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This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions,$$0.0 \leq \varPhi \leq 0.5$$, and ratios of dynamic viscosity,$$\lambda _{\mu }$$, and thermal diffusivity,$$\lambda _{\alpha }$$, within the range$$[0.1\unicode{x2013}10]$$. The Rayleigh, Prandtl, Weber and Froude numbers are held constant at$$10^8$$,$$4$$,$$6000$$and$$1$$, respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at$$\varPhi =0.2$$and$$\lambda _{\mu }=10$$. This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws. 

This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers [Formula: see text] to observe flow structures and vortex formation between the rods in porous media structures with different porosities of [Formula: see text] which corresponds to the spacing ratio of [Formula: see text], where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number. 

Laboratory experiments were conducted to study particle migration and flow properties of non-Brownian, noncolloidal suspensions ranging from 10% to 40% particle volume fraction in a pressure-driven flow over and through a porous structure at a low Reynolds number. Particle concentration maps, velocity maps, and corresponding profiles were acquired using a magnetic resonance imaging technique. The model porous medium consists of square arrays of circular rods oriented across the flow in a rectangular microchannel. It was observed that the square arrays of the circular rods modify the velocity profiles and result in heterogeneous concentration fields for various suspensions. As the bulk particle volume fraction of the suspension increases, particles tend to concentrate in the free channel relative to the porous medium while the centerline velocity profile along the lateral direction becomes increasingly blunted. Within the porous structure, concentrated suspensions exhibit smaller periodic axial velocity variations due to the geometry compared to semidilute suspensions (bulk volume fraction ranges from 10% to 20%) and show periodic concentration variations, where the average particle concentration is slightly greater between the rods than on top of the rods. For concentrated systems, high particle concentration pathways aligned with the flow direction are observed in regions that correspond to gaps between rods within the porous medium. 

This study discusses turbulent suspension flows of non-Brownian, non-colloidal, neutrally buoyant and rigid spherical particles in a Newtonian fluid over porous media with particles too large to penetrate and move through the porous layer. We consider suspension flows with the solid volume fraction $${{\varPhi _b}}$$ ranging from 0 to 0.2, and different wall permeabilities, while porosity is constant at 0.6. Direct numerical simulations with an immersed boundary method are employed to resolve the particles and flow phase, with the volume-averaged Navier–Stokes equations modelling the flow within the porous layer. The results show that in the presence of particles in the free-flow region, the mean velocity and the concentration profiles are altered with increasing porous layer permeability because of the variations in the slip velocity and wall-normal fluctuations at the suspension-porous interface. Furthermore, we show that variations in the stress condition at the interface significantly affect the particle near-wall dynamics and migration toward the channel core, thereby inducing large modulations of the overall flow drag. At the highest volume fraction investigated here, $${{\varPhi _b}}= 0.2$$ , the velocity fluctuations and the Reynolds shear stress are found to decrease, and the overall drag increases due to the increase in the particle-induced stresses. 

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. 

Flow of a semidilute neutrally buoyant and non-colloidal suspension is numerically studied in the Taylor–Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction $${\phi _b} = 0.1$$ , the radius ratio $$(\eta = {r_i}/{r_o} = 0.877)$$ and two particle size ratios $$\mathrm{\epsilon }\,( = \; d\textrm{/}a) = 60,\;200$$ , where d is the gap width ( $$= {r_o} - {r_i}$$ ) between cylinders, a is the suspended particles’ radius and $$r_i$$ and $$r_o$$ are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counter-rotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of $$\mathrm{\epsilon } = 200$$ , the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of non-axisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of $$\mathrm{\epsilon } = 60$$ ; thus, the transitions occur following the sequence of CCF → SVF → WSVF → WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow. 

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.