This paper presents the results of a comprehensive numerical study of the interaction between a supersonic air flow with a Mach number of 3.5 and a stationary jet injected through a slot in a streamlined plate. The mathematical model is based on the Reynolds-averaged Navier–Stokes equations, which are solved by the finite volume method. In the first stage, methodological calculations were performed to substantiate the choice of optimal parameters for the computational grid, the convective flow approximation scheme, and the turbulence model. It was found that the best fit to the experimental data is achieved by combining the Spalart–Allmaras turbulence model allowing for compressibility and the second-order AUSM+up scheme. After validating the computational methodology, a systematic parametric study was conducted to examine the influence of two factors: the relative pressure in the jet (in the range from 8.74 to 63.5) and the injection angle (from –30 to 30◦). It is shown that increasing the jet intensity leads to a nearly linear increase in the length of the separation zone in front of the slot, the depth of jet penetration in the cross flow, and the resulting force acting on the plate. The highest injection efficiency, characterized by the gain factor, is achieved at a relative pressure of 17.12; its further increase is accompanied by an enhancement of the shock-wave interaction and a decrease in efficiency. The study of the influence of injection angle revealed a pronounced asymmetry between the concurrent and countercurrent injected jets. The countercurrent injection leads to the formation of extensive separation zones, intense shock waves, and significant total pressure losses. By contrast, the concurrent injection forces the jet against the surface, weakens the shock-wave structure, and reduces losses.
The martensite stabilization effect significantly influences the thermomechanical response of shape memory alloys and must be properly taken into account in numerical modeling. In our previous studies, to describe this effect in TiNi alloys we developed a model using the microstructural approach. The foundation of the model was the hypothesis of damage accumulation at inter-martensitic boundaries. In this work, four approaches to the identification of material constants of this model are considered: manual fitting, the deterministic Nelder--Mead method, a stochastic genetic algorithm, and a neural network approach based on the Deep Sets architecture. The study uses the results of experiments for the Ti50Ni50 and Ti49Ni51, titanium nickelide alloys reported in the literature. These experiments reproduce three characteristic modes of applying preliminary deformation: tensile deformation in the martensitic state, cooling under constant load, and stress-induced martensite transformation. The parameter identification procedure aims to minimize the discrepancy function measuring the difference between the calculated and experimentally observed shifts in the reverse martensitic transformation temperature. A comparison of the accuracy and computational efficiency of the applied methods was carried out for both alloys. The results show that the Nelder--Mead method and the genetic algorithm provide a comparable quality of the experimental data approximation at moderate computational costs and relatively simple parameter setting. The neural network approach demonstrates less accurate agreement between the results of numerical simulation and experiments but provides fast inference after training; however, it requires pre-generation of large training datasets and exhibits increased sensitivity to the initial training conditions. The obtained results confirm the applicability of different methods of automated parameter identification for models of shape memory alloys.
The study addresses an important environmental problem related to harmful effects of greenhouse gases on Earth's temperature and climate and the need to reduce anthropogenic carbon dioxide emissions into the atmosphere. One-sided density-driven convection developed inside a porous formation during dissolution of supercritical CO2 fluid in water is investigated in reference to the technologies of carbon dioxide storage in underground water-saturated formations. The hydrodynamic model includes equations of continuity, motion (based on the Darcy's law), convection-diffusion and a non-linear equation of state that relates the density of fluid medium with the concentration of CO2. A fluid is described as a single-phase two-component medium with variable viscosity. Based on the data available in the literature, the physical properties of the CO2 + H2O system were determined in the ranges of temperature T=307.7 - 342.8 К and pressure P=8.07 - 31.42 MPa. Numerical simulation of hydrodynamic processes in this system was carried with the aid of the developed finite-difference numerical code. In particular, the code was employed to study how the characteristics of convective dissolution depend on the temperature and the pressure. It has been found that with increase of these parameters the convective dissolution of CO2 fluid in water is more intensive. For example, the time during which half of CO2 dissolves in water and is transported down by a convective flow is reduced almost twice. Thus, an increase in temperature and pressure ensures more reliable storage of carbon dioxide in underground water-saturated formations.
The article examines the phenomena caused by the mutual influence of mechanical, temperature and diffusion fields in a continuous orthotropic multicomponent cylinder under the action of unsteady external perturbations set on the cylinder surface. The cylinder does not experience volumetric perturbations. It is assumed that the physico-mechanical processes occurring in the cylinder depend only on the radial coordinate. The mathematical formulation involves a system of coupled nonstationary thermodiffusion equations in a cylindrical coordinate system. The employed heat and mass transfer model accounts for the finite velocity of thermal and diffusion wave propagation. The kinematic relations for thermal and diffusion flows are constructed based on the generalized Lord–Shulman theory. The proposed algorithm for solving a polar-symmetric problem is based on the integral representation of the desired fields in the form of time-dependent convolutions of Green's functions and the functions, describing surface thermomechanodiffusion perturbations. The Green's functions are found by applying the time-domain Laplace transform and the Fourier–Bessel series expansion, which makes it possible to reduce the initial boundary value problem to a system of linear algebraic equations with respect to the coefficients of the Fourier series. The solutions of this system are rational functions, and therefore the inverse Laplace transformation is carried out analytically using the theory of residues and tables of operational calculus. Using a three-component cylinder as an example, a numerical analysis of the interaction between mechanical, temperature and diffusion fields under external unsteady thermal action is performed and the obtained results are compared with the solutions to known problems of thermoelasticity and mechanodiffusion. The effect of the finite velocity of propagation of thermal and diffusion fluxes on the kinetics of heat and mass transfer in continuous media under different types of external thermal load is investigated.
The operation of gas turbine engine parts at elevated temperatures in aggressive environments containing oxygen and sulfur compounds leads to the formation of a corrosive film that changes the mechanical characteristics and stress state in the surface layer. This, in turn, affects the rate of propagation of the corrosion product. High-temperature salt corrosion of metal alloys is accompanied by inter-diffusion and chemical reactions between metal components and aggressive substances, swelling of the material and the occurrence of rheological strains. For this reason the description of this process must be carried out within the framework of a coupled formulation. For the theoretical description of the process, a model based on the classical thermodynamics of irreversible processes is used. It includes the equations of mass balance of the components and the equilibrium equation for the material as a whole, and takes into account the elastic-viscous-plastic behavior of corrosion products at elevated temperatures. The COMSOL Multiphysics finite element package was used to calculate the processes of high-temperature oxidation and sulfide-oxide corrosion of a two-component iron and chromium alloy. Analysis of the results obtained showed the formation of a layered structure of a corrosion film, the advance of the front of compressive residual stresses and corrosion deep into the material, and stress relaxation near the surface. A comparison of geometrically linear and nonlinear formulations of the model, considering or ignoring the influence of stresses on diffusion flows and chemical reaction rates, as well as plastic and viscous strains, revealed a significant effect of each of these factors on the propagation velocity of the corrosion front and on the stress-strain state of the material.
