Rarefaction Effects Research Articles

Estimate of the Effect of Rarefaction on the Poiseuille Number in a Long Annular Channel under Partial Accomodation of Gas Molecules

Estimate of the Effect of Rarefaction on the Poiseuille Number in a Long Annular Channel under Partial Accomodation of Gas Molecules

Numerical study of three-dimensional flow and aerodynamic characteristics of a cylindrical cavity in rarefied hypersonic flows

Cylindrical cavity configuration frequently appears on the surface of an aerospace vehicle while flow physics of rarefied hypersonic flows over it are not clear yet. This work presents a comprehensive numerical study to reveal flow structures inside the cavity and aerodynamic surface quantities, including the pressure on and heat flux to the surfaces of three-dimensional cylindrical cavities using the DSMC method. The results showed that the traditional cavity flow types based on the classical categorization are not suitable for characterizing rarefied hypersonic flows over cylindrical cavities due to more diverse flow patterns induced by the curved cylindrical sidewall, especially for the cylindrical cavity with a shallow depth. Both the pressure on and heat flux to the striped area near the top lip of downstream curved sidewall are always the strongest due to the violent airflow collision there, which is a depth range of about 0.4 y/H away from the top lip, but those for the cavity floor are usually quite weak because the gas over it moves slowly. With the increase of cavity depth, the weaker pressure on and heat flux to the cavity floor appear because the rising curved sidewall makes it more difficult for freestream to permeate into the cavity, whereas the maximum pressure on and peak heat flux to the downstream curved sidewall seem to be unchanged. The severe rarefaction effect at 90 km make the flow pattern and temperature distribution inside the cavity different from those for 50, 60, and 70 km. As the freestream Mach number is increased from 13.4 to 33.5, the streamline patterns and velocity contours around and inside the cavity only change slightly, consequently leading to similar numerical trends of both the pressure on and heat flow to the cavity surfaces.

Insight into transport performance at the interface of porous catalytic particle by means of numerical simulation

The double slip effect plays an important role in transport characteristics at the permeable porous interface between porous catalytic particle and free fluid, especially for coke deposition process. In this work, a direct pore-scale simulation is carried out via lattice Boltzmann method to investigate the mass, momentum and heat transfer process inside a porous composite system. The spatial distribution of velocity and temperature under the gas rarefaction effect is analyzed. Meanwhile, the impact of coke deposition on the double slip effect is also revealed. The results reveal that a high gas rarefaction effect can weaken the velocity double slip, which are greatly influenced by pore structural parameters. The dynamic evolution of pore structure, flow and heat transfer characteristics of the porous interface during the coke deposition process is investigated. It is found that the heat flow bifurcation phenomenon is enhanced under a high gas rarefaction effect.

Non-continuum effects on a squeezed gas film in a two-dimensional acoustic resonator

We study the effect of gas rarefaction and wall confinement on the propagation of vibroacoustic disturbances in a microchannel, generated by non-uniform (localized) time-harmonic oscillations of one of the channel walls. The problem is studied in the entire range of gas rarefaction rates, combining continuum and free-molecular limit analyses with direct simulation Monte Carlo calculations. Gas rarefaction is found to strongly increase the signal decay rate, varying between a slowly decaying propagating wave parallel to the channel walls at continuum conditions, to a near-source confined acoustic perturbation in the free-molecular regime. The impact of the stationary scattering wall is examined in detail, and the effect of replacing between fully diffuse and specular boundary reflections is found to slightly reduce the decay rate of the signal. The frequency dependence of the force generated by the gas film on the channel walls is calculated. Here, gas rarefaction smooths the transition between resonance and antiresonance behaviours observed in the continuum regime. A model set-up of a fully specular channel with a point delta source is examined, for which closed-form expressions are found for the effect of the stationary wall on the hydrodynamic perturbations and the acoustic force. These expressions assist in rationalizing the fundamental effect of the scattering wall on the system response.

Pressure- and Size-Dependent Aerodynamic Drag Effects on Mach 0.3–2.2 Microspheres for High-Precision Micro-Ballistic Characterization

The acceleration of microparticles to supersonic velocities is required for microscopic ballistic testing, a method for understanding material characteristics under extreme dynamic conditions, and for projectile gene and drug delivery, a needle-free administration technique. However, precise aerodynamic effects upon supersonic microsphere motion at sub-300 Reynolds numbers have not been quantified. We derive drag coefficients for microspheres traveling in air at subsonic, transonic, and supersonic velocities from the measured trajectories of microspheres launched by laser-induced projectile acceleration. Moreover, the observed drag effects on microspheres in atmospheric (760 Torr) and reduced pressure (76 Torr) are compared with existing empirical data and drag coefficient models. We find that the existing models adequately predict the drag coefficient for subsonic microspheres, while rarefaction effects cause a discrepancy between the model and empirical data in the supersonic regime. These results will improve microsphere flight modeling for high-precision microscopic ballistic testing and projectile gene and drug delivery.

Nonmonotonic heat flux trends of a boundary-heated granular gas.

By means of the direct simulation Monte Carlo method, the effect of rarefaction on the heat fluxes and the hydrodynamics of a granular gas bounded by thermal walls is investigated. The heat flux is found to evolve nonmonotonically with the particle inelasticity due to the competition between the particle inelasticity and rarefaction. The former enhances the heat flux, and the latter reduces the heat flux. As the particles become more inelastic, the onset of the heat flux diminishment due to rarefaction is found to be signaled by a temperature gradient collapse. The same temperature gradient convergence, which precedes the rarefied-reduced heat flux, is also found as the applied temperature gradient is increased.

Continuum breakdown in compressible mixing layers.

Gas-kinetic simulations of rarefied and compressible mixing layers are performed to characterize continuum breakdown and the effect on the Kelvin-Helmholtz instability. The unified gas-kinetic scheme (UGKS) is used to perform the simulations at different Mach and Knudsen numbers. The UGKS stress tensor and heat-flux vector fields are compared against those given by the Navier-Stokes-Fourier constitutive equations. The most significant difference is seen in the shear stress and transverse heat flux. The study demonstrates the existence of two distinct continuum breakdown regimes, one at low and the other at high convective Mach numbers. Overall, at low convective Mach numbers, the deviation from continuum stress and heat flux appears to scale exclusively with the micro-macro length scale ratio given by the Knudsen number. On the other hand, at high convective Mach numbers, the deviation depends on the global micro-macro timescale ratio given by the product of Mach and Knudsen numbers. We further demonstrate that, unlike shear stresses and transverse heat flux, the deviations in normal stresses and the streamwise heat flux depend separately on Knudsen and Mach numbers. A local parameter called the gradient Knudsen number is proposed to characterize the rarefaction effects on the local momentum and thermal transport. Noncontinuum aspects of gas-kinetic stress-tensor and heat-flux behavior that Grad's 13-moment equationmodel reasonably captures are identified.

Influence of surface roughness on methane flow in shale kerogen nano-slits

Understanding the mechanism of methane transport in real kerogen nano-pores is critical to evaluate gas productivity in shale formations accurately. This work presents a novel numerical method to generate nano-slits with different surface roughness for Type II-D kerogen in molecular dynamics (MD) simulations. The methane adsorption and transport phenomenon in the kerogen nano-slits are then studied. A modified velocity model is proposed by considering the effect of surface roughness on the slip velocity and the effect of gas rarefaction on the methane viscosity. The ratio of the mass flow rate in the adsorption region to the total flow rate is between 57% and 78% at a channel width of 2.5 nm depending on the surface roughness and pressure, but it drops to between 6% and 16% at a channel width of 10 nm. Hence, two mathematical equations are derived to estimate the mass flow rate in the adoption region from either (1) the adsorption per apparent surface area, or (2) the product of the bulk density and the width of the adsorption region, respectively. Finally, a new flow enhancement model is derived by combining the modified velocity model and the equation for mass flow rate in the adsorption region. The flow enhancement increases with the Knudsen number but decreases with the increase of surface roughness. The proposed flow enhancement model can match the MD simulation well. The proposed model for methane flow enhancement covers the slip flow and transition flow regimes and can potentially be implemented to study the large-scale flow properties, such as permeability, of the shale matrix at various conditions to better evaluate the shale gas production performance.

Rarefaction Effect, Heat Transfer, and Drag Coefficient for Gas Flow Around Square Cylinder in Transition Flow Regime

Abstract In this work, rarefaction effect, heat transfer, and drag coefficient for gas flow around a square cylinder in transition flow regime are numerically studied using unified gas kinetic scheme (UGKS). To reduce computational cost, a mirror symmetry boundary treatment for UGKS is proposed and applied in this study. It is found that: (1) velocity slip is not obvious on upwind and downwind surfaces of square cylinder due to the tangential gas flow being weak in these surfaces; (2) with the increase of local Knudsen number, velocity slip on upper surface always increases, but temperature jump can decrease, which indicates that Knudsen number is not the decisive parameter to characterize temperature jump; (3) the heat transfer between gas and square cylinder enhances with the increase of inflow Knudsen number and cylinder temperature due to the increase of temperature jump and deteriorates with the increase of inflow Mach number on account of gas stagnation; and (4) the drag coefficient increases with the increase of inflow Knudsen number, the decrease of inflow Mach number, and the increase of cylinder temperature. To further predict the variation of average Nusselt number and drag coefficient, correlations for average Nusselt number and drag coefficient with inflow Mach number ranging from 0.05 to 0.3, inflow Knudsen number ranging from 0.1 to 10, and cylinder temperature ranging from 320 K to 380 K are proposed. This research can improve the understanding for mechanisms of gas flow and heat transfer in micro-electromechanical system (MEMS) devices.

On the synchronisation of three-dimensional shock layer and laminar separation bubble instabilities in hypersonic flow over a double wedge

Linear three-dimensional instability is studied in the shock layer and the laminar separation bubble (LSB) induced by shock-wave/boundary-layer interactions in a Mach 7 flow of nitrogen over a double wedge with a$30^{\circ }\text {--}55^{\circ }$cross-sectional profile. At a free-stream unit Reynolds number$Re=5.2\times 10^{4}\,{\rm m}^{-1}$this flow exhibits rarefaction effects and has shock thicknesses comparable to the thickness of the boundary layer at separation. Flow features have been fully resolved using a high-fidelity massively parallel implementation of the direct simulation Monte Carlo method that captures the flow evolution from the inception of three-dimensionality, through linear growth of instabilities, to the early stages of nonlinear saturation. It is shown that the LSB sustains self-excited, small-amplitude perturbations that originate past the primary separation line and lead to spanwise-periodic wall striations inside the bubble and downstream of the primary reattachment line, as known from earlier experiments, simulations and instability analyses. A spanwise-periodic instability, synchronised with that in the separation zone, is identified herein for the first time, which exists in the internal structure of the separation and detached shock layers, and manifests itself as spanwise-periodic cats-eyes patterns in the global mode amplitude functions. The growth rate and the spanwise-periodicity length of linear disturbances in the shock layers and the LSB are found to be identical. Linear amplification of the most unstable three-dimensional flow perturbations leads to synchronised low-frequency unsteadiness of the triple point, with a Strouhal number of$St\approx 0.028$.

Fully Suspended Nano-beams for Quantum Fluids

Non-invasive probes are keystones of fundamental research. Their size, and maneuverability (in terms of e.g. speed, dissipated power) define their applicability range for a specific use. As such, solid state physics possesses e.g. Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), or Scanning SQUID Microscopy. In comparison, quantum fluids (superfluid $^3$He, $^4$He) are still lacking probes able to sense them (in a fully controllable manner) down to their smallest relevant lengthscales, namely the coherence length $\xi_0$. In this work we report on the fabrication and cryogenic characterization of fully suspended (hanging over an open window, with no substrate underneath) Si$_3$N$_4$ nano-beams, of width down to 50 nm and quality factor up to $10^5$. As a benchmark experiment we used them to investigate the Knudsen boundary layer of a rarefied gas: $^4$He at very low pressures. The absence of the rarefaction effect due to the nearby chip surface discussed in Gazizulin et al. [1] is attested, while we report on the effect of the probe size itself.

Kinetic modeling of fractal aggregate mobility

Although the mobility or transport parameters, such as lift drag and pitching moments for regular-shaped particulates, are widely studied, the mobility of irregular fractal-like aggregates generated by the aggregation of monomers is not well understood. These particulates which are ubiquitous in nature, and industries have very different transport mechanisms as compared to their spherical counterpart. A high-fidelity direct simulation Monte Carlo (DSMC) study of two fractal aggregates of different shapes or dimensions is undertaken in the slip and transitional gas regime to understand the underlying mechanism of gas-particle momentum transfer that manifests as the orientation-averaged mobility parameters of the particulates. The study specifically focuses on the viscous contribution of these parameters and develops a non-linear correlation for drag and lift parameters p and q obtained from DSMC by normalizing the axial and lateral forces. The drag parameter p predicted a monotonic increase in fractal particulate drag with respect to a spherical monomer while the lift parameter q shows an initial increasing trend but a decreasing tendency toward the high Mach number or high compressibility regime. The approximate model that captures the compressibility and rarefaction effects of the fractal mobility is used to study the evolution of these particulates in a canonical Rankine vortex to illustrate the wide disparity in the trajectories of the fractal aggregate vs a spherical geometry approximation generally found in the literature.

Characterization of gas transport in shale: A multi-mechanism permeability modeling approach

Accurate characterization of gas transport in shale is crucial for many industrial processes and scientific issues, such as CO2 sequestration in depleted shale and shale gas production. Gas transport in shale involves complex chemical, hydraulic, and mechanical effects and is generally characterized by permeability. Laboratory observations show some “abnormal” permeability evolution behavior which cannot be explained by classical shale permeability models. In this research, we develop a generic shale permeability model that couples multiple gas transport mechanisms and explains complex permeability evolution. Shale is idealized as an improved sugar-cube structure with inorganic flow channels and composite flow channels penetrating organic and inorganic zones. In organic zones, gas rarefaction effects, multilayer adsorption, multilayer-adsorption-induced swelling, stress sensitivity, and surface diffusion are considered. For inorganic zones, gas rarefaction effects and stress sensitivity control gas transport. Based on this conceptual geometry, the variation of flow channel size, effective stress, porosity, tortuosity, and permeability is coupled. The permeability model can be degraded into different forms that are suitable for constant confining pressure, constant effective stress, and constant average pore pressure conditions. The model is verified against experimental data involving different permeability evolution trends. The comparison among this model and several classical models further demonstrates its advantage and uniqueness. Simulation results show that shale permeability is determined by the competitive effects of gas rarefaction phenomenon, sorption-induced organic matter swelling, and effective stress variation. Before and after pore pressure reaches a switch pressure value, the dominant mechanisms for permeability evolution are different. We use the switch pressure to drawn two controlling factor diagrams that demonstrate the dominant mechanisms in different realms of permeability evolution during gas injection or depletion.

Thermal and hydrodynamic behavior of forced convection gaseous slip flow in a Kelvin cell metal foam

Porous metallic foams are a key material in numerous thermal and hydraulic applications. Gas flows in such micro/nanoporous systems deviate from classical continuum descriptions due to nonequilibrium in gas dynamics, and the resulted heat and mass transport show variation by rarefaction. This study performed a wide range of pore-level analysis of convective gas flows in a Kelvin cell model at different porosities and working conditions. Rarefaction effects onto permeability and heat transfer coefficients were calculated through Darcy to Forchheimer flow regimes. Permeability increased up to 60% by increasing rarefaction while this enhancement decreased by increasing porosity. At the same time, rarefaction lessened inertial effects such that Forchheimer coefficients decreased substantially. At high flow velocities, the increase in rarefaction considerably decreased the effect of drag forces. Hence, hydrodynamic enhancement due to rarefaction was found to increase by increasing Reynolds number. On the other hand, positive influence of boundary slip and negative influence of temperature jump developing between gas and solid almost canceled each other for the studied low heat flux region of highly conductive metal foam structures. Hence, Nusselt numbers were found mostly related to Reynolds number independent from rarefaction. We described Nusselt value based on power law model as a function of Reynolds and porosity. Results and the proposed model are important to accurately predict the thermal and hydrodynamic performance of metal foams in the 80 PPI range.

Perfusion of Brain Preautonomic Areas in Hypertension: Compensatory Absence of Capillary Rarefaction and Protective Effects of Exercise Training.

Remodeling of capillary rarefaction and deleterious arteries are characteristic hallmarks of hypertension that are partially corrected by exercise training. In addition, experimental evidence showed capillary rarefaction within the brain cortex and reduced cerebral blood flow. There is no information on hypertension- and exercise-induced effects on capillary profile and function within preautonomic nuclei. We sought now to evaluate the effects of hypertension and exercise training (T) on the capillary network within hypothalamic paraventricular (PVN) and solitary tract (NTS) nuclei, and on the remodeling of brain arteries. Age-matched spontaneously hypertensive rats (SHR) and Wistar-Kyoto (WKY), submitted to moderate T or kept sedentary (S) for three months, were chronically cannulated for hemodynamic recordings at rest. Rats were anesthetized for i.v. administration of fluorescein isothiocyanate (FITC)-dextran (capillary volume/density measurements) or 4% paraformaldehyde perfusion (basilar, middle, and posterior arteries' morphometry) followed by brain harvesting and processing. Other groups of conscious rats had carotid blood flow (CBF, ultrasound flowmeter) acquired simultaneously with hemodynamic recordings at rest and exercise. SHR-S exhibited elevated pressure and heart rate, reduced CBF, increased wall/lumen ratio of arteries, but no capillary rarefaction within the PVN and NTS. T improved performance gain and caused resting bradycardia in both groups; reduction of pressure and sympathetic vasomotor activity and normalization of the wall/lumen ratio were only observed in SHR-T. T groups responded with marked PVN and NTS capillary angiogenesis and augmented CBF during exercise; to avoid overperfusion at rest, reduced basal CBF was observed only in WKY-T. Data indicated that the absence of SHR-S capillary rarefaction and the intense SHR-T angiogenesis within autonomic areas associated with correction of deleterious arteries' remodeling are essential adjustments to hypertension and exercise training, respectively. These adaptive responses maintain adequate baseline perfusion in SHR-S and SHR-T preautonomic nuclei, augmenting it in exercised rats when a well-coordinated autonomic control is required.

Simulation applicability verification of various slip models in micro-nozzle

The micro-nozzle allows small spacecraft to realize the orbital maneuvering and precise station-keeping. Due to the rarefaction effect of the gas flow in micro-nozzles, the velocity-slip and temperature-jump exists near inner wall, and thus, affecting the operating characteristics of micro-nozzles. Various gas-solid theories and models have been developed to describe the velocity slip and temperature jump in computational fluid dynamics (CFD). In this study, numerical simulations of a micro-nozzle with five classical slip boundary models, which are based on the Maxwell scattering and Langmuir adsorption, are conducted to analyze the applicability of these models through comparing with the results obtained by direct simulated Monte Carlo (DSMC) method. The results show that the inlet pressure dramatically influences the flow regime of the micro-nozzle. The lower the inlet pressure, the higher the influence of the rarefaction effect. The results also indicate that the Langmuir slip model can accurately simulate the flow field in the transition regime. However, the modified Maxwell and Langmuir models proposed by Agrawal et al. (2008) and Le et al. (2012), respectively, are valid in the slip regime.

Heat transfer and friction factor correlations for slip gaseous fluid flow in confined porous medium with pore-scale LBM modelling

The gaseous fluid flow and heat transfer with the consideration of rarefaction effects are important at micro/nano-scales. The formulation of accurate predictive models is beneficial to optimize the heat transfer and friction across the porous domain, in micro- and nano-devices. In this work, the lattice Boltzmann method (LBM) with multiple-relaxation-time (MRT), which offers a natural and robust way to simulate the slip gaseous fluid flow and heat transfer, was applied to the confined porous medium at a pore-scale level. An efficient boundary scheme was utilized at the walls of porous media to consider the velocity slip and temperature jump effect. A two-dimensional porous domain composed of different types of micro obstacles (circle, ellipse and diamond) was established for the pore-scale simulations. Nusselt number (Nu) and friction factor (Cf) were obtained and analyzed across the obstacles with varying Knudsen number (0.0 ≤ Kn ≤ 0.1), Reynolds number (1 ≤ Re ≤ 10) and porosity (0.4 ≤ ε ≤ 0.8). With increasing Re number, Nu number shows an increasing trend for all obstacles, however, for increasing Kn number, Nu number decreases accordingly. Whereas, the friction factor Cf shows a decreasing trend for both increasing Kn and Re numbers. Based on the obtained results, the new predictive correlations for Nusselt number and friction factor were proposed, which will be valuable to understand the slip gaseous flow characteristic in confined porous space.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Pore‐scale study of reactive transfer process involving coke deposition via lattice Boltzmann method

AbstractCoke deposition during catalytic industrial processes can lead to the narrowing and blockage of pore structures inside particles so as to influence the catalyst performance. In this work, a direct pore‐scale simulation is carried out by the lattice Boltzmann method to investigate the change of pore structures caused by coke formation. Coke deposition processes in the single pore and complex porous medium are evaluated. The interaction of pore structure and mass transfer under the condition of coke deposition is analyzed. The results reveal that the pore narrowing and blockage can hinder the viscous flow and Knudsen diffusion, resulting in the change of mass transfer mechanism, which is sensitive to gas rarefaction effect and coke deposition rate as well as surface roughness. For the complex porous medium, the uniformity of pore size distribution becomes weak under the gas rarefaction effect and coke deposition.

Propagation of two-dimensional vibroacoustic disturbances in a rarefied gas

The effect of gas rarefaction on the propagation of two-dimensional vibroacoustic disturbances generated by a nonuniformly oscillating plane is studied. Closed-form descriptions are obtained in the free-molecular (left panel of the figure) and continuum (right panel) limits and complemented by direct simulation Monte Carlo results. The impacts of gas rarefaction on signal decay rate and directivity pattern are highlighted and rationalized.