Sketched in Fig. P 12.6 are the upstream [section (1) ) and...

Sketched in Fig. $P 12.6$ are the upstream [section (1) ) and downstream [section (2)] velocity triangles at the arithmetic mean tadius for flow through an axial-flow turbomachine rotor. The axial component of velocity is 50 ft/s at sections (1) and $(2) .$ (a) Label cach velocity vector appropriately. Use $\mathbf{V}$ for absolute velocity, $\mathbf{W}$ for relative velocity, and U for blade velocity, (b) Are you dealng with ¿ turbine or a fan? (c) Calculate the work per unit mass involved. (d) Sketch a reasonable blade section. Do you think that the actual blade exit angle will need to be less or greater than $15^{\circ} ?$ Why?

Sketched in Fig. $P 12.6$ are the upstream [section (1) ) and downstream [section (2)] velocity triangles at the arithmetic mean tadius for flow through an axial-flow turbomachine rotor. The axial component of velocity is 50 ft/s at sections (1) and $(2) .$ (a) Label cach velocity vector appropriately. Use $\mathbf{V}$ for absolute velocity, $\mathbf{W}$ for relative velocity, and U for blade velocity, (b) Are you dealng with
¿ turbine or a fan?
(c) Calculate the work per unit mass involved.
(d) Sketch a reasonable blade section. Do you think that the actual blade exit angle will need to be less or greater than $15^{\circ} ?$ Why?

Key Concepts

Velocity Triangles

Velocity triangles represent the vector relationships among absolute velocity (V), relative velocity (W), and blade velocity (U) in turbomachinery. They are used to visualize and analyze the flow behavior through rotor blades by decomposing velocities into their axial and tangential components, which is essential for understanding the energy transfer and direction of flow relative to the moving blades.

Euler Turbomachinery Equation

The Euler turbomachinery equation relates the work per unit mass to the change in the tangential component of the velocity across the rotor, multiplied by the blade speed. This principle is fundamental to determining the energy exchange in machines such as turbines, compressors, and fans, and it provides a basis for computing the work imparted to or extracted from the fluid.

Turbomachinery Classification

Turbomachinery can be categorized into devices like turbines, compressors, and fans based on how energy is transferred between the fluid and the rotor. Identifying whether the device acts as a turbine or a fan depends on the direction of energy exchange; turbines extract energy from the fluid while fans or compressors add energy to it. The velocity triangles and flow characteristics help in making this determination.

Blade Design Considerations

Blade design in turbomachinery requires careful attention to the blade exit angle and overall geometry to ensure aerodynamic efficiency and appropriate matching between flow velocities and blade trajectories. Factors such as the blade exit angle affect the flow turning and energy transfer, and adjustments may be necessary to optimize performance, reduce losses, or avoid issues like flow separation.

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