Journal of Applied Mechanics and Technical Physics最新文献

The characteristics of joint flows of evaporating liquid and a laminar gas stream in a plane horizontal channel are studied based on an exact partially invariant solution of thermosolutal convection equations. The influence of the liquid layer thickness and the conditions for the temperature function on the upper wall of the channel on the rate of evaporation caused by gas pumping is investigated. The exact solution is verified by comparison with experimental data. The linear stability of the exact solutions is studied. It is established that regardless of the type of boundary thermal regime, oscillatory instability in the form of cellular convection always appears in the system. Thermal insulation of the upper wall does not lead to a change in the structure of the most dangerous perturbations, slightly destabilizes the flow in the case of long-wave perturbations, and has a stabilizing effect in the case of short-wave perturbations.

Rotational sedimentation of neutrally buoyant particles in suspensions in the case of two-dimensional circular flows between two cylinders is studied by mathematical simulation. Particle separation in the absence of gravity is caused by rotation of the inner cylinder. It is revealed that sedimentation depends on particle rotation. Within the framework of the Cosserat continuum, the suspension is considered as a micropolar fluid. The effect of the eccentricity of noncoaxial cylinders on the sedimentation front is investigated.

Unsteady one-dimensional shear flows of a viscoelastic fluid are considered. A general approach is formulated for fluids with several relaxation times, which allows the known models of viscoelastic flows to be presented as evolutionary systems of first-order equations. Conditions of hyperbolicity of flow classes considered are found for the Johnson–Segalman, Giesekus, and Rolie-Poly models. The equations of motion of the viscoelastic fluid are presented in the form of a full nonlinear system of conservation laws. A method of calculating unsteady discontinuous flows within the framework of the models under consideration is proposed. The class of unsteady Couette flows in the gap between the cylinders used in rheological tests is studied numerically. The process of shear banding and its influence on the structure of steady flows are investigated. The numerical results obtained are compared with experimental data.

This paper considers hyperbolic systems of equations of a certain type that describe one-dimensional nonlinear waves propagating in the same way in both (x) directions. Each system of this type can be put into correspondence with a hyperbolic system of equations of halved order derived based on the initial system of equations. The similarity of the solutions of this system of equations and the original one is studied.

Publications dealing with investigations of screw fluid flows with collinear velocity and vortex vectors are reviewed. New solutions are presented for the Navier–Stokes equations for an incompressible fluid and second-grade fluid equations, which are two-dimensional analogs of screw flows.

One possible formulation of the inverse problem of identification of the vortex structure based on the flow velocity vectors at a set of points is considered, and an algorithmic method of its solution is proposed. The approach is based on the vortex structure presentation by a combination of the Rankine vortices. Identification is understood as determination of the number of model vortices, their intensities, centers, and radii. The method implies minimization in space of the parameters of the model system of the objective functional estimating the closeness of the known and modeled velocity vectors. The algorithm includes the following stages: search for the initial approximation for the vortex structure, refinement of the model vortex parameters, and correction of the resultant structure. Solving the direct problem of the flow development prediction is based on solving the initial-boundary value problem for the Euler equation for the ideal fluid dynamics by the spectral-vortex method. Results of test computations performed by the proposed approach are presented. It is demonstrated that the model system in all test computations ensures a sufficiently accurate description of the topology of streamlines during identification. Predictions at times corresponding to changes in the flow topology are obtained.

This paper examines two-dimensional flows near a free critical point of an incompressible viscoelastic Maxwell medium using the Johnson-Segalman convected derivative. The flow is assumed to be axisymmetric, and its velocity profile is linear along the axial coordinate. A general exact analytical solution is found for the problem of the distribution of the stress tensor components near the stagnation point.

Heat exchange in a liquid film moving along the microchannel bottom is calculated using the developed three-dimensional steady-state model of the liquid film motion. The liquid moves under the action of a cocurrent gas flow in the channel, with a square heater located at its bottom. In this case, the action of all the main physical factors during their interaction is taken into account: diffusive/convective heat transfer, dependence of the liquid properties on temperature, thermocapillary effect, occurrence/growth of surface deformations, and evaporation/condensation of the liquid. It is revealed that heater size significantly affects temperature fields, surface deformations, and temperature extremes. An equation for calculating the greatest excess of mean temperature achieved on the substrate is derived.

A nonlinear problem of unsteady motion of a circular cylinder in an ideal infinitely deep fluid under the action of arising hydrodynamic loads is considered. A method of reducing the solution of the initial mathematical problem to the solution of an equivalent integrodifferential system of equations for the function determining the shape of the sought free surface for the normal and tangential components of the fluid velocity on the free surface, and for the unknown trajectory of cylinder motion is used. The initial (in terms of time) asymptotic curve of the solution, which describes the cylinder motion from the state at rest is constructed.

The normal coordinate method is used in conservative mechanical systems to reduce two quadratic forms to a sum of squares. In this case, a system of differential equations is split into a system of independent oscillators. A linear dissipative mechanical system with a finite number of degrees of freedom is determined by three quadratic forms: kinetic and potential energy of the system, as well as the Rayleigh dissipation function, which, generally speaking, cannot be reduced to a sum of squares. Conditions are considered under which all three quadratic forms are exactly or approximately reduced to a sum of squares by a single transformation. It is revealed that such systems can be supplemented with normal coordinates in which the system is split into independent second-order systems. This allows one to construct exact or approximate analytical solutions in general form and with an estimated relative error in the case of an approximate solution. The advantages of this approach are shown for problems of theoretical mechanics and electrical engineering, in which analytical solutions are constructed and optimization analysis is carried out. In this case, traditional methods allow only for numerical calculations to be performed for given parameter values.