Investigation of secondary flow on an infinite yawed cylinder with 15 per cent. Thick Joukowski profile as section

This paper contains a theoretical investigation of the secondary flow in the laminar incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. The secondary flow profiles are obtained at different points of the wing section and for various angles of sweepback. It is found that in favourable pressure gradients and at pressure minimum, the secondary flow profiles have negative values. In regions of adverse pressure gradients after the pressure minimum the secondary flow changes sign from negative to positive values and have points of inflexion. The change of sign starts from the surface and extends to the edge of the boundary layer downstream. At some points in adverse pressure gradients the secondary flow profiles have double points of inflexion and values of both signs simultaneously. It is also found that an adverse pressure gradient produces more powerful secondary flow than a favourable pressure gradient of the same strength.     

Investigation of secondary flow on an infinite yawed cylinder in a compressible stream

In this paper a study of the secondary flow on an infinite yawed cylinder in a compressible stream is made at stagnation for unit Prandtl number and for a given Mach number. The secondary flow profiles are calculated for different edge inclination angles. The chordwise and spanwise velocity profiles given by Crabtree¹ are used here in the calculation. It is found that the secondary flow profiles are the same for complementary edge inclination angles and they are maximum for the edge inclination angle of 45°. A comparison with the incompressible flow profiles² is made. It is found that the magnitude of the secondary flow profiles in a compressible stream is less than that in an incompressible stream for the same edge inclination angle.     

An approximate method for the calculation of the incompressible laminar spanwise boundary layer on an infinite uniform yawed cylinder with distributed suction

This paper describes an approximate method to calculate the incompressible laminar spanwise boundary layer on an infinite yawed uniform cylinder with distributed suction. The calculation for the chordwise layer is supposed to be known. A similar method to calculate the laminar spanwise layer for a solid boundary is given by Rott and Crabtree, but for a porous boundary with suction no such method is known to the author at present except the one given in this paper. The present method is equally applicable to a solid boundary also. A comparison of the calculation by the present approximate method is made with the exact solutions of the spanwise layer with the chordwise velocity distribution U = Cx ^mat the edge of the layer, and the agreement is found to be quite satisfactory. Moreover, the method is very simple in operation.     

The Fredholm index of a second order elliptic system on an infinite cylinder

This paper investigates the Fredholmness of a second order elliptic system on an infinite cylinder in various weighted or non-weighted Sobolev spaces, assuming homogeneous Dirichlet boundary conditions and suitable asymptotic behavior of the coefficients. It is shown that the index coincides with the spectral flow of an associated parametrized family of elliptic systems on the cross-section of the cylinder. Dependence or independence of the index upon the functional setting is discussed along with their impact on spectral invariance and elliptic regularity.      

A note on Hydromagnetic oscillatory flow along an infinite flat plate with variable suction

The two-dimensional, incompressible flow past an infinite plate of a weakly conducting fluid in the presence of a transverse magnetic field is discussed when the suction velocity normal to the plate as well as the external flow velocity vary periodically with time. Expressions for the velocity and the skin-friction in the boundary layer have been obtained in a non-dimensional form.     

Investigation of one-dimensional problem of resource distribution on an infinite time interval

Two controlled nonlinear dynamic models of resource distribution are considered in the case of an infinite horizon. Both of the models are studied on the basis of a known theoretical result that can only be applied without any constraints to the first problem. For both of the models, optimal solutions are found and their optimality is proved.     

Note on unsteady viscous flow on the outside of an expanding or contracting cylinder

In this paper, the viscous flow on the outside of an expanding or contracting cylinder is studied. The governing Navier-Stokes equations are transformed into a similarity equation, which is solved by a shooting method. The solution is an exact solution to the unsteady Navier-Stokes equations. Results show both trivial and non-trivial solutions. For trivial solutions, there is no axial flow induced during the cylinder expansion or contraction. However, for the non-trivial solutions which only exist for cylinder expansion, an axial flow is generated and its strength increases with the increase in expansion speed.     

Free convection effects on the oscillatory flow of an incompressible viscous fluid past an infinite,vertical plate with variable suction

An analysis of a two-dimensional flow of an incompressible, viscous fluid past an infinite, vertical porous plate has been carried out under the following conditions: (i) the suction velocity normal to the plate varies periodically with time (ii) the free stream velocity oscillates in time about a constant mean (iii) the temperature difference between the constant plate temperature and the free stream temperature, causing the free convection currents in the boundary layer. Approximate solutions for the transient velocity, the transient temperature, the amplitude and the phase of the skin-friction and the rate of heat transfer are derived. The fluctuating parts of the velocity profiles, the transient velocity, the transient temperature are shown on graphs whereas the numerical values of the amplitude and the phase of the skin-friction and the rate of heat transfer are entered in tables. The results are discussed in a quantitative way.     

Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.     

Approximate torsion calculations for anisotropic members with a cross section in the form of an elongated profile

An approximate method is proposed for solving the problem of the free torsion of a prismatic anisotropic member with a narrow cross section. The material is assumed to be homogeneous with a special form of anisotropy (nonorthotropic). An arbitrary elongated section and special cases are considered. Experimental data are presented for DSP-B wood-resin laminate and the limits of applicability of the method are established.Mekhanika Polimerov, Vol. 3, No. 2, pp. 312–317, 1967     

Algebraic surfaces with an infinite set of planes of oblique symmetry. I

Translated from Ukrainskii Geometricheskii Sbornik, No. 32, pp. 47–60, 1989.     

The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure

In this paper we investigate the effect of structural flexibility on rocking motion of a system consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Motion is excited by random acceleration of the ground; instability is associated with overturning of the overall structure. The condition of instability is constructed by the stochastic Melnikov method. We demonstrate a twofold effect of structural flexibility on the rocking response. The attached structure may increase the critical angular displacement and velocity in comparison with the similar parameters of the single rigid block. At the same time, the enlargement of the domain of stability enhances the contribution of the random perturbation in the Melnikov process. As a result, a lower level of random forcing can result in overturning of the structure. As an example, an effect of a single-mass secondary structure on the dynamic behavior of the system is discussed. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitation.     

Note on a theorem of J. Folkman on transversals of infinite families with finitely many infinite members

In this note we show by a simple direct proof that Folkman's necessary and sufficient condition for an infinite family of sets with finitely many infinite members to have a transversal implies Woodall's condition. A short proof of Folkman's theorem results by combining with Woodall's proof.     

Stagnation flow on a cylinder with partial slip--an exact solution of the Navier-Stokes equations

The stagnation slip flow on an axially moving cylinder is studied.The Navier–Stokes and energy equations reduce to nonlinearordinary differential equations under a similarity transform.For large slip, the flow field decays exponentially into potentialflow. The heat transfer can be expressed as an incomplete gammafunction. In general, the heat transfer increases with slip,Prandtl number and Reynolds number.     

Effects of mass transfer on free convective flow of a dissipative,incompressible fluid past an infinite vertical porous plate with suction

An analysis of the mass transfer effects on the free convective flow of an incompressible, dissipative, viscous fluid past an infinite, vertical porous plate with constant suction, has been carried out. Approximate solutions to coupled non-linear equations governing the flow are derived. The velocity and the temperature profiles are shown graphically for air (P=0·71). The effects of Gr (Grashof number), Gc (the modified Grashof number), Sc (Schmidt number), E (Eckert number) are discussed qualitatively during the course of discussion. It is observed that due to the addition of the foreign mass, there is a rise in the velocity and a fall in the temperature. But the skin-friction increases when Sc?1 and it decreases when Sc ～1. The rate of heat transfer increases for Sc<1 and decreases for Sc>1.     

The effect of gravity on flow past a semi-circular cylinder with a constant pressure wake

The flow past a semi-cylinder with a trailing wake region is considered. In the absence of gravity the only known high Reynolds number solutions have tangential separation from the body and a cusped shape at the back of the wake. This flow can be a simple model for several situations, including the classical approximation of a constant pressure wake and the flow past an object with a region of trapped fluid of different density (or an air cavity) attached on the downstream side. Here we relax the assumption of high flow speeds to examine the effects of gravity. It is shown that there are situations in which a stagnation point can form either on the body or at the tail of the wake and that there is a minimum velocity beneath which a cavity will not form. Non-uniqueness in the parameter space is found in certain cases.     

Two-dimensional numerical simulation of a wave with a current past a circular cylinder. Part 1: Inline flow

This study considered a 2D numerical simulation with LES modeling of a sinusoidal oscillatory flow inline with an imposed uniform flow using primitive variables. The study is performed by a customized code particularly built for this simulation. This code allows an easy implementation to a customized combination of different boundary conditions and discretization schemes. The code is verified against well-recognized studies of a similar type to validate the calculated results. It is found that the drag and inertia coefficients of the wavy flow are reduced with the increased strength of the imposed uniform flow. A strong chaotic behavior was observed in the flow field structures. This behavior has a significant unpredictable influence on the resulting inline and transverse forces through the flow field pattern within the vicinity of the cylinder surface. This influence sometimes causes the exerted forces to increase when compared to the purely wavy flow. Based on this study, it is highly recommended not to uncouple wavy flows from uniform flows to simultaneously capture the combined interactions of such flow scenarios.     

On problem of the dynamics of a viscoelastic medium with memory on an infinite interval

The existence of a weak solution of a boundary value problem for a viscoelasticity model with memory on an infinite time interval is proved. The proof relies on an approximation of the original boundary value problem by regularized ones on finite time intervals and makes use of recent results concerning the solvability of Cauchy problems for systems of ordinary differential equations in the class of regular Lagrangian flows.