scholarly journals Experimental verification of theoretical approaches for radial gravity currents draining from an edge

2021 ◽  
Author(s):  
D. Petrolo ◽  
M. Ungarish ◽  
L. Chiapponi ◽  
V. Ciriello ◽  
S. Longo
Keyword(s):  
Wedge Angle ◽  
Single Layer ◽  
Gravity Currents ◽  
Ambient Fluid ◽  
Operational Conditions ◽  
Theoretical Approaches ◽  
Drainage Flows ◽  
Radial Flux ◽  
Theoretical Predictions ◽  
Set Up

AbstractWe present an experimental study of inertial gravity currents (GCs) propagating in a cylindrical wedge under different drainage directions (inward/outward), lock-release (full/partial gate width) and geometry (annulus/full cylinder). We investigate the following combinations representative of operational conditions for dam-break flows: (i) inward drainage, annular reservoir, full gate; (ii) outward drainage, full reservoir, full gate; and (iii) outward drainage, full reservoir, partial gate. A single-layer shallow-water (SW) model is used for modelling the first two cases, while a box model interprets the third case; the results of these approximations are referred to as “theoretical”. We performed a first series of experiments with water as ambient fluid and brine as intruding fluid, measuring the time evolution of the volume in the reservoir and the velocity profiles in several sections; in a second series, air was the ambient and water was the intruding fluid. Careful measurements, accompanied by comparisons with the theoretical predictions, were performed for the behaviour of the interface, radial velocity and, most important, the volume decay $${\mathcal {V}}(t)/{\mathcal {V}}(0)$$ V ( t ) / V ( 0 ) . In general, there is good agreement: the theoretical volume decay is more rapid than the measured one, but the discrepancies are a few percent and the agreement improves as the Reynolds number increases. Velocity measurements show a trend correctly reproduced by the SW model, although often a delay is observed and an over- or under-estimation of the peak values. Some experiments were conducted to verify the role of inconsistencies between experimental set-up and model assumptions, considering, for example, the presence or absence of a top lid, wedge angle much less than $$2\pi $$ 2 π , suppression of the viscous corner at the centre, reduction of disturbances in the dynamics of the ambient fluid: all these effects resulted in negligible impacts on the overall error. These experiments provide corroboration to the simple models used for capturing radial drainage flows, and also elucidate some effects (like oscillations of the radial flux) that are beyond the resolution of the models. This holds also for partial width lock-release, where axial symmetry is lost.

scholarly journals Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Andreas M. Menzel ◽  
Hartmut Löwen
Keyword(s):  
Colloidal Particles ◽  
Colloidal Particle ◽  
Theoretical Description ◽  
Point Of View ◽  
Material Behavior ◽  
Theoretical Point ◽  
Mechanical Stiffness ◽  
Theoretical Approaches ◽  
Theoretical Predictions ◽  
Particle Level

Abstract Magnetic gels and elastomers consist of magnetic or magnetizable colloidal particles embedded in an elastic polymeric matrix. Outstanding properties of these materials comprise reversible changes in their mechanical stiffness or magnetostrictive distortions under the influence of external magnetic fields. To understand such types of overall material behavior from a theoretical point of view, it is essential to characterize the substances starting from the discrete colloidal particle level. It turns out that the macroscopic material response depends sensitively on the mesoscopic particle arrangement. We have utilized and developed several theoretical approaches to this end, allowing us both to reproduce experimental observations and to make theoretical predictions. Our hope is that both these paths help to further stimulate the interest in these fascinating materials.

scholarly journals Active control of liquid film flows: beyond reduced-order models

2021 ◽  
Vol 104 (1) ◽  
pp. 267-287
Author(s):  
Radu Cimpeanu ◽  
Susana N. Gomes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Liquid Film ◽  
Information Transfer ◽  
Analytical Models ◽  
Feedback Controls ◽  
Reduced Order ◽  
Modelling Framework ◽  
Theoretical Approaches ◽  
Active Feedback ◽  
Feedback Strategies ◽  
Set Up

AbstractThe ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex to tackle directly, and reduced-order modelling is used in order to create viable representations of the target systems. The simplified setting allows for the development of rigorous control theoretical approaches, but the propagation of their effects back up the hierarchy and into real-world systems remains a significant challenge. Using the canonical set-up of a liquid film falling down an inclined plane under the action of active feedback controls in the form of blowing and suction, we develop a multi-level modelling framework containing both analytical models and direct numerical simulations acting as an in silico experimental platform. Constructing strategies at the inexpensive lower levels in the hierarchy, we find that offline control transfer is not viable; however, analytically informed feedback strategies show excellent potential, even far beyond the anticipated range of applicability of the models. The detailed effects of the controls in terms of stability and treatment of nonlinearity are examined in detail in order to gain understanding of the information transfer inside the flows, which can aid transition towards other control-rich frameworks and applications.

The Reduction of Bias Error in Transfer Function Estimates Using FFT-Based Analyzers

1984 ◽  
Vol 106 (1) ◽  
pp. 29-35 ◽  
Author(s):  
P. Cawley
Keyword(s):  
Transfer Function ◽  
Random Excitation ◽  
Analogue Computer ◽  
Bias Error ◽  
Testing Time ◽  
Theoretical Predictions ◽  
Set Up ◽  
Modal Mass ◽  
Time Required ◽  
Good Agreement

The susceptibility to bias error of two methods for computing transfer (frequency response) functions from spectra produced by FFT-based analyzers using random excitation has been investigated. Results from tests with an FFT analyzer on a single degree-of-freedom system set up on an analogue computer show good agreement with the theoretical predictions. It has been shown that, around resonance, the bias error in the transfer function estimate H2 (Syy/Sxy*) is considerably less than that in the more commonly used estimate, H1 (Sxy/Sxx). The record length, and hence the testing time, required for a given accuracy is reduced by over 50 percent if the H2 calculation procedure is used. The analysis has also shown that if shaker excitation is used on lightly damped structures with low modal mass, it is important to minimize the mass of the force gage and the moving element of the shaker.

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

Application of Wide-Band Ultrasound for the Detection of Angled Crack Features in Oil and Gas Pipelines

2018 ◽  
Author(s):  
Willem Vos ◽  
Petter Norli ◽  
Emilie Vallee
Keyword(s):  
Large Scale ◽  
Crack Detection ◽  
Oil And Gas ◽  
Wide Band ◽  
Theoretical Background ◽  
Proof Of Concept ◽  
Offshore Pipelines ◽  
Large Scale Testing ◽  
Theoretical Predictions ◽  
Set Up

This paper describes a novel technique for the detection of cracks in pipelines. The proposed in-line inspection technique has the ability to detect crack features at random angles in the pipeline, such as axial, circumferential, and any angle in between. This ability is novel to the current ILI technology offering and will also add value by detecting cracks in deformed pipes (i.e. in dents), and cracks associated with the girth weld (mid weld cracks, rapid cooling cracks and cracks parallel to the weld). Furthermore, the technology is suitable for detection of cracks in spiral welded pipes, both parallel to the spiral weld as well as perpendicular to the weld. Integrity issues around most features described above are not addressed with ILI tools, often forcing operators to perform hydrostatic tests to ensure pipeline safety. The technology described here is based on the use of wideband ultrasound inline inspection tools that are already in operation. They are designed for the inspection of structures operating in challenging environments such as offshore pipelines. Adjustments to the front-end analog system and data collection from a grid of transducers allow the tools to detect cracks in any orientation in the line. Description of changes to the test set-up are presented as well as the theoretical background behind crack detection. Historical development of the technology will be presented, such as early laboratory testing and proof of concept. The proof of concept data will be compared to the theoretical predictions. A detailed set of results are presented. These are from tests that were performed on samples sourced from North America and Europe which contain SCC features. Results from ongoing testing will be presented, which involved large-scale testing on SCC features in gas-filled pipe spools.

scholarly journals On the (un-)predictability of a large intragenic fitness landscape

2016 ◽  
Author(s):  
Claudia Bank ◽  
Sebastian Matuszewski ◽  
Ryan T. Hietpas ◽  
Jeffrey D. Jensen
Keyword(s):  
Amino Acid ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Specific Information ◽  
Theoretical Approaches ◽  
Elevated Salinity ◽  
Theoretical Predictions ◽  
Experimental Approaches ◽  
Deterministic Processes ◽  
Negative Epistasis

AbstractThe study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with NGS methods enable accurate and extensive studies of the fitness effects of mutations – allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape, and its implications for the predictability and repeatability of evolution.Here, we present a uniquely large multi-allelic fitness landscape comprised of 640 engineered mutants that represent all possible combinations of 13 amino-acid changing mutations at six sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multi-allelic fitness landscape. Using subsets of the data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino-acid specific epistatic hotspots, and that inference is additionally confounded by the non-random choice of mutations for experimental fitness landscapes.Author SummaryThe study of fitness landscapes is fundamentally concerned with understanding the relative roles of stochastic and deterministic processes in adaptive evolution. Here, the authors present a uniquely large and complete multi-allelic intragenic fitness landscape of 640 systematically engineered mutations in yeast Hsp90. Using a combination of traditional and recently proposed theoretical approaches, they study the accessibility of the global fitness peak, and the potential for predictability of the fitness landscape topography. They report local ruggedness of the landscape and the existence of epistatic hotspot mutations, which together make extrapolation and hence predictability inherently difficult, if mutation-specific information is not considered.

scholarly journals Variable Stars in Dwarf Spheroidal Galaxies

1973 ◽  
Vol 21 ◽  
pp. 35-48
Author(s):  
Steven Van Agt
Keyword(s):  
Globular Clusters ◽  
Local Group ◽  
Elliptical Galaxies ◽  
Variable Stars ◽  
Dwarf Spheroidal Galaxies ◽  
Theoretical Predictions ◽  
History Of ◽  
Set Up ◽  
Theoretical Considerations ◽  
Spheroidal Galaxies

Interest in dwarf spheroidal galaxies is motivated by a number of reasons; an important one on the occasion of this colloquium is the abundance of variable stars. The theory of stellar evolution and stellar pulsations is now able to predict from theoretical considerations characteristic properties of variable stars in the colour-magnitude diagram (Iben, 1971). By observing the variable stars in the field, and in as wide a selection of objects as possible, more insight can be obtained into the history of the oldest members of our Galaxy (the globular clusters) and of the dwarf spheroidal galaxies in the Local Group. It is worthwhile to explore the spheroidal galaxies as observational tests for the theoretical predictions of conditions in space away from our Galaxy. The numbers of variable stars in the dwarf spheroidal galaxies are such that we may expect well-defined relations to emerge once reliable magnitude sequences have been set up, the variable stars found, and their periods determined. Six dwarf spheroidal galaxies are presently known in the Local Group within a distance of 250 kpc. In Table I, which lists members of the Local Group, they are at the low-luminosity end of the sequence of elliptical galaxies (van den Bergh, 1968).

scholarly journals Entrainment in Shallow Rotating Gravity Currents: A Modeling Study

2010 ◽  
Vol 40 (8) ◽  
pp. 1819-1834 ◽  
Author(s):  
Lars Umlauf ◽  
Lars Arneborg ◽  
Richard Hofmeister ◽  
Hans Burchard
Keyword(s):  
Froude Number ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Spatial Separation ◽  
Gravity Currents ◽  
Transverse Jet ◽  
Entrainment Process ◽  
Set Up ◽  
Rotation Set ◽  
Bulk Parameters

Abstract The physics of shallow gravity currents passing through a rotating channel at subcritical Froude number is investigated here with a series of idealized numerical experiments. It is found that the combined effects of friction and rotation set up a complex transverse circulation that has some crucial implications for the entrainment process. A key component of this secondary circulation is a geostrophically balanced transverse jet in the interface that laterally drains fluid from the interface. This effect is shown to result in a strong cross-channel asymmetry and a spatial separation of the entrainment process: drained interfacial fluid is partly replaced by entrained ambient fluid on the deep side of the gravity current, whereas the downward mixing of buoyant fluid occurs on the shallow side. These results, closely corresponding to recent measurements in a shallow, channelized gravity current in the western Baltic Sea, illustrate that the description of entrainment as a strictly vertical mixing process with the help of local bulk parameters like the Froude number is not generally applicable in rotating gravity currents.

Selective withdrawal from a stably stratified fluid

1968 ◽  
Vol 32 (2) ◽  
pp. 209-223 ◽  
Author(s):  
I. R. Wood
Keyword(s):  
Single Layer ◽  
Layered System ◽  
Volume Discharge ◽  
Layer System ◽  
Minimum Width ◽  
Theoretical Predictions ◽  
Small Rise ◽  
Self Similar ◽  
The One ◽  
Dead Water

In this paper a reservoir connected through a horizontal contraction to a channel is considered. Both the reservoir and the channel are considered to contain a stable multi-layered system of fluids. The conditions under which there is a flow in only one layer, and the depth in this flowing layer decreases continuously from its depth in the reservoir to its depth in the channel, give the maximum discharge that can be obtained with a flow only from this single layer. For this case the volume discharge calculations are carried out at a single section (the section of minimum width). Where there are velocities in only two layers and the depth in each of these layers decreases continuously from their depths in the reservoir to their depths in the channel, the theory involves computations at two sections in the flow. These are the section of minimum width and a section upstream of the position of minimum width (the virtual point of control). For this flow it is shown that the solution is the one in which the velocity and density distributions are self similar and that the depths of the layers at the point of maximum contraction are two-thirds of those far upstream. It is then shown that for any stable continuous or discrete density stratification in the reservoir a self similar solution will satisfy the conditions for the depths of the flowing layers to decrease smoothly from the reservoir to downstream of the contraction. Again the ratio of the depth at the contraction to that far upstream is two-thirds.When there is a very large density difference between the fluid in the lower dead water and that in the lowest flowing streamline then this streamline becomes horizontal and may be considered as a frictionless bed. The flow when the bed is not horizontal but where there is a small rise in the channel at the position of maximum contraction is considered for the case where two discrete layers flow under a volume of dead water. In this case the velocity and density profiles are not self similar.Experiments have been carried out with a contraction in a flume for the withdrawal of two discrete layers from a three layer system and the withdrawal from a fluid with a linear density gradient. In both cases the reservoir and channel bed and hence the lowest streamline was effectively horizontal. These experiments confirmed the theoretical predictions.

Mixing in continuous gravity currents

2017 ◽  
Vol 818 ◽  
Author(s):  
Diana Sher ◽  
Andrew W. Woods
Keyword(s):  
Light Attenuation ◽  
Vertical Gradient ◽  
Gravity Currents ◽  
Mixing Zone ◽  
Ambient Fluid ◽  
Unit Width ◽  
A Value ◽  
Dense Fluid ◽  
Catch Up ◽  
High Reynolds

We present measurements of the entrainment of ambient fluid into high-Reynolds-number gravity currents produced by a steady flux of buoyancy. The currents propagate along a horizontal channel and the mixing is measured using a light attenuation technique to obtain the cross-channel average of the density throughout the current. The total volume of the current increases linearly with time, at a rate in the range $(1.8{-}2.1)Q_{o}$ for source Froude numbers, $Fr_{o}$, in the range $0.1{-}3.7$, where $Q_{o}$ is the source volume flux per unit width. Most mixing occurs either immediately downstream of the inflow or near the head of the flow, with an increasing proportion of the entrainment occurring in a mixing zone near the inflow as $Fr_{o}$ increases. A vertical gradient in the density and horizontal velocity develops in this mixing zone. This enables relatively dense fluid at the base of the current to catch up with the head, where it rises and mixes with the ambient fluid which is displaced over the head. The mixed fluid continues forward more slowly than the head, forming the relatively dilute fluid in the upper part of the current. Our data show that the depth and the depth-averaged buoyancy are primarily dependent on the position relative to the front, with the speed of the front being $\unicode[STIX]{x1D706}(Fr_{o})B_{o}^{1/3}$, where $B_{o}$ is the source buoyancy flux per unit width. Here, $\unicode[STIX]{x1D706}(Fr_{o})$ increases from 0.9 to 1.1 as $Fr_{o}$ increases from 0.1 to 3.7, while the Froude number at the head of the flow has a value of $1.1\pm 0.05$.

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