Peristaltic pumping of a second-order fluid in a planar channel

The peristaltic motion of a non-Newtonian fluid represented by the constitutive equation for a second-order fluid was studied for the case of a planar channel with harmonically undulating extensible walls. A perturbation series for the parameter ( half-width of channel/wave length) obtained explicit terms of 0(²), 0(²Re²) and 0(₁Re²) respectively representing curvature, inertia and the non-Newtonian character of the fluid. Numerical computations were performed and compared to the perturbation analysis in order to determine the range of validity of the terms.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

ON THE UNIFICATION OF THE HAMILTON PRINCIPLES IN NONHOLONOMIC SYSTEM AND IN HOLONOMIC SYSTEM

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A Limiting Solution for Flow Past a Delta Wing in the Presence of Supercritical Flow Regions

The flow past a planar delta wing is studied for strong interaction between the boundary layer and the outer supersonic flow. An analytic investigation is carried out using the Newtonian passage to the limit in which the specific heat ratio tends to unity and the Mach and Reynolds numbers to infinity. Possible flow regimes are classified for various wing aspect ratios. For determining the supercritical-subcritical flow transition line an analytic expression, correct to the second approximation, is obtained for flow past a cold wing with a fairly large aspect ratio in which the transverse boundary-layer flows are insignificant.     

Evolution of Vortex Structures on the Leeward Side of a Delta Wing

Results of an experimental study of a supersonic flow around the leeward side of a delta wing are presented. The experiments are performed on three delta wings with leading–edge sweep angles = 68°, 73°, and 78° for Mach numbers M =2—4 and angles of attack = 0—22°. Data on the structure and position of internal shock waves are obtained; the size and location of primary and secondary vortices are found. New regimes of the flow around a delta wing are identified. The chart of flow regimes around delta wings is refined and extended.     

Natural convection heat transfer through an enclosed horizontal layer of supercritical carbon dioxide

In natural convection heat transfer through a thin horizontal layer of carbon dioxide, maxima in the equivalent thermal conductivities are obtained in the vicinity of the respective pseudocritical temperatures at pressures of 75.8, 89.6 and 103.4 bar. The maxima are the more pronounced, the closer the critical point is approached.Comparison of experimental results with Nusselt equations shows good agreement except for the immediate vicinity of the pseudocritical temperature.In visual observations a distinct change in flow structure appears in the immediate vicinity of the pseudocritical temperature. A steady state polygon pattern and a boiling-like action could not be observed in this geometry.

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Zusammenfassung Beim Wärmetransport durch freie Konvektion in einer dünnen waagerechten Schicht von Kohlendioxid ergaben sich Maxima der scheinbaren Wärmeleitfähigkeit in der Nähe der pseudokritischen Temperaturen bei Drükken von 75,8, 89,6 und 103,4 bar. Die Maxima sind um so ausgeprägter, je mehr man sich dem kritischen Punkt nähert.Ein Vergleich der Versuchsergebnisse mit Nusseltbeziehungen ergibt gute Übereinstimmung außer in unmittelbarer Umgebung der pseudokritischen Temperatur. Direkte Beobachtungen der Konvektionsmuster zeigen in unmittelbarer Umgebung der pseudokritischen Temperatur eine deutliche Strukturänderung. Ein stationäres Zellmuster und siedeähnliche Vorgänge konnten in dieser Anordnung nicht beobachtet werden.

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Nomenclature A area of the heating or cooling plate - C constant in the correlation - g acceleration of gravity - h heat transfer coefficient - k thermal conductivity of fluid in the gap - k _e equivalent thermal conductivity - m, n exponents of dimensionless numbers - q heat flux - T _C,PC absolute temperature; critical C, pseudocritical PC - Gr Grashof numberg ( _h– _c) ³/ ² - Nu Nusselt numberh/k - Pr Prandtl number/ - thermal diffusivity - coefficient of volume expansion - width of gap - _c,h temperature of cooling (c)-, heating (h)-plate - _m arithmetic mean temperature ( _c+ _h)/2 - kinematic viscosity - _c,h fluid density at the temperature of the cooling (c)- or heating (h)-plate - heat flow rate through the gap     

Study of vortex breakdown by particle tracking velocimetry (PTV)

Using a quasi three-dimensional instantaneous measurement technique, which combines particle tracking velocimetry (PTV) with volume scanning, first quantitative experimental results of the unsteady and asymmetric interior region of vortex breakdown were obtained. The study was carried out in a low speed flow through a cylindrical tube. A vortex was generated by a set of guidevanes and subjected to an adverse pressure gradient causing its breakdown. By scanning a pulsed illuminated planar laser light sheet, a set of meridional and azimuthal cuts of the flow was obtained. With PTV the recorded particle paths in the cuts were processed in order to obtain the instantaneous two-dimensional velocity field, mean streamlines and vorticity distribution. Moreover, the three-dimensional shape of the appearing breakdown, visualized with fluorescent dye, was reconstructed from the cuts. The results revealed that the shape of the bubble nearly equals the streamsurface of the stagnation point. According to the conditions in the water tunnel a single tilted vortex ring at the open rear part of the bubble dominates the interior flow structure of the bubble as first noted by Sarpkaya (1971). The vortical flow is bulged over the bubble, restored and intensified at the lower end. The gathered data lead to the conclusion that the vortex axis remains parallel to the centerline.     

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.     

Effects of magnetic field and variable viscosity on forced non‐darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing

This paper presents a study of the effect of a magnetic field and variable viscosity on steady twodimensional laminar nonDarcy forced convection flow over a flat plate with variable wall temperature in a porous medium in the presence of blowing (suction). The fluid viscosity is assumed to vary as an inverse linear function of temperature. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using the finite difference method. The effects of variable viscosity, magnetic and suction (or injection) parameters on the velocity and temperature profiles as well as on the skinfriction and heattransfer coefficients were studied. It is shown that the magnetic field increases the wall skin friction while the heattransfer rate decreases.     

Correlations between porous medium flow data and turbulent tube flow results for aqueous hydroxypropylguar solutions (Part 2)

Turbulent tube flow and the flow through a porous medium of aqueous hydroxypropylguar (HPG) solutions in concentrations from 100 wppm to 5000 wppm is investigated. Taking the rheological flow curves into account reveals that the effectiveness in turbulent tube flow and the efficiency for the flow through a porous medium both start at the same onset wall shear stress of 1.3 Pa. The similarity of the curves = ( _w ) and = ( _w ), respectively, leads to a simple linear relation / =k, where the constantk or proportionality depends uponc. This offers the possibility to deduce (for turbulent tube flow) from (for flow through a porous medium). In conjunction with rheological data, will reveal whether, and if yes to what extent, drag reduction will take place (even at high concentrations).The relation of our treatment to the model-based Deborah number concept is shown and a scale-up formula for the onset in turbulent tube flow is deduced as well.     

Transverse Decay of Solutions in an Elastic Cylinder

In a semiinfinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strainenergy flux through a plane crossection decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strainenergy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes.This problem is considered in the present paper which discusses a circular semiinfinite cylinder and derives an estimate for the strainenergy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strainenergy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.Sommario. E'noto che in un cilindro semiinfinito composto da materiale elastico lineare anisotropo, caricato sulla base ed incastrato lungo la superficie laterale, la soluzione elastica, misurata, per esempio, dal flusso di energia di deformazione attraverso una sezione trasversale piana, decade con legge al più esponenziale con la distanza dalla base. C'è tuttavia, anche un decadimento radiale della soluzione, misurato, per esempio, dall'energia di deformazione che passa dalla regione vicina all'asse del cilindro a quella vicin alla superficie laterale dove l'energia si annullaQuesto problema è qui studiato. Si discute in particolare un cilindro circolare semiinfinito e si deduce una stima per l'energia di deformazione contenuta in un anello cilindrico ad una distanza assegnata dalla base e di altezza variabile, e la cui superficie esterna coincide con la superficie laterale del cilindro. Si dimostra che l'energia di deformazione decade al più con legge algebrica a zero quando il raggio interno del cilindro si avvicina a quello esterno.     

Flow in vicinity of blunt body stagnation point in diverging hypersonic stream

In the hypersonic thin shock layer approximation for a small ratio k of the densities before and after the normal shock wave the solution of [1] for the vicinity of the stagnation point of a smooth blunt body is extended to the case of nonuniform outer flow. It is shown that the effect of this nonuniformity can be taken into account with the aid of the effective shock wave radius of curvature R_*, whose introduction makes it possible to reduce to universal relations the data for different nonuniform outer flows with practically the same similarity criterion k. The results of the study are compared with numerical calculations of highly underexpanded jet flow past a sphere.Notations x, y a curvilinear coordinate system with axes directed respectively along and normal to the body surface with origin at the forward stagnation point - R radius of curvature of the meridional plane of the body surface - uV, vV., , p V ² respectively the velocity projections on the x, y axes, density, and pressure - and V freestream density and velocity The indices =0 and=1 apply to plane and axisymmetric flows Izv. AN SSSR, Mekhanika Zhidkosti i Gaza, Vol. 5, No. 3, pp. 102–105, 1970.     

Investigation of the flow past wings of infinite span with a blunt leading edge in the vorticity interaction regime

An asymptotic analysis of the Navier-Stokes equations is carried out for the case of hypersonic flow past wings of infinite span with a blunt leading edge when 0, Re , and M . Analytic solutions are obtained for an inviscid shock layer and inviscid boundary layer. The results of a numerical solution of the problems of vorticity interaction at the blunt edge and on the lateral surface of the wing are presented. These solutions are compared with the solution of the equations of a thin viscous shock layer and on the basis of this comparison the boundaries of the asymptotic regions are estimated.deceasedTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–127, November–December, 1987.     

Application of the method of integral diffusion to investigation of turbulent transfer

A number of authors have critically examined semiempirical mixing length theories [1]. A defect of these theories is connected with the fact that the magnitude of the mixing length, which is assumed to be small in constructing the theory, turns out in experiments to be comparable with the characteristic dimensions of the flow region. Thus, the concept of volume convection [2–4] or integral diffusion [5], which is understood to be a transfer mechanism in which the friction stress is not expressed in terms of the velocity gradient, is introduced along with the concept of gradient diffusion. In addition, there are a number of experimental papers [6] in which it is shown that the turbulent friction stress cannot be equal to zero at the place in the flow where the derivative of the velocity is equal to zero. Mixing length theory does not describe this effect.It is possible to generalize mixing length theory [7–9] in a way which eliminates these defects. Flow of an incompressible fluid is considered.     

Effect of the Nature of the Interaction between a Gas and a Surface on the Relations for the Knudsen Layer in the Case of Strong Evaporation

The effect of the temperature accommodation coefficient _T on the relations at the Knudsen layer edge is investigated for strong evaporation using the moment method. An explicit expression for the dimensionless density as a function of the temperature and the Mach number M is obtained for 0 < _T < 1. For _T = 0 the entire solution is obtained in explicit form. It is shown that for = 0 and a condensation coefficient << 1 the temperature outside the Knudsen layer changes sharply as M varies from 0 to a certain value much less than unity after which the temperature ceases to depend on . For the model of specular reflection of the molecules from the surface the density and the temperature outside the Knudsen layer are found in explicit form as functions of the Mach number.     

Electrode layers in flows of an inviscid plasma with good conductivity

The structure of the electromagnetic electrode layers that are produced in flows across a magnetic field by a completely ionized and inviscid plasma with good conductivity and a high magnetic Reynolds number is examined in a linear approximation. Flow past a corrugated wall and flow in a plane channel of slowly varying cross section with segmented electrodes are taken as specific examples. The possibility is demonstrated of the formation of nondissipative electrode layers with thicknesses on the order of the Debye distance or electron Larmor radius and of dissipative layers with thicknesses on the order of the skin thickness, as calculated from the diffusion rate in a magnetic field [2].In plasma flow in a transverse magnetic field, near the walls, along with the gasdynamie boundary layers, which owe their formation to viscosity, thermal conductivity, etc. (because of the presence of electromagnetic fields, their structures may vary considerably from that of ordinary gasdynamic layers), proper electromagnetic boundary layers may also be produced. An example of such layers is the Debye layer in which the quasi-neutrality of the plasma is upset. No less important, in a number of cases, is the quasi-neutral electromagnetic boundary layer, in which there is an abrupt change in the frozen-in parameter k=B/p (B is the magnetic field and p is the density of the medium). This layer plays a special role when we must explicitly allow for the Hall effect and the related formation of a longitudinal electric field (in the direction of the veloeiryv of the medium). We will call this the magnetic layer. The magnetic boundary layer can be dissipative as well as noudissipative (see below). The dissipative magnetic layer has been examined in a number of papers: for an incompressible medium with a given motion law in [1], for a compressible medium with good conductivity in [2], and with poor conductivity in [3]. In the present paper, particular attention will be devoted to nondissipative magnetic boundary layers.     

Transport in ordered and disordered porous media II: Generalized volume averaging

In this paper we develop the averaged form of the Stokes equations in terms of weighting functions. The analysis clearly indicates at what point one must choose a media-specific weighting function in order to achieve spatially smoothed transport equations. The form of the weighting function that produces the cellular average is derived, and some important geometrical theorems are presented.Roman Letters A interfacial area of the- interface associated with the local closure problem, m² - A _e area of entrances and exits for the-phase contained within the averaging system, m² - A _p surface area of a particle, m² - d _p 6V _p/A_p, effective particle diameter, m - g gravity vector, m/s² - I unit tensor - K _m permeability tensor for the weighted average form of Darcy's law, m² - L general characteristic length for volume averaged quantities, m - L _p general characteristic length for volume averaged pressure, m - L characteristic length for the porosity, m - L _v characteristic length for the volume averaged velocity, m - l characteristic length (pore scale) for the-phase - l _i i=1, 2, 3 lattice vectors, m - (y) weighting function - m(–y) (y), convolution product weighting function - _v special weighting function associated with the traditional averaging volume - m _v special convolution product weighting function associated with the traditional averaging volume - m _g general convolution product weighting function - m _V unit cell convolution product weighting function - m _C special convolution product weighting function for ordered media which produces the cellular average - m _D special convolution product weighting function for disordered media - m _M master convolution product weighting function for ordered and disordered media - n unit normal vector pointing from the-phase toward the-phase - p pressure in the-phase, N/m² - p_m superficial weighted average pressure, N/m² - p _m intrinsic weighted average pressure, N/m² - p traditional intrinsic volume averaged pressure, N/m² - p p p _m , spatial deviation pressure, N/m² - r ₀ radius of a spherical averaging volume, m - r _m support of the convolution product weighting function, m - r position vector, m - r position vector locating points in the-phase, m - V averaging volume, m³ - V volume of the-phase contained in the averaging volume, m³ - V _cell volume of a unit cell, m³ - V velocity vector in the-phase, m/s - vm superficial weighted average velocity, m/s - v _m intrinsic weighted average velocity, m/s - V volume of the-phase contained in the averaging volume, m³ - V _p volume of a particle, m³ - v traditional superficial volume averaged velocity, m/s - v v p _m spatial deviation velocity, m/s - x position vector locating the centroid of the averaging volume or the convolution product weighting function, m - y position vector relative to the centroid, m - y position vector locating points in the-phase relative to the centroid, m Greek Letters indicator function for the-phase - Dirac distribution associated with the- interface - V /V, volume average porosity - _m m * . weighted average porosity - mass density of the-phase, kg/m³ - viscosity of the-phase, Ns/m² - V /V, volume fraction of the-phase     

Generation of vortices in a partially filled,rapidly rotating cylinder

We describe a system in which vortices are shed from a cylindrical free surface approximately centered in a rotating flow. Shedding is controlled by the parameter =2 g/ ² d, where g, , d denote gravity, rotation rate and the diameter of the free surface. We find vortex shedding for >0.162 and no vortex shedding for < 0.0847. The range depends on the aspect ratio L/d, where L is the column length, in a nonmonotonic fashion. These results are independent of viscosity and surface tension for small values of these parameters.Now at Martin Marietta, Orlando Aerospace, PO Box 5837, Mail Point 150, Orlando, FL 32855, USA     

On surface waves in generalized thermoelasticity

Knowles' representation theorem for harmonically time-dependent free surface waves on a homogeneous, isotropic elastic half-space is extended to include harmonically time-dependent free processes for thermoelastic surface waves in generalized thermoelasticity of Lord and Shulman and of Green and Lindsay.r , , r , , .This work was done when author was unemployed.     

A non-dualistic unified field theory of gravitation,electromagnetism and spin

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrödinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-M) theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrödinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric formds ²=g dx ^v x ^v and the non-degenerate two-formF=(1/2> _l) dx ^vdx ^vto enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an external gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.