Blade element theory tutorial PDF

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TUTORIAL: BLADE ELEMENT THEORY AND PROPELLER BLADE DESIGN

1. What are the assumptions implicit in blade element theory for propeller design? Where are they most likely to break down? 2. Sketch a blade element with the associated aerodynamic velocity and force diagrams. 3.

From the velocity and force diagrams show that the advance angle is given by V (1 + a ) tan φ = , the incremental thrust by δ T = B( dL cos φ − dW sin φ ) and the incremental 2 π nr torque by dQ = rB (dL sin φ + dW cos φ ) . Note n is the propeller rotational speed in revolutions per second and B is the number of propeller blades. 4. From the expressions for incremental thrust and torque, show that dQ dT C sin φ + Cd cos φ 2 C cos φ − Cd sin φ 2 and . = Bcq (1+ a ) ⋅ l = Bcq(1+ a) r ⋅ l 2 sin 2 φ dr dr sin φ 5.

Normalize the expressions from Q4 to give expressions for the non-dimensional dCtorque dCthrust T thrust and torque coefficient gradients and where Cthrust = 2 4 and dx dx ρn D Q Ctorque = 2 5 . ρn D 6. Rework the microlight propeller example covered in class for a propeller diameter of 1m. Use the same lift coefficient and angle of attack, and take the blade chord as constant along the span. You will be able to use an advance ratio of 0.4. Evaluate the thrust and torque coefficient for a selected chord length, and then scale the blade chord appropriately (via the solidity) to give the required thrust (note that thrust and torque are proportional to solidity). What is the required blade chord? How much more efficient is the propeller compared to the case for D = 0.6m? Plot the twist distribution on a graph. 7.

The blade element efficiency is the local thrust power divided by the local torque dT 1 VdT r tan φ power, i.e. ηb = . From this result show that η b = . 1+ a ΩdQ dQ Hence show that η b = tan ε =

1− tanε tanφ 1 tan φ , where ε is the drag to lift ratio as follows 1+ a tan ε + tan φ

Cd . Cl

From the above show that the optimal efficiency is when φ =

π ε − . 4 2...