Publications

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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.

We develop an idealized experimental system for studying how a small amount of gas can cause large net (rectified) motion of an object in a vibrated liquid-filled housing when the drag on the object depends strongly on its position. Its components include a cylindrical housing, a cylindrical piston fitting closely within this housing, a spring suspension that supports the piston, a post penetrating partway through a hole through the piston (which produces the position-dependent drag), and compressible bellows at both ends of the housing (which are well characterized surrogates for gas regions). In this system, liquid can flow from the bottom to the top of the piston and vice versa through the thin annular gaps between the hole and the post (the inner gap) and between the housing and the piston (the outer gap). When the bellows are absent, the piston motion is highly damped because small piston velocities produce large liquid velocities and large pressure drops in the Poiseuille flows within these narrow gaps. However, when the bellows are present, the piston, the liquid, and the bellows execute a collective motion called the Couette mode in which almost no liquid is forced through the gaps. Since its damping is low, the Couette mode has a strong resonance. Near this frequency, the piston motion becomes large, and the nonlinearity associated with the position-dependent drag of the inner gap produces a net (rectified) force on the piston that can cause it to move downward against its spring suspension. Experiments are performed using two variants of this system. In the single-spring setup, the piston is pushed up against a stop by its lower supporting spring. In the two-spring setup, the piston is suspended between upper and lower springs. The equilibrium piston position is measured as a function of the vibration frequency and acceleration, and these results are compared to corresponding analytical results (Torczynski et al., 2017). A quantitative understanding of the nonlinear behavior of this system may enable the development of novel tunable dampers for sensing vibrations of specified amplitudes and frequencies.

Models and simulations are employed to analyze the motion of a spring-supported piston in a vibrated liquid-filled cylinder. The piston motion is damped by forcing liquid through a narrow gap between a hole through the piston and a post fixed to the housing. As the piston moves, the length of this gap changes, so the piston damping coefficient depends on the piston position. This produces a nonlinear damper, even for highly viscous flow. When gas is absent, the vibration response is overdamped. However, adding a little gas changes the response of this springmass-damper system to vibration. During vibration, Bjerknes forces cause some of the gas to migrate below the piston. The resulting pneumatic spring enables the liquid to move with the piston so as to force very little liquid through the gap. Thus, this "Couette mode" has low damping and a strong resonance near the frequency given by the pneumatic spring constant and the total mass of the piston and the liquid. Near this frequency, the amplitude of the piston motion is large, so the nonlinear damper produces a large net force on the piston. To analyze the effect of this nonlinear damper in detail, a surrogate system is developed by modifying the original system in two ways. First, the gas regions are replaced by upper and lower bellows with similar compressibility to give a well-defined "pneumatic" spring. Second, the upper stop against which the piston is pushed by its lower supporting spring is replaced with an upper spring, thereby removing the nonlinearity from the stop. An ordinary-differential-equation (ODE) drift model based on quasi-steady Stokes flow is used to produce a regime map of the vibration amplitudes and frequencies for which the piston is up or down for conditions of experimental interest. These results agree fairly well with Arbitrary Lagrangian Eulerian (ALE) simulations of the incompressible Navier-Stokes (NS) equations for the liquid and Newton's 2nd Law for the piston and bellows. A quantitative understanding of this nonlinear behavior may enable the development of novel tunable dampers for sensing vibrations of specified amplitudes and frequencies.

The Rayleigh-Taylor instability (RTI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, two-dimensional and three-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode-perturbed interfaces between two atmospheric-pressure monatomic gases. The DSMC simulations reproduce all qualitative features of the RTI and are in reasonable quantitative agreement with existing theoretical and empirical models in the linear, nonlinear, and self-similar regimes. At late times, the instability is seen to exhibit a self-similar behavior, in agreement with experimental observations. For the conditions simulated diffusion can influence the initial instability growth significantly.

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In this paper, 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. Finally, for the conditions simulated, diffusion can influence the initial instability growth significantly.

We show how introducing a small amount of gas can completely change the motion of a solid object in a viscous liquid during vibration. We analyze an idealized system exhibiting this behavior: a piston in a liquid-filled housing with narrow gaps between piston and housing surfaces that depend on the piston position. Recent experiments have shown that vibration causes some gas to move below the piston and the piston to subsequently move downward against its supporting spring. We analyze the analogous but simpler situation in which the gas regions are replaced by bellows with similar pressure-volume relationships. We show that the spring formed by these bellows (analogous to the pneumatic spring formed by the gas regions) enables the piston and the liquid to oscillate in a mode with low damping and a strong resonance. We further show that, near this resonance, the dependence of the gap geometry on the piston position produces a large rectified (net) force on the piston. This force can be much larger than the piston weight and tends to move the piston in the direction that decreases the flow resistance of the gap geometry.

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Analysis, simulations, and experiments are performed for a piston in a vibrated liquid-filled cylinder, where the damping caused by forcing liquid through narrow gaps depends almost linearly on the piston position. Adding a little gas completely changes the dynamics of this spring-mass-damper system when it is subject to vibration. When no gas is present, the piston's vibrational response is highly overdamped due to the viscous liquid being forced through the narrow gaps. When a small amount of gas is added, Bjerknes forces cause some gas to migrate below the piston. The resulting pneumatic spring enables the liquid to move with the piston so that little liquid is forced through the gaps. This "Couette mode" thus has low damping and a strong resonance near the frequency given by the pneumatic spring constant and the piston mass. Near this frequency, the piston response is large, and the nonlinearity from the varying gap length produces a net force on the piston. This "rectified" force can be many times the piston's weight and can cause the piston to compress its supporting spring. A surrogate system in which the gas regions are replaced by upper and lower bellows with similar compressibility is studied. A recently developed theory for the piston and bellows motions is compared to finite element simulations. The liquid obeys the unsteady incompressible Navier-Stokes equations, and the piston and the bellows obey Newton's 2nd Law. Due to the large piston displacements near resonance, an Arbitrary Lagrangian Eulerian (ALE) technique with a sliding-mesh scheme is used to limit mesh distortion. Theory and simulation results for the piston motion are in good agreement. Experiments are performed with liquid only, with gas present, and with upper and lower bellows replacing the gas. Liquid viscosity, bellows compressibility, vibration amplitude, and gap geometry are varied to determine their effects on the frequency at which the rectified force makes the piston move down. This critical frequency is found to depend on whether the frequency is increased or decreased with time.

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