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It has been found convenient to introduce an artificial density pa(r, z) to account for compressibility effects (Ghaly, see Ref.3); the artificial density is defined so as to satisfy V *PaW = O (2.18) Use of Eq.(2.17) in Eq.(2.18) yields W eV Inp, = W • 7 Inp (2.19) The artificial density has the physical meaning of fluid density in the limit of B -- oo (which is referred to as Bladed Actuator Duct flow model, Tan et al., Ref.4). We use Stokes stream function, b,to describe the mean flow ( as well as the bladed actuator duct flow). Thus the velocity components in the mean flow (also in actuator duct flow) are given as: PaWr - = r paWz 1(2.20) r az rV - rw (2.21) (2.22) r Br Substituting for Vr (= Wr) and V, (= W,) in the equation for the 0- component of the mean vorticity [ = V - Oz j= 1 Upon subtracting Eq.(2.17) from Eq.(2.16) we obtain a governing equation for the periodic velocity V as: V eV = -W Ilnp+ W Ilnp (2.24) It has been found convenient to use Fourier Series for representing the 0- depen- dence of the periodic velocity potential D (since the flow has inherent blade-to-blade 8' 1 a 82 I -+- , we arrive at a governing equation for ib: Or 8(lnpa) 8 [r'rrarz2rar z ,-zzOrrOz 8(lnPa) a ' 8arfVioyOrVo fj 0 = rP E "" ( ] (2.23)PDF Image | Radial Inflow Splitter Blades in Three-Dimensional
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