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Convection Terms (convection + term)
Selected AbstractsFinite element analysis of vortex shedding using equal order interpolationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2002Y. J. Jan Abstract An operator splitting and element-by-element conjugated gradient solver, and equal order interpolations are applied for solving time dependent Navier,Stokes (NS) equations to simulate flow induced vortex shedding in the present study. In addition, the convection term is corrected by balanced tensor diffusivity, which can stabilize the numerical simulation and overcome the numerical oscillations. The evolution of the interested flowing properties with time is analyzed by using spectral analysis. The developed code has been validated by the application of two examples: a driven cavity flow and a flow induced vortex vibration. Results from the first example for Reynolds number Re=103 and Re=104 are compared with other numerical simulations. Results from the second example, uniform flow past a square rod over a wide range of high Reynolds numbers from Re=103,105, are compared with experimental data and other numerical studies. Copyright © 2002 John Wiley & Sons, Ltd. [source] DIMENSIONLESS CORRELATIONS FOR CONVECTIVE HEAT TRANSFER IN CANNED PARTICULATE FLUIDS UNDER AXIAL ROTATION PROCESSINGJOURNAL OF FOOD PROCESS ENGINEERING, Issue 2010MRITUNJAY DWIVEDI ABSTRACT Dimensionless correlations for estimating heat transfer coefficients (U and hfp) in canned high viscosity Newtonian liquids (with and without particles) were developed using stepwise multiple nonlinear regressions of statistically significant dimensionless groups using tangent as an estimate and Newton as search method. Data on overall heat transfer coefficient U and fluid-to-particle heat transfer coefficients hfpwere obtained for several processing conditions and were analyzed separately for particle and particle-free conditions. In free axial mode, a newly developed form, combining natural and forced convection, provided higher R2 = 0.93. In the absence of particles in end-over-end mode, introducing natural convection term (Gr × Pr), improved R2 from 0.81 to 0.97. Combination of the reel radius, radius of the can and radius of the particles was chosen as characteristics length. PRACTICAL APPLICATIONS Most earlier dimensionless correlations for a canned liquid particulate mixture subjected to free axial mode of agitation are present for either U or hfp individually due to the difficulties in obtaining time,temperature profiles of the liquid and particles simultaneously; however, the time,temperature prediction at the particle center requires appropriate correlations for both U and hfp and cannot be made with only one of these coefficients. Additionally, importance of natural convection in forced convection heat transfer correlations has been demonstrated by developing the U and hfp correlations using the mixed convection approach as the combination of natural and forced convection heat transfer. These developed correlations would help in modeling the time,temperature profiles of a canned particulate mixture and will be helpful in determining the contribution of natural and forced convection heat transfer. These dimensional numbers would give a better understanding of the physical phenomenon and can also be easily used for scale-up purposes. [source] A discrete splitting finite element method for numerical simulations of incompressible Navier,Stokes flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Kenn K. Q. Zhang Abstract The presence of the pressure and the convection terms in incompressible Navier,Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill-conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non-linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite element modelling of free-surface flows with non-hydrostatic pressure and k,, turbulence modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005C. Leupi Abstract Validation of 3D finite element model for free-surface flow is conducted using a high quality and high spatial resolution data set. The commonly numerical models with the conventional hydrostatic pressure still remain the most widely used approach for the solution of practical engineering problems. However, when a 3D description of the velocity field is required, it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the presence of short waves and/or strong bathymetry gradient, and/or strong channel curvature. A numerical solution is based on the unsteady Reynolds-averaged Navier,Stokes equations on the unstructured grid. The eddy viscosity is calculated from the efficient k,, turbulence model. The model uses implicit fractional step time stepping, and the characteristics method is used to compute the convection terms in the multi-layers system (suitable for the vertical stratified fluid flow), in which the vertical grid is located at predefined heights and the number of elements in the water column depends on water depth. The bottommost and topmost elements of variable height allow a faithful representation of the bed and the time-varying free-surface, respectively. The model is applied to the 3D open channel flows of various complexity, for which experimental data are available for comparison. Computations with and without non-hydrostatic are compared for the same trench to test the validity of the conventional hydrostatic pressure assumption. Good agreement is found between numerical computations and experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] An efficient finite difference scheme for free-surface flows in narrow rivers and estuariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003XinJian ChenArticle first published online: 13 MAY 200 Abstract This paper presents a free-surface correction (FSC) method for solving laterally averaged, 2-D momentum and continuity equations. The FSC method is a predictor,corrector scheme, in which an intermediate free surface elevation is first calculated from the vertically integrated continuity equation after an intermediate, longitudinal velocity distribution is determined from the momentum equation. In the finite difference equation for the intermediate velocity, the vertical eddy viscosity term and the bottom- and sidewall friction terms are discretized implicitly, while the pressure gradient term, convection terms, and the horizontal eddy viscosity term are discretized explicitly. The intermediate free surface elevation is then adjusted by solving a FSC equation before the intermediate velocity field is corrected. The finite difference scheme is simple and can be easily implemented in existing laterally averaged 2-D models. It is unconditionally stable with respect to gravitational waves, shear stresses on the bottom and side walls, and the vertical eddy viscosity term. It has been tested and validated with analytical solutions and field data measured in a narrow, riverine estuary in southwest Florida. Model simulations show that this numerical scheme is very efficient and normally can be run with a Courant number larger than 10. It can be used for rivers where the upstream bed elevation is higher than the downstream water surface elevation without any problem. Copyright © 2003 John Wiley & Sons, Ltd. [source] Computation of unsteady viscous incompressible flows in generalized non-inertial co-ordinate system using Godunov-projection method and overlapping meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002H. Pan Abstract Time-dependent incompressible Navier,Stokes equations are formulated in generalized non-inertial co-ordinate system and numerically solved by using a modified second-order Godunov-projection method on a system of overlapped body-fitted structured grids. The projection method uses a second-order fractional step scheme in which the momentum equation is solved to obtain the intermediate velocity field which is then projected on to the space of divergence-free vector fields. The second-order Godunov method is applied for numerically approximating the non-linear convection terms in order to provide a robust discretization for simulating flows at high Reynolds number. In order to obtain the pressure field, the pressure Poisson equation is solved. Overlapping grids are used to discretize the flow domain so that the moving-boundary problem can be solved economically. Numerical results are then presented to demonstrate the performance of this projection method for a variety of unsteady two- and three-dimensional flow problems formulated in the non-inertial co-ordinate systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] An implicit velocity decoupling procedure for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002Kyoungyoun Kim Abstract An efficient numerical method to solve the unsteady incompressible Navier,Stokes equations is developed. A fully implicit time advancement is employed to avoid the Courant,Friedrichs,Lewy restriction, where the Crank,Nicolson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity,pressure decoupling is achieved in conjunction with the approximate factorization. The main emphasis is placed on the additional decoupling of the intermediate velocity components with only nth time step velocity. The temporal second-order accuracy is preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving several test cases, in particular, the turbulent minimal channel flow unit. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||