Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites

1995 ◽  
Vol 448 (1933) ◽  
pp. 161-190 ◽  
Keyword(s):  
Effective Conductivity ◽  
Main Tool ◽  
Two Dimensional ◽  
Two Phase ◽  
Fractional Linear Transformation ◽  
Optimal Bounds ◽  
Conductivity Function ◽  
Similar Class ◽  
Original Class ◽  
Class Of Functions

The effective conductivity function of a two-phase two-dimensional composite is known to be a tensor valued analytic function of the component conductivities, assumed here to be isotropic. Optimal bounds correlating the values this function can take are derived. These values may correspond to the measured effective magnetic permeabilities, thermal conductivities, or any other transport coefficient mathematically equivalent to the effective conductivity. The main tool in this derivation is a new fractional linear transformation which maps the appropriate class of conductivity functions passing through a given point to a similar class of functions which are not subject to the restriction of passing through a known point. Crude bounds on this class of functions give rise to sharp bounds on the original class of effective conductivity functions. These bounds are the best possible, being attained by sequentially layered laminate microgeometries.

Modelling the effective conductivity function of an arbitrary two–dimensional polycrystal using sequential laminates

1994 ◽  
Vol 124 (4) ◽  
pp. 757-783 ◽  
Author(s):  
Karen E. Clark ◽  
Graeme W. Milton
Keyword(s):  
Polycrystalline Material ◽  
Effective Conductivity ◽  
Dimensional Space ◽  
Conductivity Tensor ◽  
Finite Dimensional Space ◽  
Two Dimensional ◽  
Geometrical Configuration ◽  
Pure Crystal ◽  
Finite Dimensional ◽  
Conductivity Function

The effective conductivity tensor σ*of a two-dimensional polycrystalline material depends on the conductivity tensor σ0of the pure crystal from which the polycrystal is constructed and on the geometrical configuration of grains in the polycrystal, represented by a rotation fieldR(x) giving the orientation of the crystal at each pointx.Here it is established that the dependence of σ*on σ0in any polycrystal, with R (x) held fixed, can be mimicked exactly by a polycrystal constructed by sequential lamination. It is first shown that the effective conductivity function is perturbed only slightly if we truncate the Hilbert space of fields in the polycrystal to a finitedimensional space. Then the structure of this finite-dimensional space of fields is shown to be isomorphic to the structure of the finite-dimensional space of fields associated with the sequential laminate. In particular, there is an operation which corresponds to peeling away the layers in the sequential laminate and successively reducing the dimension of the space of fields.

Features of spatial shock-wave flows in vapor-gas-liquid mixtures

2014 ◽  
Vol 10 ◽  
pp. 27-31
Author(s):  
R.Kh. Bolotnova ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
High Pressure ◽  
Shock Waves ◽  
Liquid Mixture ◽  
Liquid Mixtures ◽  
Pressure Vessels ◽  
Water Mixture ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Two Phase

The two-phase model of vapor-gas-liquid medium in axisymmetric two-dimensional formulation, taking into account vaporization is constructed. The nonstationary processes of boiling vapor-water mixture outflow from high-pressure vessels as a result of depressurization are studied. The problems of shock waves action on filled by gas-liquid mixture volumes are solved.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Regularization of a two-dimensional two-phase inverse Stefan problem

1997 ◽  
Vol 13 (3) ◽  
pp. 607-619 ◽  
Author(s):  
D D Ang ◽  
A Pham Ngoc Dinh ◽  
D N Thanh
Keyword(s):  
Stefan Problem ◽  
Two Dimensional ◽  
Two Phase
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