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where KT is the transpose of the shape function vector. The Jacobian, in terms of the coordinates of ri and zi, is given as 0r Ba 8r (3.6) -if [k]_ + 2- [1] = Br The derivative of variables in the physical ]plane can be expressed in terms of those in the computational plane as follows: .7) VTq = a. ~. -aP. f'.~The 121 122 J If we use the Galerkin method, the variati onal form of equation (2.23) becomes I= f 8NN) +I(a)(' )]dA+ffTNTNqdA 2 r(3.8B)r s - 0, we obtain the Euler equation [k]it = -q (3.9) with the corresponding boundary conditions. This is done locally from element to element. To assemble the contribution from each element, we apply the direct stiffness technique to obtain the global matrix over the whole domain as + 12" + . ar r as as where q is the nodal value of [! evaluation of [k] and q is done by Gaussian Quadrature. For stationary value of I, i.e., tK]3 = -g (3.10) The above procedure is also applied for the periodic velocity potential in Eq.(2.26). The above equation can be solved directly by a method such as LU decompostion, or iteratively, such as by conjugate gradient method. As there is no need to get the exact solution for the stream function and the periodic velocity potential before the blade 1a as ar Pa ar asPDF Image | Radial Inflow Splitter Blades in Three-Dimensional
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