Rarefaction

About: Rarefaction is a research topic. Over the lifetime, 1852 publications have been published within this topic receiving 26943 citations.

On Knudsen-minimum effect and temperature bimodality in a dilute granular Poiseuille flow

Abstract: The numerical simulation of gravity-driven flow of smooth inelastic hard disks through a channel, dubbed ‘granular’ Poiseuille flow, is conducted using event-driven techniques. We find that the variation of the mass-flow rate ( ) with Knudsen number ( ) can be non-monotonic in the elastic limit (i.e. the restitution coefficient ) in channels with very smooth walls. The Knudsen-minimum effect (i.e. the minimum flow rate occurring at for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with , irrespective of the value of the wall roughness. Another rarefaction phenomenon, the bimodality of the temperature profile, with a local minimum ( ) at the channel centerline and two symmetric maxima ( ) away from the centerline, is also studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality (i.e. the ‘excess’ temperature, ) near the continuum limit ( ), but the rarefaction being its origin (as in the molecular gas) holds beyond . The dependence of the excess temperature on the restitution coefficient is compared with the predictions of a kinetic model, with reasonable agreement in the appropriate limit. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both the mass-flow rate and the temperature bimodality on and in this flow. The validity of the Navier–Stokes-order hydrodynamics for granular Poiseuille flow is discussed with reference to the prediction of bimodal temperature profiles and related surrogates.

Chapter viii – sound

Abstract: Publisher Summary This chapter discusses sound waves. A body oscillating in a fluid causes a periodic compression and rarefaction of the fluid near it, thereby producing sound waves. The energy carried away by these waves is supplied from the kinetic energy of the body. Monochromatic waves are important as any wave can be represented as a sum of superposed monochromatic plane waves with various wave vectors and frequencies. This decomposition of a wave into monochromatic waves is simply an expansion as a Fourier series or integral. The terms of this expansion are called the Fourier components of the wave. The energy flux density in a plane sound wave equals the energy density multiplied by the velocity of sound. The propagation of a sound-wave packet is accompanied by the transfer of fluid and is a second-order effect. Turbulent velocity fluctuations also are a cause of sound excitation in the surrounding fluid. If there is something in the path of propagation of a sound wave, then the sound is scattered. Beside the incident wave, there appear other scattered waves, which are propagated in all directions from the scattering body. The existence of viscosity and thermal conductivity results in the dissipation of energy in sound waves, and the sound is consequently absorbed, that is, its intensity progressively diminishes.