Discrete simulation of granular and particle-fluid flows: from fundamental study to engineering application

2017 ◽  
Vol 33 (6) ◽  
Author(s):  
Wei Ge ◽  
Limin Wang ◽  
Ji Xu ◽  
Feiguo Chen ◽  
Guangzheng Zhou ◽  
...  
Keyword(s):  
Multiscale Modeling ◽  
Chemical Engineering ◽  
Fluid Flows ◽  
Process Engineering ◽  
Continuum Approach ◽  
Engineering Applications ◽  
Discrete Simulation ◽  
Discrete Approach ◽  
Multiscale Structures ◽  
The Continuum

AbstractMultiphase chemical reactors with characteristic multiscale structures are intrinsically discrete at the elemental scale. However, due to the lack of multiscale models and the limitation of computational capability, such reactors are traditionally treated as continua through straightforward averaging in engineering simulations or as completely discrete systems in theoretical studies. The continuum approach is advantageous in terms of the scale and speed of computation but does not always give good predictions, which is, in many cases, the strength of the discrete approach. On the other hand, however, the discrete approach is too computationally expensive for engineering applications. Developments in computing science and technologies and encouraging progress in multiscale modeling have enabled discrete simulations to be extended to engineering systems and represent a promising approach to virtual process engineering (VPE, or virtual reality in process engineering). In this review, we analyze this emerging trend and emphasize that multiscale discrete simulations (MSDS), that is, considering multiscale structures in discrete simulation through rational coarse-graining and coupling between discrete and continuum methods with the effect of mesoscale structures accounted in both cases, is an effective way forward, which can be complementary to the continuum approach that is being improved by multiscale modeling also. For this purpose, our review is not meant to be a complete summary to the literature on discrete simulation, but rather a demonstration of its feasibility for engineering applications. We therefore discuss the enabling methods and technologies for MSDS, taking granular and particle-fluid flows as typical examples in chemical engineering. We cover the spectrum of modeling, numerical methods, algorithms, software implementation and even hardware-software codesign. The structural consistency among these aspects is shown to be the pivot for the success of MSDS. We conclude that with these developments, MSDS could soon become, among others, a mainstream simulation approach in chemical engineering which enables VPE.

scholarly journals Invasion front dynamics in disordered environments

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Youness Azimzade ◽  
Mahdi Sasar ◽  
Iraj Maleki
Keyword(s):  
Diffusion Constant ◽  
Continuum Approach ◽  
Perturbative Approach ◽  
Invasion Front ◽  
Discrete Approach ◽  
Individual Based Models ◽  
Large Disorder ◽  
Homogeneous Environment ◽  
Front Dynamics ◽  
The Continuum

Abstract Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher’s equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have $$\bar{v}=v_0 (1-|\xi |^2/6)$$ v ¯ = v 0 ( 1 - | ξ | 2 / 6 ) where $$|\xi |$$ | ξ | is the amplitude of disorder and $$v_0$$ v 0 is the invasion velocity in the corresponding homogeneous environment given by $$v_0=2\sqrt{RD_0}$$ v 0 = 2 R D 0 . Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: $$D_{C}= \dfrac{1}{8} \xi ^2\sqrt{RD_0 (1-|\xi |^2/3)}$$ D C = 1 8 ξ 2 R D 0 ( 1 - | ξ | 2 / 3 ) . These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.

Discrete particle simulation of particle–fluid flow: model formulations and their applicability

2010 ◽  
Vol 661 ◽  
pp. 482-510 ◽  
Author(s):  
Z. Y. ZHOU ◽  
S. B. KUANG ◽  
K. W. CHU ◽  
A. B. YU
Keyword(s):  
Fluid Flow ◽  
Fluid Flows ◽  
Particle Simulation ◽  
Pneumatic Conveying ◽  
Continuum Approach ◽  
Complex Particle ◽  
Discrete Particle Simulation ◽  
Computational Fluid Dynamics Cfd ◽  
Numerical Treatments ◽  
The Continuum

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.

Steady Hydrodynamics and Thermal Behaviors of Fluid Flows in Micro – Parallel Plates (Couette Flows)

2011 ◽  
Vol 110-116 ◽  
pp. 408-414
Author(s):  
Ahmad Al-Shyyab ◽  
Suleiman E. Al-Lubani ◽  
Muhammad M. Kwafha ◽  
A. F. Khadrawi
Keyword(s):  
Pressure Gradient ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Fluid Flows ◽  
Thermal Boundary Condition ◽  
Parallel Plates ◽  
Brinkman Number ◽  
Continuum Approach ◽  
Thermal Behaviors ◽  
The Continuum

The hydrodynamics and thermal behaviors of fluid in micro - Couette flows is investigated numerically. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number Kn, Brinkman number and the pressure gradient on the Couette microchannel hydrodynamics and thermal behaviors are investigated. It is found that as Kn increases the slip in the hydrodynamic and thermal boundary condition increases. Also, it is found that the slip velocity and the temperature jump at the boundaries increases as the Brinkman number and the pressure gradient increases.

scholarly journals Liouville quantum gravity — holography, JT and matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Thomas G. Mertens ◽  
Gustavo J. Turiaci
Keyword(s):  
String Theory ◽  
Generating Functions ◽  
Preliminary Evidence ◽  
Quantum Deformation ◽  
Dilaton Gravity ◽  
Continuum Approach ◽  
Genus Zero ◽  
Explicit Formulas ◽  
Liouville Gravity ◽  
The Continuum

Abstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

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