Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition
Abstract
:1. Introduction
2. Theoretical Background of POD
3. Methodology
3.1. Data Collection for Roof Pressure on Low-Rise Building
3.2. Analysis of the Pressure Eigenmode Using POD
3.3. Mean Reattachment Length () Evaluation Using POD and Validation
4. Results
4.1. Pressure Fluctuation Characteristics
4.2. Interpretation of the POD Eigenmode
4.2.1. Eigenvalues, Wind Angles () of 0°
4.2.2. Interpretation of the POD Eigenmodes, Wind Angles () of 0°
4.2.3. Effects of Wind Direction on POD Eigenmodes, Wind Angles () of 5°
4.3. Evaluation of the Mean Attachment Length () Using the POD Eigenmode
4.4. Validation of the POD-Based Mean Reattachment Length ()
5. Conclusions
- Primary POD eigenmode: This mode effectively characterizes the major global mechanisms influencing the roof pressure field. The regions of high magnitude in the eigenmodes are closely associated with intense pressure fluctuations, reflecting the complex and variable fluid flow within the separation bubble. Conversely, areas of low magnitudes in the eigenmode are indicative of low-pressure fluctuations, characteristic of the more stable flow found in the reattachment area. Notably, these regions are distinguished by reversed signs in the eigenmode. This comprehensive characterization captures the dynamics associated with flow separation and reattachment, demonstrating the detailed nature of the pressure field’s variability in these regions.
- Secondary POD eigenmode: This mode reveals the presence of vortex structures within the separation bubbles. This finding offers a deeper understanding of the complex flow behaviors and the underlying mechanics within the roof separation bubble.
- Third POD eigenmode: This mode exhibits pronounced effects at the windward front corners of the roof caused by the wind flow. The distribution of this eigenmode strongly correlates with the pressure fluctuations at these corners, indicating the impact of roof corners on flow dynamics.
- Estimation of the mean reattachment length () using the first POD eigenmode: By evaluating the dominant POD eigenmodes and eigenvalues, it was deduced that the mean reattachment length () can be represented as the distance from the leading edge to the first zero-valued contour line after the first POD eigenmode reaches its maximum value. This offers a clear, quantifiable measure of the mean reattachment length () on the roof.
- Validation of the POD-based mean reattachment length (): The mean reattachment length () determined via the proposed POD-based method closely aligns with those obtained from an established aerodynamic database, with observed discrepancies being less than 5%. This underscores the robustness and precision of the POD approach in estimating the mean reattachment length () using the first POD eigenmode.
- Methodological advantages: The technique’s capacity to precisely pinpoint the flow reattachment location across the entire separation region, using solely pressure data, is a significant advancement. This negates the need for specialized aerodynamic databases, making the approach adaptable to a model regardless of its shapes and flow conditions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Mode | Eigenvalue | Normalized Eigenvalue |
---|---|---|
1 | 0.91 | 0.14 |
2 | 0.77 | 0.11 |
3 | 0.49 | 0.08 |
Turbulence Intensity | ||
---|---|---|
= 12.7% | = 0.6% | |
Maximum (mm) | 410 | 694 |
Minimum (mm) | 290 | 637 |
Average (mm) | 326 | 670 |
Turbulence Intensity ( , %) | Reduced Pressure Coefficient () | Reference |
---|---|---|
4 | 0.35 | Hudy et al. [21] |
13 | 0.28 | Akon [17] |
17 | 0.25 | Akon [17] |
18 | 0.24 | Ho et al. [26] |
26 | 0.21 | Akon [17] |
Turbulence Intensity (, %) | 12.7 | 0.6 |
---|---|---|
Mean reattachment length according to the current POD-based method (, mm) | 324 | 689 |
Mean reattachment length according to Akon’s method [17] (, mm) | 340 | 657 |
Relative error (%) in the mean reattachment length () between the current POD-based method and Akon’s method [17] | 4.9 | 4.6 |
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Ham, H.J.; Lee, S.; Choi, S.H.; Kim, H.-J. Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition. Appl. Sci. 2024, 14, 88. https://doi.org/10.3390/app14010088
Ham HJ, Lee S, Choi SH, Kim H-J. Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition. Applied Sciences. 2024; 14(1):88. https://doi.org/10.3390/app14010088
Chicago/Turabian StyleHam, Hee Jung, Sungsu Lee, Seung Hun Choi, and Ho-Jeong Kim. 2024. "Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition" Applied Sciences 14, no. 1: 88. https://doi.org/10.3390/app14010088
APA StyleHam, H. J., Lee, S., Choi, S. H., & Kim, H.-J. (2024). Mean Reattachment Length of Roof Separation Bubbles Using Proper Orthogonal Decomposition. Applied Sciences, 14(1), 88. https://doi.org/10.3390/app14010088