Predicting Rotor Heat Transfer Using the Viscous Blade Element Momentum Theory and Unsteady Vortex Lattice Method
Abstract
:1. Introduction
2. Methodology
2.1. CFD Heat Transfer Simulations
2.1.1. Airfoil Average Heat Transfer Correlation
2.1.2. CFD Simulations Details
2.1.3. Convective Heat Transfer
2.1.4. Zone with Maximum Fr
2.2. BEMT-RHT
2.3. UVLM-RHT
2.3.1. Discretization and Grid Construction
2.3.2. Induced Velocities Calculation
2.3.3. Vortex Strength and Forces Calculation
2.3.4. Slow Start Method
2.3.5. Modified Viscous-Heat Transfer Coupling Algorithm
- Calculate αeff at each blade section .
- Find CL-visc by interpolating αeff in the CFD viscous database
- Check
- Adjust αeff in the first step by the found Δαvisc
- Repeat until |CL-inv − CL-visc| < ε
2.3.6. Complete UVLM-RHT Solution Procedure
3. Results
3.1. CFD Heat Transfer Results
3.1.1. Flat Plate Verification Test Case
3.1.2. Average Frossling Number Correlation
3.1.3. Maximum Frossling Number Correlation
3.2. Validation of Implemented BEMT and UVLM
3.2.1. Two-Blade Hovering Rotor
3.2.2. Four-Blade Hovering Rotor in Ground Effect
3.2.3. Two-Blade Rotor in Axial Flight
3.2.4. Two-Blade Rotor in Forward Flight
3.3. Rotor Heat Transfer Results
3.3.1. Hover Out of Ground Effect (OGE)
3.3.2. Hover in Ground Effect (IGE)
3.3.3. Axial Flight
3.3.4. Forward Flight
4. Conclusions and Future Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Without CFD Database | With CFD Database | ||
---|---|---|---|
BEMT | 1 | Guess a value for λ | |
2 | Calculate tip loss factor F | ||
3 | Calculate αeff and φ (Equations (2) and (3)) | ||
4 | Redo until convergence (|λ i+1−λ i| = 10−5) | ||
Aerodynamic Coefficients | 5 | Obtain CL-inv and CD-inv by a correlation | Obtain CL-visc and CD-visc from viscous database by interpolating αeff |
Thrust and torque | 6 | Calculate incremental dCT, dCPi and dCPo, Output CT, CP and CQ | |
Heat transfer | 7 | For every Re and αeff at every r, calculate Fr |
Step | Task | |
---|---|---|
UVLM | 1 | Blade camber line geometry and flight path kinematics |
2 | Blade influence coefficients matrix A | |
3 | Form the right-hand side matrix RHS | |
4 | Solve RHS to obtain Γ | |
5 | Pressure and forces calculation (CT, CLy, …) | |
6 | Wake rollup | |
Heat transfer | 7 | Viscous coupling algorithm (Re, CL-visc, and αeff) |
8 | For every Re and αeff at every collocation point, calculate Fr |
Constant Surface Temperature TS | Constant Surface Heat Flux QS |
---|---|
[32] | S-A CFD data, Aupoix et al. [37] |
[28] | S-A CFD data, Abdollahzadeh et al. [29] |
UVLM | BEMT | Ferlisi | Colmenares et al. | Caradonna and Tung | |
---|---|---|---|---|---|
θ = 5° | 0.00243 | 0.00290 | 0.00237 | 0.00221 | 0.00213 |
θ = 8° | 0.00477 | 0.00540 | 0.00460 | 0.00467 | 0.00459 |
θ = 12° | 0.00794 | 0.00910 | 0.00824 | 0.00821 | 0.00796 |
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Samad, A.; Tagawa, G.B.S.; Morency, F.; Volat, C. Predicting Rotor Heat Transfer Using the Viscous Blade Element Momentum Theory and Unsteady Vortex Lattice Method. Aerospace 2020, 7, 90. https://doi.org/10.3390/aerospace7070090
Samad A, Tagawa GBS, Morency F, Volat C. Predicting Rotor Heat Transfer Using the Viscous Blade Element Momentum Theory and Unsteady Vortex Lattice Method. Aerospace. 2020; 7(7):90. https://doi.org/10.3390/aerospace7070090
Chicago/Turabian StyleSamad, Abdallah, Gitsuzo B. S. Tagawa, François Morency, and Christophe Volat. 2020. "Predicting Rotor Heat Transfer Using the Viscous Blade Element Momentum Theory and Unsteady Vortex Lattice Method" Aerospace 7, no. 7: 90. https://doi.org/10.3390/aerospace7070090
APA StyleSamad, A., Tagawa, G. B. S., Morency, F., & Volat, C. (2020). Predicting Rotor Heat Transfer Using the Viscous Blade Element Momentum Theory and Unsteady Vortex Lattice Method. Aerospace, 7(7), 90. https://doi.org/10.3390/aerospace7070090