An analytical method was proposed for the prediction of the turbulent friction factor in a circular pipe under supercritical conditions. The friction factor equation was based on the new wall function by Van Direst transformation which is widely used in compressed flow. The law of the wall of two layers was used and integrated over the entire flow area to obtain the algebraic form of the turbulent friction factor. The new turbulent friction formula was first adjusted to Colebrook equation in isothermal flow at supercritical pressures. And then it was validated in heated supercritical flow by several existing correlations. Similar trends were found between them, which confirms the physical validity of the new frictional formula. The theoretical analysis also shows that the friction factor due to the variation of fluid property at supercritical pressures is mainly caused by the density and viscosity variation. In viscous sublayer, both the viscosity play the main role, while in turbulent sublayer, only the density do.

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