No-slip condition

Summary

In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition. For highly viscous foodstuffs that contain a high level of fat, such as mayonnaise and melted cheese, the no-slip condition cannot be applied, due to their "self-lubricating" properties. Physical justification Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance bring

Official source

https://en.wikipedia.org/wiki/No-slip_condition

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Partial slip at fluid-solid boundaries by multiparticle collision dynamics simulations

Maxim Belushkin, Giuseppe Foffi, Samuel Hanot

The understanding of the exact boundary conditions at the interface between a solid and a fluid is becoming increasingly important, as the limitations of the no-slip boundary condition are becoming apparent, especially in micro- and nanofluidics applications. We present a systematic study of controlled partial-slip boundary conditions in multiparticle collision dynamics simulations. By studying a plane Poiseuille flow, we demonstrate that, in general, the slip length of the fluid strongly depends on the microscopic dynamics in the vicinity of the solid surface. We empirically derive the dependence of the slip length on the properties of the MPC fluid and of the wall, and demonstrate that the wall slip in this coarse-grained simulation approach is linearly correlated with the flux of momentum across the fluid-solid interface.

Royal Soc Chemistry2013

This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top Surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry and of the prescribed boundary conditions of Dirichlet type-no-slip on the cavity walls. The top Surface of the cylindrical cavity is left open with an imposed stress-free boundary condition, while a no-slip condition with a prescribed rotational velocity is imposed on the bottom wall. The Reynolds regime corresponds to transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new flow states that were investigated based on a fully three-dimensional Solution of the Navier-Stokes equations for the free-surface cylindrical swirling flow, without resorting to any symmetry property unlike all other results available in the literature, Theses solutions are obtained through direct numerical simulations based on a Legendre spectral element method. (C) 2009 Elsevier Ltd. All rights reserved.

2009

Large Eddy Simulation of Particle Dynamics Inside a Differentially Heated Cavity

Christoph Bosshard

In nuclear safety, most severe accident scenarios lead to the presence of fission products in aerosol form in the closed containment atmosphere. It is important to understand the particle depletion process to estimate the risk of a release of radioactivity to the environment should a containment break occur. As a model for the containment, we use the three-dimensional differentially heated cavity (DHC) problem. DHC is a cubical box with a hot wall and a cold wall on vertical opposite sides. On the other walls of the cube we have adiabatic boundary conditions. For the velocity field the no-slip boundary condition is valid. The flow of the air in the cavity is described by the Boussinesq equations. Complex flow patterns develop and the flow characteristics depend on the non-dimensional Rayleigh and Prandtl numbers. The predominant flow type in the DHC is a turbulent natural convection flow. This work aims at reaching Rayleigh numbers and turbulent levels as high as possible given the available computational resources. The method used to simulate the turbulent flow is the large eddy simulation (LES) where the dynamics of the large eddies is resolved by the computational grid and the small eddies are modelled by the introduction of subgrid scale quantities using a filter function. Numerically, the LES equations are discretized by the spectral element method. Particle trajectories are computed using the Lagrangian particle tracking method, including the relevant forces (drag, gravity, thermophoresis). Four different particle sets with each set containing one million particles and diameters of 10 μm, 15 μm, 25 μm and 35 μm are simulated. The complexity and the size of the large three-dimensional problem requires the use of massively parallel supercomputers. Spectral element methods are naturally suitable for parallelisation by distributing the elements among the processors. For the Lagrangian particle tracking we use a method where equal numbers of particles are assigned to every processor. The flow field is broadcast and every particle processor tracks the assigned particles, a procedure which leads to a perfect load balancing. Simulation results for the flow field and particle sizes from 15 μm to 35 μm at a Rayleigh number of 109 are compared to previous results from a direct numerical simulation. First order statistics of the LES flow fields are in very good agreement with the direct numerical simulation while the agreement of second order moments is fair. Also the turbulent structures associated to the maximum of turbulent kinetic energy production are correctly reproduced. Particle statistics in the LES and the direct numerical simulation were similar and the settling rates practically identical. Contrary to previous particle simulations in LES, it was found that no model was necessary for the influence of the unresolved flow scales on the particle motions. This can be explained, because the important settling mechanism is through gravity and particle deposition at the walls by turbophoresis is negligible.

EPFL2012

Large Eddy Simulation of Particle Dynamics Inside a Differentially Heated Cavity

Christoph Bosshard

EPFL2012