Abstract
This work investigates fully developed turbulent flows of carbon-dioxide close to its vapour-liquid critical point in a channel with a hot and a cold wall. Two direct numerical simulations are performed at low Mach numbers, with the trans-critical transition near the channel centre and the cold wall, respectively. An additional simulation with constant transport properties is used to selectively investigate the effect of the non-linear equation of state on turbulence. Compared to the case where the pseudo-critical transition occurs in the channel center, the case with the pseudo-critical transition close to the cold wall reveals that compressibility effects can exist in the near-wall region even at low Mach numbers. An analysis of the velocity streaks near the hot and the cold walls also indicates a greater degree of streak coherence near the cold wall. A comparison between the constant and variable viscosity cases at the same Reynolds number, Mach number and having the same isothermal wall boundary conditions reveals that variable viscosity increases turbulence near the cold wall and also causes higher velocity gradients near the hot wall. We also show that the extended van Driest transformation results in a better agreement of the velocity profile with the log-law of the wall compared to the standard van Driest transformation. The semi-locally scaled turbulent velocity fluctuations and the turbulent kinetic energy budgets on the hot and the cold sides of the channel collapse on top of each other, thereby establishing the validity of Morkovin’s hypothesis.
Highlights
Fluids at temperatures and pressures above their vapour-liquid critical point are known as supercritical fluids
Compressible direct numerical simulations are performed for turbulent flows of supercritical CO2 at low Mach numbers close to the vapour-liquid critical point involving trans-critical transition
This is seen in the unusual nature of the density fluctuations, which is not observed in turbulent ideal gas flows with a wall temperature difference
Summary
Fluids at temperatures and pressures above their vapour-liquid critical point are known as supercritical fluids. The vapour-liquid critical point, the heat capacity of a supercritical fluid at constant pressure (Cp) shows a maximum value at a certain temperature, known as the pseudo-critical temperature (Tpc). This point is called the pseudo-critical point. Along any isobar above the critical point, on crossing the pseudo-critical point, all the thermodynamic and transport properties like density, isobaric heat capacity, viscosity and thermal conductivity etc., exhibit sharp gradients for small changes in temperature.
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