Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm
Abstract
:1. Introduction
2. Methodology
2.1. Original UESA
2.2. Numerical Solver for Fluid Flow
2.3. Improvement of the UESA for Compressor Cascade with Normal Shock
2.3.1. Constrained Movement of the Wall Nodes along the Spine
2.3.2. Using a Distribution of Elasticity Modulus along the Beam
2.4. Validation of Original UESA for the Cascade with High Subsonic Flow (Mach Inlet = 0.87)
2.5. Validation of UESA for the Cascade with Transonic Flow (Mach Inlet = 0.96)
- The geometry correction of the pressure surface and suction surface should be independently carried out to control the oscillations. In other words, when the pressure surface is being corrected, the suction surface should be fixed, and vice versa. According to our experience with numerical inverse design in transonic regimes, after five iterations for the geometry correction of the pressure surface, five iterations for the geometry correction of the suction surface should be applied.
- By applying the constraint of the spine for nodal displacements (ΔX = 0), the oscillations of the flexible wall through the inverse design process are significantly controlled.
3. Results and Discussion
3.1. Design of Sharp-Edged Blades in Transonic Flow
3.1.1. Initial Design with Fixed Blade Stagger Angle
- Two degrees of freedom (Y, θ) were considered for node displacement, which means the nodes can only move in the spine direction (ΔX = 0).
- The leading and trailing edges of the blade were fixed. Therefore, the blade stagger angle was fixed.
3.1.2. Second Design with Elastic Modulus Distribution and Fixed Blade Stagger Angle
- Two degrees of freedom (Y, θ) were considered for node displacement, which means the nodes could only move in the spine direction (ΔX = 0).
- The leading and trailing edges of the blade were fixed. Therefore, the blade stagger angle was fixed.
- A distribution of the beam elastic modulus along the blade surface was implemented.
3.1.3. Third Design with Elastic Modulus Distribution and Low Variable Blade Stagger Angle
- Two degrees of freedom (Y, θ) are considered for node displacement, which means the nodes can only move in the spine direction (ΔX = 0).
- Although the trailing edge of the blade is fixed, but the leading edge can freely move along the direction perpendicular to the blade chord. Therefore, the blade stagger angle is variable.
- A distribution of the beam elastic modulus along the blade surface is implemented.
3.2. Comparison of Performance Curves
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
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Boundary Condition between the Blades | Periodic | Number of Meshes on the Blade | 50 |
---|---|---|---|
Inlet boundary condition | total pressure | Blade stagger angle | 44° |
Outlet boundary condition | static pressure | Number of beam elements | 50 |
Flow equations | RANS | Type of the mesh | H-structured |
Inlet Mach number | 0.49 | Angle of attack | 1° |
Validation Case | Number of Shape Modifications | CPU Times in each Shape Modification Step (s) | CPU Time (s) | Log (CFD Residual) | ||
---|---|---|---|---|---|---|
Mesh Generation | CFD Solution | Beam Deformation | Total | |||
High subsonic | 150 | 2.1 | 61 | 1.5 | 9690 | −4 |
Transonic | 175 | 2.1 | 88 | 0.9 | 15,925 | −4 |
Grid Type | H-Structured | Inlet Total Pressure (pa) | 152,000 |
---|---|---|---|
Boundary condition between the blades | periodic | Outlet static pressure (pa) | 113,800 |
Inlet boundary condition | total pressure | Inlet static pressure (pa) | 84,305 |
Outlet boundary condition | static pressure | Blade stagger angle | 45° |
Flow equations | RANS | Blade incidence angle | 5° |
Turbulence model | k-ω-SST | Inlet Mach number | 0.96 |
Number of beam elements on each side of the blade | 50 | Maximum Mach number | 1.24 |
Design Case | Number of Shape Modifications | CPU Times in Each Shape Modification Step (s) | CPU Time (s) | Log (CFD Residual) | ||
---|---|---|---|---|---|---|
Mesh Generation | CFD Solution | Beam Deformation | Total | |||
2nd Design | 70 | 2 | 118 | 0.9 | 8463 | −4 |
3rd Design | 110 | 2 | 118 | 1.8 | 13,398 | −4 |
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Noorsalehi, M.H.; Nili-Ahmadabadi, M.; Nasrazadani, S.H.; Kim, K.-C. Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm. Appl. Sci. 2021, 11, 4845. https://doi.org/10.3390/app11114845
Noorsalehi MH, Nili-Ahmadabadi M, Nasrazadani SH, Kim K-C. Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm. Applied Sciences. 2021; 11(11):4845. https://doi.org/10.3390/app11114845
Chicago/Turabian StyleNoorsalehi, Mohammad Hossein, Mahdi Nili-Ahmadabadi, Seyed Hossein Nasrazadani, and Kyung-Chun Kim. 2021. "Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm" Applied Sciences 11, no. 11: 4845. https://doi.org/10.3390/app11114845