Introduction

Problems in real life do not regularly come in the form of a “given” computational domain in which to solve the flow-governing equations. The fact of the matter is that we are given a large flow domain, and we are interested in finding the flow behavior over just a subregion of it. In separating our subdomain, we should be careful to add the effect of the remainder of the bigger system to our subdomain of interest. Perhaps one of the most illustrative examples of such a situation is the seal segment in the secondary (or leakage) flow passage in the the pump stage shown in Figure 14.1. Note that our focus is on this secondary passage and, in particular, the seal part of it.

Leakage flow in the shroud-to-housing gap of centrifugal pumps has significant performance and rotor-integrity consequences. First, it is the leakage flow rate, as determined by the through-flow velocity component, that is typically a major source of the stage losses. The swirl velocity component, on the other hand, is perhaps the single most predominant destabilizing contributor to the impeller rotordynamic behavior [3]. Control of the through-flow velocity in the clearance gap is often achieved through use of a tight-clearance seal. Suppression of the flow swirl, however, requires a careful design of the leakage passage and/or the use of such devices as the so-called swirl brakes (e.g., [7, 13]) or straightening grooves/ribs in the inner housing surface (e.g., [12]). Unfortunately, an efficient leakage-control device, such as the labyrinth seal, may itself trigger the instability problem of fluid-induced vibration [8].