1,721,068 research outputs found
Riflessione di fronti d'onda onda stazionari di altezza finita in correnti a superficie libera
No full textWhen a uniform supercritical channel flow is sharply turned by a wedge on one channel wall, a shock wave forms and reflects from the opposite wall in three main, distinctly different configurations named regular reflection (RR), irregular reflection (IR), and Guderley/Vasilev reflection (GR/VR).
Within the framework of shallow free-surface flows, the basic equations for shock waves and shock wave reflection were first proposed by Ippen. However, Ippen limited his attention to RR problems, and since his pioneering work the study on shock wave reflection in shallow supercritical flows did not record any notable theoretical progress.
On the contrary, shock wave reflection was extensively studied in gas dynamics. In the early 1940s, von Neumann developed the two-shock theory (2ST) and three-shock theory (3ST) for RR and IR, respectively, based on mass, momentum, and energy conservation equations. However, experimental evidence pointed out that a reflection pattern similar to IR (i.e., with three shocks and a slip stream meeting at a triple point) also exists within a range of fundamental parameters where the von Neumann theory predicts neither RR nor IR. This discrepancy between theory and experiments is called the 'von Neumann paradoxâ'. The structure of the unpredicted reflection pattern was discussed in some detail by Colella and Henderson (1990), which inspired much of the recent research on weak shock wave reflection off a wedge.
Many different resolutions of this paradox have been suggested over the last 60 years. The theoretically consistent solution originally proposed by Guderley and markedly improved and formalized by Vasilev et al (2008), referred to as the four-wave theory, has recently proved to be the key to solve von Neumann paradox. Vasilev et al also suppose the existence of the afterwards called Vasilev reflection (VR), to which the solution is again provided by the four-wave theory but, unlike the GR, the flow between the slip stream and the Mach stem is subsonic (or subcritical, within the framework of shallow water flows).
Great advances have been made in the past few years, mainly thanks to improved numerical and experimental capabilities. In gas dynamics, the Guderley reflection (GR) has been simulated numerically at moderately low Mach numbers. Recently, the shock wave pattern predicted by the four wave theory has been further confirmed by Skews & Ashworth (2005) who experimentally detected the expansion fan and the supersonic patch behind the triple point using a special shock tube.
In the present work, high-resolution numerical study of the Guderley and the Vasilev reflection within the framework of shallow water flow has shown that the 4WT accurately predicts the complex flow pattern around the triple point. However, the four-wave theory does not provide a complete solution to the GR configuration. According to the present numerical results, a weak and diffused compression wave through the supercritical patch turns the flow immediately behind the Guderley stem until critical condition is achieved. On the contrary, the Vasilev reflection is completely resolved by the four-wave theory. The supercritical patch of this reflection configuration is extremely small because of the relatively high Froude number, and this work is the first time it has been resolved. Our solution is obtained within the framework of depth averaged two-dimensional inviscid shallow water flow. However, because of the strong analogy between shallow water flows and either two-dimensional gas flows or shallow granular flows, the present work can be of more general interest.
Within the framework of oriented shock wave fronts, a technique to reconstruct the steady shock wave pattern and the flow field close to the triple point of von Neumann, Guderley and Vasilev reflections has been proposed. First, the idea of orienting shock wave fronts is extended and formalized. Then, the technique for obtaining a close view of the above reflection patterns centred about the triple point is described and a numerical example, within the framework of shallow water flow, is presented and discussed. The technique proved very effective and can be profitably used both in numerical and experimental investigations to explore further the nature of the flow field within and around the supercritical patch and to assess the impact of viscosity and real fluid properties.
In the last part of the present work, open channel flow through a linear contraction has been studied, with special attention to the flow configuration with a two-dimensional jump in the contraction discussed by Akers and Bokhove (2008). A simple quasi-two-dimensional model has been proposed, in order to assess equilibrium conditions and to explore their stability. Both bed friction and bed slope were found to contribute to the stability of this flow configuration which otherwise would be unstable. Results of the theoretical model are compared with both experiments and numerical simulations, and the comparison confirms the reliability of the proposed model. Hysteresis is addressed as well, and it's showed that channel flow through a linear contraction can experience two different nested hysteretic loops.Nel corso del Dottorato di Ricerca è stato trattato il problema delle riflessioni di fronti d'onda di altezza finita in moti supercritici stazionari a superficie libera.
Nelle ipotesi di considerare un moto su fondo orizzontale ed in assenza di dissipazioni per attrito, le equazioni che reggono il fenomeno sono state proposte inizialmente da Ippen nel 1951. Tuttavia, Ippen e i suoi collaboratori hanno rivolto la loro attenzione esclusivamente al fenomeno della riflessione regolare e, dalla pubblicazione dei loro lavori originali, nel campo dei problemi di riflessione di fronti d'onda in correnti supercritiche a superficie libera non sono stati registrati progressi degni di nota.
D'altra parte, il fenomeno della riflessione è stato studiato in modo esteso e dettagliato in gasdinamica. Già nei primi anni '40 von Neumann, a partire dalle equazioni di conservazione della massa e della quantità di moto, elaborò le teorie cosiddette dei due e dei tre fronti d'onda, in grado di risolvere, rispettivamente, le riflessioni regolari e irregolari.
In seguito, evidenze sperimentali hanno mostrato come, in alcuni particolari casi per i quali la teoria di von Neumann non prevedeva l'esistenza di riflessione regolare né irregolare, si riscontrassero delle configurazioni di riflessione del tutto simili al caso di riflessione irregolare. Questa apparente discrepanza tra l'approccio teorico e quello sperimentale fu denominata 'paradosso di von Neumann'.
A partire dalla fine degli anni '90, il paradosso di Von Neumann è ritornato a destare interesse in ambito scientifico, poiché le maggiori potenzialità di indagine fornite dalle tecniche numeriche hanno permesso di indagare in maniera approfondita questi particolari fenomeni di riflessione.
In questo contesto si inserisce la prima parte del presente lavoro di ricerca, che rappresenta un contributo apprezzabile alla soluzione teorica del paradosso di von Neumann.
La seconda parte del lavoro di ricerca ha riguardato una delle possibili applicazioni degli strumenti messi a punto per la risoluzione dei problemi di riflessione nelle correnti supercritiche a superficie libera: in particolare sono state indagate alcune problematiche relative al comportamento di una corrente a superficie libera che affronta un tratto di canale linearmente convergente
Water age, exposure time, and local flushing time in semi-enclosed, tidal basins with negligible freshwater inflow
No full textWithin the framework of tidally flushed, semi-enclosed basins with negligible freshwater inflow, and under steady periodic flow conditions, three frequently used local transport time scales to quantify the efficiency of water renewal, namely water age, exposure time, and local flushing time are studied and compared to each other. In these environments, water renewal is strongly controlled by diffusion, and it is significantly affected by the return flow (i.e., the fraction of effluent water that returns into the basin on each flood tide). The definition of water age is here modified to account for the return flow, in analogy with exposure time and local flushing time. We consider approximate time scales, whose accuracy is analyzed, in order to overcome problems related to the size of the computational domain and to reduce the computational effort. A new approximate procedure is introduced to estimate water age, which is based on the water aging rate. Also, the concept of local flushing time as a relevant time scale is introduced. Under steady periodic conditions, we demonstrate that the local flushing time quantitatively corresponds to water age, and well approximates exposure time when the flow is dominated by diffusion. Since the effort required to compute water age and exposure time is greater than that required to compute the local flushing time, the present results can also have a practical interest in the assessment of water renewal efficiency of semi-enclosed water basins. The results of a modeling study, in which the lagoon of Venice is used as a benchmark, confirm the substantial quantitative equivalence between these three transport time scales in highly diffusive environments
Renewal time scales in tidal basins: Climbing the Tower of Babel
No full textTransport time scales are key parameters to assess water renewal of estuaries and tidal basins and they have long been used to this purpose. In a modern-day Tower of Babel, an ever-increasing confusion has involved terminology, use and estimation of time scales, despite valuable efforts towards a sounder theoretical framework. Within the framework of tidally flushed, semi-enclosed basins with negligible freshwater inflow, water renewal is strongly controlled by diffusion. The inlet of a tidal basin acts alternatively as a source and as a sink. A significant fraction of effluent water can return to the basin each flood tide. Accordingly, to correctly assess water renewal of such basins, a region larger than the basin itself has to be considered. To account for the effects of return flow, the concept of exposure time was introduced as an alternative to the residence time. However, deep analysis of exposure time revealed unexpected complications that, in part, are still open questions. The present contribution extends the concepts of water age and local flushing time to account for the return flow, as for exposure time. These time scales are studied and compared to each other, aided by a modelling study focusing on the Venice lagoon. Also, approximate methods to estimate the real time scales are introduced and analysed. We show that the local flushing time well approximates, quantitatively, both water age and exposure time in steady periodic hydrodynamic condition. Conversely, wind-driven advection makes exposure time to be significantly different from water age and local flushing time
La previsione in tempo reale dei livelli idrometrici di piena del fiume Bacchiglione a Ponte degli Angeli, Vicenza
Get PDFIl disastroso evento di piena che ha colpito il Veneto il primo novembre 2010, particolarmente drammatico per la città di Vicenza, ha reso evidente la necessità di disporre di metodi di previsione, soprattutto a breve termine, che siano efficaci strumenti di supporto alle decisioni. Infatti, nelle fasi concitate di un’alluvione che colpisce un’area urbana densamente popolata, è assai difficile mantenere una visione chiara dell’evoluzione dell’evento e, di conseguenza, stabilire e coordinare un piano per la gestione delle fasi dell’emergenza. Questa nota presenta un modello di previsione che adotta un metodo di tipo statistico basato sull’acquisizione in tempo reale dei dati misurati dalle stazioni idro-meteorologiche del bacino del Bacchiglione e delle previsioni di modelli meteorologici
Free surface waves induced by vortex shedding in cylinder arrays
Get PDFThe paper presents and discusses the results of an accurate and extensive experimental investigation on the waves that originate when an array of cylinders is placed in an otherwise uniform open channel flow. The study was originally aimed at providing new and more accurate data to calibrate and validate a theoretical model recently proposed in the literature. However, two interesting characteristics of the phenomenon at hand, never reported in the literature, also emerged from the experimental study, i.e. (i) the wave produced by the cylinders is actually a metachronal wave rather than a pure transverse seiche; (ii) two different resonant conditions exist for each single wave mode, i.e. two typical Strouhal numbers characterize the resonance frequency of vortex shedding from the cylinders in an array. Evidence of the metachronal wave, as well as some preliminary data on the longitudinal component of this wave, are given in the paper. Also, the double resonance condition is experimentally demonstrated and discussed
A semi-empirical model to predict the probability of capture of buoyant particles by a cylindrical collector through capillarity
Get PDFThe seeds of many aquatic plants, as well as many propagulae and larvae, are buoyant and transported at the water surface. These particles are therefore subject to surface tension, which may enhance their capture by emergent vegetation through capillary attraction. In this work, we develop a semi-empirical model that predicts the probability that a floating particle is retained by plant stems and branches piercing the water surface, due to capillarity, against the drag force exerted by the flowing water. Specific laboratory experiments are also performed to calibrate and validate the model
Open channel flow through a linear contraction
Get PDFIn this work we study the open channel flow through a linear contraction. We focus on the flow configuration with a two-dimensional jump in the contraction discussed by Akers and Bokhove Phys. Fluids 20, 056601 2008 and propose a simple quasi-two-dimensional model to assess equilibrium conditions and explore their stability. We show that both bed friction and bed slope contribute to the stability of this flow configuration, which otherwise would be unstable. Results of the theoretical model are compared to both experimental data and the results of numerical simulations, and the comparison confirms the reliability of the proposed model. We also show that channel flow through a linear contraction can experience two different nested hysteretic loops
Extended theory of hydraulic hysteresis in open channel flow
Get PDFThe occurrence of hysteresis in a supercritical, open-channel flow approaching an obstacle has been recognized and investigated both experimentally and theoretically over the last few decades. However, the available theory and experimental investigations in the literature do not include the case when subcritical flow, controlled from downstream, can establish across the obstacle. The present work fills this gap by proposing a new theory that includes this occurrence and shows that two different steady flow states can establish for the same obstacle geometry and flow conditions—one with supercritical to subcritical transition far downstream from the obstacle, and the other with supercritical to subcritical transition far upstream from the obstacle. The proposed, more general theory includes the existing theory as a special case. Finally, two specific examples are illustrated and discussed, i.e., the case of flow over a raised bed hump, and the case of flow through a channel contraction
Multiple states in the flow through a sluice gate
Get PDFThis paper addresses the problem of hydraulic hysteresis for a supercritical open channel flow approaching a sluice gate when subcritical flow can establish downstream, against the gate. The possible flow configurations across the gate are classified on the basis of the Froude number of the incoming and downstream flows, and of the ratio of gate opening to the upstream supercritical flow depth. Within the above parameter space, two regions exist in which the problem admits a dual solution, that is, two different flow configurations can establish for the same gate opening and undisturbed flow conditions. In one of these regions, both smooth flow (i.e. the fluid flows under the gate without interacting with the gate) and free outflow conditions can establish; in the other region, both smooth flow and submerged flow can establish. For flow conditions in the above regions, the configuration that actually establishes depends on the previous history of the flow, thus implying the hysteretic character of the flow
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