Blade Element Propeller Theory
Consider a cross-sectional area of a blade, shown in grey. Air particles passing through the top surface travels faster than those at the bottom. By Bernoulli’s Principle, the difference in air velocities creates a pressure differential, giving rise to a lift force. The air particles at the bottom are deflected downwards, generating frictional drag on the airfoil.
We ideally want to maximise lift and minimise drag, so that we can obtain a large thrust and reduce the resistive torque required to rotate the propeller.
Computational Fluid Dynamics
Summing up all blade elements to determine thrust and resistive torque is usually impractical, so a CFD analysis is usually performed with a software like SOLIDWORKS Flow Simulation.
As a brief summary, SOLIDWORKS Flow Simulation approximates Reynolds-Averaged Navier-Stokes (RANS) equations using the Finite Volume Method (FVM) on a rectangular (parallelepiped) computational mesh. The RANS equations are time-averaged equations of motion for fluid flow.
Sources
John D. Anderson, Jr. (2017). Fundamentals of Aerodynamics Sixth Edition. McGraw-Hill Education.
Blade Element Propeller Theory | Aerodynamics for Students. (n.d.). http://www.aerodynamics4students.com/propulsion/blade-element-propeller-theory.php
Sobachkin A., Dumnov G., Sobachkin A. (2014). Numerical Basis of CAD-Embedded CFD White Paper. https://www.solidworks.com/sw/docs/flow_basis_of_cad_embedded_cfd_whitepaper.pdf
To calculate efficiency, we define these parameters:
- Thrust (N) acting on all blade surfaces
- Axial speed (m/s) of air exiting a circular sectional area right above the fan
- Resistive torque (N m) of the motor to rotate the propeller
- Rotational speed of a defined circular rotating region of the fan (RPM)
- Standardised at 7000 RPM
- Efficiency (%)
Sources
M. Jenkins, “How to Optimize a Propeller Design,” SimScale, Jun. 01, 2023. [Online]. Available: https://www.simscale.com/blog/how-to-optimize-propeller-design/
Fan 3B 35mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.203 | 9.15 | 0.0100 | 7000 | 25.38 |
Fan 3B 25mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.208 | 9.17 | 0.00746 | 7000 | 34.9 |
Fan 6B 35mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.923 | 12.5 | 0.0315 | 7000 | 50.0 |
Toy Fan Propeller Model
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.049 | 4.16 | 0.000902 | 7000 | 30.8 |
Fan 2B 25mm Curved
Dimensions | z: 261mm | x: 103mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.0891 | 5.24 | 0.00148 | 7000 | 43.0 |
Fan 3B 25mm Curved
Dimensions | z: 345mm | x: 114mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.105 | 5.48 | 0.00163 | 7000 | 48.20 |
Fan 4B 25mm Curved
Dimensions | z: 253mm | x: 110mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.127 | 5.92 | 0.00210 | 7000 | 48.8 |
Fan 2B V1
Dimensions | z: 309mm | x: 111m
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.112 | 5.98 | 0.00195 | 7000 | 46.85 |
Fan 3B V1
Dimensions | z: 177mm | x: 106mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.155 | 6.49 | 0.00264 | 7000 | 51.98 |
Fan 4B V1
Dimensions | z: 258mm | x: 94mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.183 | 7.12 | 0.00333 | 7000 | 53.38 |
Fan 5B V1
Dimensions | z: 257mm | x: 102mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.200 | 7.37 | 0.00380 | 7000 | 52.92 |
Fan 4B V2
Dimensions | z: 255mm | x: 93mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.140 | 6.24 | 0.00203 | 7000 | 58.71 |
Fan 4B V3A
Dimensions | z: 242mm | x: 96mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.176 | 6.50 | 0.00241 | 7000 | 64.76 |
| 0.181 | 6.67 | 0.00250 | 7000 | 65.88 |
* Made minor modifications for the 2nd row.
Fan 3B V3
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.139 | 6.01 | 0.00184 | 7000 | 61.9 |
Fan 5B V3
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.168 | 6.52 | 0.00235 | 7000 | 63.6 |
Fan 4B V3B
Dimensions | z: 234mm | x: 87mm
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.1398 | 5.666 | 0.001669 | 7000 | 64.74 |
Fan 4B V3 (Further Testing)
We reduced the trailing edge pitch and found that efficiency drops if the blade curvature becomes too gentle.
| Thrust (N) | Velocity (m/s) | Torque (N m) | Rotation (RPM) | Efficiency (%) |
| 0.120 | 5.48 | 0.00166 | 7000 | 54.04 |
Fan 4B V3A Asym
Extend Mid Angle ("long boi")
|
Thrust (N) |
Velocity (m/s) |
Torque (N m) |
Rotation (RPM) |
Efficiency (%) |
|
0.145 |
6.06 |
0.00193 |
7000 |
62.1 |
Extend Small Angle
|
Thrust (N) |
Velocity (m/s) |
Torque (N m) |
Rotation (RPM) |
Efficiency (%) |
|
0.142 |
5.99 |
0.00199 |
7000 |
58.3 |
Extend Large Angle
|
Thrust (N) |
Velocity (m/s) |
Torque (N m) |
Rotation (RPM) |
Efficiency (%) |
|
0.134 |
5.82 |
0.00187 |
7000 |
56.7 |
Optimising Propeller Efficiency
All Phase 1 propellers did not achieve efficiencies higher than 50%.
Phase 2 propellers and more recent designs usually have efficiencies larger than 50%.
We achieve a record efficiency of 65.88%, close to the industry standard of 67 to 72% for axial flow fans.
Optimising Number of Blades
Across three blade designs, the highest efficiencies are achieved at 4 blades.
Optimising Pitch Angle
We varied the pitch angle of the blade end from 9 to 14 degrees, as shown below in red.
|
Pitch Angle (°) |
Thrust (N) |
Velocity (m/s) |
Torque (N m) |
Efficiency (%) |
|
9 |
0.134 |
5.63 |
0.00180 |
57.18 |
|
10.8 |
0.176 |
6.50 |
0.00241 |
64.76 |
|
12 |
0.178 |
6.58 |
0.00253 |
63.15 |
|
14 |
0.203 |
7.15 |
0.00310 |
63.87 |
We observed that both thrust and torque increases at different rates with increasing pitch angle.
As pitch angle increases after an optimal point, torque increases at a faster rate than thrust, resulting in an overall decrease in efficiency.
A pitch angle of 11 degrees is the most ideal.
Effect of Blade Curvature
|
Colour |
Thrust (N) |
Velocity (m/s) |
Torque (N m) |
Rotation (RPM) |
Efficiency (%) |
|
Red |
0.176 |
6.50 |
0.00241 |
7000 |
64.76 |
|
Blue |
0.140 |
5.67 |
0.00170 |
7000 |
64.74 |
Two different blade shapes were found to have similar theoretical efficiencies but different air velocities.
We tested both propellers and found that actual efficiencies and air velocities are lower.
This may be attributed to the rough surface finish of 3D printed parts which adversely affected the air flow.