Propeller Design Optimization and an Evaluation of Variable Rotational Speed Flight Operation Under Structural Vibration Constraints
Abstract
1. Introduction
- In the present paper, OptProp is used to formulate and solve a constrained multi-objective optimization problem (MOOP), focusing on simultaneously minimizing power consumption at two critical points in flight: takeoff and top-of-climb. The proposed problem has not yet been resolved in the literature and is a critical factor linking flight missions and energy consumption.
- Table 1 shows that most research focuses on optimization with a single aerodynamic objective. The proposed MOOP aims to generate a non-dominated solutions group strategically distributed across the Pareto front (PF). It serves as a valuable resource for decision-makers, allowing them to choose one or multiple solutions aligned with their preferences. Additionally, it is crucial to underscore the advantages of adopting a multi-objective method over several single-objective optimization formulations. A multi-objective method offers a robust solution space while mitigating the computational cost associated with creating and solving numerous single-objective optimization problems.
- As highlighted in Table 1, there has been limited exploration of employing multiple optimization algorithms and assessing their effectiveness. Employing multiple algorithms can foster greater diversity and enhance the distribution of non-dominated solutions across the PF.
- The evaluation of the solution extracted from the optimization problem in a continuously multi-rotational-speed approach, with structural frequency constraints and the no-go zones identified in the Campbell diagram, is also a significant contribution of this research. This analysis, carried out in the conceptual design stage, prevents undesirable oscillations in the propeller caused by the resonance between its rotational motion and its natural frequencies of vibration. There is a gap in the literature regarding the application and evaluation of this approach for aircraft propellers.
2. Definition of the Optimization Problem
3. The Optimization Framework
3.1. Airfoil Database and Profiles Refinement
3.2. Propeller Analysis
3.3. Coupling the Propeller Aerodynamic Analysis and the Optimization Process
4. Structural Model for a Rotating Beam
5. Optimum Design of the Propellers
5.1. Design Space Exploration
5.2. Solutions Obtained from the Optimization Problem
- Airfoil profile in Sec. 1 (design variable x(1)): FX 74-CL6-140, a high lift, low drag, and smooth stall behavior airfoil [64].
- Airfoil profile in Sec. 2 (design variable x(2)): NPL ARC CP 1372, a low drag, gradual stall, and with good lift-to-drag ratio airfoil [65].
- Airfoil profile in Sec. 3 (design variable x(3)): NACA 65(3)-218, a high lift, higher drag at high speeds, and steep stall airfoil [66].
- Airfoil profile in Sec. 4 (design variable x(4)): NACA M5, a low drag, good lift-to-drag, and mild stall behavior airfoil.
- propeller diameter (design variable x(5)): 1879 mm.
- number of blades (design variable x(6)): 8.
- hub diameter to propeller diameter ratio (design variable x(7)): .
- rotational speed (design variable x(7)): 1337.
6. Optimal Operational Procedures of the Optimized Propeller for a Given Flight Mission and with Structural Constraints
6.1. Operational Evaluation
6.2. Operational Analysis Under Structural Constraints
7. Final Considerations
- The OptProp coupled methodology for propeller optimization, which allows the consideration of different propeller geometries, such as chord distribution and twist, in addition to the airfoil section.
- The proposed MOOP delivered an optimized propeller considering minimum energy consumption at two points of interest in the flight envelope, thus enabling the design of efficient propellers systematically and pragmatically. The results obtained demonstrate its potential, providing feasible non-dominated solutions and significantly reducing computational costs using the BEM theory.
- The application of the optimized propeller in a mission, evaluating the multi-rotational-speed flight procedure to mitigate the power consumption. Also, using the Campbell diagram to predict no-go zones could prevent structural instability during the flight.
- It corroborates the various studies in the area that aim to improve aeronautical systems’ efficiencies while trying to mitigate environmental and economic impacts.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Reference | Model | Optimization Algorithm | Single or Multiple Objectives | |
---|---|---|---|---|
Aerodynamic | Structural | |||
Gur et al. [10,27] | BEM | beam | simple genetic single steepest-descent | simplex min P, fixed T and rpm min T, fixed P and rpm |
Ingraham et al. [28] | BEM | - | gradient-based | single |
Yu et al. [29] | CFD | - | PSO | single min SPL |
Hoyos et al. [12] | BEM | beam | PSO | single FSI min P, fixed T and rpm |
Zhang et al. [15] | CFD | 3D FEM | adjoint method | single max T, fixed rpm |
Guan et al. [19] | CFD | 3D FEM | NSGA II | multi FSI max T min stress |
Oliveira et al. [30]
Oliveira [31] | BEM | - | AGE-MOEA AR-MOEA NSGAII MSOPII | multi plus 7 aerodynamic problems |
Yang et al. [32] | CFD | - | adjoint method | single fixed T and rpm |
Koyuncuoglu and He [33] | CFD | 3D FEM | adjoint method | single |
Geng et al. [34] | BEM/CFD multi-fidelity | - | deep reinforcement learning | single min noise cruise |
Sedelinov et al. [35] | BEM | - | DE | single min P fixed T |
Wu et al. [36] | BEM/CFD multi-fidelity | - | neural network | single fixed T and rpm cruise |
Weigang et al. [37] | - | beam composite tapered | GA | single min mass |
Total Thrust | Flight Mach Number | Altitude | |
---|---|---|---|
Takeoff | 22.27 kN | 0.135 (47.30 m/s) | 0 m |
Top-of-climb | 7.06 kN | 0.35 (114.15 m/s) | 3048 m |
Rotational Speed [rpm] | 1st Flapwise Mode [Hz] | 1st Edgewise Mode [Hz] | 2nd Flapwise Mode [Hz] | 2nd Edgewise Mode [Hz] |
---|---|---|---|---|
0 | 47.2 | 80.0 | 155.8 | 165.0 |
100 | 62.9 | 86.3 | 156.2 | 165.6 |
200 | 77.8 | 94.0 | 157.4 | 167.5 |
300 | 91.6 | 103.0 | 159.1 | 170.6 |
400 | 104.3 | 113.0 | 161.5 | 174.8 |
500 | 115.7 | 123.8 | 164.3 | 180.0 |
600 | 126.6 | 136.1 | 170.7 | 203.0 |
700 | 137.3 | 150.3 | 182.4 | 253.3 |
800 | 146.9 | 166.0 | 197.7 | 320.2 |
900 | 154.7 | 183.0 | 214.8 | 392.6 |
1000 | 159.7 | 200.8 | 231.8 | 459.9 |
1100 | 162.7 | 220.5 | 249.6 | 523.6 |
1200 | 165.0 | 242.5 | 269.8 | 591.1 |
1300 | 166.9 | 265.7 | 291.3 | 660.4 |
1400 | 168.6 | 289.1 | 313.2 | 729.4 |
1500 | 170.1 | 311.7 | 334.6 | 796.1 |
1600 | 171.7 | 333.5 | 355.3 | 860.2 |
1700 | 173.1 | 355.0 | 376.1 | 923.2 |
1800 | 174.3 | 376.4 | 396.9 | 985.5 |
1900 | 175.5 | 397.8 | 417.8 | 1047.2 |
2000 | 176.6 | 419.2 | 438.6 | 1108.9 |
2100 | 177.6 | 440.6 | 459.4 | 1170.3 |
2200 | 178.5 | 462.0 | 480.2 | 1231.4 |
2300 | 179.4 | 483.3 | 501.1 | 1292.1 |
2400 | 180.2 | 504.6 | 521.9 | 1352.6 |
2500 | 180.9 | 525.9 | 542.8 | 1413.0 |
2600 | 181.6 | 547.2 | 563.6 | 1473.4 |
2700 | 182.2 | 568.5 | 584.5 | 1533.6 |
2800 | 182.8 | 589.7 | 605.4 | 1593.6 |
2900 | 183.3 | 611.0 | 626.2 | 1653.4 |
3000 | 183.8 | 632.2 | 647.1 | 1713.1 |
Segment (Step Number) | Velocity [m/s] | Thrust [N] | Rotational Speed [rpm] | Power [kW] | [°] | |||
---|---|---|---|---|---|---|---|---|
Takeoff (1) | 47.30 | 11137.3 | 2668 | 942.1 | 0.373 | 0.369 | 0.559 | 26.69 |
Descent (42) | 100.21 | 1417.0 | 1275 | 165.9 | 0.645 | 0.220 | 0.858 | 50.12 |
Descent (52) | 74.53 | 1445.9 | 1213 | 127.0 | 0.555 | 0.240 | 0.848 | 44.39 |
Descent (53) | 72.03 | 1555.3 | 1275 | 132.7 | 0.498 | 0.233 | 0.843 | 42.18 |
Second Descent (93) | 74.53 | 1467.9 | 1213 | 129.2 | 0.567 | 0.245 | 0.847 | 44.49 |
Second Descent (94) | 71.40 | 1567.1 | 1275 | 132.8 | 0.500 | 0.236 | 0.842 | 42.03 |
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Oliveira, N.L.; Lemonge, A.C.d.C.; Hallak, P.H.; Kyprianidis, K.; Vouros, S.; Rendón, M.A. Propeller Design Optimization and an Evaluation of Variable Rotational Speed Flight Operation Under Structural Vibration Constraints. Machines 2025, 13, 490. https://doi.org/10.3390/machines13060490
Oliveira NL, Lemonge ACdC, Hallak PH, Kyprianidis K, Vouros S, Rendón MA. Propeller Design Optimization and an Evaluation of Variable Rotational Speed Flight Operation Under Structural Vibration Constraints. Machines. 2025; 13(6):490. https://doi.org/10.3390/machines13060490
Chicago/Turabian StyleOliveira, Nicolas Lima, Afonso Celso de Castro Lemonge, Patricia Habib Hallak, Konstantinos Kyprianidis, Stavros Vouros, and Manuel A. Rendón. 2025. "Propeller Design Optimization and an Evaluation of Variable Rotational Speed Flight Operation Under Structural Vibration Constraints" Machines 13, no. 6: 490. https://doi.org/10.3390/machines13060490
APA StyleOliveira, N. L., Lemonge, A. C. d. C., Hallak, P. H., Kyprianidis, K., Vouros, S., & Rendón, M. A. (2025). Propeller Design Optimization and an Evaluation of Variable Rotational Speed Flight Operation Under Structural Vibration Constraints. Machines, 13(6), 490. https://doi.org/10.3390/machines13060490