As stated before, an uniform purely axial inlet flow is assumed. This gives that the three-dimensional flow will be of a free vortex design. The formulas from section 2.2.4 can be used.
The variation of the air angles α2, β1 and β2; the Haller numbers Hrotor and Hstator; and the degree of reaction Λ over the radius are shown below:
(a) (b)
(c)
Figure 3.4: The air angles(a), Haller numbers(b) and degree of reaction(c) over the radius.
As can be seen, the deflection β1 − β2 decreases for increasing radius. Given that the condition of constant specific work applies, this can be explained by the increasing blade speed with the radius, which means that less deflection is needed to produce the enthalpy rise. Furthermore, the Haller numbers are well above 0.72. The large Haller numbers are explained by the fact that the motor power is limited in the rotor design. Also the degree of reaction is well within bounds. From the fact that the rotor Haller number is larger than that of the stator, can be concluded that there is more diffusion in the rotor than in the stator.
This is confirmed by the degree of reaction, which is larger than 0.5 for al radii.
3.5 Blade design
Now the three-dimensional flow design is known, blades can be designed such that the designed flow is achieved. In the design the rotor blade Mach number varies between 0.72 and 1.0, therefore double circular arc blade(DCA) sections are most suitable. However, little DCA cascade data is available. On the NACA 65 series plenty cascade data is available. This
data allows to determine the optimal blade shape and the efficiency of the compressor. Also, the prototype made in section 4 can only be tested at low axial speeds due the lack of a device to create such high inlet velocities. Therefore, a blade design using NACA 65-series blade sections suffices within the scope of the experiments. For both the rotor and the stator sections with 10% thickness are used since the cascade tests are done using that thickness.
Since the cascade data is only available in figures it is not realistic to determine a contin-uous blade section design over the radius. Instead the blade sections for both the rotor and the stator are designed at 5 radii evenly spread from root to tip. The blade section shape between these five positions is obtained by interpolation in the CAD software. The blades are designed such that the blade leading edge is a straight line.
In the rotor and stator design two EDFs owned by team Air/e are used as inspiration, the Schubeler DS-98-DIA HST and the Wemotec Midi Fan evo EDF. These EDFs are shown in the figure below:
(a) (b)
Figure 3.5: The Schubeler DS-98-DIA HST(a) and the Wemotec Midi Fan evo EDF(b).
3.5.1 Rotor blade section design
The chord length c of the rotor blade is determined using the blade aspect ratio l/c. A good estimate is l/c = 3 according to [4]. Although, the Schubeler and Wemotec rotors have an aspect ratio of 1.81 and 1.66 respectively. The average, an aspect ratio of 1.7 has been chosen.
With a blade length of l = 32mm this gives a chord length of c = 18.8mm.
The number of blades is determined considering the solidity σ = c/s. Note that the solidity varies over the radius for a fixed chord length. Cascade data is available for σ = 0.5 − 1.5.
For 11 - 15 blades both the root and tip solidity lies within the range of the data. A number of 13 blades is chosen since this lies in the middle of the available range and 13 is a prime number which is beneficial, as explained in section 2.3.3. The solidity now varies between 1.2966 at the root to 0.6272 at the tip.
Method 2, explained in section 2.3.3, is used to determine the camber and stagger angle.
The table below shows all important data concerning the blade section shape at the five radii. Note that the angles are denotes in cascade notation.
Table 3.5: Important parameters to determine and describe the rotor blade section design.
Here r: radial position, α1: air inlet angle, ε: deflection, σ: solidity, Cl0: camber, AoA: angle of attack, ζ: stagger angle.
Section No. r [m] α1[°] ε[°] σ [-] Cl0 [-] AoA[°] ζ[°]
1 (root) 0.030 32.3 21.1 1.297 1.03 12.7 19.6
2 0.038 38.7 14.1 1.024 0.75 9.2 29.5
3 0.046 44.2 9.7 0.845 0.65 7.5 36.7
4 0.054 48.7 6.8 0.720 0.56 6.2 42.5
5 (tip) 0.062 52.6 4.9 0.627 0.47 5.2 47.4 3.5.2 Stator blade section design
The stator blades are structural parts of the EDF, supporting the motor and rotor. Although the forces acting on the stator blades are relatively small, there is a chance that the rotor is unbalanced which can cause violent vibrations. The stator blades must be able to withstand these vibrations. However, the exact severity of these vibrations is not known and therefore I chose to over-dimension the stator blades.
The stator blades of the Schubeler and the Wemotec EDF have an aspect ratio of 0.4 and 0.733 respectively. A lower aspect ratio gives a longer chord and stronger blades. An aspect ratio of 0.4 was chosen. This gives a chord length of 80mm.
The stator solidity of the Schubeler and the Wemotec EDFs lie between σ = 0.75 − 1.42 and σ = 0.5 − 1.2 respectively. Choosing similar range in σ would lead to 3 stator blades.
However, to over-dimension the stator 4 blades are chosen. This gives σ = 0.821 − 1.698.
Data is only available up to σ = 1.5. However, due to the linear behaviour of the data with respect with the solidity, the data can be extrapolated up to σ = 2. This has been done earlier in [16].
For the stator, the blade inlet air angle is out of the data range. Therefore, method 2(section 2.3.3) cannot be used to determine the camber and stagger angle. Instead a slight variation in method 1 is used. In method 1 i = 0° is set. However, it is not known whether i = 0° is optimal for the blade sections shape. Therefore, instead the optimal AoA is determined as a function of the camber using figure 2 from [8] just as in method 2. Now the camber angle is determined by solving:
1
2θ = α1− AoA(θ) − α2+ δ (3.6)
Here θ is the camber angle and AoA is the angle of attack which is a function of the camber. Note that the carpet plots describing AoA(θ) express the camber in terms of the design lift coefficient Cl0. Equation 2.39 can be used to convert the camber angle θ into Cl0. Furthermore, δ is the deviation which is determined using equations 2.43 and 2.44.
The table below shows all important data concerning the blade section shape at the five radii.
Table 3.6: Important parameters to determine and describe the stator blade section design.
Here r: radial position, α1: air inlet angle, ε: deflection, sigma: solidity, Cl0: camber, AoA:
angle of attack, ζ: stagger angle.
Section No. r [m] α1[°] ε[°] σ [-] Cl0 [-] AoA[°] ζ[°]
1 (root) 0.030 23.5 23.5 1.698 1.07 15.0 8.52
2 0.038 19.0 19.0 1.340 0.92 12.2 6.85
3 0.046 15.8 15.8 1.107 0.82 10.1 5.69
4 0.054 13.6 13.6 0.943 0.75 8.72 4.88
5 (tip) 0.062 11.9 11.9 0.821 0.69 7.68 4.22 3.5.3 Blade efficiency
Using the method described in section 2.3.4 the blade efficiency for both the rotor and the stator has been determined at mid-span. Using the data from [7] the profile drag coefficient of the rotor and stator have been determined at CDp = 0.014 and CDp = 0.015 respectively.
Now the blade efficiencies are ηb,rotor = 0.878 and ηb,stator = 0.125. The stator efficiency is very low. This can be explained by the fact that the isentropic static pressure rise is low.
Therefore small losses already cause a very small efficiency. Furthermore, the annulus losses of the stator are approximately 4 times as large as those of the rotor due to the large blade spacing.
The overall isentropic compressor efficiency is ηs= 0.77.
3.5.4 Off-design and static performance
Until this point only the ’On-design’ performance has been considered, which means that ratio of the inlet velocity and the rotational speed are equal to the value the EDF was designed on. Or in other words, the advance ratio is equal to the design value of J = 1.03. In this case the rotor inlet air angles and the deflections in the rotor are on their design values. During off-design operation the rotor inlet air angles are not on their design values. Because of this the deflection in the rotor will differ, influencing the EDF power and thrust.
Figure 3f in [8] can be used to determine the off-design deflection of a blade design as a function of the blade angle of attack. Appendix C shows how to use this figure. The relation below gives the mid-span deflection as function of the mid-span angle of attack.
εm = 0.8AoAm+ 3.8 (3.7)
Here AoAm is the mid-span rotor angle of attack and εm is the mid-span air deflection of the rotor blades.
When the angle of attack becomes too large or too small, the blade can stall. When this happens the blade losses will increase much and the blades do not perform as designed. The maximum angle of attack can also be determined for Figure 3f from [8] and has been set on 18.3° for the rotor mid-span. The minimum angle of attack is not given. However, no test data is available for angles of attack below 0°. Therefore, I assume the minimum allowed angle of attack to be 0°. In this report the operation region where AoAm = 0°−18.3° is called the efficient operation region. This region can also be denoted by J = 0.70 − 1.34. Equation 3.7 is only valid within the efficient operation region.
Off-design dynamic performance The theory explained in section 2.2.1 is used to de-termine the off-design performance. Here β1 is determined from the rotor rotational speed and the inlet velocity. The rotor outlet air angle is determined from the off-design deflection described by equation 3.7. The isentropic efficiency of the EDF is assumed to be constant.
Both this assumption as equation 3.7 are only valid in the efficient operation range. Because of this the theoretical estimation is expected to be more accurate within this range.
Static performance To determine the static performance, again the theory in section 2.2.1 is used. However, in static operation the forward velocity is zero and the assumption that the inlet velocity is equal to the forward velocity does not make sense. Instead, for a certain EDF input power, the equations are solved for the mass flow. Here the mass flow is calculated from the outlet velocity and density. The deflection in the rotor is again calculated using the off-design deflection given by equation 3.7.
Both the theoretical static and dynamic performance curves can be seen in the results sections of section 5.