  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.
