Relative efficiencies for parallel and perpendicular entrainment flow paths

HIGH-SPEED fluid, introduced into an otherwise quiescent region of ambient fluid, provides an effective means for inducing stream wise motion in the latter. Ejectors and jet-pumps are common technological examples of this phenomenon. The induced flow may be constrained to approach the high-speed flow with either a perpendicular or parallel orientation. The relative efficiency (as defined below) of these two entrainment flow paths is the primary subject of this paper. The general problem under consideration is most readily described in terms of the specific investigation that was executed. The experimental geometry will be described and the relative efficiency will then be defined. Figure 1 presents the parallel and perpendicular entrainment flow paths into the shear layer for the present experiment; these figures also allow a definition of the problem. Consider that a given high-speed or primary flow [viz., 50x80 cm, £/0 = 13 mps, 0(0) = 9 mm] exists and that a defined entrainment flow rate qe will be delivered to the shear layer through a rectangular passage of width 4 [viz., 4 = 150 mm = 16.7 0(0) and height = 80 cm]. If the geometries of the entrainment plenums and the entrances to the entrainment channels are identical for the two entrainment paths, then the relative efficiency of the entrainment process can be characterized by the relative plenum pressure pe to deliver the designated flow rate. The present study also provides insight into the relationship between one- and two-stream layers. A two-stream mixing layer, in the limit as the low-speed velocity U2 tends to zero, would be represented by the flow studied in Fig. la. This condition can be set in contrast to a single stream mixing layer (Fig. Ib) where the jc-component velocity is identically zero as the fluid is introduced into the entrainment flow path. Since it is convenient to consider the limiting case: U2-+ 0 to be of the same "family" as U2 = 0 (see, e.g., Brown and Roshko,1 Fig. 10). It is useful to identify the similarities and differences of these two conditions. Contents The boundary conditions for the present experiment are established by 1) the primary flow boundary layer, 2) the streamwise variation of the inviscid flow conditions of the primary stream U0 (x) or p0 (x), and 3) the conditions within the entrainment plenum. Observations were not made in the entrainment plenum; the pressure was measured by an open tube at @ in Figs, la and Ib, and it was assumed that negligible velocities (note the area ratio) existed in this region. The primary flow boundary layer (at separation) can be described by 6(x = 0) = 9 cm and #0 = 7300. Independent measurements of the velocity U0(x), and pressure p0(x), confirmed that there were no measurable accelerations in the primary flow over the region of interest -2<x/7<6. The entrainment flow rate was controlled by the use of a throttle plate and was metered by its passage through a slitjet. Since the metering and throttling functions were independent, it was possible to create virtually the same entrainment flow for the two entrainment paths. That is, the precision and repeatability of this setting was better than its accuracy. The latter is estimated to be Fe/C/0 = 0.05, 0.04, 0.03 ±0.0005 and was primarily limited by the ability to read the low ( — 2-4 mps) velocities through the metering nozzle. Note that the selected entrainment velocities bracket, and stand well above, the nominal value for a single stream shear layer, Ve/U0 = 0.032 (i.e., Liepmann and Laufer2). The primary results are presented in Table 1. (The repeated data are second trials for the same conditions). The parallel case plenum pressures are approximately 38% larger than the perpendicular case pressures for the three Ve/UQ values. This finding suggests that the entrainment processes for the parallel and perpendicular paths are rather different. The relatively large nondimensional values (based upon Ve) and their increase with decreasing ( V e /U 0) reveal a relatively large pressure drop coefficient associated with both cases. The relative constancy of the alternative nondimensional results—based upon the (Ve/UQ) product, is quite instructive. Apparently, this nondimensional form properly accounts for the combined effects of the plenum pressurization and the accelerative effects as the low-speed entrainment flow interacts with the high-speed primary flow. The velocity surveys, in the entrainment channels for the two cases, clarify the reasons for the increased plenum pressure in the parallel case; see Fig. 2. Specifically, the mean velocity profile for the parallel case is highly skewed with a high-speed region near the splitter plate. In contrast, the perpendicular case exhibits a relatively flat velocity profile. Hence, for the same mass flux, the kinetic energy flux for the parallel case is substantially larger than that of the perpendicular case. The increased plenum pressure (pe) must be present to account for this difference since the primary flow (i.e., the downstream pressure value for the entrainment flow) is identical in both cases. The kinetic energy