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(6) times gravity in practical vortex tubes), combined with an a
xial 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 approx
imation. For weak pipe rotation, the swirl is of solid-body type and soluti
ons are compact: v(z)/v(za)=1-4y(2)+3y(4) and (T-T-w)/(T-a-T-w)=(1-y(2))(3)
; where y=r/r(w), the subscripts w and a denote values of axial velocity v(
z), temperature T, and radial distance r, at the wall and on the axis. The
axial gradient of pressure, being proportional to 3y(2)-1, has opposite dir
ections near the wall, y=1, and near the axis, y=0; this explains the count
erflow. With increasing pipe rotation, the flow starts to converge to the a
xis. This causes important new effects: (i) the density and swirl velocity
maxima occur away from the wall (vortex core formation), (ii) the temperatu
re 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 (i
v) the total axial heat flux (Nu) reaches its maximum Nu(max)approximate to
4000 and then decreases as swirl increases. These features can be exploite
d for the development of a micro-heat-exchanger, e.g., for cooling computer
chips. (C) 2001 American Institute of Physics.