Buoyancy-opposed Flow Research Articles

A direct numerical simulation of transition phenomena in a mixed convection channel flow

This study intends to provide an increased understanding of the laminar–turbulent transition phenomena for the buoyancy-assisted heated vertical channel flow during the early transient stage. The spectral method with weak formulation is applied in the direct numerical simulation. Initial disturbances consist of the finite-amplitude two-dimensional TS wave and a pair of three-dimensional oblique waves for the K-type disturbances. The results from the harmonic energy competitions of different wave modes show that for the buoyancy-assisted heated flow, the ( k x =1, k z =1) or (1,1) and (1,0) modes would gain energy immediately and start to rise at almost the same rate. This phenomenon is different from that of the buoyancy-opposed flow, where the (1,1) mode decays slowly in the beginning until other modes gain enough energy and then it begins to grow quickly and overtakes the (1,0) mode after a short time period. These different transition patterns match with the experimental results that the flow transition is supercritical and subcritical for the buoyancy-assisted and -opposed flows, respectively. Buoyancy-assisted heated flow transition follows the general trend of an isothermal flow in the beginning, but the thermal-buoyant force is crucial in accelerating the instability and also causing notable differences during the subsequent transition process. All of the results for the vortex structures development, kinetic energy budget of the disturbances, flow visualization by tagged fluid particles, and the local temperature fluctuations are consistent in pointing to a clear pattern for the buoyancy-assisted heated flow transition.

Linear stability analysis of mixed-convection flow in a vertical pipe

A comprehensive numerical study on the linear stability of mixed-convection flow in a vertical pipe with constant heat flux is presented with particular emphasis on the instability mechanism and the Prandtl number effect. Three Prandtl numbers representative of different regimes in the Prandtl number spectrum are employed to simulate the stability characteristics of liquid mercury, water and oil. The results suggest that mixed-convection flow in a vertical pipe can become unstable at low Reynolds number and Rayleigh numbers irrespective of the Prandtl number, in contrast to the isothermal case. For water, the calculation predicts critical Rayleigh numbers of 80 and −120 for assisted and opposed flows, which agree very well with experimental values of Rac = 76 and −118 (Scheele & Hanratty 1962). It is found that the first azimuthal mode is always the most unstable, which also agrees with the experimental observation that the unstable pattern is a double spiral flow. Scheele & Hanratty's speculation that the instability in assisted and opposed flows can be attributed to the appearance of inflection points and separation is true only for fluids with O(1) Prandtl number. Our study on the effect of the Prandtl number discloses that it plays an active role in buoyancy-assisted flow and is an indication of the viability of kinematic or thermal disturbances. It profoundly affects the stability of assisted flow and changes the instability mechanism as well. For assisted flow with Prandtl numbers less than 0.3, the thermal–shear instability is dominant. With Prandtl numbers higher than 0.3, the assisted-thermal–buoyant instability becomes responsible. In buoyancy-opposed flow, the effect of the Prandtl number is less significant since the flow is unstably stratified. There are three distinct instability mechanisms at work independent of the Prandtl number. The Rayleigh–Taylor instability is operative when the Reynolds number is extremely low. The opposed-thermal–buoyant instability takes over when the Reynolds number becomes higher. A still higher Reynolds number eventually leads the thermal–shear instability to dominate. While the thermal–buoyant instability is present in both assisted and opposed flows, the mechanism by which it destabilizes the flow is completely different.

Combined convection heat transfer in a channel with two ribs attached to one wall

Two-dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisted flow and buoyancy-opposing flow. The effect of Reynolds number, ReL, and modified Richardson number, Ri*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy-assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999

Combined convection heat transfer in a channel with two ribs attached to one wall

Two-dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisted flow and buoyancy-opposing flow. The effect of Reynolds number, ReL, and modified Richardson number, Ri*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy-assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999

Combined convection heat transfer in a channel with two ribs attached to one wall

Two-dimensional calculations were performed for combined convection heat transfer in a channel with two ribs attached to one wall, following a previous study on the forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisted flow and buoyancy-opposing flow. The effect of Reynolds number, ReL, and modified Richardson number, Ri*, was examined keeping the space between ribs, σ, and blockage ratio, τ, constant (σ = 3.0, τ = 0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculations are stabilized in both cases. Serious deterioration of Nusselt number on the second rib suddenly occurs in a certain range of Ri* due to the flow stabilization. This is because flow unsteadiness plays an important role for heat transfer enhancement as was described in a previous study. However, in buoyancy-assisted flow, a similar deterioration of Nusselt number also appears on the second rib even if flow remains steady. This is caused by the disappearance of a strong rotating flow which exists in the cavity between both ribs and keeps the fluid in the cavity cooler. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 379–394, 1999

Unsteady conjugated mixed convection flow and heat transfer between two co-rotating discs

Abstract The problem of unsteady laminar mixed convection flow and heat transfer between two co-rotating disks with wall effects including both wall conduction and wall heat capacity was investigated numerically. In this work, both thermal boundary conditions of uniform heat flux (UHF) and uniform wall temperature (UWT) were considered. The Boussinesq approximation was used to characterize the centrifugal-buoyancy effects. The present paper particularly addressed the wall effects on the characteristics of fluid flow and thermal performance. The predicted results reveal that wall effects play important roles in the unsteady mixed convection heat transfer, especially for the early transient period. Additionally, in the situation of buoyancy-opposing flow ( Gr Ω > 0), the centrifugal buoyancy induced by the rotation has a retarding effect on the skin friction coefficient and heat transfer rate.

The mixed convection plume along a vertical adiabatic surface embedded in a non-Darcian porous medium

Abstract The mixed convection flow, from a line heat source embedded at the leading edge of an adiabatic vertical surface which is immersed in a non-Darcian porous medium, is numerically studied by employing an implicit finite difference Keller's box method. The non-Darcian effects of convective, inertia, and solid boundary are all considered. Both the buoyancy-assisting and buoyancy-opposing flow conditions have been investigated. The results are presented for the entire range of the mixed convection parameter A L = Gr L / Re L 2 , a ratio of the buoyancy-force to the inertia-force, from the purely force convection (A L = ∞) to the purely tree convection (A L -∞) regimes. It is shown that the non-Darcian effects decrease the peak velocities and increase the maximum temperatures. The criteria for the pure and mixed convection for a wall plume in porous media are established.

Combined Convection Heat Transfer in a Channel with Two Ribs Attached to One Wall.

Two dimensional calculation was performed for combined convection heat transfer in a channel with two ribs attached to one wall, following the previous study on forced convection case without buoyancy. The flow is heated from the surfaces of both ribs and the present study dealt with the two cases of buoyancy-assisting flow and buoyancy-opposing flow. The effect of Reynolds number, ReL, and modified Richardson number, Ri*, was examined keeping space between ribs, σ, and blockage ratio, τ, constant (σ=3.0, τ=0.5). Increasing the magnitude of buoyancy, unsteady flows predicted by the present calculation are stabilized in both of two cases. Serious deterioration of Nusselt number on the 2nd rib suddenly occurrs in a certain range of Ri* due to the flow stabilization. This is because flow unsteadiness plays an important roll for heat transfer enhancement as was described in the previous study. However, in buoyancy-assisting flow, similar deterioration of Nusselt number also appears on the 2nd rib even if flow remains steady. This is caused by the disappearance of strong rotating flow which exists in the cavity between the both ribs and keeps fluid in the cavity cooler.

The linear stability of mixed convection in a vertical channel flow

In this study, the linear stability of mixed-convection flow in a vertical channel is investigated for both buoyancy-assisted and -opposed conditions. The disturbance momentum and energy equations were solved by the Galerkin method. In addition to the case with a zero heat flux perturbation boundary condition, we also examined the zero temperature perturbation boundary condition. In general, the mixed-convection flow is strongly destabilized by the heat transfer and therefore the fully developed heated flow is very unstable and very difficult to maintain in nature. For buoyancy-assisted flow, the two-dimensional disturbances dominate, while for buoyancy-opposed flow, the Rayleigh–Taylor instability prevails for zero heat flux perturbation boundary condition, and for the zero temperature perturbation on the boundaries the two-dimensional disturbances dominate except at lower Reynolds numbers where the Rayleigh–Taylor instability dominates again. The instability characteristics of buoyancy-assisted flow are found to be strongly dependent on the Prandtl number whereas the Prandtl number is a weak parameter for buoyancy-opposed flow. Also the least-stable disturbances are nearly one-dimensional for liquids and heavy oils at high Reynolds numbers in buoyancy-assisted flows.From an energy budget analysis, we found that the thermal–buoyant instability is the dominant type for buoyancy-assisted flow. In buoyancy-opposed flow, under the zero temperature perturbation boundary condition the Rayleigh–Taylor instability dominates for low-Reynolds-number flow and then the thermal–shear instability takes over for the higher Reynolds numbers whereas the Rayleigh–Taylor instability dominates solely for the zero heat flux perturbation boundary condition. It is found that the instability characteristics for some cases of channel flow in this study are significantly different from previous results for heated annulus and pipe flows. Based on the distinctly different wave speed characteristics and disturbance amplification rates, we offer some suggestions regarding the totally different laminar–turbulent transition patterns for buoyancy-assisted and -opposed flows.