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Automotive Radial Turbine Expander Design WHR

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Automotive Radial Turbine Expander Design WHR ( automotive-radial-turbine-expander-design-whr )

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117 𝑕 =𝑕 +1𝐢2 (β€Ž5-38) 3 π‘œ3 23 The other thermodynamic properties can now be obtained, as shown in Equation(β€Ž5-39). The new value of mass flow rate π‘š. is obtained using equation (β€Ž5-40), and the process is repeated until convergence is achieved. 𝑆 =𝑆,𝑕 =πΈπ‘œπ‘†πœŒ,𝑇,π‘Ž,𝑃,𝑓𝑙𝑒𝑖𝑑 (β€Ž5-39) (β€Ž5-40) 3 43 3333 π‘š. π‘π‘Žπ‘™π‘ = 2πœ‹π‘Ÿ 𝜌 𝑏 𝐢 3 3 3 π‘š3 Similar to the rotor throat width, the stator throat width is calculated using equation (β€Ž5-41)[234]. 𝑠𝑣 is the vane pitch at the trailing edge, as shown in Figure β€Ž3-9. Moreover, it is related to the vane chord 𝑐𝑣 , where 𝑐𝑣 = 1.2 π‘‘π‘œ1.3. 𝑠𝑣 This limit ratio is known as solidity 𝜍, and it is implemented in the OC to reach the optimum value within the limit. If the flow at the stator exit is supersonic (𝑀3 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 β€Ž3-9. πœŒβˆ— π‘Žπ‘›π‘‘ π‘Žβˆ— are the density and speed of sound at sonic conditions, respectively. π‘œ3=𝑠𝑣𝑠𝑖𝑛𝛼3 π‘“π‘œπ‘Ÿπ‘€3<1 π‘œ3=πΆπ‘š3𝜌3 π‘“π‘œπ‘Ÿπ‘€3β‰₯1 πœŒβˆ—π‘Žβˆ— (β€Ž5-41) π‘π‘Žπ‘™π‘ The number of nozzle vanes 𝑍𝑠can be either calculated using equation (β€Ž5-42) or defined by the user. 2πœ‹π‘Ÿ (β€Ž5-42) 𝑍𝑠= 3 The stator setting angle 𝛾3 should be calculated iteratively to set the required throat width. The stator vane is positioned at the stator outlet radius π‘Ÿ3 and rotated around the trailing edge with an initial guess of 𝛾3 β‰₯ 5Β°. Subsequently, the second vane is constructed by rotating the first vane around the origin by 2πœ‹, and the throat width will be the minimum distance 𝑍𝑠 𝑠𝑣

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