Chaos Analysis of the Stable and Unstable Flows in a Natural Convection Loop

An experimental investigation has been made on the flow in a natural convection loop. Time series data of temperature oscillation were obtained for various types of the flow. Based on these data, attractors in high-dimensional space have been reconstructed by obtaining optimum delay time. The correlation dimensions Dc for these attractors were calculated by the method of correlation integration and plotted against heat inputs. The values of Dc could be classified into three regions according to the value of heat flux q, 1) Dc ≥ 13 in the laminar region (q ≤ 4.13kW/m2), 2) 1.1 ≤ Dc ≤ 2.4 in the unstable region (5.51 ≤ q ≤ 22.0), and 3) Dc ≥ 11.5 in the turbulent region (q ≥ 23.4). The values of Dc are non-integer in all regions. These results are consistent with chaotic characteristics. Observed in detail, however, the region 2) contains three types of flows: Turbulent, unstable with and without flow reversals. The last one was considered to be unstable flow in spite of non-reversal, because of its small Dc.