Том 57, № 6 (2016)

The existence of axial–radial acoustic resonance oscillations of the basic air flow in bleed channels of aviation engines is demonstrated theoretically and experimentally. Numerical and analytical methods are used to determine the frequency of acoustic resonance oscillations for the lowest modes of open and closed bleed channels of the PS-90A engine. Experimental investigations reveal new acoustic resonance phenomena arising in the air flow in bleed channel cavities in the core duct of this engine owing to instability of the basic air flow. The results of numerical, analytical, and experimental studies of the resonance frequencies reached in the flow in bleed channel cavities in the core duct of the PS-90A engine are found to be in reasonable agreement. As a result, various types of resonance oscillations in bleed channels can be accurately described.

The dynamic behavior of the magma melt saturated with a strongly compressed gas at a high temperature, which is located between two rigid boundaries aligned symmetrically with respect to the vertical axis, is considered. A constant pressure is maintained at the channel bottom, while the pressure in the medium is initially distributed in accordance with the hydrostatic law. The top of the channel is hermetically sealed with a plug, which is affected by a constant pressure equal to the atmospheric value. The state of the melt after instantaneous removal of the plug is studied.

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.

The self-gravitating instability of the present model is discussed by using a simple linear theory. The problem is formulated for a rotating fluid layer, and a dispersion relation valid for all kinds of perturbations is derived and discussed. The self-gravitating force is found to be a destabilizing factor for a small range of wavenumbers, while it is stabilizing in other ranges, depending on the density ratio of the fluids. For high values of the angular velocity, the rotational force produces a stabilizing effect and can suppress the self-gravitating instability. In the absence of the self-gravitating force, the model of a rotating fluid layer is marginally stable.

A similarity solution for a steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation point on a vertical permeable plate with a magnetic field and a buoyancy force is obtained by solving a system of nonlinear ordinary differential equations. These equations are solved analytically by using a new kind of a powerful analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). Three different types of nanoparticles, namely, copper (Cu), alumina (Al₂O₃), and titanium oxide (TiO₂), with water as the base fluid are considered. The influence of the volume fraction of nanoparticles, permeability parameter, magnetic parameter, and mixed convection parameter on the surface shear stress and surface heat transfer, as well as on the velocity and temperature profiles, is considered. It is observed that the skin friction coefficient and the local Nusselt number increase with the nanoparticle volume fraction for all types of nanoparticles considered in this study. The greatest values of the skin friction coefficient and the local Nusselt number are obtained for Cu nanoparticles.

A two-dimensional magnetohydrodynamic boundary layer flow of the Eyring–Powell fluid on a stretching surface in the presence of thermal radiation and Joule heating is analyzed. The Soret and Dufour effects are taken into account. Partial differential equations are reduced to a system of ordinary differential equations, and series solutions of the resulting system are derived. Velocity, temperature, and concentration profiles are obtained. The skin friction coefficient and the local Nusselt and Sherwood numbers are computed and analyzed.

The accelerated flow of a pseudoplastic fluid around a quiescent sphere at Reynolds numbers Re = 0–200 and dimensionless acceleration Ga = 10–10⁴ is studied by numerical simulation. It is shown that the analytical expression of the added mass force for an ideal fluid is appropriate for a pseudoplastic fluid. An expression for calculating the hereditary Basset force for a pseudoplastic fluid is proposed.

A mathematical model is proposed to describe methane–carbon dioxide replacement in gas hydrate by injecting liquid carbon dioxide into a porous medium initially saturated with methane and its hydrate. Self-similar solutions of the axisymmetric problems are constructed that describe the distribution of the main parameters of the reservoir. It is shown that there exist solutions according to which the process can occur both with and without boiling of carbon dioxide. Diagrams of the existence of each type of solution are constructed.

This research is aimed at studying the two-phase flow pattern of a top heat mode closed loop oscillating heat pipe with check valves. The working fluids used are ethanol and R141b and R11 coolants with a filling ratio of 50% of the total volume. It is found that the maximum heat flux occurs for the R11 coolant used as the working fluid in the case with the inner diameter of 1.8 mm, inclination angle of −90◦, evaporator temperature of 125◦C, and evaporator length of 50 mm. The internal flow patterns are found to be slug flow/disperse bubble flow/annular flow, slug flow/disperse bubble flow/churn flow, slug flow/bubble flow/annular flow, slug flow/disperse bubble flow, bubble flow/annular flow, and slug flow/annular flow.

The torsional and longitudinal–flexural vibrations of corrugated orthotropic shells are investigated. Relations, including the equations of motion in forces and moments and Hooke’s relations, are obtained using the Kirchhoff–Love hypotheses. The influence of the geometric parameters of the shell (corrugation amplitude and length) on the eigenfrequencies and natural vibrations modes is studied for fixed-end shells. It is found that during torsional vibrations, increasing the corrugation amplitude and increasing the number of corrugations leads to a decrease in the resonant frequencies. In the case of torsional and longitudinal–flexural vibrations, the influence of the corrugation amplitude on the natural vibration modes is investigated.

The Ramberg–Osgood stress–strain relation is used to perform a theoretical springback analysis in the problem of bending of a narrow rectangular strip made of a strain-hardening material. The maximum strip thickness is 5 mm, and its length is significantly greater than the thickness. Based on the elasticity and plasticity deformation theory and also on the Tresca and von Mises yield criteria, an expression for the springback ratio is derived. The springback ratio depends on the ratio of the yield stress to Young’s modulus, Poisson’s ratio, strain hardening coefficient, and sheet thickness.