Experimental investigation of the resistance to the flow of a conducting fluid in flat insulated ducts in the presence of a transverse magnetic field with allowance for fringe effects and wall roughness

The distribution of pressure, velocity, and electrical potential has been investigated for a mercury flow in insulated rectangular ducts with a large side ratio (Hartmann-type flow). The ranges of variation of the Reynolds, Hartmann, and Stewart numbers were 7·10²R5·10⁵, 0H490, and 0N24, respectively. Special attention is given to the sections of the channel where the flow enters and leaves the magnetic field. In these zones the pressure is sharply nonuniform and the velocity profiles in a plane perpendicular to the field acquire an M shape. A relation is established between the length of the entrance section, where the flow is three-dimensional, and the MHD similarity criteria. It is shown that ducts which are hydraulically smooth in the absence of a magnetic field become increasingly rough as the field grows stronger. Data are obtained on the resistance coefficient for a stabilized flow measured in a magnetic field and on the dependence of the critical Reynolds number on the Hartmann number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–21, July–August, 1971.     

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.     

Multiple Steady State Solutions Resulting From Coupling Between Mixed Convection And Radiation In An Inclined Channel

In this work, we present a numerical study of mixed convection coupled with radiation in an inclined channel with an aspect ratio B = L/H=10, and locally heated from one side. Convective, radiative and total Nusselt numbers, evaluated on the cold surface and at the exit of the channel, are presented for different combinations of the governing parameters namely, the surface emissivity (0 1), the Reynolds number (10 Re 50), the inclination of the channel with respect to the horizontal surface (0° 90°) and the Rayleigh number (Ra = 10⁵). The ratio, R = Q_C/Q_E, of the heat quantities, leaving the channel through the cold wall, Q_C, and through the exit, Q_E, is presented to identify the most favorable issue to the heat transfer in the studied configuration. The results obtained show that the flow structure is significantly altered by radiation which contributes to reduce or to enhance the number of the solutions obtained.     

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 a longitudinal magnetic field on the characteristics of a stabilized channel arc

The results of calculations of the temperature profiles and volt-ampere characteristics of a long cylindrical argon arc in a longitudinal uniform magnetic field are presented. The calculation was made for the following parameters: pressure p =0.1–10.0 atm; temperatures T = 1000-20,000°K; magnetic field induction B =0-10 T; diameter of cylindrical channel d = 1.0 cm. It is shown that for strongly radiating arcs (p1.0 atm) the temperature profiles become more inflated with an increase in the magnetic field, while for weakly radiating arcs (p 0.1 atm) the appearance of loops in the volt-ampere characteristics is typical for certain conditions (14,000T20,000°K, B1.0 T), indicating the impossibility of arcing under these conditions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 147–153, March–April, 1975.     

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).

     

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.     

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.     

Asymptotic Nusselt numbers for Newtonian flow through a parallel-plate channel with recycle

General expressions for evaluating the asymptotic Nusselt number for a Newtonian flow through a parallel-plate channel with recycle at the ends have been derived. Numerical results with the ratio of thicknesses as a parameter for various recycle ratios are obtained. A regression analysis shows that the results can be expressed by log Nur^0.83=0.3589 (log)² -0.2925 (log) + 0.3348 forR 3, 0.1 0.9; logNu=0.5982(log)² +0.3755 × 10^–2 (log) +0.8342 forR 10^–2, 0.1 0.9.

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Asymptotische Nusselt-Zahlen für die Newtonsche Strömung durch einen Kanal aus parallelen Platten mit Rückführung

Zusammenfassung In dieser Untersuchung wurden allgemeine Ausdrücke hergeleitet um die asymptotische Nusselt-Zahl für eine Newtonsche Strömung durch einen Kanal aus parallelen Platten mit Rückführung an den Enden berechnen zu können. Es wurden numerische Ergebnisse mit den Dicken-Verhältnissen, als Parameter für verschiedene Rückführungs-verhältnisse, erhalten. Eine Regressionsanalyse zeigt, daß die Ergebnisse wie folgt ausgedrückt werden können: log Nur^0,83=0,3589 (log)² -0,2925 (log) + 0,3348 fürR 3, 0,1 0,9; logNu=0,5982(log)² +0,3755 × 10^–2 (log) + 0,8342 fürR 10^–2, 0,1 0,9.

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Nomenclature A₁ shooting value,d(0)/d - A₂ shooting value,d(1)/d - B channel width - Gz Graetz number, U_bW²/L - h _m logarithmic average convective heat transfer coefficient - h _x average local convective heat transfer coefficient - k thermal conductivity - L channel length - Nu average local Nusselt number, 2 h_xW/k - Nu _m logarithmic average Nusselt number, 2h_mW/k - R recycle ratio, reverse volume flow rate divided by input volume flow rate - T temperature of fluid - T _m bulk temperature, Eq. (8) - T ₀ temperature of feed stream - T _s wall temperature - U velocity distribution - U _b reference velocity,V/BW - V input volume flow rate - v dimensionless velocity distribution, U/U_b - W channel thickness - x longitudinal coordinate - y transversal coordinate - Z₁-z₆ functions defined in Eq. (A1) - thermal diffusivity - least squares error, Eq. (A7) - weight, Eqs. (A8), (A9) - dimensionless coordinate,y/W - dimensionless coordinate,x/GzL - function, Eq. (7)     

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.     

Analysis of slip and temperature jump coefficients in a binary gas mixture

The possibility of simplifying the formulas obtained by the Maxwell-Loyalka method for the velocity _u, temperature _T and diffusion _d slip coefficients and the temperature jump coefficient in a binary gas mixture with frozen internal degrees of freedom of the molecules is considered. Special attention is paid to gases not having sharply different physicochemical properties. The formulas are written in a form convenient for use without linearization in the thermal diffusion coefficient. They are systematically analyzed for mixtures of inert gases, N₂, O₂, CO₂, and H₂ at temperatures extending from room temperature to 2500°K. It is shown that for the molecular weight ratios m^* = m₂/m₁ considered the expressions for _u and can be radically simplified. With an error acceptable for practical purposes (up to 10%) it is possible to employ expressions of the same structural form as for a single-component gas: for _u if 1 m^* 6, and for if 1 m^* 3. When 1 m^* 2 the expression for _T can be simplified with a maximum error of 5%. Within the limits of accuracy of the method the expression for _t can be linearized in the thermal diffusion coefficient. An approximate expression convenient for practical calculations is proposed for _d Finally, the , _u, and _T for a single-component polyatomic gas with easy excitation of the internal degrees of freedom of the molecules are similarly analyzed; it is shown that these expressions can be considerably simplified.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–159, November–December, 1990.     

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.     

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.     

Messung und Berechnung des örtlichen und mittleren Stoffübergangs an stumpf angeströmten Kreisscheiben bei unterschiedlicher Turbulenz

Zusammenfassung In einer vergleichenden Literaturübersicht zu Umströmung, Druck- bzw. Geschwindigkeitsverteilung sowie Wärme- und Stoffübergang werden bislang vorliegende Angaben zu stumpf angeströmten Kreisscheiben und -Zylindern zusammengefaßt. Wenige und zudem divergierende Ergebnisse zum Wärme- und Stoffübergang machen grundlegende experimentelle und theoretische Untersuchungen notwendig, wie sie in [l, 2] für die Eichung von Stoffübergangsmeßmethoden benötigt werden.Unter Einbeziehung des quer angeströmten Kreiszylinders wird gezeigt, daß genaue Angaben zum Wärme- und Stoffübergang bei zwei- wie dreidimensionalen Staupunktströmungen bislang nur über die Messung möglich sind. Über gemessene Geschwindigkeitsverteilungen berechnete Stoffübergangskoeffizienten werden von der Messung nicht bestätigt. Sie liegen gegenüber dem Experiment zu niedrig.Die Messungen wurden bei Turbulenzintensiten 0,8%Tu6%, Reynolds-Zahlen 2·10³5 und Scheibendurchmessern 9,3mmd73,7mm durchgeführt. Der Einfluß der Turbulenz auf den Stoffübergang im Staupunkt von Kreisscheiben kann nur näherungsweise über den Smith-Kuethe-Parameter Tu · Re/100 erfaßt werden. Differenzen zwischen Theorie nach Smith und Kuethe für Tu· Re<5 und Messung lassen sich über die Stabilitätstheorie erklären. Für eine genauere Erfassung des Stoffübergangs muß den unterschiedlichen Transportvorgängen über Turbulenzballen oder Längswirbeln sowie der Struktur der Turbulenz Rechnung getragen werden.

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Measuring and computation of local and average mass transfer to disks in cross flow at different turbulence intensities

The results of different publications concerning the flow, pressure and velocity distributions as well as the heat and mass transfer of disks and cylinders in cross flow are compared by a literature review. A few diverging results for heat and mass transfer require new experimental and theoretical approaches. The calibration of recently developed techniques for the determination of mass transfer rates as published in [1, 2] make these investigations expecially necessary. Including the cylinder in cross flow the authors show, that up to now exact data of heat and mass transfer for two- or three-dimensional flow at a forward stagnation region can be obtained by direct measuring only.Mass transfer coefficients computed from measured velocity distributions are not confirmed by the experimental results. Compared to the experimental data they are too low. The measurements were accomplished for turbulence intensities 0.8%Tu6%, Reynolds-numbers 2· 10³5 and disk diameters 9.3 mm d 73.7 mm.The influence of the turbulence on the stagnation point mass transfer of disks can be obtained only approximately by the Smith-Kuethe-parameter Tu·Re/100. Differences between theoretical results of Smith and Kuethe and experimental ones for Tu·Re/100<5 may be explained by the stability theory. For a more accurate determination of the mass transfer the different transport mechanisms of the scale of turbulence or the tree-dimensional flow pattern like Taylor-Görtler-vortices as well as the structure of the turbulence itself have to be regarded.

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Bezeichnungen a Temperaturleitkoeffizient - C_p Beiwert für den statischen Druck - C₂, C₃ Gradient der bezogenen Geschwindigkeit U⁺ am Staupunkt bei ebener, räumlicher Strömung - D_A Diffusionskoeffizient von Ammoniak in Luft - d Durchmesser - Fr=Sh/Re Frössling-Zahl für den Stoffübergang - Fr=Nu/Re Frössling-Zahl für den Wärmeübergang - Le=a/D_A Lewis-Zahl - L Bezugslänge - M Maschenweite von Turbulenzgittern - Nu=·d/ Nußbelt-Zahl - n Exponent der Prandtl-bzw. Schmidt-Zahl - Pr=/a Prandtl-Zahl - p Druck, Partialdruck - p_x statischer Druck an der Stelle x am Rand der Grenzschicht - Re=U · d/ Reynolds-Zahl - r Radius - r(x) radiale Distanz von der Rotationsachse eines Körpers zu einem Oberflächenelement - Sc=/D_A Schmidt-Zahl - Sh= _A ·d/D_A Sherwood-Zahl - T absolute Temperatur - Tu Turbulenzintensität (Turbulenzgrad) in% - U Strömungsgeschwindigkeit in x-Richtung am Rand der Grenzschicht - U Hauptströmungsgeschwindigkeit im freien Kanalquerschnitt - U⁺=U/U bezogene Geschwindigkeit in x-Richtung am Rand der Grenzschicht - u Strömungsgeschwindigkeit in x-Richtung, tangential zur Oberfläche - mittlere turbulente Geschwindig-keitsschwankung in x-Richtung - v Strömungsgeschwindigkeit in y-Richtung, normal zur Oberfläche - x Koordinate in Strömungsrichtung, tangential zur Oberfläche - x_G Entfernung vom Turbulenzgitter in Strömungsrichtung - x⁺ bezogene Länge x/r - y Koordinate normal zur Oberfläche - Wärmeübergangskoeffizient - _A Stoffübergangskoeffizient (Ammoniak) - dimensionsloses Temperaturgefälle an der Wand - Keilvariable - Wärmeleitkoeffizient - Wirbelweilenlänge (mm) - kinematische Zähigkeit - transformierte bezogene Länge - _A Partialdichte von Ammoniak Indices B mit Korrektur aufgrund der Verengung - m mittel - S bezogen auf die Kreisscheibe - Z bezogen auf den Kreiszylinder Herrn Prof. Dr.-Ing. habil. Josef Ipfelkofer zum 70. Geburtstag am 7. April 1977 gewidmet.     

A delta-function method for the n-th approximation of relaxation or retardation time spectrum from dynamic data

A function series g(x; n, m) is presented that converges in the limiting case n and m = constant to the delta-function located at x = = 1. For every finite n, there exists 2n+1(–nmn) approximations of the delta-function _(n)(x–x _n,m ). x _n,m is the argument where the function reaches its maximum. A formula for the calculation is given.The delta-function approximation is the starting point for the approximative determination of the logarithmic density function of the relaxation or retardation time spectrum. The n-th approximation of density functions based on components of the complex modulus (G*) or the complex compliance (J*) is given. It represents an easy differential operator of order n.This approach generalizes the results obtained by Schwarzl and Staverman, and Tschoegl. The symmetry properties of the approximations are explained by the symmetry properties of the function g(x; n, m). Therefore, the separate equations for each approximation given by Tschoegl can be subsumed in a single equation for G and G, and in another for J and J.     

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.     

Emergence of taylor vortices between rotating eccentric cylinders

In a linear setting we examine the stability of the flow of a viscous incompressible liquid between eccentric cylinders, the inner cylinder rotating and the outer cylinder fixed. We consider the case of a narrow gap between the cylinders, which is characteristic for problems in lubrication theory. The main flow, perturbations, and the critical Reynolds number are found in the form of expansions in powers of the eccentricity to within O (³). The results obtained agree with the known experimental data for 0 0.5 and confirm the stabilizing influence of the eccentricity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 101–106, May–June, 1973.The author wish to thank N. P. Artemenko, A. D. Myshkis, and R. Di Prima for a useful discussion of the problem.     

Comparison of Calculated and Experimental Data on Supersonic Flow past a Circular Cylinder

The supersonic perfect-gas flow past a circular cylinder is studied on the basis of a numerical analysis of the time-dependent two-dimensional Reynolds equations using a differential q– turbulence model with reference to the experimental conditions. The calculations are carried out at Reynolds and Mach numbers Re=2× 10⁵ and M=1.1, 1.3, and 1.7 and the experimental investigations at Re=1.62×10⁵–2×10⁵ and Mach numbers on the interval 0.7 M 1.7. The calculated and experimental data on the pressure coefficient distribution over the cylinder surface, the location of the separation point on the surface, and the pressure drag coefficient are compared.     

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.     

On the Ellipticity of the Middle Surface of a Shell and its Application to the Asymptotic Analysis of ‘Membrane’ Shells

We consider a surface S = (), where ² is a bounded, connected, open set with a smooth boundary and : ³ is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H¹() × H¹() × L²(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = .