Swirling flows between coaxial cylinders with injection by radial jets

Abstract

An experimental program has been carried out to investigate a class of flows which is of interest with regard to the aeroelastic flutter of flexible cylinders. The flowfield of interest is the swirling flow between two concentric cylinders, of which the inner one is stationary and the outer one rotates. Air is admitted into the annulus between the cylinders through inlets in the wall of the rotating outer cylinder near one end of the apparatus and is exhausted through an annular outlet surrounding the inner cylinder near the other end. Measurements of the resulting flowfield have been made for a wide range of flow rates, outer cylinder rotational speeds, and inlet geometries. Approximate scaling laws for the velocity field have been developed, and dimensionless parameters have been defined which correlate the effects of the various inlet conditions which were tested. Nomenclature Aan = cross-sectional area of annulus A„ = total cross-sectional area of inlets d = internal diameter of inlet tubes / = inner cylinder structural frequency I = length of inlet tubes m =mass flow, Ibm/sec M = dimensionless momentum flux quantity, Eq. (4) N = number of inlets p,pt = static pressure, pitot pressure r = radius from cylinder axis Rj = radius of inner cylinder (outside) R0 = radius of outer cylinder (inside) R = dimensionless radius = (r-Rt)/(R0 —/?/) t = dimensionless residence time quantity, Eq. (5) Um = average axial velocity in the annulus =m/pAan V = magnitude of fluid velocity Vn = average radial velocity in inlets =m/pAn Vt = tangential component of fluid velocity Vz = axial component of fluid velocity z = axial coordinate 0 = yaw angle A = pitot pressure referenced to the static pressure at the inner cylinder =prp(Ri) T =Vtr, circulation T0 =uR20, (ideal) circulation at outer cylinder oj = angular velocity of outer cylinder