scholarly journals Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces

2019 ◽  
Vol 871 ◽  
pp. 1007-1027 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Global Analysis ◽  
Companion Paper ◽  
Density Difference ◽  
Local Analysis ◽  
Instability Criterion ◽  
The Novel ◽  
Two Fluids ◽  
Buoyancy Forces ◽  
Equal Density ◽  
Time Dependent Analysis

The novel viscous fingering instability recently found in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655), involving two superposed currents of viscous fluid, has been shown to originate at the lubrication front when the fluids are of equal density. However, when the densities are unequal, additional buoyancy forces associated with the underlying layer act to suppress this instability and are largest at the lubrication front, which is where the instability originates. In this paper, we investigate the interaction between the mechanism of the instability and the stabilising influence of these buoyancy forces by performing a global and fully time-dependent analysis, which does not use the frozen-time approximation. We determine a critical condition for instability in terms of the viscosity ratio and the density difference between the two layers. Consistently with the local analysis of the companion paper, instabilities occur when the jump in hydrostatic pressure gradient across the lubrication front is negative, or, equivalently, when the intruding fluid is less viscous than the overlying fluid, provided the two fluids are of equal densities. Once there is a non-zero density difference, these driving buoyancy forces suppress the instability for large wavelengths, giving rise to wavelength selection. As the density difference increases, the instability criterion requires higher viscosity ratios for any instability to occur, and the band of unstable wavenumbers becomes bounded. Large enough density differences suppress the instability completely.

scholarly journals An Integrated Geometric and Material Survey for the Conservation of Heritage Masonry Structures

Heritage ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 585-611
Author(s):  
Michele Betti ◽  
Valentina Bonora ◽  
Luciano Galano ◽  
Eugenio Pellis ◽  
Grazia Tucci ◽  
...  
Keyword(s):  
Seismic Behavior ◽  
Laser Scanning ◽  
Global Analysis ◽  
Interdisciplinary Approach ◽  
Local Analysis ◽  
Masonry Building ◽  
In Situ Tests ◽  
Knowledge Process ◽  
Giorgio Vasari ◽  
House Museum

This paper reports the knowledge process and the analyses performed to assess the seismic behavior of a heritage masonry building. The case study is a three-story masonry building that was the house of the Renaissance architect and painter Giorgio Vasari (the Vasari’s House museum). An interdisciplinary approach was adopted, following the Italian “Guidelines for the assessment and mitigation of the seismic risk of the cultural heritage”. This document proposes a methodology of investigation and analysis based on three evaluation levels (EL1, analysis at territorial level; EL2, local analysis and EL3, global analysis), according to an increasing level of knowledge on the building. A comprehensive knowledge process, composed by a 3D survey by Terrestrial Laser Scanning (TLS) and experimental in situ tests, allowed us to identify the basic structural geometry and to assess the value of mechanical parameters subsequently needed to perform a reliable structural assessment. The museum represents a typology of masonry building extremely diffused in the Italian territory, and the assessment of its seismic behavior was performed by investigating its global behavior through the EL1 and the EL3 analyses.

GLOBAL ANALYSIS OF THE AIRCRAFT STRUCTURE AND ITS APPLICATION TO THE PRELIMINARY DESIGN STAGE

Aviation ◽  
2005 ◽  
Vol 9 (3) ◽  
pp. 29-35
Author(s):  
Jerzy Bakunowicz ◽  
Tomasz Kopecki
Keyword(s):  
Numerical Model ◽  
Global Analysis ◽  
Economic Factor ◽  
Computer Application ◽  
Local Analysis ◽  
Design Stage ◽  
Preliminary Design ◽  
Preliminary Design Stage ◽  
Sufficient Strength ◽  
Made In

Modern aircraft safety depends on sufficient strength and rigidity of the structure. This must sustain with lightest possible weight, because any excess mass has not only detrimental effect upon the performance but also is significant economic factor. The most rational way to achieve the proper structure seems to be global analysis commenced in the preliminary design stage already. The analysis outcomes provide base for local analysis of the details led parallel. Any revisions more or less relevant can be made in the numerical model with very expensive prototype changes avoiding. The paper illustrates efficiency of the airframe structure global analysis. As examples the aircrafts still in service but designed without computer application were chosen. The finite elements numerical model of each was created and some critical in-flight load cases were simulated.

scholarly journals Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear

2019 ◽  
Vol 871 ◽  
pp. 970-1006 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Viscous Fluid ◽  
Pressure Gradient ◽  
Dynamic Pressure ◽  
Jump Discontinuity ◽  
Local Analysis ◽  
Instability Criterion ◽  
Shear Stresses ◽  
Horizontal Shear ◽  
Dynamical Regimes ◽  
Inner Region

A novel viscous fingering instability, involving a less viscous fluid intruding underneath a current of more viscous fluid, was recently observed in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655). We examine the origin of the instability by asking whether the instability is an internal instability, arising from internal dynamics, or a frontal instability, arising from viscous intrusion. We find it is the latter and characterise the instability criterion in terms of viscosity difference or, equivalently, the jump in hydrostatic pressure gradient at the intrusion front. The mechanism of this instability is similar to, but contrasts with, the Saffman–Taylor instability, which occurs as a result of a jump in dynamic pressure gradient across the intrusion front. We focus on the limit in which the two viscous fluids are of equal density, in which a frontal singularity, arising at the intrusion, or lubrication, front, becomes a jump discontinuity, and perform a local analysis in an inner region near the lubrication front, which we match asymptotically to the far field. We also investigate the large-wavenumber stabilisation by transverse shear stresses in two dynamical regimes: a regime in which the wavelength of the perturbations is much smaller than the thickness of both layers of fluid, in which case the flow of the perturbations is resisted dominantly by horizontal shear stresses; and an intermediate regime, in which both vertical and horizontal shear stresses are important.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

A note on the mechanism of the instability at the interface between two shearing fluids

1984 ◽  
Vol 144 ◽  
pp. 463-465 ◽  
Author(s):  
E. J. Hinch
Keyword(s):  
Interfacial Tension ◽  
Couette Flow ◽  
Viscous Fluids ◽  
Physical Explanation ◽  
Two Fluids ◽  
Equal Density

In a recent paper Hooper & Boyd (1983) have shown that the unbounded stratified Couette flow of two viscous fluids of equal density and with no interfacial tension is always unstable. They found that the instability arises at the interface between the two fluids and occurs at short wavelengths where viscosity is more important than inertia. The purpose of this note is to provide a simple physical explanation of the mechanics of the instability.

Multi-Scale Overlapping Domain Decomposition to Consider Local Deformations in the Analysis of Thin-Walled Members

2014 ◽  
Vol 553 ◽  
pp. 667-672
Author(s):  
R. Emre Erkmen
Keyword(s):  
Numerical Technique ◽  
Global Analysis ◽  
Local Deformation ◽  
Local Analysis ◽  
Type Model ◽  
Cross Sectional ◽  
Multi Scale ◽  
Shell Type ◽  
Thin Walled ◽  
The Cross

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-column type finite element formulations. Beam-column elements however, are based on the assumption of rigid cross-section, thus they cannot consider the cross-sectional deformations such as local buckling and only allows considerations of the beam axis behaviour such as flexural or lateral-torsional buckling. Shell-type finite elements can be used to model the structure in order to consider these local deformation effects. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member.

scholarly journals Buoyancy-driven flow in a confined aquifer with a vertical gradient of permeability

2018 ◽  
Vol 848 ◽  
pp. 411-429 ◽  
Author(s):  
Edward M. Hinton ◽  
Andrew W. Woods
Keyword(s):  
Rarefaction Wave ◽  
Pore Space ◽  
Lower Boundary ◽  
Leading Edge ◽  
Vertical Gradient ◽  
Vertical Shear ◽  
Classical Solutions ◽  
The Novel ◽  
Two Fluids ◽  
Gradient Of Permeability

We examine the injection of fluid of one viscosity and density into a horizontal permeable aquifer initially saturated with a second fluid of different viscosity and density. The novel feature of the analysis is that we allow the permeability to vary vertically across the aquifer. This leads to recognition that the interface may evolve as either a rarefaction wave that spreads at a rate proportional to $t$, a shock-like front of fixed length or a mixture of shock-like regions and rarefaction-wave-type regions. The classical solutions in which there is no viscosity ratio between the fluids and in which the formation has constant permeability lead to an interface that spreads laterally at a rate proportional to $t^{1/2}$. However, these solutions are unstable to cross-layer variations in the permeability owing to the vertical shear which develops in the flow, causing the structure of the interface to evolve to the rarefaction wave or shock-like structure. In the case that the viscosities of the two fluids are different, it is possible that the solution involves a mixture of shock-like and rarefaction-type structures as a function of the distance above the lower boundary. Using the theory of characteristics, we develop a regime diagram to delineate the different situations. We consider the implications of such heterogeneity for the prediction of front locations during $\text{CO}_{2}$ sequestration. If we neglect the permeability fluctuations, the model always predicts rarefaction-type solutions, while even modest changes in the permeability across a layer can introduce shocks. This difference may be very significant since it leads to the $\text{CO}_{2}$ plume occupying a greater fraction of the pore space between the injector and the leading edge of the $\text{CO}_{2}$ front in a layer of the same mean permeability. This has important implications for estimates of the fraction of the pore space that the $\text{CO}_{2}$ may access.

A Software Model by UML for Highway Monitoring System

2013 ◽  
Vol 336-338 ◽  
pp. 2147-2151
Author(s):  
Yong Liu ◽  
Li Yan Yuan
Keyword(s):  
Monitoring System ◽  
Global Analysis ◽  
System Modeling ◽  
Theory And Practice ◽  
Local Analysis ◽  
Software System ◽  
Monitor System ◽  
System Software ◽  
Whole Process ◽  
Software Model

In order to improve the efficiency of designing monitor system software and modeling with UML, the UML application of software system modeling was researched in theory and practice. The whole process is divided into four steps, which are the global analysis, the local analysis, the global design, and the local design, and the GUI of the system is described at last. A distributed highway monitoring system is analyzed and designed by UML.

scholarly journals Multi-Scale Overlapping Domain Decomposition to Consider Elasto-Plastic Local Buckling Effects in the Analysis of Pipes

2017 ◽  
Vol 17 (01) ◽  
pp. 1750015 ◽  
Author(s):  
R. Emre Erkmen ◽  
Magdi Mohareb ◽  
Ashkan Afnani
Keyword(s):  
Domain Decomposition ◽  
Global Analysis ◽  
Computational Cost ◽  
Industrial Applications ◽  
Local Analysis ◽  
Cross Sectional ◽  
Multi Scale ◽  
Shell Type ◽  
Decomposition Procedure ◽  
Beam Type

Elevated pipelines are commonly encountered in petro-chemical and industrial applications. Within these applications, pipelines normally span hundreds of meters and are thus analyzed using one-dimensional (1D) beam-type finite elements when the global behavior of the pipeline is sought at a reasonably low computational cost. Standard beam-type elements, while computationaly economic, are based on the assumption of rigid cross-section. Thus, they are unable to capture the effects of cross-sectional localized deformations. Such effects can be captured through shell-type finite element models. For long pipelines, shell models become prohibitively expensive. Within this context, the present study formulates an efficient numerical modeling which effectively combines the efficiency of beam-type solutions while retaining the accuracy of shell-type solutions. An appealing feature of the model is that it is able to split the global analysis based on simple beam-type elements from the local analysis based on shell-type elements. This is achieved through domain-decomposition procedure within the framework of the Bridging multi-scale method of analysis. Solutions based on the present model are compared to those based on full shell-type analysis. The comparison demonstrates the accuracy and efficiency of the proposed method.

Finite Element Method for the Study of Belt Edge Delaminations in Truck Tires

2005 ◽  
Vol 78 (4) ◽  
pp. 557-571 ◽  
Author(s):  
Şebnem Özüpek ◽  
Eric B. Becker
Keyword(s):  
Finite Element ◽  
Global Analysis ◽  
Computational Procedure ◽  
Initial Crack ◽  
Local Analysis ◽  
Modeling And Analysis ◽  
Crack Growth Simulation ◽  
Truck Tires ◽  
Steady State Rolling ◽  
Critical Regions

Abstract In this study, we develop a computational procedure to predict the initiation and growth of belt layer separations in pneumatic tires. The procedure consists of finite element modeling and analysis of a tire subject to steady state rolling conditions. First, a global analysis that uses a full tire model is performed. Then, critical regions for crack initiation are determined through local analysis around the belt edges. This is followed by the placement of an initial crack in a local model. A sequence of crack configurations is analyzed and tearing energies at various crack sizes are calculated as part of the fatigue crack growth simulation. The final desired result is the prediction of fatigue life of the tire.

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