Although the EDF is not designed for static operation, it is interesting to determine the static performance since it can be of use in the design of the airplane.
5.3.1 Method
In the static tests the setup without blower is used. Furthermore, the EDF is fitted with the static test inlet. The measurements are executed as follows. First the EDF is powered at
max power and all quantities are measured and noted. Next, the power is decreased until from the sound the EDF makes can be told that the EDF is clearly ran at lower power and the quantities are measured and logged again. This way the power is decreased to zero in approximately 7 steps.
The experiments are done starting at maximum power since this way the batteries are fully charged during the experiments with the highest powers. The battery voltage drops by up to 4V when supplying high currents due to the internal resistance. Especially when the batteries are not completely fully charged, this can limit the power they can supply significantly. In every measurement the pitot tube is positioned at position 1 shown in Figure 5.7.
The following quantities are measured:
Table 5.2: Quantities measured in experiment 2
Atmospheric temperature Ta
Dynamic pressure at the outlet pdyn,4
Total pressure relative to the atmospheric pressure p04− pa 5.3.2 Processing the results
The density is assumed constant and equal to the atmospheric density, which is calculated from the atmospheric temperature and pressure. Using equations 5.2 and 5.5 the outlet velocity at the pitot tube Ca4 and the bulk outlet velocity Ca4,bulk are calculated. Since incompressible flow is assumed, the inlet bulk velocity is easily calculated using conservation of mass.
The power through the ESC is calculated using the measured voltage and current. To determine the EDF input power the efficiency of the ESC and the motor should be taken into account. The efficiency of the ESC is estimated using [19] and is set of 85%. The efficiency of the motor is specified as a function of the current by the manufacturer and is shown below for a voltage of 24V:
Figure 5.9: The motor efficiency as function of the current at a voltage of 24V.[14]
Here Imotor is the current through the motor and ηm is the motor efficiency. As can be seen the efficiency is fairly constant for higher currents and drops fast for currents below approximately 20A.
Since the EDF performs static the pressure ratio over the EDF is equal to Rs = p04/pa. The total temperature rise can be calculated from the EDF input energy using equation 2.13.
Now the isentropic efficiency is calculated using:
ηs= Ta The static performance of a propeller of EDF is often expressed in terms of CF/CF as a function of CP. Here CF is the dimensionless thrust coefficient and CP is the dimensionless power coefficient. These are explained in section 2.4.
5.3.3 Results
The figures below show the EDF input power and the inlet bulk velocity as function of the rotational speed during static operation.
(a) (b)
Figure 5.10: The EDF input power as function of the rotational speed during static op-eration(a) and the inlet bulk velocity as function of the rotational speed(b) during static operation.
Here the theoretical performance is determined in section 3.5.4. As can be seen, the theoretical and experimental performance show the same trend. Over the entire ω range the theoretical calculation over-estimates the EDF input power. The EDF was run at a maximum rotational speed of 13.8kRPM. At this point the EDF used 864W as where the theory predicted 1075W. Although the theory does over-estimate the input power, for most measurement points the prediction is within the uncertainty of the measurements. A possible explanation for the over-estimation is given by the fact that the EDF input power is a function of the rotational speed, the inlet velocity and the deflection in the rotor. Figure 5.10b shows that the theory over-estimates the inlet velocity. This explains the experimental PEDF to be lower than the theoretical. However, the lower measured inlet velocity causes the angle of attack to be higher than estimated. This gives a higher deflection in the rotor(equation
3.7), which increases the input power. The results show that the direct effect of a lower inlet velocity on the input power dominates the effect of the higher angle of attack.
The figure below shows the thrust as a function of the EDF input power.
(a) (b)
Figure 5.11: The EDF thrust as function of the input power during static operation(a) and the isentropic efficiency as function of the input power(b).
Figure 5.11a shows that the theoretical and measured thrust show the same trend. For low input powers the thrust force is predicted accurately. The accuracy decreases for increasing input power. However, the prediction is still within the uncertainty of the measurements. At the maximum power of 864W, a thrust force of 25N is predicted as where the experiment gives thrust force of 23N.
Since the thrust is lower than predicted for most powers, one expects the isentropic effi-ciency to be lower than calculated theoretically. However, Figure 5.11b shows the opposite.
The theory gives an efficiency of 0.77. For PEDF higher than 273W the experimental isen-tropic efficiency has a value of approximately 0.87. The efficiency seems to be constant here.
However, due to the large uncertainties no conclusions can be made. The large uncertainties in the isentropic efficiency are mainly caused by the uncertainties in the thrust and the current measurements. For lower input powers, the experimental isentropic efficiency is much higher with unrealistically high values between 1.0 and 1.9.
The under-estimation of the isentropic efficiency can be explained by two things. First, the pitot tube measurements are done behind the nozzle at measurement position 1(Figure 5.7), which is a position at which the flow is disturbed minimally. If the pitot tube measure-ment would have been done, for example, closer to the nozzle walls or in the wake of the stator blades, then the measurements would probably have shown a much smaller isentropic efficiency. Second, the EDF input power is determined from the power through the ESC, using an estimation of the ESC and motor efficiency. There is a chance these estimations are off. According to the manufacturers specifications, the motor efficiency decreases rapidly for decreasing current as the current comes below 20A(see Figure 5.9). Because of the low motor efficiency, the EDF input power becomes very low. Because of this, the generated thrust becomes very high for the used power. This results in an unrealistic high isentropic efficiency.
For example at the lowest measured power, the current through the EDF was only 4A which
leads to a motor efficiency of only 38%. At this point the experimental isentropic efficiency is 1.9.
The figure below shows the static performance of the EDF in terms of CF/CP as a function of CP.
Figure 5.12: The ratio of thrust coefficient over the power coefficient as a function of the power coefficient for static operation.
As can be seen the theoretical prediction and the experimental results do not match very well. This is a result of the deviations between the prediction and the measurements of the thrust and power, discussed above. The trend in the measurements does slightly resemble the typical shape of a static performance curve shown in Figure 2.9. However, due to the large uncertainties no conclusions can be made. Also, for low powers, and thus low CP, the calculation of the input power is probably not accurate, as discussed above. Therefore the peak CF/CP value of 8.9 should especially not be trusted.