1,497 research outputs found

    Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

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    Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions

    A Stokes-Brinkman model of the fluid flow in a periodic cell with a porous body using the boundary element method

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    The problem of viscous incompressible flow in a periodic cell with a porous body is solved. The Stokes flow model is adopted to describe the flow outside the body and the Brinkman equation is applied to find the filtration velocity field inside the porous domain. The conditions on the boundary between the free fluid and the porous medium for the porous body of arbitrary shape are obtained. The boundary value problem for the joint solution of the biharmonic and Brinkman equations for the stream functions outside and inside the porous body are then solved using a boundary element method. Good agreement of the numerical and analytical models for the Kuwabara circular cell model is shown for the fluid flow through a porous circular cylinder. The fluid flow past a circular, square, triangular cylinders and a circular body of uneven surface (an idealized model of a viral capsid) in a rectangular periodic cell are calculated. Comparison of the results obtained with the numerical solution from a CFD ANSYS/FLUENT model shows good accuracy of the developed mathematical model

    Simulation of Cavity Flow by the Lattice Boltzmann Method

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    A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives accurate results over a wide range of Reynolds numbers. Studies of errors and convergence rates are carried out. Compressibility effects are quantified for different maximum velocities, and parameter ranges are found for stable simulations. The paper's objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers.Comment: Submitted to J. Comput. Physics, late

    Computational fluid mechanics utilizing the variational principle of modeling damping seals

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    A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed

    Suppression of von K\'arm\'an vortex streets past porous rectangular cylinders

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    Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, where also the convective terms are retained to correctly account for the inertial effects at high values of permeability. Different aspect ratios of the cylinder are considered, varying the thickness-to-height ratios, t/d, from 0.01 (flat plate) to 1.0 (square cylinder). The results show that the permeability of the bodies has a strong effect in modifying the characteristics of the wakes and of the associated flow instabilities, while the porosity weakly affects the resulting flow patterns. In particular, the fluid flows through the porous bodies and, thus, as the permeability is progressively increased, the recirculation regions, initially attached to the rear part of the bodies, at first detach from the body and, eventually, disappear even in the near wakes. Global stability analyses lead to the identification of critical values of the permeability above which any linear instability is prevented. Moreover, a different scaling of the non-dimensional permeability allows to identify a general threshold for all the configurations here studied that ensures the suppression of vortex shedding, at least in the considered parameter space.Comment: 31 pages and 17 figure

    Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

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    The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh

    Simulation of natural convection heat transfer in a 2-D trapezoidal enclosure

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    Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energy-related applications, in case of proper design enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 10(3)<ra<10(5) and Prandtl number (Pr=0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra=10(4)). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported

    Simulation of three dimensional double-diffusive throughflow in internally heated anisotropic porous media

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    A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the steady state throughflow. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold. © 2014 Elsevier Ltd. All rights reserved
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