Analysis of centrifugal convection in rotating pipes

New exact solutions, obtained for centrifugal convection of a compressible fluid in pipes and annular pipes, explain axially elongated counterflow and energy separation—poorly understood phenomena occurring in vortex devices, e.g., hydrocyclones and Ranque tubes. Centrifugal acceleration ~which can be up to 10 times gravity in practical vortex tubes!, combined with an axial gradient of temperature ~even small!, induces an intense flow from the cold end to the hot end along the pipe wall and a backflow near the axis. To account for large density variations in vortex devices, we use the axial temperature gradient as a small parameter instead of the Boussinesq approximation. For weak pipe rotation, the swirl is of solid-body type and solutions are compact: vz /vza51 24y13y and (T2Tw)/(Ta2Tw)5(12y ); where y5r/rw , the subscripts w and a denote values of axial velocity vz , temperature T, and radial distance r, at the wall and on the axis. The axial gradient of pressure, being proportional to 3y21, has opposite directions near the wall, y 51, and near the axis, y50; this explains the counterflow. With increasing pipe rotation, the flow starts to converge to the axis. This causes important new effects: ~i! the density and swirl velocity maxima occur away from the wall ~vortex core formation!, ~ii! the temperature near the axis becomes lower than near the wall ~the Ranque effect!, ~iii! the axial gradient of temperature drops from the wall to the axis, and ~iv! the total axial heat flux ~Nu! reaches its maximum Numax '4000 and then decreases as swirl increases. These features can be exploited for the development of a micro-heat-exchanger, e.g., for cooling computer chips. © 2001 American Institute of Physics. @DOI: 10.1063/1.1384890#