A numerical study is performed for 2-D axisymmetric turbulent flow of supercritical water flowing upward in a vertical pipe with constant applied wall heat flux. This study uses Computational Fluid Dynamics (CFD) to analyze supercritical flow instability in a vertical heated channel. The governing equations are solved using two RANS models in the CFD code ANSYS CFX v14.5. Analyses of static and oscillatory flow instabilities are performed using the standard k-epsilon model with a scalable wall-function and the k-omega-based SST model. The instability threshold results of the CFD code are compared with 1-D non-linear code predictions. Also, criteria for approximating the thresholds of static and oscillatory instabilities based on steady-state results are assessed and discussed. The effect of changing the turbulent Prandtl number (Pr-t) on the instability threshold is also examined. It was observed that the instability threshold results obtained using the k-epsilon and the SST models are similar. Also, the results of the CFD and 1-D codes are different due mainly to the different pressure drop predictions between the two methodologies. Comparisons of instability threshold predictions between CFD and 1-D codes showed smaller differences for static instabilities and greater differences for oscillatory instabilities. In addition, approximating the flow instability threshold by the criteria proposed generally holds true for a CFD solution. Results also indicate that the value of Prt does not have a noticeable effect on the instability threshold for the cases examined in the present study. (C) 2016 Elsevier Ltd. All rights reserved.