On dynamical friction in a gaseous medium with a boundary

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. We study the effects of the presence of a boundary on dynamical friction by studying analytically the interaction of perturber with uniform rectilinear motion in a uniform homogeneous medium with a reflecting planar boundary. Wake reflection at a medium's boundary may occur at the edges of truncated disks perturbed by planetary or stellar companions as well as in numerical simulations of planet-disk interaction with no-outflow boundary conditions. In this paper, we show that the presence of the boundary modifies the behaviour of dynamical friction significantly. We find that perturbers are invariably pushed away from the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless of initial velocity. Dynamical friction may even be reversed for Mach numbers less than 0.37 thereby accelerating instead of decelerating the perturber. Perturbers moving parallel to the boundary feel additional friction orthogonal to the direction of motion that is much stronger than the standard friction along the direction of motion. These results indicate that the common use of the standard Chandrasekhar formula as a short hand estimate of dynamical friction may be inadequate as observed in various numerical simulations.Comment: Revised version, 28 pages, 10 figures, Accepted for publication in Astrophysics & Space Scienc

Unsteady 3D-Navier-Stokes System with Tresca's Friction Law

Motivated by extrusion problems, we consider a non-stationary incompress-ible 3D fluid flow with a non-constant (temperature dependent) viscosity, subjected to mixed boundary conditions with a given time dependent velocity on a part of the boundary and Tresca's friction law on the other part. We construct a sequence of approximate solutions by using a regularization of the free boundary condition due to friction combined with a particular penalty method, reminiscent of the " incompressibility limit " of compressible fluids, allowing to get better insights into the links between the fluid velocity and pressure fields. Then we pass to the limit with compactness arguments to obtain a solution to our original problem

Effective boundary conditions for dense granular flows

We derive an effective boundary condition for granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit between no-slip and Coulomb friction; two simple functions relating wall stress, velocity, and velocity variance are found from numerical simulations. Moreover, we show that this effective boundary condition corresponds to Navier slip condition when GDR MiDi's model is assumed to be valid, and that the slip length depends on the length scale that characterises the system, \emph{viz} the particle diameter.Comment: 4 pages, 5 figure

Direct measurements and analysis of skin friction and cooling downstream of multiple flush-slot injection into a turbulent Mach 6 boundary layer

Experiments were conducted to determine the reduction in surface skin friction and the effectiveness of surface cooling downstream of one to four successive flush slots injecting cold air at an angle of 10 deg into a turbulent Mach 6 boundary layer. Data were obtained by direct measurement of surface shear and equilibrium temperatures, respectively. Increasing the number of slots decreased the skin friction, but the incremental improvement in skin-friction reduction decreased as the number of slots was increased. Cooling effectiveness was found to improve, for a given total mass injection, as the number of slots was increased from one to four. Comparison with previously reported step-slot data, however, indicated that step slots with tangential injection are more effective for both reducing skin friction and cooling than the present flush-slot configuration. Finite-difference predictions are in reasonable agreement with skin-friction data and with boundary-layer profile data

Combined riblet and lebu drag reduction system

The invention is a system of flow control devices which result in reduced skin friction on aerodynamic and hydrodynamic surfaces. The devices cause a breakup of large-scale disturbances in the boundary layer of the flow field. The riblet device acts to reduce disturbances near the boundary layer wall by the use of longitudinal striations forming V-shaped grooves. These grooves are dimensional on the order of the wall vortices and turbulent burst dimensions. The large eddy breakup device is a small strip or airfoil which is suspended in the upper region of the boundary layer. Various physical mechanisms cause a disruption of the large-scale vortices. The combination of the devices of this invention result in a substantial reduction in skin friction drag

Study of longitudinal vibrations of stab knife refiners

The subject of research is the longitudinal vibrations of stab knife refiners. A model of the fibrous layer between the rotor and stator is developed. It is shown that it is advisable to use the Maxwell-Thomson model for liquid friction of the rotor and stator, and the Hooke elastic model for boundary friction. The formula for determining the dynamic stiffness of the fibrous layer is obtained. Dynamic and mathematical models of the refiner in the longitudinal direction are developed. The mathematical model is a system of linear differential equations with periodically varying coefficients (Mathieu-Hill equations). A method for calculating the amplitude of oscillations of the refiner rotor and stator is developed. According to this technique, Andritz 54-60-1c stab refiner was designed. Oscillation parameters of the refiner rotor and stator are determined theoretically and experimentally. The stator oscillation amplitude is 1.6-2.3 times smaller than the rotor oscillation one. In case of boundary friction, the amplitude of oscillations of the stator and rotor increases by 2-3 times in comparison with liquid friction. The oscillation amplitude of the rotor and stator in the longitudinal direction is comparable with the gap between these elements. Therefore, it is recommended while designing refiners, to develop methods and means of vibration protection, and during operation, to prevent boundary friction between headsets. The developed calculation procedure can be used in other industries, for example, mining and metallurgy. © Published under licence by IOP Publishing Ltd

Thermodynamics and kinetics of boundary friction

A deterministic theory describing the behavior of an ultrathin lubricant film between two atomically-smooth solid surfaces is proposed. For the description of lubricant state the parameter of excess volume arising due to chaotization of solid medium structure in the course of melting is introduced. Thermodynamic and shear melting are described. Dependences of friction force on temperature of lubricant, shear velocity of rubbing surfaces, and pressure upon surfaces are analyzed. Within the framework of a simple tribological model the stick-slip mode of friction, when the lubricant periodically melts and solidifies, is described. The obtained results are qualitatively compared with the experimental data. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/1808

Thermodynamics and kinetics of boundary friction

A deterministic theory describing the behavior of an ultrathin lubricant film between two atomically-smooth solid surfaces is proposed. For the description of lubricant state the parameter of excess volume arising due to chaotization of solid medium structure in the course of melting is introduced. Thermodynamic and shear melting is described consistently. Dependences of friction force on temperature of lubricant, shear velocity of rubbing surfaces, and pressure upon surfaces are analyzed. Within the framework of a simple tribological model the stick-slip mode of friction, when the lubricant periodically melts and solidifies, is described. The obtained results are qualitatively compared with the experimental data.Comment: 14 pages, 6 figures, 33 reference

Force calculation on walls and embedded particles in multiparticle collision dynamics simulations

Colloidal solutions posses a wide range of time and length scales, so that it is unfeasible to keep track of all of them within a single simulation. As a consequence some form of coarse-graining must be applied. In this work we use the Multi-Particle Collision Dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct force s on the solid bypassing the calculation of the velocity profile or the stre ss tensor in the fluid near the surface. As an application we measure the friction on a spherical particle, when it is placed in a bulk fluid and when it is confined in a slit. We show that the implementation of the no-slip boundary conditions leads to an enhanced Ensko g friction, which can be understood analytically. Because of the long-range nature of hydrodynamic interactions, the Stokes friction obtained from the simulations is sensitive of the simulation box size. We address this topic for the slit geometry, showing that that the dependence on the system size differs very much from what is expected in a 3D system, where periodic boundary conditions are used in all directions.Comment: To appear in Physical Review