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.
When subjected to certain harmonic oscillations, the gas bubble in a partially liquid-filled, closed, vertical cylinder will break up. Under certain conditions, some of the gas will migrate to the bottom due to Bjerknes forces. At sufficiently large amplitudes, the bubble will break up into gas bubbles at the top and bottom ends of the cylinder. High-speed imaging captured the dynamics of bubble breakup and gas migration. Several parameters were investigated: oscillation frequency, oscillation acceleration, gas volume fraction, and liquid viscosity.
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.
Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60-100 at a Mach number of 0.3. Conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.
The Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics (MGD) has been used for more than 50 years to simulate rarefied gas flows. Modern supercomputers have brought higher-density near-continuum flows within range. In the present paper, DSMC is used to study compressible turbulence in the Taylor-Green (TG) vortex flow. The DSMC results are compared to available numerical results from Direct Numerical Simulation (DNS) of the (continuum) Navier-Stokes equations.
Models and experiments are developed to investigate how a small amount of gas can cause large rectified motion of a piston in a vibrated liquid-filled housing when piston drag depends on piston position so that damping is nonlinear even for viscous flow. Two bellows serve as surrogates for the upper and lower gas regions maintained by Bjerknes forces. Without the bellows, piston motion is highly damped. With the bellows, the piston, the liquid, and the two bellows move together so that almost no liquid is forced through the gaps between the piston and the housing. This Couette mode has low damping and a strong resonance: the piston and the liquid vibrate against the spring formed by the two bellows (like the pneumatic spring formed by the gas regions). Near this resonance, the piston motion becomes large, and the nonlinear damping produces a large rectified force that pushes the piston downward against its spring suspension. A recently developed model based on quasi-steady Stokes flow is applied to this system. A drift model is developed from the full model and used to determine the equilibrium piston position as a function of vibration amplitude and frequency. Corresponding experiments are performed for two different systems. In the two-spring system, the piston is suspended against gravity between upper and lower springs. In the spring-stop system, the piston is pushed up against a stop by a lower spring. Model and experimental results agree closely for both systems and for different bellows properties.
The Direct Simulation Monte Carlo (DSMC) method has been used for more than 50 years to simulate rarefied gases. The advent of modern supercomputers has brought higher-density near-continuum flows within range. This in turn has revived the debate as to whether the Boltzmann equation, which assumes molecular chaos, can be used to simulate continuum flows when they become turbulent. In an effort to settle this debate, two canonical turbulent flows are examined, and the results are compared to available continuum theoretical and numerical results for the Navier-Stokes equations.
The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method's inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird's 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.
We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at Re=500. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.