In collaboration with NASA and our industrial colleagues, CSAR has selected the solid rocket boosters (SRB) of the Space Transportation System (STS)—better known as the Space Shuttle—as the device for our initial simulation. The Shuttle SRB is a well-established, commercial rocket, is globally recognized, and most importantly, basic design data and propellant configurations are available through NASA and Thiokol.
The propellant combustion interface (PCI) is the layer of combustion that separates the solid propellant from the core gases. The PCI moves normal to this interface at the nominal regression rate for the propellant. Stewart, Jackson, Xu, Fried, and Short have a project is underway that represents the motion of the PCI using the method of level sets. The rules for self-consistent motion of the surface are being constrained with the use of continuum mechanical analysis of generalized jump conditions for thermomechanical materials. The solid, sufficiently far from the PCI, is assumed to be a generalized, heat-conducting solid, and the fluid gases in the core, sufficiently far from the PCI, is assumed to be an inviscid, compressible gas. The normal jump conditions consider the heat release in the PCI and show the expected jump conditions for conservation of mass, momentum and energy, plus an additional constraint on the functional form of the regression rate argued from the dissipation inequality and the surface kinematic relations. The level-set surface representation plus the thermodynamically self-consistent conditions form the PCI model. Related studies are underway to check that conventional combustion models which included detailed models of sub-scale physics, such as pyrolysis and grain-level flame physics, have far-field averaged solutions that are consistent with the macroscale constraints on the regression rate.
A computer code for arbitrary surface topologies that can interpolate near surface fields from different meshes on either side of the PCI is being designed and written that will be capable of representing the PCI between the solid and fluid system code components. Early collaborations on the level-set methods this past year have included exploratory work with Tariq Aslam at Los Alamos National Laboratory and prototyping 3-D level set code after Aslam’s code, DKAPPA3D.
This figure shows a very early burnout of a star propellant grain computed by DKAPPA3D.
Short and Quirk have been examining effective ways of solving chemical flow problems with adaptive mesh refinement and parallelization. This has implications for the full-scale rocket simulation, in which the use of adaptive mesh refinement could substantially lower the cost of computing the model chemistry and complex flow geometries involved.
Brewster, Loner, Tang, O’Shea, and Knott worked closely in several instability analysis projects. These included developing a nonlinear, unsteady propellant (homogeneous, nonmetalized) combustion model; establishing a coupled propellant combustion and simplified motor chamber model for L* instability and generalized (i.e., homogeneous and composite) nonlinear, unsteady propellant combustion; designing a L* burner to perform experimental work to obtain modeling data necessary for simulating unsteady composite propellant combustion; and beginning the analytical modeling of composite propellant combustion.
The group’s most significant single research finding is preliminary numerical prediction of oscillatory nonlinear L* behavior—which has been observed experimentally, but never simulated computationally—involving initial high-frequency oscillations early in the firing at low pressure followed by low-frequency oscillations at high pressure. Other significant results include numerical simulation of complex extinction and chuffing behavior.
L* instability is the phenomena of low frequency oscillatory combustion coupled with spatially uniform chamber pressure fluctuation occurred in solid rocket motors with small characteristic length L* (defined as the ratio of free chamber volume to nozzle throat area). Numerical simulation of L* instability for homogeneous propellant in solid rocket motors has been performed. The model of a simplified kinetics combustion model coupled with a simplified L* combustor is used. The combustion model, which was developed by Ward, Son, and Brewster (WSB), of a new low gas activation energy analysis in the gas phase with the activation energy asymptotic thermal decomposition analysis of Lengelle in the condensed phase is used for modeling the combustion of homogeneous propellants. The quasi-steady gas and condensed phase reaction (surface reaction) were assumed in the modeling of unsteady nonlinear combustion and gas dynamics. Several nonlinear behaviors are predicted computationally for the first time, many of which are similar to observed nonlinear L* instability behavior such as extinction (Figure 3.10) and chuffing (Figure 3.11) (TO BE INSERTED). Frequency shifting has been observed experimentally in double base propellant but attributed tentatively to the two-stage flame structure of these propellants or incomplete combustion due to short gas resident time. In the present model, the initial high-frequency behavior is manifested without including a two-stage flame structure or the modeling of incomplete combustion. It therefore appears that this behavior may be due to other effects, which are currently under investigation.
Krier and Lee are performing numerical simulation of combustion instability in solid-propellant rocket motors. Combustion instability associated with the pressure dependence of the burning rate of energetic materials in solid-propellant rocket motors can lead to catastrophic failure. Combustion instability in a solid rocket motor chamber are mainly due to the interaction between the unsteady energy released by exothermic chemical reactions of energetic materials and the combustion chamber wave dynamics. Typical combustion instability can often be characterized by oscillatory pressure fluctuations coupled with unsteady heat release. The unsteady combustion of solid-propellant (SP) is highly responsive to the 3-D pressure fluctuation of high-temperature burnt gas in a rocket motor chamber. The contributions of the heat release due to SP combustion to the acoustic energy in the chamber can be described by an acoustic admittance function. For a quasi-steady gas flame, the acoustic admittance function is directly related to the propellant burning rate response function. For a rigorous description of combustion/acoustic instability in rocket motor chambers, the physical aspects such as combustion response of SP, compressibility of burnt gas, chamber volume changes due to burn-back of SP grain, and the large shear and temperature stresses along the burning interface have to be considered.
The objective of the present study is to analyze the combustion instability for both homogeneous and heterogeneous solid propellants in large motors. Murphy and Krier have extended recent unsteady burning models to heterogeneous propellants. Their statistical response function for heterogeneous SP will be implemented in the present numerical simulation. The fluid flow with nonstationary waves, governed by unsteady compressible Navier-Stokes equations, has been numerically solved by the third-order approximate Riemann solver, Flux Vector Splitting, and Advection Upstream Splitting Method, with MUSCL (Monotonic Upstream centered Scheme for Conservation Laws) extrapolation. To take account of moving SP grain, the so-called Geometric Conservation Law for a moving grid and the two-block structured grid system have been employed.
To investigate combustion instability in a solid-propellant rocket motor, a high-order Navier-Stokes solver (third-order in space and fourth-order in time) with a moving boundary capability has been developed, which is the first stage of combustion instability analysis code development. The preliminary numerical calculation for unsteady chamber filling process has reported. In those calculations a phenomenological burning rate model, i.e., rb = apn, and non-moving interface model were adopted. The quasi-steady numerical solutions have been compared with a simple gas dynamics theory, and satisfactory agreement was achieved. The steady-state flow field solution has also been perturbed by introducing a sinusoidal forcing function at head-end wall to investigate the acoustic wave dynamics inside a rocket motor chamber. In the ongoing stage of the numerical code development process, the combustion response function of heterogeneous SP is currently being implemented and parallelism introduced into the code.
Buckmaster and Jackson have collaborated in research on idealized propellant flame configurations for the purpose of identifying the key modeling ingredients needed for accurate simulations. The most significant result is the demonstration that a time dependent shear in the neighborhood of the propellant surface of the kind generated by the interaction of acoustic waves and the mean flow can generate large variations in the heat flux to the propellant, both instantaneous and time-averaged, with concomitant effect on the regression rate. There appears to be no literature on non-axisymmetric vortical rocket chamber flows, and so there are a large number of questions to be examined. They plan to increase the complexity of the propellant flame modeling, accounting for 3-D effects, more complex kinetic models, etc.
Fried has focused his attention on the formulation of a thermodynamically consistent description of the propellant combustion process, a description in which the interface between solid rocket propellant and its combusted product is modeled as a sharp surface of discontinuity in various relevant bulk fields and constitutive properties. The key aspect of this work concerns the formulation of appropriate kinematic, kinetic, and constitutive equations for the interface. This effort has been conducted using modern continuum mechanical methods developed for the study of phase transitions. The investigator has interacted closely with other members of the combustion team, including Jackson, Stewart, and Xu. Thus far, this work has yielded a 1-D model of a rocket consisting of a system of governing equations that involve bulk and interfacial partial differential equations.
During the coming year, Fried will work with Jackson and Stewart to analyze the aforementioned system of equations with a view to comparing their solutions with those obtained from standard diffuse-interface models for combustion. The goal is to obtain guidance with regard to the structure of interfacial constitutive equations that describe the kinetics of the combustion process and the evolving jump in the temperature field across the combustion front in the sharp-interface model. In addition, they will continue to work on a full 3-D sharp-interface description of the combustion process, with a focus on including in the theory the effects of interfacial energy, stress, and other thermodynamic fields. With Vanka, a turbulence model is to be included. Solvers for structural mechanics and heat conduction in SP grain will also be implemented into the code in the near future and then integrated into GEN1 or GEN2.
Fermionic path integral Monte Carlo (FPIMC) simulations have been used to study the equilibrium properties of the hydrogen and deuterium in the density and temperature range of 1.6 < rs < 14.0 and 5000K < T < 167000K. Ceperley and Militzer studied the nature of the transitions and used a cluster analysis to identify the various chemical species in each phase such as H, H+, e, H2 and H2+. They also determined the equation of state of deuterium along the Hugoniot, which is studied by laser shock wave experiments by the Lawrence Livermore group. A recent news article in Science (218, 1135, 1178, Aug. 21, 1998) has a description of the experiments and compares to their calculations. Ceperley attended a workshop at Livermore and was one of the presenters on the properties of high pressure-high density hydrogen in January 1998. The investigators have used the ACSI Blue SP2 at LLNL for developing and running the parallel FPIMC simulations. They were one of the heaviest users of machine this year. In particular, full parallelization and testing of the path integral code was an important part of this year’s computational advances.
As part of his graduate studies, Militzer spent the summer at Lawrence Livermore National Laboratory working with E. L. Pollock and others on the above research. He developed a new variational approach based on the density matrix in order to study the theory of warm condensed matter with a particular focus on hydrogen. Next year they will develop pseudopotentials for use with their path integral code (thesis work of Zong) so that they can treat the heavier atoms occurring in rocket fuel and will modify the code to use the pseudopotentials and test them on applications.
Mitas is using Quantum Monte Carlo methods for studying electronic structure of molecular and condensed systems with high-energy storage. Quantum Monte Carlo (QMC) is one of the most promising methods for high accuracy calculations of atomization and cohesive energies, heats of formation, excitation energies and barrier heights, etc., for both molecular and condensed matter systems. It is well known that current quantum chemistry and condensed matter physics methods in many cases are not capable of providing the energy differences with desired accuracy (1 kcal/mol). QMC provides a new alternative to the traditional electronic structure approaches. Some advantages:
 | The QMC method relies on explicitly correlated wave functions and stochastic techniques to solve the Schrödinger equation. This combination enables the description of the extremely complex many-body effects with high accuracy and efficiency. |
| Because of a negligible communication overhead, QMC is ideal for massively parallel architectures such as ASCI machines. Tests on Origin, SP2, Exemplar and T3E up to 512 processors show essentially perfect scalability. |
| QMC has a wide range of applicability as demonstrated by their sand others recent calculations for molecules, clusters and solids. Some of these calculations belong to the largest ever done within the correlated wave function framework (~ 200 valence electrons). |
Mitas has also initiated application of QMC to several high-energy molecular systems, in particular, to cage molecules of carbon and nitrogen. This will involve systems such as octanitrocubane and 1,3,5,7-tetranitrocubane that are highly energetic (it is estimated that octanitrocubane can be more effective than HMX by 25% or so). Fundamental difficulties with these systems lie in the fact that either their synthesis has not been successful so far or the synthesis is too expensive. Plans for the next year are to expand the usefulness of the QMC method to calculations of interatomic forces. Such development will enable descriptions for equilibrium geometries, and open possibilities for dynamical calculations in a fully correlated manner.
Martin, Stephan, and Mattson are performing quantum simulations of hydrocarbons at high pressure and temperature. The primary goal of the project is to develop efficient methods for ab initio simulation of materials under extreme conditions. They are developing "Order N" methods that simulate thermal motions of atoms and reactions directly from a quantum treatment of the electrons. These methods solve the quantum mechanical equations with computational complexity that scales linearly in the number of atoms. In contrast, the most efficient current methods scale as the square or the cube of the number. Order N methods are intrinsically parallel in nature and adaptable to parallel computers. They have simpler versions running that make certain approximations. The main efforts now are to improve the programs to include self-consistent density functional methods that are state-of-the-art in chemistry and physics. In this they are working with Soler and Ordejon (former member of the group). The codes are called SIESTA and presently are advanced and highly structured, but only for serial architectures. Mattson is working with these codes and Stephan is developing a more general Order-N package that can be used with SIESTA. The first applications are for the equation of state of carbon at high pressure and temperature. In the future, they will simulate reactions in hydrocarbons under extreme conditions.
Martinez leads a team that aims to achieve a first-principles description of molecular dynamics including electronic excitation that they will use to study combustion and detonation. In the first year, they have succeeded in implementing a multiple spawning method on parallel architectures, achieving near-linear speedups (up to 28 times faster on 30 processors) and have also performed the first ever ab initio molecular dynamics simulations including electronic excitation. However, in order to be able to apply these methods to larger systems which more accurately model true materials, they need to make significant advances in the methods used to compute interatomic potential energy surfaces, for both ground and excited electronic states. They have pursued two directions here—first, combining interpolation methods with direct ab initio evaluation of the potential energy surfaces and second, assembling intermolecular interactions from detailed information about fragments of the molecule. The first of these is most well suited to the study of large molecules, while the second is best for large systems composed of many molecules, e.g. molecular crystalline solids. They are applying the first-principles methods to investigate the reactions of ozone under high pressure and further developing their methods for solving the electronic Schrödinger equation in large systems and/or at high pressures.