scholarly journals Dynamics of non-circular finite-release gravity currents

2015 ◽  
Vol 783 ◽  
pp. 344-378 ◽  
Author(s):  
N. Zgheib ◽  
T. Bonometti ◽  
S. Balachandar
Keyword(s):  
Aspect Ratio ◽  
Density Ratio ◽  
Front Propagation ◽  
Gravity Currents ◽  
Box Model ◽  
Wall Friction ◽  
Cross Sectional ◽  
Initial Shape ◽  
Box Models ◽  
Self Similar

The present work reports some new aspects of non-axisymmetric gravity currents obtained from laboratory experiments, fully resolved simulations and box models. Following the earlier work of Zgheib et al. (Theor. Comput. Fluid Dyn., vol. 28, 2014, pp. 521–529) which demonstrated that gravity currents initiating from non-axisymmetric cross-sectional geometries do not become axisymmetric, nor do they retain their initial shape during the slumping and inertial phases of spreading, we show that such non-axisymmetric currents eventually reach a self-similar regime during which (i) the local front propagation scales as $t^{1/2}$ as in circular releases and (ii) the non-axisymmetric front has a self-similar shape that primarily depends on the aspect ratio of the initial release. Complementary experiments of non-Boussinesq currents and top-spreading currents suggest that this self-similar dynamics is independent of the density ratio, vertical aspect ratio, wall friction and Reynolds number $\mathit{Re}$, provided the last is large, i.e. $\mathit{Re}\geqslant O(10^{4})$. The local instantaneous front Froude number obtained from the fully resolved simulations is compared to existing models of Froude functions. The recently reported extended box model is capable of capturing the dynamics of such non-axisymmetric flows. Here we use the extended box model to propose a relation for the self-similar horizontal aspect ratio ${\it\chi}_{\infty }$ of the propagating front as a function of the initial horizontal aspect ratio ${\it\chi}_{0}$, namely ${\it\chi}_{\infty }=1+(\ln {\it\chi}_{0})/3$. The experimental and numerical results are in good agreement with the proposed relation.

scholarly journals Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150070 ◽  
Author(s):  
S. Longo ◽  
V. Di Federico ◽  
L. Chiapponi
Keyword(s):  
Cross Sections ◽  
Rheological Behaviour ◽  
Gravity Currents ◽  
Channel Cross Section ◽  
Rigid Boundary ◽  
Cross Sectional ◽  
Self Similar ◽  
Similar Solutions ◽  
Fluid Rheology ◽  
Asymptotic Validity

A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n . The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b ≥0. The cases k ⋛ 1 are associated with wide, triangular and narrow cross sections. For b >0, the cases k ≷ 1 describe widening channels and squeezing fractures; b =0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like t α , scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume ( α ), the fluid rheological behaviour ( n ), and the transversal ( k ) and longitudinal ( b ) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.

On the application of box models to particle-driven gravity currents

2000 ◽  
Vol 416 ◽  
pp. 187-195 ◽  
Author(s):  
CHARLOTTE GLADSTONE ◽  
ANDREW W. WOODS
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Laboratory Experiments ◽  
Interstitial Fluid ◽  
Gravity Currents ◽  
Box Model ◽  
Monodisperse Particle ◽  
Box Models ◽  
Exchange Particle ◽  
Different Types

New laboratory experiments on different types of lock-exchange particle-driven gravity currents advancing into a flume of fresh water are presented. These include purely saline currents, monodisperse particle-laden gravity currents with both fresh and saline interstitial fluid, and bidisperse particle-laden currents. For each case a simple box model is developed. These agree well with the experimental data. We find that particulate gravity currents with saline interstitial fluid flowing into ambient fresh fluid are best described using a Froude number of 0.52 in the box model (cf. Huppert & Simpson 1980). However, particulate gravity currents with fresh interstitial fluid are best described using a higher Froude number of 0.67. The change in Froude number reflects the different shape and structure associated with the different density of interstitial fluid. For all experiments, box models provide accurate predictions for up to twenty lock-lengths.

Self-similar gravity currents with variable inflow revisited: plane currents

1994 ◽  
Vol 258 ◽  
pp. 77-104 ◽  
Author(s):  
Julio Gratton ◽  
Claudio Vigo
Keyword(s):  
Density Ratio ◽  
Gravity Currents ◽  
Type I ◽  
Type Ii ◽  
Ambient Fluid ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Self Similar ◽  
Similar Solutions ◽  
Transition Type

We use shallow-water theory to study the self-similar gravity currents that describe the intrusion of a heavy fluid below a lighter ambient fluid. We consider in detail the case of currents with planar symmetry produced by a source with variable inflow, such that the volume of the intruding fluid varies in time according to a power law of the type tα. The resistance of the ambient fluid is taken into account by a boundary condition of the von Kármán type, that depends on a parameter β that is a function of the density ratio of the fluids. The flow is characterized by β, α, and the Froude number [Fscr ]0 near the source. We find four kinds of self-similar solutions: subcritical continuous solutions (Type I), continuous solutions with a supercritical-subcritical transition (Type II), discontinuous solutions (Type III) that have a hydraulic jump, and discontinuous solutions having hydraulic jumps and a subcritical-supercritical transition (Type IV). The current is always subcritical near the front, but near the source it is subcritical ([Fscr ]0 < 1) for Type I currents, and supercritical ([Fscr ]0 > 1) for Types II, III, and IV. Type I solutions have already been found by other authors, but Type II, III, and IV currents are novel. We find the intervals of parameters for which these solutions exist, and discuss their properties. For constant-volume currents one obtains Type I solutions for any β that, when β > 2, have a ‘dry’ region near the origin. For steady inflow one finds Type I currents for O < β < ∞ and Type II and III Currents for and β, if [Fscr ]0 is sufficiently large.

Non-self-similar viscous gravity currents

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
Bruce R. Sutherland ◽  
Kristen Cote ◽  
Youn Sub (Dominic) Hong ◽  
Luke Steverango ◽  
Chris Surma
Keyword(s):  
Gravity Currents ◽  
Self Similar

scholarly journals Microcrystal alignment in drawn fiber over sub-meter to kilometer length scales

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Laurel Tauzer ◽  
Ann Mescher
Keyword(s):  
Aspect Ratio ◽  
Composite Fiber ◽  
Polymer Surfaces ◽  
Crystal Length ◽  
Cross Sectional ◽  
Length Scales ◽  
Grapeseed Oil ◽  
The Mean ◽  
Width Reduction ◽  
Uniform Reduction

AbstractThis paper describes a method for aligning stiff, high-aspect-ratio microcrystals over macro-length scales using a polymer fiber drawing process. A composite preform was constructed with an interfacial, liquid shell layer of grapeseed oil suspending ytterbium-doped potassium lutetium fluoride microcrystals (30% Yb:K2LuF5, KLF) between adjacent cylindrical surfaces of acrylic (polymethyl methacrylate, PMMA). The mean length of synthesized KLF microcrystals was 67 microns, and the mean aspect ratio, equivalent to crystal length divided by diameter, was eight. The acrylic-host preform was drawn into fiber, resulting in uniform reduction of all cross-sectional dimensions by a factor of approximately 20 in the final fiber. A corresponding width reduction of the interstitial liquid-filled gap, containing microcrystals between the polymer surfaces, constrains the microcrystals and causes alignment of the crystal long axes parallel to the axis of the drawn composite fiber. Alignment was best for clearly separated microcrystals and improved even further with the longest lengths, or highest aspect-ratio microcrystals.

scholarly journals Comparison of Different Approaches to Predict the Performance of Pumps As Turbines (PATs)

Energies ◽  
2018 ◽  
Vol 11 (4) ◽  
pp. 1016 ◽  
Author(s):  
Mauro Venturini ◽  
Stefano Alvisi ◽  
Silvio Simani ◽  
Lucrezia Manservigi
Keyword(s):  
Simulation Model ◽  
Ad Hoc ◽  
Polynomial Regression ◽  
Point Of View ◽  
Box Model ◽  
Physical Point ◽  
Evolutionary Polynomial Regression ◽  
Box Models ◽  
Performance Curves ◽  
Physics Based Simulation

This paper deals with the comparison of different methods which can be used for the prediction of the performance curves of pumps as turbines (PATs). The considered approaches are four, i.e., one physics-based simulation model (“white box” model), two “gray box” models, which integrate theory on turbomachines with specific data correlations, and one “black box” model. More in detail, the modeling approaches are: (1) a physics-based simulation model developed by the same authors, which includes the equations for estimating head, power, and efficiency and uses loss coefficients and specific parameters; (2) a model developed by Derakhshan and Nourbakhsh, which first predicts the best efficiency point of a PAT and then reconstructs their complete characteristic curves by means of two ad hoc equations; (3) the prediction model developed by Singh and Nestmann, which predicts the complete turbine characteristics based on pump shape and size; (4) an Evolutionary Polynomial Regression model, which represents a data-driven hybrid scheme which can be used for identifying the explicit mathematical relationship between PAT and pump curves. All approaches are applied to literature data, relying on both pump and PAT performance curves of head, power, and efficiency over the entire range of operation. The experimental data were provided by Derakhshan and Nourbakhsh for four different turbomachines, working in both pump and PAT mode with specific speed values in the range 1.53–5.82. This paper provides a quantitative assessment of the predictions made by means of the considered approaches and also analyzes consistency from a physical point of view. Advantages and drawbacks of each method are also analyzed and discussed.

Hierarchical Structure Enhances and Tunes the Damping Behavior of Load-Bearing Biological Materials

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Mahan Qwamizadeh ◽  
Pan Liu ◽  
Zuoqi Zhang ◽  
Kun Zhou ◽  
Yong Wei Zhang
Keyword(s):  
Aspect Ratio ◽  
Biological Materials ◽  
Damping Capacity ◽  
Geometrical Parameters ◽  
Loading Frequency ◽  
Load Bearing ◽  
Damage And Fracture ◽  
Damping Behavior ◽  
Specific Loading ◽  
Self Similar

One of the most crucial functionalities of load-bearing biological materials such as shell and bone is to protect their interior organs from damage and fracture arising from external dynamic impacts. However, how this class of materials effectively damp stress waves traveling through their structure is still largely unknown. With a self-similar hierarchical model, a theoretical approach was established to investigate the damping properties of load-bearing biological materials in relation to the biopolymer viscous characteristics, the loading frequency, the geometrical parameters of reinforcements, as well as the hierarchy number. It was found that the damping behavior originates from the viscous characteristics of the organic (biopolymer) constituents and is greatly tuned and enhanced by the staggered and hierarchical organization of the organic and inorganic constituents. For verification purpose, numerical experiments via finite-element method (FEM) have also been conducted and shown results consistent with the theoretical predictions. Furthermore, the results suggest that for the self-similar hierarchical design, there is an optimal aspect ratio of reinforcements for a specific loading frequency and a peak loading frequency for a specific aspect ratio of reinforcements, at which the damping capacity of the composite is maximized. Our findings not only add valuable insights into the stress wave damping mechanisms of load-bearing biological materials, but also provide useful guidelines for designing bioinspired synthetic composites for protective applications.

Effects of cross-sessional area and aspect ratio coupled with orientation on mechanical properties and deformation behavior of Cu nanowires

2021 ◽  
Author(s):  
Hui Cao ◽  
Wenke Chen ◽  
Zhiyuan Rui ◽  
Changfeng Yan
Keyword(s):  
Mechanical Properties ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cu Nanowires ◽  
The Cross

Abstract Metal nanomaterials exhibit excellent mechanical properties compared with corresponding bulk materials and have potential applications in various areas. Despite a number of studies of the size effect on Cu nanowires mechanical properties with square cross-sectional, investigations of them in rectangular cross-sectional with various sizes at constant volume are rare, and lack of multifactor coupling effect on mechanical properties and quantitative investigation. In this work, the dependence of mechanical properties and deformation mechanisms of Cu nanowires/nanoplates under tension on cross-sessional area, aspect ratio of cross-sectional coupled with orientation were investigated using molecular dynamics simulations and the semi-empirical expressions related to mechanical properties were proposed. The simulation results show that the Young’s modulus and the yield stress sharply increase with the aspect ratio except for the <110>{110}{001} Cu nanowires/nanoplates at the same cross-sectional area. And the Young’s modulus increases while the yield stress decreases with the cross-sectional area of Cu nanowires. However, both of them increase with the cross-sectional area of Cu nanoplates. Besides, the Young’s modulus increases with the cross-sectional area at all the orientations. The yield stress shows a mildly downward trend except for the <111> Cu nanowires with increased cross-sectional area. For the Cu nanowires with a small cross-sectional area, the surface force increases with the aspect ratio. In contrast, it decreases with the aspect ratio increase at a large cross-sectional area. At the cross-sectional area of 13.068 nm2, the surface force decreases with the aspect ratio of the <110> Cu nanowires while it increases at other orientations. The surface force is a linearly decreasing function of the cross-sectional area at different orientations. Quantitative studies show that Young’s modulus and yield stress to the aspect ratio of the Cu nanowires satisfy exponent relationship. In addition, the main deformation mechanism of Cu nanowires is the nucleation and propagation of partial dislocations while it is the twinning-dominated reorientation for Cu nanoplates.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

2019 ◽  
Vol 869 ◽  
pp. 610-633 ◽  
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
D. Petrolo ◽  
V. Di Federico ◽  
S. Longo
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Density Ratio ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Numerical Code ◽  
Long Distance ◽  
Front Speed

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

scholarly journals Comparison between 1-D and grey-box models of a SOFC

2019 ◽  
Vol 128 ◽  
pp. 01007
Author(s):  
Ramin Moradi ◽  
Andrea Di Carlo ◽  
Federico Testa ◽  
Luca Del Zotto ◽  
Enrico Bocci ◽  
...  
Keyword(s):  
Power Systems ◽  
Solid Electrolyte ◽  
Gas Turbines ◽  
Internal Combustion Engines ◽  
Box Model ◽  
System Level ◽  
Internal Temperature ◽  
Box Models ◽  
The Impact ◽  
D Model

Solid Oxide Fuel Cells (SOFCs) have shown unique performance in terms of greater electrical efficiency and thermochemical integrity with the power systems compared to gas turbines and internal combustion engines. Nonetheless, simple and reliable models still must be defined. In this paper, a comparisonbetween a grey-box model and a 1-D model of a SOFC is performed to understand the impact of the heat transfer inside the cell on the internal temperature distribution of the solid electrolyte. Hence, a significant internal temperature peak of the solid electrolyte is observed for a known difference between anode and cathode inlet temperatures. Indeed, it highlights the difference between the 1-D model andthe grey-box model regarding the thermal conditioning of the SOFC. Therefore, the results of this study can be used to investigate the reliability of the thermal results of box models in system-level simulations.

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