Buoyancy effects on a fully-developed flow inside a vertical pipe in laminar and turbulent regimes

Natural and forced mixed convection of an ascending hot fluid in a vertical pipe surrounded by a colder medium is found in various applications including electronics cooling, building heating and cooling, fires in tall buildings, nuclear reactors, and solar chimney power plants. The ascending air becomes denser and heavier near the cooler wall, which in turn, reverses the flow toward the descending direction near the wall. As a result, air velocity near the centerline increases in the ascending direction to satisfy the continuity equation, which causes an inflection point in the velocity profile, where the emerging mixing layer becomes a source of turbulence. An analytical solution is used to reveal such a reverse flow in an infinitely long vertical pipe with laminar flow regime. The axisymmetric analytical solutions for the longitudinal velocity (u) and temperature (T) profiles are compared with the corresponding numerical solutions in the Ra ≤ 264 and Re < 1372 range (with Ra and Re being the Rayleigh and Reynolds numbers, respectively. These results agree well with an accuracy of ±3%, with the analytical solution serving as a benchmark for the numerical code. In addition, experiments in a vertical pipe of a finite height of H = 2 m were conducted for both laminar and turbulent flows with changing the inlet air temperature or/and the mass flowrate. For validations, the distributions of the longitudinal velocity (u) and temperature (T) predicted numerically and measured experimentally are compared and the difference is found to be less than ±5%. For turbulent flows in the Ra < 5175 or/and Re > 2795 ranges, it was found that the ascending fluid is always dominated by inertia and no inflection point in the velocity profile is found. Accordingly, an increase in fluid density due to cooling is negligible in turbulent flows.