DESIGN OF A NEW PROPELLER

This section deals mainly with the aerodynamic considerations of design­ing a new propeller. The optimum blade loading is prescribed by the Betz condition, which requires the trailing vortex system to lie along a helical surface in the ultimate wake. This condition will be met if

wr tan (ф + a,) = constant

= У + wo (6.60)

Wo is a fictitious velocity called the impact velocity. Given the design advance ratio, one can arbitrarily choose a value of wJwR. From the geometry of Figure 6.10, it follows that

sin (ф + ad cos (Ф + ai)

where

Substituting Equation 6.61 into Equation 6.42 leads to the product aCi as a function of x. One must then decide how to choose between a and Q. The procedure for doing so is not well defined. First, one must choose the number of blades. This may be done on the basis of experience or arbitrarily as a first step in a design iteration. Similarly, a radial distribution of thickness is chosen. Ultimately, stress calculations must be made. Based on these results, the thickness may be changed.

A very practical and completely nonaerodynamic consideration in the choice of an airfoil section for a propeller blade is the question of stress concentrations resulting from leading and trailing edge nicks and scratches, particularly leading edge nicks. To elaborate on this point, consider the two airfoil sections pictured in Figure 6.22. From a stress-concentration view­point, the symmetrical airfoil on the left is preferred since, in bending, stresses are directly proportional to the distance from the neutral axis. From an aerodynamic viewpoint, the cambered section is preferred. Hence, the engineer is faced once again with another compromise, a practice that characterizes much of the engineering profession.

M (b)

Figure 6.22 Susceptibility of airfoil shapes to leading and trailing edge stress concentrations, (a) Edges close to neutral axis. (b) Edges removed from neutral axis.

Having selected an airfoil family such as the NACA series-16 or the newer supercritical airfoil, one now chooses at each x a design C, that will avoid compressibility effects. The steps for doing this are:

1. Choose С/.

2. Calculate c from aCt.

3. Determine Mcr from tic and C(.

4. Compare Ma with the resultant local M.

5. If Mcr is less than M, decrease C( and repeat.

If Mach number is not a consideration in the design, then one can choose C(j to give the lowest Cd to C( ratio for the chosen airfoil family.

Having determined the radial distribution of c (and hence cr) and С/, the corresponding Cd values are calculated. These, together with (ф + a,), are substituted into Equations 6.32a and 6.32b to determine thrust and power. The entire design process is performed with different vv0 values until the desired value of Cr or Cp is achieved. Generally, increasing w0 will increase either of these coefficients.

Most propellers are designed to operate immediately in front of a fuselage or nacelle. The inflow velocity in this case is no longer a constant but is, indeed, a function of x, the dimensionless radial station. This three – dimensional flow field can be determined by the potential flow methods presented in Chapter Two. With V a function of x, the resultant flow angle, ф, becomes

or

For this case of a nonuniform, potential inflow, the Betz condition is not

V(x) + w0 = constant Instead, one should impose only

w0 = constant (6.65)

Equation 6.65 follows from superimposing the potential flow from the propeller on that produced by the body. In the ultimate wake V(x) will approach V0 and w0 will approach 2w0, so that the Betz condition is again satisfied.