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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.
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Heat and momentum transfer to a particle in a laminar boundary layer
Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas–solids mixture. Previous efforts to resolve the solids’ heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle–wall separation distance and asymptotically decays to zero for large particle–wall separation distances, seaming together the unbounded and near-wall regions.
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- Award ID(s):
- 1707046
- PAR ID:
- 10310922
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 889
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin ( J. Fluid Mech. , vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number ( Pe ) and the particle volume fraction ( ϕ ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $$({\phi _b})$$ ranging from 0 to 0.3. The critical Rayleigh number $$(R{a_c})$$ grows gradually by increasing $${\phi _b}$$ from the critical value $$(R{a_c} = 1708)$$ for a pure Newtonian fluid, while the critical wavenumber $$({k_c})$$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $$({\phi _b} = 0)$$ . The heat transfer in moderately dense suspensions $$({\phi _b} = 0.2\text{--}0.3)$$ is significantly enhanced by convection rolls for small Rayleigh number ( Ra ) close to $$R{a_c}$$ . We also found a power-law increase of the Nusselt number ( Nu ) with Ra , namely, $$Nu\sim R{a^b}$$ for relatively large values of Ra where the scaling exponent b decreases with $${\phi _b}$$ . Finally, it turns out that the shear-induced migration of particles can modify the heat transfer.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.45
