The numerical analysis of heat transfer by finite element method (FEM) has been used widely. It is usually assumed that the parameters relevant to the heat transfer process are accurately known. However, many of these parameters may vary in a random way in reality. The reliability of the heat transfer performance is needed to be evaluated. The paper introduces an accurate, efficient sensitivity analysis method to compute the FEM response with respect to input parameters. Combining this sensitivity analysis, first order reliability method (FORM) algorithm based stochastic finite element method (SFEM) method is used to evaluate the reliability of the limit state for heat conduction of a benchmark plate with input uncertainties.

Solar chimney is a new method to produce electrical power. It employs solar radiation to raise the temperature of the air and the buoyancy of warm air to accelerate the air stream flowing through the system. By converting thermal energy into the kinetic energy of air movement, solar chimneys have a number of different applications such as ventilation, passive solar heating and cooling of buildings, solar-energy drying, and power generation. Moreover, it can be employed as an energy conversion system from solar to mechanical. A component, such as a turbine or piezoelectric component, set in the path of the air current, converts the kinetic energy of the flowing air into electricity. In this paper, a numerical investigation on a prototypal solar chimney system integrated in a south facade of a building is presented. The chimney is 4.0 m high, 1.5 m wide whereas the thickness is 0.20 m for the vertical parallel walls configuration and at the inlet 0.34 m and at the outlet 0.20 m for convergent configuration. The chimney consists of a converging channel with one vertical wall and one inclined of 2°. The analysis is carried out on a three-dimensional model in airflow and the governing equations are given in terms of k-ε turbulence model. The problem is solved by means of the commercial code Ansys-Fluent. The numerical analysis was intended to examine the effect of the solar chimney’s height and spacing. Further, comparison between radiative and non-radiative model is examined and discussed. Results are given in terms of wall temperature distributions, air velocity and temperature fields and transversal profiles for a uniform wall heat flux on the vertical wall equal to 300 W/m 2 . Thermal and fluid dynamics behaviors are evaluated in order to have some indications to improve the energy efficiency of the system.

Free vibration of cantilever beam with an electromagnetic actuator is studied. The governing equation of motion of the system is developed and the electromagnetic actuation part is added to the system. The system is modeled by 1DOF vibration mode. Three different analytical solution methods, namely, Krylov and Bogoliubov, Energy Balance and Modified Energy Balance are utilized to obtain the equations of motion and the frequency response of the system. Expression for the fundamental frequency is obtained using different types of analytical procedures. Frequency responses of the system are obtained using different numerical methods and the accuracy of the proposed approaches is studied. The influence of the initial conditions on the system performance is studied and the point where, the system starts to show an unstable behavior and quasi-periodic response is identified. Phase-plane trajectories are presented to elaborately analyze the dynamical behaviors of the system. Variations of the natural frequencies for different values of actuation parameter and the initial conditions are plotted to reveal the sensitivity of the objective system.

Counter current flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. This paper describes experimental and numerical results obtained in a circular column of 240 mm inner diameter with two inner pipes. The counter current flow studied concerns an upward flow of air and a downward flow of water at ambient temperature and pressure. The following range of operating conditions is analyzed: superficial air velocities up to 0.25 m/s and superficial water velocities up to 0.04 m/s, corresponding to global void fractions up to 27.7%. The experimental investigations concerns (i) flow visualization, (ii) local data from a double optical probe and (iii) global void fraction data. Images obtained from an optical camera are used to observe the general flow pattern and to support the boundary conditions of the numerical simulations, in terms of average bubble diameter. Data obtained from the double optical probe are used to study local flow characteristics. The gas disengagement technique is used to obtain the global void fraction over a range of superficial air velocities for the validation of the numerical method. Numerical calculations are performed with an Eulerian two-fluid model using the commercial code ANSYS Fluent Release 14.5.7 and results are compared with experimental data. The effects of bubble diameter and various interfacial drag coefficients are studied. The formulation of the drag coefficient is found to have significant effects on the global void fraction predictions. However, using merely the drag law, numerical results are inaccurate.

In many industrial applications, some measurement instruments must be placed in a pipe in which fluid flows. Two phase cross flows around a body have seldom been studied until now and considering these flows can play a significant role in long-term reliability and safety of industrial systems. In this paper drag coefficient, pressure coefficient and void fraction around triangular bodies with different leading edge angles were considered. Also effect of Reynolds number and inlet void fraction on drag coefficient and pressure coefficient has been investigated and flow treatment behind the triangular obstacle has been examined. To achieve this aim, main equations of flow have been developed for investigation of drag coefficient in air-water two phase. Our numerical analyses were performed by a designed and written CFD package which is based on Eulerian-Eulerian approach. Geometries, which have been studied in this article, are triangle, with different leading edge angle. Other parameters such as two phase Reynolds number, free stream void fraction and bubble size were considered, too. Drag coefficient is closely relates to the turbulence and the bubble motion. Since these mechanisms vary over time, we used final value of drag coefficient after convergence. The results showed that drag coefficient is strongly depended of Reynolds number. In this simulation it can be seen that both the drag coefficient and pressure drag coefficient decrease whit increase in two phase Reynolds number and increase with decrease in inlet void fraction.

The flow patterns in two phase and multi-phase flows is a significant factor which influences many other parameters such as drag force, drag coefficient and pressure drop in pipe lines. One of the major streams in the gas and oil industries is oil-water two phase flow. The main flow patterns in oil-water flows are bubbly, slug, dual continuous, stratified and annular. In the present work flow patterns in two phase oil-water flow were investigated in a 0.5in diameter pipe with length of 2m. 3D simulation was used for this pipe and six types of mesh grid were used to investigate mesh independency of the simulation. The proposed numerical analyses were performed by a CFD package which is based both on volume of fluid (VOF) and Eulerian-Eulerian methods. The results showed that some flow patterns can be simulated better with VOF method and some other maybe in Eulerian-Eulerian method, so these two methods were compared with together for all flow patterns. The flow patterns may be a function of many parameters in flow. One of the important parameter which may affect flow patterns in pipe line is pipe inclination angle; therefore flow patterns in the different pipe inclination angles were investigated in two phase oil-water flow. The range of inclinations has been varied between −45 to +45 degree about the horizon. In the presented simulation oil is mixed with water via a circular hole at center of the pipe, the ratio of oil surface to water surface at entrance is 2/3 so water phase was considered as the main phase. Flow patterns were investigated for every angle of pipe and numerical results were compared with available experimental data for verification. Also the flow patterns simulated by numerical approaches were compared with available flow regime maps in the previous literatures. Finally, effect of pipe inclination angle and flow patterns on the pressure loss were investigated comprehensively.

A numerical analysis of mixed convection in a vertical channel filled with metal foam partially heated at uniform heat flux is studied numerically. Local thermal non-equilibrium and Brinkman-Forchheimer-extended Darcy model are assumed. Boussinesq approximation with constant thermophysical proprieties are considered. Results are carried out for an aluminium foam with 10 pore per inch (PPI) and ε=0.909, the fluid is air. Results, for different Reynolds numbers and geometrical aspect ratios, are given in terms of solid and fluid temperatures, at heated walls and inside the channel at several heights, velocity profile along the channel, local and average Nusselt numbers. Results show that diffusive effect resulted lower temperature values inside the solid and the fluid temperatures are higher in all considered cases. For heated channel with smaller aspect ratios, an average Nusselt number increase is found for solid and fluid phases.

This paper handles numerical analyses that give attention to the relation between the thermal performance of concentric tube heat exchangers and its operational parameters. For this purpose, an iterative computational code is developed to compute thermal performance. The computations are based on supplying the code with the exchanger length, inner/outer diameters, inner/outer fluids, inner/outer flow rates and inner/outer inlet temperatures. A parametric analysis that examines the relation between the thermal performance of heat exchanger and inner/outer flow rates is presented. It is originated that the thermal performance and the overall heat transfer coefficient of a concentric tube heat exchanger increase through a rational function with the inner and outer flow rates.

The present work aims to develop a steel ferrule forming by a low-contact deformation process using numerical analysis. Two Finite Elements (FE) models have been developed within ABAQUS. The first one is a 3D model that can both calculate the forming geometry of the part and the forces applied on the roller. The second one is a 2D axisymmetric model allowing reducing the CPU time without important loss of accuracy on the final part geometry. We present in this paper a mixed experimental/numerical comparison performed with each model and discuss the results with measurements coming from a part manufacturing by the industrial partner.

Cold spray is a rapidly developing coating technology for depositing materials in the solid state. In this deposition process, the spray particles are accelerated to a high velocity by a high-speed gas flow, and then form a dense and high quality coating due to plastic deformation of particles impinged upon the solid surface of substrate. 2D and 3D modelling of particle impacting behaviours in cold spray deposition process by using ABAQUS/Explicit was conducted for four couples of materials (i.e. impacting particle/impacted substrate): copper/aluminium, aluminium/copper, copper/copper, and aluminium/aluminium. A systematic analysis of a single impact was carried out considering different parameters, such as the initial impact velocity, initial temperature and contact angle, which affect the deposition process and subsequently the mechanical properties of coating. Three numerical methods have been evaluated and their performances are discussed for various simulation settings: (i) modelling in a Lagrangian reference frame; (ii) modelling using adaptive remeshing in an Arbitrary Lagrangian Eulerian (ALE) reference frame; and (iii), modelling in a CEL reference frame. It is found that the Coupled Eulerian Lagrangian (CEL) method has more advantages to simulate the large deformation of materials, and is also more efficient to prevent the excessive distortion of the mesh. A comparison between simulation results and experimental data from the literature was performed. Nevertheless, the CEL method is implicitly isothermal for ABAQUS v6.10, whereas the modelling in the classical Lagrangian reference frame does include coupled thermo-mechanical effects with a local increase of the temperature near the interface — due to friction — and for the highly plastically deformed elements — due to the heat dissipation linked to plasticity. A local rise of temperature at the impact surface may also be observed for oblique impacts. Finally a first attempt to simulate the deposition of several particles is made with a 3D CEL model, resulting in the creation of porosity at the interface between particles.

The paper deals with the effect of stress state on inelastic deformation and failure behavior of ductile solids. The continuum model takes into account stress-state-dependence of the damage and failure criteria with different branches corresponding to different micro-mechanical mechanisms depending on the stress triaxiality and the Lode parameter. Basic material parameters are identified using various tests with smooth and differently notched tension and shear specimens. To get more insight in the complex damage and failure mechanisms on the micro-scale additional series of three-dimensional micro-mechanical numerical analyses of void-containing unit cells have been performed. These calculations cover a wide range of stress triaxialities and Lode parameters in tension, shear and compression domains. The numerical results are used to discuss general trends, to develop equations for the damage and failure criteria, and to identify corresponding parameters of the continuum model.

The Boundary Element Method (BEM) allows efficient solution of partial differential equations whose kernel functions are known. The heat equation is one of these candidates when the thermal parameters are assumed constant (linear model). When the model involves large physical domains and time simulation intervals the amount of information that must be stored increases significantly. This drawback can be circumvented by using advanced strategies, as for example the multi-poles technique. We propose radically different approach that leads to a separated solution of the space and time problems within a non-incremental integration strategy. The technique is based on the use of a space-time separated representation of the unknown field that, introduced in the residual weighting formulation, allows to define a separated solution of the resulting weak form. The spatial step can be then treated by invoking the standard BEM for solving the resulting steady state problem defined in the physical space. Then, the time problem that results in an ordinary first order differential equation is solved using any standard appropriate integration technique (e.g. backward finite differences). When considering the nonlinear heat equation, the BEM cannot be easily applied because its Green’s kernel is generally not known but the use of the PGD presents the advantage of rewriting the problem in such a way that the kernel is now clearly known. Indeed, the system obtained by the PGD is composed of a Poisson equation in space coupled with an ODE in time so that the use of the BEM for solving the spatial part of the problem is efficient. During the solving, we must however separate the nonlinear term into a space-time representation that can limit the method in terms of CPU time and storage, that is why we introduce in the second part of the paper a new approach combining the PGD and the Asymptotic Numerical Method (ANM) in order to efficiently treat the nonlinearity.

For a steady state convection problem, assuming given concentration field values in a few measurement points and hydraulic head values in the same piezometers, the source of the concentration, and its intensity are deduced using Artificial Neural Networks (ANNs). ANNs are trained with data extracted from Finite Difference (FD) solution of a classical convection problem for small Peclet number. The numerical analysis is exemplified for vanishing, homogeneous and non-homogeneous field of velocity. It is shown that the diffusivity vector can also be identified. The complexity of the problem is discussed for each studied case.

The simulation of multiphase compressible flows through high pressure nozzles is presented. The study uses the developed numerical approach. There are many important engineering applications which are concerned with multiphase flows and convergent-divergent nozzles. This work presents the developed extension of the model and numerical algorithm based on the so called parent model earlier introduced by Saurel and Abgrall [Saurel, R. and Abgrall, R., A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys. 150 (1999), 425–467]. This model which consists of conservation laws for each phase complemented with the volume fraction evolution equation is modified by adding a source term to simulate area variation. The model is strictly hyperbolic and non-conservative due to the existence of non-conservative terms. The model is able to deal with compressible and incompressible flows. Moreover, it can deal with mixtures and pure fluids, where each fluid has its own pressure and velocity. The presence of velocity and pressure relaxation terms in the governing equations has made the velocity and pressure relaxation processes essential to tackle the boundary conditions at the interface. The interface separating phases is considered as a numerical diffusion zone in this method. The model is solved using an efficient Eulerian numerical method. A second order Godunov-type scheme with approximate Riemann solver is used to enable capturing of a physical interface by the resolution of the Riemann problem. The solution is obtained by splitting the hyperbolic part and source terms parts in the numerical algorithm. The source terms, including relaxation parts of the model, are tackled in succession using Strang splitting technique. The governing equations are solved at each computational cell using the same numerical algorithm for the whole domain including the interface. The main aim of this work has been to study different flow regimes with respect to pressure boundary conditions through the numerical solutions of single and multiphase flows. The performance of the programme has been verified via well established benchmark test problems for multiphase flows.

This work deals with the complete stability analysis in the case of two dimensional fluid flows searching for steady and Hopf bifurcations. The stability analysis starts with the computation of steady bifurcations. It is realized by first considering the monitoring of an indicator which is a scalar function. The indicator is computed via a perturbation method: the Asymptotic Numerical Method. Steady bifurcation point corresponds to the zero of this indicator. From this singular point, all the steady bifurcated branches are computed by using the perturbation method. Then the stability analysis is pursued with the computation of Hopf bifurcations by a hybrid method. This latter consists in coupling a continuation method with a direct Newton solver. The continuation method allows the bifurcation indicator to be determined using alternating reduced order and full size steps resolution. The quantities coming from the bifurcation indicator are used as initial approximations for the direct method iterations. Then an augmented system whose solutions are Hopf bifurcation is solved by a direct method of Newton kind. The examples of the one side and two sides lid driven cavities show the reliability and the efficiency of the proposed numerical tools.

Despite constantly improving computer capabilities, classical numerical methods (DNS, LES,…) are still out of reach in fluid flow control strategies. To make this problem tractable almost in real-time, reduced-order models are used here. The spatial basis is obtained by POD (Proper Orthogonal Decomposition), which is the most commonly used technique in fluid mechanics. The advantage of the POD basis is its energetic optimality: few modes contain almost the totality of energy. The ROM is achieved with the recent developed optimal projection [1], unlike classical methods which use Galerkin projection. This projection method is based on the minimization of the residual equations in order to have a stabilizing effect. It enables moreover to access pressure field. Here, the projection method is slightly different from [1]: a formulation without the Poisson equation is proposed and developed. Then, the ROM obtained by optimal projection is introduced within an optimal control loop. The flow control strategy is illustrated on an isothermal square lid-driven cavity and an anisothermal square ventilated cavity. The aim is to reach a target temperature (or target pollutant concentration) in the cavity, with an interior initial temperature (or initial pollutant concentration), by adjusting the inlet fluid flow rate.

As two bodies come into contact, attractive forces occur wherever a gap exists between the two surfaces. The forces are significant at distances of atomic order but become negligible at much larger separations. Their effect is insignificant in most situations for which engineers wish to understand the state of the contact since the adhesive forces are usually much smaller than the net load applied and/or surface roughness results in non-contacting areas being far enough apart that the attractive force is negligible. There are, however, certain cases in which adhesion forces do contribute to the contact mechanics and must be accounted for in any valid analysis. Materials with low elastic modulus, such as rubber, may deform sufficiently around surface asperities such that the surface separation is small and adhesion is apparent. A model for arbitrary geometry (with surface roughness) that includes adhesive forces is reported here. It is based upon the multi-level method of contact analysis developed by Venner and Lubrecht [1]. Adhesion has been implemented using the Lennard-Jones potential as applied to two parallel surfaces, adding the requirement of specific negative pressures for the separated surface nodes [2]. The model is then compared to theoretical and numerical analysis of smooth spherical contacts and to rough contacts of different scales and material properties.

In the field of aeroelasticity, flutter is a well known instability phenomenon. Flutter is a synchronized vibration which takes place in a flexible structure moving through a fluid medium. It occurs when two regular, rhythmic motions coincide in such a way that one feeds the other, drawing additional energy from surrounding flow. A classic case of wing flutter might combine wing bending with either wing twisting. This article explores the flutter phenomenon in water. An important difference from the flutter phenomenon in air is the fact that the flexible structure is evolving in heavy fluid; this implies in particular added mass effects and important fluid damping. Flutter appeared for the first time on racing yacht keels with composite fins, so in water, in 2004: • On the IMOCA 60 feet boat POUJOULAT-ARMORLUX of Bernard STAMM during the transatlantic race ‘The Transat’: he lost his keel and capsized. • On the IMOCA 60 feet boat SILL Rolland JOURDAIN: the keel and the boat were saved. Following these problems — particularly following the loss of the keel of Bernard STAMM sailboat, accident that could have dramatic consequences for the skipper — HDS company focused on the phenomenon. Flutter has occurred only for canting keels with composite fins on IMOCA 60 feet and Volvo 70 feet racing yacht. The main questions asked are “Why are composite keels susceptible to flutter, and is it possible to predict and prevent this behaviour?”, then “Can a fair indication of the flutter critical speed of the keel be given at low cost?”. This presentation will introduce the strategy of HDS faced to the problem and the analytical and numerical methods implemented to estimate the flutter critical speed. Our model is based on a truncated modal basis for the most energetic modes which are generally, for a bulb keel, the lateral bending predominant mode and the torsion predominant mode. One of our requirements was to make a simple model in order to integrate the calculation of the flutter critical speed in the first design loops of a composite or steel keel. This model has worked well for the two cases of flutter appeared on IMOCA sailboat keels. Besides, to verify the quality of the model and to complete our analysis of flutter phenomenon on racing yacht keels, a 3 dimensional multi-physics simulation has been developed using the software ADINA.

Carbon black has been widely used in industry, especially in rubber and plastic production. The present study is concerned with measuring and simulating the carbon black formation process in Propane-air and Acetylene-Air diffusion flames. The carbon black concentrations in the furnace have been measured by means of a soot pump and gravimetric method. The flue gas analysis is also done by means of Testo XL-350 Gas Analyzer. The numerical predictions are carried out with the CFD code, Fluent. The chemical reaction formulation relates the production of the carbon black to the incomplete combustion and pyrolysis of propane and Acetylene as both the main gas and the feedstock. The effects of feedstock mass flow rate, the position of feedstock injection, the feedstock material and the shape of the furnace on carbon black are studied. The results show the effect of temperature on soot and carbon black formation in which as the temperature increases the soot and carbon black mass fraction is also increased. The results also show that as the feedstock mass flow rate increases the formation of the carbon black is increased up to point where the mass flow rate of feed stock is three times greater than the mass flow rate of the main gas and after that the carbon black production rate starts decreasing because of the decreasing of temperature due to cold fuel injection to the furnace. The position of feedstock injection affects the mixing process of air and fuel, and complete mixing causes the temperature to be increased. The injection of feedstock in the pre-combustion zone influences the maximum of the flame temperature. As the hydrocarbon initially pyrolyzes to acetylene and afterwards acetylene breaks into soot and carbon black in the present study acetylene is used as feedstock, the results show huge increasing of soot and carbon black mass fraction in the products. The results also show that predictions and the experimental measurements are in good agreement.

In this study, axial compression behavior of grooved thin-walled steel cylinders is investigated using experimental and numerical methods. Circumferential grooves are generated by means of a special forming tools and the effect of interval between the grooves and their total number on the load-displacement curve, energy absorption-displacement curves and initial buckling load are investigated. It is revealed that having circumferential grooves on the tubes can decrease the initial peak load in load-displacement curve and also increase the amount of absorbed energy. Then explicit Finite Element Model of aforementioned grooved tubes under axial loading are generated using ANSYS software and solved utilizing LSDYNA solver. Result of the FE models (containing the amount of absorbed energy, the peak load and the load-displacement curve during axial compression) are validated by comparing them with those of experimental test. The outcome of comparisons confirms the FE model to be in a good agreement with experimental results.