Liquid Helium Turbulent Pipe Flow and Magnetic Levitation Research

Liquid helium-4 undergoes a phase transition below about 2.17 K where it is called the superfluid (He II). He II is a non-classical fluid which is one of the very few macroscopic manifestation of the quantum mechanics. He II entails several bizarre properties including an extremely low kinematic viscosity. Due to this, He II has been proposed as an exceptional working fluid for turbulence research. The primary goal of the current thesis is to design a pioneering experiments to investigate the possibility and potential non-classical behavior of a law of the wall scaling in turbulent He II pipe flow. Here we report assembling a 5-m long He II flow facility so-called Liquid Helium Flow Visualization Facility which can generate He II turbulent flows with Reynolds numbers ($Re$) larger than a million. Inside an optically-accessible square flow pipe of $2 \times 2$ cm$^2$ cross-section, we generate fully-turbulent He II forced flows using an automated bellows-linear actuator pump. We also report the incorporation of a quantitative flow visualization technique called molecular tagging velocimetry (MTV) using metastable triplet helium molecules as tracers. This visualization technique is based on a combination of a femtosecond laser-field ionization together with a 905-nm laser-induced fluorescence scheme to generate and illuminate the metastable helium molecules, respectively. We have designed and implemented a novel optical system to guide and satisfy the optical criteria for visualization of He II. Using this one-of-a-kind facility, we report the first quantitative flow visualization study of the law of the wall in He II turbulent pipe flow. We acquire the mean velocity profile near the wall region using a robust image processing algorithm, specifically developed for the type of images we acquire in our flow pipe and we compare it with the existing data in classical fluid research. Our data shows the existence of a logarithmic profile of "the near-wall mean velocity profile in turbulent pipe flow (NVP) in He II". By fitting the velocity profile using the law of the wall formula, we determined the two fitting coefficients including the von K\'arm\'an coefficient $\kappa$ and the additive constant $B$ in He II. We also conducted a comprehensive uncertainty analysis of data to evaluate the associated error. It turns out $\kappa=0.160\pm 0.015$ and $\kappa=0.154\pm 0.010$, and $B=-23.2\pm 0.4$ and $B=-24.0\pm 0.4$ for $Re_D=1.01\times 10^6$ and $Re_D=1.21\times 10^6$, respectively. On the other hand, the values of these two constants in classical turbulent pipe flow are determined about $\kappa=(0.37-0.42)$ and $B=(4-6)$. This significant difference suggests that the non-classical properties of He II affects the velocity profile in extremely high $Re$ He II pipe flow. This deviation from classical turbulence is of great significance for future numerical research as well as engineering designs of the He II pipe systems.