We present that 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. Lastly, 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.
Here, 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. Finally, 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.
We provide the first demonstration that molecular-level methods based on gas kinetic theory and molecular chaos can simulate turbulence and its decay. The direct simulation Monte Carlo (DSMC) method, a molecular-level technique for simulating gas flows that resolves phenomena from molecular to hydrodynamic (continuum) length scales, is applied to simulate the Taylor-Green vortex flow. The DSMC simulations reproduce the Kolmogorov -5/3 law and agree well with the turbulent kinetic energy and energy dissipation rate obtained from direct numerical simulation of the Navier-Stokes equations using a spectral method. This agreement provides strong evidence that molecular-level methods for gases can be used to investigate turbulent flows quantitatively.
The Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. For the conditions simulated, diffusion can influence the initial instability growth significantly.