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Register a new userCombined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nano-particles transport in buoyancy driven flow
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The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the Navier-Stokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines Newtons method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that Stream Upwind Petrov-Galerkin regularization approach is required to solve properly the ill-posed Buongiorno transport model being tackled as a variational problem under mean value constraint. Non-trivial numerical computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature. The numerical experiments demonstrate that by accounting for only the thermophoresis and Brownian motion forces in the concentration transport equation, the model is not able to reproduce the heat transfer impairment due to the presence of suspended nanoparticles in the base fluid. It reveals, however, the significant role that these two terms play in the vicinity of the hot and cold walls.
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We investigate the ability of discontinuous Galerkin (DG) methods to simulate under-resolved turbulent flows in large-eddy simulation. The role of the Riemann solver and the subgrid-scale model in the prediction of a variety of flow regimes, including transition to turbulence, wall-free turbulence and wall-bounded turbulence, are examined. Numerical and theoretical results show the Riemann solver in the DG scheme plays the role of an implicit subgrid-scale model and introduces numerical dissipation in under-resolved turbulent regions of the flow. This implicit model behaves like a dynamic model and vanishes for flows that do not contain subgrid scales, such as laminar flows, which is a critical feature to accurately predict transition to turbulence. In addition, for the moderate-Reynolds-number turbulence problems considered, the implicit model provides a more accurate representation of the actual subgrid scales in the flow than state-of-the-art explicit eddy viscosity models, including dynamic Smagorinsky, WALE and Vreman. The results in this paper indicate new best practices for subgrid-scale modeling are needed with high-order DG methods.
The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, is limited owing to its computational complexity. Here, we propose a wavelet-based adaptive version of the POD (the wPOD), in order to overcome this limitation. The amount of data to be analyzed is reduced by compressing them using biorthogonal wavelets, yielding a sparse representation while conveniently providing control of the compression error. Numerical analysis shows how the distinct error contributions of wavelet compression and POD truncation can be balanced under certain assumptions, allowing us to efficiently process high-resolution data from three-dimensional simulations of flow problems. Using a synthetic academic test case, we compare our algorithm with the randomized singular value decomposition. Furthermore, we demonstrate the ability of our method analyzing data of a 2D wake flow and a 3D flow generated by a flapping insect computed with direct numerical simulation.
Rayleigh--Taylor fluid turbulence through a bed of rigid, finite-size, spheres is investigated by means of high-resolution Direct Numerical Simulations (DNS), fully coupling the fluid and the solid phase via a state-of-the art Immersed Boundary Method (IBM). The porous character of the medium reveals a totally different physics for the mixing process when compared to the well-known phenomenology of classical RT mixing. For sufficiently small porosity, the growth-rate of the mixing layer is linear in time (instead of quadratical) and the velocity fluctuations tend to saturate to a constant value (instead of linearly growing). We propose an effective continuum model to fully explain these results where porosity originated by the finite-size spheres is parameterized by a friction coefficient.
The behaviour of the turbulent Prandtl number ($Pr_t$) for buoyancy-affected flows near a vertical surface is investigated as an extension study of {Gibson & Leslie, emph{Int. Comm. Heat Mass Transfer}, Vol. 11, pp. 73-84 (1984)}. By analysing the location of mean velocity maxima in a differentially heated vertical planar channel, we {identify an} {infinity anomaly} for the eddy viscosity $ u_t$ and the turbulent Prandtl number $Pr_t$, as both terms are divided by the mean velocity gradient according to the standard definition, in vertical buoyant flow. To predict the quantities of interest, e.g. the Nusselt number, a machine learning framework via symbolic regression is used with various cost functions, e.g. the mean velocity gradient, with the aid of the latest direct numerical simulation (DNS) dataset for vertical natural and mixed convection. The study has yielded two key outcomes: $(i)$ the new machine learnt algebraic models, as the reciprocal of $Pr_t$, successfully handle the infinity issue for both vertical natural and mixed convection; and $(ii)$ the proposed models with embedded coordinate frame invariance can be conveniently implemented in the Reynolds-averaged scalar equation and are proven to be robust and accurate in the current parameter space, where the Rayleigh number spans from $10^5$ to $10^9 $ for vertical natural convection and the bulk Richardson number $Ri_b $ is in the range of $ 0$ and $ 0.1$ for vertical mixed convection.
We use well-resolved numerical simulations to study the combined effects of buoyancy, pressure-driven shear and rotation on the melt rate and morphology of a layer of pure solid overlying its liquid phase in three dimensions at a Rayleigh number $Ra=1.25times10^5$. During thermal convection we find that the rate of melting of the solid phase varies non-monotonically with the strength of the imposed shear flow. In the absence of rotation, depending on whether buoyancy or shear is dominant, we observe either domes or ridges aligned in the direction of the shear flow respectively. Furthermore, we show that the geometry of the phase boundary has important effects on the magnitude and evolution of the heat flux in the liquid layer. In the presence of rotation, the strength of which is characterized by the Rossby number ($Ro$), we observe that for $Ro = mathcal{O}(1)$ the mean flow in the interior is perpendicular to the direction of the constant applied pressure gradient. As the magnitude of the applied horizontal pressure gradient increases, the geometry of solid-liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular to or aligned at an oblique angle to the applied pressure gradient.
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