blastFoam: Implementation and Validation of New Equations of State (EOS)
The Synthetik Applied Technologies team is excited to announce the implementation and validation of three new Equations of State (EOS) as part of our free and open-source CFD airblast code blastFoam.
1) LSZK Equation of State
There are several advantages of the Landau-Stanyukovich-Zeldovich and Kompaneets (LSZK) EOS with regard to use in hydrodynamics codes:
The function is smooth and has smooth derivatives.
The derivative of pressure with respect to density (used to calculate sound speed) is always positive. This is not, in general, true for the popular JWL EOS.
It is possible to integrate the equations of motion analytically to define the parameters behind the detonation wave as a function of position relative to the detonation front.
2) BKW Equation of State
The Becker–Kistiakowsky–Wilson (BKW) EOS is a non-ideal, semi-empirical, full EOS that can explicitly represent temperature (unlike the JWL EoS) and is widely used to describe detonation products (high-pressure regime) and, due to its physical basis, also provides good agreement in the mid- and low-pressure regimes.
Thanks to its simplicity the BKW EOS is used in many practical applications in the explosives field with derivation of an accurate solution for a specific high explosive achieved via the employment of calibrated BKW constants.
3) Doan-Nickel Equation of State
For many applications the assumption that air is an ideal gas with a constant value of gamma (the ratio of specific heats of the gas – usually assumed to be 1.4) is a very good approximation. However, air is a mixture of real gasses (predominantly nitrogen and oxygen) and it is important to understand the limitations of this assumption.
When incident blast pressures exceed about 250 psi (1,725 kPa), gamma begins to deviate from the constant value of 1.4, and this can have significant impacts on calculation outputs, with up to 60% errors in shock density values, and 50% errors in dynamic pressures.
Consequently, the Doan-Nickel EOS provides a fit to data from Hilsenrath (1957), which accounts for excitation and ionization of nitrogen and oxygen in air at higher energies (temperatures).
blastFoam is available for free download here: https://github.com/synthetik-technologies/blastfoam
Synthetik YouTube Channel: https://www.youtube.com/channel/UCjWIYiONQ312lUlncFG3sQA
REFERENCES:
1. Lutsky, M.: The Flow Behind a Spherical Detonation in TNT using the Landau-Stanyukovich Equation of State for Detonation Products, NOL-TR 64–40. U.S. Naval Ordnance Laboratory, White Oak, Maryland (1965)
2. Laurence E. Fried and P. Clark Souers, “BKWC: An empirical BKW parametrization based on cylinder test data,” Propellants, Explosives, and Pyrotechnics, Oct, 1996.
3. Doan, L. R., Nickel, G. H.: A subroutine for the equation of state of air. RTD (WLR) TN63–2. Air Force Weapons Laboratory, (1963)
4. Hilsenrath, J., Green, M.S., Beckett, C.W.: Thermodynamic Properties of Highly Ionized air, SWC-TR-56-35. National Bureau of Standards, Washington D.C. (1957)