Inlet triangle

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Inlet triangle

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The inlet triangle is defined by inflow parameters and geometrical dimensions on leading edge.

Between inlet area and leading edge the swirl is constant because transmission of energy from rotating impeller to fluid occurs in blade area only. Cross sections 0 and 1 (see Main dimensions) are different only due to blockage of the flow channel by blades (τ1) in section 1. This results in an increased meridional velocity cm.


(const. inflow swirl)



Selected blade angle β1B does only indirectly influence the velocity triangle due to blade blockage. Differences between selected blade angle β1B and flow angle β1 is referred as the incidence angle: i = β1B1

In general an inflow without any incidence is intended (i=0). If i0 the flow around the leading edge shows high local velocities and low static pressure:

i > 0: β1 < β1B stagnation point on pressure side

i < 0: β1 > β1B stagnation point on suction side

A small incidence angle i can be profitable for best efficiency point. Calculation of β1B inside CFturbo gives inflow without incidence.

Typical inlet blade angles are:

Pumps, Fans

β1B < 40° due to best efficiency


β1B as small as possible due to cavitation; with regard to efficiency not smaller then 15…18°


optimal blade angle β1B is about 30°

If the radius of leading edge varies from hub to shroud the blade angle β1B does not remain constant. A higher radius on shroud results in a lower value for β1B- the blade is curved on leading edge.

Possible warnings


Possible solutions

Leading edge blade angle βB1 > xx°

Unusual high inlet blade angles.

The warning level can be adjusted under Preferences: Warning level.

Too high values indicate too small inlet cross section. Increase leading edge dimensions (Main dimensions)

Leading edge blade angle ßB1 < xx°

Unusual low inlet blade angles.

The warning level can be adjusted under Preferences: Warning level.

Too small inlet angles indicate too high inlet cross section. Decrease leading edge dimensions (Main dimensions)

Vaned Stator downstream swirl  differs significantly from defined value at cu,cm specification [axial turbines only]

If a vaned stator is located prior the rotor, its blade angles might yield circumferential velocities that are significantly different from those defined by cu, cm specification.

Adjust the precursor stator trailing edge blade angles manually or by using the soft button "Set αTE" in the blade properties of the stator.

Calculation of LE blade angles not possible. Change blade shape, blade thickness or inlet diameters.

The combination of the inlet state (mass flow, swirl, pressure and temperature), diameters and blade setup does not allow for the calculation of the blade angles. There are no blade angles that fulfill all the above mentioned constraints. E.g., the blockage τ might be too big in case the inlet swirl is high.

Adjust the inlet swirl (e.g. by adjusting a precursor stator trailing edge), or the diameters (main dimensions or LE in meridional contour), or the LE thickness.

A reasonable thermodynamic state could not be calculated @LE. Consider change of blade angles or thickness, main dimensions or global setup.

[ for compressors and turbines only ]

The geometry does not allow for the establishment of a physically valid state. E.g. the mass flow is too high.

Adjust the leading edge blade angles or thickness values or main dimensions or the global setup (e.g. mass flow or inlet conditions).

The blade angles are not within the valid range.

Usage of CFturbo is limited to inlet angles between 0° and 180°.

Blade angle calculation is impossible (see below) or adjust unsuitable user input for blade angles.

ßB indeterminate. It's not possible to determine blade angle ßB.

Blade angle calculation failed.

Check input values and geometry.

[ Turbine rotors only ]

In case of turbines the calculation of the incidence by Aungier can be used.

According to decreased energy transmission the slip coefficient γ is defined: