Reynolds Number Of Fluid Flow Research Articles

Motion Behavior of Nonmetallic Inclusions at the Interface of Steel and Slag. Part I: Model Development, Validation, and Preliminary Analysis

Abstract The motion behavior of nonmetallic inclusions at the interface of molten steel and slag fundamentally affects the removal of inclusions. Therefore, from an analysis of forces, this study constructed a mathematical model of inclusion movement. Compared with other models that only consider the forces acting on nonmetallic inclusions at the interface, the proposed model considers not only cases in the inclusions which enter the slag interior and rebound into the molten steel, but also the effect of fluid flow containing the inclusions with different Re numbers on the drag force. The application of this established model has not taken Reynolds number of fluid flow into consideration. The model can predict the motion of inclusions at the interface and in nearby areas and provide a curve of inclusion displacement vs time. The mathematical model was verified with a physical model, with the curve of displacement vs time obtained from physical experiment being consistent with the calculated curve. The preliminary calculation results show that inclusions having liquid film at their surfaces are rebounded into the steel when they have size within a certain range but enter the slag phase directly when they are beyond that size range.

Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear

Coupled shear-flow tests were conducted on two artificial rock fractures with natural rock fracture characteristics under constant normal loading boundary conditions. Numerical simulations using the 3-D Navier–Stokes equations taking account of the inertial effects of fluid were conducted using the void space geometry models obtained from the coupled shear-flow tests. The test and numerical simulation results show that the evolutions of geometrical and hydraulic characteristics of rock fracture exhibit a three-stage behavior. Transmissivity of a certain void space geometry within a fracture is related to the Reynolds number of fluid flow due to the inertial effects of fluid, which can be represented by the Navier–Stokes equations, but cannot be represented by some simplified equations, such as the cubic law, the Reynolds equation or the Stokes equations. The mechanical aperture is usually larger than the hydraulic aperture back-calculated from measured flow rate, and the difference between them is found strongly related to the geometrical characteristics of the fractures. A mathematical equation is proposed to describe the relation between hydraulic aperture and mechanical aperture by means of the ratio of the standard deviation of local mechanical aperture to its mean value, the standard deviation of local slope of fracture surface and Reynolds number.

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (ks), thermal conductivity of flush-mounted discrete heat source (kc), Reynolds number of fluid flow (Res), modified Richardson number (Ri+) and aspect ratio (AR) of the channel. The standard k-e turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T*) using the asymptotic computational fluid dynamics (ACFD) technique.

Computation of Leading Eigenvalues and Eigenvectors in the Linearized Navier-Stokes Equations using Krylov Subspace Method

In the hydrodynamic stability analysis of fluid flow, an eigenproblem with a large asymmetric matrix can be produced by the linearized Navier-Stokes equations. To find the leading eigenvalues and eigenvectors is one of the key issues in the stability analysis. In this study, the Krylov subspace method has been used to develop a general algorithm and then solve the eigenproblem with a large asymmetric matrix in the linearized Navier-Stokes equations. The Krylov subspace method is to construct a set of linearly independent vectors from the linearized equations in which the leading eigenvalues with the largest real parts are included, and orthonormalize the vectors. Then, the Arnoldi's method is used for extracting the desirable eigenvalues with the largest real parts. The advantage of the present method is its ability to calculate a given number of leading eigenvalues including the largest real parts, and corresponding eigenvectors in a large asymmetric matrix. Therefore, this algorithm is general for the hydrodynamic stability analysis with asymmetric matrices resulting from the linearized Navier-Stokes equations. This method has been verified and applied to detect the critical Reynolds number of fluid flow past a circular cylinder. The finite element method with equal-order interpolation was used in this application for discretization of the linearized Navier-Stokes equations.

Theory and modeling of phase change materials with and without mushy regions

The continuous-properties model has been developed to numerically solve problems of melting and solidification of substances with a mushy region. The new method is applicable to negligibly small mushy regions. Therefore, it can also be used to numerically calculate the behaviour of materials showing a discontinuous (first-order) phase transition. A stress number, comparable to the Reynolds number of fluid flow, can be introduced to quantify the difficulty of the computational task.