Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number

2021 ◽  
Author(s):  
John Carter ◽  
Nan Jiang
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Magnetic Reynolds Number ◽  
Second Order ◽  
Ensemble Method ◽  
Magnetohydrodynamics Equations

scholarly journals Second-order Solutions for Steady Magnetohydrodynamic Channel Flow with Anisotropic Conductivity

1972 ◽  
Vol 25 (6) ◽  
pp. 719
Author(s):  
DM Panton
Keyword(s):  
Reynolds Number ◽  
Perturbation Expansion ◽  
Magnetic Reynolds Number ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Anisotropic Conductivity ◽  
Square Channel ◽  
Flow Parameters ◽  
Flow Through ◽  
Magnetohydrodynamic Channel

Further investigation of steady magnetohydrodynamic flow through a straight channel of arbitrary cross section with nonconducting walls is considered, in the presence of anisotropic conductivity due to the Hall effect, where no restriction is made on the Reynolds number or magnetic Reynolds number. An approximate solution is provided by a perturbation expansion in terms of the Hall parameter, assumed small. Corrections are made to the first-order solutions established by Panton and Hosking (1971) and the solutions are then extended to the second order for a square channel. It is found that both the Reynolds number and magnetic Reynolds number terms have a significant influence on the mass transport, the former far outweighing the contribution to the flow established by Tani (1962) for the values of the flow parameters assumed.

Numerical Analysis of the Turbulent Flow Field Applied to Thermal Spallation Drilling

2004 ◽  
Author(s):  
Angela O. Nieckele ◽  
Luis Fernando Figueira da Silva ◽  
Joa˜o Carlos R. Pla´cido
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Flow Field ◽  
Gas Phase ◽  
Accurate Determination ◽  
Rock Surface ◽  
Drilling Technique ◽  
High Reynolds ◽  
Drilling Conditions ◽  
Volume Method

Thermal spallation is a possible drilling technique which consists of using hot supersonic jets as heat source to perforate hard rocks at high rates. This work presents a numerical analysis of a typical spallation drilling configuration, by the finite volume method. The time-averaged conservation equations of mass, momentum and energy are solved to determine the turbulent compressible gas phase flow field. Turbulence is predicted by the classical high Reynolds number κ-ε model, as well as with a low Reynolds number κ-ε model. The influence of the jet Reynolds number is investigated. Special attention is given to the rock surface temperature, since its accurate determination is required to predict spallation rates under field-drilling conditions.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

A Numerical Simulation Algorithm of the Inviscid Dynamics of Axisymmetric Swirling Flows in a Pipe

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
J. Granata ◽  
L. Xu ◽  
Z. Rusak ◽  
S. Wang
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Difference Scheme ◽  
Second Order ◽  
Swirling Flows ◽  
Inviscid Limit ◽  
Simulation Algorithm ◽  
Spatial Integration ◽  
Order Difference ◽  
Breakdown Process

Current simulations of swirling flows in pipes are limited to relatively low Reynolds number flows (Re < 6000); however, the characteristic Reynolds number is much higher (Re > 20,000) in most of engineering applications. To address this difficulty, this paper presents a numerical simulation algorithm of the dynamics of incompressible, inviscid-limit, axisymmetric swirling flows in a pipe, including the vortex breakdown process. It is based on an explicit, first-order difference scheme in time and an upwind, second-order difference scheme in space for the time integration of the circulation and azimuthal vorticity. A second-order Poisson equation solver for the spatial integration of the stream function in terms of azimuthal vorticity is used. In addition, when reversed flow zones appear, an averaging step of properties is applied at designated time steps. This adds slight artificial viscosity to the algorithm and prevents growth of localized high-frequency numerical noise inside the breakdown zone that is related to the expected singularity that must appear in any flow simulation based on the Euler equations. Mesh refinement studies show agreement of computations for various mesh sizes. Computed examples of flow dynamics demonstrate agreement with linear and nonlinear stability theories of vortex flows in a finite-length pipe. Agreement is also found with theoretically predicted steady axisymmetric breakdown states in a pipe as flow evolves to a time-asymptotic state. These findings indicate that the present algorithm provides an accurate prediction of the inviscid-limit, axisymmetric breakdown process. Also, the numerical results support the theoretical predictions and shed light on vortex dynamics at high Re.

Numerical Analysis of an Actively Cooled Low-Reynolds-Number Hypersonic Diffuser

2019 ◽  
Vol 33 (1) ◽  
pp. 32-48 ◽  
Author(s):  
Andrew J. Brune ◽  
Serhat Hosder ◽  
David Campbell ◽  
Stefano Gulli ◽  
Luca Maddalena
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Low Reynolds Number ◽  
Low Reynolds

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

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