Figure 12. Surfaces of turbulent kinetic energy near sleeve and seal face.

interfaces. This situation is advantageous for promoting heat transfer by way of increased mixing in the precise locations where heat exchange is most critical, i.e., near the warmer interface regions of the seal faces (Figure 4), and near the cooler fluid moving through the channel.

Figure 13 depicts a cross-sectional view of the secondary flow velocities for a conventional design having a narrow (1 mm) radial gap, with no axial tapers on any of the barrier fluid bounding surfaces. In this view, the in-plane (axial-radial) components of the flow at the bottom (6:00 o'clock) position midway between the inlet and outlet planes (Figure 10) are displayed. The Reynolds Number corresponding to this set of design/operating conditions is about 13,300, based on the radial gap, the surface speed of the rotating sleeve, and the kinematic viscosity of water at 38 C. The velocity vectors, as well as the wall boundaries,

Figure 13. Secondary flow velocity vectors for 1-mm untapered radial gap.

are shown colored by temperature. Note that the cooler fluid circulating in the channel does not communicate well with the warmer flow near the interface regions. For this case the rate of convective heat removal by the barrier fluid is less than 0.5 kW, based on the throughflow and the predicted rise in fluid temperature between the inlet and outlet surfaces of the flow domain.

If the width of the radial gap is doubled (Figure 14), thereby also doubling the Reynolds Number, we notice that the cooler fluid within the channel circulates more effectively in the axial direction. This intuitive result produces a more efficient axial exchange of heat, and a 56% increase in the net heat removed by the barrier fluid.

Figure 14. Secondary flow velocity vectors for 2-mm untapered radial gap.

Finally, model predictions for the tapered-surface design are shown in Figure 15. In this configuration both the rotating and stationary boundaries are radially inclined in the axial direction. As in the previous case, the radial gap is approximately 2 mm. The fluid circulation cells, now span the entire axial distances between the flow channel and the interface regions of the seal. This more efficient transfer of mass, made possible by the axial pumping action induced by the rotating tapered sleeve, produces an even greater

Figure 15. Secondary flow velocity vectors for 2-mm tapered radial gap.

increase in cooling efficiency (roughly 130% compared with that of the narrow-gap case,Figure 13). The results illustrated in Figure 15 correspond to those representing the same geometric configuration and operating conditions presented in Figures 9-12.

Continuing with the tapered surface design, Figure 16 shows a 3-dimensional 'snapshot' of temperature colored flow trajectories for two fluid particles (represented as spherical glyphs) released immediately downstream of the (magenta) inlet plane. In this view, the yellow glyphed particle travels along the cooler inboard side of the seal, while the red glyphed particle travels through the warmer outboard side. The trajectories are rendered as 2D streamribbons onto which any scalar variable (here local fluid temperature) can be mapped. The twisting nature of the ribbons is indicative of the local swirl (vorticity) of

Figure 16. Streamribbon trajectories of fluid particles released near flow inlet.

the flow, with regions of stronger vorticity corresponding to those of greater turbulence (Figure 12), mixing, and heat transfer. Figure 16 is actually a single frame image of a flow trajectory animation wherein the flow speed (m/s) of the red outboard particle is displayed in the lower left, and the elapsed time (ms) from release is shown in the upper left of the frame. For this example, the fluid particles complete their journey from the flow channel to their respective interfaces and back in approximately 100 ms. During this time the rotating shaft/sleeve completes about six revolutions.