Experimental and numerical investigations of simultaneously developing laminar-turbulent transitional regime of mixed convection flows in a vertical tube

Abstract

Combined free and forced convection, most often called mixed convection, has practical importance in many engineering applications like heat exchangers, solar energy systems, cooling of electronic equipment, extraction of geothermal energy, and many areas because of its varying nature of heat transfer. This present study investigates the heat transfer, pressure drop, and flow characteristics of buoyancy-assisting (heated upward) and opposing (heated downward) flows of water in the simultaneously hydrodynamically and thermally developing laminar-turbulent transitional regime of mixed convection in a vertical tube. To accomplish this, both numerical and experimental investigations were carried out for the range of Reynolds number, (102 ≤ 𝑅𝑒 ≤ 1.5×104), Grashof number (103 ≤ 𝐺𝑟 ≤ 108), Richardson number (0.01 ≤ 𝑅𝑖 ≤ 1.5) and Prandtl number ( 3 ≤ 𝑃𝑟 ≤ 7) in a vertical tube with a length-to diameter (𝐿/𝐷) ratio of ≤ 500. 2D axisymmetric, steady-state simulations were performed by employing a SIMPLE/Coupled scheme for pressure-velocity coupling in momentum equations and a second-order UPWIND scheme for solving convective terms. Numerical results show that buoyancy plays a significant role in laminar turbulent transitions between assisting and opposing flows. In the case of laminar mixed convection, it can be inferred from the velocity profile that the velocity gradient is sharper near the walls in assisting flow. In contrast, in the case of opposing flow, the velocity gradient is sharper at a distance from the wall. With increasing 𝑅𝑖, both 𝑓 and � �𝑢 exhibit increasing and decreasing trend for buoyancy-aided and opposed flows, respectively. It is worth mentioning that the developing region exhibits higher 𝑁𝑢 compared to fully developed states for both aided and opposed flows. The effect of heat flux on the entry length is also analyzed in buoyancy-assisting and opposing flows. The hydrodynamic development length (𝐿ℎ) increases as we increase the 𝑅𝑖 for both assisting and opposing flow, but the thermal entry length (𝐿𝑡) decreases in the case of assisting flow in contrast to the opposing flow. In contrast, in turbulent mixed convection, there is not much of a difference between buoyancy-aiding and opposing flows due to the dominance of turbulence. It has been observed that the pressure drop (quantified by 𝑓) and heat transfer (quantified by 𝑁𝑢) both are higher in buoyancy opposing flow than buoyancy-assisting flow. The entry length is also short, and the flow is developed early. The hydrodynamically fully developed conditions in buoyancy assisting and opposing flow were achieved by 𝐿/𝐷~21 and ~17 and the thermally developed condition by 𝐿/𝐷~25 and ~20, respectively. The laminar-turbulent transitional regime shows a compromise between pressure drop and heat transfer. The increase in 𝑅𝑒 and 𝐺𝑟 keeping 𝑅𝑖 constant first increases 𝑓 and then decreases, whereas the 𝑁𝑢 increases in both buoyancy assisting and opposing flow. Furthermore, the mixed convection experimental set-up was built to perform experiments in the laminar, transitional, and lower ranges of turbulent regimes for aiding and opposing flows. The effects of varying 𝐺𝑟 and 𝑅𝑒, at fixed 𝑅𝑖 on pressure drop and heat transfer were investigated for both buoyancy-assisting and buoyancy-opposing flows. Experimental results showed that the average 𝑓 decreases with the increase in 𝑅𝑒 in the laminar regime, increased in the transitional regime and decreased again with the further increase in 𝑅𝑒 in the turbulent regime. The average 𝑁𝑢 increases continuously with the increase in 𝑅𝑒 in all laminar, transitional, and turbulent regimes. The inception of transition occurs earlier in the opposing flow as compared to the assisting flow for the same 𝑅𝑒 and 𝐺𝑟. It has also been observed that the transition is delayed with the increase in 𝑅𝑖 in both flows. The numerical results were also compared with my experiments. Finally, correlations were developed to quantify the friction factor, 𝑓 = 𝑓(𝑅𝑒,𝐺𝑟), Colburn j-factor, 𝑓/𝑗 = 𝑓(𝑅𝑒,𝐺𝑟,𝑃𝑟), and Nusselt number, 𝑁𝑢 = 𝑓(𝑅𝑒,𝐺𝑟,𝑃𝑟,𝐿/𝐷) in developing and fully developed regime of laminar, transitional, and turbulent mixed convection under both the flow conditions.