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Show (3) where V c is the mean axial core velocity from 0 to Rh, and Va is the mean axial velocity component in the outer annulus. The main assumption is that velocity is uniform within the core and within the annulus. However, Vc and Va are not necessarily identical as they are affected by the screen blockage in the inner tube. Figure 2 shows the functional dependence of Sy on the two important parameters, V /U a and RhlR for a vane-swider with a = 37°. As Sy scales by tan( u), the general shapes of these curves remains the same for different u. These curves show that the proper limits are achieved by our defmition of Sv. At R h ~ R, i.e. tube flow without swid, Sv reduces to zero, and when V c = 0 as in the case of a solid hub, Sv is identical to Eq. (2). Figure 2 also shows that varying RhlR of the hub swider (solid line) from 0 to 0.9 only changes S by 50%. Note that Eq. (2) becomes meaningless at the limit ofRhlR = 1.0. For our new design where core flow is allowed, Sv can be conveniently varied by changing U/Ua or RhlR. To seek a vane-swider that works with the WSB, it was more convenient to vary U /V a by fitting the inner tube with screens with differing amounts of blockage than by varying RhlR because new fins would need to be fabricated for different Rh. Increased blockage increase Sv because the higher pressure drop through the inner tube forces more flow through the annular region. As shall be discussed later, once the regime of Sv for flame stabilization has been established for different velocities and equivalence ratios, the phase plane of Figure 2 would be useful as a design tool for scaling the WSB to different power ratings and physical dimensions. LDA Measurement of Non-reacting flows Experimental test conditions of a vane swider with a = 37° and Rh / R = 0.776 are marked by symbols (+) on Figure 2. They include the four screens of Table I, the open tube (no screen) case and the closed tube (hub) case. All velocity profiles were obtained at 5 mm above the burner tube. The definition of Sv in its present form requires empirical input for V c and Va. Our approach is us an averaged velocity from r = -20.5 to r = +20.5 mm as Vc. Va was then calculated from the mass flow rate of the total flow 7 |