Some duct flow problems at high Hartmann number

AbstractIn this paper we propose a development of the finite difference method, called the tailored finite point method, for solving steady magnetohydrodynamic (MHD) duct flow problems with a high Hartmann number. When the Hartmann number is large, the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer. Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy. However, the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh. Firstly, we devise the tailored finite point method for the scalar inhomogeneous convection-diffusion problem, and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations. For each interior grid point of a given rectangular mesh, we construct a finite-point difference operator at that point with some nearby grid points, where the coefficients of the difference operator are tailored to some particular properties of the problem. Numerical examples are provided to show the high performance of the proposed method.

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The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100046752 ◽

1971 ◽

Vol 69 (2) ◽

pp. 337-351 ◽

Cited By ~ 16

Author(s):

D. J. Temperley ◽

L. Todd

Keyword(s):

Magnetic Field ◽

Electrical Conductivity ◽

Applied Magnetic Field ◽

Hartmann Number ◽

Classical Model ◽

Critical Discussion ◽

Duct Flow ◽

Rectangular Duct ◽

Wall Conductivity ◽

Expansion Procedure

AbstractLaminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

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An exponential compact difference scheme for solving 2D steady magnetohydrodynamic (MHD) duct flow problems

Journal of Computational Physics ◽

10.1016/j.jcp.2012.05.010 ◽

2012 ◽

Vol 231 (16) ◽

pp. 5443-5468 ◽

Cited By ~ 12

Author(s):

Yan Li ◽

Zhen F. Tian

Keyword(s):

Difference Scheme ◽

Duct Flow ◽

Compact Difference Scheme ◽

Flow Problems ◽

Compact Difference

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Second-order far field computational boundary conditions for inviscid duct flow problems

10.2514/6.1991-633 ◽

1991 ◽

Cited By ~ 1

Author(s):

A. VERHOFF ◽

D. STOOKESBERRY

Keyword(s):

Boundary Conditions ◽

Second Order ◽

Far Field ◽

Duct Flow ◽

Flow Problems

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Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

Journal of Computational Physics ◽

10.1016/j.jcp.2010.08.034 ◽

2010 ◽

Vol 229 (24) ◽

pp. 9216-9234 ◽

Cited By ~ 15

Author(s):

Po-Wen Hsieh ◽

Suh-Yuh Yang

Keyword(s):

Coupled System ◽

Difference Schemes ◽

Diffusion Equations ◽

Duct Flow ◽

Convection Diffusion ◽

Flow Problems

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Simple Approximate Treatments of Certain Incompressible Duct Flow Problems Involving Separation

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1975_017_011_02 ◽

1975 ◽

Vol 17 (2) ◽

pp. 57-64 ◽

Cited By ~ 8

Author(s):

G. D. Matthew

Keyword(s):

Momentum Equation ◽

Head Loss ◽

Sudden Expansion ◽

Duct Flow ◽

Flow Problems ◽

Teaching Context ◽

Flow Geometry ◽

Simplifying Assumptions ◽

Satisfactory Approximation ◽

Good Agreement

Many examples of abrupt conduit change, for example, sudden or gradual contractions, mitre bends etc., have been treated by free-streamline, potential flow theory in conjunction with the classical Borda result for sudden expansion loss. These analyses have provided results which show moderate but rarely close agreement with experimental evidence. Here a fresh and simpler look is taken at such problems, on the basis of radical simplifying assumptions about the flow geometry and pressure distribution. It is demonstrated that direct application of the linear momentum equation, in association, where appropriate, with the Bernoulli equation, can yield results for head loss and contraction coefficients which are in consistently good agreement with experimental data (especially as far as head loss is concerned). It is shown in passing that these simplified arguments can even be used to provide a satisfactory approximation to the profile of a contracting jet, suggesting wider applications of the method in more complex geometrical situations. The analysis is advanced in a teaching context to illustrate the power of momentum and energy methods in providing immediately useful solutions to certain problems involving abrupt change.

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