Proper orthogonal decomposition analysis of turbulent natural convection in an air–water system with evaporation across the free surface

Abstract

In this paper, we analyze the properties of turbulent natural convection in a water-air system via Proper Orthogonal Decomposition (POD). The flow domain is an open-top cuboid uniformly heated from below, while the water and air are separated by an evaporative interface. Direct numerical simulations of this problem were presented in an earlier publication of ours; herein we investigate in detail the emerging flow structures and the interaction between the two phases. In the water, the flow is organized around a dominant convective roll. In the gas the flow is due to combined thermal-concentration convection. The flow pattern is more complex and consists of an outer circulation plus an inner dual-roll structure with one roll above the other. First we discuss spectra of the thermal fluctuations. In the gas, the spectrum is bimodal. The high-frequency peak is due to natural convection while the low-frequency one is due to the interaction with water at the free surface. Then, we present the results of our POD analysis and elaborate on the properties of the dominant spatial and temporal modes. The spectra of the temporal modes are also examined herein. Our analysis shows that there is high correlation and coherence between the low-frequency signals in the dominant modes of the two phases, which implies that the convective patterns in the two phases influence each other. We also present the reconstructed snapshots with the dominant POD modes and discuss their influence. Our analysis shows that they provide a fairly accurate approximation of the instantaneous flow patterns. Further, in the water, the dominant mode modifies the length of the main convective roll, whereas the second mode tends to rotate its impingement point.