The secondary flow and its stability for natural convection in a tall vertical enclosure

Abstract

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air, and the time-periodic flow of oil (Prandtl numbers of 0.71 and 1000, respectively) are investigated and descriptions of these flows using both physical and spectral approaches are presented. The details of the time dependency of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The spectra of kinetic energy and thermal variance for air are found to be smooth and viscously dominated. Similar spectra for oil are bumpier, and the dynamics of the time-dependent flow are determined to be confined to the lower end of the spectrum alone.The three-dimensional linear stability of the multicellular flow of air is parametrically studied. The domain of stable two-dimensional cellular motion was found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550 (with the critical Grashof number for the base flow being 8037). Therefore the flow of air in a sufficiently tall vertical enclosure should be considered to be three-dimensional for most practical applications.

The modelling of buoyancy driven flow in bubble columns

“…In the prediction of the lateral convection of heat, it is beneficial to the numerical solution of the transport equations to split the flow into basic flow and secondary mean flow quantities [21][22].…”

“…The basic profile for the gas-liquid flow (40) was obtained from the reported experimental velocity profiles of Degaleesan et al [13][ [17][18][19] and the lateral heat convection profile (39) was the laminar flow profile of Chait and Korpela [22]. Reynolds stresses therefore are intrinsically important in attempting to capture the turbulence effects in the fluid flow that arises from the differences in density.…”

“…2) and plane fields (Fig. 3a.), when solving gas-liquid motion with k-ε the two-dimensional turbulence model [22]. The corresponding structures are only observed within the fully three-dimensional simulation where the corresponding vector fields are depicted in Fig.…”

“…Heat transport has been long established in the modelling of turbulent flows particularly when simulating natural convection in cavities with large height to diameter ratios [21][22]. The convection of heat across the width of the mesh provides an excellent example of how to simulate the turbulent interactions in buoyancy driven flows.…”

“…The investigations of Chait and Korpela [22] provide the basis for the simulation of buoyancy driven flows where heat causes local differences in the fluid density.…”