Oscillating Gas Flow Research Articles

Frequency-domain Monte Carlo method for linear oscillatory gas flows

Gas flows generated by resonating nanoscale devices inherently occur in the non-continuum, low Mach number regime. Numerical simulations of such flows using the standard direct simulation Monte Carlo (DSMC) method are hindered by high statistical noise, which has motivated the development of several alternate Monte Carlo methods for low Mach number flows. Here, we present a frequency-domain low Mach number Monte Carlo method based on the Boltzmann–BGK equation, for the simulation of oscillatory gas flows. This circumvents the need for temporal simulations, as is currently required, and provides direct access to both amplitude and phase information using a pseudo-steady algorithm. The proposed method is validated for oscillatory Couette flow and the flow generated by an oscillating sphere. Good agreement is found with an existing time-domain method and accurate numerical solutions of the Boltzmann–BGK equation. Analysis of these simulations using a rigorous statistical approach shows that the frequency-domain method provides a significant improvement in computational speed.

Experimental study of heat transfer in oscillatory gas flow inside a parallel-plate channel with imposed axial temperature gradient

Understanding of heat transfer processes between a solid boundary and an oscillatory gas flow is important for the design of internal components such as heat exchangers, regenerators and thermal buffer tubes in thermoacoustic and Stirling thermodynamic machines where the flow oscillations are part of the power production or transfer processes. The heat transfer between the flow and an arrangement of hot and cold plates forming a parallel-plate channel is studied experimentally and numerically. Here, the particular focus is on the processes occurring within the thermal and viscous boundary layers. The measured phase-dependent temperature fields combined with the velocity fields are studied in detail. Near wall temperature minima and maxima of the cross sectional temperature profiles are observed when the gas moves from cold to hot or from hot to cold parts of the channel. They are referred to as “temperature undershoot” and “overshoot”, respectively. The existence of these temperature minima and maxima causes large local temperature gradients in the direction normal to the wall, which result in large heat diffusion between gas layers in the direction normal to the wall. It is observed that the flow history has a strong impact on the temperature fields. This invalidates the so-called “Iguchi hypothesis”, based on which the heat transfer data for steady flows is being applied to oscillatory flow conditions. General guidelines for the design of heat exchangers used in thermoacoustic devices are discussed.

Oscillatory rarefied gas flow inside rectangular cavities

AbstractTwo-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry.

Lattice Boltzmann method for linear oscillatory noncontinuum flows.

Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.

Oscillating gas flow induces reptation of granular droplets

We report on the reptation of vertically vibrated droplets of fine particles lying on a solid incline. On the one hand, time-resolved measurements show that the gas pressure in the gap between the droplet bottom and the solid surface can be accounted for by a Darcy law. The cumulative effect of the viscous drag is responsible for the droplet formation. On the other hand, we show that the gap pressure is responsible for an effective horizontal acceleration whose cumulative effect is the upward reptation of the droplets. Using various geometries of the solid substrate, we manipulate the droplets and study the effects of the substrate geometry and of the experimental parameters on the droplet shape and dynamics. The experimental results are discussed in the light of theoretical arguments. This study demonstrates that, by the choice of a suitable geometry of the surface and characteristics of the vibration, one can develop tools for precise powder handling and control.

Enhancement of CO2 capture at Ca-looping conditions by high-intensity acoustic fields

The Ca-Looping (CaL) technology, based on a dual gas-fluidized bed system of CaO/CaCO3 particles operated at high temperature, is a viable technological process for highly efficient pre-combustion and post-combustion CO2 capture. In this paper we show a lab-scale experimental study on the carbonation/decarbonation of a fluidized bed of CaO particles at CaL conditions as affected by the application of a high-intensity acoustic field. The results obtained demonstrate that both carbonation and decarbonation are remarkably enhanced for sound intensity levels above 140dB and frequencies of about 100Hz. Fine particles (of size smaller than dp∼100μm) are entrained in the oscillating gas flow induced by an acoustic field of such low frequency, which yields a strong agitation of the bed and improves the gas–solid contact efficiency. On the other hand, an intense convection of gas flow (acoustic streaming) is generated on the surface of larger particles unmovable by the sound wave, which promotes the heat/mass transfer at the gas–solid boundary in this case. Either of these mechanisms, whose relative importance will depend on the average particle size and sound frequency, will contribute to increase the carbonation and decarbonation rates of CaO fluidized beds in the CaL technology.

Lattice Boltzmann approach for the simulation of rarefied gas flow in the slip flow regime

For rarefied gas flows in micro-devices, the rarefaction effect becomes significant and the slip at the solid wall becomes an important flow feature. The lattice Boltzmann equation (LBE) method has been used to simulate rarefied gas flows in micro-systems and proved its accuracy in capturing rarefied effect. However, the results of previous studies are not in accordance with each other even though they were started from the same governing equation to solve the same problem, and show only qualitative agreements with those of experimental or analytic approaches. The discrepancies of the results come from the boundary condition and the relation between Knudsennumber and relaxation-time. In this work, the best combination of LBE approach, which employs an equilibrium wall boundary condition and a Knudsen-number-relaxation-time relation derived using the viscosity-based mean free path and mean thermal speed, is suggested. The results of the simulations are compared with the analytic solutions. The present 2D results of microchannel and oscillatory shear-driven gas flows are in excellent agreement with the analytical solution. The results of 3D microchannel flow are also compared with the analytic solutions, and are in good agreement.

Basic Operation of Cryocoolers and Related Thermal Machines

This paper deals with the basics of cryocoolers and related thermodynamic systems. The treatment is based on the first and second law of thermodynamics for inhomogeneous, open systems using enthalpy flow, entropy flow, and entropy production. Various types of machines, which use an oscillating gas flow, are discussed such as: Stirling refrigerators, GM coolers, pulse-tube refrigerators, and thermoacoustic coolers and engines. Furthermore the paper deals with Joule-Thomson and dilution refrigerators which use a constant flow of the working medium.

Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow

Accurate evaluation of damping in laterally oscillating microstructures is challenging due to the complex flow behavior. In addition, device fabrication techniques and surface properties will have an important effect on the flow characteristics. Although kinetic approaches such as the direct simulation Monte Carlo (DSMC) method and directly solving the Boltzmann equation can address these challenges, they are beyond the reach of current computer technology for large scale simulation. As the continuum Navier-Stokes equations become invalid for nonequilibrium flows, we take advantage of the computationally efficient lattice Boltzmann method to investigate nonequilibrium oscillating flows. We have analyzed the effects of the Stokes number, Knudsen number, and tangential momentum accommodation coefficient for oscillating Couette flow and Stokes' second problem. Our results are in excellent agreement with DSMC data for Knudsen numbers up to Kn=O(1) and show good agreement for Knudsen numbers as large as 2.5. In addition to increasing the Stokes number, we demonstrate that increasing the Knudsen number or decreasing the accommodation coefficient can also expedite the breakdown of symmetry for oscillating Couette flow. This results in an earlier transition from quasisteady to unsteady flow. Our paper also highlights the deviation in velocity slip between Stokes' second problem and the confined Couette case.

Quantification of energy dissipation for laterally oscillating microstructures

Fluid film damping in laterally oscillating microstructures is investigated in the entire Knudsen regime and a wide Stokes number range using analytical and numerical results from Park et al. [“Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime,” Phys. Fluids 16, 317 (2004)] and Hadjiconstantinou [“Oscillatory shear driven gas flows in the transition and free-molecular-flow regimes,” Phys. Fluids 17, 100611 (2005)]. An energy dissipation parameter per oscillation cycle that allows a consistent interpretation of the quality factor utilized in the design of microelectromechanical system devices is presented.

Grouping and trapping of evaporating droplets in an oscillating gas flow

A new approach to the analysis of droplet grouping in an oscillating gas flow is suggested. This is based on the investigation of droplet trajectories in the frame of reference moving with the phase velocity of the wave. Although the equations involved are relatively simple, the analysis shows distinctive characteristics of grouping and non-grouping cases. In the case of grouping, droplet trajectories converge to the points for which the ratio of flow velocity in this frame of reference and the amplitude of flow oscillations is less than 1, and the cosine of the arc sine of this ratio is positive. In the case of non-grouping, droplet trajectories in this frame of reference oscillate around the translational velocity close to the velocity of flow in the same frame of reference. The effect of droplet size on the grouping pattern is investigated. It has been pointed out that for the smaller droplets much more stable grouping is observed. The effect of droplet evaporation is studied in the limiting case when the contribution of the heat-up period can be ignored. It is shown that evaporation can lead to droplet grouping even in the case when the non-evaporating droplets are not grouped. This is related to the reduction in droplet diameter during the evaporation process. Coupling between gas and droplets is shown to decrease the grouping tendency. A qualitative agreement between predictions of the model and in-house experimental observations referring to Diesel engine sprays has been demonstrated.

Oscillatory Gas Flow in a Circular Nanotube

Gas flow through nanoscale conduits shows distinctly different physics compared to flow at the macroscale. One of the first manifestations of this is the appearance of wall slip. Here we consider the oscillatory flow of an incom- pressible Newtonian gas through a circular nanotube, with first order wall slip due to rarefaction. It was found that the ma- jor effect of wall slip at lower oscillation frequencies is to alter the instantaneous velocity profiles from Poiseuille-like to more plug-like, with an overall enhancement to the fluid velocity magnitude. However, at higher frequencies the en- hancement to velocity magnitude due to wall slip is greatly diminished, and rarefaction introduces a region of backflow near the centerline of the nanotube. These flow characteristics may have important implications for the design of various practical applications of unsteady gas flow through nanoscale conduits, from fuel cell membranes to gas-powered nanomachines constructed from carbon nanotubes.

Oscillatory Gas Flow in a Circular Nanotube

Oscillatory Gas Flow in a Circular Nanotube

Simulation study of air-induced segregation of equal-sized bronze and glass particles

We have investigated the effect of air on the density segregation of fine, equal-sized bronze and glass particles under vertical sinusoidal vibrations by numerical simulation, using a hybrid granular dynamics-computational fluid dynamics model. We find both the bronze-on-top and the sandwich configurations as observed in previous experiments. The simulations allow us to give a detailed explanation of the phenomena. The key observation is the precise timing of the decompaction of the bed with the oscillating gas flow, which will cause the bronze to move to the top, due to the difference in acceleration from the air drag. For higher frequencies, the different inertia in collisions will cause the bronze clusters on top to sink through the bed, leading to a sandwich formation.

Experimental and Computational Analysis of Periodic Flow Structure in Oscillatory Gas Flow Meters

AbstractThe oscillatory characteristics and dynamic structure of periodic flow in an oscillatory gas flow meter were studied experimentally and numerically. The flow oscillations were triggered by the Coanda effect and an universal correlation between Strouhal number and Reynolds number, Str = 1.09 × 10−3 for ReHD >800, was deduced based on spectral analysis of the pressure fluctuations in the flow channel. Numerical simulation indicated that the evolution of the flow patterns was classified into stages of induction and sustainable periodic oscillation. The transformation between the two stages was noticeably affected by the design of the feedback channels. The results further revealed that the development of the main vortex in the oscillating chamber and the small vortices at the entrance of the feedback channels concurrently modulate the mechanism of oscillation. The small vortices located at both entrances of the feedback channels play the role of a pair of modulating valves, which alternatively switch on and off the bypass flow through each feedback channel, thus reinforcing the periodic oscillation.

Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes

We investigate oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes. Analytical results valid through slip flow and the early transition regime are obtained using a recently proposed, rigorous second-order slip model with no adjustable coefficients. Analytical solution of the collisionless Boltzmann equation provides a description of the high Knudsen number limit (Kn⪢1) including the bounded shear layers present in the limit of high oscillation frequency. These layers are analogous to the Stokes layers observed in the Kn⪡1 limit, but contrary to the latter, they exhibit a nonconstant wave speed as demonstrated by Park, Bahukudumbi, and Beskok in Phys. Fluids. 16, 317 (2004). All theoretical results are validated by direct Monte Carlo simulations. We find that the second-order slip results are in good agreement with direct simulation Monte Carlo (DSMC) solutions up to Kn≈0.4; in some cases these results continue to provide useful approximations to quantities of engineering interest, such as the shear stress, well beyond Kn≈0.5. The collisionless theory provides, in general, a good description of DSMC results for Kn≳10, while in the high frequency limit the agreement is very good for Knundsen numbers as low as Kn≈5.

Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime

A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo (DSMC) method. Computations are performed as a function of the Knudsen (Kn) and Stokes (β) numbers, in the entire Knudsen regime (Kn⩽100) and a wide range of Stokes numbers (β⩽7.5). The DSMC results are validated using a recently developed semianalytical/empirical model that is applicable for quasisteady flows (β⩽0.25) in the entire Knudsen regime, and for any Stokes number flow in the slip flow regime (Kn⩽0.1). In addition, we derived an analytical solution of the linearized collisionless Boltzmann equation for oscillatory Couette flows, and utilized this to validate the DSMC results in the free-molecular flow regime. Dynamic response of the flow, including the velocity profiles, phase angle, wave speed, shear stress, and the penetration depth for high Stokes number flows are presented. Increasing the Stokes number at fixed Kn, we observed formation of “bounded Stokes layers,” as expected. However, increasing the Knudsen number at fixed β results in “bounded rarefaction layers,” where the penetration depth continuously decreases with increasing the Kn. Interplay between the rarefaction and unsteadiness contributes to this interesting flow physics, and also introduces a new characteristic length scale to the problem.

Hydrodynamic simulation of methanol synthesis in gas–liquid slurry bubble column reactors

A transient, two-dimensional hydrodynamic model for the production of methanol from syn-gas in an Air Products/DOE LaPorte slurry bubble column reactor was developed. The model predicts downflow of catalyst at the walls and oscillatory particle and gas flow at the center, with a frequency of about 0.7 H. The computed temperature variation in the reactor with heat exchangers was only about 5°K, indicating good thermal management. The computed slurry height, the gas holdup and the rate of methanol production agree with LaPorte's reported data. Unlike the previous models in the literature, this model computes the gas and the particle holdups and the particle rheology. The only adjustable parameter in the model is the effective particle restitution coefficient. It gives values of granular temperature, random particle oscillating velocities, that agree with measurements in a laboratory slurry bubble column containing the methanol catalyst that was built to approximate the La Porte reactor. The computed turbulent kinetic energy or the granular temperature agrees with similar measurements at Ohio State University in a bubble column extrapolated to no particles.

The effect of the ageing procedure upon the activity of a three-way catalyst working under transient conditions

The mode of ageing of a model three-way catalyst has been studied. The comparison of stationnary or cycling ageing and of a conventionnal thermal ageing shows very different results. The catalysts have been characterised by their reactivity under transient conditions and by Temperature Programmed Reduction. Under an oscillating gas flow, closed to real conditions, there is formation of destruction of a pre-existing alloy while a thermal ageing leads to a severe sintering of the metallic phase Pt-Rh.

Oscillatory Electrohydrodynamic Gas Flows

Prior numerical solutions of electrohydrodynamic flows in a positive-corona, wire-plate electrostatic precipitator are extended to reveal steady-periodic electrohydrodynamic flows. Previously, only steady solutions were reported. The present study includes results for flows with Reynolds numbers from 0 to 4800 and with dimensionless electric number ranging from 0.06 to ∞. Results indicate that two regimes of low frequency oscillatory flow occur. The first regime is characterized by a single recirculating vortex that oscillates in strength between one and five Hertz. The second regime is characterized by two counter-rotating vortices that oscillate in strength at a frequency near one Hertz.