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"fluid flow"
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Discrete particle simulation of particle–fluid flow: model formulations and their applicability
The approach of combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been increasingly used to study the fundamentals of coupled particle–fluid flows. Different CFD–DEM models have been used. However, the origin and the applicability of these models are not clearly understood. In this paper, the origin of different model formulations is discussed first. It shows that, in connection with the continuum approach, three sets of formulations exist in the CFD–DEM approach: an original format set I, and subsequent derivations of set II and set III, respectively, corresponding to the so-called model A and model B in the literature. A comparison and the applicability of the three models are assessed theoretically and then verified from the study of three representative particle–fluid flow systems: fluidization, pneumatic conveying and hydrocyclones. It is demonstrated that sets I and II are essentially the same, with small differences resulting from different mathematical or numerical treatments of a few terms in the original equation. Set III is however a simplified version of set I. The testing cases show that all the three models are applicable to gas fluidization and, to a large extent, pneumatic conveying. However, the application of set III is conditional, as demonstrated in the case of hydrocyclones. Strictly speaking, set III is only valid when fluid flow is steady and uniform. Set II and, in particular, set I, which is somehow forgotten in the literature, are recommended for the future CFD–DEM modelling of complex particle–fluid flow.
Journal Article
Interface-resolved simulations of small inertial particles in turbulent channel flow
We present a direct comparison between interface-resolved and one-way-coupled point-particle direct numerical simulations (DNS) of gravity-free turbulent channel flow laden with small inertial particles, with high particle-to-fluid density ratio and diameter of approximately three viscous units. The most dilute flow considered, solid volume fraction$O(10^{-5})$, shows the particle feedback on the flow to be negligible, whereas differences with respect to the unladen case, notably a drag increase of approximately 10 %, are found for a volume fraction$O(10^{-4})$. This is attributed to a dense layer of particles at the wall, caused by turbophoresis, flowing with large particle-to-fluid apparent slip velocity. The most dilute case is therefore taken as the benchmark for assessing the validity of a widely used point-particle model, where the particle dynamics results only from inertial and nonlinear drag forces. In the bulk of the channel, the first- and second-order moments of the particle velocity from the point-particle DNS agree well with those from the interface-resolved DNS. Close to the wall, however, most of the statistics show major qualitative differences. We show that this difference originates from the strong shear-induced lift force acting on the particles in the near-wall region. This mechanism is well captured by the lift force model due to Saffman ( J. Fluid Mech. , vol. 22 (2), 1965, pp. 385–400), while other widely used, more elaborate, approaches aiming at extending the lift model for a wider range of particle Reynolds numbers can actually underpredict the magnitude of the near-wall particle velocity fluctuations for the cases analysed here.
Journal Article
Short‐Lived and Voluminous Fluid‐Flow in a Single Fracture Related to Seismic Events in the Middle Crust
This study focuses on samples that underwent rapid hydration (∼10 hr) and evolved in permeability (∼10−9 to 10−8 m2) as a result of crustal fracturing. A coupled reactive transport model and thermodynamic analyses, focusing on Si alteration processes within reaction zones, are used to estimate the fluid volume required to induce fluid‐driven seismic activity. Estimated fluid volumes (101–104 m3) are used to approximate the moment magnitudes of potential seismic events. The resulting moment magnitudes (−0.6 to 3.8) and short timescales of fluid infiltration (∼10 hr) are comparable to some slow‐slip events, such as tremors and low‐frequency earthquakes. This indicates that the voluminous fluid flow in a single fracture could be a key control on the generation of crustal fracturing and the induction of seismic activity above the tremor and slow slip events source regions in the lower–middle crust. Plain Language Summary Short‐lived fluid flow in the crust modifies the hydrological properties of rocks and controls the earthquakes triggering. However, there are limited numerical constraints on the fluid volumes that can be rapidly transported. This study focuses on fluid flow through a single fracture in metamorphic rocks. We discuss the relationship between estimated fluid volumes and a series of low‐magnitude fracturing events, such as tremors and other types of slow slip events in the lower‐middle crust. Specifically, we analyze unique geological and geochemical evidence preserved in fluid‐rock reaction zones to approximate the duration of fluid infiltration and the volume of fluids transported. We use two independent methods for constraining generated seismic moment and magnitude based on fluid volumes and single fracture geometry. The transportation of fluid volumes through a fracture (101–104 m3) may be related to short seismic events, as suggested by duration (∼10 hr) and cumulative magnitude, representing the maximum values as 2.0–3.8. We observed a dramatic change in hydrological properties: from low permeable rocks to high‐permeable fractures, which are not dead‐end and can effectively transport a large volume of fluids in a short time. Such fluid infiltration can possibly trigger seismic activity above the earthquake source regions. Key Points Fluid volumes estimated via reactive‐transport modeling and thermodynamic analyses are used to approximate the moment magnitudes Moment magnitudes (−0.6 to 3.8) and short timescales of fluid infiltration (∼10 hr) are comparable to slow‐slip events Voluminous fluid flow in a single fracture may be related to the generation of crustal fracturing and the induction of short seismic events
Journal Article
Numerical simulations of a sphere settling in simple shear flows of yield stress fluids
We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito ( J. Non-Newtonian Fluid Mech. , vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.
Journal Article
The reciprocal theorem in fluid dynamics and transport phenomena
In the study of fluid dynamics and transport phenomena, key quantities of interest are often the force and torque on objects and total rate of heat/mass transfer from them. Conventionally, these integrated quantities are determined by first solving the governing equations for the detailed distribution of the field variables (i.e. velocity, pressure, temperature, concentration, etc.) and then integrating the variables or their derivatives on the surface of the objects. On the other hand, the divergence form of the conservation equations opens the door for establishing integral identities that can be used for directly calculating the integrated quantities without requiring the detailed knowledge of the distribution of the primary variables. This shortcut approach constitutes the idea of the reciprocal theorem, whose closest relative is Green’s second identity, which readers may recall from studies of partial differential equations. Despite its importance and practicality, the theorem may not be so familiar to many in the research community. Ironically, some believe that the extreme simplicity and generality of the theorem are responsible for suppressing its application! In this Perspectives piece, we provide a pedagogical introduction to the concept and application of the reciprocal theorem, with the hope of facilitating its use. Specifically, a brief history on the development of the theorem is given as a background, followed by the discussion of the main ideas in the context of elementary boundary-value problems. After that, we demonstrate how the reciprocal theorem can be utilized to solve fundamental problems in low-Reynolds-number hydrodynamics, aerodynamics, acoustics and heat/mass transfer, including convection. Throughout the article, we strive to make the materials accessible to early career researchers while keeping it interesting for more experienced scientists and engineers.
Journal Article
A review on non-Newtonian fluid models for multi-layered blood rheology in constricted arteries
Haemodynamics is a branch of fluid mechanics which investigates the features of blood when it flows not only via blood vessels of smaller/larger diameter, but also under normal as well as abnormal flow states, such as in the presence of stenosis, aneurysm, and thrombosis. This review aims to discuss the rheological properties of blood, geometry of constrictions, dilations and the emergence of single-layered fluid to four-layered fluid models. To discuss further the influence of the aforesaid parameters on the physiologically important flow quantities, the mathematical formulation and solution methodology of the two-layered and four layered arterial blood flow problems studied by the authors (Afiqah and Sankar in ARPN J Eng Appl Sci 15:1129--1143, 2020, Comput Methods Programs Biomed 199:105907, 2021. 10.1016/j.cmpb.2020.105907) are recalled. It should be pointed out that the increasing resistive impedance to flow in three distinct states encompassing healthy, anaemic, and diabetic demonstrates that the greater the restriction in the artery, very few blood is carried to the pathetic organs, leading to subjects' death. It is also discovered that the pulsatile nature of blood movement produces a dynamic environment that poses a slew of intriguing and unstable fluid mechanical state. It is hoped that the intriguing results gathered from this literature survey and review conducted may help the medical practitioners to forecast blood behaviour mobility in stenotic arteries. Furthermore, the physiological information gathered from the available clinical data from the literature on patients diagnosed with diabetes and anaemia may be beneficial to doctors in deciding the therapeutic procedure for treating some particular cardiovascular disease.
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