Dimensionless scaling of heat-release-induced planar shock waves in near-critical CO2

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 of 150 μm in length with adiabatic hard ends filled with CO2 at initial pressures p*0 = 1:00; 1:04; 1:40 p*c, where p*c = 7:3773 MPa is the critical pressure of CO2 and the superscript (*) denotes dimensional quantities. 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 of 50 μm from one end, with heat release intensities per unit area, Ω* spanning the range 103 -1011 W/m2, generating isentropic compression waves for Ω* < 109 W=m2. 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 Π = 2. Long-term time integration reveals resonance behavior of the compression waves, raising the mean pressure and temperature at every (near-acoustic) resonance cycle. This phenomenon is known in the literature as “Piston Effect”. 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. Future efforts will focus on developing appropriate wall-impedance conditions for near-critical fluids.