近临界CO2中热释放诱导的平面shock waves的无标度性
Dimensionless scaling of heat-release-induced planar shock waves in near-critical CO2
摘要：
我们进行了高分辨率的一维完全可压缩的Navier-Stokes模拟的热释放引起的压缩波在近临界CO2。受Miura等人实验装置的启发，2006年，由一个封闭的无粘性（一维）管道组成，在三个超临界压力下，绝热硬端填充有CO2。相应的初始温度值沿拟沸腾线取。采用Peng-Robinson状态方程和Chung方法模拟了近临界条件下CO2的热力学和输运性质。在距离一端一定距离处施加热源，其热释放强度范围为10^3-10^11 W/m^2，产生的等熵压缩波的值小于10^9 W/m^2。对于更高的放热率，这种压缩与明显的类似激波的特征（例如，非等熵性和可测得的大于1的传播马赫数）结合在一起，并且由于强烈的热力学非线性，存在非均匀的激波后状态。由此产生的压缩波强度已经通过热膨胀系数，在近临界流体中高度可变，作为参考能量的标度参数之一崩溃。建议的缩放适用于等熵热声波以及冲击波的冲击强度2。长期的时间积分揭示了压缩波的共振行为，在每个共振周期提高了平均压力和温度。当热注入停止时，产生膨胀波，膨胀波抵消压缩波，使传导成为唯一的热弛豫过程。在长期演化过程中，利用等温边界条件定性地再现了实验中观察到的共振波振幅衰减。
英文摘要：
We performed highly resolved one-dimensional fully compressible Navier-Stokes simulations of heat-release-induced compression waves in near-critical CO2. The computational setup, inspired by the experimental setup of Miura et al., Phys. Rev. E, 2006, is composed of a closed inviscid (one-dimensional) duct with adiabatic hard ends filled with CO2 at three supercritical pressures. The corresponding initial temperature values are taken along the pseudo-boiling line. Thermodynamic and transport properties of CO2 in near-critical conditions are modeled via the Peng-Robinson equation of state and Chung's Method. A heat source is applied at a distance from one end, with heat release intensities spanning the range 10^3-10^11 W/m^2, generating isentropic compression waves for values < 10^9 W/m^2. For higher heat-release rates such compressions are coalescent with distinct shock-like features (e.g. non-isentropicity and propagation Mach numbers measurably greater than unity) and a non-uniform post-shock state is present due to the strong thermodynamic nonlinearities. The resulting compression wave intensities have been collapsed via the thermal expansion coefficient, highly variable in near-critical fluids, used as one of the scaling parameters for the reference energy. The proposed scaling applies to isentropic thermoacoustic waves as well as shock waves up to shock strength 2. Long-term time integration reveals resonance behavior of the compression waves, raising the mean pressure and temperature at every resonance cycle. When the heat injection is halted, expansion waves are generated, which counteract the compression waves leaving conduction as the only thermal relaxation process. In the long term evolution, the decay in amplitude of the resonating waves observed in the experiments is qualitatively reproduced by using isothermal boundary conditions.
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