New Mechanism of Buoyant Plume Transition Unveiled by Large Eddy Simulations

A wide range of engineering applications are convection-driven, such as passive heat exchanger, submerged pipelines, HVAC system and electronic cooling. The design and analysis of these systems are based on the interaction between the fluid flow and heat transfer of the natural convection. Most studies on natural convection around horizontal cylinders focus on heat transfer characteristics to establish the empirical correlation between the Rayleigh and Nusselt numbers. However, natural convection around single horizontal cylinders is rather complicated due to the highly unstable buoyant plume that causes a transition from laminar to turbulent flow. The transition improves the heat transfer on cylinder surfaces. Unfortunately, the transition occurs above the heated cylinder as which presents an additional challenge. Thus, a thorough understanding of the transitional behavior of thermal plumes would effectively contribute to both fluid dynamics and heat transfer communities.

Considering the key factors affecting the computational fluid dynamics such as modeling, mesh adequacy, and boundary condition settings, large eddy simulation (LES) has been identified as a promising scheme for studying free convention thermal plume turbulence for idealized geometries. However, LES of buoyant plumes has remained largely underexplored. Consequently, natural convection around single horizontal cylinders has been extensively studied in the literature, but only for heat transfer characteristics. When the fluid flow is incorporated, the modeling of laminar-turbulent transition in buoyant plumes becomes more complex and challenging. Therefore, it is of great significance to improve LES’s computational reliability and accuracy in the free convection of horizontal cylinders.

To address this issue, Dr. Haiteng Ma from Shanghai Jiao Tong and Professor Li He from the University of Oxford used the high-fidelity LES method to investigate the physical mechanisms responsible for developing buoyant plumes for unconfined single horizontal cylinders in water. The study was conducted at a Rayleigh number of and it was complemented by the Reynolds-Averaged Navier-Stokes (RANS) computations. The boundary condition, ensemble-averaging period, numerical sensitivity and mesh resolution associated with LES were thoroughly tested. The CFD results were compared to the existing experimental data to validate the feasibility of the approach in terms of Nusselt number and velocity evolution for cylinder surface and buoyant plume, respectively. The transitional behavior was discussed to understand the physical mechanism behind the transitional buoyant plume. The work is published in the International Journal of Thermal Sciences.

The authors showed that the LES is more sensitive to both boundary conditions and mesh resolution settings than RANS. Due to its inferior accuracy, an alarm was set to enable the use of periodic conditions in LES on the lateral boundaries of the computational domain. As such, well-calibrated LES with pressure conditions produced reliable results consistent with the experimental data as far as buoyant plume velocity and heat transfer on the cylinder were concerned. In addition, the authors observed that buoyant plume accelerates immediately downstream of the heated cylinder, subject to the work done by buoyancy force, until the plume becomes unstable and begins transitioning to turbulence at a streamwise Grashof number of 1.5 x 10⁸. The plume velocity continues to increase until the fluctuation in horizontal velocity is peaked at a streamwise Grashof number of . It then declines towards asymptotic value to end the transition. Thereafter, the buoyant plume then entered a fully-developed turbulent state.

“New physical insights about buoyant plume evolution are presented”, as concluded in the original paper. “After leaving the heated cylinder, buoyant plume accelerates while its temperature keeps decreasing due to heat loss to the atmosphere. This is because buoyancy force exerts work on thermal plume, contributing to increase of mean kinetic energy and thus, plume acceleration. In this region, buoyant plume is laminar or at the initial stage of transition. So the loss of mean kinetic energy mainly comes from molecular viscosity, which is much smaller than the generation of mean kinetic energy from work done by buoyancy force. The plume continues to accelerate until it begins to sway at 2.3 diameters downstream cylinder center, which is near the middle of transitional regime. Thereafter, energy dissipation from mean flow to turbulence increases quickly to become the major loss mechanism, overriding that by molecular viscosity. As a result, diffusivity of thermal plume is augmented notably due to turbulent stresses, leading to the smoothing of transverse mean velocity distribution. Transversely-averaged mean kinetic energy reduces and finally stabilizes after thermal plume enters fully-turbulent regime (x₂/D≥3.8). Overall speaking, buoyancy work prevails over energy dissipation into turbulence and molecular viscosity, leading to monotonic increase of transversely-integrated mean kinetic energy along the streamwise direction of thermal plume. Production of turbulent kinetic energy, however, mainly comes from mean shear rather than buoyancy.”.

In summary, the researchers successfully conducted a high-fidelity LES study of natural convection heat transfer and fluid flow around a horizontal cylinder. This is the first LES study to provide insights into the laminar-to-turbulent transition associated with buoyant plume in heated cylinders. In a statement to Advances in Engineering, the authors explained their study would advance modeling in natural convection to expand its industrial applications. One particular application the authors are working on now is thermal-to-kinetic energy conversion associated with passive heat exchangers.