Direct numerical simulations of turbulent channel flow under transcritical conditions

TL;DR

This study uses direct numerical simulations with a real-fluid equation of state to explore turbulent channel flows under transcritical conditions, revealing insights into flow behavior and supporting the attached eddy hypothesis.

Contribution

It introduces a DNS approach with a Peng-Robinson equation of state for transcritical flows and compares fully and quasi-conservative schemes, advancing understanding of turbulence under such conditions.

Findings

Qualitative agreement between FC and QC schemes with some velocity oscillations.

Streamwise energy spectrum shows inverse wavenumber scaling.

Velocity structure function follows a logarithmic scaling, supporting the attached eddy model.

Abstract

Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to investigate the turbulent flows under transcritical conditions using DNS of turbulent channel flows. A fully compressible solver is used in conjunction with a Peng-Robinson real-fluid equation of state to describe the transcritical flows. A channel flow with two isothermal walls is simulated with one heated and one cooled boundary layers. The grid resolution adopted in this study is slightly finer than that required for DNS of incompressible channel flows. The simulations are conducted using both fully (FC) and quasi-conservative (QC) schemes to assess their performance for transcritical wall-bounded flows. The instantaneous flows and the statistics are analyzed and compared with the canonical theories. It is found that results from both FC and QC schemes qualitatively agree well with noticeable difference near the top heated wall, where spurious oscillations in velocity can be observed. Using the DNS data, we then examine the usefulness of Townsend attached eddy hypothesis in the context of flows at transcritical conditions. It is shown that the streamwise energy spectrum exhibits the inverse wavenumber scaling and that the streamwise velocity structure function follows a logarithmic scaling, thus providing support to the attached eddy model at transcritical conditions.