Cool-down of a vertical line with liquid nitrogen

Abstract

Analytical and numerical modeling is presented for predicting the thermofluid parameters of the cool-down process of an open-to-air vertical tube carrying liquid nitrogen. A two-fluid mathematical model is employed to describe the flowfield. In this model four distinct flow regions were analyzed: 1) fully liquid, 2) inverted annular film boiling, 3) dispersed flow, and 4) fully vapor. These flow regimes were observed in an experimental investigation constructed for validating the mathematical model, and also in previous experiments by other investigators. For the single-phase regions, the one-dimensional form of mass, momentum, and energy equations were used. For the two-phase regions, the volume-averaged, phasic one-dimensional form of conservation equations were applied. The one-dimensional energy equation was formulated to determine the tube wall temperature history. The numerical procedure is based on the semi-implicit, finite-difference technique. The calculations for the inverted annular film boiling were performed implicitly. The computations for the tube wall, fully liquid, and dispersed flow regions were performed explicitly. In each region, the appropriate models for heat transfer and shear stress rates are used. Results and comparisons of the predicted numerical models with the experimental data for several constant inlet flow rates of liquid nitrogen into a vertical, insulated tube are presented. Nomenclature Aw = cross-sectional area of the flow channel, m2 cp = specific heat capacity, J/kg °C Da = area-averaged, population-mean diameter of drops, m ALix = maximum entrainable diameter of drops, m £&ax = maximum stable diameter of drops, m Dsmd = Sauter mean diameter of a droplet population, m Dv = volume averaged, population-mean diameter of drops, m d = diameter of the flow channel, m g = local acceleration of gravity, m/s2 h = enthalpy, J/kg hc = convective heat transfer coefficient, W/m2 °C hnb = heat transfer coefficient for nucleate boiling, W/m2 °C ^,sat = saturation enthalpy of either liquid or vapor, J/kg k = thermal conductivity, W/m °C Lfg = latent heat of vaporization, J/kg m' = interfacial mass transfer rate, kg/m3s q = heat flux per unit area, W/m2 q' = heat transfer rate per unit volume, W/m3 <7evaP - vaporization heat flux, W/m2 #rad = wa ^ to liquid radiation, W/m2 q% = vapor to drop radiation heat flux, W/m2 q^d = wall to drop radiation heat flux, W/m2 q'^v = wall to vapor radiation heat flux, W/m2 Pi = inner perimeter of tubular flow channel, Pr = Prandtl number, cpiji/kl p = pressure, N/m2 m