The design process begins with the construction of velocity triangles.
Gone are the days of simple one-dimensional calculations. Moustapha advocates for detailed loss breakdowns:
For radial turbines, the incidence loss at the rotor inlet is a major focus of optimization. For axial turbines, tip leakage remains the enemy of efficiency. axial and radial turbines by hany moustaphapdf 2021
Before distinguishing between the two types, it is essential to establish the shared thermodynamic and kinematic foundations.
To characterize performance irrespective of physical size, engineers utilize dimensionless parameters: The design process begins with the construction of
The governing equation for all turbomachinery is the Euler Turbine Equation, derived from the conservation of angular momentum. The specific work done by the fluid on the rotor ($W$) is given by:
$$ W = U_1 C_\theta 1 - U_2 C_\theta 2 $$ For radial turbines, the incidence loss at the
Where:
This equation highlights a fundamental design difference: In axial turbines, $U$ is constant across the stage (ignoring radial variations), simplifying the energy transfer analysis. In radial turbines, the change in radius from inlet to outlet provides a significant contribution to the work output via the $U_1 C_\theta 1$ term, allowing for high pressure drops across a single stage.
Some novel designs blur the line – e.g., mixed-flow turbines (intermediate between radial and axial) for turbochargers operating at high altitude.