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Conceptual Design of a Supersonic Jet Engine

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Conceptual Design of a Supersonic Jet Engine ( conceptual-design-supersonic-jet-engine )

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Figure 4: Velocity triangles for a typical compressor stage [19] In this work the axial velocity has been determined assuming values of 𝑀𝑎𝑥,𝑖𝑛 and 𝑀𝑎𝑥,𝑜𝑢𝑡 based on guidelines given in [18] with a linear interpolation within the component. The velocity triangles have been calculated at the hub, mean, and tip of each blade of the turbomachinery components. With regard to radial equilibrium, the exponential blading method was used to determine the angles and the velocities at the hub and the tip. The necessary equations and formulas can be found in [19]. A number of aerodynamic properties have been evaluated to achieve an adequate turbomachinery performance including: degree of reaction, diffusion factor, De Haller number, stage loading, flow coefficient and deflection. Detailed formulas are provided in appendix A. Degree of reaction The degree of reaction is defined as the ratio between the static enthalpy change in the rotor and that of the whole stage. It provides a measure to the extent of which the rotor contributes to the overall pressure difference in the stage [19]. For a compressor, this should typically be in the range of 0,5 – 0,8 [20], while for a turbine 0,3 – 0,5 [11]. Diffusion factor The air passing over an airfoil will accelerate on the convex side, leading to a drop in static pressure. On the concave side, the air will decelerate. The losses in a blade row arise primarily from growth of boundary layers on the two blade sides. At the blade trailing edge the boundary layers come together forming a wake, causing a local drop in total pressure. Thick boundary layers, causing high losses have been found in regions where rapid velocity changes occur. The diffusion factor concept was developed by NACA based on cascade testing. For the rotor hub region and stators the losses are unaffected up to a diffusion factor of 0,6. In the rotor tip region, the losses grow rapidly at a diffusion factor above 0,4 [19]. 22

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