UCRL-ID-117240CHEETAH: A Next Generation Thermochemical Code L. Fried P. Suers November 1994 *_ L Work performed under the auspices of the U S Department of Energy by the .. Lawrence Livermore National Laboratory under Contract W-7405-ENG-48. , DISCLAIMER "his document was prepared a an account o work sponsored by an agency of the United States Government. Neither s f t e United states Governmentnor khe University of California nor any of t e r employees, makes any warranty, express h hi or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness o any f information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. 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Box 6 ,Oak Ridge, TN 37831 2 P i available from ( 1 ) 7 . 4 1 FIS G&8401 r m 655680, Available to the public from the ehia National T c n c l Information Service U.S. Department of commerce 5 8 Port Royal R . 25 d, Springfield, VA 2 1 1 26 L DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. CHEETM has been made simpler to use than TIGER. A wide variety of improvements have been made in Version 1.g. so CHEETAH can predict the properties of this state.CHEETAH: A next generation thermochemical code Laurence E. It solves thermodynamic equations between product species to find chemical equilibrium. We have improved the robustness and ease of use of TIGER. We have also made an extensive effort to improve over the results of TIGER. 1 Overview 1. no guesses for the C-J state) than TIGER did. in a system comprised solely of condensed carbon. typical use of the code occurs with the new standard run command. For instance. A kinetics capability will be added to the code that will predict reaction zone thickness.1 What CHEETAH does Below we give a non-technical explanation of what CHEETAH does. Further ease of use features will eventually be added. typical run times are under 10 seconds on a workstation.0. CHEETAH is a thermochemical code. and gaseous CO2. C-J theory says that the detonation point is a state in thermodynamic and chemical equilibrium. 1 . In the future we plan to improve the underlying science in CHEETAH. something that other BKW parameter sets have been unable to do. CHEETAH can find the equilibrium of the reaction c + co*-2co at a specified pressure and temperature. Fried and l? Clark Souers (510) 422-7796 Abstract CHEETAH[ 11 is an effort to bring the TIGER thermochemical code[2] into the 1990s. CHEETAH'S version of the BKW equation of state (BKWC) is able to accurately reproduce energies from cylinder tests. CHEETAH will make the use of thermochemical codes more attractive to practical explosive formulators. More accurate equations of state will be used in the gas and the condensed phase. Calculations performed with BKWC execute very quickly. All of TIGER'S solvers have been replaced by new algorithms. an automatic formulator that adjusts concentrations to match desired properties is planned. We find that CHEETAH solves a wider variety of problems with no user intervention (e. gaseous CO. explicitly specified in CHEETAH. The first two reactions are trivial and therefore have no effect on the chemical equilibrium.e. i.S) points play an important role when undertaking an adiabatic expansion from the C-J state. This reaction is an internal construct of the code and does not have to occur physically. you might ask. The above carbon example leads to the equation The chemical potentials of condensed species are just functions of pressure and temperature. These types of calculations implicitly define pressure and temperature. 2CO-c t--L - Since decomposition reactions in CHEETAH aren’t real. For example CHEETAH might choose C and CO as components. + Pco* = 2pco Here. How then. as long as there are enough of them to change concentrations arbitrarily. the number of molecules of COz. they can have negative stoichiometric coefficients. CHEETAH manufactures a decomposition reaction for each product molecule. The decomposition reactions would then be: c . does CHEETAH get the chemical reactions for balancing chemical potentials ? The answer is that the reactions used don’t matter. -VCO. the answer will come out the same no matter what reactions are used. we can specify the volume and the entropy instead of the pressure and temperature. CHEETAH can calculate thermodynamic states where the pressure and temperature are not explicitly indicated.c co co co.T) = s o Thermodynamic equilibriumcan be found by balancing chemical potentials.T) = S(P. For instance. The number of components is equal to the number of elements in the problem. There are no chemical reactions. In fact many thermochemical codes (notably CHEQ[3]) numerically minimize G instead of bothering with chemical potentials. V(P. . while the potentials of gaseous species depend on concentrations: Pc (V.From these properties and elementary detonation theory come the detonation velocity and other performance indicators. The product molecule (called a “constituent” in the language of TIGER) decomposes into a small number of “component” molecules. Recall that the chemical potential is the Gibbs free is energy difference obtained from adding one more molecule into the system: Balancing the chemical potentials is the same as minimizing G. where users can send questions or suggestions. 0 0 0 0 0 CHEETAH supports a startup file that loads initialization commands automatically. CHEETAH has a reactant database containing most frequently used explosives and binders. etc. It is now possible to run CHEETAH by giving only the composition and density. CHEETAH supports user-defined and relative units for input.The equations solved by CHEETAH are ~ Here Z C is the concentration of COZ. The input routines of TIGER have been re-written. CHEETAH[ has a single command standard run.2. CHEETAH 1. We have started an electronic mail hotline for C&ETAH users. Quattro.O User's Manual[ 11. CHEETAH is nothing but a complicated chemical potential balancer. names can'be used. This file is readable by Excel. CHEETAH produces a single sheet summary of a run. The output of CHEETAH can be exported to a spreadsheet file. The manual includes a tutorial to help new users. 3 0 0 0 . 1. This saves the user the inconvenience of looking up thermodynamic constants. Since then. industry. More than 80 pages of discussions have been logged on the hotline since July. CHEETAH has been released to more than 30 beta testers at DoD and DOE laboratories.0 was released to beta testers in the Office of Munitions Technical Coordinating Group in July 1994. CHEETAH has a simple macro facility for frequently used commands. new algorithms.1 User convenience 0 CHEETAH has been extensively documented. more logical. In words the equations say: balance the chemical potentials while keeping the total moles of each element fixed. A 140 page user's manual[ 11 was prepared and professionally published. detailed description of code features is given in the CHEETAH 1. Wc is the concentration of the element C in the system. Input files now accept comments. 1. and new capabilities. The hotline is an informal discussion group. Longer.2 FY94 Accomplishments A list of accomplishments made in the CHEETAH project during FY94 is given b l w A more eo. The summary sheet has all the information that most users require. and academia. Work on CHEETAH has fallen into one of three categories: enhanced user convenience. . 2 Code improvements in CHEETAH 1. CHEETAH has a new C-J solver that is more reliable than TIGER’S. The reparametrization was done through exhaustive computer search techniques. CHEETAH estimates the portion of the detonation energy that is available for doing mechanical work. C-J pressures. CHEETAH estimates cylinder test wall velocities for comparison with experiment. 1. CHEETAH has a JWL fitting program built in. 0 1.2. and final energies of detonation.0 The following sections describe changes to TIGER made in developing CHEETAH.3 New capabiiities 0 CHEETAH has wide variety of thermodynamic point types. Most notably. The program is not limited to 640K of memory and can be resized to take advantage of available memory. CHEETAH supports multiple product libraries. 0 0 0 0 0 CHEETAH can be dynamically resized to run large problems or accomodate small computers.2. A version of CHEETAH for MS-Windows was developed. CHEETAH has a new Hugoniot solver that is faster and more robust than TIGERS.2. The new parameters are capable of generating reliable detonation velocities.2 Algorithmic improvements 0 CHEETAH has a new solver for chemical equilibrium that is more reliable than TIGER’S. 0 0 0 1.3 Improved equation of state The BKW equation of state has been reparametrized for CNOH explosives. T-S points are available for freezing along an adiabat.0 Product libraries now have titles. This allows the library used to be clearly identified in the output files. There is also a stand-alone program for fitting experimental cylinder test data to a JWL. CHEETAH has a new solver for solid-liquid phase coexistence. adiabat energies. Difficultieswith freezing concentrations in TIGER have been fixed. t. The load file command is particularly useful in conjunction with relative units (see below). 5 spreadsheet.3 Startup file Any commands in the file startup. Favorite input units. .0 in TIGER. 200000 stop 5 .in. Because of this. p . it returns to running commands from the original input file. myfile:!. myfile-dat. or frequently used reactants are good candidates for inclusion into the startup file. s. h. tab isoline. close point. in the file string. 2. Comments are echoed into the output file but are otherwise ignored. user-defined names cannot. p. Spaces in words are now recognized. 1200.2 Load f i l e command The command instructs CHEETAH to execute the commands contained in myf ile . 3 0 0 0 . The '&' must be the last character on the line. CHEETAH keeps a "dictionary" of strings that it has learned in previous runs and while loading the library. e point. For instance. a set of modifications were made to the entire code that replaced al the input with a modem token-based input system. l To solve this problem. This had nightmarish consequences for the readability of the code. 2. After the commands are executed. since one had to be sure that no two constituents shared the same first three letters. For example. Any input line beginning with a "##" character is a comment. in will be executed before the regular input file.in. s. v.4 Spreadsheet output CHEETAH can create an auxiliary output file consisting of specified thermodynamic variables. t . (like Dan Calef's PC version) were limited to recognizing only the first three characters of a string. v. While commands may be abbreviated to three letters. This is to help reduce errors in library files. p. load file. the authors translated character strings into floating point numbers. 10 0 . Single-precision versions of TIGER.1 New input routines TIGER was written before FORTRAN had character string types. Although commands can be abbreviated. This made the creation of constituent libraries very error-prone.2. in a form readable by most spreadsheets and plotting packages. t.h 2. spreadsheet. the string 'ALPHA' appears as the number 1526302215.dat. equation of state set commands. further letters are now significant. myfi1e. An '&' is provided as a continuation character for long lines. It also had subtle consequences for the user. 20000 spreadsheet. v. columns are separated by commas. Other separator options are comma and space.dat be created.g. P. The problem with the two-step scheme is that if a difficult or unphysical set of 7‘s was chosen. and maintains the exceptional speed of the original TIGER solver. in which case the set of variables used in the first spreadsheet command is inherited by the second.5 Improvements to the freeze command The freeze command in TIGER used an algorithm that was susceptible to roundoff errors. containing values of p.v. Other exotica. not all p-v states are attainable).6 Reformulated concentration solver For every calculation type (point. are possible.s. 2.t. such as p-t.a. etc. This occurred for two reasons: the two-step solver used in TIGER could get trapped in local minima that a single-step solver would avoid. isoline). The qs have now been eliminated as basic variables in CHEETAH.v.g. the inner concentration solver would fail. and K . The columns in the file are to be separated by tabs. Most notably.. 6 .9 for information on Hugoniot points.specifies that a spreadsheet file m y f ile . CHEETAH can report the concentrations of selected constituents.T). the Newton solvers in TIGER used a poor backtracking mechanism that often led to poor convergence. the new point types require that you first run an ordinary point. Spreadsheet commands can follow one another without an intervening close. in which case CHEETAH will be unable to find a solution. In the two-step solver the concentrations were adjusted at fixed q values (the q were related to chemical potentials). The freezing algorithm was modified in CHEETAH to make it more reliable. and specific volume are adjusted simultaneously in a single solver. the log concentrations.e. c-j. t.t. TIGER solves at least once for the concentrations of the non-frozen constituents at a specified thermodynamic state (e. Spreadsheet can report the following variables: p. 2. p-v.p.. The new solver is more robust than the TIGER solver. By default. The new thermo solver also incorporates bounds so that no concentration can exceed the maximum allowed by stoichiometry. h. In the above example. vgS. so that freezing had to be done in multiple steps. Currently.h. The consequence of this to the user was that TIGER would frequently refuse to freeze concentrations. This should be useful. such as H-S points. 2. a.Hugoniot). T-S points can be given. and S. by giving the constituent name. The original solver would often fail to converge. Sometimes the state specified does not exist (e. See section 2. temperature. The new solver implements a different set of equations than TIGER. The close command is necessary to make sure that unwanted points do not end up in the spreadsheet file. Instead. Secondly.7 New point types CHEETAH allows the user to specify the thermodynamicstate (“point”) by giving any two functions from the list (p. then the qs were adjusted. s.for freezing along an isentrope. e. C. In addition. the point at 3000K and 2oooO atm would be put in the spreadsheet file were it not for the close command. The first argument to spreadsheet must be either a filename or close. p .Hugoniot) can be held constant. and IE is the adiabatic exponent.11 User-defined units units.9. v.e. as in TIGER.e0 = (PI PO)(VO . (2) with Brent’s method.v. CHEETAH implements a Hugoniot point in a different way than TIGER rather than solving for a successive number of ( p . Using these points as brackets. it finds the root of Eq. p .h. 2. The c. Units to use when entering pressures or volumes can be specified with the commands 7 . w) points. isoline accepts new variables. 2 units.j command doesn’t take any arguments. hugoniot calculations are performed until a pressure is found that satisfies the equation is satisfied. Isentrope integrals are only calculated for p-s or v-s lines. Unfortunately. similarly to the specification of the reference state in TIGER’S c. The c. For example.j command also has a new syntax.9 New Hugoniot solver TIGER used a simple iteration scheme to find a point on a shock Hugoniot. saying that we are on the Hugoniot plays the same role in CHEETAH as saying that the pressure is 1OOkBar. it uses the equation (1) e1 . CHEETAH’S solver takes advantage of the hugoniot point type. The reference state (PO.t. Thus.8 New isoline types Corresponding to the new point types.2. + 2. 2. Any thermodynamic variable from the list (p. A series of p. 2‘ is the volume at the specifiedpressure on the Hugoniot line. 100 units. The reference point on the Hugoniot is specified with the hug0 command described in Sec. The detonation pressure is assumed to be between the constant volume explosion point and 500kBar.10 New C-J solver CHEETAH has a new C-J solver that should be more robust than TIGER’S solver. eo) is specified through the new hug0 command. Here. iterative methods don’t always converge.w1)/2 as an implicit definition of the thermodynamic state. The same iteration was used within the C-J solver.s. the C-J and Hugoniot solvers in TIGER often ran into difficulties. while any other variable from the list can be changed. 2. It behaves very VO.j or hugoniot command. This volume should have been previously set through the hug0 command or the standard run command.: is the molar volume of the reactant in its standard state. The v0 command gives volumes in reference to the initial explosive volume. which is the number of cylinder runs to use in the fit. j wlf i t takes a single argument. The summary command with a blank argument closes the current summary file. At least three runs must be used. so V . Units can be set for p . sv indicates that the standard volume is the new input unit of volume. The second command sets the input unit of relative volume to be 2 cc / gm. This should be followed by the det energy command. 2. v. in which case the JWL fitter will find the best possible fit to the points. The appropriate command is j wl f i t.H . In this case the unit of volume is set to be the shock Hugoniot reference volume VO. 2. which finds the detonation energy.The first command sets the input unit of pressure to be 100 Atm. This command should be given after finding the C-J point and at least 3 points along the adiabat. myfile-sum where myf ile . all quantities with the dimensions of energy ( E . The S-V points correspond to cylinder test results. can generally be regarded as the TMD of the reactant mixture. The units in the output file are unaffected by the units command. The command units.12 Summary sheet output A file summarizing the run can be generated by using the command: summary.o u t is created as the default summary file if the summary command is not given. all the previous cylinder runs are used. If E units are specified.p . therefore it is of particular use in specifying expansion volumes. =Ex& I (3) where xj is the mole fraction of reactant i and V. . C-J parameters. The unit of S is the unit of E divided by the unit of 7'. and the volumes and energies of any subsequent S-V points. There are two special ways to set the unit of volume.13 JWL-Fitting CHEETAH will automaticallydetermine a JWL fit to the C-J point and the adiabat.sum is the name of the summary file. G) are input with the new E units. The third command sets the unit of pressure to be the current pressure. The file summary. This is particularly useful when specifying pressures or volumes relative to the last thermodynamic state in the calculation. The second way to define the unit of volume is through the command units. The molar volume in the standard state is usually the same as the inverse of the TMD divided by the molecular weight. v0. The summary file contains the initial composition. More than 3 points along the adiabat can also be used. E and T . The standard volume is defined as: v. Subsequent summary commands close the previous summary file. By default. and 20. calculating points at relative volumes equal to 2. standard run assumes that the density is equal to TMD. The use of a formulacommand in the input file discontinues searching of the database for all formulas. 2. The first line of the database gives a title that will be echoed to the main output and summary files.82 is the density of the formulated explosive.16 Formula library command to specify the reactant formulas is no longer necessary. The first line of the standard. . Next the freezing temperature is given. The energy of detonation is then found and finally. Longer versions of the command (e.0. Without the rho argument.in. The standaid CHEETAH run performed at LLNL can be executed with the standard run command.4.0 if freezing is not desired.6. starting with the first character in the line.in file is the number of points to calculate along the adiabat.17 Configuration directory All startup and configuration files are now put in a configuration directory.in. Formulas in the database must begin with the command for. 1. This command is used to find the detonation energy. 2.1. By default.arched for the appropriate formula. The composition is frozen at 1 0 K along 80 the adiabat. rho. Next follows the relative volumes at each of the points. The standard run can be customized by modifying the file config/s tandard. It then proceeds along the adiabat. InThe old for. The old subroutine CHKPHA has been replaced by the C subroutine checkphase.82 where 1. the adiabat points are fit to a JWL equation of state.4 D e t energycommand . assuming a reference pressure of I atm for the Hugoniot.2.5 S t a n d a r d r u n command standard run. The syntax is: 21 .0. The command first finds the C-J point. . The formula command can be used in the input file to override database values.in file controls whether JWL fitting is done or not. The last line of the standard.21 . A 1 indicates that the adiabat is to be fit to a JWL equation of state. the directory is conf i g .18 New mixture solver The mixture solving and detection routines from TIGER have been replaced with new routines in CHEETAH. 10.g. 2. formula. enter 0. The energy of detonation is broken out into a mechanical and a thermal part. ) cannot be used in the database file. while a 0 indicates that fitting is not to be done. The following algorithm is used to check the condensed phase assumptions: if condensed phase 9 . these commands have been put into a database file config/formula.5. . stead. the database is se. When the components command is given. You then run CHEETAH on a library file: cheetah 1ibrary. It is then concluded that the ith condensed constituent should be in a mixture state. Finally the fourth number is the maximum number of reactants.P ) values. The command library file. until all possible assumptions are exhausted. CHEETAH will store and read the library in the file cheetah. 2. checkphase0 then looks through all previously tried guesses to find a candidate for the melting compound. c h l should be placed in the library prior to running it with CHEETAH. The first number is the maximum number of gaseous products (called constituents in the language of TIGER) The second is the maximum number of condensed products. CHEETAH’S array sizes are controlled by the file conf ig/alloc .while CHEETM can be kept small for PC’s or other systems with little memory. library files may be selected with the command library file. the mixmaster() routine is somewhat slower than the iteration method used in TIGER. The melting compound is identified when the following conditions are met: there exists two guesses identical in all assumptions except the ith. but it should be more reliable. 2.assumptions are violated. called mixmaster. The liquid fraction fi is then determined in a new subroutine. Then. The alloc . In general. chl.h 1ibrary.19 Dynamic memory allocation The size of internal arrays in CHEETAH cart be easily changed by the user. mylib. rather than the default cheetah. Naming libraries is highly recommended as a mechanism for documenting io . a unique set of new assumptions are generated. P ) ) are recalculated using these assumptions. This subroutine uses Brent’s method to find the value of fr such that the chemical potential of the solid is equal to that of the liquid for condensed constituent i.in. checkphase0 concludes that the state of the system must be a solid-liquid mixture. chl. For these two guesses the chemical potential conditions are satisfied for all but the ith condition. and the changes then take effect upon running CHEETAH. mylib. chl in the input file or conf ig/startup.If the library file command is not used.20 Library file command CHEETAH can keep track of more than one pre-compiled library file at a time through the use of the library f i l e command. At this point. which is violated in both of the guesses.chl.i n file can be edited to change the default array sizes. If the assumptions are again incorrect.in.21 Library titles Product libraries can now be titled. CHEETAH prints the title of the current library in the output and summary files. Large numbers of products or reactants can be run on computers with sufficient memory (RAM).out The 1 ibrary f i l e command specifies that the compiled library will be stored in my l i b . The thermodynamic state (and hence (T. new assumptions are generated which are correct for the current ( T . The third number is the maximum number of elements (called components in TIGER). 2. 1 Introduction C-J detonation theoryC41 implies that the performance of an explosive is determined by themodyn a m k states-the C-J state and the C-J adiabat. This point of tangency can be found. This title is recorded i the binary library file and is reported for each subsequent CHEETAH run using that n library. and total energies of detonation were used to reparametrize the BKW equation of state for the CHEETAH thermochemical code. reproduces detonation velocities and adiabat energies better than previous BKW parametrizations. the reporting of these functions is restored. F. referred to as BKWC.H. given that the equation of state P = P( V. and IC. SO 11 .2 a = = -(-)p 1 de P dv dlnp -(-). 7') of the products is known. The resulting detonation velocities. adiabat energies. C-J theory states that a stable detonation occurs when the Rayleigh line is tangent to the shock Hugonlot. By using the details command.the library associated with a particula output fil command above to switch between libraries. The allowed thermodynamic states behind a shock are intersections of the Rayleigh line (expressing conservation of mass and momentum). the following information is shown: the constant volume heat capacity. and hence obtain a prediction of explosive performance. and the shock Hugoniot (expressing conservation of energy). After the details command. By default. C-J pressures. The chemical composition of the products changes with the thermodynamic state. enter the command title. To give a library a title. and C1 was collected. d. The resulting parameter set.N. IC was called ADEXP in TIGER. Thermochemical codes use thermodynamics to calculate these states. CHEETM shows fewer thermodynamic functions than TIGER did.O. 3. The BKWR equation of state is found to be slightly better in yielding C-J pressures. The definitions are as follows: 2 2 Details command . the hydrodynamic constants cy.= dlnv K a+l B 3 BKWC: A new parametrization of the BKW equation of state A database containing mostly cylinder test data for 42 explosives composed of C. an example library especially when ising the library file immediately after the start of library command in the library input file. K . and R is the gas constant. 61 gaseous equation of state (EOS) has a long and venerable history in the explosives field. Finger et. The new code. the C-J state is attained behind a planar detonation wave traveling through an infinite medium after an infinite period of time. but chemical equilibrium is not completely achieved. Even the concept of a sonic point. To that end we have employed a modern stochastic optimization algorithm to find the global parameters and covolumes that best match available experimental data. we will cease to distinguish between the sonic point and the C-J state. and 8 are adjustable equation of state parameters. The work of Baer and Hobbs was critical in reviving interest in the BKW equation of state and extending its use to a wide range of inorganic compounds. but rather by a spatial distribution of states. There have been a number of different parameter sets proposed for the BKW EOS. we decided to explore the limits of accuracy possible within the BKW framework. Thus the C-J state is never exactly attained in any real experiment. Since geometric (e-g. al. however.thermochemical codes must simultaneously solve for state variables and chemical concentrations.given that the equation of state of the gaseous and solid products is known. According to Zeldovich-Von Neumann-Doering (ZND) theoryC41. Notionally we may say that the C-J state is replaced by a frozen "sonic point"[ 11. BKWS gave better results for the adiabat. . the developing C-J state is disrupted by rarefaction waves. Caution must be employed when comparing predicted C-J properties from an equilibrium code and experimental data. We have undertaken a project to update and extend the TIGER[2] thermochemicalcode at LLNL. while Baer and Hobbs[8] proposed the BKWS parameter set. Of course. is simplified. Kury and Souers[9] have critically reviewed these equations of state by comparing their predictions to a database of cylinder tests performed at Lawrence Livermore National Laboratory (LLNL). Finite system size reduces the effective time available for equilibration. Mader[6] used two BKW parameter sets for high oxygen and high carbon explosives. but failed to reproduce the shape of the adiabat without the use of empirical scaling factors.[7] proposed the BKWR (for renormalized) parameters. p. The BKW EOS has the following form: p v = nRT x = k/u(T+8)" k = KC$. As apoint of departure.c is achieved. n. We hope to address some of the above issues in the near future. This is consistent with our 12 . however. sample shape and confinement) effects determine the behavior of an explosive. named CHEETAH[ 11. v is the molar gas volume. For the present time. its properties cannot be described by a single thermodynamic state. ni is the mole fraction of species i and the ki are covolumes. We refer to the new parameters as BKWC (for CHEETAH). however. The performance of the BKWC equation of state will serve as a practical test of the utility of other equations of state that we will pursue in the future. Despite its simplicity and lack of rigorous derivation.ki 1 + zexp(Pz) Here. 121 where the condition D = U p -t. The Becker-Kistiakowski-Wilson(BKW)[S. the BKW EOS is used in many practical applications in the explosives field. cy. p is the pressure. currently implements the BKW and JCZ3[ 101 equations of state. One of the most difficult parts of this problem is accurately describing the equation of state of the gases. (8) . real experiments are always carried out on finite systems. This problem is relatively straightforward. More sophisticatedequations of state will likely be addedinthe future. but suffered from poorer prediction of detonation veiocites. They concluded that BKWR gave the best predictions for detonation velocities and CJ pressures. K. While it is always safer to do calculations with a large number of product species than it is to have too few. since it gives good results without scaling factors. we ran calculations on all the CNOH compounds in the data base. These values are much less than typical disagreements between thermochemcal code results and experiment. We kept all species attaining a maximum concentration of 0. In each calculation the C-J state was found. A further expansion was then done along the adiabat to 1 ATM or 298 K. 4. Most explosives of wide practical utility are included in the database. we now discuss the adjustment of parameters to match the experimencal database.15]. volume. it was necessary to determine the minimal number of products needed to obtain good results for "usual" explosives. The database contains compounds lacking hydrogen (BTF. Carbon rich (TATB. heat of formation. the VOiUme error was 0. We started with BKWS as an initial parameter set. For each CNOH product in the Sandia library. however. We repeated the runs with the abbreviated BKWS library. with the exception of CH3. mostly consisting of cylinder tests performed at LLNLE 13. we found the fractional root mean square ( W S ) enor in the pressure. The resulting maximum concentrations are reported in Table 3.. temperature. . 0 Although ANFO has notoriously strong size dependences. and energy across all the thermodynamic states in the calculation. The reason for the 298K criterion is that BKW equations of state occasionally predict very cold (loOK or below) product gases after expansion. we expect the ANFO values to be fully size converged. Calculations of the C-J state and the adlabat 13 . Having determmed a minimal acceptable set of product species. H20.03 %. whichever condition came first. N..desire to make a predictive model that can be directly compared to experimental data. the data reported for this explosive is based on a large scale underground explosion of more than a kiloton[ 161. the abbreviated library does not cause significant errors. and the energy error was 0. . Table 1 gives the composition. There are several non-ideal explosives. and 8 given in Table 2. and NH3 are among the most common species. A wide range of stoichiometries was chosen. a number modestly greater than the 12 species used in BKWR. we found the maximum concentration that the product obtained across all the explosives and all thermodynamic states. the temperature error was 0. then points I ? along the explosive adiabat at 2.2 Method We have collected a database of explosive performance properties. The heat capacity fits used in CHEETAH break down in this regime. most notably .07 %. This yields 17 product species. Radicals never achieved significant concentrations.TNM) and carbon (RX-23-AA).1.05 mol/kg or greater in the BKWC library. We used BKWS values for CY. For instance. and density of the compounds in the database. Since we envisioned the BKWC library as an everyday tool for explosive formulators. we performed a final calculation at 298 K and 1 ATM. A similar procedure was followed to determine the necessary F and C1 products. After the end of the adiabat was found. By comparing the results Of the abbreviated BKWS with the full BKWS. The BKWS library. and H. To this end.2. contains a large number of product species. 0. The RMS pressure error was 0.14. in practice the use of so many products slows calculations dramatically. there are 6 1 product species containing C. CO?. We define this point to be the end of the adiabat. 3. but much less than the 6 1 species of BKWS. TNT) as well as high oxyygen (TNM) explosives were included.5 relative volumes were found. As might be expected. and 6.05 %.1 1 %. 176 0.4 F 26.75 0.Name BTF HMX HMX2 HNB LX14 PETN PETN2 PETN3 TNM HNS HNS2 HNS3 HNS4 NM FZ-23-AA TATB TNT FX-26-AF ANFO QMlOOR DP12 AFX902 FEFO FMl PF RX-36-AH RX-41-AB LX17 RX-27-AD RX-45-AA RX-47-AA RX-48-AA C H 6 4 8 4 8 6 15.7 -27.64 0.1 19.6 1.83 1.4 28.177.5 c P(glC4 1 1. and heat of formation of compounds in the performance database.3 25.6 -30.61 1.74 1.83 1.26 1.0 .6 O 6 8 8 12 27.7 1.9 61.0 51.83 1.5 10 33.3 44.20 1.4 2.3 3 29.89 1.1 -62.50 1.0 40. For mixtures.66 1.84 0.7 4 4 4 4 6 6 6 6 1 29.3 17.7 7.50 6620 10.6 1.1 6 3 25.7 .2 1 2.159.9 5 6 20.7 -36.8 -48.18 1.8 18.5 0.7 118.7 18.1 2.3 23. the composition is given as mole fractions.1 2.3 17.0 4 13.85 1.1 5 8 5 8 5 8 1 14 6 14 6 6 14 14 6 1 3 51.7 18.1 6 6 25.13 1.7 30.40 1.8 -20.80 1.3 3.6 -86.5 12 12 12 8 12 12 12 12 2 19.403 CY 3 ri (ccK*) B(K) 11.5 1.2 2.7 4.7 40.51 1.0 35.0 -27.76 1.9 23.4 -64. Table 1: Composition.6 18.80 1850 10.oo 1.82 0.51 1.6 N 6 8 8 6 26.0 8.26 1..3 35.0 10. EOS BKWR BKWS 0.8 23.2 6 2 22.0 17.9 29.15.17.8 4.7 1. density.5 17.2 6 29.2 37.7 30.8 20.7 -30.9 17.2 14.6 17.9 .7 18.1 25.128.97 1.86 0.6 29.9 13.9 28.5 27.65 1.4 -128.4 47.9 -62.8 23.0 33.4 24.6 23.7 1.298 BKWC 0.83 1.8 -8.9 20.0 30.2 25.3 12.9 .7 16.5 .8 6 6 5 7 20.7 2 3.5 0.85 H f (kcdmol) 144.42 1.63 1.5 0.4 1.5 2.86 544 1 Table 2: BKW parameters used in the calculations 14 .0 28.5 .7 -128.2 24.91 0.7 15. lOE-08 7.43E-07 9.02E-03 8.75E-0 1 2.32E-12 1.3OE-05 2.98E-02 3.73E-04 1.03E-03 1.55E-04 5.46E-02 4.S 1E-04 1.68E+O1 1.72E-16 Table 3: Maximum concentrations ( .39Ei-00 3.7OE-02 3.71E-03 2.53E+01 5.65E-01 8.58E-03 .85E-06 1.89E-02 1S3E-02 1.19E-06 3.54E-08 3.18E-04 1.01E-05 3.12 1.96E-02 2..42E-05 4.4OE-04 3.29E-05 1.28E-02 2.84E-04 3.34E-04 2.17E-02 1.75E+01 1. 15 . & ) found with BKWS when performing C-J and adiabat calculations on all compounds in the performance database.79Ei-00 3.62E-02 7.19E-04 2.99E-05 2SOE-05 2.38E-02 5.61E-07 2.04E+OO l.46E-05 2.74E+Q 1 1.32E-02 4.19E-06 1.O9E+OO 5.09E-04 6.01E-06 8.72E+O1 1.95E+OO 5.33E-03 2. a- (morng) 1S8E-03 1.Compound -Ymas (moykg) 2.26E-02 2.15E-04 7.16E.17E-01 1.53E-02 3.34E-02 6. Some energies of detonation were determined through fitting the cylinder data to a JWL equation of state.1 rnm/ps. The error in the adiabat endpoint. C-J pressure) can have disparate error bars. We adjusted BKW parameters and covolumes to find the “best fit” to the experimental data.5 to 1%. For 25 and 50mm cylinders of 300mm length. the error to be minimized) in order to obtain the parameter set that best describes physical reality. have a variance between runs of 0. indicates that thermodynamic equilibrium is not fully achieved through a typical adiabatic expansion. The presence of substantial concentrations of CO in detontion products. The difficulty in matching to experimental data is that different quantities (e. TATB. In the present treatment. The measured velocity is thus across a distance of 200mm. After consulting previous work. Detonation velocities are determined from pin rings attached to the cylinders.6%[19]. Since our data is at SOmm.e. but rather how well the finite size measurement approximates an infinite system.better than 1%. 5% errors were E estimated for adiabat energies. The difficulty arises in relating cylinder velocities to infinite diameter theoretical predictions. Thus an overall error of 3% was used. To this effect. Most of the data is collected from cylinder tests. which in turn was based on JANAF table data[ 181. detonation velocity. Standard pressure reference data (heat of formation. we estimated an error of 10%. cylinder).g. with the exception of ANFO and QMlOOR. those quantities with largest error bars would dominate the fitting process. the pin rings are set at 90 and 290mm. so that the accuracy is much. Our approach was to optimize the EOS to give results that are within experimental error bars. The performance data we used is given in Table 4. BKWC uses the same standard pressure data as BKWS. E is the experimental value. This was based largely on the use of streak camera data. however. for example. we defined the discrepancy between a theoretical and a measured quantity to be: Here T is the theoretical value. The difference between D at 50mm diameter and l O O m m diameter is 0. The discrepancy is defined to be zero if we are inside 16 . as found by OrnellasC 171. is probably higher. Total energies of detonation. The relevant error is not how well a quantity in a particular finite sized experiment was measured (e. In effect we would be trying to reproduce experimental errors. we took 1% as an error estimate. If the difference between experiment and theory was minimized without regard to the underlying error bars. The problem is compounded by the fact that experimental error bars are often difficult to find. and d is the discrepancy. Comparison with Omellas’[ 171 data yielded an error estimate of 5%. This is based on a comparison of C-J pressure measurements for P m using various experimental techniques[ 121. we arrived at the following rough error estimates. and heat capacity as a function of temperature) were not adjusted.g. Some thought must be put into the definition of the objective function (i. F is the estimated fractional experimental error bar.were performed as described above. the detonation velocity in a 2 in. we take the freezing temperature to be an adjustable parameter. It has been standard practice at LLNL to freeze concentrations along the adiabat at 181)o K. entropy of formation. Some explosives ( e g TNT) show variable results according to confinement. has a strong detonation velocity size dependence. with the exception that concentrations were frozen at a temperature Tj. For the C-J pressure. which typically has velocities of about 2 5 0. as determined by bomb calorimetry[171. This error can be reduced to perhaps f1% with the use of Fabry-Perot interferometry. 2 7. S C C C C -5.480 1 6.63 C C C.54 -4.0 16.77 -5.4 13.61 -3.19 -8.07 -6.77 -5.70 -7.15 -5.928 1 7.O 8.0 7.5 7.0 26.72 -7.10 -5-91 E(6.2 E(2.10 -3.5 3.7 1 5.18 -4.39 -4.3 7.09 -9.630 1 6.0 31.60 -8.0 ECd 11.590 1 8.0 30.7 5.57 -5.23 -5.82 -6.5 43.57 -5.280 1 8.6 7.8 9.2 13.1) -8.24 -3.65 -5.340 1 5.0 21.13 -5.2 10.5 15.66 -4.54 -3.1 10.0 40.451 1 6.0 27.6 3.19 -5.511 1 8.19 -4.8 1 -4.67 -4.45 Ref. 3 indicates a strongly non-ideal explosive.2 8.814 2 7.0 26.20 -6.97 E(4.0 10.1 Em 11.87 -6.93 -3.31 -3.0 24.54 -4.83 -7.14 -6.74 -5.100 1 6.5 3.54 -2.740 1 5.8 4.4 1 -2.08 -4.9 8. All energies are reported in kJ/cc.3 8.3 6.5 19.68 -4.3 8.64 -4.290 1 8.17 -10.2) -6.640 2 7.59 -9.97 i 8.4 7.63 -3.7 3 7.Compound BTF I HMXl HMx2 HNB HNS 1 1 8.93 -3.33 -3.72 -4.2 11.0 9.344 1 7.5 6.06 -2.335 D(mm/ps) HNs2 HNs3 HNs4 NM PETN 1 PETN2 PETN3. J 12.82 -5.0 34.7 7.760 Pu(GPa) 34.69 -5.36 -8.710 1 7.8 26.5 12.04 -4.71 -6. Ecd is the total energy of detonation measured by bomb calorimetry.5 20.87 -6.0 33.3 7.656 1 7.0 6.J.45 -6.5) -9.40 -1.5 5.55 -6.19 -6.08 -8.88 -3.40 -4.88 -8.31 -5.59 -4.53 -3.49 1 9. E(z) is the adiabat energy at a relative volume of 2.5 7.2 7.5 -5.800 1 8.6 4.05 -2.78 -5.59 -7.580 1 6.0 26.0 25.5 39.5 16. 3 indicates partially ideal.674 1 9.19 -7.89 -3.51 -4 .95 7.60 -4.10 1 6.0 24.12 -5.0 15. E J w L is the total energy of detonation determined by fitting the adiabat to a JWL equation of state.030 1 6.72 C C C C C C. C C C C C C C C C C.32 -4.3 12. I is the explosive ideality.2 6. S N N C C 25.74 -2. 17 .1 C.5 35.0 6.0 11. RXA23A TATB TNT TNM LX14 RX26AF ANFO QMlOOR DP12 AFX902 FEFO FM1 PF RX36AH RX4 1AB LX17 RX27AD FX45AA RX47AA RX48AA 1 7.58 -4.449 2 7.9 7.09 -4.42 -6.3 11.569 I 7.65 -7.08 -5.0 7 .78 -8.070 1 8.240 3 4.J.5 37.35 -6.O 7. 1 indicates an ideal explosive. R C C C C Table 4:The LLNL performance database.18 -6.85 -6.274 1 7.70 -3. the heat of formation of diamond was increased by van Thiel and Ree[22] to empirically account for surface effects in carbon clusters. however.3 Results The optimized parameter set is given in Tables 2 and 5. The total error function is the weighted root mean squared discrepancy: Here. which corresponds to 60. 8 . but require many more function evaluations. Freezing is a rough way of incorporating kinetics into a thermochemical code. The stochastic minimizer was run about 2000 cycles. 211. and 25 % for the adiabat. the covoiume acts as an effective molecular volume multiplied by a stiffness factor. the carbon equation of state was adjusted. Some care is appropriate when considering the covolumes. covolumes can be related to virial coefficients. 20. The algorithm makes random steps in each parameter. For instance. There is no general relation. In addition to the gaseous parameters. Only a single phase (graphite) is present. where E. IC. is the activation energy for the reaction. The parameters involved are the usual BKW parameters: a. the error function is evaluated by running CHEETAH on all of the problems in the database. The motivation for this is that other workers have found that empirical “nonequilibrium” carbon models give better results for detonation properties than rigorous equilibrium carbon modelsE3. such as simulated annealing[24]. minimize the error. we can say that reactions where I. + + 3. should be frozen. Given a set of parameters. The term “covolume” is somewhat of a misnomer. We would like to find the parameter set that yields the global minimum error. between molecular volume and the virial coefficient. The freeze temperature was raised from 1800K to 2 1OOK. In the high density limit. and the covolumes ki.000 separate CHEETAH runs. zoi is a weight given to each explosive property. Intuitively. Having defined the error function e that is to be minimized. By “non-equilibrium”. Of course. Most multidimensional minimization algorithms head directly to the nearest local minimum. We chose weights of 50% for the detonation velocity. In the low density limit. Setting the freezing temperature is equivalent to stating an “average” activation energy. with the reduced set of species described above. a host of reactions occur in detonation. the freezing temperature Tj. we next discuss the method used to p.*T < E. however. 25 % for the C-J pressure. We have used the stochastic “record to record travel” algorithm[23]. the equation of state is: V = V aT bP o (11) I All three parameters (& a. This algorithm is similar to other stochastic minimizers. each with its own activation energy. we mean that model parameters have been adjusted to empirically take into account the difference between the carbon material formed under detonation and the properties of equilibrium carbon. b) were adjusted.experimental errors. 18 . then accepts the step if it leads to an error that is within a given tolerance of the best run so far. We have used an extremely simple carbon model. We started with the BKWS equation of state. but it does not require the determination of an annealing schedule. Therefore covolumes cannot be uniquely identified with a physical molecular property. Stochastic minimizers are better at finding global minima. Parameter 2 145 Tf (K) VO(cdmole) 4. however. since BKWC was specifically designed to minimize 19 . For instance NH3 has a i.378 x 376 376 663 6 14 3 16 418 153 493 865 832 394 270 404 610 440 325 384 98 550 722 Covolumes: HzO ?. The effectivecarbon model has a 7 9% lower specific volume than the BKWS carbon model. It is best think of covolumes as effective interaction parameters that lie somewhere between the molecular volume and viriai limits.for instance. C02.993 4.068 x BKWC value BKWS value B K W R value 1800 4.378 x -6. I \ CO:! eo 0 2 Hz CH4 C HzO2 CzH6 i0 V CH3OH C H3 -YO2 :V H3 c H4 2 C HzU HF CHFO C FZU C H F3 C H2 F2 HC L cc LzU 188 374 511 372 306 550 270 420 737 1095 394 649 1159 732 533 727 684 8 10 682 906 953 332 1661 800 626 50 1 834 795 654 770 795 757 786 570 1450 NA 386 800 NA NA NA NA 389 NA NA NA NA 643 NA Table 5: The BKWC parameters and covolumes. In the following series of figures we graph theoretical values versus experimental vaiues for a range of parameters.e BKW EOS.963 ~ 1 0 ‘ ~ -6.637 ct (cdmole-K) 3. We also give R M S errors.This is a consequence of the empirical and highly simp ified nature of t. In general the covolumes correlate roughly with molecular volume. There are exceptions to this rule. as opposed to RMS discrepancies. The coefficient of thermal expansion and the compressibility have been decreased as well. ! s ia large covolume than CO. we will now evaluate the results obtained with the BKWC EOS.993 3.584 x b (cc/mole-atm) -6.trger covolume than C H4.963 xIO-’ 3. 4% 6 =20 . It is thus difficult to ascertain how much of the increased disagreement is due to experimental error. however. This yields a fairer comparison between the various parametrizations. CHEETAH[ l]. For this set of compounds.0 30 . Larger disagreement with experiment is found for the C-J pressure. 3.0 3 0 5 0 7. gives too negative a number) the adiabat energy. BKWR.0 . BKWC and BKWS predict values of PCJ that are lower than the experimental ones. In the present case. The BKWS calculations were done with the reduced product set described above. In Figure 1 we show the detonation velocity for BKWC.2 is displayed. The biggest difference between the parameter sets occurs when D is low (under 6 mm/ps). BKWC predicts somewhat low values for low and high performance materials. It is interesting to note that most equilibrium codes (e. BKWR overestimates D in this case. and shows no bias for intermediate performance ( E = -6 to -4 kJ/cc). It is important to remember. with the exception of PETN.0 9. Here the BKWR equation of state fairs slightly better than BKWC. that the C-J pressure has much higher experimental error bars associated with it than the detonation velocity. In Figure 3 the adiabat energy at a relative volume of 2. PCJ was determined from a JWL[25] fit to cylinder test results. nearly identical results were obtained in test cases with the full product set. and how much is due to the EOS. . and is also significantly better than BKWS. which was determined by supracompression experiments[26]. In the past this was fixed empirically by using scale factors determined to match PETN cylinder test results[9]. C-J pressure measurements are usually indirect extrapolations.0 . Figure 2 compares experimental and theoretical C-J pressures. and BKWS.% Theory g 7. O 3. and too high for low performance explosives. BKWS adiabat energies also were systematically too low for high performance explosives.0 3 0 5.0 Experiment 3.CHEQ[3]) predict C-J pressures which are systematically lower than measured values.g. while BKWS tends to underestimate D.0 5.0 . ti = 0. One of the most significant improvements made with BKWC is that the shape of the adiabat is reproduced.0 7. TIGER[2]. showing a 0.8% D(BKWC) 6 = 1.0 5. 5. BKWC has the best match with experiment.8% RMS error. BKWC is a dramatic improvement over BKWR.the RMS discrepancy.e. BKWC shows very good agreement with experiment in the low D limit.0 9. I Figure 1: Theoretical versus experimental detonation velocities for the BKW EOS in mmlps. The BKWR equation of state systematically underestimates (i.0 9. The reason for this is unknown. 20 .:: D(BKWR) D(BKWS) ~ 50 . Scale factors were not used in the reported calculations. "irJ.0 7. 1% . 45. 'a * I J* ? 1 Experiment (W/cc) Figure 3: Experimental and theoretical adiabat energies at a relative volume of 2.0- . E(4.0 15.01 m = 2.0 2 .2)(BKWS) 6 = 3.6% E(4.9% -3.0- a Theory -5..2)(8KWR) -1.0- 6 = 5.0 50 50 .0 25.0 /' .0-7.0-9.* -8.1)(BKWR) -2.0 25.0 ..3% * u ** .0 .0- b = 4.9% E(2.1)(BKWC) -2. 5 0 15. .0-4.1)(BKWS) b = 3.0 -2.N' .0 3 .0- ry' . E(2. tr -8.* 4 "t 8 . 50 Figure 2: Experimental and theoretical C-J pressures for the BKW EOS.0 -6.Theory 5. .0 3 . 45.0 45. 50 Experiment (GPa) 5 0 15.2 for the BKW EOS . 35. E(4. The mechanical energy of detonation is thus a measure of the total PV work an explosive is capable of delivering.\. BKWR is the worst. with an RMS error of 2.* . The end of the adiabat is taken to be 1 ATM or 298K. 6 = 2.5.0 -8. BKWR tends to be too low. -4.J .0 to -5. -14. with a 3.E(6.0 -8.1 and 6.0 -12.0 -12. whichever is encountered first along the expansion. BKWC again shows the smallest errors.0 Figure 5: Experimental and theoretical adiabat energies at a relative volume of 6.3% RMS error.0 -4. As a final comparison.0 -12.T/cc.0 k.3% E(rnech)(BKWR) -2. The temperature condition is necessary because thermochemical reference data used in CHEETAH is not reliable at low temperatures. and high in the range -5.0 -10. 80 -8.0 -6.3 %.0 -6...5)(BKWC) s = 2.1% E(rnech)(BKWS) Theory -10.0 I . BKWS shows the greatest scatter n for low performing explosives with E between -4 and -2 kJ/cc.T/cc. J .0 Experiment (kJ/cc) -8.5 for the BKW EOS. The adiabat at larger volumes is also well reproduced.0 -6.O -14. 6 -10.0 -4. ’ .0 -12. we plot the mechanical energy of detonation in Figure 6.0 6 = 3.0 -12. For v = 4.5)(BKWS) 6 = 3.2.6% E(6.0 k. 4a 7. Similar trends are seen when v = 6.5)(BKWR) 6 = 4.3% E(rnech)(BKWC) -2. BKWC performs well in predicting the mechanical energy of detonation.0 -8.5.0 6 = 3. We define the mechanical energy of detonation to be the energy difference between the reactants and the products at the end of the adiabat.0 -10./.0 Experiment (kJ/cc) -2 Figure 6: Experimental and theoretical mechanical energies of detonation for the BKW EOS. In Figures 4 and 5 we show the adiabat energy at a relative volume of 4.1 It tends to be low i the range -8. by roughly the same amount as when v = 2. .0 to -2.0 -14.1% E(6.O.0 Theory -.0 -14. 22 .0 -2.11 - !O .3% -4. BKWC is the best parameter set for reproducing the detonation velocity database. In all. References COVering well-studied explosives ( U N L . and thus have a lower density than crystalline carbon. and recent experiments on TNAZ[30].the materials of greatest interest to the Department of Energy. For instance. BKWC does well and will probably be a useful tool €or fast thermochemical calculations. it is important to remember that BKWC was specifically fit to the performance database. This question can only be resolved through careful. size-converged experiments on unusual materials. In judging this comparison. and therefore the values of the parameters themselves have no independent physical meaning. the recent review article by Anderson[29].4 Conclusion Our zoal in performing the calculations described here wai to obtain a BKW parametrization that worked well for the whole detonation process when applied to a wide range of compounds. We would also like to caution researchers about using the BKWC EOS for properties other than the ones considered here. thermochemical codes predict chemical concentrations along the adiabat. Within the group of properties considered here. It is possible that the parameter set would fair less well when applied to materials outside the database. an alternative explanation could hold: the rarer explosives have unusual properties that are not well reproduced by the BKW equation of state. We have no idea how well such properties will be predicted by BKWC (or any other equation of state. we have compared the performance of the BKWC parameter set to other BKW parameter sets in predicting the performance database. We have collected a detonation velocity database that covers many materials not included in the cylinder test performance database. accurate experiments are rarely done on materials of little practical interest. however.In the results so far. The TNAZ data. There is an interesting variation in the RMS error with reference. 3. Meyer's handbook[28]. Another interesting feature of our work is the use of an empirical carbon model. only reflects two experiments whereas the other references have a much larger number of experiments. we give RMS errors for the detonation velocities. This is probably due to the quality of the experimental data: large scale. it is possible to find detonation velocities for a wide range of materials. In Table 7. For the properties that we have considered. sorted by reference. however. 23 . On the other hand. the BKWC EOS yields results that are usually within estimated error bars of the experimental results. It may very well be that the empirical carbon model is compensating for other EOS errors. for that matter) since there is no reliable experimental data to compare to. Detonation velocities were taken from several reference works: the LLNL explosives handbook[27]. the detonation velocity database contained 127 entries. A parallel effort at LLNL on the CHEQ thermochemical code produced a non-equilibriumcarbon model with a higher density than standard carbon[3. Comparatively few experiments were done on other materials. Anderson) are better reproduced by BKWC than references covering more exotic explosives (Meyer). Intuitively one would expect non-equilibrium carbon to resemble amorphous carbon. For instance. 211. the majority of cylinder tests performed at LLNL were formulated HMX and TATB . It has the lowest RMS errors for every reference except the recent TNAZ measurements. Nonetheless. It is a difficult task to find experimental data for properties that are truly independent of the performance database. We find this to be a puzzling result. 22 1. No.59 4.15 2.72 2.7 1 Tabie 7: RMS percent errors in predicting detonation velocites 24 .48 1.34 5.52 3. 1 4 1 MEN-2 1 2 1 1 1 3 2 1 I 1 Methyl nitrate MHN Nitropentanon Nitroglycerine Nitroglycol NM NQ NTO octo1 75 Octo1 70 1 1 1 1 1 3 1 2 2 2 2 1 I 1 1 I I I 1 1 1 1 1 2 1 1 3 1 1 1 1 1 1 1 1 1 PBX9007 PBx9010 PBX9011 PBX9205 PBX9407 PBX9501 PBX9503 Pentastit Pentolite PEW Picryl chloride Picric acid RDX Tacot TAGN TATB Tetryl TNA WAN TNAZ TNB TNC TNGU TNM TNP TNT TNPEN 1 1 1 1 1 1 1 1 1 3 2 3 4 2 1 3 5 2 1 1 2 1 1 1 1 1 6 1 Table 6: Compounds contained in the detonation velocity database. Reference LLNL TNAZ Anderson Meyer No. 3 2 I 1 Compound LX14 LX4 LX17 No.01 BKWS 4.57 3. is the number of entries for the particular compound.12 6. entries 68 2 10 47 BKWC BKWR 2.Compound Ammonium picrate Ammonium nitrate (AN) BTF Comp 8-3 Comp B Comp C-3 Comp C-4 Cyclotol75 Cyclotol60 Cyclotrimethylenenitsamine Cyanuric triazide DATB DEGN DINA Dinitmdimthy loxamide Diazodinimphenol Diethyleneglycol dinitrate Dinitdimethyloxamide Dinimphenoxyethy Initrate DIPAM DIPEHN DNB EDD EDNA Ethyl picrate Ethriol trinitrate Ethyl nirrate FEFO HMX HNAB HNDP HNS Hydrazine nitrate LXOl LX04 LX07 LX09 LX 10-0 LX10-1 LX11 No.03 2. CHEETAH 1. Coronado. ”The Effect of Elemental Composition on the Detonation Behavior of Explosives”. 1990. Craig Tarver has made several insightful suggestions.R. Hornig. p. CAY 1979. University of California Press. his help has been invaluable. Clark has also assembled the reactant library described in the User’s Manual[ 11. Zwisler. [3] A. Hobbs and M. [6] C. Davis. Hobbs and M. and M. [2] M. Office of Naval Research. Fickett and W. ”Report on the prediction of detonation velocities of solid explosives”. VA. SRI Publication No. The cylinder test data reported here were generated over a thirty year period by Howard Homig. R. References [ 11 L. Helm. [ 5 ] G. Berkeley. Guidry. Don Breithaupt. H. E. Nichols I11 and E R e .0 User’s Manual. Arlington. 24. Zwisler. McGuire. “Nonideal Themoequilibrium Calculations Using a Large Producf Species Darn Base ”. B. Albuquerque. D. 1973. Nichols I11 and E H. 1979. H. Milt Finger provided initial funding. L.Acknowledgements CHEETAH owes an obvious debt to M. CHEQ 2. C. €owperwaithe and W. Ed James and Mark Hoffman were the first brave users of the PC version.R. Cowan and W. “TIGER Computer Program Documentation”. Hayes. Chem. MA ( 1994). E. Mike Murphy loaned me computer hardware nkcessary to develop CHEETAH for the PC and helped with numerous file transfers.L. UCRL-MA-106754.H. Finally. NM.0 User’s Manual. the developers of TIGER[2]. CAY24-27 August 1976. F. Baer. Baer. and Milt Finger. M. Sandia Report SAND92-0482( 1992). blader. H. Kahara. Kistiakowsky and E. ACR-22 1. Wilson. Fickett. Jim McDonnell. Frank.932( 1956). Finger. University of California. Don Omellas. P. and has been instrumental in testing the program. Fried. Many of the capabilities that will be put into CHEETAH are inspired by the thermochemical code CHEQ. Cowperthwaite and W. Randall Simpson and AI Holt have been relentless proponents of the project. 87185: M. 2106.L. E71 M.. Office of Scientific Research and Development report OSRD-69 (1941). 7 10-722. B. Detonation. “Calibrating the BKW-EOS with a Large Product Species Data Base and Measured C-J Properties”. I have had many useful conversations with Albert Nichols 111.Helm. B. Berkeley. Lee. Ree. Phys. R. written by A. [81 M. ”Numerical Modeling of Detonations”. Proceedings of the Sixth Symposium (International) on Detonation. Clark Souers first advanced the idea of improving TIGER. 75 . UCRL-MA-117541. L. Boston. [31 W. J. Tenth Symposium (Internstional) on Detonation. Sandia National Laboratories. University of California. 1994. University of California Press. M.E. Propellants. USA. private communication. New York. Tarver. Ornellas. Souers and L.[9] P.W. Ree. Berkeley. Report UCRL-52821 (1982). C. J. Hornig.H D ’ . [ 131 Lawrence Livermore National Laboratory. Supplement No. D. R.D. 1251(1984). Science. and M. 18. C. “Comparison of cylinder. Sixth Detonation Symposium. Vecchi Optimization by simuZated annealing. “The JCZ equations of state for detonation products [ 111 A. private communication.5845(1986).). Kirkpatrick. White Oak. Appl. C. CA. 1993. Cowperthwaithe and W. 81. 9.. Kirkpatrick. C. Amarillo. MD 12. Popolato (eds.. VanThiel. Wilkins. University of California Press. and C. J. Proceedings of the Fourth Symposium (International) on Detonation. Gelatt. 1986.975( 1984). 3-12. Phys. [211 M. Stat. Lawrence Livermore National Laboratory. Ree. EM. and M.R. J. USA. Optimization by simulated annealing: quantitative studies. Gamer.175( 1993). [22] M. 1994. 1976-1991”. Jr. Phys. Lawrence Livermore National Laboratory. Chem. 162. “Performance calculations on the ANFO explosive m .USA. 1994. Vol. “Calorimetric determinations of the heat and products of detonation for explosives: October 1961 to April 1982”. Detonation Equation o State at LWL. p. Zwisler.H. Mason and Hanger-Silas Mason Co. Omellas. Phys. Souers. 1985. Explosives.L. [ 191 A. “Metal Acceleration by Chemical Explosives”. LLNL.15 October 1965. J. Finger. H. University of California. [25] J.L. McDonnel.. Report MHSMP-75-17 (1973. American Institute of Physics. Nichols III. Campbell. Lee. Larson. 14. E171 D. L. Kury.L. 26 . 84. E201 F. [24] S. 1994.data and code calculationsfor homogeneous explosives. 34. Livermore. T.. Gibbs and A. 183(1984).C. “New Optimization Heuristics: The Great Deluge Algorithm and the Record-toRecord Travel”.116113. Phys. (1976). [ 151 P. University of California. “High Explosive Applications Laboratory Records. 104. 1993.. Journal of Physical and Chemical Reference Data. W. 220 67 1( 1983). CA.. M. 62. 3rd ed.W. and Pyrotechnics. 1980. TX. [16] P. [ 103 M. 8-92( 1993). 1761-1767(1987).L.C. Souers and J. UCRL-ID. Jr. Chem. 1.H. [23] G. [ 121 P.. J. van Thiel and F. Livermore.L.. [ 181 “JANAF Thermochemical Tables”. Phys. H. and their incorporation into the TIGER code”. Kury. Explosives. Dueck.. Haselman. UCRLIDf 116113. Pantex Plant. Comp. “HNS Cylinder Tests”. Strange. S .P. p. A loose-leaf Cylinder Handbook contains much of the data. Propellants. [ 141 “LASL Explosive Property Data”. Pyrotechnics. .J. D. E. C. Washington. International Symposium on Pyrotechnics and Explosives.M.[26] L. P. [28] R. in Tactical Missile Warheads. 1987. Anderson. (-301 S . Livermore. . 1994. 155 of Progress in Astronautics and Aeronautics. ISBN 1-56347-067-5. CA. [29] E. private communication. UCRL-52997. WUMNME. Meyer.. Explosives. B. LLNL Explosives Handbook. VCH. ed. “Shock Measurements on Explosives in the SupraCompressive Region”. and J. China. J. 77 . Beijing. Weinheim. [27] Dobratz. Explosives. 1985. Vol. N. Green. Holmes. American Institute of Aeronautics and Astronautics. Report UCRL-95461 (1987). and Crawford. Aubert. USA. DC. Lawrence Livermore National Laboratory. 12-15 October 1987. A. Kury. Carleone.
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