Dimensionless Scaling and Prediction of Vortex Tube Temperature Separation

Abstract

Ranque–Hilsch vortex tubes split an incoming fluid stream into two outgoing streams: one with a higher total temperature than the incoming fluid and the other with a lower total temperature. This 90-year-old device accomplishes its temperature separation with no moving parts and no external power sources, and despite a diversity of extant theories regarding the underlying mechanism, it is clear that a rapidly swirling flow inside the tube is key to its operation. While many parametric studies have characterized the degree of temperature separation as a function of a host of variables (e.g., inlet pressure, inlet temperature, working gas, tube geometry), no previous effort has identified the governing nondimensional parameters that would simplify further characterization. In the present work, we nondimensionalize the energy equation as it applies to Ranque–Hilsch vortex tubes and identify the governing nondimensional parameters and nondimensional dependent variables. The governing nondimensional parameters are shown to be the Reynolds number, the Péclet number, and a lesser-known nondimensionalization of the Joule–Thomson coefficient, . To discern the dependence of temperature separation on these nondimensional parameters, experimental data were analyzed. We show that a unique dimensionless form of the product of the total temperature, density, and specific heat collapses across a wide range of the aforementioned governing nondimensional parameters, although some dependence remains evident, particularly in the case of , for which an extremely wide range of values were obtained through comparison of carbon dioxide with air. A method is demonstrated to predict temperature separation for new cooling scenarios, reducing the experimental burden for new applications.