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 Title
 An analysis of mushchimney structure.
 Creator

Yang, YoungKyun., Florida State University
 Abstract/Description

When a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its...
Show moreWhen a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its permeability to the liquid flow. In particular, if a binary alloy (for example, NH$\sb4$ClH$\sb2$O solution) is cooled at bottom and a dense component (for example, NH$\sb4$Cl) is solidified, buoyant material released during freezing in the pores returns to the melt only through thin, vertical, but widely separated, 'chimneys', the flow through the matrix between them being organized to supply these chimneys., We presented photos of a mushchimney system obtained from the ammonium chloride experiment, and we studied how convection with horizontal divergence affects the structure and flow of the mushchimney system. We use a simple ODE system in the mush derived by assuming that the temperature depends on vertical coordinate only. We find that the mass fraction of solid increases and the depth of a mush decreases when the strength of convection increases., We present an axisymmetric model containing only one chimney to analyze the structure of the mushchimney system. We find solutions of the temperature, the solid fraction, and the pressure in the chimney wall. In particular, the pressure expression shows that the fluid flow needs a huge pressure in order to pass through the chimney wall if its permeability is very small., We assume that a ratio of composition is large, which allows us to neglect the pressure contribution of the chimney wall. We use the knowledge of the variables in the mush, evaluated on the chimney wall, to find the fluid flow in the chimney and the radius of chimney. Our procedure employs the von KarmanPohlhausen technique for determining chimney flow (Roberts & Loper, 1983) and makes use of the fact that the radius of the chimney is much less than the thickness of the mush. We find a relation between a parameter measuring the ratio of viscous and buoyancy forces in the chimney and the vertical velocity component on the top of the mush, and estimate numerically the value of this velocity measuring the strength of convection. The results obtained show reasonably good agreement with theoretical and experimental works (Roberts & Loper (1983), Chen & Chen (1991), Tait & Jaupart (1992), Hellawell etc. (1993), Worster (1991)).
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9540067, 3088707, FSDT3088707, fsu:77509
 Format
 Document (PDF)
 Title
 On the characterization of turbulent thermal convection as spatiotemporal chaos.
 Creator

Jayakumar, P. K., Florida State University
 Abstract/Description

Direct numerical simulation of two dimensional turbulent thermal convection of an incompressible fluid (Prandtl number = 0.71) in a laterally heated rigid box has been carried out for a range of Rayleigh numbers. The nonlinear dynamics of the turbulent convection is studied using tools of Dynamical Systems Theory. The KarhunenLoeve dimension of the turbulent flow is found to vary from 49 at Rayleigh number $Ra = 4\times10\sp8$ to 127 at $Ra = 10\sp9$. The characterization of turbulence as...
Show moreDirect numerical simulation of two dimensional turbulent thermal convection of an incompressible fluid (Prandtl number = 0.71) in a laterally heated rigid box has been carried out for a range of Rayleigh numbers. The nonlinear dynamics of the turbulent convection is studied using tools of Dynamical Systems Theory. The KarhunenLoeve dimension of the turbulent flow is found to vary from 49 at Rayleigh number $Ra = 4\times10\sp8$ to 127 at $Ra = 10\sp9$. The characterization of turbulence as spatiotemporal chaos has been investigated in detail by studying the spatial variation of local dynamics whose properties vary throughout the domain. Spatial maps of the dimensional complexity and Lyapunov exponent of the local dynamics are constructed. Analysis of the spatial variation of these quantities revealed significant heterogeneity and sharp gradients. Numerical support for the relationship between the distribution of local Lyapunov exponents and that of the energy dissipation rate as conjectured earlier by Ruelle (1991) is presented. The implications of the factorization of the global dynamics due to the spatial localization of the local chaotic dynamics are discussed. It is shown that hierarchical partitioning of the global system into spatially coherent subsystems can in principle lead to a lower dimensional description of turbulence. A quantity called coherence parameter is introduced for detecting the spatiotemporal coherence of a turbulent flow.
Show less  Date Issued
 1992, 1992
 Identifier
 AAI9306036, 3087995, FSDT3087995, fsu:76802
 Format
 Document (PDF)
 Title
 On the motion of a rigid cylinder parallel to its axis in a rotating electrically conducting fluid.
 Creator

Ruan, Kezhi., Florida State University
 Abstract/Description

In an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder...
Show moreIn an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder. The flow structure is found by solving a twodimensional (independent of the axial coordinate) mixed boundary value problem. Approximate analytic solutions for velocity field and perturbed magnetic field are obtained. The buoyancy driven rise speed of the cylinder is calculated. The results are consistent with the those derived from Moore and Saffman (1969) and given by Hasimoto (1960) as limiting cases. The numerical value of dimensional rise speed obtained is in good agreement with the typically quoted rise speed in geophysics.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9525925, 3088642, FSDT3088642, fsu:77444
 Format
 Document (PDF)