A study of the jwl equation of state parameters of dynamite for use in airblast models b. The jwl eos is of the miegruneisen form with a constant gruneisen coefficient and a constants specific heat. U is the vector of conservative variables, volume fraction, mass, momentum, and energy. This model is implemented in a form referred to as a programmed burn, which means that the reaction and initiation of the explosive is not determined by shock in the material. The williamsburg is a thermodynamically complete equation of state for detonation products. Dunnett awe aldermaston, reading rg7 4pr, united kingdom d. Aug 01, 2020 jwl equation of state for expansion of detonating products after explosion has been studied for several high explosives and simplified approach with p v. At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. Theory and calibration of jwl and jwlb thermodynamic equations. The resulting equation of state was evaluated b6y simulating cylinder tests with a hydrocode. This methodology has been assessed with thirteen data sets for a number of commercial explosives of the anfo and emulsion type 6, 10. Air was modeled using the ideal gas equation of state with an adiabatic gamma of 1. Pdf theory and calibration of jwl and jwlb thermodynamic.
Capturing the material behavior is crucial, as these characteristics determine the failure method, particle velocities, and energy coupling factors. Jwl equation of state, joneswilkinslee equation of state for explosives. On exact conservation for the euler equations with complex. The joneswilkinslee jwl equation of state eos has long been used to accurately calculate the chapman jouguet cj state of condensed phase explosive detonation waves and the subsequent expansion of the reaction products as they do work on surrounding materials. Estimation of joneswilkinslee parameters of emulsion. It describes in a correct manner the behaviour of detonation products within the whole range of pressure changes and becomes an equation of an ideal gas for small densities.
The joneswillcinslee jwl eos is much more flexible, but assumes the griineisen gamma coefficient is constant, and is not a complete. In this modeling, the equation of state for the detonation products is the primary modeling description of the work output from the explosive that causes the. The mapping of a bomb shape to the cartesian grid means that it will be di. Because there is no founding document for the jwl equation of state, there exist different interpretations of the equation, which is the source of substantial confusion. Scaling of the detonation product state with reactant kinetic. Jwl eos the jwl eos has the form exp v v v v v 1 i os i os i r r w p we a. Comparison of bkw and jwl equations of state for explosion. A set of mixture equations to describe the states attained as the reactions proceed. This process, when applied to a large range of explosives, seems to show that the exponent increases with increasing energy density and is grouped based on ideality. The parameters are iterated until the best match can be made between simulation and experiment. Analysis of the copper wall expansion can be used to determine parameters for the joneswilkinslee jwl. Optimizing code calibration of the jwl explosive equation. Jwl equation of state coefficients for high explosives unt digital.
These arrays are listed during the package setup phase. A complete equation of state for nonideal condensed phase. The joneswilkinslee jwl equation of state is speci. From this code, both the parameters of the jwl equation of state of a given composition are calibrated from the calculated adiabatic curve and tabulated equations of state are constructed. For this work, emphasis is place on nonideal equations of state and a joneswilkinslee jwl eos is chosen. The jwl equation of state describing the adiabatic expansion of detonation products is revisited to complete the description of the principal eigenvalue, to reset the secondary eigenvalue to produce a wellbehaved adiabatic gamma profile, and to normalize the characteristic equation of state in terms of conventional parameters having a clear experimental interpretation. Pdf the jwl eos is widely used in different forms two, three terms according to the level of accuracy in the pressurevolume domain that. Study on jwl equation of state for the numerical simulation. Modeling of shock wave propagation through energetic solid. Beckerkistiakowskiwilson bkw and joneswilkinslee jwl are among the most widely used eos. Aneos analytic equations of state for shock physics codes. The jwl equation of state describing the adiabatic expansion of detonation products is revisited to complete the description of the principal eigenvalue, t. Jwl equation of state for expansion of detonating products after explosion has. Parametric study of the dynamic jwleos for detonation products.
Theory and detonation products equations of state for. Theory and detonation products equations of state for a new. Therefore, high explosive burn, the joneswilkinslee equation of state jwl eos, elastic. Oct 12, 2018 a thermochemical code, siame, dedicated to the study of high explosives, is currently being validated. The jwl and gurney energy are then used in analytical and hydrocode simulations to assess fox7 perfomance in fragmenting and slow stretching jet warheads and compared against other high performance explosives. User guide for shock and blast simulation with the octvce. Adjustment of parameters in the jwl equation changes the expansion pro le of the simulated wall expansion. Available cylinder test data for five high explosives are used for the calculation of jwl parameters. However, in the case of modern composite materials, the commonly used jc strength model has limitations. U is the vector of conservative variables, volume fraction, mass, momentum, and energy, f are the uxes corresponding to the respective conservative.
The resulting eigenvalue jwlb equation of state is more accurate at early detonation products expansion compared to an eigenvalue jwl equation of state. View the article pdf and any associated supplements and figures for a period of 48 hours. The most popular equation of state used in numerical codes is the semiempirical joneswilkinslee jwl equation, which can be easily applied in numerical algorithms. Nearfield effects cause severe effects on the structures leading to. An equation of state model except the ideal gas equation of state can also be used with the tensile failure model dynamic failure models, section 18. The joneswilkinslee jwl equation of state is an empirical model useful in describing the thermodynamic properties i. The purpose of this paper is to provide a thermodynamic and mathematical background of the jwl and jwlb equations of state, as well as parameterization methodology. In this modeling, the equation of state for the detonation products is the primary modeling description of the work output from the explosive that causes the subsequent air blast. Joneswilkinslee equation of state for explosives jwl equation the equation of state from joneswilkinslee is used to describe the detonation products of explosives. Thompson computational physics and mechanics division i sandia national laboratories albuquerque, new mexico 87185 abstract aneos is an inline software package which provides thermodynamic information for. For relatively fast aluminum reaction, an eigenvalue jwlb equation of state and calibration methodology was developed. We have introduced via the algebraic expansion swhere 0 to later plot jwl data at volumes relative to those of.
The joneswilkinslee or jwl equation of state models the pressure generated by the release of chemical energy in an explosive. Williamsburg equation of state for modelling nonideal detonation. I 2 in this equation, p is the pressure and a, b, r1, r2, and n are the jwl coefficients, v is the relative volume which can be computed as eo e, where is the density of the detonation products, and e is the energy. The standard joneswilkenslee equation of state for modeling detonation of high explosives was modified to allow. Parametric study of the dynamic jwleos for detonation. Jwl equation of state for expansion of detonating products after explosion has been studied for several high explosives and simplified approach with p v. The initial jwl or jwlb explosive or chemical energy e 0 for the bomb is also assumed this value is reported for various explosives in 10, 4.
Williamsburg parameters have were obtained for nitromethane by fitting to the results of chemical equilibrium calculations. The physical processes involved in a detonation phenomenon, though, are extremely complex. The contents of the aneos storage arrays are given in appendix b. Theory and detonation products equations of state for a. The numerical methods used in the paper are developed in section 4. Jwl equation of statesimilar to unreacted eos, the jwl equation of state of. The jwl equation of state eos is frequently used for the products and sometimes reactants of a high explosive he. Numerical simulation of shock initiation on solid rocket. Therefore, the common practice is to resort to empirical or semiempirical equations of state eoss describing the detonation properties of explosives.
Swift fluid gravity engineering ltd, 11 bell street, st andrews, fife ky16 9ur, scotland m. The unreacted jwl equation of state is fitted to the available experimental data. The model relies on analysis of the metal cylinder expansion by detonation products. The joneswilkinslee jwl equation of state for detonation products is probably the currently most used equation of state for detonation and blast modeling. A study of the jwl equation of state parameters of dynamite. The jwl thermodynamic equation of state 1 was deve loped to provide an accurate description of high explosive products expansion work output and detonation chapmanjouguet state. Joneswilkinslee jwl reaction product equations of state. Detailed descriptions of the models are given elsewhere 7,8,9,10. Two jwl equations of state, one of them is for the unreacted explosive and another is for reaction products, in the form.
There have been a number of versions of the aneos package. Jwl equation of state coefficients for high explosives showing 14 of 10 pages in this report. Jwl equation of state and gurney energy is described and the results compared with other published data. Simulating underbelly blast events using abaqusexplicit cel. Theory and calibration of jwl and jwlb thermodynamic. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. These initial sets of parameters are then used as starting points for simulations of the cylinder expansion tests with the explicit fem code lsdyna. The jwl equation of state can be written in terms of the initial energy per unit mass, as. Study on jwl equation of state for the numerical simulation of near. The jwl equation of state 1, 2, 9, 14 is commonly used in explosives modelling for describing the pressurevolumeenergy relationship of the detonation products. Jwl equation of state parameters based on the cylinder test is proposed. Determination of properties for emulsion explosives using.
A study of the jwl equation of state parameters of. Braithwaite wilton centre, middlesborough, cleveland ts90 8je, united kingdom. Gpa, using the jwl equation of state dobratz and crawford, 1985 and the specific explosion energy of tnt. It can be seen that the jwl takes the form of a modified perfect gas eos, with the exponential terms acting to stiffen the eos at high densities. One ver model covers the principles described above. A solution strategy for the riemann problem with general convex equations of state is presented in section 3.
It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. Analytic equations of state for shock physics codes input manual samuel l. Reference frame at detonation velocity isentropic products expansion constant properties along. Capturing the material behavior is crucial, as these characteristics determine the failure method, particle velocities, and. Thus jwl eos is used for calculating pressure of detonation products with. The ideal detonation code vixeni is used to obtain initial sets of parameters for the jwl equation of state for the emulsion explosives used. Equation 1 expresses the pressure of the detonation products as a function of the volume expansion from the initial state of the. The standard joneswilkenslee equationofstate for modeling detonation of high. The jwl miller equation of state 14 fordescribing the detonation product of aluminized explosives are adopted as p a1.
The equation of state of the detonation product of aluminized explosives should be able to establish the essential relationship among pressure, density, internal energy and the reaction process variable. Scaling of the detonation product state with reactant. The joneswilkinsleebaker jwlb equation of state is an extension of the jwl equation of state that we commonly use. Review of joneswilkinslee equation of state researchgate. A new derivation of jwl eos is proposed, using a less restrictive assumption for the gruneisen coefficient suggested by.
Jwl standard japan light alloy wheel standard, a set of requirements for alloy wheels set by the ministry of land, infrastructure, transport and tourism japan that must be met for all passenger cars in japan. Plane chapmanjouguet detonation and a partial form of the wbl model were used to. The explosive then burns iven explosive subscripted e and v is up. Numerical results for the application of these schemes to a riemann problem are presented in section 5. Figure 1 shows the composition b unreacted equation of state defined by the parameters listed in table 2, along with seven linear shock velocity u s particle velocity u p fits to various sets of experimental data listed in dobratz and crawford 6. This is a pdf file of an unedited manuscript that has been accepted for publication. The tensile failure model uses the hydrostatic pressure stress as a failure measure and offers a number of failure choices. Both the mechanical and thermal equations might be considered when modeling mixtures of multiple materials for example, but for this single gas case the mechanical eos is su cient.
Determination of the equation of state for the detonation. Investigation of jwl equation of state for detonation products at low pressure with radio interferometry figures. Dec 01, 2018 seven equations were established to determine the jwl equation of state parameters a, b, c, r 1, r 2, e 0. Weggel department of civil and environmental engineering, unc charlotte, usa abstract two separate blast tests were conducted inside a conventional, unreinforced, brick building scheduled to be demolished. Determination of the jwl constants for anfo and emulsion. Investigation of jwl equation of state for detonation products at. Jwl equation of state coefficients for high explosives unt.
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