Boundary-fitted Method Research Articles

Multiphysics Analyeses of Curvilinear Structures using Finite Difference Method with Boundary-fitted Method

In the present study, a multiphysics formulation coupled among thermal, dynamically elastic and electric effects was proposed in consideration of strain gradient and electric gradient. Some two-dimensional curvilinear structures of a smooth circular disk with and without a corrugated outer were analyzed under the applied temperature or pressure by finite difference method using boundary-fitted method. Dynamic behaviors under a stepped pressure and a constant temperature at the outer perimeter were examined for the verification of the proposed scheme. Compared the obtained results with the analytical solution, they show a good agreement and the shape effect of curvilinear structure was multiphysically discussed.

Statistical analysis of pulsating non-Newtonian flow in a corrugated channel using Lattice-Boltzmann method

Pulsating non-Newtonian flow in a corrugated channel was studied by using the Lattice Boltzmann Method (LBM) and utilizing the Boundary Fitting Method (BFM). A wide range of fluctuation amplitudes of pulsating flow was studied (0≤Apulse≤0.35) where Apulse=0 represents the steady flow. Various Reynolds numbers (50, 100, 150 and 200) and power law indices (0.6, 0.8, 1.0, 1.2 and 1.4) were also investigated with the Strouhal number set to 0.25. Spatial and temporal variations of streamlines, shear stress contours, recirculation zones, and skin-friction factor and velocity profiles were analyzed when non-Newtonian behavior transitions from shear-thinning to shear-thickening. Results demonstrated that skin friction factor is directly proportional to the power-law index and indirectly related with the Reynolds number. Plug-like velocity profiles are formed when fluid shows pseudoplastic behavior. Pulse amplitude, power-law index and Reynolds number were identified as key parameters affecting the behaviors of the pulsating flow. Fidelity of the numerical method was verified for both Newtonian and non-Newtonian regimes by comparison with available analytic solutions.

Optimizing Design of Two-dimensional Forging Preform by Bi-directional Evolutionary Structural Optimization Method

Abstract Preform is a step between blanking and finish forming. Design and optimization of the preform for forging would affect the material flow, forming load, dimension accuracy and tool wear. In this study, analysis, simulation and optimization process are carried out by utilizing MATLAB codes as well as using finite element analysis software (DEFORM-2D package) and CAD software as auxiliary tools. The results of this study are as following: using “Curve Fitting” method and two times of reference length are the better options for the boundary fitting method. Besides, the differences between using mean stress and normal pressure as an addition criterion were considered. In terms of strain, the average of effective strain is 0.643 and the standard deviation is 0.298 when using normal pressure as an addition criterion. These values are smaller than those using mean stress as an addition criterion, in which the values are 0.674 and 0.308, respectively. In terms of forming load, the value of the former is 70.616 tons. It is greater than value of the other criterion that forming load is 70.207 tons. Finally, in terms of shape, the results from normal pressure are more complex than those from mean stress.

Convection heat transfer of SWCNT-nanofluid in a corrugated channel under pulsating velocity profile

This study focuses on the effects of single-walled carbon nanotubes (SWCNT) on convection heat transfer in a corrugated channel under a pulsating velocity profile. The volume fraction of added nanotubes to water as base fluid is lower than 1% to make dilute suspensions. A theoretical model is used for effective thermal conductivity of the nanofluid containing carbon nanotubes. This model covers different phenomena of energy transport in nanofluids. Also, an analytical model is applied for effective viscosity of the nanofluid which includes the Brownian effect and other physical properties of nanofluids. The Strouhal number and amplitude of pulsating velocity are studied at the range of 0.05–0.25 and 0–0.5, respectively, for various Reynolds numbers (50, 100 and 150). The study uses lattice Boltzmann method based on boundary fitting method to simulate flow and thermal fields. The time-averaged values of Nusselt number and relative pressure drop along a pulse period time are calculated and presented as the target outcomes. The results approved that the use of SWCNT particles in convectional channels can be an applicable method to enhance convection rate and also to reduce the pressure drop.

Wall Shape Effects on Convection Heat Transfer Over a Corrugated Channel

This study investigates the effects of the wall waviness on forced convection and its fluid flow in a channel bound by two wavy walls. The lattice Boltzmann method based on the boundary fitting method is used to simulate flow and thermal fields in the corrugated channel. The problem is investigated for different Reynolds numbers (50 to 150), wall amplitudes (0 to 0.35), number of wall wavelength (2 to 8), and phase difference of the walls (0 to 270) when the Prandtl number is equal to 0.71 for air flow. The study represents the significant effects of wavy walls on flow and thermal fields in a two‐dimensional channel. It is found when the phase difference between the channel walls has a value equal to 90°; the best heat transfer rate can be achieved in comparison with other geometrical conditions and the flow is likely to be periodically unsteady at lower Reynolds numbers.

Pulsating flow effects on convection heat transfer in a corrugated channel: A LBM approach

At the present study, the effects of the pulsating flow on forced convection in a corrugated channel are investigated using Lattice Boltzmann Method (LBM) based on Boundary Fitting Method (BFM). The dimensionless frequency of pulsating velocity (at a form of Strouhal number) and oscillation amplitude are studied at a wide range (0.05≤St≤1 and 0≤Apulse≤0.25) which Apulse=0 represents the steady constant flow. The study is carried out for different Reynolds numbers (50, 100 and 150) when the Prandtl number is equal to 3.103. Temporal variations of streamlines, isotherms, and relative pressure drop and Nusselt number are presented for appropriate dimensionless groups. Also, the time-averaged values of Nusselt number and relative pressure drop along a pulse period time are calculated and presented in the form of relevant correlations aspect to the Strouhal number. The results show that the role of flow pulsation on the heat transfer enhancement on the target surface is highly dependent on pulsating velocity parameters. It is found that the variation of heat transfer rate according to Strouhal number has an extremum peak. In this extremum value pulsating velocity gradient has best effects on heat transfer rate and heat transfer rate start to drop for higher frequencies.

Lattice Boltzmann simulation of mixed convection heat transfer in a corrugated wall cavity utilizing water‐based nanofluids

AbstractIn the present study, the effects of Cu and CuO nanoparticles' presence on mixed convection heat transfer in a lid‐driven cavity with a corrugated wall are investigated using the lattice Boltzmann method. The boundary fitting method with second‐order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different Richardson numbers (0.1–10), volume fractions of nanoparticles (0–0.05), curve amplitudes (0.05–0.25), and phase shifts of corrugated wall (0–270) when the Reynolds number is equal to 25. The volume fraction of added nanoparticles to the water‐based fluid is less than 0.05 to make dilute suspensions. Results show that adding nanoparticles enhances the rate of heat transfer. It is found that nanoparticles have significant effects on both fluid flow and heat transfer of the mixed convection, especially for low Richardson numbers. A comparison between Cu and CuO nanoparticles shows the Cu nanoparticles have a better effect on heat transfer enhancement for all tested conditions. The results also represent the effective role of a corrugated wall on the rate of nanofluid heat transfer. It is observed that increasing the wavy wall's amplitude leads to a decrease of the average Nusselt numberfor a high Richardson number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21024

Large-eddy simulation of sheared interfacial flow

Large-eddy simulations (LES) of a turbulent interfacial gas-liquid flows are described in this paper. The variational multiscale approach (VMS) introduced by Hughes for single-phase flows is systematically assessed against direct numerical simulation (DNS) data obtained at a shear Reynolds number Re⋆=171, and compared to LES results obtained with the Smagorinsky model, modified by a near-interface turbulence decay treatment. The models are incorporated in the same pseudospectral DNS solver built within the boundary fitting method used by Fulgosi et al. for air-water flow. The LES are performed for physical conditions allowing low interface deformations that fall in the range of capillary waves of wave slope ak=0.01. The LES results show that both the modified Smagorinsky model and the VMS are capable to predict the boundary layer structure in the gas side, including the decay process, and to cope with the anisotropy of turbulence in the liquid blockage layer underneath the interface. Higher-order turbulence statistics, including the transfer of energy between the normal stresses is also well predicted by both approaches, but qualitatively the VMS results remain overall better than the modified Smagorinsky model. The study has demonstrated that the key to the prediction of the energy transfer mechanism is in the proper prediction of the fluctuating pressure field, which has been found out of reach of any of the LES methodologies. The superiority of the VMS is demonstrated through the analysis of the subgrid transport and exchange terms in the resolved kinetic energy, where it is indeed shown to be self-adaptive with regard to the eddy viscosity. Although VMS is shown to be sensitive to filter scale partition and model constant, the optimal setting can be easily translated in the interface tracking/finite-volume context, which makes it very useful for practical purposes. An important point is that the VMS approach yields very satisfactory results without the need for prescribing an ad-hoc damping function and the required distance to the interface.

Numerical analysis of crystal growth of an InAs-GaAs binarysemiconductor under microgravity conditions

We investigate the possibility of growing a uniform binary compoundcrystal in space, proposing a new crystal growth method. We develop anumerical calculation method for the growth of binary crystals, in whichconvection induced by temperature and concentration differences in thesolution is taken into account. How to determine the shape and movement of thesolution-crystal interface during the crystal growth is clearly explained forbinary crystals, which is more complicated than for single-component crystals.The boundary fit method is employed to solve this moving boundary phasetransition problem. The calculation method is applied to the crystal growthanalysis of an InAs-GaAs binary semiconductor and the effect of buoyancyconvection induced under microgravity conditions on the crystal growth processis investigated. It is found that the concentration field is disturbed and, asa result, the solution-crystal interface is deformed by buoyancy convection,even when the gravitational acceleration is as low as 10-6 g, which issupposed to be the gravity level in the International Space Station which willstart operation in 2004. It is also found that the direction of the residualgravity has a strong effect on the concentration field in the solution and thecrystal growth process. Next, we analyse the influence of g-jitters and theSorét effect on the crystal growth process. In fact, it is found thatg-jitters and the Sorét effect have little influence on the macroscopiccrystal growth process. The dependence of the generation of supercooling inthe solution on convection is also investigated. It is found that supercoolingis not induced by convection if residual gravity is 10-6 g. Finally, wediscuss the possibility of growing high-quality InGaAs crystals of uniformcompositions in space.

Constitutional supercooling induced by convection during InP solution growth

Abstract We studied InP solution growth by the travelling heater method numerically. We developed a numerical model of solution growth and a calculation method based on the boundary fit method and the finite difference method. We investigated the effect of buoyancy convection and Marangoni convection on the flow, temperature and concentration fields, the crystal growth rate, the shape of solution-crystal interface and the generation of constitutional supercooling. Through this analysis, the following results were obtained; (1) Constitutional supercooling is induced by buoyancy convection when the Rayleigh number is larger than 1000. (2) Constitutional supercooling is also induced by Marangoni convection when the Marangoni number is larger than 100. (3) The degree of supercooling is lower in the case of Marangoni convection than in the case of buoyancy convection. (4) The solution-crystal interface becomes wavy in the case of Marangoni convection but it becomes concave in the case of buoyancy convection.

A flexible automatic hexahedral mesh generation by boundary-fit method

A general-purpose automatic hexahedral mesh generation system for FEA (Finite Element Analysis) was developed, based on a shape recognition technique and the boundary-fit method. In this system, a solid model is analyzed and decomposed into single-connected sub-models. Then, other sub-models topologically identical to the original ones are constructed using only orthogonal angles. Cubes are used to construct intermediate models, which reassemble these, and finally, hexahedral meshes are generated by mapping the cubes back onto the original solid model. In order to make the automatic system more flexible and friendly to the user, this system also has the capability to interact with the user to modify the intermediate models used in the system to improve the quality of generated mesh, or to help the system to circumvent various topological difficulties.

Numerical analysis of InP solution growth by travelling heater method: transient response in the case of no heater movement

We carried out a numerical simulation of InP solution growth by the travelling heater method (THM). We introduced the governing equations and made clear the parameters which govern solution growth by THM. The velocity, temperature and concentration fields and the solidification processes were simulated by the finite difference method and the boundary fit method. The effect of thermal convection on the crystal growth rate and the constitutional supercooling occurring in indium solvent was investigated.

Automatic Hexahedral Mesh Generation System with Element Distortion Control Capability.

This paper describes an interactive FEA (finite element analysis) mesh refinement technique in an automatic hexahedral mesh generation system based on the shape recognition technique and boundary-fit method. In this system, a solid model is analyzed, and cubes are put together to construct a corresponding mapping model. Hexahedral meshes are then generated by mapping the cubes onto the solid model. If users are not satisfied with the automatic mesh generation results, they can remake the intermediate models interactively. Furthermore, if this system fails to construct the intermediate models automatically, users can interactively aid its construction. The advantages of this technique are: (1) more types of solid models can be meshed, and (2) users can direct the creation of higher quality meshes.

Solidification Analysis by FVM on Irregular Grid.

A method of numerical simulation of the solidification of castings, particularly of complicated shapes, is developed. The proposed method is based on the finite volume method (FVM) and uses an irregular grid system. The irregular grid system is obtained by the boundary fit method. The coordinates lines of the grid are formed to coincide with the complicated boundaries of the castings. Nodal points are placed inside the each cell of the grid. Using the local oblique Cartesian Coordinates which are formed by connecting neighboring nodal points, the energy balance equation is directly solved by the vector analysis technique in the generalized coordinates. Some calculation results of two-dimensional sections are shown and the accuracy of the method is checked. The proposed method has the following advantages : (1) The algorithm is simple and calculation time is short comparable to the conventional finite difference method (FDM), and (2) It can handle castings of complicated shapes which could not be handled by the conventional FDM.

Numerical Analysis for Lock-In Phenomenon of Vibrating Cylinder in Uniform Flow. Investigation of Analyzing Technique for Moving Boundary Problem.

It is well known that a cyclic Karman vortex street is periodically thrown out from a cylinder whose axis is vertical to the bulk flow. When the cylinder is vibrated at a frequency close to that of the Karman vortex street, the frequency is locked in to that of the cylinder. While there are many experimental studies of this phenomenon, analytical studies by numerical calculation are few. In this study, a new algorithm for a moving boundary problem is proposed, and a simulator, which can deal with this phenomenon is developed. The simulator is based on the boundary-fit method and MAC method. This lock-in phenomenon is analyzed by it and the following results are obtained. The lock-in phenomenon is confirmed to exist by this simulator. The bandwidth of the frequency in which it is locked in coincides with that from experimental results. For the near-wake of the cylinder, the velocity profile corresponds to the experimental one.