On the Interaction between vortex-induced vibrations and galloping in rectangular cylinders of low side ratio Dissertation VXEPLWWHGWRDQGDSSURYHGE\WKH 'HSDUWPHQWRI$UFKLWHFWXUH&LYLO(QJLQHHULQJDQG(QYLURQPHQWDO6FLHQFHV 8QLYHUVLW\RI%UDXQVFKZHLJ±,QVWLWXWHRI7HFKQRORJ\ DQGWKH 'HSDUWPHQWRI&LYLODQG(QYLURQPHQWDO(QJLQHHULQJ 8QLYHUVLW\RI)ORUHQFH LQFDQGLGDF\IRUWKHGHJUHHRID Doktor-Ingenieur (Dr.-Ing.) / Dottore di Ricerca in Processes, Materials and Constructions in Civil and Environmental Engineering and for the Protection of the Historic- Monumental Heritage*) E\ 7RPPDVR0DVVDL ERUQ IURP%DJQRD5LSROL ), ,WDO\ 6XEPLWWHGRQ 2UDOH[DPLQDWLRQRQ 3URIHVVRULDODGYLVRUV 3URI*LDQQL%DUWROL 3URI.ODXV7KLHOH 2016 (LWKHUWKH*HUPDQRUWKH,WDOLDQIRUPRIWKHWLWOHPD\EHXVHG Statement of Originality I, Tommaso Massai, the undersigned, declare that this thesis and the material presented in it are, to the best of my knowledge and belief, original and my own work and contains no material previously published or written by another person, except where due reference is made in the text of the thesis. I confirm that: ● The work was done during candidature for the research degree at the International PhD between the University of Florence and the Technische Universit¨at Carolo- Wilhelmina zu Braunschweig. ● Where I have consulted the published work of others, it is clearly attributed. ● Where I have quoted from the work of others, the source is always given. ● I have mainly used Open-Source Software and they are cited within the dissertation; where I have used proprietary software they are declared and covered by license under my Institutions. ● I have acknowledged all sources of help. ● Where the thesis is based on work done by myself jointly with others, the contributions by each party are attributed. Signed: Date: i Abstract On the Interaction between vortex-induced vibrations and galloping in rectangular cylinders of low side ratio by Tommaso Massai The present work deals with the interaction between vortex-induced vibrations (VIV) and galloping for rectangular cylinders of low side ratio, which is defined as the body width on the body depth facing the fluid flow (SR = B/D). In particular, the interaction mech- anism has been characterized for a wide range of Reynolds numbers (Re)andmassratios (m∗), aiming to provide a complete description of the response in several flow situations (smooth and turbulent, air and water) for bodies which exhibited, or were known to have, a pronounced proneness to this type of instability. This type of flow-induced vibrations (FIV) phenomenon occurs for particular combinations of both aerodynamic and dynamic characteristics of a system. The present study consists in two main parts, both of them aimed at proposing a complete framework for scientific and designing purposes. The first one investigates the phenomenon occurring in sectional models purposely designed and experimentally tested. Therefore, the experimental activity has been dichotomously carried out in air- and water flow to characterize two different ranges of m∗ and Re for smooth flow, while turbulent measures were performed in wind tunnel only. It is worth noting that for SR = 1.5and0.67 such a low m∗ range has never been investigated. Then, the second part is devoted to the implementation of a predictive model for the interaction, implying also further experimental measures to assess the model key-parameter. Despite extensive works have been already undertaken in the study of the interaction mech- anism, there are still many issues to fully comprehend the variety of responses exhibited by different low SR cross-sections, in turns characterized by different properties related to flow regimes and system dynamics. Several sectional models of a SR = 1.5 have been tested given that this section demonstrated to be particularly prone to the interaction between VIV and galloping. Nevertheless, the majority of former literature investigations were per- formed on the square section. The response features of such a phenomenon are still not fully understood. In order to have a deeper insight and to give a comprehensive description of the interaction, the present investigation was conducted focusing particularly on the SR = 1.5 rectangular section: this is a soft oscillator respect to the incipient instability, while the same rotated section with an angle of attack α = 90○,thatisSR = 0.67, is generally re- ferred to as a hard-type one. Results in air flow showed peculiar amplitude response curves differently shaped depending on Re, m∗ and corners sharpness accuracy; in some cases the arise of a super-harmonic resonance at one third of K´arm´an-resonance velocity has been observed, in agreement with literature. Turbulent flow measurements showed a delayed onset for galloping instability, either interacting with vortex-shedding or not, suppressing the response for high turbulence intensity and integral length scale. Results in water flow showed the response in amplitude and frequency to be strongly influenced by the abrupt change of m∗, recalling the different responses in air- and water flow regime reported in literature for a circular cylinder, though related to VIV only. The afterbody has a remarkable effect too, as SR = 0.67 shows a completely different response, although remaining, differently from air flow measurements, a soft oscillator. Further tests on m∗ variation constituted an integration for the data so far available in literature about these sections. ii Finally, although big efforts have been done in assessing the sensitive parameter of the cho- sen model for the interaction, numerical results have been not satisfying, showing a good capability for the model to predict the instability onset, though exhibiting also a poor ac- cordance between modelled stable amplitudes and experimental values in the post-critical branch. Sommario La tesi tratta dell’interazione fra vibrazioni indotte da distacco di vortici (VIV) e galoppo in corpi a sezione rettangolare con basso il rapporto fra i lati (SR = B/D). In particolare il fenomeno dell’interazione `e stato caratterizzato in un vasto range relativo al numero di Reynolds (Re) e fattore di massa (m∗), con lo scopo di fornire una descrizione com- pleta della risposta in qualsiasi condizione di flusso (laminare e turbolento, aria ed acqua), per quei corpi caratterizzati da una spiccata tendenza a questo tipo di instabilit`a. Tale fenomeno si manifesta per paricolari combinazioni di caratteristiche dinamiche ed aerodi- namiche del sistema. Il lavoro consta di due parti, entrambe concorrenti nella formulazione di un quadro utile per scopi sia scientifici sia progettuali. La prima relativa alla sperimen- tazione su modelli sezionali, appositamente progettati e testati in laboratorio: l’attivit`a sperimentale `e stata suddivisa in prove in aria ed acqua, per cos`ı caratterizzare due distinti intervalli di fattori di massa e Re, aventi ordini di grandezza diversi, in flusso laminare, mentre misure in flusso turbolento sono state eseguite solo in galleria del vento. In seguito, una seconda parte descrive l’implementazione di un modello predittivo per l’interazione, che ha comportato la necessit`a di effettuare ulteriori test di laboratorio per determinare il parametro fondamentale del modello. Nonostante la vasta letteratura al riguardo, ci sono ancora molte questioni aperte nel tenta- tivo di chiarire completamente la variet`a di tipi di risposta, osservata per differenti sezioni rettangolari, caratterizzata a sua volta da diversi propriet`a dinamiche e tipologie di flusso. Data la straordinaria predisposizione all’interazione tra distacco di vortici e galoppo per il rettangolo con SR = 1.5, sono stati testati diversi modelli sezionali del medesimo per cercare di descrivere al meglio il fenomeno, considerando anche i molti studi sperimentali, numerici e teorici gi`a pubblicati sulla sezione quadrata; tale sezione `e ben nota per essere un oscillatore soft rispetto all’incipiente instabilit`a, mentre la stessa sezione ruotata per un angolo di attacco pari a α = 90○,cio`e SR = 0.67, `e generalmente considerato un oscil- latore hard. I risultati ottenuti in galleria del vento hanno mostrato diversi tipi di curve di risposta che cambiano dipendentemente dal modello sezionale utilizzato; talvolta `e stato osservato il manifestarsi di una risonanza super-armonica ad un terzo della velocit`acritica di risonanza. Misure in flusso turbolento hanno messo in luce un ritardo nella velocit`adi innesco dell’instabili`a, sia in regime di interazione con VIV sia di galoppo, sopprimendo le vibrazioni per alti valori di intensit´a di turbolenza e scala integrale. Negli esperimenti in canaletta si `e registrata una risposta in ampiezza e frequenza molto influenzata dal valore completamente differente di m∗, ricordando una simile differenza ri- portata per il cilindro circolare nel passaggio fra test in aria e acqua, sebbene per questo solo la risposta in distacco di vortici sia possibile. Anche l’effetto del retrocorpo `e risultato molto marcato, dal momento che il rettangolo con SR = 0.67 risponde in maniera comple- tamente diversa, tuttavia rimanendo un oscillatore soft, diversamente da quanto accade in flusso d’aria. Ulteriori test sulla variazione del fattore di massa hanno colmato vuoti di letteratura per queste sezioni rettangolari, a valori molto bassi di quest’ultimo, fin’ora mai sperimentati. Infine, nonostante sia stata dedicata una notevole cura nella determinazione sperimentale dei parametri cui il modello `e sensibile, i risultati finali non sono soddisfacenti, mostrando una