Artificial neural networks (ANNs) are widely used to approximate nonlinear mappings, yet their ability to capture thermodynamic behaviour in dynamic physical systems remains insufficiently characterised. This study investigates how representational capacity influences surrogate modelling accuracy for a crank-angle-resolved internal combustion engine (ICE) simulation with a maximum dynamic state dimension of six. Two feedforward ANN configurations are evaluated: a low-capacity 5-5 architecture containing 84 trainable parameters and a high-capacity 25-25-25 architecture containing 1554 parameters (18.5 & times; larger). Both networks approximate the nonlinear mapping from five embedded operating parameters to four peak thermodynamic outputs (maximum pressure, pressure phasing, maximum temperature, and temperature phasing). Evaluation across 53,178 operating points demonstrates that the high-capacity configuration reduces root mean squared error by factors of 30-50 & times; relative to the low-capacity network, decreasing peak temperature error from 17.68 K to 0.36 K and peak pressure error from 0.116 MPa to 0.0025 MPa. Although both models achieve coefficients of determination exceeding 0.99, the low-capacity network exhibits heavy-tailed residual distributions and regime-dependent error amplification, whereas the high-capacity model reduces both central dispersion and extreme-case error. These results demonstrate that high correlation alone does not guarantee engineering reliability in nonlinear thermodynamic systems. Distribution-level analysis, including percentile and extreme-case characterisation, is required to evaluate engineering robustness. The findings provide a quantitative framework linking ANN capacity, nonlinear dynamic system representation, and predictive robustness.

The study addresses how numerical simulation has been developed and applied to the investigation of intra-chamber processes in solid rocket motors (SRMs). The existence of non-spherical condensed phase particles is a feature of internal flows in the SRM channels and nozzles. The simultaneous occurrence of events on several temporal and spatial scales that characterize the production of agglomeration particles, their burning, and their transport in the flow of combustion products in internal channels and nozzles are mathematical difficulties in this field. A multi-scale strategy that integrates models expressing the system’s status at the micro-, meso- and macro-sizes is one way to solve these issues. A summary of models with different levels of depth and complexity is provided. In order to simulate two-phase flows with metal-oxide agglomerates generated in the propellant channel and simulating drops of molten metal with oxide particles attached to their surface, the design of multi-scale models is taken into consideration. The developed approach capabilities are exhibited through the computation of combustion product flows in propulsion system nozzles and channels that contain agglomeration particles.

The paper presents a numerical study of aerosol particle deposition in the human nasal cavity taking into account airflow velocity, inhaled air temperature, and soft tissue deformation. A coupled multiphysics model was used for simulation, including the Navier-Stokes equations with the SST k-omega turbulent model, the Lagrangian discrete phase model (DPM) for tracking particle motion, heat transfer, and a hyperelastic material model (Neo-Hookean material) to describe soft tissue mechanics. The results showed a nonlinear dependence of the deposition efficiency on the flow velocity: with an increase in velocity from 1.41 to 2.82 m/s, deposition increases due to the inertial mechanism, whereas at 4.22 m/s, the efficiency decreases, probably due to increased turbulence. Temperature affects deposition differently: at low velocities, a strong negative correlation was found, while at high velocities, the effect is weakened. Soft tissue deformation increases significantly with velocity and temperature, but has only a moderate effect on particle deposition. The findings highlight the importance of integrating aerodynamics, heat transfer, and biomechanics into the analysis of aerosol transport in the upper respiratory tract. The proposed approach can be used to optimize the delivery of inhaled drugs and develop personalized treatment regimens.

The structure and memory organization of graphics processor units (GPUs) manufactured by NVIDIA and the use of CUDA programming technology to solve computational fluid dynamics (CFD) problems is reviewed and discussed. The potential of using a general-purpose GPU to solve fluid dynamics problems is examined. The code optimization with the utilization of various memory types is considered. Some CFD benchmark problems focused on simulation of viscous incompressible fluid flows are solved on GPUs. Consideration is given to the application of the finite volume method and projection method. Programming implementation of various components of the computational procedure, solution of Poisson equation for pressure and multigrid method to solve the system of algebraic equations, is provided. By using meshes of varying resolutions and different techniques for dividing up the input data into blocks, the speedup of the GPU solution is compared to the CPU approach.

A continuum model for describing pseudo-turbulent flows of a dispersed phase is developed using a statistical approach based on the kinetic equation for the probability density of particle velocity and temperature. The introduction of the probability density function enables a statistical description of the particle ensemble through equations for the first and second moments, replacing the dynamic description of individual particles derived from Langevin-type equations of motion and heat transfer. The lack of detailed dynamic information on individual particle behavior is compensated by a richer statistical characterization of the motion and heat transfer within the particle continuum. A numerical simulation of the unsteady flow of a gas–particle suspension generated by the interaction of a shock wave with a particle cloud is performed using an interpenetrating continua model and equations for the first and second moments of both gas and particles. Numerical methods for solving the two-phase gas dynamics equations—formulated using a two-velocity and two-temperature model—are discussed. Each phase is governed by conservation equations for mass, momentum, and energy, written in a conservative hyperbolic form. These equations are solved using a high-order Godunov-type numerical method, with time discretization performed by a third-order Runge–Kutta scheme. The study analyzes the influence of two-dimensional effects on the formation of shock-wave flow structures and explores the spatial and temporal evolution of particle concentration and other flow parameters. The results enable an estimation of shock wave attenuation by a granular backfill. The extended pressure relaxation region is observed behind the cloud of particles.

The study of the process of laser action on powder materials requires the construction of mathematical models of the interaction of laser radiation with powder particles that take into account the features of energy supply and are applicable in a wide range of beam parameters and properties of the particle material. A model of the interaction of pulsed or pulse-periodic laser radiation with a spherical metal particle is developed. To find the temperature distribution in the particle volume, the non-stationary three-dimensional heat conductivity equation with a source term that takes into account the action of laser radiation is solved. In the plane normal to the direction of propagation of laser radiation, the change in the radiation intensity obeys the Gaussian law. It is possible to take into account changes in the intensity of laser radiation in space due to its absorption by the environment. To accelerate numerical calculations, a computational algorithm is used based on the use of vectorized data structures and parallel implementation of operations on general-purpose graphics accelerators. The features of the software implementation of the method for solving a system of difference equations that arises as a result of finite-volume discretization of the heat conductivity equation with implicit scheme by the iterative method are presented. The model developed describes the heating and melting of a spherical metal particle exposed by multi-pulsed laser radiation. The implementation of the computational algorithm developed is based on the use of vectorized data structures and GPU resources. The model and calculation results are of interest for constructing a two-phase flow model describing the interaction of test particles with laser radiation on the scale of the entire calculation domain. Such a model is implemented using a discrete-trajectory approach to modeling the motion and heat exchange of a dispersed admixture.

This paper presents a model of working processes in the combustion chambers of micro gas turbine engines, taking into account turbulence, combustion, the detailed mechanism of chemical reactions, radiation, swirling flow, and the presence of oil in the fuel mixture. The results of calculations and experiments with the combustion chamber of the JetCat P100-RX engine are presented. Estimates of the addition of oil to fuel for fuel consumption are given.

A computational study is conducted on shock wave propagation and diffraction in an annular duct. The curved geometry and central obstruction of the annular configuration generate complex wave phenomena not typically observed in linear channels. The evolution of incident shock fronts, their interactions with the inner and outer walls, and the resulting diffraction patterns are analysed in detail. Particular focus is placed on the formation of reflected and transmitted waves, as well as the effects of curvature and channel dimensions on shock strength and propagation speed. High-resolution computational fluid dynamics (CFD) simulations are used to capture transient flow features, and results are validated against available experimental data. Simulations are performed across a range of annular geometries with varying radii of curvature and inlet Mach numbers. Simulations across a range of inlet Mach numbers (1.5–3.0) and radii of curvature show that increasing curvature intensifies shock focusing near the inner wall, raising local pressure peaks by up to 20%, while promoting faster attenuation of the transmitted wave downstream. At higher Mach numbers, the reflected shock transitions from regular to Mach reflection, producing triple-point structures. The comparison of shock structures across configurations shows good agreement with experimental observations. The findings enhance understanding of shock dynamics in non-standard geometries and have implications for the design of detonation engines, pulse detonation systems, and safety analyses in confined environments.

The propagation of smoke and hot gases in mechanically ventilated nuclear compartments has been highlighted as one of the main issues of significance. It may lead to the failure of several systems such as clogging of filters located in the ventilation network or electrical devices. To address this issue, the continuous improvement of the predictive capability of existing models with regards to liquid pool fires is of high importance. Computational fluid dynamics (CFD) is widely used for fire simulations. It is worth noting that most pool fire simulations in open atmosphere, under-ventilated and mechanically ventilated compartments have relied on pre-defined/prescribed fuel mass loss rate (MLR) or heat release rates (HRR) from correlations or experimental data when available. Therefore, the prediction of fuel MLR and HRR based on the specific actual fire conditions rather than prescribed data, remains a key development area for the fire community. The present work aims to provide some contribution and advances on this issue. Building on existing liquid evaporation models, the study develops an approach which in then implemented in an in-house version of the CFD code FireFOAM in which a mechanical ventilation model has been embedded, to predict the fuel MLR in both open atmosphere and mechanically ventilated compartments. Validations of the implemented model includes comparison with experimental fuel MLR and previous studies that made use of correlations and experimental data. The results show acceptable fuel MLR predictions with reasonable accuracy and provide further insights into fire behaviour in mechanically ventilated compartments.

The combustion chamber is one of the main components that determine the energy and mass characteristics of the propulsion system. A detailed description of the combustion chambers of some model engines running on kerosene is given. The results of fire tests and numerical studies of combustion chambers of model small-sized gas turbine engines are considered. To qualitatively compare the results of calculations with the data of a physical experiment, annealed colors are used. Based on the results of the research, a map of tem perature distribution on the walls of the combustion chamber was compiled. The internal and external surfaces of the combustion chamber are unevenly colored with tarnished colors. This coloring is a consequence of non-uniform distributions of temperature and concentration of various components of combustion products, and also indicates the formation of a spatial flow in the combustion chamber.

The influence of the preliminary ionization of a combustible mixture and the excitation of its molecules by an electron beam and an external electric field on the intensity of burning of this mixture at diff erent rates of its excitation was considered. Results of calculations of the ignition temperatures of a dry mixture of propane and air as well as of their wet mixture are presented. Recommendations for the exposure of a subsonic flow of such a mixture to an electron beam in an external electric field for increasing the efficiency of burning of the mixture are given.

Numerical modeling of the interaction of a vortex ring with a normally located flat obstacle was performed based on the nonstationary Navier–Stokes equations, for discretization of which the finite volume method was used. A qualitative picture of the change in the structure of a vortex ring during its interaction with the obstacle is presented. The distributions of pressure in time on the obstacle and the change in the longitudinal force acting on the obstacle are determined.

The possibilities of simulation of viscous incompressible fluid flows with lattice Boltzmann method are considered. Unlike the traditional discretization approach based on the use of Navier–Stokes equations, the lattice Boltzmann method uses a mesoscopic model to simulate incompressible fluid flows. Macroscopic parameters of a fluid, such as density and velocity, are expressed through the moments of the discrete probability distribution function. Discretization of the lattice Boltzmann equation is carried out using schemes D2Q9 (two-dimensional case) and D3Q19 (three-dimensional case). To simulate collisions between pseudo-particles, the Bhatnaga r–Gross–Crooke approximation with one relaxation time is used. The specification of initial and boundary conditions (no penetration and no-slip conditions, outflow conditions, periodic conditions) is discussed. The patterns of formation and development of vortical flows in a square cavity and cubic cavities are computed. The results of calculations of flow characteristics in a square and cubic cavity at various Reynolds numbers are compared with data available in the literature and obtained based on the finite difference method and the finite volume method. The dependence of the numerical solution and location of critical points on faces of cubic cavity on the lattice size is studied. Computational time is compared with performance of fine difference and finite volume methods. The developed implementation of the lattice Boltzmann method is of interest for the transition to further modeling non-isothermal and high-speed compressible flows.

The opportunities provided by new information technologies, object-oriented programming tools, and modern operating systems for solving boundary value problems in CFD described by partial differential equations are discussed. An approach to organizing vectorized calculations and implementing finite-difference methods for solving boundary value problems in CFD is considered. Vectorization in CFD problems, eliminating nested loops, is ensured through the appropriate data organization and the use of vectorized operations with arrays. The implementation of numerical algorithms with vectorized mesh structures, including access to internal and boundary mesh cells, is discussed. Specific examples are reported and the implementation of the developed computational algorithms is discussed. Despite the fact that the capabilities of the developed algorithms are illustrated by solving benchmark CFD problems, they enable a relatively simple generalization to more complex problems described by three-dimensional equations.

An approach to modelling the unsteady axisymmetric vortex flows of a gas-dispersed mixture with an incompressible carrier phase is developed. Numerical modelling of formation of a vortex ring, its capture of dispersed particles and particle transfer is carried out, taking into account the influence of the dispersed phase on the vortex structure of the flow. For numerical simulations, the unsteady Navier–Stokes equations for a viscous incompressible fluid are used. The movement of particles is described based on the discrete-trajectory approach of sample particles. The calculation results make it possible to establish the features of the transfer and behavior of particles of different inertia in vortex rings, as well as changes in the characteristics of the vortex ring in the presence of particles of different sizes and concentrations.

A numerical simulation of the gasdynamic processes accompanying the formation and propagation of vortex rings obtained with the use of a piston-type generator has been performed. The formation of a vortex ring, the capture of particles of a disperse admixture by it, and their carry by the ring are considered. The numerical calculations were conducted with the use of nonstationary Navier–Stokes equations, and the movement of particles was defined using the discrete-trajectory method. The distribution of the admixture particles in a vortex ring was determined depending on the conditions of its formation. The influence of the characteristics of a vortex ring on the carry of a passive admixture by it was investigated. The reasons for the qualitative and quantitative differences between the losses of particles in a vortex ring in the path of its movement in different regimes are discussed.

The principles and methods of improvement of thrust, efficiency and cooling of rocket engines for space flight safety are of great interest for aerospace industry. The development of reliable and durable low-thrust rocket engines for space missions seems to be one of the important areas of development of the rocket and space industry. Issues related to the implementation of a new direction related to the design of propulsion systems for orientation systems of upper stages of launch vehicles using environmentally friendly fuel components are considered. A mathematical model is developed and numerical modelling of processes in the combustion chamber of a low-thrust rocket engine with gaseous fuel components (hydrogen and oxygen) is carried out. The model takes into account the presence of a cooling jacket. The mathematical model includes the effects of turbulence, combustion of a gaseous fuel mixture, kinetics of hydrogen combustion, and radiation. As a result of calculations, distributions of flow quantities in the combustion chamber and thermal loads on its walls are obtained. The influence of hydrogen mass flow rate on the efficiency of the working process and the dependence of thrust on hydrogen mass flow rate are discussed. The results of numerical modelling are compared with the data of a physical experiment obtained through fire tests of an engine model made of stainless steel on a three-dimensional printer.

The need to develop models and methods for calculating unsteady gas and fluid flows with concentrated vorticity is determined by the wide distribution of such flows in nature and technology. Numerical simulation of the formation of a vortex ring, its propagation and interaction with a flat target oriented normal to the direction of movement of the ring is considered. The construction of a model of a virtual generator of vortex rings and the choice of a set of parameters describing the generating pulse (pulse duration and its amplitude) are discussed. The computational domain consists of the internal region of the vortex ring generator and the external space region behind its outlet, in which the formation and movement of the vortex ring occurs. For numerical calculations, unsteady Navier–Stokes equations in an axisymmetric formulation are used, for discretization of which the finite volume method is applied. To simulate the flow generated by the movement of the piston in the tube, unsteady boundary conditions are used at the outlet of the generating tube, describing the distribution of mass flow rate over time. The distribution of pressure over the target and the change in the longitudinal force acting on the target over time, as well as the change in the characteristics of the vortex ring during its interaction with the target are given. The results of numerical calculations are compared with the data of a physical experiment. A qualitative pattern of the flow that occurs when a vortex ring approaches a wall is presented, and the key features of the flow and critical points that are formed during the interaction of the vortex ring with the wall are discussed.

The article explores flow behavior around thick airfoils at low Reynolds numbers and the potential application of energy methods to manipulate the flow field for increased lift and reduced drag. The study relies on a set of propulsion airfoils calculated using a combined approach of solving the inverse problem of aerodynamics and applying stochastic global optimization methods. The calculations consider the transition from laminar to turbulent flow regimes, which significantly affects lift and airfoil drag. The suitability of different turbulence models for airfoil modeling in low Reynolds numbers is discussed, and numerical simulation results determine the lift coefficient dependence on angle of attack and the optimal air flow rate taken from the airfoil surface for each angle of attack. The accuracy of different turbulence models is analyzed by comparing numerical simulation results to physical experiment data.

Mathematical and numerical models of the combustion of a fuel mixture in the combustion chamber of a microturbine engine have been developed. Complexity of the models can vary, which gives developers a fairly convenient calculation and design tool. Models allow to take into account the required design tasks by considering and not taking into account various physical processes, and create an optimal complexity model for each specific case. The development of the required configuration begins with the consideration of a simple model of the global kerosene in air combustion reaction without conjugate heat exchange with solids. Step by step, models of extended kinetics, swirling flow, radiation, heat exchange with walls, and the presence of lubricant oil in kerosene are added to the calculation methodology. The results of calculating the wall temperature and combustion completeness were compared with those of JetCat P100-RX and P550-PRO turbojet engines, the integral characteristics of which are well known. In the course of the performed computational and experimental studies, a comparison of the run-off spots on the walls of the combustion chamber with the calculated temperature distributions was performed. A good agreement of the results was obtained for the complete mathematical model. The effect of better cooling of the combustion chamber and increasing the completeness of combustion by twisting the flow behind the compressor is revealed. The effect of the addition of oil to kerosene on an increase in specific fuel consumption by 1–4 % has been determined. The significance of the results obtained lies in the possibility of applying the proposed calculation methodology in engineering practice. The considered modifications of the model represent an important stage in the creation and verification of a mathematical model of in-chamber processes.