Effects of thermal buoyancy on the dynamics of a rising or falling sphere

This study investigates the effects of thermal buoyancy on the ascent or descent dynamics and path instabilities of a finite-size sphere through direct numerical simulations with the immersed boundary method. By parametrically varying the density ratio (ρ ᵣ) , Richardson number (Ri) and Galileo number (Ga) , four distinct motion regimes are identified: stable vertical, zigzagging, spiralling and chaotic regimes. These regimes emerge from the competition between particle inertial, gravitational forces and fluid thermal-buoyant forces. Compared with isothermal cases, particles with positive Richardson numbers exhibit accelerated motion due to thermal buoyancy. The critical Reynolds numbers Rep,cr for their path instability are significantly reduced by amplifying wake recirculation zones and triggering vortex shedding. This destabilization mechanism is markedly more pronounced for light particles (ρ ᵣ < 1) than heavy particles (ρ ᵣ > 1) . The present results reveal that the dynamics of heated light particles (ρ ᵣ=0.5, Ri> 0) are governed by the codependent interplay of thermal-buoyancy intensity ( Ri ) and gravitational force ( Ga ), which collectively dictate velocity modulation and path instability patterns. Notably, thermal buoyancy elevates particle Reynolds numbers (Reₚ) while could reduce Nusselt numbers, arising from competing mechanisms between intensified convective transport and impaired conductive heat transfer – particularly pronounced for low Ga particles. These findings bridge the gap between fundamental fluid mechanics and thermal engineering, offering insights to optimize thermal management in particle-laden flows systems, such as industrial heat exchangers and fluidized bed reactors, where thermohydrodynamic coupling effect plays a key role in the performance.