Prikladnaâ matematika i mehanika

Prikladnaâ matematika i mehanika. 2025;89(5):677-678

677-678

Influence of solid surfaces on the evolution of incompressible fluid jets. Part 1. Jets emerging from an orifice perpendicular to an infinite solid plane

Gaifullin A., Shcheglov A.

摘要

A review of works on submerged jets, the evolution of which occurs in the presence of infinite solid planes, is presented. In the first part of the review, problems related to jets emerging from an orifice perpendicular to an infinite plane are considered. The second part of the review will be devoted to jets emerging parallel to an infinite plane, as well as the interaction of jets.

Prikladnaâ matematika i mehanika. 2025;89(5):679-702

679-702

Structure of a locally turbulent flow formed when a part of the fluid leaves into the side branch of a circular tube

Smirnov E., Gataulin Y., Kolesnik E.

摘要

The results of a numerical study of unsteady viscous fluid flow in the area of the branching of a circular cross-section channel at an angle of 60° are presented for four values of the inlet Re number that are less than or equal to 1475; in the upstream region, the channel flow is assumed to be unperturbed and fully-developed. The main results relate to the case of equality of the flow rates in two branches, with flow separation regions in both branches. It was shown, in particular, that at Re = 750, intense quasi-periodic oscillations develop in the computational domain due to the Kelvin-Helmholtz instability. At Re = 1475, a zone of locally turbulent motion is formed in the flow, the size of which depends on the proportion of the flow going into the side branch. The vortex pattern of the flow and the type of the velocity pulsation spectrum at various points in the region are analyzed.

Prikladnaâ matematika i mehanika. 2025;89(5):703-717

703-717

Experience of direct numerical simulation of turbulent boundary layers in complex flows

Garbaruk A., Stabnikov A., Strelets M., Travin A., Shur M.

摘要

A survey is presented of numerical studies of near-wall turbulent flows conducted in different years using Direct Numerical Simulation (DNS) by representatives of three generations of L.G. Loitsyansky's students, currently working in the laboratory “Computational Hydroaeroacoustics and Turbulence” of SPbPU. Based on the experience accumulated in the course of these studies, a conclusion is drawn that despite the high computational costs required to carry out DNS, this method already today represents a powerful universal tool not only for fundamental research into turbulence, but also for solving important applied problems.

Prikladnaâ matematika i mehanika. 2025;89(5):718-751

718-751

Stability of a three-dimensional boundary layer with s-shaped spanwise velocity profiles

Boiko A., Demidenko N.

摘要

The hydrodynamic stability of the flow with S-shaped spanwise velocity profiles simulating an incompressible flow in three-dimensional boundary layers is analyzed in a wide range of Reynolds numbers. The existence of an instability different from the known crossflow vortices and Tollmien-Schlichting waves is confirmed. The boundaries of the instabilities are estimated in terms of the wave vector angle.

Prikladnaâ matematika i mehanika. 2025;89(5):752-764

752-764

On the Flow Field of a Submerged Swirling Non-Self-Similar Jet of Viscous Incompressible Fluid Determined by Exact Integrals of Motion

Yavorsky N.

摘要

The flow field of a submerged swirling non-self-similar jet is considered, determined by exact integrals of motion: conservation of the total momentum flow, the total angular momentum flow, the total mass flow and the hidden integral of motion. The impact of the twist parameter, flow rate, and hidden integral of motion on the flow is investigated for three physical models of motion sources: a swirling jet flowing from a tube, a jet from a fan with zero flow, and a flow from a vortex vacuum cleaner when the liquid flow rate is negative. A number of nontrivial physical features of the velocity field of a non-self-similar swirling jet due to the nonlinear interaction of motion integrals are revealed. It is shown that the physical effects found in the work can be controlled by setting different values to these integrals of motion, which makes the results of the work universal and have the potential for practical application.

Prikladnaâ matematika i mehanika. 2025;89(5):765-783

765-783

Generalized Helical Flows

Meleshko S., Petrova A., Pukhnachev V.

摘要

This paper studies the compatibility conditions for a system of equations describing nonuniform helical flows of an inviscid incompressible fluid. The class of flows considered traces back to the works of I. S. Gromeka and E. Beltrami, who independently discovered stationary solutions of the Euler equations satisfying the collinearity condition between the velocity and vorticity vectors. Their results laid the foundation for the theory of helical flows, identifying special solution classes of hydrodynamic equations. The system under consideration comprises the Euler equations supplemented by differential constraints that relate the velocity and vorticity vectors. Gromeka showed that if the function α is constant, the system becomes involutive. However, when α(x, y, z) is variable, the analysis becomes significantly more complex, and in general, the system is not involutive. A group analysis is performed for the resulting closed nonlinear system relating the velocity components and the function α\alpha. An optimal system of subgroups of the six-dimensional Lie algebra admitted by the system is constructed. Invariant solutions with respect to one-parameter subgroups are derived and are described by quasilinear equations with two independent variables.

Prikladnaâ matematika i mehanika. 2025;89(5):784-796

784-796

Influence of viscosity on the behavior of a drop (bubble) in liquid under the influence of vibrations

Lyubimova T., Ivantsov A.

摘要

The paper studies the effect of viscosity on oscillations of a liquid or gaseous inclusion (a drop or a gas bubble) in a fluid of uniform density under the action of external vibrations. It is assumed that the vibration amplitude is small and the frequency is high, however, the vibration velocity and the thickness of the dynamic boundary layers are finite. Numerical modeling of the inclusion behavior in a non-averaged formulation using the liquid volume method is performed. The effect of viscous dissipation on the amplitude of inclusion oscillations and its averaged shape is studied. The fields of flows generated by vibrations near the inclusion for different vibration parameters are obtained. The numerical data are compared with known analytical results. Corrections are proposed that take into account viscous dissipation that occurs when the vibration frequency decreases.

Prikladnaâ matematika i mehanika. 2025;89(5):797-810

797-810

On a partially invariant solution of gas dynamics equations

Chupakhin A., Stetsyak E.

摘要

The present paper is devoted to the study concerning partially invariant multidimensional solutions of gas dynamics equations, generalizing classical stationary two-dimensional gas flows. It is proved that the gas dynamics equations for such solutions reduce to a third-order dynamical system on a manifold. The singular manifolds of this system are investigated. The main attention is paid to the structure of invariant and non-invariant components of the solution, as well as the features of solutions near singular points. The existence of solutions conjugated through a shock wave, which correspond to the transition of integral curves from one sheet of the manifold to another, is proved.

Prikladnaâ matematika i mehanika. 2025;89(5):811-824

811-824

Modeling dissipative processes in open and closed hydrodynamic systems

Rudyak V.

摘要

In this paper, the modeling of transport processes in both closed and open hydrodynamic systems is discussed. The main focus is on reviewing the relevant mechanisms. It is shown that in weakly nonequilibrium systems, dissipative processes are caused by microscopic thermal molecular fluctuations, and their irreversibility is associated with the non-potential nature of intermolecular interactions. In open hydrodynamic systems the rheology of the fluid changes at sufficiently high shear rates. The nature of these changes is demonstrated using molecular dynamics simulations. It is established that with increasing shear rate, both simple liquid and nanofluids become pseudoplastic. In the latter case, the critical shear rate of rheology change depends on the concentration of nanoparticles and their size. However, at sufficiently high shear rates, dissipative processes cease to depend on the sizes of the internal structural elements of the medium. Its viscosity drops sharply. In all cases, the change in the rheology of the medium is associated with the transformation of its structure. In particular, with the degradation of the short-range order.

Prikladnaâ matematika i mehanika. 2025;89(5):825-842

825-842

Potential Jet Flows of Burning Fluids

Rashkovskiy S.

摘要

Within the framework of the theory of jets flows in an ideal fluid, the combustion of a liquid monopropellant jet flowing out of a vessel with flat walls is investigated. An exact solution to the problem is obtained and a parametric study of the influence of the vessel geometry and combustion parameters on the shape, flow rate coefficient and length of the jet is carried out. This work expands the class of problems solved by methods of the theory of plane potential jets in an ideal fluid.

Prikladnaâ matematika i mehanika. 2025;89(5):843-860

843-860

Power-law elliptical bodies of minimum drag in approximation of newton pressure coefficient law

Takovitskii S.

摘要

Newton's classical problem of constructing bodies with minimum drag is being developed in the direction of studying the characteristics of bodies with non-circular cross-sections. The examples of pyramidal bodies, the elliptical cone, and the power-law elliptical body demonstrate the possibility of reducing drag compared to axisymmetric bodies, provided that the length and the base area are preserved. The obtained results correct the erroneous results and conclusions, published in the journals “Applied Mathematics and Mechanics” (Nguyen V.L. Power-Law Elliptical Bodies of Minimum Drag in a Gas Flow // Applied Mathematics and Mechanics, 2023, vol. 87, no. 3, pp. 454–460) and “Fluid Dynamics” (Nguyen, V.L. Power-Law Elliptical Bodies of Minimum Drag in a Gas Flow // Fluid Dyn 58, 1367–1372 (2023)).

Prikladnaâ matematika i mehanika. 2025;89(5):861-876

861-876

The Stability in Couette–Taylor Flow of a Viscoelastic Kelvin–Voigt Fluid

Proskurin A.

摘要

This paper considers the stability of a flow of a weak polymer solution between concentric cylinders, the inner of which rotates. A case of Kelvin–Voight model, frequently called Oskolkov model, was used to describe the movement of the fluid. This model is applicable for highly diluted solutions, where the relaxation time is much less than the typical flow time scale and the elastic forces are much less the viscous. The stability was investigated by the linear approach using the differential sweep numerical method. It is found that for axisymmetric perturbations, as well as in the case of small gap between the cylinders, the critical Reynolds numbers are close to the case of Newtonian fluid. In the case of medium and small values of the inner cylinder radius, the viscoelastic fluid is less stable with respect to the non-axisymmetric disturbances than the viscous one. The critical Reynolds numbers for the non-axisymmetric spiral perturbations may be lower than for the axisymmetric Taylor vortices.

Prikladnaâ matematika i mehanika. 2025;89(5):877-888

877-888