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<< Click to Display Table of Contents >> Outlet triangle |
  
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<< Click to Display Table of Contents >> Outlet triangle |
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The outlet triangle is determined by geometrical dimensions of flow channel and selected blade angle β2B. The blade angle β2B strongly affects the transmission of energy in the impeller therefore it has to be chosen very carefully.
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Similar to the inlet the velocity triangles in cross sections 2 and 3 are different due to blockage of the flow channel by blades τ2 in section 2.
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For determination of β2B it is important to be aware about the deviation between flow angle and blade angle. The direction of the relative flow w2 at impeller outlet does not follow exactly with the blade contour at angle β2B. The flow angle β2 is always smaller than blade angle β2B due to the slip velocity. This difference is called deviation angle δ:
The deviation angle should not exceed 10°…14°, in order to limit increased turbulence losses by asymmetric flow distribution.
A reduced flow angle β2 results in smaller circumferential component of absolute speed cu2, which is - according to Euler's equation - dominant for the transmission of energy. Blade angle β2B is estimated by cu2,∞ for blade congruent flow (see figure). Therefore an estimation of slip is necessary.
Slip can be estimated by empirical models. The following models are available in CFturbo (not for Radial-inflow Turbines):
Blade angle β2B must be determined to reach the desired energy transmission - respectively the required head/ pressure difference - under consideration of slip velocity.
The following recommendations for common blade angles β2B exist due to optimal efficiency:
Pumps |
15°...45°, commonly used 20°...27° |
Fans |
not higher than 50° |
Compressors |
35°...50°, unshrouded impellers up to 70°...90° |
Turbines |
radius dependent, see sine rule |
Centrifugal machines - except for radial-inflow gas turbines - with low specific speed nq usually have similar values for β2B. The blades for this type of impellers are often designed with a straight trailing edge (β2B=const.). For radial-inflow gas turbine rotors and for Francis runners the radii along the trailing edge from hub to shroud are very different, resulting in very different values for β2B and twisted blades.
Problem |
Possible solutions |
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Trailing edge blade angle ßB2 < xx° |
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Unusual low outlet blade angles. The warning level can be adjusted under Preferences: Warning level. |
Too small outlet angles indicate too high outlet cross section. Decrease trailing edge dimensions |
Deviation δ (slip) between blade and flow is pretty high. |
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Unusual high deviation (slip) between blade and flow direction at outlet. This indicates too high blade loading. The warning level can be adjusted under Preferences: Warning level. |
Possible solutions could be: increase the impeller diameter (Main dimensions), increase the number of blades, increase meridional blade length (Meridional contour), select a different slip model |
Trailing edge blade angle ßB2 > xx°. |
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Unusual high blade angles at trailing edge. This can be caused by overloading the impeller. The warning level can be adjusted under Preferences: Warning level. |
Increase trailing edge dimensions (Main dimensions) and/or the slip coefficient γ. |
A reasonable thermodynamic state could not be calculated @TE. Consider change of blade angles or thickness, main dimensions or global setup. [ for compressors and gas turbines only ] |
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The geometry does not allow for the establishment of a physically valid state. E.g. the mass flow is too high. |
Adjust the trailing edge blade angles or thickness values or main dimensions or the global setup (e.g. mass flow or inlet conditions). |
Calculation of TE blade angles not possible. Change blade shape or blade angles or inlet/outlet diameters. |
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The combination of Global setup settings, main dimensions 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. |
Adjust main dimensions or the global setup (e.g. mass flow or inlet conditions) or the Blade properties (e.g. blade shape, blade thickness, slip coefficient γ/ slip model, number of blades). |
Blade angles are not within the valid range. |
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Usage of CFturbo is limited to blade angles between 0° and 180°. |
Blade angle calculation is impossible (see below) or adjust unsuitable user input for blade angles. |
No possibility to determine Blade angles ßB. |
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Blade angle calculation failed. |
Try to increase the impeller diameter d2 or outlet width b2 and/or the slip coefficient γ. |
Deviation δ (slip) between blade and flow is too high. |
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The slip calculation results in an extremely high slip angle, which is unrealistic. The blades could be overloaded or the wrong slip model is used. The error level can be adjusted under Preferences: Warning level. |
Possible solutions could be: increase the impeller diameter (Main dimensions), increase the number of blades, increase meridional blade length (Meridional contour), select a different slip model |
