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21 pages, 3755 KB

Open AccessArticle

Effect of Pore-Scale Anisotropic and Heterogeneous Structure on Rarefied Gas Flow in Three-Dimensional Porous Media

by Wenqiang Guo, Jinshan Zhao, Gang Wang, Ming Fang and Ke Zhu

Fluids 2025, 10(7), 175; https://doi.org/10.3390/fluids10070175 - 3 Jul 2025

Viewed by 594

Porous media have great application prospects, such as transpiration cooling for the aerospace industry. The main challenge for the prediction of gas permeability includes the geometrical complexity and high Knudsen number of gas flow at the nano-scale to micro-scale, leading to failure of the conventional Darcy’s law. To address these issues, the Quartet Structure Generation Set (QSGS) method is improved to construct anisotropic and heterogeneous three-dimensional porous media, and the lattice Boltzmann method (LBM) with the multiple relaxation time (MRT) collision operator is adopted. Using MRT-LBM, the pressure boundary conditions at the inlet and outlet are firstly dealt with using the moment-based boundary conditions, demonstrating good agreement with the analytical solutions in two benchmark tests of three-dimensional Poiseuille flow and flow through a body-centered cubic array of spheres. Combined with the Bosanquet-type effective viscosity model and Maxwellian diffuse reflection boundary condition, the gas flow at high Knudsen (Kn) numbers in three-dimensional porous media is simulated to study the relationship between pore-scale anisotropy, heterogeneity and Kn, and permeability and micro-scale slip effects in porous media. The slip factor is positively correlated with the anisotropic factor, which means that the high Kn effect is stronger in anisotropic structures. There is no obvious correlation between the slip factor and heterogeneity factor. Full article

(This article belongs to the Section Flow of Multi-Phase Fluids and Granular Materials)

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18 pages, 2280 KB

Open AccessArticle

Poiseuille-Type Approximations for Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall

by Kristina Kaulakytė, Nikolajus Kozulinas, Grigory Panasenko, Konstantinas Pileckas and Vytenis Šumskas

Mathematics 2023, 11(9), 2106; https://doi.org/10.3390/math11092106 - 28 Apr 2023

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Abstract

An asymptotic ansatz for the solution of the axisymmetric problem of interaction between a thin cylindrical elastic tube and a viscous fluid filling the thin interior of the elastic tube was recently introduced and justified by G. Panasenko and R. Stavre. The thickness [...] Read more.

ε

) and that of the fluid domain (

ε_{1}

) are small parameters with

ε < < ε_{1} < < 1

, while the scale of the longitudinal characteristic size is of order one. At the same time, the magnitude of the stiffness and density of the elastic tube may be large or finite parameters with respect to the viscosity and density of the fluid when the characteristic time is of order one. This ansatz can be considered as a Poiseuille-type solution for the fluid–structure interaction problem. Its substitution to the Stokes fluid–elastic wall coupled problem generates a one-dimensional model. We present a numerical experiment comparing this model with the solution of the full-dimensional fluid–structure interaction problem. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

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16 pages, 4566 KB

Open AccessArticle

A Parametric Analysis of Capillary Height in Single-Layer, Small-Scale Microfluidic Artificial Lungs

by Lindsay J. Ma, Emmanuel A. Akor, Alex J. Thompson and Joseph A. Potkay

Micromachines 2022, 13(6), 822; https://doi.org/10.3390/mi13060822 - 25 May 2022

Cited by 4 | Viewed by 3092

Abstract

Microfluidic artificial lungs (μALs) are being investigated for their ability to closely mimic the size scale and cellular environment of natural lungs. Researchers have developed μALs with small artificial capillary diameters (10–50 µm; to increase gas exchange efficiency) and with large capillary diameters (~100 µm; to simplify design and construction). However, no study has directly investigated the impact of capillary height on μAL properties. Here, we use Murray’s law and the Hagen-Poiseuille equation to design single-layer, small-scale μALs with capillary heights between 10 and 100 µm. Each µAL contained two blood channel types: capillaries for gas exchange; and distribution channels for delivering blood to/from capillaries. Three designs with capillary heights of 30, 60, and 100 µm were chosen for further modeling, implementation and testing with blood. Flow simulations were used to validate and ensure equal pressures. Designs were fabricated using soft lithography. Gas exchange and pressure drop were tested using whole bovine blood. All three designs exhibited similar pressure drops and gas exchange; however, the μAL with 60 µm tall capillaries had a significantly higher wall shear rate (although physiologic), smaller priming volume and smaller total blood contacting surface area than the 30 and 100 µm designs. Future μAL designs may need to consider the impact of capillary height when optimizing performance. Full article

(This article belongs to the Special Issue Women’s Special Issue Series: Micromachines)

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20 pages, 4270 KB

Open AccessArticle

Migration and Alignment of Three Interacting Particles in Poiseuille Flow of Giesekus Fluids

by Bing-Rui Liu, Jian-Zhong Lin and Xiao-Ke Ku

Fluids 2021, 6(6), 218; https://doi.org/10.3390/fluids6060218 - 11 Jun 2021

Cited by 2 | Viewed by 2801

Abstract

Effect of rheological property on the migration and alignment of three interacting particles in Poiseuille flow of Giesekus fluids is studied with the direct-forcing fictitious domain method for the Weissenberg number (Wi) ranging from 0.1 to 1.5, the mobility parameter ranging from 0.1 to 0.7, the ratio of particle diameter to channel height ranging from 0.2 to 0.4, the ratio of the solvent viscosity to the total viscosity being 0.3 and the initial distance (y₀) of particles from the centerline ranging from 0 to 0.2. The results showed that the effect of y₀ on the migration and alignment of particles is significant. The variation of off-centerline (y₀ ≠ 0) particle spacing is completely different from that of on-centerline (y₀ = 0) particle spacing. As the initial vertical distance y₀ increased, the various types of particle spacing are more diversified. For the off-centerline particle, the change of particle spacing is mainly concentrated in the process of cross-flow migration. Additionally, the polymer extension is proportional to both the Weissenberg number and confinement ratio. The bigger the Wi and confinement ratio is, the bigger the increment of spacing is. The memory of shear-thinning is responsible for the reduction of d₁. Furthermore, the particles migrate abnormally due to the interparticle interaction. Full article

(This article belongs to the Special Issue Transport in Viscoelastic Fluids)

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23 pages, 5338 KB

Open AccessArticle

Analysis of the Moment Method and the Discrete Velocity Method in Modeling Non-Equilibrium Rarefied Gas Flows: A Comparative Study

by Weiqi Yang, Shuo Tang and Hui Yang

Appl. Sci. 2019, 9(13), 2733; https://doi.org/10.3390/app9132733 - 5 Jul 2019

Cited by 5 | Viewed by 3326

Abstract

In the present study, the performance of the moment method, in terms of accuracy and computational efficiency, was evaluated at both the macro- and microscopic levels. Three different types of non-equilibrium gas flows, including the force-driven Poiseuille flow, lid-driven and thermally induced cavity flows, were simulated in the slip and transition regimes. Choosing the flow fields obtained from the Boltzmann model equation as the benchmark, the accuracy and validation of Navier–Stokes–Fourier (NSF), regularized 13 (R13) and regularized 26 (R26) equations were explored at the macroscopic level. Meanwhile, we reconstructed the velocity distribution functions (VDFs) using the Hermite polynomials with different-order of molecular velocity moments, and compared them with the Boltzmann solutions at the microscopic level. Moreover, we developed a kinetic criterion to indirectly assess the errors of the reconstructed VDFs. The results have shown that the R13 and R26 moment methods can be faithfully used for non-equilibrium rarefied gas flows in the slip and transition regimes. However, as indicated from the thermally induced case, all of the reconstructed VDFs are still very close to the equilibrium state, and none of them can reproduce the accurate VDF profile when the Knudsen number is above 0.5. Full article

(This article belongs to the Special Issue Heat and Mass Transfer: Fundamentals and Applications in Thermal Energy)

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15 pages, 1860 KB

Open AccessArticle

Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow

by Sukhendu Ghosh

Fluids 2017, 2(4), 66; https://doi.org/10.3390/fluids2040066 - 1 Dec 2017

Cited by 5 | Viewed by 5033

Abstract

The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr–Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow. Full article

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11 pages, 329 KB

Open AccessArticle

A New Approach to Laminar Flowmeters

by Fernando Lopez Pena, Alvaro Deibe Diaz, Marcos Rodriguez Lema and Santiago Vazquez Rodriguez

Sensors 2010, 10(12), 10560-10570; https://doi.org/10.3390/s101210560 - 29 Nov 2010

Cited by 15 | Viewed by 8970

Abstract

After studying the performance and characteristics of actual laminar flowmeters a new disposition for this type of sensors is proposed in such a way that the measurement errors introduced by the intrinsic nature of the device can be minimized. The preliminary study shows that the developing entry region introduces non-linearity effects in all these devices. These effects bring about not only errors, but also a change in the slope of the linear calibration respect of the Poiseuille relation. After a subsequent analysis on how these non-linearity errors can be reduced, a new disposition of this type of flowmeters is introduced. This device makes used of flow elements having pressure taps at three locations along its length and connected to three isolated chambers. In this way, the static pressure can be measured at three locations and contributed to by the pressure taps at the level of each chamber. Thus the linearization error is reduced with an additional advantage of producing a reduced pressure drop. Full article

(This article belongs to the Section Physical Sensors)

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