“…The numerical results are plotted in figure 2; they agree very well with those by Majlesara et al. (2020). Figure 2.Code validation for a settling particle at fixed temperature in a long vertical channel.…”
Section: Numerical Methods and Validationsupporting
confidence: 85%
“…Our code is applied to simulate the same cases as those presented by Majlesara et al. (2020), facilitating a direct comparison of the normalized terminal velocity across various and values, where is the characteristic buoyancy velocity. The numerical results are plotted in figure 2; they agree very well with those by Majlesara et al.…”
Section: Numerical Methods and Validationmentioning
For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al., Eur. Phys. J. E, vol. 39, 2016, pp. 1–9). In this study we numerically analyse the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by the Péclet number
$Pe$
). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by the Galileo number
$Ga$
; and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number
$Ra$
. We analyse how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters
$Pe$
,
$Ga$
and
$Ra$
. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large
$Ra$
, even collisions between the droplets can take place. Our study on the effect of
$Ga$
further shows that with increasing
$Ga$
, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number
$Re_d$
, is proportional to
$Ra^{1/4}/( \ell /R)$
, where
$\ell /R$
is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number
$Re_{rep}$
, which is proportional to
$PeRa^{-0.38}$
. The balance of attractive and repulsive effect leads to
$Pe\sim Ra^{0.63}$
, which agrees well with the transition curve between the regimes with and without collision.
“…The numerical results are plotted in figure 2; they agree very well with those by Majlesara et al. (2020). Figure 2.Code validation for a settling particle at fixed temperature in a long vertical channel.…”
Section: Numerical Methods and Validationsupporting
confidence: 85%
“…Our code is applied to simulate the same cases as those presented by Majlesara et al. (2020), facilitating a direct comparison of the normalized terminal velocity across various and values, where is the characteristic buoyancy velocity. The numerical results are plotted in figure 2; they agree very well with those by Majlesara et al.…”
Section: Numerical Methods and Validationmentioning
For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al., Eur. Phys. J. E, vol. 39, 2016, pp. 1–9). In this study we numerically analyse the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by the Péclet number
$Pe$
). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by the Galileo number
$Ga$
; and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number
$Ra$
. We analyse how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters
$Pe$
,
$Ga$
and
$Ra$
. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large
$Ra$
, even collisions between the droplets can take place. Our study on the effect of
$Ga$
further shows that with increasing
$Ga$
, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number
$Re_d$
, is proportional to
$Ra^{1/4}/( \ell /R)$
, where
$\ell /R$
is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number
$Re_{rep}$
, which is proportional to
$PeRa^{-0.38}$
. The balance of attractive and repulsive effect leads to
$Pe\sim Ra^{0.63}$
, which agrees well with the transition curve between the regimes with and without collision.
“…(2018 a , b ) and Majlesara et al. (2020) for the heat transfer in particle-laden flows. Furthermore, direct comparison of the numerical results with the experimental measurements of Zade (2019) at dense regimes verified the excellent accuracy of the numerical code.…”
Section: Methodsmentioning
confidence: 99%
“…A volume of fluid (VoF) approach (Hirt & Nichols 1981) is coupled to the IBM to solve the temperature equation in the two phases (Ström & Sasic 2013). The method has been used extensively with several validations reported by Picano, Breugem & Brandt (2015), Lashgari et al (2016) and Ardekani et al (2016) for the fluid-solid interactions and by Ardekani et al (2018a,b) and Majlesara et al (2020) for the heat transfer in particle-laden flows. Furthermore, direct comparison of the numerical results with the experimental measurements of Zade (2019) at dense regimes verified the excellent accuracy of the numerical code.…”
This study presents direct numerical simulations of turbulent Rayleigh–Bénard convection in non-colloidal suspensions, with special focus on the heat transfer modifications in the flow. Adopting a Rayleigh number of
$10^8$
and Prandtl number of 7, parametric investigations of the particle volume fraction
$0\leq \varPhi \leq 40\,\%$
and particle diameter
$1/20\leq d^*_p\leq 1/10$
with respect to the cavity height, are carried out. The particles are neutrally buoyant, rigid spheres with physical properties that match the fluid phase. Up to
$\varPhi =25\,\%$
, the Nusselt number increases weakly but steadily, mainly due to the increased thermal agitation that overcomes the decreased kinetic energy of the flow. Beyond
$\varPhi =30\,\%$
, the Nusselt number exhibits a substantial drop, down to approximately 1/3 of the single-phase value. This decrease is attributed to the dense particle layering in the near-wall region, confirmed by the time-averaged local volume fraction. The dense particle layer reduces the convection in the near-wall region and negates the formation of any coherent structures within one particle diameter from the wall. Significant differences between
$\varPhi \leq 30\,\%$
and 40 % are observed in all statistical quantities, including heat transfer and turbulent kinetic energy budgets, and two-point correlations. Special attention is also given to the role of particle rotation, which is shown to contribute to maintaining high heat transfer rates in moderate volume fractions. Furthermore, decreasing the particle size promotes the particle layering next to the wall, inducing a similar heat transfer reduction as in the highest particle volume fraction case.
“…( 5) in the two phases (Ström and Sasic, 2013). The method has been used extensively with several validations reported by Picano et al (2015), Lashgari et al (2016) and Ardekani et al (2016), considering fluid-solid interactions and by Ardekani et al (2017), Ardekani et al (2018) and Majlesara et al (2020) for the heat transfer in particle-laden flows. All the details of this implementation are presented in the mentioned references; for the sake of completeness, only a brief description of the method is therefore presented here.…”
We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrallybuoyant spherical particles for solid volume fractions up to 35% and bulk Reynolds numbers from 500 to 5600. An Immersed Boundary-Volume of Fluid method is used to solve the energy equation in the fluid and solid phase. We relate the heat transfer to the regimes of particle motion previously identified, i.e. a viscous regime at low volume fractions and low Reynolds number, particle-laden turbulence at high Reynolds and moderate volume fraction and particulate regime at high volume fractions. We show that in the viscous dominated regime, the heat transfer is mainly due to thermal diffusion with enhancement due to the particleinduced fluctuations. In the turbulent-like regime, we observe the largest enhancement of the global heat transfer, dominated by the turbulent heat flux. In the particulate shear-thickening regime, however, the heat transfer enhancement decreases as mixing is quenched by the particle migration towards the channel core. As a result, a compact loosely-packed core region forms and the contribution of thermal diffusion to the total heat transfer becomes significant once again. The global heat transfer becomes, in these flows at volume fractions larger than 25%, lower than in single phase turbulence.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
