Becker - Kistiakowsky - Wilson

Halford was an active contributor to this equation of state study 

Kisciakowsky Wilson attribute to D.P. MacDougall L. Epstein the addn of /3 to the repulsive term, which gives  

Cowan Fickett (Addnl Ref E) added the 6 to T to prevent pressure from tending to infinity as the temperature tends to zero and to keep (dp/e T)v positive over the range of volumes of interest. They found that the values a =0.5 and /3 = 0.09 were satisfactory for reporducing experimental detonation velocity-density curve and C-J pressure of Comp B. The value of 6 they used was 400 k was defined as /tSx -k(, where K was 11,85, x was the mole fraction and kz- were the individual geometrical covolumes. The final version of Cowan-Fickett equation is given here under Kistiakowsky-Wilson Equation of State 

With this historical background given by Mader (Addnl Ref N,. pp 7-8), it becomes apparent that the BKW equation of state is based upon a repulsive potential applied to the virial equation of state  

Replacing B/v with x and neglecting higher order terms, there was obtained pv/RT = l+x+xe x or to a first approximation pv/RT = 1 +xe x 

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Fur die Berechnung des Detonationsdruckes, sowie der Geschwindig-keit der ebenen Detonationswelle nach der - Chapman-Jouget Theo-rie, wurden wahrend der letzten funfzig Jahre hauptsachlich die Becker-Kistiakowsky-Wilson (BKW)-, die Lennard-Jones-Devonshire (LJD)- und die Jacobs-Cowperthwaite-Zwisler (JCZ)-Zustandsglei-chung verwendet. 

CHEMKIN REAL-GAS A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, Schmitt, R. G., Butler, P. B. and French, N. B. The University of Iowa, Iowa City, IA. Report UIME PBB 93-006,1993. A Fortran program (rglib.f and rgin-terp.f) used in connection with CHEMKIN-II that incorporates several real-gas equations of state into kinetic and thermodynamic calculations. The real-gas equations of state provided include the van der Waals, Redlich-Kwong, Soave, Peng-Robinson, Becker-Kistiakowsky-Wilson, and Nobel-Abel. 

Mader, C. L., Detonation Properties of Condensed Explosives Computed Using the Becker-Kistiakowsky-Wilson Equation of State, Report LA-2900, Los Alamos Scientific Laboratory, Los Alamos, New Mexico, 1963. 

Relative performance" of various HE s was predicted by Kury et al (Ref 7, p 11) on calcn using Becker-Kistiakowsky-Wilson equation in a thermodynamic-hydrodynamic code, such as RUBY (qv). To do this the energy release (AE) for the reaction ... 

N) C.L. Mader, "Detonation Properties of Condensed Explosives Using BeCker-Kistiakowsky-Wilson Equation of State , LASL Rept LA-2900(1963) O) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT Using the Landau-Stanyukovich Equation of State for Detonation Products , USNavalOrdnanceLaboratory, White Oak, Md, NOLTR 64-40(1964) (The equation discussed in Rept is the one modified by Zel dovich Kompaneets and is referred to by Lutzky as "LSZK Equation of State ) Oi) M.L. Wilkins, Univ of Calif, LawrenceRadLab, Livermore, Calif, Rept UCRL-7797(1964) P) H. Hurwitz, "Calculation of the Detonation Parameters With... 

IBM-7030 STRETCH Computer using the Becker-Kistiakowsky-Wilson equation of state. These parameters are listed by us under "Detonation (and Explosion), Equations of State Used in . He also detd several Chapman-Jouguet parameters... 

Becker-Kistiakowsky-Wilson (deton) equation of state 4 D272... 

Equations of state (detonation and expin), listing of Abel, Allan, Beattie-Bridgeman, Becker, Becker-Kistiakowsky-Wilson, Benedict-Webb-Rubin, Berthelot, Boltzman, Brinkley-Wilson, Caldirola Paterson, Callendar,... 

BITA = aziridine curing agent 34 bi-trinitroethylnitramine 34 bi-trinitroethylurea 35 BKW = Becker Kistiakowsky Wilson state equation... 

Next to the - Chapman-Jouget theory, during the last 50 years, the principal methods of calculating detonation pressure and the velocity of flat detonation waves have been the Becker-Kistiakowsky-Wilson (BKW), the Lennard-Jones-Devonshire (LJD) and the Jacobs-Cow-perthwaite-Zwisler (JCZ) equations of state. 

To calculate the detonation pressure, this equation is however not good enough, because there are strong deviations from the ideal gas behavior. The Becker-Kistiakowsky-Wilson equation of state (BKW-EOS)... 

One of the most difficult parts of this problem is accurately describing the equation of state of the fluid components. Despite its simplicity and lack of rigorous derivation, the Becker-Kistiakowski-Wilson (BKW) is used in many practical energetic material applications. There have been a number of different parameter sets proposed for the BKW EOS [5-8]. Kury and Souers [9] have critically reviewed these equations of state by comparing their predictions to a database of detonation tests. They... 

The Becker-Kistiakowsky-Wilson (BKW) equation of state described in Appendix E is the most used and best calibrated of those used to calculate detonation properties assuming steady-state and chemical equilibrium. Comparison of the calculated and experimental detonation properties permits evaluation of the errors to be expected from steady-state modeling of detonation products. Table 2.1 lists the calculated and experimental C-J properties of various explosives and mixtures. The calculated detonation product compositions of some of the explosives are given in Table 2.2. 

The gamma-law equation of state means that the gamma-law equation is used to describe the isentrope through the C-J state and the constant beta equation is used to calculate off the isentrope. The BKW equation of state means that the Becker-Kistiakowsky-Wilson equation of state (Appendix E) is used to describe the isentrope through the C-J state and a variable beta equation of state is used to calculate off the isentrope, with beta a function of volume as defined by the BKW equation of state. 

The historical background of the Becker-Kistiakowsky-Wilson (BKW) equation of state is of some value, since it gives an insight into its theoretical basis. 

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