Asymptotic analysis of a three-dimensional Bridgman furnace at large Rayleigh number

1999 ◽  
Vol 11 (7) ◽  
pp. 1827-1846 ◽  
Author(s):  
M. R. Foster
Keyword(s):  
Rayleigh Number ◽  
Asymptotic Analysis ◽  
Three Dimensional ◽  
Large Rayleigh Number

A local nonlinear solution as an approximation to low-frequency spanwise jitter in thermoconvective flows

2002 ◽  
Vol 469 ◽  
pp. 343-367
Author(s):  
P. GRASSIA ◽  
D. RICHARDSON
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temperature Fields ◽  
Microgravity Environment ◽  
Anomalous Scaling ◽  
Dimensional Complexity ◽  
Large Rayleigh Number

A shallow fluid-filled cavity with a longitudinal applied temperature gradient is subjected to spanwise accelerations (g-jitter) representing the space-based microgravity environment. A simplified slot model is introduced to describe the buoyancy-driven flow and advected temperature fields produced in the cavity. Numerical solutions indicate that boundary layer behaviour can manifest itself in the limit of strong g-jitter (large Rayleigh number Ra). However, boundary layer thicknesses do not obey the conventional Ra−1/4 scaling that typically arises in free thermal convection problems. This anomalous scaling results from the three-dimensional complexity of the flow and advected temperature fields, which are not themselves produced by a single fixed applied temperature change. Three different regimes are identified at large Rayleigh number characterized by the shapes of the advected temperature profiles. These regimes are selected according to the values of the Biot number Bi and an aspect ratio parameter. Simple models are presented of the boundary layer behaviour which reproduce, in each regime, the numerically predicted scalings for boundary layer thickness and advected temperature. These models give a succinct overall picture of the slot behaviour in the buoyancy-dominated limit.

Three-dimensional asymptotic analysis of multiple-electroded piezoelectric laminates

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 317-324 ◽  
Author(s):  
Zhen-Qiang Cheng ◽  
R. C. Batra
Keyword(s):  
Asymptotic Analysis ◽  
Three Dimensional

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

scholarly journals Spectral properties of magnetohydrodynamic convection with mean horizontal temperature gradient

2006 ◽  
Vol 2 (S239) ◽  
pp. 513-513
Author(s):  
D. Skandera ◽  
W.-Ch. Müller
Keyword(s):  
Temperature Field ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Numerical Code ◽  
Dimensional System ◽  
Horizontal Temperature Gradient ◽  
Mhd Turbulence

AbstractSpectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations (Skandera D. & Müller W.-C. 2006). The investigated system is set up with a mean horizontal temperature gradient in order to avoid a development of elevator instabilities in a fully periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equation are solved by a numerical code (Müller & Biskamp 2000) that uses a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Obtained results are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence (Müller & Biskamp 2000). While the three-dimensional system is found to operate in a Kolmogorov-like regime where buoyant forces have a negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra ∼106), the two-dimensional system exhibits interesting irregular quasi-oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime of turbulence and a standard Iroshnikov-Kraichnan-like regime of turbulence (Müller & Biskamp 2000). The most important parameter determining the turbulent regime of 2D magnetoconvection, apart from a high Rayleigh number, seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer in spectral space. Kinetic, magnetic and temperature energy are transported by a turbulent cascade from large to smaller scales. The local/nonlocal character of the transport is tested for several individual terms in the governing equations. Moreover, other statistical quantities, e.g. probability density functions, are computed as well. A passive character of the temperature field in the investigated three-dimensional magnetoconvection is supported by computations of intermittency using extended self-similarity. The intermittency of the Elsasser field z+ is in agreement with results from numerical simulations of isotropic MHD turbulence (Müller & Biskamp 2000). The intermittency of the temperature field is found to approximately agree with results of passive scalar measurements in hydrodynamic turbulence (Ruiz-Chavarria, Baudet & Ciliberto 1996).

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

Convection fluid dynamics in a model of a fault zone in the earth's crust

1978 ◽  
Vol 88 (4) ◽  
pp. 769-792 ◽  
Author(s):  
D. R. Kassoy ◽  
A. Zebib
Keyword(s):  
Fluid Dynamics ◽  
Rayleigh Number ◽  
Porous Material ◽  
Fault Zone ◽  
Slug Flow ◽  
Tectonic Activity ◽  
Two Dimensional ◽  
Core Flow ◽  
Number Flow ◽  
Large Rayleigh Number

Faulted regions associated with geothermal areas are assumed to be composed of rock which has been heavily fractured within the fault zone by continuous tectonic activity. The fractured zone is modelled as a vertical, slender, two-dimensional channel of saturated porous material with impermeable walls on which the temperature increases linearly with depth. The development of an isothermal slug flow entering the fault at a large depth is examined. An entry solution and the subsequent approach to the fully developed configuration are obtained for large Rayleigh number flow. The former is characterized by growing thermal boundary layers adjacent to the walls and a slightly accelerated isothermal core flow. Further downstream the development is described by a parabolic system. It is shown that a class of fully developed solutions is not spatially stable.

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