The stability of a finitely inflated cylindrical elastic membrane under axial compression

The stability under overall axial compression of a finitely inflated cylindrical membrane composed of highly elastic material is investigated. The critical loads for inflated tubes with closed ends and with either simply-supported or fixed ends are determined in terms of the material properties of the membrane. For long tubes the results are compared with the Euler formulae for the buckling load for struts in compression. An equivalent Young's modulus is derived, and it is shown that the critical loads can be obtained from the Euler formulae by using the dimensions of the inflated state and the equivalent Young's modulus.     

Flow Asymptotics of a Viscous Compressible Fluid with Discontinuous Initial Data

Asymptotics of a continuous solution to a plane problem on the motion of a viscous incompressible fluid with discontinuous initial velocity and pressure fields is studied by the boundarylayer method with simultaneous stretching of space and time coordinates.     

Thermal Growth of a Vapor Bubble Moving in a Superheated Liquid

The problem of thermal growth of a vapor bubble moving in a superheated liquid is solved for two models of the phase interface, namely: a rigid (no-slip condition) and a pliable (slip condition) spherical surface. The second self-similar solution of the problem of the motion of a vapor bubble with a pliable surface is found. On the basis of this solution, an approximate dependence of the nondimensional heat flux into the bubble on the Jacob and Péclet numbers is constructed. For two limiting cases, namely, for a bubble growing at rest and a moving bubble of constant radius, this dependence coincides with the known solutions. The calculation results are compared with the experimental data obtained for vapor bubbles rising in a superheated liquid.     

Computations of Interaction of an Incident Oblique Shock Wave with a Turbulent Boundary Layer on a Flat Plate

Results of numerical simulation of interaction between an oblique shock wave and a turbulent boundary layer formed in a supersonic (Mach number M =5) flow past a flat plate are presented. The computations are performed for three cases of interaction of different intensity, which result in an attached or detached flow. Numerical results are compared with experimental data. The effect of flow turbulence and shockwave unsteadiness on flow parameters is studied.     

Turbulent boundary layer over a smooth wall with widely separated transverse square cavities

Laser-Doppler velocimetry (LDV) measurements and flow visualizations are used to study a turbulent boundary layer over a smooth wall with transverse square cavities at two values of the momentum thickness Reynolds number (R =400 and 1300). The cavities are spaced 20 element widths apart in the streamwise direction. Flow visualizations reveal a significant communication between the cavities and the overlying shear layer, with frequent inflows and ejections of fluid to and from cavities. There is evidence to suggest that quasi-streamwise near-wall vortices are responsible for the ejections of fluid out of the cavities. The wall shear stress, which is measured accurately, increases sharply immediately downstream of the cavity. This increase is followed by a sudden decrease and a slower return to the smooth wall value. Integration of the wall shear stress in the streamwise direction indicates that there is an increase in drag of 3.4% at bothR .Nomenclature C _f skin friction coefficient - C _fsw friction coefficient for a continuous smooth wall - k height of the cavity - k ⁺ ku / - R Reynolds number based on momentum thickness (U ₁ /v) - Rx Reynolds number based on streamwise distance (U ₁ x/) - s streamwise distance between two cavities - t time - t ⁺ tu ₂ / - U ₁ freestream velocity - mean velocity inx direction - u,v,w rms turbulent intensities inx,y andz directions - u local friction velocity - u _sw friction velocity for a continuous smooth wall - w width of the cavity - x streamwise co-ordinate measured from the downstream edge of the cavity - y co-ordinate normal to the wall - z spanwise co-ordinate - y ⁺ yu / - boundary layer thickness - ₀ boundary layer thickness near the upstream edge of the cavity - _i thickness of internal layer - kinematic viscosity of water - ⁺ zu / - momentum thickness     

Effect of a Short Roughness Strip on a Turbulent Boundary Layer

The response of a turbulent boundary layer to a short roughness strip is investigated using laser Doppler velocimetry (LDV) and laser induced fluorescence (LIF). Skin friction coefficients are inferred from accurate near-wall measurements. There is an undershoot in , where is the undisturbed smooth wall skin friction coefficient, immediately after the strip. Downstream of the strip, overshoots before relaxing back to unity in an oscillatory manner. The roughness strip has a major effect on the turbulent stresses ; these quantities increase, relative to the undisturbed smooth wall, in the region between the two internal layers originating at the upstream and downstream edges of the strip. The increase in the ratio suggests a decrease in near-wall anisotropy. From the flow visualizations, it is inferred that streamwise vortical structures are weakened immediately downstream of the strip. Consistently, streamwise length scales are also reduced; direct support for this is provided by measured two-point velocity correlations.     

On near-wall turbulence-generating events in a turbulent boundary layer on a riblet surface

The boundary layer over a drag reducing riblet surface is investigated using hot-wire anemometry and flow visualisation. The concept of a riblet sublayer is introduced, and a definition is proposed in terms of a region of reduced turbulence energy production formed near the wall by the addition of riblets. The hot wire records are examined using a modified form of quadrant analysis, and results obtained over plain and riblet surfaces are compared. Close to the wall, the addition of riblets produces a marked reduction in the occurrence of ejection (2nd quadrant) events. A corresponding increase in the incidence of sweep (4th quadrant) events is accompanied by the development of a strong tendency toward a preferred event duration, and a preferred interval between events. These changes diminish rapidly with distance from the surface, becoming almost undetectable beyondy ⁺=40. They are discussed in the light of flow visualisation results, and interpreted in terms of mechanisms associated with the interaction between the riblets and the inner boundary layer flow structures. A conceptual model of the flow mechanisms in the riblet sublayer is proposed.     

Effect of Boundary-Layer Thickness on the Structure of a Near-Wall Flow with a Two-Dimensional Obstacle

Results of physical and numerical experiments on investigating the effect of the depth of immersion of a two-dimensional obstacle with a square cross section into a developed turbulent boundary layer on the length of the separated flow region are presented. The numerical simulation is based on solving averaged Navier–Stokes equations with the use of the k– model of turbulence. The near-wall flow is visualized in the experiments, and the fields of mean and fluctuating velocities are measured. Flow regions where the results of numerical simulation agree with experimental data are determined. It is shown that the length of the recirculation flow region in the near wake increases with decreasing depth of immersion of the two-dimensional obstacle into the turbulent boundary layer.     

On the vanishing of the additive measures of strain and rotation for finite deformations

Explicit formulae for the finite strain and rotation measures are given, in the cases when either one of the infinitesimal tensors of strain and rotation vanishes. Conversely, when the finite strain or rotation measure vanishes, explicit formulae for the infinitesimal tensors of strain and rotation are also obtained.     

Natural convection from a horizontal permeable surface in a porous medium - numerical and asymptotic solutions

The equations which govern the similarity solution for free convection boundary-layer flow above a permeable, horizontal surface in a fluid-saturated porous medium are considered. These are seen to depend on the dimensionless parameters and m measuring mass transport rate and the wall temperature variation, respectively. Numerical solutions are presented for a wide range of values of and m. Asymptotic solutions are obtained for ¦¦ large (for both fluid injection, > 0, and fluid withdrawal, < 0) and for m large. These are compared with the numerical solutions.     

Analytic Solution to a Problem of Seepage in a Chequer-Board Porous Massif

A study is made of steady two-dimensional seepage in a porous massif composed by a double-periodic system of white and black chequers of arbitrary conductivity. Rigorous matching of Darcy's flows in zones of different conductivity is accomplished. Using the methods of complex analysis, explicit formulae for specific discharge are derived. Stream lines, travel times, and effective conductivity are evaluated. Deflection of marked particles from the natural direction of imposed gradient and stretching of prescribed composition of these particles enables the elucidation of the phenomena of transversal and longitudinal dispersion. A model of pure advection is related with the classical one-dimensional vective dispersion equation by selection of dispersivity which minimizes the difference between the breakthrough curves calculated from the two models.     

Spin-up in a saturated porous medium

It is shown that, on the Brinkman model, spin-up is confined to boundary layers whose thickness is of order k ^1/2, and the spin-up is established in a time of order k/, where k, , and denote permeability, density, porosity and dynamic viscosity, respectively.     

Transmission in a rectangular waveguide loaded with an arbitrary number of capacitive screens

Summary Green's theorem is applied to individual domains consisting of the walls of a rectangular waveguide and two neighbouring slotted capacitive screens. In addition this theorem is applied to the two end domains, that is, the one containing the incident field and the other containing the transmitted field only. Using the continuity of the electromagnetic field intensities in the slits, a system of simultaneous integral equations is obtained in terms of field intensity functions within the slits. By a change of variables a system of ² linear algebraic equations is derived, and formulae for the principal mode transmission and reflection coefficients are given to any approximation desired. Conditions for a full transmission are derived, especially to a first order approximation. Some applications with regard to the filter properties of the waveguide system are discussed and the theory developed is compared with measurements.     

Stability and Transition on a Swept Cylinder in a Supersonic Flow

Results of experimental investigations of the evolution of natural disturbances and laminar–turbulent transition in a supersonic boundary layer on the attachment line of a circular cylinder with a sweep angle of 68° and a freestream Mach number M = 2 are presented. The experimental studies are supplemented by calculations of the mean flow and stability characteristics. Flow regimes in the boundary layer on the attachment line are determined by a hotwire technique as functions of the Reynolds number and height of twodimensional roughness elements. The results are compared with NASA (Ames) experiments.     

Free Convection from a Vertical Plate in a Porous Medium Subjected to a Porous Medium Subjected to a Sudden Change in Surface Heat Flux

An analysis is made of the transient free convection from a vertical flat plate which is embedded in a fluid-saturated porous medium. It is assumed that for time a steady state temperature or velocity has been obtained in the boundary-layer which occurs due to a uniform flux dissipation rate . Then at time the heat flux on the plate is suddenly changed to and maintained at this value for 0$$ " align="middle" border="0"> . An analytical solution has been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjacent to the plate. These effects cause a new steady boundary layer. A numerical solution of the full boundary-layer equations is then obtained for the whole transient from to the steady state, firstly by means of a step-by-step method and then by a matching technique. The transition between the two distinct solution methods is always observed to occur very near to the turning point of the plate surface temperature, a time at which the fluid temperature is close to its steady state profile. The solution obtained using the step-by-step method shows excellent agreement with the small time analytical solution. Results are presented to illustrate the occurrence of transients from both small and large increases and decreases in the levels of existing energy inputs.     

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.     

Buoyancy- and pressure-driven motion in a vertical porous layer: Effects of quadratic drag

The seepage velocity arising from pressure and buoyancy driving forces in a slender vertical layer of fluid-saturated porous media is considered. Quadratic drag (Forcheimer effects) and Brinkman viscous forces are included in the analysis. Parameters are identified which characterize the influence of matrix permeability, quadratic drag and buoyancy. An explicit solution is obtained for pressure-driven flow which illustrates the influence of quadratic drag and the strong boundary layer behavior expected for low permeability media. The experimental data of Givler and Altobelli [2] for water seepage through a high porosity foam is found to yield good agreement with the present analysis. For the case of buoyancy-driven flow, a uniformly valid approximate solution is found for low permeability media. Comparison with the pressure-driven case shows strong similarities in the near-wall region.Nomenclature B function of - d layer thickness - D discriminant defined by Equation (9) - modified Darcy number - F Forcheimer constant - g gravitational acceleration - k porous matrix permeability - m parameter defined by Equation (11) - p pressure - p modified pressure - pressure gradient - R buoyancy parameter - T ₀ nominal layer temperature - u seepage velocity - dimensionless seepage velocity - _c composite approximation - _i boundary layer velocity - _o outer or core flow approximation - _m midplane velocity - U matching velocity - V cross-sectional average velocity - w variable defined by Equation (12) - x, z Cartesian coordinates - , dimensionless Cartesian coordinates - inertia parameter - T layer temperature difference - larger root of cubic given by Equation (8) - fluid dynamic viscosity - _e effective viscosity of fluid saturated medium - variable defined by Equation (18) - 0 fluid density - smaller root of cubic given by Equation (8) - variable defined by Equation (18) - stretched inner coordinate - porosity - function of      

Pressure development in a non-Newtonian flow through a tapered tube

Summary The flow of viscous fluids through a tapered tube is very interesting from the standpoint of blood flow in blood vessels. The taper of the tube is an important factor in the pressure development. In the first place, we have given a brief summary of our theory of the steady convergent flow of non-Newtonian fluids characterized by an arbitrary time-independent flow curve through a slightly tapered tube. Based on our general formula for the flow per unit time, explicit formulae of the pressure gradient are obtained in several cases of non-Newtonian fluids specified by particular flow curves: power law fluid,Bingham body, and the fluid obeyingCassons equation. In all these cases it is shown that the pressure gradient is not constant along the axis but increases with decrease in the radius of the tapered tube. If we neglect quantities of order ² (: angle of taper), then the pressure gradient increases linearly with the distance along the axis of the tube.With 2 figures