Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

A system-approach to the elastohydrodynamic lubrication point-contact problem

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed

Weak-inertial flow between two rough surfaces

“Oseen–Poiseuille” equations are developed from an asymptotic formulation of the three-dimensional Navier–Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier–Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media

Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

The effect of disjoining pressure on the shape of condensing films in a fin-groove corner

Thin film condensation is commonly present in numerous natural and artificial processes. Phase-change driven passive heat spreaders such as heat pipes, which are widely used in electronics cooling, employ a continuous condensation process at the condenser region. When the wick structure of a heat pipe is composed of grooves, the top surfaces of the walls (fins) located between consecutive grooves function as the major source of condensation and the condensate flows along the fin top into the grooves. Modeling of this condensation problem is vital for the proper estimation of condensation heat transfer, which constitutes the basis for the overall performance of an heat pipe together with the evaporation process. In the current study, a solution methodology is developed to model the condensation and associated liquid flow in a fin-groove system. Conservation of mass and momentum equations, augmented Young-Laplace equation and Kucherov-Rikenglaz equation are solved simultaneously to calculate the film thickness profile. The model proposed enables the investigation of the effect of disjoining pressure on the film profile by keeping the fin-groove corner, where the film becomes thinnest, inside the solution domain. The results show that dispersion forces become effective for near isothermal systems with sharp fin-groove corners and the film profile experiences an abrupt change, a slope break, in the close proximity of the corner. The current study is the first computational confirmation of this behavior in the literature