The figures below shows the plane drag and EDF thrust as a function of the flying velocity.
(a) Plane with one EDF (b) Plane with two EDFs
(c) Plane with three EDFs
Figure 6.3: Drag and thrust force for planes with one, two and three EDFs. The legend holds for all figures.
Here the dotted lines show the thrust for advance ratios of 0.5 and 0.81, where the max-imum thrust is limited by the motor. The dash-dotted line shows the maxmax-imum thrust for advance ratios between 0.2 and approximately 1.04. J = 1.04 is the point where CF becomes negative. A minimum J of 0.2 was chosen since this is approximately the minimum advance ratio encountered in the experiments. The discontinuity at Cplane≈ 160m/s is caused by the discontinuity in the polynomial fit of CF.
As can be seen for all EDF configurations the drag force is larger than the thrust force at a flying velocity of 750km/h=208.3m/s. This means that using the current EDF design it is not possible to break the Guinness world speed record. Using one, two or three EDFs a maximum velocity of 160m/s=576km/h , 170m/s=612km/h and 178m/s =640km/h is possible. When using two or three EDFs plenty of thrust is available for Cplane< 160m/s. However for higher Cplane, maximum thrust is given by advance ratios higher than approximately 0.81. Figure 5.16 shows that for J larger than approximately 0.81, CF rapidly decreases for increasing J . This causes the maximum thrust force to rapidly decrease for flying speeds above 160m/s.
Because of this, the EDF cannot generate sufficient thrust at the goal flying velocity. To create sufficient lift at 208.3m/s, the thrust coefficient of the EDF must be improved for
advance ratios up to at least 1.03. How much CF must be improved depends on both the size of the model airplane as on the number of EDFs used. Again assuming a plane with a wing size of Awing = 0.47m2, the thrust coefficient at J = 1.03 must be improved from CF ≈ 0.051 to at least CF = 1.03 given that the LMT3080/7 is used and that the plane is propelled using 3 EDFs. At J = 1.03, the theoretical CF = 0.91. This shows that the designed EDF is not powerful enough and a redesign of the EDF or a smaller plane with less drag is needed.
Chapter 7
Conclusion and recommendations
A high speed EDF was designed with the goal to propel a model airplane at velocities up to 750 km/h=208.3m/s to break the Guinness world speed record for model airplanes.
An EDF was designed using axial compressor theory and NACA 65-series cascade test data. The EDF is designed such that the root radius of the rotor and the stator is equal to the outer radius of the electric motor. In the chosen EDF concept the electric motor is glued directly on the stator blades. Because of this the EDF is kept compact and the motor is in direct contact with the flow, which enhances cooling. The EDF is powered by the LMT3080 electric motor with 7 windings. The LMT3080 series are the most powerful electric motors suitable for model airplane applications that could be found. The number of windings of the motor and the mid-span design of the EDF was determined by choosing a maximum tip Mach number of 1.0. From the mid-span design a three-dimensional flow and a corresponding rotor and stator blade geometry were designed. The designed EDF produces maximum 95.1N of thrust and has an isentropic efficiency of 0.77.
A prototype was designed and produced. The prototype is designed to operate at lower speeds and uses a smaller motor to save costs. Since a smaller motor is used, the motor cannot be glued directly to the stator blades and is mounted in a housing. Because of this, extra features were needed proper cooling of the motor. The EDF is produced using mainly SLS 3D printing. Assuming on-design performance, this prototype can be operated at inlet velocities up to 84m/s. A working EDF was designed and made.
An experimental setup was made so that the input power, thrust force, the outlet velocity and rotational speed of the EDF could be measured in both static and dynamic tests. For the dynamic tests, a blower was used to create a non-zero inlet velocity. The blower was developed in a separate project[18].
The static performance was tested by running the EDF in still air at different powers.
The results showed that the theory predicts the static performance with reasonable accuracy.
At the maximum measured power of 864W, 25N of thrust was expected as where 23N was measured.
The dynamical performance of the EDF can be described conveniently using dimensionless parameters: the advance ratio J , the power coefficient CP and the thrust coefficient CF. Here J describes the operating point of the EDF and is defined as the ratio of the inlet velocity over the mid-span rotor blade velocity. CP and CF are dimensionless equivalents of the input power and thrust force. The dynamic performance of the EDF was measured at inlet velocities of approximately 19, 38 and 49m/s. The measured input power agreed with the theory relatively
well. Although the theory did over-estimate the input power, the prediction was within the uncertainty bounds for most measurement points. Larger and more interesting differences were found between the theoretical and experimental thrust. For J at the design operating point, the measured CF was much lower than expected. Where the theory predicted a thrust coefficient of CF = 0.91, the experiments gave CF = 0.045. This showed that the isentropic efficiency at this point was much lower than expected. Possible explanations include decreased isentropic efficiency due to the surface roughness of the 3D printed blades and a decreased performance due to non-uniform inlet velocity. For lower J the theory under-estimated the thrust. A lower J corresponds with a lower inlet velocity or higher blade velocity. This is surprising since at these operating points, a drop is efficiency was expected due to blade stall.
No explanations were found for this behaviour.
The experimental results were used to predict the maximum flying velocity of a plane with a wing area of 0.47m2. Using one, two and three EDFs, maximum velocities flying velocities of 576km/h, 612km/h and 640km/h are possible. To reach the target velocity, the performance at the design point of the EDF must be improved. This shows that a redesign of the EDF is needed.
Concluding, a working EDF was designed and made and the used methods and gained experience can be used in later projects to further build on. Although the theory suggests it is possible to create sufficient thrust to propel a small plane at high flying velocities, the experiments show that still some improvements in the EDF design are needed.
Recommendations
The choices of the number of windings in the motor and mid-span design are based on a maximum rotor tip Mach number of 1.0. However, this Mach number is quite arbitrary and different choices and designs are possible. Another method would be to determine an optimal EDF size that corresponds with the plane and to base the design on this. A first step in this has been made in appendix B. In the analysis done here, a certain plane shape concept is assumed, where the EDFs are mounted on top of the plane. This concept is in no means claimed to be optimal. It would be interesting to do more work on integral design process of the plane and the EDF with all corresponding electronic parts. This way, one gains insight in the overall optimal design point, which increases the chance that the Guinness speed record will be broken at one point.
The dynamic test showed surprising results. The thrust coefficient CF in the efficient op-eration region of the EDF was much lower than expected and CF for lower advance ratios was higher than expected. Several possible explanations are given for the reduced CF. However, no explanations were found for the high CF values for low J . One possible explanation for the worse performance is the high surface roughness of the prototype EDF, which might increase the losses in the blade cascade. The low quality surface finish is caused by the manufacturing method: SLS 3D printing. It would be interesting do manufacture a rotor with a smooth surface and test the EDF performance using this. The rotor is the most important part of the EDF to have a smooth surface since the rotor contributes most to the pressure ratio over the EDF. Another possible explanation is the fact that it is likely that the inlet velocity profile of the EDF in the tests is non-uniform. This might reduce the performance of the EDF since it is designed on a uniform inlet velocity. It might be interesting to measure the inlet velocity profile of the EDF.
When operating the EDF at decreasing J , one would expect a steep drop in CF at one point due to blade stall. However, this is not encountered in the experiments. It would be interesting to perform tests at lower J to investigate whether stall occurs. This can be done by decreasing the inlet velocity or by increasing the rotational speed of the EDF.
Decreasing the inlet velocity can easily be done by closing the valves on the blower. A higher rotational speed can be achieved by operating the EDF at a higher voltage. At 57.6V the LMT2280/10 can deliver maximum 9kW at 41.0kRPM. In the performed experiments the motor was operated at approximately 24V, giving a maximum motor output power of 1.3kW at 15.5kRPM. To perform experiments at higher power, different batteries, a different ESC and different equipment to measure the current and voltage over the ESC are needed due to the higher voltage and the higher current.
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Appendix A
Naca 65-series shape data
In the table below the thickness distribution and mean-line ordinates are given at a series of stations along the chord length. All, thickness ordinates, mean-line ordinates and stations are given in percentages of the chord length. Furthermore the leading edge radius in percentages of the chord line and the mean-line slope are given. The mean-line slope at the leading and trailing edge (station 0 and 100) is infinite due to the definition of the mean-line.
Table A.1: Geometry description of a NACA 65-series profile with Cl0 = 1.0 camber and 0.1c thickness. Here x denotes the station along the chord line, yt is the thickness ordinate, ym is the mean-line ordinate, and dydxm is the slope of the mean-line. x, yt and ym are given in percentages of the chord length. [7]
Station x Thickness ordinate yt Mean-line ordinate ym Mean-line slope dydxm
0 0 0
Appendix B
Analysis on EDF configuration and potential plane size
In this chapter an analysis is done on the most promising EDF configuration and the sizing of a high speed plane. In the analysis below, first the drag force on the plane and the EDF and the input power of the EDF are determined as a function of plane and EDF size and the mass flow through the EDFs. As explained in section 2.2, an increase in mass flow through the EDFs ˙m on a plane gives an increase in propulsion efficiency ηp. However, an increase in mass flow comes with an increase in EDF size which creates more drag. Using this, the optimum mass flow as function of the plane size is determined. After this, the performance of single-stage and two-stage EDFs are compared at maximum flying velocity(750km/h). Next, the most promising number of single-stage EDFs is determined, taking into account a number of constraints on the EDF and plane design. Finally, an analysis on the limitations in plane sizing is done.
B.1 Drag force and EDF input power
Assuming isentropic conversion of energy in the EDF, substituting and rewriting equations 2.10 to 2.18 gives the equation below for the needed EDF input power:
PEDF = 1 2
F2
˙
m + CplaneF (B.1)
Here FT is the thrust which is equal to the drag is steady flight. The drag of an EDF and the effect that the EDF has on the drag of the plane and the other way around are complicated phenomena which are often analysed using CFD simulations or by doing experimental tests.
Due to time limitations, in this project only a simple analytic analysis can be done. In a crude estimation, the total drag on an airplane with and EDF can be determined by:
FD = 1 Here the first term denotes the airplane drag and can be derived using equations 2.1 and 2.2. The second term denotes the EDF drag using equation 2.1. Here the EDF CD is assumed to be constant and equal to the zero-lift CD of the airplane. For the EDF, reference surface AEDF is defined as the outer surface of the housing. For the airplane drag the wing
area is used as reference area. In steady flight the lift force is equal to the gravitational force acting on the plane. To determine the lift dependent part of the drag, the plane mass must be determined. The total mass of the plane mplane is the sum of the mass of the empty plane structure mhull, the battery mass mbattery and the motor mass mmotor. Other components adding to the mass are for example the EDF housing and blades, cables, other electronic components, etc. However, the contribution of these latter ones is small and can be neglected. The mass of the empty plane structure is assumed to be determined by:
mhull = −1.86 + 14.2Awing (B.3)
This equation is based on the weight and wing area of the two planes owned by team Air/e, the fun-jet ultra and the hot-shot. The fun-jet and the hot-shot are considered a relatively small and an average sized model airplane. Both planes are shown in Figure B.1. The Table below gives the wing area, aspect ratio and the plane structure weight of both planes.
Table B.1: Properties of the fun-jet ultra and hot-shot.
Awing [m2] AR [-] mhull [kg]
Fun-jet ultra 0.1725 3.527 0.6
Hot-shot 0.6238 2.179 7
(a) (b)
Figure B.1: Two model airplanes owned by team Air/e. (a) The fun-jet Ultra, (b) the hot-shot(in building state)
The mass of the motors and batteries is given by:
mmotor = PEDF Here PEDF is the input power of the EDF, ρpower,mass is the power density of an electric motor in W/kg, ρenergy,mass is the energy density of the batteries in J/kg and tf light is the duration of a speed record attempt.
The root radius of the EDF is determined by the outer diameter of the motor, since the motor choice is fixed this gives rr= 0.03m. Now the total surface area of all the EDF housings AEDF is given by:
AEDF = 2 π rt LEDF nEDF (B.6)
rt= s
˙
m/nEDF
Cplaneρπ + rr2 (B.7)
Here nEDF is the number of (single- or two-stage) EDFs and LEDF is the length of the EDF. The length of the EDFs is fixed by the length of the motor. Each stage is assumed to be as long as the motor.