CFD STUDIO: AN EDUCATIONAL SOFTWARE FOR CFD ANALYSIS

This paper explores the application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [1] in solution of coupled heat transfer and fluid flow problems associated with solidification of a binary alloy. The involved temperature, velocity, species and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The energy and momentum equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local continuity equation violation [2,3]. The solution procedure is demonstrated in simulation of solidification of 8 wt % Pb-Sn alloy and 5 wt % Sn-Pb alloy in rectangular cavity at conditions, defined in [4]. The numerical examples include studies with different uniform discretization and its influence on final macrosegregation map. The solution is assessed by comparison with the reference results of the finite volume and finite element method. The advantages of the method are simplicity, accuracy and straightforward applicability in non-uniform node arrangements. The methodology will be use in complementing our heat transfer model [5] of the continuous casting of steel.

A Meshless Radial Basis Function Method for Fluid Flow with Heat Transfer K Nagamani Devi1, D.W. Pepper2 Summary Over the past few years, efforts have been made to solve fluid flow and heat transfer problems using radial basis functions. This approach is meshless, easy to understand, and simple to implement. Preliminary results indicate accuracies on the order of finely meshed conventional techniques, but with considerably less computational effort. In this study, a projection-based technique is used to solve the primitive equations of motion and energy using radial basis functions. Three benchmark test cases are examined: (1) lid-driven cavity flow, (2) natural convection in a square enclosure, and (3) flow with forced convection over backward facing step. Results are compared with COMSOL and FLUENT – two popular commercial CFD packages.

Numerical evaluation of the latent heat thermal energy storage performance enhancement by installing longitudinal fins

PurposeStudying the effect of localized wall discharge on the fluid flow and heat transfer for a flow over backward facing step is the main purpose of this paper. Jet is used to control the reattachment length which controls the fluid flow and heat transfer downstream the step. Several parameters are to be investigated: geometric; expansion ratio, location of the jet, and jet angle flow; Reynolds number, jet velocity.Design/methodology/approachNumerical simulation using both the standard K−ε and renormalized group turbulence theory (RNG) K−ε models are used to model flow in the computational domain. The energy equation is also used to model the heat transfer characteristics of the flow. The model equations are solved numerically using a finite volume code.FindingsIt is found that the presence of the wall jet at a proper location can significantly influence the flow and heat characteristics of the problem. Furthermore, varying the ratio of the jet velocity to the main stream velocity could play an important role in controlling the size of the circulating bubble and, therefore, the fluid and heat transfer characteristics of the flow, whereas, the expansion ratio has less influence. It is also found that increasing Reynolds number increases the value of maximum heat transfer but has less influence on either its location or the reattachment length.Research limitations/implicationsThe range of the Reynolds number considered in this research covers only the turbulent regime. The research does not cover laminar flows. The results and conclusions cover only three values of expansion ratios. Namely (expansion ratio (ER)=1.67, 1.8 and 2). Conclusions should not be read beyond these values of ER.Practical implicationsThis work gives designers of similar flows a new method of controlling the fluid flow and heat transfer by varying jet angle.Originality/valueThis work has not been done before and it can initiate additional research projects as investigating the effect of applying wall jets in combustors.

Purpose The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

Transient 3D heat transfer analysis up to the state of Dryout in fuel rods

A mathematical model has been developed for the prediction of cracks in the continuously cast steel beam blank through the fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell. Fluid flow and heat transfer in the strand mold were analyzed with a three-dimensional (3-D) finite-volume method (FVM). For the complex geometry of the beam blank, a body-fitted coordinate (BFC) system was employed. Thermo-elastic-plastic deformation behavior in the strand was analyzed using the finite-element method (FEM) based on the two-dimensional (2-D) slice model. The thermal fields of the strand calculated with the FVM were used in the analysis of the deformation behavior of the strand. Through the iterative analysis of the fluid flow, heat-transfer, and deformation behavior, the coupling parameter of the heat-transfer coefficient between the strand and the mold was obtained. In order to describe the thermophysical properties and thermomechanical behavior of steel in the mushy zone, the microsegregation of solute elements was assessed. Consequently, some characteristic temperatures of steel as well as variations of phase fractions with temperature were determined. The probability of cracking in the strand, originating from an interdendritic liquid film, was quantified as a crack susceptibility coefficient. Recirculating flows were developed in the web and flange-tip regions. The development of a solidifying shell in the flange-center region was retarded by the inlet flow from a submerged entry nozzle (SEN). An air gap was formed mainly near the flange-tip corner. Surface cracks in the web and fillet regions and internal cracks in the flange-tip region were predicted.

A comparative analysis of thermal models in the lattice Boltzmann method(LBM) for the simulation of laminar natural convection in a square cavity is presented. A HYBRID method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum conservation are resolved by the lattice Boltzmann method, is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred correction method to ensure stability of the solutions. The HYBRID method and the double-population method are applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the conventional Navier-Stokes equation method. In general, the present HYBRID method is as accurate as the Navier-Stokes equation method and the double-population method. The HYBRID method shows better convergence and stability than the double-population method. These observations indicate that this HYBRID method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problem with the LBM.

A new hybrid method is proposed for solving the problems of fluid dynamics and heat transfer in complex hydraulic systems. The peculiarity of the method consists in the idea that some elements of the model are represented as network elements, where the solving of the flow distribution problem is carried out on the basis of the hydraulic circuit theory, whereas the flow in the remaining elements is calculated by the spatial methods of computational fluid dynamics (CFD). The results are presented of testing the proposed hybrid method for the problems of fluid dynamics and heat transfer in microchannels. The test calculations demonstrate high efficiency of the method.

A molecular dynamics study on the supercritical evaporation of liquid ammonia under forced convection conditions

The analysis of the time-dependent and two-dimensional fluid flow and heat transfer around a single row of tubes in a channel is performed numerically. Due to its fundamental significance and practical importance, aerodynamic and heat transfer characteristics of tube bundle have been paid great attention by many researchers. In the present study, the immersed boundary method is applied by using a Cartesian grid system. Numerical solution for the governing equations of mass, momentum and energy conservation is obtained with the finite volume method. To validate the numerical approach with the immersed boundary method, the results have been compared with published data. The generation and evolution of vortical structures, wake interactions and their effects on the drag, lift and heat transfer are analyzed at different Reynolds numbers. The effect of hydraulic boundary layer development on the fluid flow and heat transfer is also investigated.

Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow and heat transfer based on the finite volume method using staggered and Rhie-Chow’s momentum interpolation collocated grids, the second part contains the comparative computations being conducted on Rhie-Chow’s momentum interpolation collocated grid and Thiart’s finite difference scheme based nonstaggered grid. Three 3-D cases that have analytical or benchmark solutions are adopted. For the first part, the results of computations indicate that, all the six schemes have the same numerical accuracy when the diffusion term is predominant. With the increase of convection, the FUDS, HDS and PLDS almost have the same accuracy in two of those grid systems, while the SUDS and QUICK have higher accuracy than the former. The accuracy of CDS is something in between. For the same under-relaxation factors and convergence criterion, the convergence rate of each scheme on those two grid systems are nearly equal with that on the staggered grid being a little bit faster. For QUICK and CDS, smooth, non-oscillating solutions can be obtained even when local Peclet number may be as large as 31.2–31.3. For the second part, it is concluded that simplified collocated grid system is preferable from numerical accuracy, grid Peclet number limit, sensitivity to the under-relaxation factor and the freedom in choosing finite difference scheme for convection term.

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

Four problems of fluid flow and heat transfer were designed in which non‐orthogonal, boundary‐fitted grids were to be used. These are proposed to serve as test cases for testing new solution methods. This paper presents solutions of the test problems obtained by using a multigrid finite volume method with grids of up to 320 × 320 control volumes. Starting from zero fields, iterations were performed until the sum of the absolute residuals had fallen seven orders of magnitude, thus ensuring that the variable values did not change to six most significant digits. By comparing the solutions for successive grids at moderate Reynolds and Rayleigh numbers, the discretization errors were estimated to be lower than 0·1%. The results presented in this paper may thus serve for comparison purposes as bench‐mark solutions.

Chapter IX - Elliptical Ducts