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It is mentioned in section 3.2 that for nozzle and impeller blades not only end walls have boundary layers which need to be taken into account when estimating the losses. There are also boundary layers building up on the blade surfaces. A simple blade loading diagram is used to approximate the velocity distribution on the pressure surface and the suction surface. An example of such a diagram is presented in figure 3.9. c3 c2s c2 c2p c1 Δc Δc Meridional distance Figure 3.9.: Simple blade loading diagram used to approximate the surface distri- bution on the pressure surface and the suction surface. Figure adapted from [2]. The velocity difference, ∆c, in figure 3.9 is approximated according to the following relationship. ∆c = 2π(r6c6θ − r4c4θ) (3.62) LNN It is possible for the flow to be choked and a check needs to be performed to control whether this is the case or not. The throat is the station at which the flow will choke first. Consequently the check will be performed at this station. The mass flow which is associated with a choked flow is. m ̇∗ =NNbtho(1−∆)ρ∗c∗ (3.63) In this equation, ∆ is taken from equation (3.32). The static pressure which is desired under supersonic conditions is less than the static pressure at sonic conditions. This ultimately requires the calculation process to make additional iterations. An isentropic expansion from the choked solution will be assumed to yield the right static pressure. This however, is only possible as long as the static pressure does not yield a meridional velocity greater than the sonic velocity. c6m = m ̇ a6 (3.64) (1 − ∆)2πr6b6ρ6 31 Suction surface Mean surface Pressure surfacePDF Image | A Detailed Analysis of Radial Turbines
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