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117 π =π +1πΆ2 (β5-38) 3 π3 23 The other thermodynamic properties can now be obtained, as shown in Equation(β5-39). The new value of mass flow rate π. is obtained using equation (β5-40), and the process is repeated until convergence is achieved. π =π,π =πΈπππ,π,π,π,πππ’ππ (β5-39) (β5-40) 3 43 3333 π. ππππ = 2ππ π π πΆ 3 3 3 π3 Similar to the rotor throat width, the stator throat width is calculated using equation (β5-41)[234]. π π£ is the vane pitch at the trailing edge, as shown in Figure β3-9. Moreover, it is related to the vane chord ππ£ , where ππ£ = 1.2 π‘π1.3. π π£ This limit ratio is known as solidity π, and it is implemented in the OC to reach the optimum value within the limit. If the flow at the stator exit is supersonic (π3 β₯ 1), then the nozzle throat width is calculated using the mass continuity equation between the throat passage and the exit station, as shown in Figure β3-9. πβ πππ πβ are the density and speed of sound at sonic conditions, respectively. π3=π π£π πππΌ3 ππππ3<1 π3=πΆπ3π3 ππππ3β₯1 πβπβ (β5-41) ππππ The number of nozzle vanes ππ can be either calculated using equation (β5-42) or defined by the user. 2ππ (β5-42) ππ = 3 The stator setting angle πΎ3 should be calculated iteratively to set the required throat width. The stator vane is positioned at the stator outlet radius π3 and rotated around the trailing edge with an initial guess of πΎ3 β₯ 5Β°. Subsequently, the second vane is constructed by rotating the first vane around the origin by 2π, and the throat width will be the minimum distance ππ π π£PDF Image | Automotive Radial Turbine Expander Design WHR
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