Understanding Parsons' Reaction Turbine Velocity Diagrams

Parsons' reaction turbine is a significant design in steam turbine technology, primarily known for its 50% degree of reaction. This means the process of energy conversion is equally distributed between the stationary blades (nozzles) and the moving blades (rotor). A key characteristic resulting from this design principle is observed in the velocity diagrams at the inlet and outlet of the moving blades.

Velocity Diagrams Explained

Velocity diagrams are essential tools in turbomachinery analysis. They graphically represent the relationship between three key velocities:

• Absolute Velocity ($V$): The velocity of the fluid (steam in this case) relative to a stationary observer or the turbine casing.
• Blade Velocity ($U$): The tangential velocity of the turbine rotor blades.
• Relative Velocity ($W$): The velocity of the fluid relative to the moving blades.

These velocities form vector triangles at the inlet and outlet points of the moving blades, providing insights into the energy transfer and flow dynamics.

Parsons' Turbine: Congruent Velocity Triangles

In a Parsons' reaction turbine, the specific condition of a 50% reaction implies a balance in how the steam expands and accelerates through the stationary and moving blade rows. This balance leads to a specific relationship between the inlet and outlet velocity triangles for the moving blades.

For a 50% reaction turbine, the following conditions are met:

• The relative velocity at the inlet of the moving blade ($W_1$) is equal in magnitude to the relative velocity at the outlet of the moving blade ($W_2$). That is, $W_1 = W_2$.
• The absolute velocity at the outlet of the moving blade ($V_2$) is equal in magnitude to the absolute velocity at the inlet of the moving blade ($V_1$). That is, $V_1 = V_2$.
• The blade velocity ($U$) is constant for both the inlet and outlet triangles.

Because the corresponding sides and angles are equal ($W_1 = W_2$, $V_1 = V_2$, and $U$ is common), the velocity triangles formed at the inlet and outlet of the moving blades are identical. This means the triangles are congruent.

Conclusion on Velocity Diagram Shape

The defining characteristic of the velocity diagram triangles at the inlet and outlet of the moving blades in a Parsons' reaction turbine is their congruence. This congruence is a direct consequence of the turbine's 50% reaction design, ensuring an even distribution of energy conversion across both stator and rotor stages.