Reconstruction of Gappy Data for Cavity Flow Using Gappy Proper Orthogonal Decomposition

Subject Areas : Analytical and Numerical Methods in Mechanical Design

Matin Hoseini ¹ , Nader Montazerin ² , Ghasem Akbari ³

1 - Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
2 - Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
3 - Department of Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Received: 2022-09-19 Accepted : 2022-09-19 Published : 2022-06-01

Keywords: reconstruction, Proper Orthogonal Decomposition, Cavity Flow, Gappy Data, Energy mode,

Abstract :

The present study examines the possibility of completing gappy flow fields with the method of gappy proper orthogonal decomposition (GPOD). The procedure is performed on a numerically simulated cavity flow. The DNS data is artificially made incomplete by randomly omitting localized data. Two levels of gappiness are examined to evaluate the GPOD procedure. The results indicate that the relative error between the GPOD estimation and the real field directly depends on the level of gappiness. As the gappiness increases, the prediction accuracy decreases. It is shown that the relative error does not monotonically decrease because of inherent noise in higher-level modes of energy. The optimal count of modes in GPOD procedure is obtained and discussed. The contribution of GPOD procedure on spatial experimental data is also addressed.

References:

1. Zeman, O., and Lumley, J.L., 1974. ”Modeling buoyancy driven mixed layers”. J. Atm. Sci., 33, pp. 1974-1988.


2. Everson, R. and Sirovich, L., 1995. “Karhunen-Leoeve procedure for gappy data”. J. Opt. Soc. Am., 12, pp. 1657-1664.


3. Venturi, D. and Karniadakis, G.E., 2004. “Gappy data and reconstruction procedures for flow past a cylinder”. J. Fluid Mech., 519, pp. 315-336.


4. Gunes, H., Sirisup, S., and Karniadakis, G.E., 2006. “Gappy data: To krig or not to krig?”. J. Comput. Phys., 212, pp. 358-382.


5. Venturi, D., 2006. “On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate”. J. Fluid Mech., 559, pp. 215-254.


6. Druault, P., and Chaillou, C., 2007. “Use of proper orthogonal decomposition for reconstructing the 3D in cylinder mean-flow field from PIV data”. C. R. Mecanique, 335, pp. 42-47.


7. Peyret, R., and Taylor, T.D., 1983. “Computational methods for fluid flow”. Springer Press.


8. Nobari, M.R.H., Ahrabi, B.R., and Akbari, G., 2009. “A numerical analysis of developing flow and heat transfer in a curved annular pipe”. Int. J. Therm. Sci., 48, pp. 1542-1551.


9. Fukunaga, K., 1990. “Introduction to statistical pattern recognition”. 2^nd


10. Meyer, K.E., Pederson, J.M., and Oktayozcan, 2007. “A turbulent jet in cross flow analyzed with proper orthogonal decomposition”. J. Fluid Mech., 583, pp. 199-227.


11. Akbari, G., Montazerin, N., and Akbarizadeh, M., 2012. “Stereoscopic particle image velocimetry of the flow field in the rotor exit region of a forward-blade centrifugal turbomachine”. J. Power Energy, 226, pp. 163-181.