Multi-spatial scale and multi-frequency resolution Proper Orthogonal Decomposition for patterns of wall-streamwise pressure gradient fluctuation of impinging jets

Abstract

In the coating industry, seemingly ordered millimeter-scale W or X-like patterns inevitably appear on the coating wiped by jets. Considering the dynamic control of coating thickness by the maximum wall-streamwise pressure gradient on the impinging wall, exploring its fluctuation characteristics may provide insights into W or X-like patterns formation and suppression. Large Eddy Simulation is conducted to simulate jets impinging on a dry wall. The computed pressure gradient is processed by a two-dimensional Discrete Wavelet Transform using Coif2 wavelet, helping determine the spatial scale dominated by its fluctuation energy and providing snapshots on specific spatial scales. Afterward, snapshots on selected spatial scales undergo processing using either multi-scale Proper Orthogonal Decomposition (mPOD) or spectral POD, depending on the presence of some distinguishable peaks in its spectrum. This process can extract modes with spectral purity on the corresponding spatial scale, providing an advantage in addressing problems strongly linked to spatial scales. Applying this methodology, the study unveiled the evolution of the pressure gradient modes with frequency on the energy-dominant spatial scale, ranging from 0.625 mm × 0.785 mm to 1.25 mm × 1.57 mm. This evolution may be the cause of W or X-like patterns and suggests introducing a guiding jet to mitigate them.

KEYWORDS:

• Modal analysis
• MRA
• wavelet transform
• impinging jets
• LES

Acknowledgments

The authors are grateful to Prof. You for providing computational resources and insightful reviews. They also express appreciation to Ninni D, Mendez MA, Towne A, Schmidt OT, and their colleagues for generously sharing their Matlab source code.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author, Prof. You, upon reasonable request.

Additional information

Funding

This work was financially supported by the Natural Science Foundation of China (NSFC No. 12072245).