Universal Scaling of Acoustic and Thermoacoustic Waves in Compressible Fluids

We have derived the set of reference scaling parameters yielding collapse of isentropic acoustic and thermoacoustic (or heat-release-induced) waves across different pure compressible fluids with an assigned equation of state. The resulting reference pressure and velocity are consistent with classic acoustic scaling. The reference temperature and heat release rate need to be expressed in terms of the isobaric thermal expansion coefficient $\alpha^*_{p_0}$ to ensure collapse of all thermo-fluid-dynamic fluctuations across all fluids. The proposed scaling is extended to non-isentropic waves and verified against data from highly-resolved one-dimensional Navier-Stokes simulations. Conditions tested include freely propagating isentropic acoustic waves and thermoacoustic compression waves up to shock strength of 4.27, for six different supercritical fluids in states ranging from compressible liquid to near-ideal gas, and spanning seven orders of magnitude of imposed heat release rate.