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The meridional distances can then be calculated by a numerical integration. m 0 The throat radius can then be estimated. Aungier [2] derives an expression which is recited here. ∂r o2 rth = r6 − ∂m 2s (3.48) 66 In the equation above s6 corresponds to the exit nozzle pitch. The first derivative of r (3.49) (3.50) m2 = dr2+dz2 (3.47) with respect to m can be approximated, according to Aungier, as follows. ∂r m6(r6 −r5) (m6 −m5)(r6 −r4) ∂m = m (m −m ) − m m 656556 The pitch at every station is defined as. s = 2πr NN When the throat radius, rth, is determined it is possible to calculate the exit flow angle. First the throat flow angle has to be determined. This is done, as cited in [2], by slightly modifying the sine rule, specified earlier. sinαth = btho s6 b6 Then the exit flow angle is determined according to. tan α6 = r6 tan αth rth (3.51) (3.52) Finally it is possible to calculate the deviation angle, δ6. Deviation results from the fact that the flow does not follow the blade at the trailing edge, much like incidence for the leading edge. Baines, [12], explains the deviation comes from an underturning caused by the fact that the flow is diffusing from the throat to the trailing edge but it also exposed to a sudden expansion caused by the finite trailing edge thickness. Baines also shows how the deviation depends on nozzle exit mach number, the deviation tends to be a bit higher for high mach number. He also mentions how difficult it is to predict the deviation and gives an example of how the sine rule, equation (3.51), predicts the flow angle rather poorly for nozzles of radial turbines. Instead Baines proposes another model, [3] For M < 0.3 : α4 = a0 + a1 cos−1(o/s) (3.53) ForM>0.3: α4 =a0 +a1cos−1(o/s)+a2(M−0.3) (3.54) 29PDF Image | A Detailed Analysis of Radial Turbines
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