Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.

STUDY OF A DIRECT SAMPLING METHOD FOR THE INVERSE MEDIUM SCATTERING PROBLEM

Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.

MEASURING HEAD IMPACT CONTACT PRESSURE IN COLLEGIATE FOOTBALL GAMES TO CORRELATE HEAD KINEMATICS TO BRAIN KINETICS ELUCIDATING BRAIN INJURY DYNAMICS

Does a brain store thoughts and memories the way a computer saves its files? How can a single hit or a fall erase all those memories? Brain Mapping and traumatic brain injuries (TBIs) have become widely researched fields today. Many researchers have been studying TBIs caused to adult American football players however youth athletes have been rarely considered for these studies, contradicting to the fact that American football enrolls highest number of collegiate and high-school children than adults. This research is an attempt to contribute to the field of youth TBIs. Earlier studies have related head kinematics (linear and angular accelerations) to TBIs. However, fewer studies have dealt with brain kinetics (impact pressures and stresses) occurring during head-on collisions. The National Operating Committee on Standards for Athletic Equipment (NOCSAE) drop tests were conducted for linear impact accelerations and the Head Impact Contact Pressures (HICP) calculated from them were applied to a validated FE model. The results showed lateral region of the head as the most vulnerable region to damage from any drop height or impact distance followed by posterior region. The TBI tolerance levels in terms of Von-Mises and Maximum Principal Stresses deduced for lateral impact were 30 MPa and 18 MPa respectively. These levels were corresponding to 2.625 feet drop height. The drop heights beyond this value will result in TBI causing stress concentrations in human head without any detectable structural damage to the brain tissue. This data can be utilized for designing helmets that provide cushioning to brain along with providing a resistance to shear.

SAMPLING BIAS IN EVALUATING THE PROBABILITY OF SEISMICALLY INDUCED SOIL LIQUEFACTION WITH SPT & CPT CASE HISTORIES

Several deterministic and probabilistic methods are used to evaluate the probability of seismically induced liquefaction of a soil. The probabilistic models usually possess some uncertainty in that model and uncertainties in the parameters used to develop that model. These model uncertainties vary from one statistical model to another. Most of the model uncertainties are epistemic, and can be addressed through appropriate knowledge of the statistical model. One such epistemic model uncertainty in evaluating liquefaction potential using a probabilistic model such as logistic regression is sampling bias. Sampling bias is the difference between the class distribution in the sample used for developing the statistical model and the true population distribution of liquefaction and non-liquefaction instances. Recent studies have shown that sampling bias can significantly affect the predicted probability using a statistical model. To address this epistemic uncertainty, a new approach was developed for evaluating the probability of seismically-induced soil liquefaction, in which a logistic regression model in combination with Hosmer-Lemeshow statistic was used. This approach was used to estimate the population (true) distribution of liquefaction to non-liquefaction instances of standard penetration test (SPT) and cone penetration test (CPT) based most updated case histories. Apart from this, other model uncertainties such as distribution of explanatory variables and significance of explanatory variables were also addressed using KS test and Wald statistic respectively. Moreover, based on estimated population distribution, logistic regression equations were proposed to calculate the probability of liquefaction for both SPT and CPT based case history. Additionally, the proposed probability curves were compared with existing probability curves based on SPT and CPT case histories.