Transition to turbulence in the wake of a fixed sphere in mixed convection

Abstract

International audienceThe thermal effect on axisymmetry breaking and transition to turbulence in the wake of a fixed heated sphere is investigated in the mixed convection configurations commonly known as 'assisting'and 'opposing' flows in which the buoyancy tends, respectively, to accelerate and decelerate the flow. The study is carried out in the Ri –Re parameter plane (Ri being the mixed convection parameter – the Richardson number) for two values of Prandtl number – 0.72 (≈air and many gases) and 7 (≈water). We show that convection affects considerably the transition (as compared to that observed in the wake of an unheated sphere) even at moderate Richardson numbers. The latter are taken to be positive in assisting flow and negative in opposing one. In this notation, it can be said that convection shifts the primary-instability threshold to higher Reynolds numbers with increasing Richardson number. In assisting flow, the primary bifurcation is always regular, but at Ri > 0.6 it appears in azimuthal subspaces associated with higher azimuthal wavenumbers m > 1. The transition scenario is characterized by a large variety of regimes explainable by nonlinear interactions between different azimuthal subspaces. On the side of higher (positive) Richardson numbers the axisymmetric flow is found stable up to Re = 1400 at Pr = 0.72 and Ri = 0.7. In opposing flow, the m = 1 subspace is always the most unstable, but the regular bifurcation gives way to a Hopf one at Ri < −0.1. Close to the junction of both bifurcations a similar variety of regimes precedes the transition to chaos as in assisting flow. On the side of negative Richardson numbers the primary (Hopf) bifurcation threshold is found as low as Re = 100 at Ri = −0.25 and at both investigated Prandtl numbers. After a primary periodic regime characterized by vortex shedding with a symmetry plane, the transition proceeds via a series of increasingly irregular helical regimes

Supersaturation in the Wake of a Precipitating Hydrometeor and Its Impact on Aerosol Activation

“…is the Reynolds number (with being the kinematic viscosity of air), Pr = ∕ is the Prandtl number (with being the thermal diffusivity of air), and Sc = ∕ v is Schmidt number (with v being the water vapor diffusivity). Following Kotouč et al (2009) and Krayer et al (2020), as a first approximation, we neglect evaporation feedback on the momentum and particle temperature in the simulations (see section S4 in the supporting information). We solve the model equations with the lattice Boltzmann method (LBM) (Guo et al, 2002;Krüger et al, 2017;Qian et al, 1992;Silva & Semiao, 2012;Succi, 2001;Tian et al, 2018) within the open-source LBM library Palabos (Latt et al, 2020).…”

Heat and water vapor transfer in the wake of a falling ice sphere and its implication for secondary ice formation in clouds

“…(4)). The system is described in a dimensionless form with reference quantities chosen as in Kotouč et al (2009) and , where u p represents the velocity of the sphere and u corresponds to the fluid velocity with respect to a fixed frame (0, x * , y * , z * ) and evaluated on a grid (x, y, z) moving with the sphere center as represented in figure 2. Here lengths are made non-dimensional with respect to the particle diameter, velocity components with the gravitational velocity u g , timescale with the gravitational timescale D/u g , pressure with r ¥ u g 2 .…”

“…We suggest therefore to investigate configurations featuring larger Richardson numbers ( -( ) 10 3 ) and above to test if buoyancy can modify the wake. It is not clear whether buoyancy would potentially affect the system, since the literature showed that weak buoyancy (Ri=0.1) can modify the flow structure (Kotouč et al 2009). This issue will also be addressed in the current study.…”

“…Kotouč et al (2008) also observed that convection tends to stabilize the flow in the assisting flow configuration by preventing detachment of the boundary layer and the formation of a recirculation zone, while in the case of opposing flow a destabilizing effect is observed with a decrease of the critical Reynolds number for the onset of recirculation (Kotouč et al 2009). The transition scenario remains unchanged for weakly heated spheres, while new regimes appear for larger values of the Richardson number (of the order of 0.3, Kotouč et al 2008Kotouč et al , 2009. One can cite for example steady flow regimes with four or six vorticity threads and respectively two and three symmetry planes.…”

On the ice-nucleating potential of warm hydrometeors in mixed-phase clouds

“…The dynamics of the flow around spherical objects are, under the assumptions stated in the previous section, fully parametrized by the Reynolds number, which depends on the diameter and indirectly, through modulation of the terminal velocity, on the density of the hydrometeor. Depending on the Reynolds number value, various flow states emerge in the wake (Johnson and Patel, 1999;Kotouč et al, 2009). At low values the wake is axisymmetric and steady.…”