Here αm is the mean flow angle is the blade row and CD is the overall drag coefficient given by:
αm= 1/2 (tan α1+ tan α2) (2.51)
CD = CDp+ CDA+ CDS (2.52)
Here CDp is the profile drag coefficient over the blade section, CDA is the annulus drag coefficient and CDS is the secondary losses drag coefficient. The profile drag coefficient of a NACA 65-series section can be determined from Figures 7 to 84 from [7]. CDA and CDS are given by:
Here l is the blade length and CL is the section lift coefficient that can be from the same figures as the profile drag coefficient[7] or with the equation below:
CL= 2 1 σ
(tan α1− tan α2) cos αm− CDp tan αm (2.55) Now the blade efficiencies for the rotor and stator can be determined using the equations above. Although the ηb and the isentropic efficiency ηsare different things, their actual values are very close and without much error ηb = ηs can be used. The isentropic efficiency can be calculated using:
ηs = Λ ηb,rotor+ (1 − Λ) ηb,stator (2.56)
2.4 Dimensionless parameters
The performance of propellers and EDFs is often expressed using dimensionless numbers.
Important dimensionless numbers are shown below:
CP = PEDF
ρω3rm5 (2.57)
CF = FT
ρω2rm4 (2.58)
J = Cplane ωrm
(2.59) Here CP and CF are the power and thrust coefficient. These are non-dimensional measures for the EDF power and thrust. The can be interpreted just as the lift coefficient describes the lift of a wing. The advance ratio is a measure for the working point of the rotor. The advance ratio is equivalent to the relative rotor inlet angle β1 and the rotor angle of attack AoA at mid-span.
The static thrust is often presented as CF/CP as a function of CP. The figure below shows a typical shape of a static thrust curve for a propeller.
Figure 2.9: Typical shape of a CF/CP vs CP curve describing the static performance of a propeller. Image from [20]
The performance of an EDF is expected to have a similar shape since an EDF is basically a propeller with a housing.
Chapter 3
Design
In this section the design of a high speed EDF is discussed. Since the high speed plane is not yet designed, it is not exactly known what the exact requirements of the EDF are. Because of this, an analysis is done of the potential size of the plane and the optimal size of the EDF to go with this plane. Next, a design for a high speed EDF is made. Finally, a low-speed prototype is designed using the high-speed design as a basis.
3.1 Requirements and concept
The model airplane used for the current Guinness world speed record of 750 km/h=208.3m/s, is propelled by a Behotec 180 model jet engine [11]. According to manufacturer specification, this jet engine can generate 180N of thrust[12]. This means that the useful work the jet engine must deliver at top speed is FT · Cplane = 180 · 208.3 = 37.5kW . The Schubeler DS-98-DIA HST EDF owned by team Air/e can deliver up to 130N of static thrust. However, this EDF has a maximum power of only 10kW and therefore will never be able to create enough thrust at high speeds[13]. To create a plane capable of flying 750 km/h a new high power EDF must be designed.
The general requirements and preferences for the EDF are stated below:
Requirements:
1. The EDF must be able to propel a, yet to be designed model airplane up to speeds of 750 km/h
2. The EDF must be compatible with typical model airplane electronics 3. The used motor must be commercially available.
4. The EDF must provide cooling for the electric motor .
Preferences:
1. The EDF must be as light as possible 2. The EDF must be as efficient as possible
Here should be kept in mind that the maximum weight of a model airplane is 25kg. In case that the mass of the EDF is too large or the efficiency is too low, this can cause problems.
Keeping the requirements and preferences in mind a layout for the EDF has been chosen:
Figure 3.1: Schematic layout of the EDF that is designed. The rotor is directly mounted on the axle of the electric motor. The motor is glued onto the stator blades. The nozzle is a separate part and is mounted after the stator.
To keep the EDF compact and light, the rotor is mounted directly on the motor shaft, instead of supporting is separately. The motor is supported by the stator blades and in direct contact with the airflow to enhance cooling. In this configuration, the root-radius of the stator is determined by the outer diameter of the stator. Furthermore, the stator blades are structural parts that need to be strong and stiff enough to support the vibrations and forces working on the motor and rotor. The EDF is mounted using brackets on the housing. The nozzle inner and outer surfaces are separate parts for easy production and such that in later research different nozzle shapes can be tested. The nozzle inner surface smoothly converges to minimize losses in the wake of the EDF.
In the section B the viability of a two-stage EDF is considered. The schubeler EDF, by manufacturer specifications, has a maximum outlet velocity of 82m/s. This is obviously not enough the propel a plane flying at 208.3m/s(=750km/h). In an earlier project a two stage EDF using a separate motor for each rotor was proposed[21]. Here two motors are used to drive the two rotors to make a more powerful EDF. Another advantage of two motors is the fact that this way the rotational speed of the rotors can be controlled separately, which might be beneficial for the performance. Since each stage has a separate motor, the layout of a two-stage EDF is very similar to that of a single-stage EDF:
Figure 3.2: Schematic layout of a two-stage EDF. Two rotor-stator pairs are places behind each other. Each rotor is powered by its own motor.
When searching for the optimal EDF, the mass flow is an important parameter to consider.
A larger mass flow gives a higher propulsion efficiency, as explained in section 2.2. However, a larger mass flow also gives a larger EDF which gives a higher drag force on the EDF housing. Clearly an optimum mass flow, giving a minimum EDF input power can be found.
In section B an analysis on the optimal EDF configuration is done. Here, the optimal mass flow through the EDFs is determined as function of the mass flow. Next, two different EDF configurations were compared, two single-stage EDFs and one two-stage EDF. Note that in both configurations two motors are used. The analysis showed that a propulsion using two single-stage EDFs uses less input power. This is caused by the fact that a two stage EDF has a slightly lower optimal mass flow than a configuration using single-stage EDFs, but not low enough to create such a small EDF that the drag force on the EDF housing is becomes smaller. From this can be concluded that a propulsion using single-stage EDFs is the most promising. In the rest of this report is focused on the design of a single-stage EDF.