A DAE-based quasi-1-D numerical framework for analysis of regenerative cooling channel in liquid rocket engines

Regenerative cooling channel (RCC) analysis is crucial for the design and parametric study of liquid rocket engines (LREs), requiring computational methods that are both accurate and efficient, covering both supercritical and subcritical two-phase flows. This paper presents a novel quasi-1-D numerical framework based on a differential-algebraic equations (DAEs) formulation for the coupled thermal–hydraulic analysis of RCCs. The framework selects pressure and specific enthalpy as the primary solution variables, proven to be optimal for this coupled problem, to ensure consistency and numerical stability across all flow regimes. This unified formulation enables the use of an identical numerical procedure from the liquid and supercritical states through the two-phase region to the gaseous state. It avoids the accuracy degradation and excessive iterations associated with traditional methods that rely on tracking variables like specific heat or latent heat to handle phase change. A Runge-Kutta method extended for DAEs is employed for efficient solution. The model is validated against the example of the Space Shuttle Main Engine (SSME) Main Combustion Chamber (MCC), demonstrating good agreement with reference data. Numerical tests reveal that second-order methods provide an optimal balance between cost and accuracy for global parameters (temperature increase, pressure drop), even on coarse grids. The framework is further applied to a LOx/LCH4 engine case at subcritical pressure involving methane boiling, successfully capturing two-phase heat transfer characteristics without numerical instability. The proposed method offers a unified, efficient, and reliable tool for RCC performance prediction, particularly suited for preliminary design and system-level studies of LREs.