In pressurized water reactors (PWRs), steam generators play a critical role in transferring heat between the primary and secondary circuits. Partial blockage of the spacer grid foliage within the tube bundle can significantly increase pressure losses, particularly in the upper two-phase region where void fraction is high. Under transient operating conditions, such clogging may amplify depressurization and lead to oscillations in reactor control parameters. These oscillations are associated with the propagation of two-phase density waves within the heated region, a well-known mechanism of hydrodynamic instability. This work focuses on Type II density wave oscillations, which are primarily driven by frictional effects and are identified as the dominant instability mechanism in clogged steam generators. The study builds upon system-scale numerical simulations previously conducted using the CATHARE 3 thermal-hydraulic code. Within the framework of an industrial PhD, the objective is to establish a rigorous mathematical foundation to support and interpret these numerical observations. A simplified physical model of a vertical heated channel operating under forced convection is introduced. The two-phase flow is described using averaged conservation equations for mass, momentum, and energy. To reduce computational complexity, a reduced-order model is derived, leading to a system of ordinary differential equations governing the evolution of the boiling front position, an auxiliary dynamic variable, and the inlet flow velocity. The system behavior depends on several dimensionless design and operating parameters, including phase-change, subcooling, friction, and Froude numbers. The research program aims to conduct a detailed bifurcation analysis, with particular emphasis on the identification and characterization of Hopf bifurcations responsible for the onset of self-sustained oscillations. A second objective is to establish theoretical links between reduced-order models and the full two-fluid equations implemented in CATHARE. Ultimately, this work seeks to improve the predictive capability of thermal-hydraulic models for clogged steam generators.