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A generalization of Darcy's law relating the velocity averaged over the transverse coordinate and the pressure gradient is obtained for flows in a thin layer. A nonlinear Darcy's law with a limiting gradient is derived taking into account microrotations and the yield stress. It is shown that the micropolarity of fluids manifests itself as an increase in the apparent viscosity and the limiting pressure gradient. A generalization of Darcy's law for the case of pseudo–plastic and dilatant Herschel—Bulkley fluids is obtained.

We consider a one–dimensional model of hemodynamics–blood flow in the blood vessels-which is based on the Navier—Stokes equations averaged over the cross section of the vessel, and conjugate with a linear or nonlinear model for the elastic wall of the vessel. The objective is to study traveling wave solutions using this model. For such solutions, the system of partial differential equations reduces to an ordinary differential equation of the fourth order. The only singular point of the corresponding system of differential equations is found. It is established that at the singular point, the linearization matrix of the system has real or complex roots for different values of the parameters of the problem. With a special choice of the parameters, it has four complex conjugate roots with a nonzero real part or purely imaginary roots. For this case, the effect of the model parameter corresponding to the viscoelastic response of the vessel wall on the solution is investigated. Numerical experiments are performed to verify and analyze the results, and various modes of blood movement are discussed.

In this work, we present the poloidal beta β_p and internal inductance l_i by solving the simplest Grad—Shafranov equation (GSE), using the Solov'ev assumption for an HT–7 tokamak with a circular cross section. The poloidal beta and internal inductance are measured by using diamagnetic and compensation loops, combined with poloidal magnetic probe array signals. In this paper, theoretical and experimental results of determining β_p and l_i are presented. The calculated poloidal beta and internal inductance are demonstrated to depend on the kind of the discharge or plasma current.

Based on numerical simulations of flight trajectories with ramjet–powered flying vehicles, it is found that all possible flight trajectories can be classified into three groups: ballistic trajectories, trajectories with a horizontal segment, and skipping trajectories. Trajectories of each group can be optimized, for instance, to ensure the maximum flight range under given initial conditions and constraints. Examples of optimal trajectories for a given amount of available fuel are presented as functions of the initial slope of the trajectory, angle of attack of the vehicle, instants of engine actuation, and engine operation time.

An approximate analytical model of the flow structure in a plane λ–shaped pseudoshock consisting of a viscous boundary layer and an inviscid core flow is proposed. It is assumed that the boundary layer edge is a streamline with a specified pressure distribution along the channel and that the flow in the pseudoshock consists of an input segment (Mach reflection of an oblique shock wave) and a sequence of internal segments with an identical structure (shock train). Comparisons with experimental data and results of numerical calculations are performed. It is shown that the model provides a sufficiently accurate description of the pseudoshock flow structure.

In this article, turbulent single–phase and two-phase (air–water) bubbly fluid flows in a vertical helical coil are analyzed by using computational fluid dynamics (CFD). The effects of the pipe diameter, coil diameter, coil pitch, Reynolds number, and void fraction on the pressure loss, friction coefficient, and flow characteristics are investigated. The Eulerian—Eulerian model is used in this work to simulate the two–phase fluid flow. Three–dimensional governing equations of continuity, momentum, and energy are solved by using the finite volume method. The κ–ε turbulence model is used to calculate turbulence fluctuations. The SIMPLE algorithm is employed to solve the velocity and pressure fields. Due to the effect of a secondary force in helical pipes, the friction coefficient is found to be higher in helical pipes than in straight pipes. The friction coefficient increases with an increase in the curvature, pipe diameter, and coil pitch and decreases with an increase in the coil diameter and void fraction. The close correlation between the numerical results obtained in this study and the numerical and empirical results of other researchers confirm the accuracy of the applied method. For void fractions up to 0.1, the numerical results indicate that the friction coefficient increases with increasing the pipe diameter and keeping the coil pitch and diameter constant and decreases with increasing the coil diameter. Finally, with an increase in the Reynolds number, the friction coefficient decreases, while the void fraction increases.

The paper presents a method of recovery of gas flow pressure from the results of measurements by a piezoelectric pressure sensor in short–duration wind tunnels. It is assumed that the measuring system is a linear dynamic object. A quasisolution of linear Volterra integral equation of the first kind is constructed based on the condition that the equation holds on average in successive intervals into which the time interval of the measurement is divided. An experimental technique for determining the normal response of the sensor (transfer function) is proposed, and an example of recovery of air flow pressure in a wind tunnel is given.

A model describing long–wave dimensional perturbations in a liquid film is developed that takes into account the presence of shear stress on the interfacial surface. This model is based on the decomposition of the liquid velocity vector components in a series in linearly independent basis functions (harmonics) and does not use the assumption of self–similarity of the velocity profile. A linear analysis of the stability of film flow with respect to three–dimensional perturbations, and a numerical simulation of nonlinear waves were performed.