Abstract
A low-dimensional representation of transitional, buoyancy-induced flow in a vertical channel with discrete heaters is developed. The governing equations are solved using a spectral element method. Proper Orthogonal Decomposition (POD) is applied to extract the most energetic eigenfunctions (coherent structures) from time-independent numerical solutions of the full model equations. Using the computed eigenfunctions we are able to reconstruct the original flow and temperature fields in an optimal way. It is found that almost all the flow energy is captured by the first 6 modes. A low-dimensional set of nonlinear ordinary differential equations that describes the dynamics of the flow and temperature fields is also derived. It is found that low-order models based on retaining at least 4 eigenmodes for each field result in stable, self-sustained oscillations with correct amplitude.
Original language | English |
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Pages (from-to) | 125-137 |
Number of pages | 13 |
Journal | American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD |
Volume | 303 |
Issue number | 1 |
Publication status | Published - 1995 |
Externally published | Yes |
Event | Proceedings of the 1995 30th National Heat Transfer Conference. Part 1 - Portland, OR, USA Duration: 6 Aug 1995 → 8 Aug 1995 |