An Equation of State for Compressible Liquid Water for CFD Applications

Computational fluid dynamics simulations of water typically assume the fluid to be truly incompressible; however, resolving acoustic behaviors such as turbulent boundary layer self-noise in simulations requires the flow to have finite speed of sound, but this can place severe time-step restrictions on most solvers. Advances in entropy-stable CFD methods for ideal gases have provable non-linear stability, and such methods appear to be extensible to weakly compressible fluids if a closed-form expression for thermodynamic entropy is available. Classical state equations like Tumlirz-Tait cannot accurately predict both speed of sound and entropy, while the IAPWS 95 formulation is unwieldy for some applications. In this work, a state equation has been developed to calculate specific volume of water at modest conditions. The method defines specific volume as a function of speed of sound and entropy, then correlates experimental data to find equations for these quantities as functions of pressure and temperature, allowing intermediate quantities to be extracted directly. Comparing the results of this equation on its domain of 5 °C to 30 °C to NIST data yields at most a 0.24% deviation in specific volume.