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Viero, Daniele Pietro (2010) Riflessione di fronti d'onda onda stazionari di altezza finita in correnti a superficie libera. [Tesi di dottorato]

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Abstract (inglese)

When 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.

Abstract (italiano)

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.

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Tipo di EPrint:Tesi di dottorato
Relatore:Defina, Andrea
Dottorato (corsi e scuole):Ciclo 22 > Scuole per il 22simo ciclo > SCIENZE DELL'INGEGNERIA CIVILE E AMBIENTALE
Data di deposito della tesi:NON SPECIFICATO
Anno di Pubblicazione:29 Gennaio 2010
Parole chiave (italiano / inglese):Fronti d'onda, Riflessione di fronti d'onda, Paradosso di von Neumann, Correnti supercritiche, Convergente lineare, Isteresi, Stabilità  del risalto idraulico
Settori scientifico-disciplinari MIUR:Area 08 - Ingegneria civile e Architettura > ICAR/01 Idraulica
Struttura di riferimento:Dipartimenti > pre 2012 - Dipartimento di Ingegneria Idraulica, Marittima, Ambientale e Geotecnica
Codice ID:2828
Depositato il:05 Nov 2010 11:42
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