Experiments on transition regime flow through a short tube with a bellmouth entry.

Abstract

Experiments were conducted to determine the mass flow rate and longitudinal pressure distribution along a short tube with a bellmouth entry for conditions ranging from free molecule to continuum. The tube has an inside diameter of 0.452 in., and the radius of the bellmouth entry is 0.75 in. The ratio of upstream stagnation pressure to downstream stagnation pressure was varied from 1.5 to more than 100. As the conditions departed from continuum toward free molecule, the effect of over all pressure ratio became quite pronounced until at free molecule conditions the effect was that predicted by Clausing. The transition could be seen in the pressure distribution (relatively flat under continuum conditions and linear between the two reservoir pressures under free molecule conditions) and in the mass flow (the discharge coefficient decreases rapidly until it reaches a constant under free molecule conditions). The Reynolds numbers of the tests ranged from 0.1 to 1500 and the pressures from 10 IJL to 10 mm. Nitrogen at 300°Kwas the test gas. Nomenclature A = cross-sectional area of tube CD = discharge coefficient D = diameter of tube m = mass flow P = pressure Q • =F a quantity related to mass flow being a product of pressure and volumetric flow rate Qc = value of Q according to the theory of Clausing Rex = Reynolds number based on length RBD ~ Reynolds number based on diameter T = temperature U = gas velocity X — longitudinal distance from beginning of constant area tube X = mean free path length v = kinematic viscosity p = density X = dynamic viscosity; also used as an abbreviation for microns of mercury