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Geometries containing a narrow gap are characterized by strong quasi-periodical flow oscillations in the narrow gap region. The above mentioned phenomena are of inherently unstable nature and, even if no conclusive theoretical study on the subject has been published, the evidence shown to this point suggests that the oscillations are connected to interactions between eddy structures of turbulent flows on opposite sides of the gap. These coherent structures travel in the direction of homogeneous turbulence, in a fashion that strongly recalls a vortex street. Analogous behaviours have been observed for arrays of arbitrarily shaped channels, within certain range of the geometric parameters. A modelling for these phenomena is at least problematic to achieve since they are turbulence driven. This work aims to address the use of Proper Orthogonal Decomposition (POD) to reduce the Navier–Stokes equations to a set of ordinary differential equations and better understand the dynamics underlying these oscillations. Both experimental and numerical data are used to carry out the POD.

In this document, the proof of the existence of an infinite prime flow, by showing that a Proximal Orbit Dense flow is prime, is examined. This proof has been given by Furstenberg, Keynes and Shapiro in the year 1973. This document investigates this proof thoroughly, as it is quite intricate and it requires a proficient amount of theory. As a side result, an improvement has been found on the Mean Ergodic Theorem. Moreover, proximal orbit dense flows are disjoint from other prime flows.

Because of their high efficiency and their ability to provide high heat transfer rates, impinging jets are applied for rapid cooling and heating in a wide variety of industrial processes. However, the physical phenomena controlling the heat transfer from impinging jets are to a large degree unknown. The goal of the present project was to gain a better understanding of the interaction between the flow and heat transfer in impinging jet arrays. Experiments were performed in two different configurations: a single impinging jet and multiple impinging jet arrays. LDA and PIV velocity measurements in the single jet were compared: these measurements were aimed at serving as a reference for comparison of the multiple jet features. In a hexagonal and an in-line array of jets PIV was used to provide instantaneous velocity fields over the flow area of interest, what proved to be essential for detecting some salient features of the multiple-jet dynamics. These dynamics were investigated on the basis of POD filtered snapshots of the flow. In both arrays, large scale eddies in the development zone cause the impinging jets to break up or be severely displaced in the out-of-plane direction. A horse-shoe vortex appears around the outer jets of the hexagonal array, whereas the in-line array does not show this feature. This is most likely caused by the higher pitch in the in-line configuration. On the other hand, the flow field in the in-line arrangement appears to be diagonally asymmetrical, even though the symmetry of the nozzle arrangement would imply a symmetrical flow field. This flow asymmetry causes an elliptical heat transfer pattern in the impingement zone of the center jet. The flow asymmetry was also found in numerical simulations of a similar configuration, conducted in a parallel project. Heat transfer measurements were performed in the impingement surface for seven multiple jet arrays using LCT, which provided insight in the influence of different geometrical parameters of the arrays on the heat transfer. Additionally, a non-dimensional correlation was derived linking heat transfer to geometrical and flow parameters. Heat transfer profiles were subsequently compared to velocity and turbulence quantities just above the impingement plate to investigate the effect of the mean flow features on the heat transfer. The apparent correlation between the Nusselt number and the normal contribution to the production of turbulent kinetic energy is coincidental: the cause of the increased Nusselt number in the impingement points of the jets is a combination of an oscillating impingement position due to large vortical structures and a very strong acceleration of the fluid from the impingement point outwards. In the impingement point the boundary layer is very thin and the temperature gradient is very steep, enabling impinging vortices to encapsulate and remove heat in an effective way. The results presented in this thesis should aid in better understanding the role of turbulence and vortical structures in the interaction between adjacent impinging jets, and in the heat transfer from impinging jets. With the advent of a measurement technique capable of capturing instantaneous heat transfer distributions, a potential extension of the present work is a more detailed analysis of the influence of individual vortical structures on impingement heat transfer.