On the interaction of a vortex pair and a vortex ring with a flat shield

The approximate method of calculation of nonstationary flow in the interaction of a vortex pair and a vortex ring with a parallel and respectively perpendicular flat shield is presented. It is shown that these primary vortices induce transverse wall flow on the shield in the ideal-fluid approximation; in this flow, with allowance for the fluid’s viscosity, a boundary layer is generated which represents vortex flow with sign opposite to that of the primary vortices. Boundary-layer separations occur on the portion of the shield with a positive longitudinal pressure gradient. Secondary flows interact with the primary ones due to which the flow is rearranged; the transverse displacement of the initial vortex pair with a loop-shaped trajectory of its motion is observed in the plane problem, whereas the formation of ascending flow along the axis of the vortex ring is observed in the axisymmetric problem. The effect found in the latter case in laminar and turbulent regimes of flow is confirmed for the laminar regime by experiment and by the data of numerical simulation of Navier–Stokes and Reynolds equations.     

The flow of a viscous liquid down a variable incline

Summary The flow of a thin film of almost inviscid fluid down a slope of variable inclination is considered. The equations governing the flow are the boundary-layer equations, and a numerical solution of these equations is obtained. It is found that in cases where the liquid film attempts to flow against gravity the flow will separate. The numerical solution indicates a singularity at the separation point. The nature of this singularity is discussed.     

Separation from a smooth surface in a slender conical flow

Summary High Reynolds number flow of an incompressible fluid past a smooth surface in a slender conical flow is considered. Attention is focused upon the flow properties in the neighbourhood of the separation line. The analysis incorporates the results of a recent inviscid-flow investigation by Smith [1], and the ideas of Sychev [2] for flow separation in two dimensions.     

Spin-up and spin-down of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force

Summary The hydromagnetic spin-up and spin-down of an incompressible electrically conducting fluid on a heated infinite disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force have been studied. The flow is non-axisymmetric due to the imposition of the buoyancy force. We have considered the situation where there is an initial steady state which is perturbed by suddenly changing the angular velocity of the disk. By using suitable transformations the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (,t ^*). Also, these transformations uncouple the momentum and energy equations, resulting in a primary axisymmetric flow with an axial magnetic field, in an energy equation dependent on the primary flow and in a buoyancy induced secondary cross flow dependent on both primary flow and energy.The results indicate that the effect of the step-change in the angular velocity of the disk is more pronounced on the primary flow than on the secondary flow and the temperature field. For both spin-up and spin-down cases the surface shear stress in the non-axial direction normal to gravity for the primary flow and the surface shear stresses for the secondary flow increase with the magnetic parameter, whilst the surface shear stress in the vertical direction and the heat transfer at the surface decrease as the magnetic parameter increases. Also, the secondary flow near the disk dominates the primary flow. We have also developed an asymptotic analysis for large magnetic parameters which complements well the numerical results obtained in the lower magnetic parameter range.     

Structural characteristics of a gas–liquid flow in a microchannel with a T-shaped mixer

The results of experimental studies of the structural characteristics of a nitrogen–water mixture flow in a horizontal microchannel provided with a T-shaped mixer are presented. The experiments are performed in a channel with a rectangular cross section of 250 × 315 μm under the conditions of a dominating influence of capillary forces. Structural characteristics of the flow are determined using the two-beam laser scanning and high-speed video capture at a distance of 500 calibers from the inlet in a wide range of reduced gas- and liquid-flow rates. A new method for the identification of flow regimes is proposed based on the statistical treatment of the laser-scanning data, and a map of flow patterns is constructed.     

Liquid metal flow through a thin walled elbow in a plane perpendicular to a uniform magnetic field

This paper presents analytical solutions for the liquid-metal flow through two straight pipes connected by a smooth elbow with the same inside radius. The pipes and the elbow lie in a plane which is perpendicular to a uniform, applied magnetic field. The strength of the magnetic field is assumed to be sufficiently strong that inertial and viscous effects are negligible. This assumption is appropriate for the liquid-lithium flow in the blanket of a magnetic confinement fusion reactor, such as a tokamak. The pipes and the elbow have thin metal walls.The flow tends toward the inside surface of the elbow, approaching a vortex about the center of curvature of the elbow. This flow migration away from the uniform fully developed flow in the pipes leads to voltage variations along the pipes. These voltage variations drive four electric current circulations in planes perpendicular to the magnetic field. These current circulations produce significant pressure variations in the cross sections of the pipes and elbow. A long length of pipe is required on both sides of the elbow for the completion of the circuits for these electric current circulations and for the decay of the disturbances to the fully developed flow in the straight pipes. All pressure drops and rises due to the three-dimensional electric current circulations cancel. The total pressure drop is the same as that for fully developed flow in a single straight pipe with the same length. While the analysis treats pipes and elbows with circular cross sections, the absence of a pressure drop in addition to that for fully developed flow is true for any smooth elbow.     

Endwall boundary layer separation in a single-stage axial-flow low-speed compressor and a high-stagger compressor cascade

The paper describes an investigation of the overtip endwall flow in a single-stage axial-flow low-speed compressor (absolute flow) and in a corresponding compressor cascade (simulated relative flow) with a tip clearance on one side. The clearance to chord ratio is 3% in both cases. Oil flow pictures of the rotor casingwall and cascade endwall are used to visualize and analyse the boundary layers on the walls at various flow rates and corresponding inlet angles, respectively. The results enable the different sources of endwall blockage to be identified and changes with flow rate or inlet angle to be determined.     

Endwall boundary layer separation in a single-stage axial-flow low-speed compressor and a high-stagger compressor cascade

The paper describes an investigation of the overtip endwall flow in a single-stage axial-flow low-speed compressor (absolute flow) and in a corresponding compressor cascade (simulated relative flow) with a tip clearance on one side. The clearance to chord ratio is 3% in both cases. Oil flow pictures of the rotor casingwall and cascade endwall are used to visualize and analyse the boundary layers on the walls at various flow rates and corresponding inlet angles, respectively. The results enable the different sources of endwall blockage to be identified and changes with flow rate or inlet angle to be determined.     

Flow of a micropolar fluid in a diverging channel

The steady flow of an incompressible micropolar fluid in a diverging channel is studied. An approximate solution for the equations of motion is obtained in the presence of the inertia terms. It is observed that in the case of a micropolar fluid, the radial flow pattern of a Newtonian fluid is accompanied by a cross flow which is more pronounced near the apex of the channel. The variation of the streamlines and the micro-rotation are plotted and discussed.     

Modeling the Effect of Bubbles on a Pattern and Heat Transfer in a Turbulent Polydisperse Upward Two-Phase Flow after Sudden Enlargement in a Tube

In this work, the numerical modeling of the flow pattern and heat transfer in a polydisperse bubbly turbulent flow after sudden enlargement in a tube is performed. The pattern of average and fluctuation twophase flows at small volumetric gas flow rate ratios (β ≤ 10%) is qualitatively similar to the one-phase liquid flow pattern. It is shown that small bubbles are present almost throughout the entire cross section of a tube, while great bubbles generally pass through the flow core and the shear mixing layer. The addition of air bubbles to a one-phase liquid flow appreciably intensifies heat transfer (up to two times), and these effects become stronger with an increase in the diameter of bubbles and the volumetric gas flow rate ratios gasratios.     

Visualization of oscillating flow in a double-inlet pulse tube refrigerator with a diaphragm inserted in a bypass-tube

The double-inlet pulse tube refrigerator that has a diaphragm inserted in a bypass-tube, which enabled it to transmit a pressure oscillation whereas to obstruct a DC gas flow, was manufactured and tested. The oscillating flow behavior inside of the refrigerator was studied by using a smoke-wire flow visualization technique. It was found that if the diaphragm was optimized, the performance would be improved more than that of the refrigerator with a bypass valve due to the increase in the P–V work of the gas and the decrease in the convective heat loss caused by a secondary flow.     

The interaction of shock waves with a boundary layer on a sharp plate and a blunted plate

The interaction of shock waves with a turbulent boundary layer on a sharp plate and a blunted plate is numerically investigated. The shock waves in the flow are generated by wedges installed on the flat plate. The flow is simulated by the dynamic equations of a viscous perfect gas. The effect of the blunting radius of the plate’s leading edge and the wedge angle on the flow field and the local aerodynamic coefficients is shown. The calculated results are in agreement with the experimental data.     

Direct resonance analysis and modeling for a turbulent boundary layer over a corrugated surface

Summary Effects of surface corrugation on turbulent flow in a boundary layer are studied using a model based on the direct resonance theory. The induced mean flow due to weakly nonlinear waves, superimposed on the mean and fluctuating components of turbulence, is determined. The mean turbulent flow is affected by the surface corrugation throughout the boundary layer. The corrugated surface generates higher harmonics and affects the streamwise vortices generated by the waves superimposed on turbulence whose mean flow includes secondary induced mean flow components due to the corrugation.     

Oscillating flow of a simple fluid in a pipe

Poiseuille flow of an elastico-viscous liquid in a straight, circular pipe driven by a pressure gradient oscillating about a non-zero mean is investigated. The simple fluid of the multiple integral type presents a flow enhancement which depends on the frequency and amplitude of the oscillation, magnitude of the mean pressure gradient and the material functions of the fluid. A closed form expression for the flow rate alteration, independent of any explicit representations for the material functions, is developed at the lowest order in the perturbation algorithm where nonlinear effects appear. Asymptotic analyses of the flow rate enhancement at small and large frequencies are presented.     

Steady flow of a buoyant plume into a constant-density layer

The upward flow of a buoyant plume emanating from a horizontal fissure into a two-layered fluid region is considered. Solutions are computed numerically for a range of fissure widths and water depths. It is shown that for a given fluid depth and fissure size there is a minimum flow rate beneath which no steady solutions exist. At this limiting flow, the fluid detaches from the wall of the fissure via a stagnation point. Solutions exist for all values of flow rate above this minimum. Exact solutions are presented for very large flow rates.     

Pulsating flow of a couple stress fluid in a channel with permeable walls

The paper is concerned with an analytical study of the oscillatory flow of a couple stress fluid in a channel, bounded by two permeable walls. The couple stress fluid is considered to be injected into the medium through one of the walls with a given velocity and to be sucked off by the other wall with an equal velocity. The problem is solved by using a perturbation technique. Analytical expressions for the velocity and volumetric flow rate are derived for the oscillatory flow of the couple stress fluid flowing in the channel. By using the method of parametric variation, distribution of the velocity of the couple stress fluid, change in velocity profiles at different instants of time, change in volumetric flow rate with change in frequency and cross-flow Reynolds number are computed, by considering an illustrative example. The study reveals that both the velocity and the volumetric flow rate are quite sensitive to the couple stress parameter, the frequency of oscillation and also to the cross-flow Reynolds number. The study will be immensely useful in resolving different problems associated with oil industries.     

Flow Expansion behind a Shock Wave Discharged from a Channel

The results are given of experimental and numerical investigations of the structure of flow behind a shock wave discharged from open ends of round and square channels. It is demonstrated that the expansion regions arising in a flow behind a diffracted wave are characterized by a larger volume and a higher expansion ratio than those arising in a stationary underexpanded jet with the same value of the Mach number of flow at the channel exit section.     

Shear flow over a protuberance on a plane wall

Simple shear flow over a protuberance with an axisymmetric shape projecting from a plane wall with its axis normal to the wall is studied by means of a boundary-integral method that is suitable for computing three-dimensional Stokes flow in axisymmetric domains. The problem is formulated in terms of a system of three scalar Fredholm integral equations of the first kind for the distribution of traction over the surface of the protuberance and the wall, and is solved by means of a boundary-element method. Numerical computations are performed for a family of protuberances whose exposed surface is a section of a sphere or of an oblate spheroid with its minor axis normal to the wall, and the results are in agreement with those of previous analytical computations for hemi-spherical and spherical shapes. The numerical computations provide accurate information on the hydrodynamic force and torque exerted on the protuberances due to the shear flow, and the distribution of shear stresses, and illustrate the kinematical structure of the flow with reference to the development of stagnation points and flow reversal.     

Instability of a two-phase flow in a rectangular channel

A two-phase (liquid-gas) flow in a short horizontal slit channel of a rectangular cross section with a height of 440 μm has been experimentally studied using a fluorescent method, which allowed the flow pattern to be monitored and its quantitative characteristics to be measured. It is established that two-phase flow regimes in this channel substantially differ from the classical regimes of flow in extended channels of large cross section. It is demonstrated that the formation of various two-phase flow regimes and the transitions between them in short narrow rectangular slits are determined by instability of the liquid-gas flow at the side-walls of the channel.     

Stokes flow driven by a Stokeslet in a cone

We consider an axisymmetric Stokes flow in an infinite right circular cone, which has a source of momentum (a Stokeslet) on its axis. It produces an infinite sequence of eddies in the conical flow region. A boundary problem for a stream function is solved. The picture of the streamlines is obtained. We investigate an eddy structure of the flow. The results can be used for constructing nanoreactors while carrying out chemical reactions in strictly localized nanosized spatial regions.