Two-component convection flow driven by a heat-releasing concentration field

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In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for $1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$ and $0.01\le {\textit {St}} \le 10$ , where the Rayleigh number ${\textit {Ra}}$ and Stokes number ${\textit {St}}$ measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with ${\textit {Ra}}$ and show minor dependences on ${\textit {St}}$ . The volume-averaged temperature and convective flux exhibit non-monotonic variations as ${\textit {St}}$ increases and reach their minimums at intermediate ${\textit {St}}$ . The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on ${\textit {St}}$ as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

Section: Introductionmentioning

confidence: 94%

Wall-bounded thermal turbulent convection driven by heat-releasing point particles

Yang

2022

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“…Further details of the code can be found in Van Der Poel et al (2015), Ostilla-Mónico et al (2015) and Kim & Moin (1985). The code has been used for stratified flows in Jain et al (2022), Yang et al (2015Yang et al ( , 2020, Du, Zhang & Yang (2021), Bin et al (2022) and Li & Yang (2021), among others. Here, a single R20F02 or R20F10 case requires approximately 2000 CPU hours; a single R20F50 realization requires 3000 CPU hours due to the increased simulation time; and a single R50F50 realization requires approximately 9000 CPU hours.…”

Section: Initial Conditionsmentioning

confidence: 99%

“…(2022), Yang et al. (2015, 2020), Du, Zhang & Yang (2021), Bin et al. (2022) and Li & Yang (2021), among others.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Direct numerical simulation of temporally evolving stratified wakes with ensemble average

Li,

Yang,

Kunz

2024

Direct numerical simulations are conducted for temporally evolving stratified wake flows at Reynolds numbers from $10\,000$ to $50\,000$ and Froude numbers from $2$ to 50. Unlike previous studies that obtained statistics from a single realization, we take ensemble averages among 80–100 realizations. Our analysis shows that data from one realization incur large convergence errors. These errors reduce quickly as the number of statistical samples increases, with the benefit of ensemble average diminishing beyond 40–60 realizations. The data with ensemble average allow us to test the previously established scalings and arrive at new scaling estimates. Specifically, the data do not support power-law scaling in the centreline velocity deficit $U_0$ beyond the near wake. Its decay rate increases continuously from 0.1 at the onset of the non-equilibrium regime until the end of our calculations without reaching any asymptote. Additionally, while no power-law scalings could be found in the wake width ( $L_H$ ) and wake height ( $L_V$ ) in the late wake, $L_H\sim (Nt)^{1/3}$ is a good working approximation of the wake's horizontal size, where $N$ is buoyancy frequency and $t$ is time. Besides the low-order statistics, we also report the transverse integrated terms and the vertically integrated terms in the turbulent kinetic energy budget equation as a function of the vertical and transverse coordinates. The data indicate that there are two peaks in the vertically integrated production and transport terms, and one peak when the two terms are integrated horizontally.

“…The code has been extensively used for stratified flows (Yang et al. 2015, 2020; Du, Zhang & Yang 2021; Li & Yang 2021), and we present a validation in Appendix A.…”

Section: Computational Detailsmentioning

confidence: 99%

“…Further details of the numerics can be found in Ostilla-Monico et al (2015), van der Poel et al (2015) and Kim & Moin (1985). The code has been extensively used for stratified flows (Yang et al 2015(Yang et al , 2020Du, Zhang & Yang 2021;Li & Yang 2021), and we present a validation in Appendix A.…”

Section: Further Detailsmentioning

confidence: 99%

Evolution of two counter-rotating vortices in a stratified turbulent environment

Bin

Yang

et al. 2022

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We conduct direct numerical simulations and study the evolution of a pair of counter-rotating vortices in a stratified and turbulent environment beyond the first vortex linking (which is due to the Crow instability). The initial position of the two vortices is perpendicular to the direction of thermal stratification. We vary the Froude number, the background turbulence intensity and the Reynolds number, covering strong, weak and neutral stratification; low, moderate and high background turbulence; and low and moderate Reynolds numbers. We observe a second vortex linking in a weakly stratified environment for the first time. The second vortex linking is followed by turbulence bursts that lead to the rapid decay of the residual vortices after the first vortex linking, leading to a short-living vortex pair. This challenges the conventional view that residual vortices have a long life span, which is true only in an unstratified environment. In addition to the second vortex linking, we observe the following. First, strong background turbulence quickly breaks the two vortices. Second, the two vortices induce secondary and tertiary vortices and lose energy to gravitational waves in a strongly stratified ( $Fr\leqslant 0.7$ ) environment.