In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. We investigate decaying turbulence produced by the Taylor-Green vortex and find that in the dissipation range the molecular-gas-dynamics spectra grow quadratically with wave number due to thermal fluctuations, in agreement with previous predictions, while the Navier-Stokes spectra decay exponentially. Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the Navier-Stokes equations are widely believed to describe. In fact, our results suggest that the Navier-Stokes equations are not guaranteed to describe the smallest scales of gas turbulence for any positive Knudsen number.
We report flow statistics and visualizations from gas-kinetic simulations using the Direct Simulation Monte Carlo (DSMC) method of compressible turbulent Couette flow over a porous substrate composed of an array of circular cylinders for which the Knudsen number is O(10-1). Comparisons are made with both smooth-wall DSMC simulations and direct numerical simulations of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed.
The commercial software package Barracuda, developed by CPFD Software for simulating particle-laden fluid flows, is evaluated as a means to simulate the motion of bubbles in vibrating liquid-filled containers. Demonstration simulations of bubbles rising due to buoyancy forces in a cylinder filled with silicone oil and angled at 0, 30, 45, and 60 degrees from the vertical were performed by CPFD Software. The results of these simulations are discussed, and the capabilities of Barracuda for simulating bubble motion are assessed. It was determined that at present Barracuda does not meet the needs of the desired application. Further developments that would enable its use for this application are highlighted.
The Smoothed Particle Hydrodynamics (SPH) package within LAMMPS is explored as a possible tool for simulating the motion of bubbles in a vibrating liquid-filled container. As an initial test case, the unphysical but computationally less intense situation of a two-dimensional single bubble rising in a quiescent liquid under the influence of gravity is considered herein. Although physically plausible behavior was obtained under certain conditions, this behavior depends strongly on the system parameters. Moreover, the large density ratio between the liquid and bubble requires extremely small timesteps, which make the simulations undesirably computationally expensive. Ultimately, it was determined that this method is not feasible for providing quantitatively accurate results for the desired application.