Numerical Effects on the Prediction of Flow Instabilities in Channels With Sudden-Expansions

Author(s):  
S. Patel ◽  
D. Drikakis

We have considered the problem of flow through a suddenly-expanded channel and performed a computational investigation to examine numerical effects on the prediction of flow instability and bifurcation phenomena. The results revealed that the solution of the flow depends on the numerical method employed. We have employed Godunov-type methods in conjunction with first-, second- and third-order accurate interpolation schemes. It is shown that the order of accuracy of the interpolation used in the discretisation of the wave-speed dependent term and averaged part of the intercell flux affects the prediction of the instability. Computations using first-order discretisation for the calculation of the flux components results in symmetric stable flow, whereas second- and third-order discretisations lead to a symmetry-breaking bifurcation.

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.


Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.


Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3053
Author(s):  
Ming Cheng ◽  
Yuhong Lei ◽  
Xiaorong Luo ◽  
Likuan Zhang ◽  
Xiangzeng Wang ◽  
...  

Organic-rich lacustrine shales in the Upper Triassic Yanchang Formation with thermal maturity mainly in the oil window are the main shale oil and shale gas system in the lacustrine strata of the Ordos Basin, China. Pore systems are important for the storage and transfer of shale oil and gas. The main objectives of this study are to identify the pore types and pore structures and investigate the controlling factors for pore types, pore structures, and total porosities of the lacustrine Yanchang Shale. In this study, organic-rich mudstones, mudstones with siltstone interlayers, siltstone, and sandstones were selected from 15 wells in the southern Ordos Basin. X-ray diffraction, pyrolysis, scanning electron microscopy (SEM), low-pressure nitrogen adsorption analysis, and helium porosimetry were conducted to investigate the mineral compositions, pore types, pore structures, porosities, and controlling factors. Siltstone and sandstone interlayers heterogeneously developed in the Yanchang Shale. The petrology, mineral composition, geochemistry, pore type, pore structure, and porosity of siltstone interlayers are different from those of mudstones. The siltstone and sandstone interlayers usually have more quartz and feldspars, greater detrital grain sizes, and relatively better grain sorting but are lower in clay minerals, total organic carbon (TOC), amount of free liquid hydrocarbons values (S1), and total residual hydrocarbons values (S2), compared to mudstones. Interparticle (interP), intraparticle (intraP) pores, and organic pores (OPs) were developed in both siltstones and mudstones. OPs were observed in samples with lower thermal maturity (e.g., 0.5–0.85%). The inorganic pore size is greater than that of OPs. Additionally, the inorganic pore diameters in siltstone interlayers are also greater than those in mudstones. Organic-rich mudstones generally have higher pore volumes (PVs) of pores with sizes less than 10 nm, pore volumes of pores with sizes between 10 and 50 nm (PV, 10–50 nm), and specific surface area (SSA), but they have lower PVs of pores with sizes greater than 50 nm, total PV, and porosity when compared to siltstone and sandstone interlayers. The dominant pore type in mudstones is OPs and TOC (first order), sources and OM types (second order), and thermal maturity (third order), while the abundances of rigid grains with greater sizes and grain sorting are the main controlling factors of pore structures, SSA and PV. Both inorganic pores and organic pores are abundant in the siltstone interlayers. The pore size distribution (PSD), PV, and porosity of siltstone interlayers are related to the abundance of rigid grains (first order), grain sorting (second order), grain size (third order), and carbonate cement content. The total PV and porosity of Yanchang Shale reservoirs may have increased with the increased abundance of siltstone and sandstone interlayers.


2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.


Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1252
Author(s):  
Hadar Elyashiv ◽  
Revital Bookman ◽  
Lennart Siemann ◽  
Uri ten Brink ◽  
Katrin Huhn

The Discrete Element Method has been widely used to simulate geo-materials due to time and scale limitations met in the field and laboratories. While cohesionless geo-materials were the focus of many previous studies, the deformation of cohesive geo-materials in 3D remained poorly characterized. Here, we aimed to generate a range of numerical ‘sediments’, assess their mechanical response to stress and compare their response with laboratory tests, focusing on differences between the micro- and macro-material properties. We simulated two endmembers—clay (cohesive) and sand (cohesionless). The materials were tested in a 3D triaxial numerical setup, under different simulated burial stresses and consolidation states. Variations in particle contact or individual bond strengths generate first order influence on the stress–strain response, i.e., a different deformation style of the numerical sand or clay. Increased burial depth generates a second order influence, elevating peak shear strength. Loose and dense consolidation states generate a third order influence of the endmember level. The results replicate a range of sediment compositions, empirical behaviors and conditions. We propose a procedure to characterize sediments numerically. The numerical ‘sediments’ can be applied to simulate processes in sediments exhibiting variations in strength due to post-seismic consolidation, bioturbation or variations in sedimentation rates.


2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.


1993 ◽  
Vol 71 (4) ◽  
pp. 523-532 ◽  
Author(s):  
Joanna Fraser ◽  
Eric G. Kokko

The initial stages of panicle, spikelet, and floret development in field-grown 'Kay' orchardgrass were examined using scanning electron microscopy. Spikelets arose from a complex multilevelled sequence of initiation from branch apices. Spikelets developed indirectly in a two-tiered progression: (i) an acropetal and basipetal sequence of first order, second-order, and third-order inflorescence apices, and (ii) an acropetal development within subclusters of higher-order lateral branch inflorescence apices. The panicle had the unique feature of dorsiventrality as well as bilateral symmetry. The basal apex from first-order, second-order, or third-order apices developed on the same side of the main axis as the first-order apex. The two glumes subtending each spikelet primordium developed alternately and acropetally. Development and initiation of florets within spikelets was basipetal within the panicle, basipetal within clusters and subclusters of spikelets on lateral branches, and acropetal within spikelets. Within florets, paleas developed later than lemmas. Key words: Dactylis glomerata, cocksfoot, scanning electron microscopy, development, panicle.


1990 ◽  
Vol 205 ◽  
Author(s):  
E. S. K. Menon ◽  
P. Huang ◽  
M. Kraitchman ◽  
J. J. Hoyt ◽  
P. Chow ◽  
...  

AbstractAlternate layers of pure copper and gold were vapor deposited on a sodium chloride substrate, the average concentration of the films being Cu-16at% Au and the layering periodicity (modulation wavelength) being 3.31 nm. The composition modulation gives rise to satellite diffraction peaks around the (200) Bragg reflections. Synchrotron radiation at SSRL was able to detect up to third order satellite intensity the evolution of which was measured as a function of annealing time at 515 K. Although the first order satellite intensity decayed as expected exponentially with time, intensities of both second and third order satellites decreased very rapidly at first, then increased before decaying exponentially. These results are in conformity with theoretical models of satellite evolution during annealing in a onedimensional modulated system governed by a nonlinear diffusion equation.


In this work, bifurcation characteristics of unsteady, viscous, Newtonian laminar flow in two-dimensional sudden expansion and sudden contraction-expansion channels have been studied for different values of expansion ratio. The governing equations have been solved using finite volume method and FLUENT software has been employed to visualize the simulation results. Three different mesh studies have been performed to calculate critical Reynolds number (Recr) for different types of bifurcation phenomena. It is found that Recr decreases with the increase in expansion ratio (ER).


Author(s):  
Satyajit Ambike ◽  
James P. Schmiedeler ◽  
Michael M. Stanisˇic´

Path tracking can be accomplished by separating the control of the desired trajectory geometry and the control of the path variable. Existing methods accomplish tracking of up to third-order geometric properties of planar paths and up to second-order properties of spatial paths using non-redundant manipulators, but only in special cases. This paper presents a novel methodology that enables the geometric tracking of a desired planar or spatial path to any order with any non-redundant regional manipulator. The governing first-order coordination equation for a spatial path-tracking problem is developed, the repeated differentiation of which generates the coordination equation of the desired order. In contrast to previous work, the equations are developed in a fixed global frame rather than a configuration-dependent canonical frame, providing a significant practical advantage. The equations are shown to be linear, and therefore, computationally efficient. As an example, the results are applied to a spatial 3-revolute mechanism that tracks a spatial path. Spatial, rigid-body guidance is achieved by applying the technique to three points on the end-effector of a six degree-of-freedom robot. A spatial 6-revolute robot is used as an illustration.


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