A Navier-Stokes-Based Validity Framework for Linear and Nonlinear Transient Pressure-Wave Modeling in Spacecraft Pumped-Fluid Loops
Abstract
Transient pressure disturbances in spacecraft pumped-fluid loops are commonly represented by linearized one-dimensional models, yet the error introduced by linearization is rarely quantified against a nonlinear formulation derived from the same conservation laws. This study develops a Navier-Stokes-based validity framework for single-phase spacecraft pumped-fluid loops. Mass conservation and axial momentum balance for a slightly compressible Newtonian liquid are reduced to coupled pressure-velocity equations that retain convective inertia and flow-regime-dependent wall friction. A consistent linear model is obtained by perturbation about a nonzero steady circulation state. The equations are solved with fourth-order spatial differencing and classical fourth-order Runge-Kutta integration. Verification against an exact smooth nonlinear characteristic solution gives the designed fourth-order convergence, with relative error decreasing to 2.72×10⁻¹⁰ at 800 grid points, and the nonlinear solution recovers the moving-base linear limit as the acoustic Mach number tends to zero. Two spacecraft-informed applications are examined: a turbulent HFE-7200 external thermal-control loop and a laminar 50/50 propylene-glycol/water internal loop. For a 20% smooth pump disturbance, the global linear-versus-nonlinear pressure discrepancies are 0.0667% and 0.0116%, respectively, with peak transient pressure excursions of approximately 74.8 and 13.6 kPa. Even at the largest tested disturbance amplitude (45%), the discrepancies remain 0.1481% and 0.0260%. A broader dimensionless map shows that errors above 1% require simultaneously larger acoustic Mach number and disturbance amplitude, while the 5% threshold in the tested turbulent family appears only near M ≳ 0.08 with strong forcing. The results show that the consistent linear model is quantitatively sufficient for the representative low-Mach spacecraft loops studied, while the nonlinear formulation provides a verified criterion for identifying conditions under which that simplification ceases to be adequate.