B'  Blade loading

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B'  Blade loading

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The blade is designed by a blade loading distribution B'(M) and can be therefore seen as inverse design. B' is defined as:

with the following components:


Circumferential abs. velocity




Meridional coordinate (not m')


angular speed

By integrating B' w.r.t M/Mmax one gets the swirl Δcu˖r that is to say the Euler work Y. The B' curve is consisting of 3 parabola. The inner parabola's third coefficient is zero which results in a linear piece of the curve. Parameters of the curve are the absolute values of B' at LE and TE, the M-coordinate of the inner control points and the slope of the inner linear piece of the curve. The dotted line is parallel to the linear piece and can be seen as a see-saw to adjust the slope. There is a corresponding set of meridional velocities to each B' curve coming from the solution of the meridional flow calculation. The result of the definition of the B' curve is a certain cu-distribution that will be used for the calculate the relative βF (impeller) and the absolute flow angle αF (stator) resp.:

Using the information of incidence and deviation from the blade properties the absolute blade angle βB (or αB for stators) is determined.

The value B' at TE is zero to obey the Kutta-condition. Therefore, the associated control point is fixed. After switching from a different design mode to blade loading, control points of the see-saw as well as of the LE are automatically fitted to get a geometry close to the one before the design mode change. Only active spans are converted that way. All blade loading curves of dependent spans are calculated based on the resulting geometry (see blade-to-blade flow 1D). That is why deviations from the Kutta-condition may occur.

The meridional velocities cm are stored and kept constant when Update global parameters is deactivated. The same applies for the Revolutions. If Update global parameters is activated the velocities are updated with the results of the solution of the meridional flow calculation and the Revolutions is held synchronized with the Global setup or Main dimension value. The latter is used if the impeller has an alternative speed.

The Euler work is derived from the respective value defined in the Global setup when the Update blade parameters is activated. Also the incidence angles are updated in that state and are taken from the Blade properties. If Update blade parameters is deactivated the Euler work as well as the incidence angles at hub and shroud can be set directly. Incidences at the inner spans will be interpolated linearly.

In the area Angular positions the stacking position can be defined. Only at this position the tangential coordinate ϕ can be specified directly, all other points along the meanline are calculated automatically. Therefore, the blade wrap angle of each span is a result of the given blade loading.