The paper presents the results of numerical simulation of heat exchange during cooling of a heated metal cylinder by a laminar gas–liquid flow in a vertical annular channel. The results were obtained based on a mathematical model of conjugate heat exchange between a gas–liquid flow and a metal cylinder in a two-dimensional nonstationary formulation that takes into account the axisymmetry of the ascending flow of the cooling medium relative to the longitudinal axis of the cylinder. The control volume method was used to solve the system of differential equations. The flow field parameters were calculated using the SIMPLE algorithm. The Gauss–Seidel method with lower relaxation was used for the iterative solution of systems of linear algebraic equations. The heat exchange parameters were obtained for cooling a high-temperature metal cylinder by a gas–liquid flow taking into account vaporization. The dynamics of changes in the structural-phase transformations of the cylinder material depending on the cooling rate is analyzed.

This paper presents a study of flammability and downward flame spread rate in an opposed oxidizer flow over glass fiber-reinforced epoxy resin (GFRER) with the added flame retardants 6,6 '-((methylenebis(4,1-phenylene))bis(azanediyl)) bis(6 H-dibenzo[c,e][1,2]oxaphosphinine 6-oxide) (DDM-DOPO) and graphene and with a binder content (BC) of similar to 35 wt% and similar to 52 wt%; the mass ratio of the glass fiber to the binder in the composite was 2:1 and 1:1, respectively. To evaluate the flammability and thermal stability of the obtained materials, the LOI test, the UL-94HB test, and thermogravimetric analysis were conducted. The effective DDM-DOPO concentration for decreasing the flammability of GFRER was found based on the LOI results. During the flame spread experiment with an opposed oxidizer flow, the addition of flame retardants resulted in an increase in the limiting oxygen concentration (LOC). Oxygen concentration increase in the oxidizer flow led to a decrease in the flame retardant effect on the rate of flame spread (ROS) for samples with a BC of similar to 35 wt%. The flame retardant effectiveness for samples with a BC of similar to 52 wt% remained almost the same at 40-60 vol% O-2 concentrations. The relationship among the LOI, LOC, and ROS was experimentally established. A numerical simulation of flame spread over reinforced material was performed using a coupled gas-solid heat and mass transfer model to predict the ROS over GFRER with and without flame retardants. The model correctly predicted the ROS for GFRER with similar to 35 wt% BC, while for samples with similar to 52 wt% BC, the model gave lower ROS compared to experiment.

The findings of this research have implications for fire safety engineering and risk assessment. A more accurate understanding of the flame behavior can lead to the development of improved fire detection and suppression systems. Furthermore, the numerical modeling approach can be extended to investigate a wide range of fire scenarios providing valuable data for the validation and refinement of fire models. This work presents a numerical study of turbulent diffusion flames on a vertical polymethyl methacrylate (PMMA) surface using the Fire Dynamics Simulator (FDS) employing LES method for turbulent transfer. LES method is used with Deardoff model for subgrid-scale viscosity; reactant concentrations are determined using the generalized reaction coordinate within the framework of the Eddy Dissipation Concept (EDC) model. Methylmethacrylate (product of PMMA pyrolysis) is assigned as the gaseous fuel component of gas-phase combustion reaction with corresponding values of molar weight and heat release. Series of numerical experiments were performed for different heights of the burning surface (5 cm, 20 cm, 50 cm, and 1 m) to investigate the flame height dependence on the pyrolysis zone size. Based on the calculated temperature fields, the flame height dependence on the pyrolysis zone size on the vertical surface was determined. The results of the simulations demonstrated good agreement with existing experimental and theoretical data.

A mixture fraction approach was applied to predict the combustion behavior of polymeric materials. In comparison to the combustion of gaseous mixtures, the presence of solid fuels complicates the description of the combustion. Accurate predictions of burning characteristics can only be achieved through the proper resolution of heat and mass transfer between the gas-phase flame and the solid fuel. We focused on a model case of flame spread over a solid fuel surface. Polymethyl methacrylate (PMMA) was selected as a polymeric material. An approach was proposed to account for heat loss from the gas phase to the solid material through calculations of counterflow diffusion flames with the flame positioned closely to the fuel supply. A combination of these solutions was applied to restore temperature and species mass fractions from tabulated chemistry. An analysis of the numerical results from previous studies on flame spread over PMMA, based on one-step combustion reaction and calculating the chemical source term at each time step, demonstrated a monotonic distribution of the mixture fraction in the flame region between the fuel and oxidizer streams. The shape of the flame tip was satisfactorily resolved using the proposed approach that employs a skeletal chemical mechanism for gas-phase combustion consisting of 29 species and 33 reactions. However, the heat flux from the flame to the solid fuel was overpredicted, resulting in higher flame spread rates compared to experimental data and previous calculations. Preliminary results show a promising opportunity for the mixture fraction approach to describe the combustion behavior of polymers. An analysis showed that oversimplifying the heat transfer process in the flame tip area is a main source of prediction inaccuracies. Multidimensional heat transfer has to be properly incorporated into a tabulated chemistry approach. Several potential directions for future work have been outlined.

The paper presents the mathematical model, numerical algorithm and results of parametric study for the parameters of multi-nozzle solid propellant propulsion supplied with the stepper regulators of mass flow rate.

The flammability of various materials used in industry is an important issue in the modern world. This work is devoted to the study of the effect of flame retardants, graphene and DDM-DOPO (9,10-dihydro-9-oxa-10-phosphaphenanthrene-10-oxide-4,4′-diamino-diphenyl methane), on the flammability of glass-fiber-reinforced epoxy resin (GFRER). Samples were made without additives and with additives of fire retardants: graphene and DDM-DOPO in various proportions. To study the flammability of the samples, standard flammability tests were carried out, such as thermogravimetric analysis, the limiting oxygen index (LOI) test, and cone calorimetry. In addition, in order to test the effectiveness of fire retardants under real fire conditions, for the first time, the thermal structure of downward flame propagation over GFRER composites was measured using thin thermocouples. For the first time, the measured thermal structure of the flame was compared with the results of numerical simulations of flame propagation over GFRER.

The flame spread over a non-planar surface of solid fuel has been studied numerically by the coupled model of heat transfer using the proposed approach for the evaluation of burning surface regression. The boundary conditions for the surface regression rate are formulated by the combination of flame spread modes over the vertical and horizontal surfaces resulted from the staircase shape of the burning surface. Numerical results showed a good agreement with the experiment on surface regression profile and mass loss of PMMA solid fuel.

The flow of gas in a solid-fuel rocket engine is determined by the peculiarities of the physico-chemical processes occurring in the combustion chamber and the process of gas outflow from the nozzle. The paper proposes a method for modeling internal unsteady turbulent flows in a rocket engine with a solid fuel charge of a telescopic type. A system of defining equations written in a cylindrical coordinate system describing the flow of a compressible viscous gas is given. A computational algorithm is proposed that belongs to the class of methods using the Godunov approach, developed on the basis of a modified flow vector splitting scheme. The obtained results of a numerical study of the flow in a model rocket engine show the dependence of the gas temperature on the engine wall on the combustion rate of a low-temperature external charge of a telescopic charge.

Axisymmetric direct numerical simulation (DNS) has been carried out to predict supersonic base flow behavior. Substantially fine grid has been used to perform calculations for the flow with Reynolds number up to 106. Optimal grid resolution was established through test calculations for affordable run time and solution convergence determined by the vorticity value. Numerical scheme provides fourth-order approximation for dissipative, fifth-order for convective and second-order for unsteady terms of conservation equations. Reynolds Averaged Navier-Stokes (RANS) approach has been employed to obtain input flow profiles for DNS calculations. Series of calculations have been carried out for Mach number 1.5 with Reynolds numbers 104, 105, 106 and for Mach number 2.46 with Reynolds number 1.65 center dot 106. It has been found that local base pressure coefficient calculated by DNS is a bit overestimated in a zone close to symmetry axis in comparison with experiment while integrated base drag coefficient shows good agreement with experimental data and noticeably better than one obtained by RANS approach.

In the present review, using an integrated approach based on the experimental and theoretical study of the processes of thermal decomposition and combustion of practically important polymers, such as polymethyl methacrylate, polyethylene, and glass-fiber-reinforced epoxy resin, the features of the mechanism for reducing the combustibility of these materials with phosphorus-containing flame-retardants (FR), as well as graphene, are identified. A set of original experimental methods was developed and applied that make it possible to study the kinetics of thermal decomposition and the thermal and chemical structure of the flames of the studied materials, including those with FR additives, as well as to measure the flame propagation velocity, the mass burning rate, and the heat fluxes from the flame on the surface of a material. Numerical models were developed and tested to describe the key parameters of the flames of the studied polymeric materials. An analysis of the experimental and numerical simulation data presented showed that the main effect of phosphorus-containing fire-retardants on reducing the combustibility of these materials is associated with the inhibition of combustion processes in the gas phase, and the effect of adding graphene manifests itself in both gas and condensed phases.

For the first time, a comprehensive study of downward flame spread over glass-fiber-reinforced epoxy resin (GFRER) slabs in oxidizer flow has been carried out experimentally and numerically. Microthermocouples were used to measure the temperature profiles on the solid fuel’s surface and in the flame, and a video camera was used to measure the rate of flame spread (ROS). The ROS was found to be linearly dependent on the oxygen concentration, to be inversely proportional to the slab thickness and not to depend on the direction of the flame spread over the slab. The absence of the influence of the forced oxidizing flow velocity and the weak influence of the GFRER pyrolysis kinetics on the ROS were observed. For the first time, a numerical model of flame spread over reinforced material with thermal conductivity anisotropy was developed on the basis of a coupled ‘gas–solid’ heat and mass transfer model, using modifications of the OpenFOAM open-source code. The sensitivity analysis of the model showed that the thermal conductivity in the normal direction to the GFRER surface had a much greater effect on the ROS than the thermal conductivity along the direction of flame propagation. The numerical results show good agreement with the experimental data on the dependences of the ROS on oxygen concentration, slab thickness and the N2/O2 mixture flow velocity, as well as temperature distributions on the fuel surface, the maximum flame temperatures and the flame zone length.

For the first time, next to the flammability tests (LOI, UL-94 HB, VBB, TGA), experimental tests and computer simulation have been conducted on the flame spread and combustion of glass fiber-reinforced epoxy resins (GFRER) with 6% graphene and 6% DDM-DOPO flame-retardant additives. The downward rates of flame spread (ROS) in opposed flow with oxidizer and the upward ROS along GFRER composites have been first measured as well as the distribution of temperature over the combustion surface of the composites with flame-retardant additives and without them. The LOI and UL-94 HB tests showed a reduction in the flammability of GFRER when flame retardants were added and predicted a higher effectiveness of DDM-DOPO compared to graphene. Adding DDM-DOPO resulted in increasing the rate of formation of the volatile pyrolysis products and their yield, indicating, together with the other data obtained, the gas phase mechanism of the flame retardant’s action. Adding graphene resulted in an increase in the soot release on the burning surface and an increase in the amount of non-volatile pyrolysis products on the burning surface, reducing the amount of fuel that participated in the oxidation reactions in the gas phase. The developed numerical combustion model for GFRER with a DDM-DOPO additive, based on the action of DDM-DOPO as a flame retardant acting in the gas phase, satisfactorily predicts the effect of this flame retardant on the reduction in downward ROS over GFRER for 45–50% oxygen concentrations. The developed model for GFRER with graphene additive, based on a reduction in the amount of fuel and increase in the amount of incombustible volatile pyrolysis products when graphene is added, predicts with good accuracy downward ROS over GFRER depending on oxygen concentration.

Numerical algorithm for the prediction of the stationary flame propagation velocity over premixed gas mixture has been formulated by using the foundations of non-equilibrium thermodynamics. Considering the combustion as a set of irreversible processes, the steady-state regime of flame propagation is identified with the stationary state of the non-equilibrium thermodynamic system. The generalized form of functional has been stated allowing its minimization relatively to the sought stationary flame propagation velocity treated as additional variable. Based on this variational statement an integral relationship for the flame propagation velocity has been obtained. The calculations of the stationary flame propagation velocity over model premixed gas mixture performed by proposed algorithm showed a faster convergence at the initial steps of iteration process in comparison with the commonly used approach based on the mass conservation of combustion chemical traction. The combined algorithm has been formulated, which benefits from the proposed 'thermodynamic' approach at the initial steps and converges to final solution satisfying the general mass balance.

Аннотация.Проводится численное исследование параметров турбулентного диффузионного пламени на поверхности твердого горючего материла.Расчеты проведены с использованием пакета с открытым кодом Fire Dynamic Simulator (FDS), использующего подход LES для моделирования турбулентного переноса.В качестве газообразного горючего принят метилметакрилат (как продукт пиролиза ПММА) с соответствующими значениями молярной массы и теплоты реакции горения.По полученным распределениям мгновенных значений температуры определена высота от поверхности горения твердого материала, на которой происходит формирование турбулентных вихревых структур

The effect of triphenyl phosphate (TPP) retardant inhibition on flame propagation over the horizontal surface of polymethyl methacrylate (PMMA) has been studied experimentally and numerically. Regarding the flame spread behavior over the surface of PMMA (pure and inhibited by TPP), the following parameters were measured: thermal decomposition with TG / DTG analyzer, the flame spread rate, the pyrolysis zone length, the mass loss rate and spatial distribution of temperature by thermocouples and species concentration in the gas-phase flame by probing mass spectrometry. The previously developed coupled heat and mass transfer mathematical model describing the feedback interaction between flame and solid fuel, as well as volatilization of pyrolysis products, was modified to resolve the effect of TPP on flame spread by introducing the correcting factor of the gas-phase combustion reaction rate relating to the inhibitor concentration in the solid material. Good agreement between the measured and calculated flame spread parameters (flame spread velocity, mass burn-out rate, pyrolysis zone length), as well as a detailed flame structure (gas phase temperature and species concentration), has been obtained for pure PMMA and PMMA+10%TPP. It has been shown that the proposed approach describes a satisfactory retardant effect of TPP on the flame spread over PMMA surface by inhibiting the gas-phase combustion reaction.

Numerical modeling of the spatial gas flow in an adjustable nozzle with an asymmetric critical section caused by the overlap of a part of the flow area by a gas flow regulator has been carried out. The mathematical model is based on three-dimensional models of gas dynamics, the method of large particles is used for calculation. When describing the unsteady flow of an inviscid gas, the system of Euler equations is used, written for a computational rectangular plane, taking into account the function of nozzle geometry. The results of calculations of flow parameters along a nozzle path with a uniform outlet section and with an obliquely cut outlet nozzle are presented. Calculations were carried out for completely open critical sections and for half overlapped. For oblique cut nozzles, the overlap of the critical section from the side of the short part and from the side of the long part of the oblique nozzle is considered.

Аннотация.Проведено численное исследование распространения ламинарного диффузионного пламени по поверхности образцов

A mathematical model of conjugate heat transfer during the laminar movement of oil fluid in the well is proposed. The motion of a gas-liquid medium in a two-dimensional axisymmetric stationary formulation is described by the equations of the boundary layer. A case of well operation in which oil is lifted to the surface due to reservoir energyis considered. A three-component medium is presented as a mixture of two components: formation of oil with dissolved gas and formation of water. The results of numerical modeling are presented, which make it possible to analyze the thermobaric state of the well under the condition of the developing flow in the pipe at the initial stage of stabilization and taking into account the phase transition associated with the formation of paraffin deposits.

A comprehensive study of thermal decomposition and combustion of a horizontally placed polyoxymethylene (POM) slab was performed. The kinetic parameters of thermal degradation of POM in supposition of two parallel reactions were determined and were used for simulation of the flame spread over the POM. The following main characteristics of the POM slab's combustion were measured: the flame spread rate, the slab's mass loss rate, the width of the pyrolysis zone, the flame height, the temperature profile of the upper and lower surfaces of the slab, the temperature field and the fields of the main flame species concentrations over the burning slab, and the conductive heat flux from the flame onto the fuel surface. It was concluded from analysis of experimental data that two global gas phase reactions may be identified: the reaction of formaldehyde pyrolysis with light combustible gas formed (with the properties close to those of СО) and the subsequent reaction of its oxidation in the flame to the end combustion products (СО2+H2O). This approach was implemented as the coupled combustion model was modified, taking into account a two-step reaction in the gas phase. The results of the calculations made showed good agreement with the experimental data.

Introduction. Polymer materials are widely used, however the actual object is to provide polymers combustion ­model to predict their behavior under fire, and reducing flammability. The work is devoted to the experimental ­study and numerical simulation of flame propagation over the surface of horizontally and vertically placed slabs of polymer in still air. Methods. The object of the investigation was cast polymethylmethacrylate (PMMA). The experiment was focused on measurement of the spatial distributions of the temperature and species concentrations of the PMMA pyrolysis and combustion products in the gas-phase over the surface of PMMA. Temperature was measured by micro­thermocouple with diameter of 50 microns. Probe mass-spectrometry was used for the measurement of the spa­tial distribution of species concentrations in the flame. Results and discussion. The main species (mehylmethacrylate (MMA), O2, CO2, H2O, N2, C2H4 (ethylene), C3H6 (propylene)) were identified and their concentration profiles were measured on the different distance from the flame front. The chemical structure of the flame was established to be in good agreement with the thermal one. The size of the “dark zone” of the flame, in which the temperature near the surface of the polymer is minimal, correlated well with the size of the oxygen-free zone. The mass burning rate, the velocity of flame propagation, the width of the pyrolysis zone and the temperature distribution in the condensed phase were also measured. Based on the experimental results, densities of conductive and radiation heat fluxes from the flame to the fuel surface were deter­mined. Calcula­tion of the radiation heat flux density was carried out under the assumption of an optically thin ­model. Modeling of the horizontal flame propagation over the PMMA surface was carried out using a two-dimen­sional conjugated laminar combustion model that takes into account one-step reactions — the decomposition reaction of PMMA in the condensed phase and the oxidation of decomposition products in the gas phase. Modeling of the vertical flame propagation over the PMMA surface was carried out using economical model of FDS. Conclusion. The model was shown to describe satisfactorily the experimental data such as the mass burning rate, flame propagation velocity, as well as the temperature distribution and concentration of species near the flame front.