Becker-Kistiakowsky-Wilson equation of state

The Becker-Kistiakowsky-Wilson equation of state according to Richard Becker , George Bogdan Kistiakowsky and Robert R. Wilson is an equation of state in physics that is used to calculate detonation products.

{\ displaystyle {\ frac {p \ cdot \ nu} {RT}} = 1 + X \ cdot e ^ {\ beta \ cdot X}}

With

{\ displaystyle X = {\ frac {\ kappa \ sum x_ {i} k_ {i}} {\ nu \ cdot (T + \ Theta) ^ {\ alpha}}}}

where the pressure, the molar volume of the reaction gases , the gas constant , the molar fraction and the individual geometric co-volume of the -th component denotes. The sum extends over all components of the gaseous mixture of substances . The parameters α , β , k , Θ are empirical constants. The size was added to prevent the pressure from becoming infinite when the temperature goes to zero. At first it was arbitrarily assigned the value = 4000 K. is generally around 0.5, while and iteratively fitting data from high pressure experiments. There are three different parameter sets in use for the BKW equation of state: BKWC, BKWR and BKWS. The BKWS parameterization uses a physically based covolume, while the covolume was used as the fit parameter for the empirical parameter sets BKWC and BKWR. The BKW equation of state delivers sufficiently accurate results at high pressures, especially with the BKWS parameterization. ${\ displaystyle p}$ ${\ displaystyle \ nu}$ ${\ displaystyle R = 8 {,} 31441 \, \ mathrm {J / (molK)}}$ ${\ displaystyle x_ {i}}$ ${\ displaystyle k_ {i}}$ ${\ displaystyle i}$ ${\ displaystyle \ Theta}$ ${\ displaystyle \ Theta \;}$ ${\ displaystyle \ alpha}$ ${\ displaystyle \ beta}$ ${\ displaystyle k}$

The renormalized BKWR parameter set uses 12 product species and has the global parameters:

{\ displaystyle \ alpha = 0 {,} 51}

; ; ;

{\ displaystyle \ beta = 0 {,} 402}

{\ displaystyle \ kappa = 12 {,} 31}

{\ displaystyle \ Theta = 3856757}

it is based on 10 measured detonation velocities, 10 measured detonation pressures and 4 measured detonation temperatures of CHNOF explosives. (see Finger et al., 1976)

The BKWS parameter set uses 61 product species with C, H, N, O and has the global parameters:

{\ displaystyle \ alpha = 0 {,} 50}

; ; ;

{\ displaystyle \ beta = 0 {,} 398}

{\ displaystyle \ kappa = 10 {,} 50}

{\ displaystyle \ Theta = 6620}

The BKWS library has also been tested for explosives containing aluminum. (see Hobbs and Baer, 1993)

The BKWC parameter set takes 17 product species into account. It was determined with a modern stochastic optimization algorithm and has the global parameters:

{\ displaystyle \ alpha = 0 {,} 50}

; ; ;

{\ displaystyle \ beta = 0 {,} 403}

{\ displaystyle \ kappa = 10 {,} 86}

{\ displaystyle \ Theta = 5441}

literature

R. Becker: An equation of state for nitrogen at high densities . In: Journal of Physics . 4, 393 (1921)
R. Becker: Physics about solid and gaseous explosives . In: Journal for Technical Physics . 3, 249 (1922)
M. Finger, E. Lee, FH Helm, B. Hayes, H. Hornig, R. McGuire, M. Kahara, M. Guidra: The Effect of elemental Composition on the Detonation Behavior of Explosives . 6th International Symposium on Detonation, Colorado, August 24-27, 1972, pp.710-722
ML Hobbs, MR Baer: Calibrating the BKW-EOS with a Large Product Species Database and measured CJ Properties . 10th International symposium on Detonation, Boston, July 12-16, 1993, pp. 409-418.
LE Fried, WM Howard, PC Sours: CHEETAH 2.0 User's Manual. UCRL-MA-117541 Rev.5 . Lawrence Livermore National Laboratory, August 1998.