OCR Text |
Show outwards in the clockwise direction. This is the same sort of feature you might find if you cut through the cross section of a threaded fastener. If we assume that this feature corresponds to the large scale structures which we observed turning outwards in the r-z plane, this suggests that these structures are connected in the form of a left-handed helix and that the lead of the helix is of the order of the throat diameter. Figure 11 shows a cross-stream view taken one throat diameter (z = d) into the furnace. This image shows the structures formed by azimuthal shear between the annular jet and the internal recirculation zone and between the annular jet and the outer furnace fluid. Note that there is no evidence of the helix in this image. This is true for about half of the data set at z = d/2 and z = d. Figures 12 and 13 show images at z = 3d/2 and z = 2d. At these locations helical connections have not been observed. The image of Fig. 12 looks similar to that of Fig. 11 but with a larger cross section. The image of Fig. 13 appears to be slightly different, showing deep penetration of the unseeded fluid into the jet. The scale of these cells is of the order of the throat diameter, suggesting that the jet may be breaking up due to three-dimensional effects. DISCUSSION The instantaneous results (Figs. 6 through 13) lead to a different mental picture of the annular swirling jet than the time-averaged data (Figs. 3 through 5). While the data of those figures (3 - 5) suggests a picture consistent with the velocity-pressure viewpoint that many of us are accustomed to, the data of the subsequent figures suggests a structure more in keeping with a vorticity view of the flow. In this section we attempt to construct a description of the flow which is consistent with: (1) our experimental findings, (2) the vorticity fed into the flowfield at the inlet plane, and (3) the dynamics of vorticity as determined by the Biot-Savart law (Batchelor, 1967). We begin this description by analyzing the vorticity entering the furnace at the inlet plane. Since the vorticity vector is Ctl = curl v (where v is the velocity vector), the vorticity flux fed into the furnace may be evaluated by examining the velocity field near the inlet plane. In terms of the velocity components, the inlet vorticity is given by _ {l d(rve) 1 dVr} 1\ {l dVz ave} 1\ {avr avz} 1\ Ctl - r dr - r de ez + r ae - dz er + az - dr ee If we assume for this purpose that the flow is axisymmetric and neglect streamwise gradients,2 2While we have no direct measurements to confirm this assumption, the primary effect of including axial gradients would be the introduction of a radial component of vorticity. If the flow at the inlet is considered to be steady and in viscid as well as axisymmetric, it can be shown (Batchelor, 1967) that the ratio of axial to radial components of vorticity is equal to the ratio of the same components of velocity. Since the radial velocity at the inlet is approximately one order of magnitude less than the axial velocity, we conclude that the radial component of vorticity is small and neglect it. - 5 - |