Micropolar fluid jet impingement on a curved surface

This paper deals with an analysis of a normally impinging micropolar fluid jet on a curved surface. The flow near the stagnation point in the impingement region is divided into inviscid and viscous flow regions. The inviscid flow solution is governed by Euler's equations of motion expressed in curvilinear coordinate system. The viscous flow solution is governed by the zeroth and the first order boundary layer equations. These boundary layer equations are solved by assuming power series expansions for both velocity and microrotation fields which give rise to two systems of ordinary coupled differential equations. The effects of surface curvature and material parameters on boundary layer characteristics have been studied and presented graphically. The gradients of zeroth order velocity and microrotation at the wall decrease and the zeroth order displacement and momentum thicknesses increase with decrease in the value of surface curvature. The reduction in curvature results in the reduction in the gradients of first order velocity and microrotation at the wall as well as first order displacement and momentum thicknesses.     

Propagation of a jet along a porous wall

A numerical solution of the problem of self-similar development of a jet of viscous incompressible fluid moving along a porous wall is obtained within the framework of laminar boundary layer theory.     

Non-linear waves along a rotating non-Newtonian liquid jet

A liquid jet may be curved due to the influence of wind or gravity but more commonly, as is the case in industrial prilling, due to the rotation of the container from which it emerges. In prilling, pellets are manufactured by utilising the breakup of a curved liquid jet, and liquids commonly used in prilling are non-Newtonian. In this paper we investigate the influence of rotation, surface tension and viscosity on the breakup of a spiralling slender power-law liquid jet with applications to industrial prilling. The non-linear evolution equations for the jet radius and axial velocity are solved numerically using the method of finite differences. Numerical simulations allow us to explore the effects of changing the amplitude (or alternatively the frequency) of initial disturbances on breakup lengths and the size of main and satellite droplets.     

Surface-tension-driven flow on a moving curved surface

The leading-order equations governing the flow of a thin viscous film over a moving curved substrate are derived using lubrication theory. Three possible distinguished limits are identified. In the first, the substrate is nearly flat and its curvature enters the lubrication equation for the film thickness as a body force. In the second, the substrate curvature is constant but an order of magnitude larger; this introduces an extra destabilising term to the equation. In the final regime, the radius of curvature of the substrate is comparable to the lengthscale of the film. The leading-order evolution equation for the thin film is then hyperbolic, and hence can be solved using the method of characteristics. The solution can develop finite-time singularities, which are regularised by surface tension over a short lengthscale. General inner solutions are found for the neighbourhoods of such singularities and matched with the solution of the outer hyperbolic problem. The theory is applied to two special cases: flow over a torus, which is the prototype for flow over a general curved tube, and flow on the inside of a flexible axisymmetric tube, a regime of interest in modelling pulmonary airways.     

Laminar weakly swirled jet propagating along a straight circular cone

The propagation of a laminar, nonisothermal, weakly swirled liquid jet along the nonconducting surface of a straight circular cone is examined. An explanation is given of the influence of the temperature dependence of the viscosity (assumed to be linear) on the hydrodynamic characteristics of the jet.     

Flow of a micropolar fluid over a curved stretching surface

The paper is devoted to the numerical solution of the problem of flow of a micropolar fluid over a curved stretching surface. A similarity transformation is applied to reduce a system of partial differential equations to a system of ordinary differential equations. The numerical solution of these coupled equations is carried out by the shooting method using the Runge–Kutta algorithm. The physical quantities of interest, like the fluid velocity, microrotation velocity, and pressure, are obtained and discussed as functions of the nondimensional curvature radius. It is evident from the results that the pressure inside the boundary layer cannot be neglected for a curved stretching sheet, as distinct from a flat stretching sheet.     

Experimental studies of a plane buoyant surface jet

Results are presented from an experimental study of the conditions of formation of a plane buoyant jet with different initial values of the density Froude number.     

Propagation of a turbulent fan jet along plane and concave surfaces

The flows associated with the propagation of a fan-shaped turbulent jet along plane and concave surfaces are theoretically and experimentally investigated.     

Tensor calculus of locally cartesian coordinates on a curved surface

A tensor calculus is developed for locally cartesian coordinates on a curved surface which is regarded as elementarily flat. In this tensor calculus the sequence of repeated differentiation of tensors is immaterial for all shapes of surface—unlike the situation for covariant differentiation.The paper concludes with a few notes pertaining to the application of locally cartesian coordinates in classical shell theory, vis-à-vis finite element analysis which uses flat elements.     

Reduction of the classical electromagnetism to a two-dimensional curved surface

The reduction of the three-dimensional classical electromagnetism to a two-dimensional curved surface is performed in a twofold way. In the first case, the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing along the surface. The electric field is a two-vector tangent to the surface and magnetic field is a scalar quantity. In the second approach, the reduced theory is that of the two-vector magnetic field and a scalar electric one. The only source coupled to the fields is now a scalar, subject to no conservation law. In the redefined theory, this scalar source may be converted into an eddy magnetic current flowing in the surface. No magnetic monopoles appear. Our results can find some applications in the electrodynamics of thin layers and of metal-dielectric interfaces.     

曲面片的可展切曲面及其映射分析

论文以微分几何可展曲面理论为基础,提出了过曲面曲线构造其可展切曲面的方法,得出了可展切曲面的表达形式,对可展切曲面进行了分类,通过建立两曲面间的映射关系,实现了它们间整体与局部的映射分析,较准确地把握曲面的变形情况,并通过实例对方法进行了验证.曲面片可展切曲面的方法可以应用于曲面设计、曲面近似展开和纹理映射等方面.     

Flow of a liquid film along a vertical surface

Results are shown of a study, by the photographic method, concerning the flow of a water film along a vertical glass plate by wave and by turbulent motion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 3, pp. 494–498, March 1972.     

Heat transfer for a planar air jet striking a concave surface

Results are presented from an experimental study of the local and mean heat transfer rates when a rectangular jet enters a relatively short concave body of parabolic profile.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 5, pp. 785–790, November, 1969.     

A turbulent jet in a concurrent stream at a permeable surface

The average and pulsation velocity profiles are measured in a rectangular channel during combined pore-slot blowing. Universal functions are proposed which generalize the experimental data obtained in different cross sections and in a wide range of intensities of pore blowing.

     

The flip-through of a plane inviscid jet with a free surface

The growth of a two-dimensional liquid jet is modelled, in which an inviscid incompressible fluid is in irrotational flow. On the moving free surface, the pressure is constant. The flow is symmetric with respect to the y-axis. The free-surface fluid particle that lies on the y-axis is Q and it has position y = Y(t). A velocity potential is presented that describes the local features of the flow near the centreline, and which contains essentially two unknowns: the velocity V(t) = d Y/d t of Q, and a length L(t). Near Q the free surface is a time-dependent parabola, whose curvature is directly proportional to a third unknown, F(t). The kinematic and dynamic free-surface boundary conditions constrain V, L and F to satisfy three ordinary differential equations. The solutions are a one-parameter family that separate into five types. For one type the free-surface curvature changes sign during the motion, so that the free surface changes from concave to convex—it executes flip-through. Soon after flip-through, there is a local maximum in the pressure, with respect to time and space. A short time later there is a maximum in the acceleration of Q. As t tends to infinity, V tends to a constant, V _∞. An estimate is made of the time scale for flip-through, based on pressure changes, and it is found to decrease as V _∞ increases. When V _∞ is chosen very large, the values of the large maxima in pressure and acceleration become sensitive to small changes in the initial conditions. The results focus on the highly transient pressure field. The findings may help to describe the flip-through of a steep fronted water wave meeting a plane impermeable wall.     

Heat-transfer characteristics of a jet flame impinging on a heat-sensing surface

Experimental data and analytical relations are given for the heat transfer from direct-jet and swirl-jet flames impinging on a heat-sensing surface.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 12–15, January, 1981.     

High-voltage pulse discharge propagating along a water surface

The results are presented of experimental studies of electrical discharge occurring in the atmosphere along a free water surface between a spike above the water surface and a remote submerged electrode during quasi-rectangular high voltage pulses. Three stages of such discharge are identified, and the stage of the discharge gliding along the water surface is investigated.     

Three-dimensional image construction by curved surface scratches

Scratches on the surface of transparent or nontransparent media reflect, refract, or diffract incident light. Under parallel illumination each length element of a scratch produces a fan beam (in the absence of diffuse scattering). Looking at a curved scratch, the right and left eyes are hit by different fan beams. Thus each eye sees a separate light spot on the scratch, which is the origin of the fan beam. In certain circumstances these spots can be stereoscopically combined by both eyes and only one light spot in space is seen. Three-dimensional images can be created by a large number of such spots originating from circular or semicircular scratches. These scratches can easily be produced on the surface of Plexiglas or other materials by using a compass. Some experiments and the theory of the so-called scratchograms are given. A comparison with holographic images is made.