The EDF is designed to generate thrust at high speeds. Dynamic experiments are done to validate the calculations and the EDF design.
5.4.1 Method
The dynamic performance is measured by creating a non-zero inlet velocity using the blower.
The performance was measured at three inlet velocities. The created inlet velocity is controlled by two valves set in series, a butterfly valve and a gate valve. The butterfly valve was always set on setting three. For the three inlet velocities, the gate valve was opened 2, 3 and 3.5 turns.
This corresponds with inlet velocities of approximately 19 m/s, 38 m/s and 49 m/s. For every inlet velocity the EDF power was varied in the same manner as in the static experiments.
When the gate valve was opened 3.5 turn the inlet velocity was observed to decrease quickly in time. This indicates that the buffer vessel was depleted. To make sure the buffer vessel was not depleted too far, during these measurements the hand-logged quantities were only noted 3 times instead of 10 times, as has been done in experiments 1 and 2. At this inlet velocity the EDF performance was also only measured at 3 powers.
Except for the exit total pressure, the same quantities are measured as in experiment 2.
In the experiments above, the density was determined using the atmospheric pressure and temperature. In this experiment however, this is not accurate since the inlet circumstances are governed by the blower outlet. Instead, the outlet density will be determined using the exit temperature and static pressure. To allow an accurate calculation of the density, the static pressure at the outlet is measured instead of the total pressure, as has been done in experiment 2.
5.4.2 Processing the results
The processing of the results mostly uses the same equations as in experiment 2. A few small changes have been made. The density is determined using the outlet temperature and static pressure, instead of the atmospheric ones. Furthermore, instead of using the motor efficiency as function of the current, a constant motor efficiency of 92% was assumed. This has been done because the results of experiment 2 showed that the motor efficiency as specified by the manufacturer was probably not accurate for low currents. When interpreting the results one should keep in mind that, for low powers, the actual EDF input power might deviate much from the used one.
Finally, the dynamic performance of an EDF is often expressed in CP and CF as a function of the advance ratio J . The equations for these dimensionless parameters are given in section 2.4.
5.4.3 Results
The figure below shows the EDF input power as function of the rotational speed for an inlet velocity of approximately 19m/s, 38m/s and 49m/s. Both the theoretical as the experimental performance are shown. The theoretical performance is determined using the method ex-plained in section 3.5.4. Here the isentropic efficiency is assumed constant and the deflection in the rotor is assumed proportional to the angle of attack according to equation 3.7. There should be noted that these assumptions only hold when the rotor is operating within its ef-ficient operation range. When in this region, the mid-span angle of attack is between 0° and 18.3°.
Figure 5.13: The EDF input power as function of the rotational speed for different inlet velocities. The dotted part of the theoretic line denotes where the rotor is outside its efficient operation range.
Here the inlet velocity given in the legend is the mean. The inlet velocity is not exactly constant for each measurement series and differs maximum 13% from the average. The theoretical line is subdivided into a solid and a dotted part. The solid part denotes the efficient operation range of the rotor.
From the figure can be concluded that the theoretical and experimental performance show the same trend. The theoretical prediction seems to be more accurate for rotational speeds within the efficient operation range and lower. For rotational speeds above the efficient range, the prediction over-estimated the EDF input power. This can be explained by the fact that for a constant inlet velocity a higher rotational speed gives a higher angle of attack. The theoretical performance assumes that a higher angle of attack gives a higher deflection in the rotor and thus a higher input power. However, for angles of attack above the efficient operation range, this assumption does not hold. The actual deflection is lower, giving a lower input power.
The figure below shows the thrust force as function of the rotational speed for different inlet velocities.
Figure 5.14: The thrust force as function of the rotational speed for different inlet velocities.
The inlet velocity differs maximum 13% from the average in a measurement series. The dotted part of the theoretic line denotes the operation range of the rotor in which the mid-span angle of attack is outside its efficient operation range.
As can be seen the EDF is able to create thrust in case of non-zero inlet velocities. The in the measurements the EDF creates maximum 16N, 21N and 22N of thrust at 19m/s, 38m/s and 49m/s respectively. The fact that the maximum thrust increases for increasing inlet velocity can be explained by the fact that the EDF input power also increases as shown by Figure 5.13.
The figure shows that for very low rotational speeds the thrust becomes negative. This is expected since at low rotational speeds not enough energy can be transferred to the flow to overcome the drag forces caused by the non-zero inlet velocity. The theoretical prediction over-estimates(less negative) the negative thrust forces. This can be explained by the fact that in the theoretical model, negative thrust forces are caused by a negative deflection due to a too small angle of attack. In the experiment however, the drag forces on the blades and the annulus also contribute to the negative thrust. In the model these drag forces are taken into account in the isentropic efficiency. However, in case of negative deflection, and thus negative total temperature rise, a lower isentropic efficiency increases the pressure ratio and therefore gives less negative thrust. So in the model the drag forces in the EDF have the opposite effect of what happens in the experiments.
For an inlet velocity of 19m/s, the theory predicts the thrust force with good accuracy.
For all measurement points the prediction is well within the uncertainty bounds. For inlet velocities of 38m/s and 49m/s, the accuracy is slightly lower. However, the prediction is still within uncertainty bounds for most measurement points. It is surprising that the thrust force is over-estimated in the efficient operation range and the thrust force is under-estimated for higher rotational speeds. One would expect the prediction to be more accurate in the efficient operation range since the assumptions on the relation between the angle of attack and the deflection and on a constant isentropic efficiency are valid here. The thrust force is expected
to be over-estimated for higher rotational speeds for the same reason and because of the fact that Figure 5.13 already showed that the power is over-estimated for high rotational speeds.
The performance of an EDF can be conveniently plotted using the power and thrust coefficients and the advance ratio J . Here the advance ratio is defined as the inlet velocity over the mid-span rotor blade velocity. The advance ratio is equivalent to the angle of attack at mid-span, related by the equation below.
AoAm= atan 1 J
− ζm (5.7)
Here AoAm is the mid-span angle of attack and ζm is the mid-span blade stagger angle.
The figure below shows the power coefficient as function of the advance ratio.
Figure 5.15: The power coefficient as function of the advance ratio. The dotted part of the theoretic line denotes the operation range of the rotor in which the mid-span angle of attack is outside its efficient operation range.
The theoretical and experimental results generally show the same trend. The theoretical prediction is more accurate for advance ratios in the efficient operation region and higher.
This corresponds with the conclusions based on Figure 5.13.
For low advance ratios(high rotational speeds), the theoretical prediction over-estimates the CP. Figure 5.13 showed that the theoretical prediction over-estimates the input power as function of the rotational speed. Therefore it makes sense that the power coefficient is also over estimated, and that the over-estimation is more profound for low advance ratios.
In the dimensionless plot, the different measurement series tend to condense on a single curve. This is beneficial since this means that it is reasonable to assume that CP is inde-pendent on the inlet velocity. Because of this the measured CP can be used to predict the performance of the high speed version of the EDF.
The figure below shows the thrust coefficient as function of the advance ratio.
Figure 5.16: The thrust coefficient as function of the advance ratio. The dotted part of the theoretic line denotes the operation range of the rotor in which the mid-span angle of attack is outside its efficient operation range.
As can be seen, also here the different measurement series tent to condense onto a single curve. This is again beneficial for predicting the performance of the high speed version of the EDF.
For advance ratios above the efficient operation region(low rotational speeds) the thrust coefficient is overestimated. This corresponds with the trends already shown by Figure 5.14.
The theoretical model does not predict negative thrust forces well.
For advance ratios between 0.5 and 0.85 the thrust coefficient is under-estimated for all inlet velocities. This corresponds with what was seen in Figure 5.14 and is again surprising since all measurement points with J < 0.7 are outside the efficient operation range. For J = 0.85 to J = 1.3, the thrust coefficient is over-estimated. This is unexpected since on-design operation is at J = 1.03 and the EDF should perform well here. However, the test results show the opposite.
Two possible explanations are given for the worse performance. First, experiments on isolated NACA wing sections showed that roughness near the leading edge strongly affects the section drag coefficient. For example for an isolated NACA0012 wing section at 0 angle of attack, the drag coefficient goes from 0.006 to 0.01 when going from a smooth wing to a wing with ’standard roughness’ near the leading edge. The rotor and stator blades of the prototype are 3D printed using SLS. This manufacturing method leaves a relatively rough finish which causes small notches at the leading and trailing edge of the blade. Due to these notches the section drag coefficient might be higher than expected which causes a lower isentropic efficiency and thus a lower thrust force. This, however, does not explain why the EDF does perform well at lower advance ratios. A second possible explanation for the worse performance at on-design operation is that in the determination of the advance ratio the inlet velocity is assumed uniform over the inlet. However, it is very likely that this is not the case for two reasons. First, the flow created by the blower does not have a uniform velocity. The velocity
in the middle of the exit is higher[18]. Secondly, the blower creates a circular flow as where the EDF has an annular flow area. At the EDF inlet, the flow from the middle is pushed outwards. Because of the non-uniform inlet air velocity, the inlet air angle distribution over the inlet might deviate much from the design. However, also this explanation does not explain why the EDF performs better than expected at lower advance ratios.
Due to blade stall at high angles of attack, one would expect to encounter a rapid drop in CF for decreasing J around J = 0.7. In the test results, this drop is not encountered. It would be interesting to perform extra tests to find whether and at which J a rapid drop in CF can be found.
Chapter 6
Estimation of the maximum plane velocity using the designed EDF
Using the experimentally determined prototype performance, it is checked whether it is indeed possible to propel a plane up to 750km/h using the designed high-speed EDF. First, the drag force of the plane as function of the velocity is determined assuming a fixed wing size. Next, a fits of the dimensionless experimental performance is made. Using these fits the EDF input power and thrust force is determined for a flying velocity up to 750km/h = 208.3 m/s.
6.1 Plane drag
The plane drag is determined using the method explained in section B. Here the plane is assumed to be a delta-shaped flying wing with the EDFs mounted on top of the plane. Both the drag of the plane as the drag of the EDF housing is taken into account. In the analysis in section B, three different zero-lift drag coefficients are considered. In this section the mean of the three is used: CD0= 0.020. Furthermore, a wing area of Awing = 0.47m2 is used since the analysis in section B showed that this wing size is most promising.
Three EDF configurations are considered: one, two and three EDFs. The plane drag as function of the flight speed is shown in Figure 6.3. The table below gives the drag at 750km/h and the weight of the plane and the batteries.
Table 6.1: Properties of the model airplanes for three different EDF configurations.
Number of EDFs Maximum FD [N] mplane [kg] mbattery [kg]
1 272 24.0 17.5
2 297 27.6 19.4
3 321 31.2 21.4
The maximum legal weight of a model airplane is 25kg. As can be seen the weight of the planes with 2 and 3 EDFs is above this legal limit. In the analysis a flight time of 2 minutes is assumed. This is based on the flight time of the current record holder. As can be seen the majority of the plane mass is given by the battery mass. By decreasing the flight time, the battery mass and thus the plane mass can be reduced easily.
Although the two planes in Table 6.1 are not legal, they are used in this analysis to give a first estimation of the possible performance of the high-speed plane.