scholarly journals Analysis of one-dimensional models for exchange flows under strong stratification

2019 ◽  
Vol 70 (1) ◽  
pp. 41-56
Author(s):  
Steven J. Kaptein ◽  
Koen J. van de Wal ◽  
Leon P. J. Kamp ◽  
Vincenzo Armenio ◽  
Herman J. H. Clercx ◽  
...  
Keyword(s):  
Density Gradient ◽  
Turbulent Mixing ◽  
Schmidt Number ◽  
Density Gradients ◽  
One Dimensional ◽  
Exchange Flows ◽  
Dimensional Models ◽  
The One ◽  
Horizontal Density Gradient ◽  
Classical Constant

AbstractOne-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Reg, the Schmidt number Sc, and the aspect ratio of the channel Γ. For small values of RegΓ, when diffusion dominates, all models perform well. However, as RegΓ increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

scholarly journals Channelization of plumes beneath ice shelves

2015 ◽  
Vol 785 ◽  
pp. 109-134 ◽  
Author(s):  
M. C. Dallaston ◽  
I. J. Hewitt ◽  
A. J. Wells
Keyword(s):  
Turbulent Mixing ◽  
Simplified Model ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ice Shelves ◽  
Narrow Channels ◽  
One Dimensional ◽  
Grounding Line ◽  
The One

We study a simplified model of ice–ocean interaction beneath a floating ice shelf, and investigate the possibility for channels to form in the ice shelf base due to spatial variations in conditions at the grounding line. The model combines an extensional thin-film description of viscous ice flow in the shelf, with melting at its base driven by a turbulent ocean plume. Small transverse perturbations to the one-dimensional steady state are considered, driven either by ice thickness or subglacial discharge variations across the grounding line. Either forcing leads to the growth of channels downstream, with melting driven by locally enhanced ocean velocities, and thus heat transfer. Narrow channels are smoothed out due to turbulent mixing in the ocean plume, leading to a preferred wavelength for channel growth. In the absence of perturbations at the grounding line, linear stability analysis suggests that the one-dimensional state is stable to initial perturbations, chiefly due to the background ice advection.

scholarly journals Rayleigh-Ritz variational method with suitable asymptotic behaviour

Open Physics ◽  
2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Francisco Fernández ◽  
Javier Garcia
Keyword(s):  
Variational Method ◽  
Asymptotic Behaviour ◽  
Orthogonal Polynomial ◽  
Rate Of Convergence ◽  
Orthogonal Basis ◽  
Basis Sets ◽  
One Dimensional ◽  
Variational Calculations ◽  
Dimensional Models ◽  
The One

AbstractThis paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.

Sputtering and heating of Titan's upper atmosphere

2008 ◽  
Vol 367 (1889) ◽  
pp. 753-771 ◽  
Author(s):  
Robert E Johnson
Keyword(s):  
Loss Rate ◽  
Particle Production ◽  
Fluid Dynamic ◽  
Recent Analysis ◽  
Upward Flow ◽  
One Dimensional ◽  
Atmospheric Structure ◽  
Dimensional Models ◽  
The One ◽  
Loss Rates

Titan is an important endpoint for understanding atmospheric evolution. Prior to Cassini's arrival at Saturn, modelling based on Voyager data indicated that the hydrogen escape rate was large (1–3×10 28  amu s −1 ), but the escape rates for carbon and nitrogen species were relatively small (5×10 26  amu s −1 ) and dominated by atmospheric sputtering. Recent analysis of the structure of Titan's thermosphere and corona attained from the Ion and Neutral Mass Spectrometer and the Huygens Atmospheric Structure Instrument on Cassini have led to substantially larger estimates of the loss rate for heavy species (0.3–5×10 28  amu s −1 ). At the largest rate suggested, a mass that is a significant fraction of the present atmosphere would have been lost to space in 4 Gyr; hence, understanding the nature of the processes driving escape is critical. The recent estimates of neutral escape are reviewed here, with particular emphasis on plasma-induced sputtering and heating. Whereas the loss of hydrogen is clearly indicated by the altitude dependence of the H 2 density, three different one-dimensional models were used to estimate the heavy-molecule loss rate using the Cassini data for atmospheric density versus altitude. The solar heating rate and the nitrogen density profile versus altitude were used in a fluid dynamic model to extract an average net upward flux below the exobase; the diffusion of methane through nitrogen was described below the exobase using a model that allowed for outward flow; and the coronal structure above the exobase was simulated by presuming that the observed atmospheric structure was due to solar- and plasma-induced hot particle production. In the latter, it was hypothesized that hot recoils from photochemistry or plasma-ion-induced heating were required. In the other two models, the upward flow extracted is driven by heat conduction from below, which is assumed to continue to act above the nominal exobase, producing a process referred to as ‘slow hydrodynamic’ escape. These models and the resulting loss rates are reviewed and compared. It is pointed out that preliminary estimates of the composition of the magnetospheric plasma at Titan's orbit appear to be inconsistent with the largest loss rates suggested for the heavy species, and the mean upward flow extracted in the one-dimensional models could be consistent with atmospheric loss by other mechanisms or with transport to other regions of Titan's atmosphere.

Modeling of Combustion in Gasoline Direct Injection Engines for the Optimization of Engine Management System Through Reduction of Three-Dimensional Models to (n × One-Dimensional) Models

2003 ◽  
Vol 125 (3) ◽  
pp. 520-532 ◽  
Author(s):  
P. Emery ◽  
F. Maroteaux ◽  
M. Sorine
Keyword(s):  
Direct Injection ◽  
Three Dimensional ◽  
Gasoline Direct Injection ◽  
Computational Time ◽  
Combustion Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
The One

Gasoline direct injection (GDI) spark ignition engines may be able to run over a wide range of operating conditions. The GDI process allows combustion with lean mixtures which may lead to improved fuel economy and emissions relative to homogeneous spark ignition (SI) engines. To satisfy the different modes of operation, the tuning of GDI engines requires a large number of engine tests which are time-consuming and very expensive. To reduce the number of tests, a model with a very short computational time to simulate the engines in the whole operating range is needed; therefore the objective of this paper is to present a reduced model to analyze the combustion process in GDI engines, applied to a homogeneous stoichiometric mode. The objective of the model is to reproduce the same tendencies as those obtained by three-dimensional models, but with a reduced computational time. The one-dimensional model is obtained thanks to a reduction methodology based on the geometry of the combustion front computed with three-dimensional models of the KIVA-GSM code, a modified version of KIVA-II code including a CFM combustion model. The model is a set of n one-dimensional equations (i.e., for n rays), taking into account a thin flame front, described with the flamelet assumption. It includes a CFM combustion model and a (k,ε)-model including the mean air motions (swirl and tumble). The results of the one-dimensional model are compared to those obtained by the KIVA IIGSM under different engine conditions. The comparison shows that the one-dimensional model overestimates the maximum cylinder pressure, which has an insignificant effect on the net indicated work per cycle. The results obtained by the numerical simulations are close to those given by the three-dimensional model, with a much reduced computation time.

A Comparison Study of One-Dimensional Models for Stratified Thermal Storage Tanks

1989 ◽  
Vol 111 (3) ◽  
pp. 204-210 ◽  
Author(s):  
Y. H. Zurigat ◽  
K. J. Maloney ◽  
A. J. Ghajar
Keyword(s):  
Three Dimensional ◽  
Thermal Storage ◽  
Comparison Study ◽  
Storage Tanks ◽  
Factors Affecting ◽  
One Dimensional ◽  
Mixing Parameters ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
The One

A survey of the stratified thermal storage tank one-dimensional models available in the literature has been conducted. Six of these models were tested and compared against the experimental data obtained at our laboratories and from the literature. Although various factors affecting the performance of a stratified tank can be accounted for by the higher order models, i.e. two- and three-dimensional models, the introduction of empirically-based mixing parameters into the one-dimensional models renders them widely applicable and practical in the simulation of energy systems incorporating thermal storage tanks.

scholarly journals Improving the parameterisation of horizontal density gradient in one-dimensional water column models for estuarine circulation

Ocean Science ◽  
2008 ◽  
Vol 4 (4) ◽  
pp. 239-246 ◽  
Author(s):  
S. Blaise ◽  
E. Deleersnijder
Keyword(s):  
Finite Difference ◽  
Water Column ◽  
Density Gradient ◽  
Lower Bounds ◽  
A Priori ◽  
Upwind Scheme ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
First Order ◽  
Horizontal Density Gradient

Abstract. A new parameterisation of horizontal density gradient for a one-dimensional water column estuarine model, inspired by the first-order finite-difference upwind scheme, is presented. This parameterisation prevents stratification from growing indefinitely, a deficiency usually referred to as "runaway stratification". It is seen that, using this upwind-like parameterisation, the salinity must remain comprised between upper and lower bounds set a priori and that any initial over- or under-shooting is progressively eliminated. Simulations of idealised and realistic estuarine regimes indicate that the new parameterisation lead to results that are devoid of the runaway stratification phenomenon, as opposed to previously used models.

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