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Pressure fluctuation signals at the inlet/outlet of an oxygen phase-change heat exchanger are analyzed using non-linear method. Chaotic characteristic parameters such as correlation dimension, Kolomogrov entropy and the largest singular value decomposition (SVD) for the covariance matrix of an established 10-dimensional phase space are analyzed. Results prove that the heat exchanger is a non-linear system with chaotic characteristics. Correlations between these parameters and Prantl Number are also examined for the thermal behavior of oxygen in the critical region. The strong dependence of these characteristic parameters on Pr indicates that they can be used to investigate effectively the phase change behavior of pure substance.