Radial Inflow Splitter Blades in Three-Dimensional

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Radial Inflow Splitter Blades in Three-Dimensional ( radial-inflow-splitter-blades-three-dimensional )

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In cylindrical coordinate system, blade surfaces may be represented by n2ir aj(r0,,z)= 0 - fi(r,z) = f for n = 0, 1,2,3,..., (B - 1) (2.5) where (r, 0, z) is the right-handed coordinate system, f is the angular coordinate of a point on the blade surface (also called the Wrap angle), B is the number of blades, and n is a nonnegative integer. The subscript j can assume a value of 1 or 2; the value of 1 pertains to the main blade while the value 2 pertains to the splitter blade. Thus the main blade surfaces correspond to a1 assuming a value of ± "22; likewise a 2 = "2 are the splitter blade surfaces. Hence the blade surfaces are at 0 = fj(r,z) ±i or j =J2 forn=0,1,2,3,...,(B-1). The only vorticity in the flow field is located at the blade surfaces, and under these assumptions they can therefore be conveniently represented in terms of generalized function 6, as follows: 2 f= Zfj6(a,) j=1 where 6,(aj) is the periodic delta function (Ref.2), given as (2.6) (2.7) (2.8) 6(aj Bn2= and the over bar "-" defines a tangential mean: einBai 2 rn=-oo n=--oo -B~ A(r, z) = 2 f A(r, O,z)dO Using Clebsch formulation (Ref.5), the velocity vector may be written as the sum of a potential and a rotational part: V=v +AVi (2.9) where 4(r, 0, z), A(r, 0, z) and t(r, 0, z) are scalars (also called Clebsch variables). Tak- ing the curl of the above equation, we obtain S=Vx v = VA xV'L (2.10)

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