Blade loading is the single most important aerodynamic design parameter in turbomachinery blades, it defines both the amount of work made, or extracted, by the blade and the distribution of such work from hub to tip / shroud.
In TURBOdesign1 the design is based on a distribution of swirl velocity or rVθ. In practice the rVθ distribution is not specified directly but through the specification of ∂rVθ/∂m, which directly relates to the pressure loading on the blade. For example, in incompressible potential flow:
B : blade number
ρ : density
Wmbl : average of meridional velocity across the blade
r : radius
rVθ : circumferentially mean tangential velocity
m : meridional distance
To fully define the blade loading specification for a given design we follow 3 steps:
- Impose rVθ spanwise distribution at the INLET section
- Impose rVθ spanwise distribution at the OUTLET section
- Impose ∂rVθ/∂m distribution on streamwise sections inside the blade
Step 1: Impose rVθ spanwise distribution at the INLET section
Spanwise distribution of rVθ is specified based on exit swirl distribution from the upstream blade row. In the absence of any blade row zero swirl distribution is specified.
Step 2: Impose rVθ spanwise distribution at the OUTLET section
r : local radius
Vθ: tangential velocity
The exit rVθ is directly related to:
Work input coefficient (rotor): W=ω(r2Vθ2 - r1Vθ1)
Spanwise work distribution (rotor)
Outlet flow conditions (stator)
Step 3: Impose ∂rVθ/∂m (blade loading) inside the blade
How do I choose the optimum blade loading distribution?
The optimum blade loading distribution to control given aspects of the 3D flow field has strong generality across designs. The below publications give an introduction to the typical blade loadings used in some common applications. For information related to your specific application, our team is on hand to answer your questions to talk with you about it
- Secondary flow suppression for centrifugal impellers
Secondary flows are reduced by specifying fore-loading at the shroud and rear-loading at the hub. This type of loading has been found to be applicable to both pumps and centrifugal compressors. Zangeneh et al (1998).
- Suppression of corner separation in vaned diffusers
For 3D diffuser design, users typically specify fore-loading at the hub and aft-loading at the shroud. This type of loading helps to remove corner separation in both pump vaned bowl diffusers and centrifugal compressor vaned diffusers. Goto and Zangeneh (1998).
- Improving pump suction performance whilst maintaining performance
A blade loading distribution in which there is little shroud loading in the first 10% of chord followed by fore-loading results in good suction performance and efficiency. This type of loading has been found to have generality across a wide range of pump sizes and specific speeds. Bonaiuti et al (2010).