier-Stokes equations for flow of gas around a rectangle

A difference scheme of the Lax-Wendroff type was used to solve the Navier-Stokes equations for the problem of flow of a perfect gas around a rectangle (cylinder of rectangular cross section) with and without a front plate for subsonic, transonic, and small supersonic flow velocities (Mach numbers 0.3M2 and Reynolds numbers 1R250). The occurrence and development of front, lateral, and rear separation of the flow are discussed, and the aerodynamic characteristics of the considered bodies are determined.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–17, July–August, 1972.     

Unsteady forced convection heat/mass transfer from a flat plate

Numerical methods are used to investigate the transient, forced convection heat/mass transfer from a finite flat plate to a steady stream of viscous, incompressible fluid. The temperature/concentration inside the plate is considered uniform. The heat/mass balance equations were solved in elliptic cylindrical coordinates by a finite difference implicit ADI method. These solutions span the parameter ranges 10 Re 400 and 0.1 Pr 10. The computations were focused on the influence of the product (aspect ratio) × (volume heat capacity ratio/Henry number) on the heat/mass transfer rate. The occurrence on the plates surface of heat/mass wake phenomena was also studied.     

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.