On the Virtual Nonexistence of Multiple Instability Regions for Some Heat-Exchanger Arrays in Crossflow

Abstract

In fluidelastic analyses involving a time delay (or phase lag) between the motions of cylinders in an array and the resultant unsteady fluid forces on the cylinders, a succession of instability-stability regions is predicted theoretically at low values of the mass-damping parameter, mδ/ρD2 , below the “ultimate” fluidelastic instability, beyond which the system is not restabilized. However, as experimenters have had difficulty in verifying the existence of these regions of instability, it is legitimate to ask (i) do these regions really exist, and (ii) why are they so rarely observed? In this paper, with the aid of the quasi-steady model of Price and Païdoussis and with expanded measurements of lift and drag coefficients for a parallel triangular array with P/D = 1.375, it is shown that (a) the stability of the array strongly depends on geometric asymmetries; (b) whereas for a perfectly symmetric geometry the system may have several sub-ultimate instability regions, an asymmetry of as little as 0.02D may quench them and leave only the ultimate instability region intact. This suggests a possible explanation as to why the instability regions in question are so difficult to “find” experimentally. It also suggests that they may be of rather less practical importance for operating engineering systems than had heretofore been assumed, at least for some array geometries.