An approximate integral model for the burning rate of a thermoplastic-like material

An approximate integral model is formulated and solved to describe the pyrolysis or burning rate of a thermoplastic-like material. A constant temperature gasification process is assumed to occur at the solid–atmosphere interface. The preheating ignition problem is also solved by a matching integral method. The ignition problem leads to a solution involving a non-linear algebraic equation, but the gasification problem yields an exact solution provided the convective heat transfer coefficient is unaffected by the fuel mass loss or blowing effect. The results are compared to numerical solution in the literature and show good agreement. Comparisons with experimental data for PMMA are limited.     

Approximate estimates of the characteristics of propellant ignition using radiant flux through shields with various properties

An analytical solution to the problem of propellant ignition using radiant flux is presented in a conjugate statement. The solution generalizes and supplements the results obtained earlier. The cases of ignition through absolutely transparent and opaque shields are considered. Approximate formulas for estimation of the time and temperature of the chemical-reaction onset and the time and temperature of the loss of quasi-stationary equilibrium in different limiting cases are obtained. Estimates of the influence of heat transfer into the environment (by the conductive mechanism) on the ignition characteristics are given. A comparison of the ignition characteristics of the propellant and shields is made.Translated from Fizika Goreniya i Vzryva, Vol. 32, No. 1, pp. 26–41, January–February, 1996.     

Thermal-balanced integral model for pyrolysis and ignition of wood

The pyrolysis and ignition of wood is of great importance to understand the initial stage of combustion, helping control the occurrence and spread of unwanted building and forestry fires. The development of a thermal-balanced model is introduced for examining the analytical relationship between the ignition time and external heat flux. The critical heat flux, one of the important fire-retardant characteristics of combustible solid, is determined from a correlation study between the ignition time and external heat flux. One of the thermal-balanced integral models, considering the effect of surface heat losses, average absorptivity and moisture content, is employed to give the prediction of surface temperature rise, ignition time and ignition temperature of the Aspen. The results show that the model readily and satisfactorily predicts ignition temperature and ignition time of wood with different moisture contents.     

恒热流竖壁层流降膜换热特性研究

将能量边界层积分法应用于恒热流竖壁层流降膜热发展段,求得了无量纲热发展段长度和包括热发展段及热定型段的平均换热系数表达式。进行了降膜破裂和换热的实际,理论和实验结果的比较证明本文的理论分析是可行的。     

On the Solution of Non-Isothermal Reaction-Diffusion Model Equations in a Spherical Catalyst by the Modified Adomian Method

We investigate the reactant diffusion within a porous catalytic pellet including the heat of reaction. The Lane–Emden boundary value problem with an Arrhenius reaction rate is used to model the reactant concentration. We combine the Volterra integral form with the Adomian decomposition method to solve the equivalent Fredholm–Volterra integral equation. We then estimate the reactant concentration at the center of the catalytic pellet and the iterated Shanks transform is used to improve the accuracy of the approximations. The objective error analysis formulas are used to demonstrate a high accuracy and rapid rate of convergence, which does not depend on a priori knowledge of the exact solution or comparison with an alternate approximation method. Thus low-stage approximations by the Adomian decomposition method are validated for parametric simulations of the reactant concentration profiles and the effectiveness factor profiles. Our approach demonstrates enhancements over previous investigations, and is readily extensible to more general diffusion reaction models in catalytic reactor engineering.     

On the thermal ignition of combustible materials

Formulas are derived for the time to achieve the ignition temperature as a function of the incident heat flux and the various thermophysical material parameters for thermally thick, thermally thin and thermally intermediate solid combustibles. Predictions are compared with recent experimental data for various natural wood species and wood products, and to previous data for wood and thermoplastics. The correlations are excellent when (1) the physical parameters used as the axes of the plots are chosen consistent with those of the theoretical formulas and (2) the experiments and the materials do not violate any of the restrictions imposed by the theory. From these plots it is easy to estimate the minimum heat flux for ignition, which is of great importance both in practice and for making theoretical predictions.     

Flammability characteristics at applied heat flux levels up to 200 kW/m2

This paper documents the first of the two interrelated studies that were conducted to more fundamentally understand the scalability of flame heat flux, the motivation being that it has been reported that flame heat flux back to the burning surface in bench‐scale experiments is not the same as for large‐scale fires. The key aspect was the use of real scale applied heat flux up to 200kW/m² which is well beyond that typically considered in contemporary testing. The main conclusions are that decomposition kinetics needs to be included in the study of ignition and the energy balance for steady burning is too simplistic to represent the physics occurring. An unexpected non‐linear trend is observed in the typical plotting methods currently used in fire protection engineering for ignition and mass loss flux data for several materials tested and this non‐linearity is a true material response. Using measured temperature profiles in the condensed phase shows that viewing ignition as an inert material process is inaccurate at predicting the surface temperature at higher heat fluxes. The steady burning temperature profiles appear to be invariant with applied heat flux. This possible inaccuracy was investigated by obtaining the heat of gasification via the ‘typical technique’ using the mass loss flux data and comparing it to the commonly considered ‘fundamental’ value obtained from differential scanning calorimetry measurements. This comparison suggests that the ‘typical technique’ energy balance is too simplified to represent the physics occurring for any range of applied heat flux. Observed bubbling and melting phenomena provide a possible direction of study. Copyright © 2007 John Wiley & Sons, Ltd.     

Ignition of a Solid Through a Detachable Shield

The problem of ignition of a solid by heat flux through a detachable shield is analyzed in a simple formulation. An approximate analytical solution of the problem is obtained, which shows that the dependence of the ignition time of the solid (with gaseous reaction products) becomes nonmonotonic if the thickness of the shield is small. Qualitative conclusions agree with numerical results.     

Extension and evaluation of the integral model for transient pyrolysis of charring materials

In most numerical simulations of fire growth and fire spread, pyrolysis models are required to calculate the reaction of the solid material to an incident heat flux. Important results of the pyrolysis model are the mass release rate of combustible pyrolysis gases and the surface temperature. In this paper an integral model is evaluated for the prediction of pyrolysis of charring materials. An existing integral model is extended with a finite and semi‐infinite cooling state. In this state both char and virgin material are present but the pyrolysis reactions have been interrupted due to insufficient heat supply. The results show that such a cooling state can occur in flame spread calculations. Simulations with the integral model are further compared with the results of a moving grid model, which has the same physical basis. Unlike the integral model, the moving grid model does not require any assumption for the temperature profile in the solid. The influence of the quadratic assumed temperature profile in the integral model on the accuracy of the predictions of the mass release rate of pyrolysis gases is evaluated for several cases. It is shown that the integral model has problems with sudden variations of the external heat flux. Copyright © 2005 John Wiley & Sons, Ltd.     

Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.     

New formula for calculating time to ignition of semi‐infinite solids

An analytical closed form formula is presented for explicitly calculating time to reach ignition temperature of semi‐infinite solids exposed to constant incident radiation and gas temperature as for example in the cone calorimeter. The non‐linear boundary condition due to the emitted radiation from the surface being proportional to the surface temperature raised to the fourth power according to the Stephan–Boltzmann law is accurately considered. The formula works for a wide range of the parameter values like the thermal inertia of the solid, the emissivity of the exposed surface and the convective heat transfer coefficient. They are all assumed constant. The new formula contains a single constant coefficient, which has been derived by comparing results obtained by accurate numerical finite element simulations using two different codes, comsol and TASEF , as well as calculations based on a Duhamel superposition scheme. Thus, the formula can be classified as semi‐empirical. It offers a simple approximate solution of a non‐linear problem that requires cumbersome numerical calculation methods to obtain more exact results. Any exact analytical solution is not available. The new method is carefully verified by comparisons with numerical solutions. However, as it is an analysis of well‐defined theoretical methods, any validation and comparisons with test data are not required and has therefore not been made.In comparison with other similar approximation formulas found in the literature, the accuracy as well as simplicity of applying the new formula is outstanding. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability and interval selection in the numerical integration of the equations describing ignition in a turbulent flow

An analysis is carried out of the stability of a linearized system of telegraphic equations, proposed as a model for studying the ignition of gas mixtures containing toxic components (methyl mercaptan etc.). The ignition is assumed to be related to the set of aerodynamic and kinetic parameters at which the system begins to be unstable. An analysis of the spectrum of growing disturbances indicates that their short-period part cannot be described sufficiently accurately using the difference methods of second-order accuracy usually applied in numerical studies. Instead a difference method correct to terms of fourth order must be used. The proposed method provides an efficient determination of the intervals of the time and space coordinates as functions of the main turbulent and kinetic parameters for the solution of ignition problems.St. Petersburg. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 3, pp. 85–88, May–June, 1993.     

Numerical simulation of transients in the ignition of two-component propellants by intense heat fluxes

An ignition model is developed for quasi-homogeneous propellants consisting of two perfectly mixed compnents which decompose independently in the condensed phase and then react in the gas phase. The model describes the heat propagation in the condensed and gas phases as well as the diffusion of components in the gas phase. The transition processes from ignition to self-sustaining combustion under pulsed irradiation are studied numerically for the simplest case of a monopropellant. It is shown that the critical value of heat flux for stable ignition of monopropellant and the shape of the stable ignition peninsula in the exposure time-heat flux coordinates depend on the extinction criterion.Tomsk. Novosibirsk. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 3, pp. 16–20, May–June, 1993.     

Flame spread measurements on wood products using the ASTM E 1321 LIFT apparatus and a reduced scale adaptation of the cone calorimeter

Flame spread experiments were conducted in an ASTM E 1321 lateral ignition and flame transport (LIFT) apparatus and a reduced scale ignition and flame spread test (RIFT) adaptation of the cone calorimeter. Wood‐based products were tested and a flame spread model was applied to the results to obtain the flame spread parameter and the minimum heat flux required for flame spread. The materials used were plywood, medium density fibreboard, hardboard, two‐particle board products, Melamine (Melteca) covered products with two types of wood substrate along with New Zealand grown Rimu, Beech, Macrocarpa and Radiata Pine. The RIFT gave comparable results to the LIFT for several of the materials investigated. There appeared to be an effective limit on suitable materials that can be successfully tested in the RIFT to those that have a minimum flux for flame spread of less than 7kW/m². This limitation was due to the rapid decay of the heat flux profile along the sample and the lower resolution dictated by the smaller size of the RIFT apparatus. It was found that the limit on the minimum heat flux for flame spread was approximately equivalent to a minimum ignition flux of 18kW/m². Copyright © 2009 John Wiley & Sons, Ltd.     

Calculation of ignition parameters and the transition to combustion in a heterogeneous system

A model for ignition of a heterogeneous condensed system by a pulsed heat flux is studied. Pyrolysis of condensed components and ignition of the pyrolysis products in the gaseous phase are assumed. The dependences of various ignition characteristics on the external parameters are studied. The conditions for stable ignition of a heterogeneous system are investigated. The region of stable transition to self-sustained combustion after removal of the external heat flux is calculated.Tomsk. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 3, pp. 124–129, May–June, 1993.     

Analysis of laminar flow forced convection heat transfer with uniform heating in the entrance region of a circular tube

A new integral or boundary-layer solution for laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux. The solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to hydrodynamically developing flow through a circular tube. Unlike available boundary-layer solutions, the new analysis provides results which join smoothly and asymptotically to the fully developed values. Results for the Nusselt number were found to agree favorably with available numerical solutions.     

Mathematical Model of Ignition of Condensed Systems by a High-Temperature Supersonic Underexpanded Jet

An approximate mathematical model is constructed and characteristics are calculated of ignition of a reactive plane infinite obstacle by a high-temperature nonstationary axisymmetric supersonic jet of combustion products escaping from the igniter. The approximate model data are compared with the results of numerical calculations using the system of equations of motion of an ideal gas, nonstationary equations of heat conduction and chemical kinetics, and conditions of conjugate heat exchange at the gas–condensed medium interface. The suggested approximate model adequately describes the ignition process and can be used for proximate evaluation of ignition time and temperature. Key words: ignition, jet, gas dynamics, supersonic flow, mathematical simulation.     

Modification of Thermal Theories to Solid Propellant Ignitibility

The conventional thermal theories are inventively modified for analyzing the ignition behaviors of solid propellants. Based on the modification of the thermal theory with the boundary condition of constant heat flux, the effects of heat flux, pressure, threshold of heat flux and absorbability on the radiant ignition of solid propellant are elaborated. The innovations of theoretical analyses are consistent with most of experimental results depicted in literatures. That the increase of hot gas velocity increases the ignition time of solid propellant is verified to be attributable to the decrease of hot gas temperature, ascertaining insight of the thermal theory with the boundary condition of flowing hot gas. In addition, a tentative estimation of pressurization rate effect on ignition time of solid propellant is proposed.     

液态金属钠在环管进口段湍流换热研究

对等热流密度边界条件下的进口效应进行了研究.推导出可借助有限差分法求解的微分-积分方程组,编制了计算机计算程序,并根据计算结果拟合出湍流放热计算关系式.实验采用环管内径为12.34mm,外径为19.00mm,通道外壁绝热,内壁为恒热流.研究结果表明,理论和实验结果与其他研究结果吻合良好.本研究参数范围:Re=2×10~4～1.35×10~5,Pe=128～854.