Numerical analysis of three-dimensional MHD natural convection flow in a short horizontal cylindrical annulus

Li, Ben-Wen; Varghese, Philip-Leslie; Leng, Xue-Yuan; Tian, Xi-Yan

doi:10.1016/j.icheatmasstransfer.2018.09.009

Cited by 13 publications

(5 citation statements)

References 30 publications

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“…The present results are compared with those benchmark results as shown in Tables I and II. It is obvious that the present results of average Nusselt number Nutrue¯ on the isothermal walls match well with those results in these works (Wang et al , 2018; Li et al , 2016; Peng et al , 2004; Tric et al , 2000; Fusegi et al , 1991) under different Ra with Pr = 0.71. In Table II, a comparison of the average Nusselt number Nutrue¯ on isothermal walls is shown under different nodes.…”

Section: Resultssupporting

confidence: 91%

“…In Table II, a comparison of the average Nusselt number Nutrue¯ on isothermal walls is shown under different nodes. The results are obtained by Wang et al (2018) with node number of 80 × 80 × 80, 100 × 100 × 100 and 150 × 150 × 150, while the present results are obtained only with node number of 20 × 20 × 20, 30 × 30 × 30 and 40 × 40 × 40. We can find that the present results with much fewer nodes can reach almost the same results for Ra = 10 4 , 10 5 and 10 6 .…”

Section: Resultscontrasting

confidence: 56%

“…The steady results can be obtained through solving the unsteady N-S equations when the pseudo time derivatives approach to zero. As a simplified, efficient and implementable method, the ACM has been widely applied to the solution of incompressible or weakly compressible fluid flow as shown in these works (Ramachandran and Puri, 2019; Vermeire et al , 2019; Wang et al , 2018; Kajzer and Pozorski, 2018; Bogaers et al , 2015; Silva and Semiao, 2012).…”

Section: Introductionmentioning

confidence: 99%

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Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Zhang

Cui

et al. 2020

HFF

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Purpose The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

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Section: Resultssupporting

confidence: 91%

Section: Resultscontrasting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

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Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Zhang

Cui

et al. 2020

HFF

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“…More than 200 papers were retrieved by database searches for 2015-2020 using the terms artificial compressibility, pseudo compressibility, and dual time stepping. These studies include analysis of the relationships between AC and fractional step methods [86,87], studies of turbulent flow [88][89][90], development of discontinuous Galerkin methods [91][92][93], parallel solution of large-scale problems [94][95][96], multi-fluid simulations [97], further advances to entropically-damped AC methods [98][99][100], implementation high-order numerical schemes [101][102][103], use of characteristic methods [104][105][106], application for non-hydrostatic effects [107,108], magneto-hydrodynamic simulations [109][110][111], solution with lattice Boltzmann methods [112], and solution by smoothed particle hydrodynamics [113,114]. Note the above are examples and should not be considered an exhaustive list of recent work.…”

Section: Recent Development Of the Artificial Compressibility Methodsmentioning

confidence: 99%

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Hodges

2020

Water

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Piping systems (e.g., storm sewers) that transition between free-surface flow and surcharged flow are challenging to model in one-dimensional (1D) networks as the continuity equation changes from hyperbolic to elliptic as the water surface reaches the pipe ceiling. Previous network models are known to have poor mass conservation or unpredictable convergence behavior at such transitions. To address this problem, a new algorithm is developed for simulating unsteady 1D flow in closed conduits with both free-surface and surcharged flow. The shallow-water (hydrostatic) approximation is used as the governing equations. The artificial compressibility (AC) method is implemented as a dual-time-stepping discretization for a finite-volume solver with timescale interpolation used for face reconstruction. A new formulation for the AC celerity parameter is proposed such that the AC celerity matches the equivalent gravity wave speed for the local hydraulic head—which has some similarities to the classic Preissmann Slot used to approximate pressurized flow in conduits. The new approach allows the AC celerity to be set locally by the flow (i.e., non-uniform in space) and removes it as a free parameter of the AC solution method. The derivation of the AC method provides for only a minor change in the form of the solution equations when a computational element switches from free-surface to surcharged. The new solver is tested for both unsteady free-surface (supercritical, subcritical) and surcharged flow transitions in a circular pipe and is implemented in an open-source Python code available under the name “PipeAC.” The results are compared to laboratory experiments that include rapid flow changes due to opening/closing of gates. Results show that the new algorithm is satisfactory for 1D representation of unsteady transition behavior with two caveats: (i) sufficient grid resolution must be applied, and (ii) the shallow-water equation approximations (hydrostatic, single-fluid) limit the accuracy of the solution with regards to the celerity of the turbulent unsteady bore that propagates upstream. This research might benefit any piping network model that must smoothly handle unsteady transitions from free surface to surcharged flow.

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“…In that case, the bottom disk was heated and the top disk was cooled, both isothermally, resulting in a combined convection under the magnetic field. Wang et al [19] numerically computed the natural convection in a horizontal cylindrical annulus whose inner and outer cylinders were heated and cooled, respectively, under the presence of an axial magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric Natural Convection of Liquid Metal in an Annular Enclosure under the Influence of Azimuthal Magnetic Field

Masuda

Tagawa

2020

Energies

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Natural convection of liquid metal in an annular enclosure under the influence of azimuthal static magnetic field was numerically studied. The liquid metal in the enclosure whose cross-sectional area is square was heated from an inner vertical wall and cooled from an outer vertical wall both isothermally whereas the other two horizontal walls were assumed to be adiabatic. The static azimuthal magnetic field was imposed by a long straight electric coil that was located at the central axis of the annular enclosure. The computations were carried out for the Prandtl number 0.025, the Rayleigh number 104, 5 × 105 and 107, and the Hartmann number 0–100,000 by using an in-house code. It was found that the contour map of the electric potential was similar to that of the Stokes stream function of the velocity regardless of the Hartmann number. Likewise, the contour map of the pressure was similar to the Stokes stream function of the electric current density in the case of the high Hartmann number. The average Nusselt number was decreased in proportion to the square of the Hartmann number in the high Hartmann number regime.

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Numerical analysis of three-dimensional MHD natural convection flow in a short horizontal cylindrical annulus

Cited by 13 publications

References 30 publications

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Axisymmetric Natural Convection of Liquid Metal in an Annular Enclosure under the Influence of Azimuthal Magnetic Field

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