Journal of Theoretical and Applied Mechanics, Sofia, vol. 53 Issue 3 (2023)

This special issue is dedicated to Prof. Stefan Radev, an eminent scientist in the field of applied mathematics and mechanics, and a long-standing editor-in-chief of the Journal of Theoretical and Applied Mechanics since 1999. On 25th September 2022 he celebrated his 80th birthday.

In this article, we present several remarks on selected topics of research in fluid mechanics at the Institute of Mechanics of the Bulgarian Academy of Sciences. A large part of the discussed results are from the years when Professor Stefan Radev was the Chair of the Department of Fluid Mechanics at the Institute of Mechanics. The topics include the optimum theory of turbulence, methodology for solving differential equations related to the motion of waves in fluids, and the application of time series analysis to problems in environmental fluid mechanics. Special attention is given to Professor Radev’s participation in this research.

The Poiseuille flows of non-Newtonian fluids may have complicated structures depending on the rheological characteristics of the fluid. The Carreau-Yasuda viscosity model is often used to describe the behaviour of many complex fluids. The Poiseuille flow of such fluids has many applications and occurs as a fundamental problem from a practical and theoretical point of view. At high shear rates, the flow may become unstable, then the Poiseuille flow problem may have no solution. In this paper, we prove the condition for the existence of its classical solution.

Authors solves the problem of spots chain dynamics with initial intervals of mixed liquid in stratified environment, and viscous flow using the numerical splitting method for studying incompressible fluid flows (SMIF method). The SMIF method is characterized by minimal scheme dissipation and dispersion. The finite difference scheme has the second order of approximation in terms of spatial variables. The fields of the stream function are obtained, which are used to study the spots chain dynamics using the example of characteristic variant with given parameters of the values of the Reynolds and Froude numbers and initial intervals between spots.

We study the effect of slip boundary conditions on the kinetics, dynamics, and heat transfer in a strongly nonequilibrium flow with coupled vibrational relaxation, state-specific gas-phase and surface reactions. Two types of kinetic boundary conditions are introduced: whereas one ensures number flux conservation, the second conserves the mass flux. Both kinetic boundary conditions are suitable for state-to-state flow simulations and take into account gain and loss of particles on the surface due to recombination and excitation/ deactivation of vibrational states. On the basis of the proposed kinetic conditions, the velocity slip, temperature jump and species normal mass fluxes on the surface are derived. The models are used for numerical simulations of a five-component air mixture along stagnation line. The effects of kinetic boundary condition, diffusion model, accommodation coefficients are evaluated for different rarefaction degree. Important effect of diffusion model and temperature jump on the fluid-dynamic variables and heat flux is shown.

In this work, the influence of interactions between multi-component plasma systems on their equilibrium compositions is studied. Equilibrium densities of atoms, ions and free electrons in these systems are determined by integration of distribution functions over the space of momentum and summation over electronic energy levels. These functions correspond to the maximum entropy for the combination of systems under different conditions of their interaction. Special attention is given to monatomic plasma mixtures under following situations: 1) the systems may exchange only energy; 2) the systems may exchange energy and electrons; 3) the systems may exchange energy, electrons and some chemical elements.

A stochastic numerical approach for the operation problem concerning the removal of contaminants in Horizontal Subsurface Flow Constructed Wetlands (HSF CW) is presented. Emphasis is given to uncertain-but-bounded input-parameters, which are considered as interval parameters with known upper and lower bounds. For the treatment of this uncertainty, the Monte Carlo method is used. The proposed methodology consists of applying the Monte Carlo procedure by solving the deterministic problem for each of the datasamples. Atypical case of a HSF CW unit, concerning Total Phosphorus (TP) removal, is used in a numerical example. The reliability of the proposed stochastic approach is proved by comparing the numerical results with available experimental ones.

The Civil Engineering structural mechanics praxis includes framed buildings of reinforced concrete (RC). The present study deals with a stochastic numerical treatment for the pounding problem concerning the seismic interaction between adjacent RC framed structures strengthened by cable-ties when the input parameters are uncertain-but-bounded. This problem concerns here the unilateral contact between neighbouring RC structures during earthquakes and is considered as an inequality problem of dynamic structural contact mechanics. The Monte Carlo method is used for treating the uncertainty concerning input parameters. The purpose here is to estimate numerically and to control actively the influence of the cable-ties on the seismic response of the adjacent structures. Finally, in a practical case of two seismically interacting framed RC structures, the effectiveness of the proposed methodology is shown.