  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.
