Upwind Scheme For Convective Terms Research Articles

Numerical modeling of copper macro-segregation in the binary alloy Al-4Cu

In this paper, the modeling of the solidification of Al-4Cu alloy was studied. The calculation code is developed to model the equiaxed globular solidification of the Al-4Cu alloy in a square mold. The mold walls are subjected to constant temperatures and the velocity components are equal to 0, the exchange coefficient ’H’ between the interface of the melt and the mold is estimated at 500 W/( m2 K) and the initial melt temperature ’T0’ is equal to 900 K. The resolution method used is finite differences, the upwind scheme for convective terms, and the space-centered scheme for diffusive terms. The calculated profiles are temperature, solid fraction, concentration and macro-segregation of copper. At the beginning of cooling, the solidification of the Al-4Cu alloy started in the four corners of the plate. The grains formed at the walls could not move in the studied surface. With cooling time, the solidification of the casting developed rapidly in the lower part; because, the grains formed away from the walls sedimented and accumulated in this part of the plate. On other hand, the liquid was located mainly in the upper part. The segregation of copper in the two-phase mixture is due to its continuous rejection from the solid to the liquid.

CFD analysis of thermal stratification and sensitivity study of model parameters for k–ɛ model in a cylindrical hot plenum

A sensitivity analysis of various numerical parameters on the prediction of thermal stratification in a 2D axi-symmetric domain has been carried out by using commercial code FLUENT 6.3. The analysis is carried out for both steady and unsteady flow conditions. The Reynolds number in all the cases has been considered as Re=19,200. The effect of under relaxation parameters, numerical schemes on convergence while solving mass, momentum and turbulence equations was first studied for steady state conditions. An optimal range for under relaxation parameters was found which ensures the stability of the numerical solutions and ensures faster convergence. Further, 1st order upwind scheme for convective terms of turbulent equations (k and ɛ) is found to give a better convergence in comparison with higher order schemes. The study was then extended to transient flow conditions and the stratification characteristics like rising of the stratification interface was studied. The turbulence model parameters of the standard k–ɛ model were changed and predictions were observed. It is observed that the values used for turbulence model parameters (Cμ, C1, C2) while solving the standard k–ɛ model for studying stratification characteristics are different than the model values used in k–ɛ equation. In the lower part of reactor vessel, k–ɛ model with standard value of model parameters have a very good agreement with the experimental observations of Moriya et al. (1987) while in the upper part the model parameters take different values than the standard values.

A stable second-order mass-weighted upwind scheme for unstructured meshes

In this paper, an original second-order upwind scheme for convection terms is described and implemented in the context of a Control-Volume Finite-Element Method (CVFEM). The proposed scheme is a second-order extension of the first-order MAss-Weighted upwind (MAW) scheme proposed by Saabas and Baliga (Numer. Heat Transfer 1994; 26B:381–407). The proposed second-order scheme inherits the well-known stability characteristics of the MAW scheme, but exhibits less artificial viscosity and ensures much higher accuracy. Consequently, and in contrast with nearly all second-order upwind schemes available in the literature, the proposed second-order MAW scheme does not need limiters. Some test cases including two pure convection problems, the driven cavity and steady and unsteady flows over a circular cylinder, have been undertaken successfully to validate the new scheme. The verification tests show that the proposed scheme exhibits a low level of artificial viscosity in the pure convection problems; exhibits second-order accuracy for the driven cavity; gives accurate reattachment lengths for low-Reynolds steady flow over a circular cylinder; and gives constant-amplitude vortex shedding for the case of high-Reynolds unsteady flow over a circular cylinder. Copyright © 2005 John Wiley & Sons, Ltd.

Numerical study on flow characteristics at blade passage and tip clearance in a linear cascade of high performance turbine blade

A numerical analysis has been conducted in order to simulate the characteristics of complex flow through linear cascades of high performance turbine blade with/without tip clearance by using a pressure-correction based, generalized 3D incompressible Navier-Stokes CFD code. The development and generation of horseshoe vortex, passage vortex, leakage vortex, tip vortex within tip clearance, etc. are clearly identified through the present simulation which uses the RNG k-e turbulent model with wall function method and a second-order linear upwind scheme for convective terms. The present simulation results are consistent with the generally known tendency that occurs in the blade passage and tip clearance. A 3D model for secondary and leakage flows through turbine cascades with/without tip clearance is also suggested from the present simulation results, including the effects of tip clearance height.

Numerical Analysis of Nonstationary Thermal Response Characteristics for a Fluid-Structure Interaction System

Nonstationary thermal response analysis for a fundamental sodium experiment simulating thermal striping phenomena was carried out using a quasi-direct numerical thermohydraulics simulation code with a third-order upwind scheme for convection terms and a boundary element method code for thermal response evaluation of structures due to random sodium temperature fluctuations developed at Power Reactor and Nuclear Fuel Development Corporation (PNC). Discussions centered on an applicability of the numerical method for the damping effects of the temperature fluctuations in the course of heat transfer to the inside of structures from the fully turbulent region of sodium flows through the comparisons with the experiment. From these comparisons, it was confirmed that the numerical method has a sufficiently high potential in accuracy to predict the damping effects of the temperature fluctuations related to the thermal striping phenomena. Consequently, it is concluded that the numerical prediction by the method developed in this study can replace conventional experimental approaches using 1:1 or other scale model aiming at the simulation of the thermal striping phenomena in actual liquid metal fast breeder reactor (LMFBR) plants. Furthermore, economical improvements in the FBR plants can be carried out based on the discussions of optimization and rationalization of the structural design using the numerical methods.

A locally modified second order upwind scheme for convection terms discretization

A finite difference scheme for convection term discretization, called BSOU (stands for Bounded Second Order Upwind), is developed and its performance is assessed against exact or benchmark solutions in linear and non‐linear cases. It employs a flux blending technique between first order upwind and second order upwind schemes only in those regions of the flow field where spurious oscillations are likely to occur. The blending factors are calculated with the aid of the convection boundedness criterion. In all cases the scheme performed very well, minimizing the numerical diffusion errors. The scheme is transportive, conservative, bounded, stable and accurate enough so as to be suitable for inclusion into a general purpose solution algorithm.

A higher-order accurate computation of three-dimensional flow in the intake process of a reciprocal engine.

A three-dimensional flow in the intake process of a reciprocal engine is calculated numerically under such complicated boundary conditions as moving valves and arbitary intake-port and combustion chamber configurations. A finite difference method using a third-order upwind scheme for convective terms is applied to solve incompressible Navier-Stokes equations. This model enables us to simulate the occurence of small vortices near the valve and valve seat or caused by curvature of the intake port, as well as the influence on flow in a cylinder of the vortices. The difference in flow pattern between single and double intake valves is compared as an application of this model. LDV measurements at 126 points inside an engine cylinder at an engine speed of 1 400 rpm are also performed in this study to evaluate the calculation results. It is clarified that the calculation flow field agrees fairly well with the measured results.