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Register a new userRegimes of heat transfer in particle suspensions
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We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrally-buoyant 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 particle-induced 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.
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We develop a two-fluid model (TFM) for simulation of thermal transport coupled to particle migration in flows of non-Brownian suspensions. Specifically, we propose a closure relation for the inter-phase heat transfer coefficient of the TFM as a function of the particle volume fraction, particle diameter, magnitude of the particle phases shear-rate tensor, and the thermal diffusivity of the particles. The effect of shear-induced migration in the particulate phase is captured through the use of state-of-the-art rheological closures. We validate the proposed interphase heat transfer coupling by calibrating it against previous experiments in a Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, the shear and thermal gradients aid each other to increase the particle migration when temperature difference between the inner and outer walls, $Delta T = T_mathrm{in} - T_mathrm{out} < 0$. Meanwhile, for $Delta T > 0$, the shear and thermal gradients oppose each other, resulting in diminished particle migration, and a more uniform distribution of the particulate phase across the gap. Within the TFM framework, we identify the origin and functional form of a thermo-rheological migration force that rationalizes our observations. We also investigate the interplay of shear and thermal gradients in the presence of recirculating regions in an eccentric Couette cell (with offset axis and rotating inner cylinder). Simulations reveal that the system Nusselt number increases with the eccentricity $E$ for $Delta T > 0$, but a maximum occurs for $Delta T < 0$ at $E = 0.4$. This observation is explained by showing that, for $E>0.4$ and $Delta T < 0$, significant flow recirculation enhances particle inhomogeneity, which in turn reduces heat transfer in the system (compared to $Delta T > 0$).
We report heat transfer and temperature profile measurements in laboratory experiments of rapidly rotating convection in water under intense thermal forcing (Rayleigh number $Ra$ as high as $sim 10^{13}$) and unprecedentedly strong rotational influence (Ekman numbers $E$ as low as $10^{-8}$). Measurements of the mid-height vertical temperature gradient connect quantitatively to predictions from numerical models of asymptotically rapidly rotating convection, separating various flow phenomenologies. Past the limit of validity of the asymptotically-reduced models, we find novel behaviors in a regime we refer to as rotationally-influenced turbulence, where rotation is important but not as dominant as in the known geostrophic turbulence regime. The temperature gradients collapse to a Rayleigh-number scaling as $Ra^{-0.2}$ in this new regime. It is bounded from above by a critical convective Rossby number $Ro^*=0.06$ independent of domain aspect ratio $Gamma$, clearly distinguishing it from well-studied rotation-affected convection.
To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Benard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{text{vol}}$, the wall-averaged $Nu_{text{wall}}$, the kinetic energy dissipation based $Nu_{text{kinetic}}$, and the thermal energy dissipation based $Nu_{text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{text{vol}}$ and the kinetic energy dissipation based $Nu_{text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{text{wall}}$ and the thermal energy dissipation based $Nu_{text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary will not cause an ``energy-like temperature functional to increase over time, irrespective of the state of flow on the open boundary. It is effective in coping with thermal open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.
The 2D second-mode is a potent instability in hypersonic boundary layers (HBLs). We study its linear and nonlinear evolution, followed by its role in transition and eventual breakdown of the HBL into a fully turbulent state. Linear stability theory (LST) is utilized to identify the second-mode wave through FS-synchronization, which is then recreated in linearly and nonlinearly forced 2D direct numerical simulations (DNSs). The nonlinear DNS shows saturation of the fundamental frequency, and the resulting superharmonics induce tightly braided ``rope-like patterns near the generalized inflection point (GIP). The instability exhibits a second region of growth constituted by the fundamental frequency, downstream of the primary envelope, which is absent in the linear scenario. Subsequent 3D DNS identifies this region to be crucial in amplifying oblique instabilities riding on the 2D second-mode ``rollers. This results in lambda vortices below the GIP, which are detached from the ``rollers in the inner boundary layer. Streamwise vortex-stretching results in a localized peak in length-scales inside the HBL, eventually forming haripin vortices. Spectral analyses track the transformation of harmonic peaks into a turbulent spectrum, and appearance of oblique modes at the fundamental frequency, which suggests that fundamental resonance is the most dominant mechanism of transition. Bispectrum reveals coupled nonlinear interactions between the fundamental and its superharmonics leading to spectral broadening, and traces of subharmonic resonance as well.
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