Moving-Boundary Model of Cryogenic Fuel Loading, II: Theory Versus Experiments

Abstract

A moving-boundary model of two-phase cryogenic flow, which was developed in the companion paper (Hafiychuk, V., Foygel, M., Ponizovskaya-Devine, E., Smelyanskiy, V., Watson, M., Brown, B., and Goodrich, C., "Moving-Boundary Model of Cryogenic Fuel Loading, I: Two-Phase Flow in a Long Pipe," Journal of Thermophysics and Heat Transfer (to be published)), is applied toward simulation of liquid nitrogen flow data collected for the cooldown regime in two different experimental fuel transfer lines: 1) the 1966 National Bureau of Standards (now the National Institute of Standards and Technology) setup and 2) the novel NASA Kennedy Space Center cryogenic testbed. With relatively small computational effort compared to full-scale schemes, the model describes pressure and temperature histories, kinetics of the vapor void fraction, and interphase boundary motion in two different parts of the transfer lines. The aforementioned time-dependent characteristics are shown to be in a good agreement with the experimental data on the cooldown stage of liquid nitrogen loading obtained at the National Bureau of Standards setup (with no fitting parameters used) and in a fair agreement with the NASA Kennedy Space Center testbed setup (with a small fitting) for chilldown and fast fill operations. The fast and accurate modeling procedure accounts for cryogen fueling operations in both the nominal and major fault regimes. Nomenclature A = internal cross-sectional area of pipe, nozzle, or vent valve, m 2 C = constant pressure (volume) specific heat, J∕K∕kg D = diameter of pipe, m t = time, s κ = thermal conductivity, W∕m · K ρ = density, kg∕m 3Subscripts O = outer vent = vent w = tube wall

Hierarchy of two-phase flow models for autonomous control of cryogenic loading operation

“…An extensive numerical testing revealed that this can be done e.g. by adding to the hierarchy homogeneous moving-boundary quasi-steady model of two-phase cryogenic flow [16,17] as will be discussed below.…”

“…To speed up integration of the model [16,17] the momentum equation is solved in the quasisteady approximation, neglecting inertia terms ( () ,z denote spatial derivative)…”

“…The integration of the HM is described in details in [16]. The solution of the HM was substantially sped up by using quasi-steady approximation [16] that allows to decouple calculations of the mass fluxes from the integration of the conservation equations for the mass and energy. The resulting algorithm is using only the two first sub-steps of the SM algorithm described above and explicit Euler time stepping.…”

“…Both models were extensively verified using a number of numerical tests [17,27] and comparison with results obtained using SINDA/FLUINT model of the transfer line [28]. The models were validated by comparison with real data obtained during chilldown of a cryogenic transfer at National Bureau of Standards (NBS) [29] and those from the cryo-testbed at KSC [3].…”

“…We have coded and tested a number of solvers for this hierarchy that include quasi-steady homogeneous moving front [16,17], semi-implicit and nearly-implicit [4] solvers for homogeneous and separated cryogenic flow.…”