The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration.The investigation is carried out b...The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration.The investigation is carried out by assuming a two-dimensional laminar in-compressible fluid flow subject to Neumann boundary conditions throughout the numerical iterations in a transient analysis.All the walls of the square cavity are perfectly insulated and the top moving lid produces a constant finite heat flux even though the fluid flow attains the steady-state condition.The objective is to examine the effects of viscous heating in the fully insulated lid-driven cavity under no-slip and free-slip Neumann boundary conditions coupled with variations in Reynolds and Prandtl numbers.The partial differential equations of time-dependent vorticity-stream function and thermal energy are discretized and solved using a self-developed finite difference code in MATLAB®environment.Time dependence of fluid thermodynamics is envisaged through contour and image plots.A commercial simulation software,Ansys Fluent®utilizing a finite element code is employed to verify the finite difference results produced.Although the effect of viscous heating is very minimal,Neumann no-slip and free-slip boundary conditions are able to trap the heat inside the fully insulated cavity as the heat flux is constantly supplied at the top lid.A lower Reynolds number and a greater Prandtl number with free-slip effects reduce temperature distribution in the cavity with a faster velocity than in the no-slip condition as the free-slip behaves as a lubricant.展开更多
Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system.In this work the accelerating motion of a single solid particle is mathematically formu...Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system.In this work the accelerating motion of a single solid particle is mathematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvilinear coordinate system.The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number(Re)from 10 to 200 and the dimensionless acceleration(A)between2.0 to 2.0.The simulation demonstrates that the total drag is heavily correlated with A,and large deceleration even drops the drag force to a negative value.It is found that the value of virtual mass force coefficient(CV)of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re.However,the total drag coefficient(CDV)is successfully correlated as a function of Re and A,and it increases as A is increased.The proposed correlation of total drag coefficient may be used for simulation of solid–liquid flow with better accuracy.展开更多
In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flow...In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flows because the regions near to the boundaries generally play an important role on the defined solutions. Using the vorticity-stream function form of the N-S equations as governing equations in the flow field simulation with irregular mesh, the determining/calculating wall vorticity under irregular mesh is very important. In this paper, one first order formula of wall vorticity under irregular mesh was derived based on the 2-D Taylor expansion and was tested numerically through an example of a flow with the Z type, shape of boundaries. A satisfactory result was found which was compared with one obtained by FEM.展开更多
The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for ...The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.展开更多
基金funding received from the Ministry of Higher Education,Malaysia and University of Malaya(https://umresearch.um.edu.my/)under the Project No:IIRG006C-19IISS leaded by Z.Siri for this study。
文摘The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration.The investigation is carried out by assuming a two-dimensional laminar in-compressible fluid flow subject to Neumann boundary conditions throughout the numerical iterations in a transient analysis.All the walls of the square cavity are perfectly insulated and the top moving lid produces a constant finite heat flux even though the fluid flow attains the steady-state condition.The objective is to examine the effects of viscous heating in the fully insulated lid-driven cavity under no-slip and free-slip Neumann boundary conditions coupled with variations in Reynolds and Prandtl numbers.The partial differential equations of time-dependent vorticity-stream function and thermal energy are discretized and solved using a self-developed finite difference code in MATLAB®environment.Time dependence of fluid thermodynamics is envisaged through contour and image plots.A commercial simulation software,Ansys Fluent®utilizing a finite element code is employed to verify the finite difference results produced.Although the effect of viscous heating is very minimal,Neumann no-slip and free-slip boundary conditions are able to trap the heat inside the fully insulated cavity as the heat flux is constantly supplied at the top lid.A lower Reynolds number and a greater Prandtl number with free-slip effects reduce temperature distribution in the cavity with a faster velocity than in the no-slip condition as the free-slip behaves as a lubricant.
基金supported by the National Key Research and Development Program(2020YFA0906804)the National Natural Science Foundation of China(22035007,91934301)+1 种基金External Cooperation Program of BIC,Chinese Academy of Sciences(122111KYSB20190032)Chemistry and Chemical Engineering Guangdong Laboratory,Shantou(No.1922006).
文摘Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system.In this work the accelerating motion of a single solid particle is mathematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvilinear coordinate system.The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number(Re)from 10 to 200 and the dimensionless acceleration(A)between2.0 to 2.0.The simulation demonstrates that the total drag is heavily correlated with A,and large deceleration even drops the drag force to a negative value.It is found that the value of virtual mass force coefficient(CV)of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re.However,the total drag coefficient(CDV)is successfully correlated as a function of Re and A,and it increases as A is increased.The proposed correlation of total drag coefficient may be used for simulation of solid–liquid flow with better accuracy.
文摘In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flows because the regions near to the boundaries generally play an important role on the defined solutions. Using the vorticity-stream function form of the N-S equations as governing equations in the flow field simulation with irregular mesh, the determining/calculating wall vorticity under irregular mesh is very important. In this paper, one first order formula of wall vorticity under irregular mesh was derived based on the 2-D Taylor expansion and was tested numerically through an example of a flow with the Z type, shape of boundaries. A satisfactory result was found which was compared with one obtained by FEM.
文摘The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.
