ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Swirling flows have a wide range of applications and exhibit a variety of interesting features. Gas cooling near the axis in these flows, the so-called Ranque–Hilsch effect, is one of them. To gain insight into this phenomenon, we have analyzed the thermal, near-axis boundary layer of a gas jet driven by a class of conical inviscid quasi-incompressible flows whose axial and azimuthal velocity components, w and v, and stagnation temperature, Tt, behave near the axis as w=W0rm−2,v=LW0rm−2, and Tt−Tr=T0r2(m−2), where z and r are the axial and radial coordinates, L is the Squire number directly related to the swirl strength, m is any real number such as 1≤m〈2, Tr is a reference temperature, and W0 and T0 are arbitrary dimensional constants; W0 is assumed to be positive while T0 may be either positive or negative. To simplify the boundary layer analysis, low Mach number flows with small relative variations in the gas density have been considered. Radial profiles of axial and azimuthal velocity components, and static and stagnation temperatures are found to depend on the Squire parameter L, the Prandtl number, Pr, and the rest of the parameters of the problem. Even for the case of inviscid vortices with positive values of T0, for which the stagnation temperature increases towards the axis, is found that the stagnation temperature decreases substantially in the vortex core for some range of values of both L and Pr (Ranque–Hilsch effect) when the effect of both heat conduction and the work done by viscous forces are taken into account. It is also found that there exists an optimum value Lop for which the cooling effect reaches a sharp maximum and that small deviations of L from Lop reduce drastically the cooling effect. The appropriate tuning of Lop can be dramatically important for the efficient operation of Ranque–Hilsch tubes. The influence of the Prandtl number and the rest of the parameters of the problem has been also considered. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870231
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