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.

中文翻译：

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二氧化碳在超临界压力和跨临界温度下的完全可压缩低马赫数模拟

这项工作研究了二氧化碳在具有热壁和冷壁的通道中接近其气液临界点的完全发展的湍流流动。两个直接数值模拟在低马赫数下进行，分别在通道中心和冷壁附近具有跨临界转变。具有恒定输运特性的附加模拟用于有选择地研究非线性状态方程对湍流的影响。与在通道中心发生伪临界转变的情况相比，靠近冷壁的伪临界转变的情况表明，即使在低马赫数下，近壁区域也可能存在压缩效应。对热壁和冷壁附近的速度条纹的分析也表明冷壁附近的条纹相干程度更高。在相同雷诺数、马赫数和具有相同等温壁边界条件下的恒定和可变粘度情况之间的比较表明，可变粘度会增加冷壁附近的湍流，并且还会导致热壁附近更高的速度梯度。我们还表明，与标准 van Driest 变换相比，扩展的 van Driest 变换使速度剖面与壁的对数定律更好地吻合。通道的热侧和冷侧的半局部尺度湍流速度波动和湍流动能收支相互重叠，从而建立了 Morkovin 假设的有效性。