3D particle tracking velocimetry and statistical analysis of turbulent pipe flow

Abstract

Air pollution and industrial mixing processes are just two examples of processes in which dispersion of particles in turbulent flows is of importance. Particle dispersion can be described by means of stochastic models. For most practical flow geometries, knowledge of Lagrangian flow statistics is necessary to determine the coefficients present in such models. Because numerical methods are either too inaccurate or limited to low Reynolds numbers, this thesis looks at the possibility of determining these model coefficients by means of experiments. An inhomogeneous turbulent flow is generated in a pipe geometry and the Lagrangian experimental technique 3D particle tracking velocimetry (3D PTV) is used to determine Lagrangian velocity statistics. An experimental set-up for 3D PTV measurements in turbulent pipe flow is designed. Important design parameters and the final design are discussed. 3D PTV experiments are carried out at two moderate Reynolds numbers. Special care has to be taken to ensure correct analysis of the measured particle tracks. Two possible particle sampling methods to avoid biased statistics are presented. To our knowledge, no experimentally determined Lagrangian statistics are available in literature for turbulent pipe flow. Furthermore, the only numerical Lagrangian results are those generated by the DNS code of Veenman as presented in [56, 62]. Eulerian as well as Lagrangian 3D PTV results are compared with results from literature and all compared quantities show good agreement. A stochastic model for particle velocity is presented for the case of turbulent pipe flow, regarding the particle acceleration as a Markov process. In this way, the model neglects viscosity effects and is therefore not able to resolve the small scale effects of low Reynolds number flow. It is, however, asymptotically exact for infinitely high Reynolds numbers. The model coefficients, being the Kolmogorov constant and damping coefficients, are determined from 3D PTV and DNS results. The model results are in agreement with the available experimental and DNS results at the moderate Reynolds numbers presented in this thesis. For Lagrangian results, this agreement is restricted to times much larger than the Kolmogorov time as a result of the Markovian assumption. As most practical examples of turbulent flows, as well as the validity of the presented model, are restricted to high Reynolds numbers, the real challenge is to obtain model coefficients at high Reynolds numbers. Upper Reynolds numbers limits for the experimental method are discussed and suggestions on how to raise these limits for the current geometry are given.