Determination of Mean Reattachment Length for Roof-Separation Bubbles using Proper Orthogonal Decomposition

Investigations of flow separation regions on building roof surfaces in turbulent wind flows are important because of the large aerodynamic loads that the flows cause (Fig. 1). The extreme pressure occurred in separation bubbles makes roof components of buildings vulnerable (Fig. 2).

          

Various methods have been applied to determine the mean size of roof separation bubbles by evaluating the reattachment length through wind tunnel experiments. Among them, the mean reattachment length evaluated using Particle Image Velocimetry shows high accuracy (Fang and Tachie, 2019). However, there are limits to the method of estimating the mean reattachment length only with the measured pressure data without flow measurement. Recently, a methodology for estimating mean reattachment length using a database of previously evaluated pressure coefficients and mean reattachment lengths has been proposed (Akon, 2017). However, with this method, it is difficult to evaluate the mean reattachment length for cases with different geometries of building model or flow characteristics that are not in the database.
 
The Proper Orthogonal Decomposition (POD) can decompose physical fields according to the variables they affect. If the variables decomposed by the POD have physical meanings, separation and reattachment phenomena occurring on the roof can be identified using these variables. 

In this study, the eigenmode of the roof pressure measured in the wind tunnel experiment is identified using the POD, and based on this, the mean reattachment length of roof-separation bubbles is evaluated (Figs. 3 and 4). The POD results are also validated by comparing mean reattachment lengths evaluated using the POD and aerodynamic database.

               

In the case of the roof centreline, it can be seen that the mean reattachment length based on the POD is in good agreement with that using the aerodynamic database with a difference of within 5%. It can be concluded that the application of the POD proposed in this study is useful when the mean reattachment length needs to be evaluated using pressure data.

ACKNOWLEGEMENTS
This research was supported by a grant (RS-2022-00155691) of Disaster-Safety Industry Technology Commercialization R&D Program, funded by Ministry of Interior and Safety (MOIS, Korea).

REFERENCES 
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2. Fang, X. and Tachie, M. F., 2019. Flows over surface-mounted bluff bodies with different spanwise widths submerged in a deep turbulent boundary layer. Journal of Fluid Mechanics 877, 717-758.
3. Simiu, E., 2011. Design of Buildings for wind: a guide for ASCE 7–10 standard users and designers of special structures. Wiley.
4. Stevenson, S. A., Kopp, G. A., and El Ansary, A. M., 2018. Framing failures in wood-frame hip roofs under extreme wind loads. Front. Built Environ.