Shock-induced ignition of thermally sensitive explosives

The process of planar detonation ignition, induced by a constant-velocitypiston or equivalently by a shock reflected from a stationarywall, is investigated using high-resolution one-dimensionalnumerical simulations. The standard one-step model with Arrheniuskinetics, which models thermally sensitive explosives, is employed.Emphasis is on comparing and contrasting the results of thefinite activation temperature simulations with high activationtemperature asymptotic predictions and previous simulations.During the induction phase, it is shown that the asymptoticresults give qualitatively good predictions. However, for parametersrepresentative of gaseous explosives, subsequent to thermalrunaway at the piston and the formation of a reaction wave,the high activation temperature asymptotic theory is qualitativelyincorrect for moderately high activation temperatures. It isshown that the results are very sensitive to the value of theactivation temperature, especially the distance from the pistonat which a secondary shock forms and the degree of unsteadinessin the reaction wave which moves away from the piston. The dependenceof the ignition evolution on the other parameters (initial shockMach number, heat of reaction and polytropic index) is alsoinvestigated. It is shown that qualitative predictions regardingthe dependence of the ignition evolution on each of the parameterscan be elucidated from finite activation temperature homogeneousexplosion calculations together with the high activation temperatureasymptotic shock ignition results. It is found that for sufficientlystrong initiating shocks the ignition evolution is qualitativelydifferent from cases studied previously in that no secondaryshock forms. For a high polytropic index, corresponding to asimple equation of state model for condensed phase explosives,the results are in much better qualitative agreement with theasymptotic theory.     

Analytical description of the radiative-conductive heat transfer in a gray medium contained between two diffuse parallel plates

Explicit analytical solutions for the temperature and heat flux in a gray medium contained between two diffuse parallel plates are derived for both pure thermal radiation and coupled conduction-radiation heat transfer. This is achieved by combining the integral equations for the heat flux and temperature predicted by the radiative transfer equation with the corresponding predictions of the discrete ordinates method. The algebraic formulation of this well-known method is used to derive analytical results that agree with their corresponding numerical ones with an accuracy greater than 99.9%, for a large interval of optical thicknesses and conduction-to-radiation factors. The explicit and original solutions, for both pure radiation and radiative-conductive heat transfer, therefore solve the problem of one dimensional steady-state heat transfer in gray cavities.     

A simulation code for investigating 2D heating of material bodies by low frequency electric fields

The finite difference method has been used to simultaneously solve in two dimensions Maxwell's equations and the heat transfer equation in forms which are appropriate to modelling low frequency electrical heating of solid materials. The nonlinear coupling of these modelling equations, which is due to temperature dependent electrical conductivities, necessitates the use of an explicit-sequential solution method and the limiting of the timestep size to ensure stability. The finite difference equations were modified to account for sharp electrical conductivity differences between different media in the body being heated.The simulation code was tested by comparison of the simulator predictions with the measured results of a physical scale model experiment. The simulation code was able to accurately predict the resistance between the electrodes used for heating, the energy deposition and the temperature rise in the bulk of the physical model.     

Flow,heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer

In this paper, we investigate the flow, heat and mass transfer of a viscous fluid flow over a stretching sheet by including the blowing effects of mass transfer under high flux conditions. Mass transfer in this work means species transfer and is different from mass transpiration for permeable walls. The new contribution from this work is, for the first time, to consider the coupled blowing effects from massive species transfer on flow, heat, and species transfer for a stretching plate. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy and mass transfer equations are solved exactly and the effects of the blowing parameter, the Schmidt number, and the Prandtl number on the flow, heat and mass transfer are presented and discussed. The solution is given in terms of an incomplete Gamma function. It is found the coupled blowing effects due to mass transfer can have significant influences on velocity profiles, drag, heat flux, as well as temperature and concentration profiles. These solutions provide rare results with closed form analytical expressions and can be used as benchmark problem for numerical code validation.     

CFD modelling of waste heat recovery boiler

A model has been developed of a waste heat recovery boiler utilising typical plant off-gas consisting of both gaseous and particulate combustibles. The model allows the calculation of temperatures of gas and particles within the boiler and hence the likelihood of deposition onto the boiler walls. The model was applied to a typical waste heat boiler geometry, and a typical off-gas composition including a mixture of combustibles (char) and non-combustible particulates. Mixing in the burner region, char burnout and char particle temperature were analysed using the model. Combustion stability was also studied using a simple Eddy break-up model which accounts for combustion kinetics and the results compared with a Mixed-is-burnt model.     

Verification and validation of numerical solutions of two-dimensional reactive flow in rocket engine nozzles

Two-dimensional mathematical models for gaseous H₂/O₂ reactive flows are solved for two geometries: a conical and a parabolic one. Five different physical models are studied: two one-species and three multi-species models (frozen, equilibrium and non-equilibrium flows). In the mathematical model, temperature is used as unknown in the energy equation and velocity is obtained for all speed flows. For all analyses, a non-orthogonal finite volume code was implemented, taking into account first (UDS) and second (CDS) order interpolation schemes and co-located grid arrangement. Model predictions of the pressure distribution and Mach number in the nozzle with a conical geometry, calculated using a CDS scheme, were found to agree well with experimental results. For both geometries, numerical results for apparent orders of convergence agreed well with the asymptotic (expected) ones for one-species flows. Some other analyses were provided for mixture of gases flows; in this case, for frozen flow, the apparent order values tend to the asymptotic ones in all cases; for local equilibrium flow, the use of CDS degenerated the apparent order to unity; this fact can be associated to the use of UDS interpolation scheme in the source term of the energy equation. Numerical solutions, including their error estimates, are provided for UDS and CDS schemes. Their analysis shows that global variables of interest (such as thrust and specific impulse) are less affected by the chosen physical model than are local variables of interest (such as the temperature at the symmetry line).     

Investigation of boundary-value problem for slow flow of a sphere by viscous non-isothermal gas

We obtain a solution to a boundary-value problem of a flow of spherical form particle for stationary system of equations of viscous non-isothermal gaseous medium including the Stokes equation, heat conductivity equation, and state equation with account taken of dependence of viscosity, heat conductivity, and density of gaseous medium on temperature.     

Prediction of risers’ tubes temperature in water tube boilers

A dynamic model is developed which enables the prediction of risers’ tubes temperature of water tube boilers under various operating conditions. The model is composed of fluid dynamics model representing the fluid flow in the drum-downcomer-riser loop and a dynamic thermal model of the riser’s temperature. The model gives a detailed account of the two-phase heat transfer process which takes place between the risers’ inner walls and the water–steam mixture flow inside the tubes. The model is used to simulate various operational scenarios of water tube boilers. Results of the simulation provide insight into the dynamic interactions of the boiler’s main variables including the drum pressure, water volume, steam quality and risers’ temperature. Such a model is useful in checking operational scenarios before their actual plant implementation, can be a basis for developing boiler start up procedures and online temperature predictions to prevent eminent tube overheating.     

Al2O3-47 nm and Al2O3-36 nm characterizations of nonlinear differential equations for biomedical applications: Magnetized peristaltic transport

Current research models the Al₂O₃ 47nm and Al₂O₃ 36nm nanoparticles transportation through peristalsis with entropy optimization. Conservation laws for mass, momentum and energy are used to model the present flow situation. These equations elaborates the magnetohydrodynamics, Hall, thermal radiation, Joule heating, heat generation and absorption. Convective heat transfer impacts are studied at channel walls. Entropy is modeled in view of thermodynamics second law. Two different expressions for effective viscosity are accounted. Simplification of the modeled equations is done through lubrication assumptions. Solution for momentum equation is obtained analytically and for numerically for temperature equation. Built-in shooting procedure is utilized to obtain the desired numerical results. Later on these obtained results are used to sketch and discussed the flow quantities of interest for the influential parameters accounted in the problem.     

Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method

A study of MHD mixed convection flow through porous space in the presence of a temperature dependent heat source in a vertical channel with radiation has been analyzed. The Rosseland approximation is considered in the modeling of the conduction radiation heat transfer and temperatures of the walls are assumed constants. The governing equations are expressed in non-dimensional form and the series solutions of coupled system of equations are constructed for velocity and temperature using homotopy analysis method (HAM). The effects of various involved parameters on the velocity and temperature field are shown and discussed. The coefficient of skin friction, and the rate of heat transfer coefficient are obtained and illustrated graphically.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

A Lagrangian simulation of particle deposition in a turbulent boundary layer in the presence of thermophoresis

Knowledge of particle deposition in turbulent flows is often required in engineering situations. Examples include fouling of turbine blades, plate-out in nuclear reactors and soot deposition. Thus it is important for numerical simulations to be able to predict particle deposition. Particle deposition is often principally determined by the forces acting on the particles in the boundary layer. The particle tracking facility in the CFD code uses the eddy lifetime model to simulate turbulent particle dispersion, no specific boundary layer being modelled. The particle tracking code has been modified to include a boundary layer. The non-dimensional yplus, y⁺, distance of the particle from the wall is determined and then values for the fluid velocity, fluctuating fluid velocity and eddy lifetime appropriate for a turbulent boundary layer used. Predictions including the boundary layer have been compared against experimental data for particle deposition in turbulent pipe flow. The results giving much better agreement. Many engineering problems also involve heat transfer and hence temperature gradients. Thermophoresis is a phenomena by which small particles experience a force in the opposite direction to the temperature gradient. Thus particles will tend to deposit on cold walls and be repulsed by hot walls. The effect of thermophoresis on the deposition of particles can be significant. The modifications of the particle tracking facility have been extended to include the effect of thermophoresis. A preliminary test case involving the deposition of particles in a heated pipe has been simulated. Comparison with experimental data from an extensive experimental programme undertaken at ISPRA, known as STORM (Simplified Tests on Resuspension Mechanisms), has been made.     

A numerical analysis of solid–liquid phase change heat transfer around a horizontal cylinder

A numerical study is conducted to analyze the melting process around a horizontal circular cylinder in the presence of the natural convection in the melt phase. Two boundary conditions are investigated one of constant wall temperature over the surface of the cylinder and the other of constant heat flux. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid–liquid phase change. The validity of the numerical code used is ascertained by comparing our results with previously published results.     

Global solution for a one-dimensional model problem in thermally radiative magnetohydrodynamics

The dynamics of gaseous stars is often described by magnetic fields coupled to self-gravitation and radiation effects. In this paper we consider an initial-boundary value problem for nonlinear planar magnetohydrodynamics (MHD) in the case that the effect of self-gravitation as well as the influence of radiation on the dynamics at high temperature regimes are taken into account. Based on the fundamental local existence results and global-in-time a priori estimates, we establish the global existence of a unique classical solution with large initial data to the initial-boundary value problem under quite general assumptions on the heat conductivity.     

Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation

The effect of thermal radiation with a regular three-parameter perturbation analysis has been studied for the effects in some free convection flows of Newtonian fluid-saturated porous medium. The effects of the thermal radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface, uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source, and, a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge–Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and a heat transfer and total heat and mass convected downstream are presented in a tabular form with the parameters characterizing the radiation, permeability of the porous medium, pressure stress work and viscous dissipation. The obtained results are compared and a representative set is displayed graphically to illustrate the influences of the radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles.     

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T_m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.     

Mixed convective heat and mass transfer in an asymmetric channel with peristalsis

This paper describes the fluid mechanics effects of mixed convective heat and mass transfer in an asymmetric channel with peristalsis. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The momentum, energy and concentration equations have been linearized under long wavelength approximation. The analytical solutions for temperature, concentration, velocity and stream function are obtained. The effects of various parameters such as local temperature Grashof number, local mass Grashof number and geometrical parameters on flow variables have been discussed numerically and explained graphically.     

Transient conduction in a plate with counteracting convection and thermal radiation at the boundaries

During the flash dehydroxylation of powdered kaolinite it is desirable that a rapidly propagating thermal wave penetrates the cold powder particles in a way that raises the particle interior to the reaction temperature of 600°C without the particle exterior being heated beyond 1000°C. In a production unit this is achieved by performing the heat treatment in a device where particles are heated by convection from hot gas and are subject to heat loss by thermal radiation to cool walls. This paper concerns the fundamental heat transfer problem of the process, decoupled from the thermal effects of the dehydroxylation reaction. Using a plate as the approximation for the particle shape a semi-analytical solution for the plate temperature distribution is obtained as a function of the five dimensionless process parameters: Biot number, radiation number, wall/gas and particle/gas temperature ratios and mode of convection. Accuracy is demonstrated by comparison with an existing numerical solution for the limiting case of pure radiative heating of a plate initially at absolute zero.     

转臂式离心机工作室内的瞬态温度求解与分析

考虑大型转臂式离心机圆柱形工作室各墙壁(顶板、底板和侧壁)的瞬态导热,建立各墙壁的瞬态温度控制方程,对控制方程进行Laplace变换并求解,得到了透过墙壁内表面的总热流量与工作室内空气温度的关系.同时,综合考虑离心机驱动系统输出功率与工作室内空气和固体部件吸热、墙壁系统的吸热和导热、出风口带出的热量,以及动能与进风口带入的热量和动能之差等供能与耗能之间的平衡关系,建立工作室内瞬态温度控制方程,导出了工作室内空气瞬态温度的Laplace变换像函数的解析表达式.然后,采用求解Laplace逆变换的展开定理,导出了工作室内空气瞬态温度随时间变化的级数型显式表达式.最后,以一台多用途离心机为例,进行了工作室内空气温度的理论计算,与以前只考虑墙壁稳态导热的理论计算相比,瞬态计算结果与实测结果更加接近.所建瞬态温度公式提高了工作室温度的预测精度,有助于提升大型转臂式离心机工作室温控设计的水平.     

Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface

The present paper is concerned with the study of flow and heat transfer characteristics in the unsteady laminar boundary layer flow of an incompressible viscous fluid over continuously stretching permeable surface in the presence of a non-uniform heat source/sink and thermal radiation. The unsteadiness in the flow and temperature fields is because of the time-dependent stretching velocity and surface temperature. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum and thermal energy are reduced to a system of nonlinear ordinary differential equations containing Prandtl number, non-uniform heat source/sink parameter, thermal radiation and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge–Kutta–Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the unsteadiness parameter, thermal radiation, suction/injection parameter, non-uniform heat source/sink parameter on flow and heat transfer characteristics as well as on the local Nusselt number are shown graphically.