A Reinterpretation of the Results of the Moby Dick Experiments in Terms of the Nonequilibrium Model

Abstract

The topological pattern of the set of measured pressure distributions included in the Moby Dick series of experiments on critical flow through a slender channel provided with a throat does not agree with that expected on the basis of the rigorous mathematical theory which predicts the appearance of a singular point, most likely, of a saddle point at or near the throat. This is considered to be paradoxical. The paper provides an alternative interpretation of these results. The Moby Dick experiments have clearly demonstrated the profound influence of the existence of metastable conditions near the flash point. For this reason, among others, the paper undertakes a re-evaluation of some of the Moby Dick results in terms of the nonequilibrium model first suggested by L. J. F. Broer in 1958 for use in flows of chemically reacting gases. Since the Moby Dick data contain measurements of the distribution α(z) of void fractions, it becomes possible to calculate local relaxation times, θ[α(z)], and so to close the system of differential equations of the model. Extensive numerical calculations reproduce the measured pressure distributions with an error of 6–10 percent at most. More importantly, the topological features of the calculated pressures, Pth(z), turn out to be identical with the measured ones, Pex(z). The most important, and totally unexpected, result is that the flow in the Moby Dick channel remained subcritical everywhere. In particular, the channel was not choked at the throat. Since the mass-flow rates were independent of back-pressure, it is concluded that the flows were choked at or near the exit. The paper advances additional reasons for the feasibility of this alternative interpretation, but emphasizes and re-emphasizes its provisional nature.