 Award ID(s):
 2031701
 NSFPAR ID:
 10342265
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 944
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Natural convection in porous media is a fundamental process for the longterm storage of CO 2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volumeaveraged Darcy–Oberbeck–Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number ( $Ra$ ) for high values of $Ra$ ( $Ra\gg 1300$ ). Here, we perform direct numerical simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega and protoplume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the porescale parameters, which is consistent with experimental studies.more » « less

null (Ed.)This study explores thermal convection in suspensions of neutrally buoyant, noncolloidal 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 shearinduced 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 powerlaw 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 shearinduced migration of particles can modify the heat transfer.more » « less

A numerical investigation of an asymptotically reduced model for quasigeostrophic RayleighBénard convection is conducted in which the depthaveraged flows are numerically suppressed by modifying the governing equations. At the largest accessible values of the Rayleigh number Ra, the Reynolds number and Nusselt number show evidence of approaching the diffusionfree scalings of Re ∼ RaE/Pr and Nu ∼ Pr−1/2Ra3/2E2, respectively, where E is the Ekman number and Pr is the Prandtl number. For large Ra, the presence of depthinvariant flows, such as largescale vortices, yield heat and momentum transport scalings that exceed those of the diffusionfree scaling laws. The Taylor microscale does not vary significantly with increasing Ra, whereas the integral length scale grows weakly. The computed length scales remain O(1) with respect to the linearly unstable critical wave number; we therefore conclude that these scales remain viscously controlled. We do not find a pointwise CoriolisinertiaArchimedean (CIA) force balance in the turbulent regime; interior dynamics are instead dominated by horizontal advection (inertia), vortex stretching (Coriolis) and the vertical pressure gradient. A secondary, subdominant balance between the Archimedean buoyancy force and the viscous force occurs in the interior and the ratio of the root mean square (rms) of these two forces is found to approach unity with increasing Ra. This secondary balance is attributed to the turbulent fluid interior acting as the dominant control on the heat transport. These findings indicate that a pointwise CIA balance does not occur in the high Rayleigh number regime of quasigeostrophic convection in the plane layer geometry. Instead, simulations are characterized by what may be termed a nonlocal CIA balance in which the buoyancy force is dominant within the thermal boundary layers and is spatially separated from the interior Coriolis and inertial forces.more » « less

SUMMARY We present investigations of rapidly rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from quasigeostrophic (QG), 3D and hybrid QG3D models. The 170 reported calculations span Ekman numbers, Ek, between 10−4 and 10−10, Rayleigh numbers, Ra, between 2 and 150 times supercritical and Prandtl numbers, Pr, between 10 and 10−2. The default boundary conditions are noslip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peaktopeak amplitude of the pattern divided by its mean, taking values up to 5. The QG model is based on the opensource pizza code. We extend this in a hybrid approach to include the temperature field on a 3D grid. In general, we find convection is dominated by zonal jets at middepths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, $Ra \le 10 \, Ra_c$ when Pr = 1, and departs from the 3D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatoriallyantisymmetric motions and zcorrelations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two data sets at Pr ≥ 0.1, with the QG model effectively more strongly driven than the hybrid case due to its cylindrically averaged thermal boundary conditions. When Pr is decreased, the range of agreement between the hybrid and 3D models expands, for example up to $Ra \le 15 \, Ra_c$ at Pr = 0.1, indicating the hybrid method may be better suited to study convection in the low Pr regime. We thus observe a transition between two regimes: (i) at Pr ≥ 0.1 the QG and 3D models agree in the studied range of Ra/Rac while the hybrid model fails when $Ra\gt 15\, Ra_c$ and (ii) at Pr = 0.01 the QG and 3D models disagree for $Ra\gt 10\, Ra_c$ while the hybrid and 3D models agree fairly well up to $Ra \sim 20\, Ra_c$. Models that include laterally varying heat flux at the outer boundary reproduce regional convection patterns that compare well with those found in similarly forced 3D models. Previously proposed scaling laws for rapidly rotating convection are tested; our simulations are overall well described by a triple balance between Coriolis, inertia and Archimedean forces with the lengthscale of the convection following the diffusionfree Rhinesscaling. The magnitude of Pr affects the number and the size of the jets with larger structures obtained at lower Pr. Higher velocities and lower heat transport are seen on decreasing Pr with the scaling behaviour of the convective velocity displaying a strong dependence on Pr. This study is an intermediate step towards a hybrid model of core convection also including 3D magnetic effects.

null (Ed.)We use well resolved numerical simulations with the lattice Boltzmann method to study Rayleigh–Bénard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $Ra \in \left [10^7, 10^{10}\right ]$ , where Pr and Ra are the Prandtl and Rayleigh numbers. The fractal boundaries are functions characterized by power spectral densities $S(k)$ that decay with wavenumber, $k$ , as $S(k) \sim k^{p}$ ( $p < 0$ ). The degree of roughness is quantified by the exponent $p$ with $p < 3$ for smooth (differentiable) surfaces and $3 \le p < 1$ for rough surfaces with Hausdorff dimension $D_f=\frac {1}{2}(p+5)$ . By computing the exponent $\beta$ using power law fits of $Nu \sim Ra^{\beta }$ , where $Nu$ is the Nusselt number, we find that the heat transport scaling increases with roughness through the top two decades of $Ra \in \left [10^8, 10^{10}\right ]$ . For $p$ $= 3.0$ , $2.0$ and $1.5$ we find $\beta = 0.288 \pm 0.005, 0.329 \pm 0.006$ and $0.352 \pm 0.011$ , respectively. We also find that the Reynolds number, $Re$ , scales as $Re \sim Ra^{\xi }$ , where $\xi \approx 0.57$ over $Ra \in \left [10^7, 10^{10}\right ]$ , for all $p$ used in the study. For a given value of $p$ , the averaged $Nu$ and $Re$ are insensitive to the specific realization of the roughness.more » « less