Overview
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Combustion of solid propellant is the driving mechanism in the operation of solid rockets. Correct description of the solid propellant regression rate is critical to the success of the multi-disciplinary, whole-system simulation of solid rocket motors. Simulations of fluid dynamics, turbulence, heat transfer, structural dynamics, and the interactions among different mechanisms depend on the regression rate. Accurate knowledge of the chemistry associated with the combustion rate (or burning rate) of solid propellants is important. Chemical processes determine these rates, both condensed phase and gas phase. Also necessary are descriptions of the transport of heat, mass and species across the propellant-combustion interface. In addition, fundamental atomic and molecular physics of the transition states of energetic materials must be an integral part of the simulation. Ongoing efforts include research and code development to understand aluminum droplet combustion, gas and particle radiative heat transfer, and aluminum distributed two-phase reacting flow analyses.
The combustion region at the interface between the core flow and the solid propellant (SP) is extremely thin, on the order of 100 µm. In contrast, the overall dimensions of the burning surface inside the Solid Rocket Booster (SRB) are measured in meters. Hence, the integrated system simulation will treat the combustion layer as an interface across which mass, momentum, and energy are injected into the core flow. The mesoscale Propellant Combustion Interface (PCI) is a moving boundary that propagates normal to the propellant surface at a speed that changes dynamically in response to the ballistic core flow on one side and SP on the other. The rule for propagation comes from examining the detailed combustion physics within the PCI.
The detailed chemistry and surface morphology of the heterogeneous combustion zone are not well understood, partly due to a lack of experimental resolution at the microscale. However, a great deal of experimental data are available for the macroscopic regression rate, which express an average over the microscale interactions. Thus, a first approach for the prescription of the propagation law will be to carry out a quasi-static flame zone analysis for the burning zone that incorporates steady-state experimental data in the determination of the expression for the propellant regression rate. The normal regression rate will be calculated in terms of the pressure presented by the core flow, as computed by the LES simulation. For rapid transients on time scales less than the thermal relaxation time of the propellant (1 to 10 µs), the quasi-static approximation fails and an effective modification of the Zeldovich-Novozhilov (ZN) method developed by researchers at UIUC will be used [28,29].
The topology of the mesoscale PCI in the rocket core can be quite complex depending on the fins and the variety of segments in the grain. One way of computing its motion is by level-set methods, which can efficiently propagate single and multiply disjoint regions of the PCI. Such methods have recently been developed at UIUC for the propagation of 2- and 3-D detonation waves in condensed phase explosives [30].
Alongside the meso-scale PCI model in the system simulation, a detailed microscale propellant combustion model at 1 to 10 µm resolution, a scale well below current experimental resolution, will be developed to describe the detailed physics of the combustion zone. The 3-D micromechanical simulation will include energetic grains, oxidizers, binder, differentiated solids, melt layers, flames, and burnt gases. The microscale simulation will necessarily be a collaborative effort among the Combustion and Energetic Materials, Hydrodynamics, and Structural Analysis & Materials Teams and will use code resources developed by each team to model the details of phase transitions, chemical reactions, and heat transfer in the solid, fluid, and reactive layers. The coordinated modeling and simulation will mirror that required for the SRB. Validation will be based on experimental data obtained through the CNEM and the existing experimental and simulation database in the propellant research community.
Simulation of normal burn scenarios will define the average regression rate in terms of pressure/velocity gradients imposed by the outer core flow and determine overall mass, momentum, and energy fluxes. A parametric suite of microsimulations that vary outflow boundary conditions and material properties will be performed and compared with the mesoscale PCI model approach (described earlier) to yield refinements. Principal abnormal scenarios include the interaction of a crack in the surface that descends deeply below the surrounding combusting surface into the solid regions. Another is the debonding of propellant at an interface.
Representative solid propellants used in launch vehicles are composites composed of 70% ammonium perchlorate (AP) grains bimodally distributed around 200 and 30 µm, 14% binder, typically HTPB, hydroxyl-terminated polybutadiene plus curative, and substantial amounts of small aluminum particles of about 30 µm. More energetic SPs have explosive (e.g., HMX) grains. The temperature of the exhaust gases is typically 3000° C, and operating pressure in the core flow of the SRB is between 50 and 100 atmospheres and are envisioned to be double that or higher for new SP designs.
At 1 to 10 µm resolution, the microscale PCI is complex
and layered. Deep in
the interior of the SP, solids are surrounded by binder. A multiphase "melt
layer" on the order of 10µm lies at the boundary of the burning surface. Surface
flames with heights of 1 mm or less lie above the melt layer, and beyond that lies a
hydrodynamic outflow region that in turn matches with the fluid dynamics that derives from
the interior ballistic core region of the SRB (see figure, left).
Simulations for a microscale unit cell will include a large AP particle and a corresponding number of surrounding smaller AP particles plus binder. Much larger (in dimension) ensemble simulations will contain sufficiently many unit cells, for statistical averaging purposes, to match the outer core flow. A large ensemble with twenty 100 µm-sized grains across (2 mm square) with a 20 µm resolved melt layer, solid propellant resolved to a depth of at least 4 or 5 mm, as well as the flame/hydrodynamic region resolved to capture self-flames and diffusion flames out to 4 or 5 mm, lead to a computational volume of 2 mm x 2 mm x 10 mm. For a representative simulation, we estimate using 20 million nodes, split evenly between finely meshed (1 µm) and coarsely meshed (10 µm) regions.
The solid models in the SP region are described elsewhere. The melt layer model will be based on some recent modeling efforts at UIUC, (supported by USAF) on melting and phase-transition in energetic materials such as HMX [31]. Flame modeling requires the specification of a minimal set of relevant gas species. Initially we plan to use a reduced scheme calibrated to reproduce full-scheme modeling of propellant sandwich flames (like those carried out at Yale by M. Smooke and his colleagues) in standard (AP and HTPB) and novel energetic materials. Validation of reduced chemical models include testing their ability to reproduce the edge flame observed in experiments [32]. More advanced, computationally efficient, full-kinetics schemes for the combustion chemistry based on reduced manifold methods of Ulrich Mass can also be implemented.
The deflagration to detonation (DDT) transition scenario in an SRB context involves a transition of combustion in confined or damaged SP into a detonation. A DDT occurrence is fatal to the operation of an SRB. A micromechanical simulation of DDT in damaged propellant will be used to evaluate the sensitivity of damaged propellant to hazardous mechanical insults. Validation of the simulations will be based on comparison with DDT experiments and dynamic experiments in granular materials carried out by various DOE/DOD laboratories. UIUC has extensive experience in this area, with current collaborations and projects sponsored by DOE-DP labs to study DDT in condensed phase high explosives (HE) [33-37].
A DDT event usually requires a pre-existing state of damage in the propellant, and such damage is often modeled by studying the behavior of porous energetic material (powders) to mimic the accumulated microcracks and voids within the SP. Mechanical energy stimulus is converted through recompaction into localized energy deposited at energetic grain boundaries. Unlike the normal surface burn scenario, energy release occurs through melting and surface pyrolysis of the solid in a distributed volume within the material, followed by gaseous combustion in interstitial pores that pressurizes the bed and loads the solids. Bed pressurization furthers the damage mechanism of individual grains, which in turn enhances the energy release process. As reaction grows, a runaway to detonation can occur. If combustion of the SP occurs on an exposed surface and then runs into a confined crack that connects to a damaged region, then transition to detonation can occur.
Our microscale DDT simulation will first simulate the impact of a piston with prescribed velocity with a bed of porous SP (or HE). A proposed simulation involves a 3-D volume of material with at least ten 100 µm grains on a side and 100 to 500 grains deep, a volume of dimension 1 mm x 1 mm x 50 mm. (Experiments show that with 100 m/sec impact piston velocities in HMX powder, 100 mm is a typical distance to detonation in about 100 ms.) At 10 µm resolution, this simulation requires approximately 5 to 10 million nodes.
The same models for the thermomechanical behavior and properties of the SP model for the microscale PCI simulation can be used for the DDT micro-simulation, with extensions of the constitutive behavior to high pressures that support strong shock states. A major geometrical difference in the microscale PCI model and the micro-DDT simulation is that in the latter the interstitial voids are distributed throughout the volume. Lagrangian FEM technology has the capability to maintain the identity of the grains without numerical diffusion. Another strategy that we are likely to employ uses level-set methods to track the boundaries between different materials, in this case solid and gas. The initial microstructure topology defines the energetic grain boundaries and the normal distance function, which is input to the level-set method. Subsequent tracking of phase boundaries delineates the regions where different sets of discretized PDEs apply. Codes developed at UIUC in recent USAF and DOE sponsored projects are available to propagate 3-D level curves [30].
The combustion of aluminum droplets in the internal SRB core flow field will be simulated using a vapor-phase, diffusion-limited, droplet burning model. Existing codes developed at UIUC will provide 3-D numerical solutions to the governing differential equations for a droplet burning in a convective, radiative environment. Parametric studies will vary droplet Reynolds number, external strain-rate, etc., and will build on our past work [38], which included the effect of variable ambient gas (oxidizer) composition. Previous work also showed that it is important to include not only variable gas composition but also thermal radiation. From these simulations a "d-squared" correlation will be extracted for use in the multiphase LES simulation of the core flow.
Solid propellants are the main pyrothenic materials used in the tens of millions of automotive airbags installed each year as the gas generators to inflate the airbags in less than 50 ms. A detailed simulation is planned to model the highly unsteady, two-phase, multicomponent reacting events associated with ignition and combustion dynamics. About 80 coupled equations for heat, mass, species, and momentum conservation and related constitutive equations must be solved for complex 3-D configurations for a wide variety of propellants [39,40]. Experiments at UIUC will provide an important independent validation of the combustion models.
Presently, the molecular basis of such phenomena as detonation and age-related deterioration of polymeric and energetic materials are poorly understood, yet both of these play a major role in the complete simulation of an SRB. Furthermore, these processes are of great interest in the broader context of the ASCI mission, since both polymeric and energetic materials are ubiquitous in weapons systems. We plan to study these processes using a multifaceted approach combining detailed atomistic simulation, effective fragment Hamiltonians, and analytical theory. One of the ultimate goals is a complete multiresolution simulation of detonation in a realistically-sized portion of energetic material, including the effects of electronic excitation. We will use this simulation to elucidate the effect of material defects on DDT, and thus infer the effects of aging on sensitivity for materials like the propellants used in an SRB. A second goal is the combination of atomistic polymer dynamics simulation and analytical theory for realistic prediction of aging effects in polymeric materials on arbitrarily long time scales. Extensive contacts with national laboratories have already been established for such work.
We will use ab initio nonadiabatic molecular dynamics [41,42], which solves both the electronic and nuclear Schrödinger equations simultaneously, to study the role of electronic excitation in energetic materials. The ab initio potential energy surfaces will be able to provide a realistic description of the highly nonadditive interactions between excited-state molecules. The multiple electronic state character of the dynamics will allow us to probe the assertion that "curve crossings" may play a fundamental role in detonation initiation and propagation. These simulations will be guided by investigations of potential energy surfaces using Quantum Monte Carlo (QMC) methods [43,44], which account for electron correlation with high accuracy. We will also use QMC to study the electronic properties of energetic materials, particularly their dependence on pressure. Newly developed linear scaling electronic structure theory methods [45,46] will be used to study ground electronic state reaction dynamics of hydrocarbons at high temperatures, large inhomogeneous stresses and strains, and adhesion of grain boundaries. Path integral Monte Carlo [47] will be used to develop equations of state for propellants undergoing combustion. This method is unique in its accuracy and its ability to treat highly excited electronic states. The parallel path integral code PUPI will be extended to perform simulation of atoms with pseudopotentials (needed for atoms with core electrons) and to treat many more electrons using the linear scaling methods mentioned above. These approaches are complementary and our vision is to synthesize them to simulate a large fragment of detonating energetic material. We will develop a multispatial resolution model that allows for electronic excitation at the detonation front on the shortest length scale, and linear scaling dynamics on either side of the front at an intermediate length scale. On a longer length scale, this system will be embedded using effective Hamiltonians developed from QMC calculations. Finally, equations of state determined by path integral Monte Carlo will be used to model the longest length scale, removed from the front.
The long-term degradation of polymeric materials, such as those used in an SRB, is often due to diffusion-limited reaction of penetrants such as oxygen. Unfortunately, molecular dynamics simulations for chemically realistic atomistic models of polymers, and the very long times relevant to this diffusion and stockpile lifetime, are impossible. We will develop a hybrid simulation/theoretical approach that retains quantitative chemical predictability by using massively parallel MD simulations to obtain detailed local information concerning the short time/distance dynamics. This will be used as input to a nonequilibrium statistical mechanical theory [48,49] treating the influence of long time/distance dynamical processes. We will apply the new hybrid simulation/theory approach to the prediction of penetrant mobility and clustering, macromolecular diffusion, viscoelastic properties, and rheological response of rubbery, glassy, multiphase, and composite (filled) polymeric materials of importance to SRB simulation and the DOE/ASCI mission.
[29] T. B. Schroeder, Unsteady combustion of homogeneous energetic solids, Proceedings of the Fourth International Symposium on Special Topics in Chemical Propulsion, May 27-31, 1996, Stockholm, Sweden; Begell House, Inc.
[30] T. Aslam, J. B. Bdzil, and D. S. Stewart. Level-set methods applied to modeling detonation shock dynamics. J. Comput. Phys., 126:390-409, 1996.
[31] G. A. Ruderman, D. S. Stewart, and E. Fried. Modeling the mechanical ignition of energetic materials. In 16th International Colloquium on Dynamics of Explosions and Reactive Systems, Cracow, Poland, 1997.
[32] J. Buckmaster, Edge-flames and their stability, Combustion Science and Technology (1996), 115:41-68.
[33] J. M. Powers, D. S. Stewart, and H. Krier. Analysis of steady compaction waves in porous materials. J. Appl. Mech., 111:15-24, 1989.
[34] J. M. Powers, D. S. Stewart, and H. Krier. Theory of two-phase detonation, part I. Combustion and Flame, 80:264-279, 1990.
[35] J. M. Powers, D. S. Stewart, and H. Krier. Theory of two-phase detonation, part II: Structure. Combustion and Flame, 80:280-303, 1990.
[36] S. Xu and D. S. Stewart. Deflagration to detonation transition in porous energetic materials: A comparative model study. J. Engineering Math., 1997. To appear.
[37] S. Xu, T. Aslam, and D. S. Stewart. High resolution numerical simulation of ideal and nonideal compressible reaction flow with embedded internal boundaries. Combustion Theory and Modeling, 1(1):113-142, 1997.
[38] E. G. Bradley and M. Q. Brewster. Effect of gas/particle coupling on combustion efficiency in aluminized solid rockets. AIAA J. Propulsion and Power 7(6):1078-1080, 1991.
[39] P. B. Butler, and H. Krier, Modeling andsimulation of the internal thermochemistry of automotive airbag inflators, Progress in Energy and Combustion Sciences, Vol 19; pp. 365-382 (1993).
[40] P. B. Butler, and H. Krier, Numerical simulation of passenger-side automotive inflators, Society of Automotive Engineers, SAE Paper No. 920848 (1992).
[41] T. J. Martinez and R. D. Levine, First-principles molecular dynamics on multiple electronic states: a case study of NaI, J. Chem. Phys. 105:6334 (1996).
[42] T. J. Martinez, M. Ben-Nun, and R. D. Levine, Multi-electronic state molecular dynamics: a wave function approach with applications, J. Phys. Chem. 100:7884 (1996).
[43] L. Mitas, Electronic structure by quantum Monte Carlo: atoms, molecules and solids, Comp. Phys. Comm. 97:107 (1996).
[44] D. M. Ceperley and L. Mitas, Monte Carlo methods in quantum chemistry, Adv. Chem. Phys. 93:1 (1996).
[45] P. Ordejon, D. A. Drabold, R. M. Martin, and M. P. Grumbach, Linear system size scaling methods for electronic structure calculations, Phys. Rev. B 51:1456 (1995).
[46] M. P. Grumbach and R. M. Martin, Phase diagram of carbon at high pressures and temperatures, Phys.Rev.B 54:15730 (1996).
[47] D. M. Ceperley, Path integrals in the theory of condensed helium, Rev. Mod. Phys. 67 279, (1995).
[48] K. S. Schweizer and J. G. Curro, Integral equation theories of the structure, thermodynamics and phase transitions of polymer fluids, Adv. Chem. Phys. 98:1 (1997).
[49] H. Tang and K. S. Schweizer, Microscopic theory of self-diffusion in polymer blends, J. Chem. Phys. 105:779 (1996).
