Transient modelling of flow distribution in automotive catalytic converters

The transient catalytic converter performance is governed by complex interactions between exhaust gas flow and the monolithic structure of the catalytic converter. Therefore, during typical operating conditions of interest, one has to take into account the effect of the inlet diffuser on the flow field at the entrance. Computational fluid dynamics (CFD) is a powerful tool for calculating the flow field inside the catalytic converter. Radial velocity profiles, obtained by a commercial CFD code, present very good agreement with respective experimental results published in the literature. However the applicability of CFD for transient simulations is limited by the high CPU demands.The present study proposes an alternative computational method for the prediction of transient flow fields in axi-symmetric converters time-efficiently. The method is based on the use of equivalent flow resistances to simulate the flow paths in the inlet and outlet catalyst sections. The proposed flow resistance modelling (FRM) method is validated against the results of CFD predictions over a wide range of operating conditions. Apart from the apparent CPU advantages, the proposed methodology can be readily coupled with already available transient models for the chemical reactions in the catalyst. A transient model for heat transfer inside the monolith is presented. An example of coupling between FRM and transient heat transfer inside the converter is included. This example illustrates the effect of flow distribution in the thermal response of a catalytic converter, during the critical phase of catalytic converter warm-up.     

Similarity solutions for magneto-forced-unsteady free convective laminar boundary-layer flow

The group theoretic method is applied for solving problem of a unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical plate under the effect of an external velocity and a magnetic field normal to the plate. The application of two-parameter transformation group reduces the number of independent variables, by two, and consequently the system of governing partial differential equations with the boundary and initial conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. The Runge–Kutta shooting method used to find the numerical solution of the velocity field, shear stress, heat transfer and heat flux has been obtained. The effect of the magnetic field on the velocity field and the Prandtl number on the heat transfer and heat flux has been discussed.     

Development and experimental validation of a control-oriented Diesel engine model for fuel consumption and brake torque predictions

This article describes the development and experimental validation of a control-oriented, real-time capable, Diesel engine instantaneous fuel consumption and brake torque model under warmed-up conditions with only two inputs: torque request and the engine speed and no other measurements. Such a model, with the capability of reliably and computationally efficiently estimating the aforementioned variables at both steady-state and transient engine-operating conditions, can be utilized in the context of real-time control and optimization of hybrid power train systems. Although Diesel engine dynamics are highly non-linear and very complex, by considering the Diesel engine and its control system, that is, engine control unit together as an entity, it becomes possible to predict the engine instantaneous fuel consumption and torque based on only those two inputs. A synergy between different modelling methodologies including physically based grey-box and data-driven black-box approaches were integrated in the Diesel engine model. The fuelling and torque predictions have been validated by means of experimental data from a medium-duty Diesel engine at both steady-state and transient operations, including engine start-ups and shutdowns.     

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.     

A method and a computer program for determining the thermal diffusivity in a solid slab

The authors describe a method for computing the thermal diffusivity of a solid, based on a computer assisted evaluation of the solution of the transient inverse heat conduction problem.The program computes either the unknown diffusivity or simulates the one-dimensional unsteady heat transfer problem. The user may model the boundary conditions by a choice of different functions.The program provides instruction and information at all stages of input and provides tabular output of results. It may be used by anybody wishing to solve or simulate heat transfer processes.     

Normalized Dynamic Characterization and Application of Multiple Heat Storage Materials Based on Standard Thermal Resistance北大核心CSCD

基于标准热阻和能量流法,推导出储热材料与换热流体的瞬态换热热阻,通过类比电路分析法,获得了储热-换热过程的瞬态热量流模型及动态响应时间常数。进一步引入节点温度,重新定义换热热阻,获得了储热与换热过程耦合的三阶电路瞬态热量流模型,求解得到了加热、储热和释热三类时间常数,可用于协同表征储热材料中储热与释热的快慢程度,从而实现了多类储热材料的归一化动态表征。通过数值模拟验证与应用对比分析,发现基于多时间常数的归一化动态模型用于表征储热材料的动态特性是可行的,可直接对不同换热、储热材料进行对比分析。案例分析发现与固体储热材料换热时,液态金属的动态换热能力优于熔融盐,而相比于水蒸气和CO₂,空气与陶瓷材料换热能更快达到稳态。     

Implementation of EOQ and Lambert W function in 1-D engine simulation model for optimizing fuel injection in GDI engine

The aim of this study was to implement Economic Order Quantity method (EOQ) together with the Lambert W function in a 1-D engine simulation model in order to develop a fuel control strategy for a Gasoline direct injection (GDI) engine. Previous work of the co-author demonstrated the possibility of optimizing fuel injection quantity in GDI engine using the EOQ that is commonly used in supply chain of perishable products. This work extends the previous work and implements it in a 1-D, crank angle resolved, engine simulation model for the application of model based calibration process. The present work uses a validated engine simulation model, which is based on predictive combustion modelling approach, and couples the 1-D engine simulation model with SIMULINK to add the evaporation, wall- wetting and heat transfer models. It employs FORTRAN subroutines to modify the internal code of the 1-D simulation software in order to add crank angle resolved evaporation model. Finally, EOQ with Lambert W function was added to the model using MATLAB with special attention to the decimal control for the solution. This study demonstrated that EOQ and Lambert W functions together are a suitable method to develop fuel control strategy for a model based calibration procedure when implemented in crank angle resolved 1-D simulation model.     

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.     

CFD predictions for cement kilns including flame modelling,heat transfer and clinker chemistry

Clinker formation in coal-fired rotary cement kilns under realistic operation conditions has been modelled with a commercial axisymmetric CFD code for the gaseous phase including a Monte Carlo method for radiation, a finite-volume code for the energy equation in the kiln walls, and a novel code for the species and energy conservation equations, including chemical reactions, for the clinker. An iterative procedure between the predictions for the temperature field of the gaseous phase, the radiative heat flux to the walls, and the kiln and clinker temperature is used to predict the distribution of the inner wall temperature explicitly, including the calculation of heat flow to the clinker. It was found that the dominant mode of heat transfer between the gas and the kiln walls is by radiation and that the heat lost through the refractories to the environment is about 10% of the heat input and a further 40% is used for charge heating and clinker formation. The predictions are consistent with trends based on experience and limited measurements in a full-scale cement kiln.     

Nonlinear thermoelastic analysis of layered structures

The nonlinear thermoelastic behavior of orthotropic layered slabs and cylinders including radiation boundaries, temperature-dependent material properties, and stress-dependent layer interface conditions is investigated. A one-dimensional finite element formulation employing quadratic layer and linear interface elements is used to perform the analyses. The transient heat conduction portion of the program is temporally discretized via an implicit linear time interpolation algorithm which includes Crank-Nicolson, Galerkin, and Euler backward differencing. The nonlinear heat conduction equations are iteratively evaluated using a modified Newton-Raphson scheme. Direct iteration between heat conduction and stress analysis is employed when stress-dependent interface thermal resistance coefficients are utilized. Verification problems are presented to demonstrate the accuracy of the finite element code.     

Transient nonlinear optically-thick radiative–convective double-diffusive boundary layers in a Darcian porous medium adjacent to an impulsively started surface: Network simulation solutions

A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X¹,Y¹,t¹) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation–conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τ_X) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da → ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251–8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in debris-laden environments (cosmic dust), heat transfer in forest fire spread, geochemical contamination and ceramic materials processing.     

Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng &; Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H,and it is shown that these thermal non-equilibrium effects are strongest when H is small.     

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

Minimum quench energies of uncooled low temperature superconductors with temperature dependent thermophysical parameters

An analytical method for calculation of minimum quench energies (MQEs) of uncooled composite low temperature superconductors is presented. The method takes into account transient heat transfer in the conductor as well as temperature dependent ohmic heat generation and temperature dependent thermophysical properties of the conductor. MQE of the conductor is calculated based on the analysis of evolution of peak temperature in the normal zone. The method is validated by comparison of the obtained results with the experimental data as well as with analytical and numerical results taken from literature.     

Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.     

Numerical Computation of Heat and Mass Transfer in Fluidized Beds with Liquid Injection

The goal of this work is the simulation of concentration and temperature distributions insides fluidized bed with a uniform liquid distribution. Further, a physically based 2D model is developed for the heat and mass transfer processes in fluidized beds with a spray nozzle. The model is a coupled and semi-linear system of convection-reaction-diffusion equations. We considered the numerical solution of these semi-linear partial differential equations with discrete boundary conditions using linear finite elements on an adaptive triangular grid in space and implicit methods in time. We present calculations using, semi implicit and implicit methods in time, and different solvers for solving the linear systems. The complex correlations of mass and liquid flow rates, mass transfer, heat transfer, drying, and transient two dimensional air humidity, air temperature, degree of wetness, liquid film temperature and particle temperature were simulated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical and numerical simulation investigation in effects of radiation and porosity on a non-orthogonal stagnation-point flow towards a stretching sheet

The steady two-dimensional non-orthogonal flow near the stagnation point on a stretching sheet embedded in a porous medium in the presence of radiation effects is studied. Using similarity variables, the nonlinear boundary-layer equations are solved analytically by homotopy perturbation method (HPM) employing Padé technique. Comparison between the results of HPM-Padé solution and numerical simulation as well as some other results which are available in the literature, demonstrates a very good agreement between them and the HPM-Padé solution provides a convenient way to control and adjust the convergence region of a system of nonlinear boundary-layer problems with high accurate. The effect of involved parameters such as striking angle, radiation parameter, porosity parameter and the Prandtl number on flow and heat transfer characteristics have been discussed with more details.     

Heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions

This paper investigates the transient heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions. Using local volumetric average approach, one-dimensional non-equilibrium heat and mass transfer models are developed to describe the humid air and liquid desiccant interaction at counter flow configuration. Using triethylene glycol solution as desiccant, some experimental studies are completed. Experimental results are used to justify the numerical models. Numerical results are then obtained to demonstrate process characteristics. The models include a transient desiccant flow model for initial liquid desiccant building-up process, empirical wetted specific surface ratio for mass transfer, and heat and mass transfer coefficients. The objective of this research is to develop a process analytical tool for liquid desiccant air-conditioner design.     

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.     

Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux

The effects of suction/injection on the laminar mixed convection boundary-layer flow on a vertical wall with a prescribed heat flux are considered. The conditions which allow the equations to be reduced to similarity form are derived and numerical solutions of the resulting equations are obtained for a range of values of the suction/injection and buoyancy parameters. Two specific cases, corresponding to a stagnation point flow and uniform wall heat flux, are treated in detail. Results are presented in terms of the skin friction and wall temperature with a selection of velocity and temperature profiles also being given. Dual solutions are found to exist for assisting flow, these are an addition to what has been reported previously for opposing flows. Solutions for some limiting values of the parameters are also derived.