Two topics from nuclear engineering field are included in this dissertation. One study is the air-ingress phenomenon during a loss of coolant accident (LOCA) scenario, and the other is a 5-by-5 bundle assembly problem under a design of PWRs. The objectives are to investigate the Kelvin-Helmholtz instability of the gravity-driven stratified flows inside a coaxial pipe and the effects caused by two types of spacers at the downstream of the rod bundle problem. Richardson extrapolation is used for the grid independent study. Simulation results give good agreements with the experiments. Wavelet analysis and Proper Orthogonal Decomposition (POD) are used to study the flow behaviors and flow patterns. For the air-ingress phenomenon, Brunt-Vaisala frequency, or buoyancy frequency, predicts a frequency of 2.34 Hz, which is confirmed by the dominant frequency of 2.4 Hz obtained from the wavelet analysis between times 1.2 s and 1.85 s. For the rod bundle study, the dominant frequency at the center of the subchannel is given as 2.4 Hz with a secondary dominant frequency of 4 Hz and a much minor frequency of 6 Hz. Generally, wavelet analysis has much better performance than POD in the air-ingress phenomenon that is a strongly transient scenario; they both appropriate for the rod bundle study. Based on this study, when the fluid pair in a real condition is used, the time which air intrudes into the reactor is predictable.
