Katsuyoshi Kamakura

Experimental and numerical analyses of double diffusive natural convection heated and cooled from opposing vertical walls with an initial condition of a vertically linear concentration gradient

Abstract When a solution having a vertically linear concentration gradient is heated from a vertical wall and cooled from an opposing vertical wall, multi-layered roll cells separated by almost-horizontal sharp interfaces are observed. A Galerkin finite element method was employed for the numerical analyses of this double diffusive convection. Computations were carried out for the Prandtl number Pr = 6, the Lewis number Le = 100, an aspect ratio A = 4, the Rayleigh number Ra = 10 6 and a buoyancy ratio N = 10 or 20. Multi-layered roll cells with sharp and almost-horizontal interfaces were formed in the numerical simulation and then the concentration in each layer became almost uniform. The experiment confirmed the numerical results.

Oscillatory phenomena of low-Prandtl-number fluids in a rectangular cavity

The oscillatory phenomena in natural convection of low-Prandtl-number fluids were studied numerically in a rectangular cavity with horizontal temperature gradient at Prandtl number Pr = 0.01, aspect ratio A = 1, 2, or 4, and Rayleigh number Ra = 10{sup 4}, 10{sup 5}, or 10{sup 6}. In the case of A = 1 a main strong round roll cell was formed at Ra = 10{sup 4}. However, at Ra = 10{sup 5} and 10{sup 6}, two secondary roll cells in the core of a main roll cell were formed and rotated around the center of the system. The flow was oscillating. In the case of A = 2, i.e., a taller regime, the shape of the main roll cell varied with time at and above Ra = 10{sup 4}, and then the secondary complicated weak roll cells were formed above and below the main roll cell. This resulted in oscillatory phenomena even at Ra = 10{sup 4}. In the case of A = 4, three main roll cells were formed. At Ra = 10{sup 5}, secondary roll cells were formed between the main roll cells and then oscillation of flow occurred.

Numerical analyses of transient formation and degradation process of multilayered roll cells with double-diffusive natural convection in an enclosure

When a solution having a linear concentration gradient along the gravitational direction is heated from a vertical wall and cooled from an opposing vertical wall, multilayered roll cells separated by near-horiwntal sharp interfaces are observed. This paper presents a finite-element computational scheme to simulate this phenomenon. Computations were carried out for Pr = 6, Le = 100, A = 8, N = 2 or S, and Ra = I04 or 105. In the numerical simulation, two roll cells appeared, one just below the top free surface and one just above the bottom plane. Subsequently, one or several roll cells appeared between them, and finally they converged to a single roll cell.

Effect of the temperature dependence of fluid properties on the migration of an interface in double-diffusive natural convection

Experimental observation has shown that a slightly tilted sharp interface between two convection layers in double-diffusive natural convection migrates perpetually upward gradually with time. This movement of an interface cannot be explained by a simple mathematical model of constant physical properties. The present paper studies the numerical analyses of two-layer convection with the temperature dependence of the properties of the fluid. The perpetual upward migration of an interface was found to be promoted mainly by the temperature dependence of the volumetric coefficient of thermal expansion and also by that of the kinematic viscosity. However, the diffusion coefficient was independent of the migration. The upward migration of an interface appears to be caused by the difference between the intensity of etching due to the flow along the hot wall in the lower layer and that along the cold wall in the upper layer.

Onset of Multilayer Convection in a Partially Heated Circular Cavity

In this article, the time-dependent double-diffusive natural convection is investigated inside a circular cavity containing stably stratified brine solution. The container is heated partially through its sidewalls by a constant heat flux rate. By using Galerkin finite element method, numerical solutions to the Navier-Stokes equations under the Boussinesq flow assumptions have been systematically organized and developed. The evolutions of the stream function, temperature and concentration fields are presented in each evaluated case. Steep and sharp concentration variation in the interfaces together with wavy distribution of temperature within the layers is observed. At first a length scale, which is the vertical displacement of a heated element of the fluid, in a stably stratified solution under Neumann boundary condition is defined. Then a special form of Rayleigh number based on the length scale is obtained and named as universal Rayleigh number. A categorization based on single, two and multilayer formation is established. Temperature distribution along the cavity in the different cases shows a correlation between heat transfer coefficient and the rate of formation and degradation of the layers.

Double diffusive natural convection of smoke in a main flow

The double diffusive natural convection of smoke in a horizontal main flow was numerically studied at the Prandtl number Pr = 0.71, the aspect ratio A = 1, the Rayleigh number Ra = 107 – 109, the Peclet number Pe = Re·Pr = 1000–3000, the buoyancy ratio N = 0.8 – 1.2 and the Lewis number Le = 0.5 – 5. Double diffusive phenomena with plumes occurred downstream at Ra = 109. When the Peclet number is small, the smoke was extensively disordered downstream. When the Lewis number is smaller or greater than unity, the smoke was disordered downstream and separated into the thermal and solutal plumes. Then the lower side of smoke had strong plumes at Le > 1 and the upper side had strong plumes at Le < 1.