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defined as. Y = p0,inlet − p0,exit (3.10) p0,exit − pexit ξ = hexit − hexit,s = c2exit (3.11) h0,exit − hexit c2exit,s In equation (3.11), hexit,s is the exit static enthalpy which would be attained in an isentropic expansion. The enthalpy loss can be modified and described as a velocity loss coefficient given by. L = c2exit,s − c2exit (3.12) This subchapter presents different ways of modeling the various losses surrounding the flow in a radial turbine. It is however naive to think that a one-dimensional analysis can be able to completely predict the nature of the flow. Initially the volute is concerned, it is followed by the nozzle, the impeller and finally the diffusor and vaneless spaces but before going into the different components, the theory of profile loss which is defined in [2] and used extensively of Aungier is presented. Boundary layer analysis When performing a mean-line analysis of a radial turbine it is convenient to use a simple one-dimensional boundary layer model. This can help predict the profile and viscous losses in the various components of the radial turbine. In a radial turbine the flow is accelerating in each component, except for the diffusor. This results in a decrease in both total and static pressure which, unlike in compressors where the flow is decelerating and give rise to an adverse pressure gradient, provides thin boundary layers. The flow is also more unlikely to separate because of the thin boundary layers that this accelerating flow give rise to. According to Aungier [2], the model takes extensive use of four parameters namely the boundary layer thickness, δ, the boundary layer displacement thickness, δ∗, the boundary layer momentum thickness θ and the skin friction coefficient, cf. These parameters are well defined in most elementary textbooks on fluid mechanics, for example in reference [8]. The boundary layer thickness is defined in figure 3.5. The boundary layer momentum thickness is defined as. δ 0 21 ρeu2eθ = ρu[ue − u]dy (3.13)PDF Image | A Detailed Analysis of Radial Turbines
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