Leszek Wawrzonek and Ryszard A. Białecki
This paper seeks to develop a reliable simulation technique and experimental equipment applicable to thermal analysis of disk brakes. The application is focused on safety issues…
Abstract
Purpose
This paper seeks to develop a reliable simulation technique and experimental equipment applicable to thermal analysis of disk brakes. The application is focused on safety issues arising in coal mines and other hazardous explosive environments.
Design/methodology/approach
The experimental rig provides data on the friction power generated by the disk‐pad pair for a user‐defined squeezing force program. The developed software predicts the temperature field in the brake and pad. The code is based on the finite volume approach and is formulated in Lagrangian coordinates frame.
Findings
In the circumferential direction advection due to the rotation of the disk dominates over the conduction. The energy transfer problem could be formulated in a Lagrange coordinates system as 2D. A novel approach to the estimation of the uncertainty of numerical simulations has been proposed. The technique is based on the GUM methodology and uses sensitivity coefficients determined numerically. Very good agreement of simulated and measured values of temperature in the brake has been found.
Research limitations/implications
The results apply for simple disk and pad geometries for which the correlations of the Nusselt number versus Reynolds and Prandtl are known. Moreover, the model should not be used in the last braking period where the assumption of negligible circumferential conduction is not applicable. Though the code models a situation of constant rotation speed, the deceleration profile of the disk can readily be accounted for. The next step of the research should be to couple the heat conduction in the brake with CFD simulation of the surrounding air.
Practical implications
The highest temperature in the system is at the pad‐disk interface. The depth of penetration of the temperature into the disk is relatively low. The heat dissipation from the disk is controlled by convection.
Originality/value
The novelty of the paper is in the simplified and robust simulation model of the brake, the concept of the experimental rig and the methodology of uncertainty assessment. The developed methodology can be useful to researchers and industry involved in safety investigations and determining safety standards, specifically in explosive atmospheres. It may also be of interest to the automotive industry.
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Gustav Amberg and Minh Do‐Quang
In welding there is an intricate coupling between the composition of the material and the shape and depth of the weld pool. In certain materials, the weld pool may not penetrate…
Abstract
Purpose
In welding there is an intricate coupling between the composition of the material and the shape and depth of the weld pool. In certain materials, the weld pool may not penetrate the material easily, so that it is difficult or impossible to weld, while other seemingly quite similar materials may be well suited for welding. This is due to the convective heat transfer in the melt, where the flow is driven primarily by surface tension gradients. This paper aims to study how surface active agents affect the flow and thus the welding properties by surveying some recent 3D simulations of weld pools.
Design/methodology/approach
Some basic concepts in the modelling of flow in a weld pool are reviewed. The mathematical models for a convecting melt, with a detailed model for the surface tension and the Marangoni stress in the presence of surfactants, are presented. The effect of the sign of the Marangoni coefficient on the flow pattern, and thus, via melting and freezing, on the shape of the weld pool, is discussed.
Findings
It is seen that it is beneficial to have surfactants present at the pool surface, in order to have good penetration. Results from a refined surface tension model that accounts for non‐equilibrium redistribution of surfactants are presented. It is seen that the surfactant concentration is significantly modified by the fluid flow. Thereby, the effective surface tension and the Marangoni stresses are altered, and the redistribution of surfactants will affect the penetration depth of the weld pool.
Originality/value
The importance of surfactants for weld pool shapes, and in particular the convective redistribution of surfactants, is clarified.
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Bamdad Lessani and Miltiadis V. Papalexandris
This paper sets out to perform a detailed numerical study of turbulent channel flow with strong temperature gradients using large‐eddy simulations.
Abstract
Purpose
This paper sets out to perform a detailed numerical study of turbulent channel flow with strong temperature gradients using large‐eddy simulations.
Design/methodology/approach
A recently developed time‐accurate algorithm based on a predictor‐corrector time integration scheme is used in the simulations. Spatial discretization is performed on a collocated grid system using a flux interpolation technique. This interpolation technique avoids the pressure odd‐even decoupling problem that is typically encountered in collocated grids. The eddy viscosity is calculated with the extension of the dynamic Smagorinsky model to variable‐density flows.
Findings
The mean velocity profile at the cold side deviates from the classical isothermal logarithmic law of the wall. Nonetheless, at the hot side, there is a better agreement between the present results and the isothermal law of the wall. Further, the numerical study predicts that the turbulence kinetic energy near the cold wall is higher than near the hot one. In other words heat addition tends to laminarize the channel flow. The temperature fluctuations were also higher in the vicinity of the cold wall, even though the peak of these fluctuations occurs at the side of the hot wall.
Practical implications
The findings of the paper have applications in the design and analysis of convective heat transfer equipment such as heat exchangers and cooling systems of nuclear reactors.
Originality/value
The paper presents the first numerical results for non‐isothermal turbulent channel flow with high wall‐temperature ratios (up to 9). These findings can be of interest to scientists carrying out research in turbulent flows.
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Piotr Furmański and Jerzy Banaszek
This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing…
Abstract
Purpose
This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing during alloy solidification. These different appearances of the momentum equation are compared and the issue is addressed of how the choice of the particular form affects velocity and temperature fields.
Design/methodology/approach
Attention is focused on the ensemble averaging method, which, owing to its stochastic nature, is a new promising tool for setting up the macroscopic transport equations in highly inhomogeneous multiphase micro‐ and macro‐structures, with morphology continuously changing in time when the solidification proceeds. The basic assumptions of the two other continuum models, i.e. based on the classical mixture theory and on the volume‐averaging technique, are also unveiled. These three different forms of the momentum equation are then compared analytically and their impact on calculated velocity and temperature distribution in the mushy zone is studied for the selected test problem of binary alloy solidification driven by diffusion and thermal natural convection in a square mould.
Findings
It is found that a chosen appearance of the momentum equation mildly affects temporal velocity/temperature, and shapes of the phase interface at longer times of the solidification.
Research limitations/implications
This mainly results from small variations of the liquid fraction across the mushy zone and from a low solidification rate, and it may change drastically when anisotropic properties of the mushy zone, solutal convection, different phase densities and cooling conditions are considered. Therefore, further comprehensive study is needed.
Originality/value
The paper addresses how the different focus of the momentum equation for liquid flow is compared.
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This paper seeks to discuss a mechanistic modeling concept for local phenomena governing two‐ and multi‐phase flows and heat transfer.
Abstract
Purpose
This paper seeks to discuss a mechanistic modeling concept for local phenomena governing two‐ and multi‐phase flows and heat transfer.
Design/methodology/approach
An overview is given of selected issues concerning the formulation of multidimensional models of two‐phase flow and heat transfer. A complete computational multiphase fluid dynamics (CMFD) model of two‐phase flow is presented, including local constitutive models applicable to two‐phase flows in heated channels. Results are shown of model testing and validation.
Findings
It has been demonstrated that the overall model is capable of capturing various local flow and heat transfer phenomena in general, and the onset of temperature excursion (CHF) in low quality forced‐convection boiling, in particular.
Research limitations/implications
Whereas the multiphase model formulation is applicable to a large class of problems, geometries and operating conditions, the closure laws and results are focused on forced‐convection boiling in heated channels.
Practical implications
The proposed approach can be used to predict multidimensional velocity field and phase distribution in two‐phase flow devices and components used in thermal power plants, nuclear power plants and chemical processing plants.
Originality/value
A complete mechanistic multidimensional model of forced‐convection boiling in heated channels is given. The potential of a CMFD approach is demonstrated to perform virtual experiments that can be used in system design and optimization, and in safety analysis.
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Eligiusz W. Postek, Roland W. Lewis and David T. Gethin
This paper sets out to present developments of a numerical model of squeeze casting process.
Abstract
Purpose
This paper sets out to present developments of a numerical model of squeeze casting process.
Design/methodology/approach
The entire process is modelled using the finite element method. The mould filling, associated thermal and thermomechanical equations are discretized using the Galerkin method. The front in the filling analysis is followed using volume of fluid method and the advection equation is discretized using the Taylor Galerkin method. The coupling between mould filling and the thermal problem is achieved by solving the thermal equation explicitly at the end of each time step of the Navier Stokes and advection equations, which allows one to consider the actual position of the front of the filling material. The thermomechanical problem is defined as elasto‐visco‐plastic described in a Lagrangian frame and is solved in the staggered mode. A parallel version of the thermomechanical program is presented. A microstructural solidification model is applied.
Findings
During mould filling a quasi‐static Arbitrary Lagrangian Eulerian (ALE) is applied and the resulting temperatures distribution is used as the initial condition for the cooling phase. During mould filling the applied pressure can be used as a control for steering the distribution of the solidified fractions.
Practical implications
The presented model can be used in engineering practice. The industrial examples are shown.
Originality/value
The quasi‐static ALE approach was found to be applicable to model the industrial SQC processes. It was found that the staggered scheme of the solution of the thermomechanical problem could parallelize using a multifrontal parallel solver.
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Miha Založnik, Shihe Xin and Božidar Šarler
This paper aims to point out the critical problems in numerical verification of solidification simulation codes and the complexity of the verification and to propose and apply a…
Abstract
Purpose
This paper aims to point out the critical problems in numerical verification of solidification simulation codes and the complexity of the verification and to propose and apply a procedure of generalized verification for macrosegregation simulation.
Design/methodology/approach
A partial verification of a finite‐volume computational model of macrosegregation in direct chill (DC) casting of binary aluminum alloys, including the coupled transport phenomena of heat transfer, fluid flow and species transport, is performed. The verification procedure is conducted on numerical test problems, defined as subproblems with respect to the complexity of the physical model, geometry, and boundary conditions. The studied cases are thermal convection with solidification in DC casting, thermal natural convection of a low‐Prandtl‐number liquid metal in a rectangular cavity and 1D directional solidification of a binary Al‐Cu alloy. Grid‐convergence studies, code comparison with an alternative Chebyshev‐collocation method, and comparison with a reference similarity solution are used for verification.
Findings
An excellent ability of the model to accurately resolve the thermal convection in the pertinent range of Prandtl and Rayleigh numbers is shown. Concerns regarding the solution of species transport in the mushy zone remain.
Research limitations/implications
The proposed verification procedure is not completed in its entirety. Further verification of the solutal and thermosolutal convection problems is required.
Originality/value
This paper proposes verification techniques for complex coupled solidification problems involving significant convection in the melt.
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Dominique Gobin and Benoit Goyeau
This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.
Abstract
Purpose
This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.
Design/methodology/approach
Since the pioneer study by Beavers and Joseph, the problem of interface continuity and/or jump conditions at a fluid‐porous interface has been of interest to the fluid mechanics and heat and mass transfer community. The paper is concerned both with numerical simulations of heat and fluid flow in such systems, and with the linear stability problems.
Findings
The one‐ and two‐domain formulations are equivalent. Using the Darcy‐Brinkman extension instead of the Darcy model reduces the number of ad hoc parameters in this configuration.
Research limitations/implications
The problem of double diffusive convection has still to be solved and analyzed.
Practical implications
The discussion on the interface conditions is of great relevance to many industrial and practical situations.
Originality/value
The important question of the macroscopic formulation of the problem is tackled in the paper.
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Kevin Erhart, Eduardo Divo and Alain Kassab
This paper aims to develop and describe an improved process for determining the rate of heat generation in living tissue.
Abstract
Purpose
This paper aims to develop and describe an improved process for determining the rate of heat generation in living tissue.
Design/methodology/approach
Previous work by the authors on solving the bioheat equation has been updated to include a new localized meshless method which will create a more robust and computationally efficient technique. Inclusion of this technique will allow for the solution of more complex and realistic geometries, which are typical of living tissue. Additionally, the unknown heat generation rates are found through genetic algorithm optimization.
Findings
The localized technique showed superior accuracy and significant savings in memory and processor time. The computational efficiency of the newly proposed meshless solver allows the optimization process to be carried to a higher level, leading to more accurate solutions for the inverse technique. Several example cases are presented to demonstrate these conclusions.
Research limitations/implications
This work includes only 2D development of the approach, while any realistic modeling for patient‐specific cases would be inherently 3D. The extension to 3D, as well as studies to improve the technique by decreasing the sensitivity to measurement noise and to incorporate non‐invasive measurement positioning, are under way.
Practical implications
As medical imaging continuously improves, such techniques may prove useful in patient diagonosis, as heat generation can be correlated to the presence of tumors, infections, or other conditions.
Originality/value
This paper describes a new application of meshless methods. Such methods are becoming attractive due to their decreased pre‐processing requirements, especially for problems involving complex geometries (such as patient specific tissues), as well as optimization problems, where geometries may be constantly changing.
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This paper seeks to discuss the numerical modeling of the transport processes that frequently arise in practical thermal systems and involve complexities such as property…
Abstract
Purpose
This paper seeks to discuss the numerical modeling of the transport processes that frequently arise in practical thermal systems and involve complexities such as property variations with temperature or with the shear rate in the flow, complicated regions, conjugate mechanisms, chemical reactions and combined mass transfer, and intricate boundary conditions.
Design/methodology/approach
The basic approaches that may be adopted in order to study such processes are discussed. Considerations for accurate numerical modeling are also discussed. The link between the process and the resulting product is critical in many systems such as those in manufacturing. The computational difficulties that result from the non‐Newtonian behavior of the fluid or from the strong temperature dependence of viscosity are considered in detail. Similarly, complex geometry, free surface flow, moving boundaries, combined mechanisms, and simulation of appropriate boundary conditions are important in several processes and are discussed.
Findings
Some of the important techniques to treat the problems that arise in numerical simulation are presented. Common errors that lead to inaccurate or invalid results are outlined. A few practical processes are considered in greater detail to quantify and illustrate these approaches. Validation of the numerical model is a particularly important aspect and is discussed in terms of existing results, as well as development of experimental arrangements to provide inputs for satisfactory validation.
Originality/value
Practical thermal processes involve a wide variety of complexities. The paper presents some of the important ones and discusses approaches to deal with them. The paper will be of particular value to the numerical simulation of complicated thermal processes in order to design, control or optimize them to achieve desired thermal processing.