Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method

2016 ◽  
Author(s):  
Diogo B. Pitz ◽  
John W. Chew ◽  
Olaf Marxen ◽  
Nicholas J. Hills
Keyword(s):  
Numerical Method ◽  
Boussinesq Approximation ◽  
Spectral Element ◽  
High Order ◽  
Element Approximation ◽  
Cavity Flows ◽  
Governing Equations ◽  
Stable Algorithm ◽  
Numerical Predictions ◽  
Rotating Cavity

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, similarly to a finite element method, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation, and no subgrid modelling is included in the governing equations. Numerical results obtained for the rotor/stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. For the buoyancy-driven flow, the energy equation is coupled to the momentum equations via the Boussinesq approximation, which has been implemented in the code considering two different formulations. Numerical predictions of the Nusselt number obtained using the traditional Boussinesq approximation are considerably higher than available experimental data. Much better agreement is obtained when the extended Boussinesq approximation is employed. It is concluded that the numerical method employed has considerable potential for further investigations of rotating cavity flows.

Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Diogo B. Pitz ◽  
John W. Chew ◽  
Olaf Marxen ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fourier Method ◽  
Spectral Element ◽  
Two Dimensions ◽  
High Order ◽  
Experimental Results ◽  
Element Approximation ◽  
Stable Algorithm ◽  
Element Discretization

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretization in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretize the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretization. Numerical results obtained for the rotor/stator cavity compare favorably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.

scholarly journals Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements

2019 ◽  
Vol 148 (1) ◽  
pp. 415-436
Author(s):  
Tae-Hyeong Yi ◽  
Francis X. Giraldo
Keyword(s):  
Computational Cost ◽  
Element Model ◽  
Atmospheric Model ◽  
Spectral Element ◽  
High Order ◽  
Spectral Elements ◽  
Test Cases ◽  
Governing Equations ◽  
Discretization Methods ◽  
Element Approach

Abstract This study addresses the treatment of vertical discretization for a high-order, spectral element model of a nonhydrostatic atmosphere in which the governing equations of the model are separated into horizontal and vertical components by introducing a coordinate transformation, so that one can use different orders and types of approximations in both directions. The vertical terms of the decoupled governing equations are discretized using finite elements based on either Lagrange or basis-spline polynomial functions in the sigma coordinate, while maintaining the high-order spectral elements for the discretization of the horizontal terms. This leads to the fact that the high-order model of spectral elements with a nonuniform grid, interpolated within an element, can be easily accommodated with existing physical parameterizations. Idealized tests are performed to compare the accuracy and efficiency of the vertical discretization methods, in addition to the central finite differences, with those of the standard high-order spectral element approach. Our results show, through all the test cases, that the finite element with the cubic basis-spline function is more accurate than the other vertical discretization methods at moderate computational cost. Furthermore, grid dependency studies in the tests with and without orography indicate that the convergence rate of the vertical discretization methods is lower than the expected level of discretization accuracy, especially in the Schär mountain test, which yields approximately first-order convergence.

scholarly journals Effect of magnetic field on nanofluid free convection in Conical Partially Annular Space

2020 ◽  
Vol 330 ◽  
pp. 01005
Author(s):  
Abderrahmane AISSA ◽  
Mohamed Amine MEDEBBER ◽  
Khaled Al-Farhany ◽  
Mohammed SAHNOUN ◽  
Ali Khaleel Kareem ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Boussinesq Approximation ◽  
Simulation Software ◽  
Comsol Multiphysics ◽  
Governing Equations ◽  
Element Analysis ◽  
Vertical Side ◽  
Side Walls

Natural convection of a magneto hydrodynamic nanofluid in a porous cavity in the presence of a magnetic field is investigated. The two vertical side walls are held isothermally at temperatures Th and Tc, while the horizontal walls of the outer cone are adiabatic. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Impact of Rayleigh number (Ra), Hartmann number (Ha) and nanofluid volume fraction (ϕ) are depicted. Results indicated that temperature gradient increases considerably with enhance of Ra and ϕ but it reduces with increases of Ha.

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

2016 ◽  
Vol 8 (4) ◽  
pp. 693-702
Author(s):  
Hongqiang Lu ◽  
Kai Cao ◽  
Lechao Bian ◽  
Yizhao Wu
Keyword(s):  
Finite Element Method ◽  
Discontinuous Galerkin ◽  
Mesh Generation ◽  
Discontinuous Galerkin Methods ◽  
Elasticity Modulus ◽  
High Order ◽  
Galerkin Methods ◽  
Governing Equations ◽  
Numerical Tests ◽  
Cubic Polynomial

AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

scholarly journals A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes

2016 ◽  
Vol 139 ◽  
pp. 148-160 ◽  
Author(s):  
David A. Kopriva ◽  
Andrew R. Winters ◽  
Marvin Bohm ◽  
Gregor J. Gassner
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element ◽  
Element Approximation ◽  
Hexahedral Meshes
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