Numerical analysis of transient combustion response to acoustic oscillations in axisymmetric rocket motors

A numerical analysis of unsteady motions in solid rocket motors with a nozzle has been conducted. The formulation treats the complete conservation equations for the gas phase and the one-dimensional equations in the radial direction for the condensed phase. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. After obtaining a steady state solution, periodic pressure oscillations are imposed at the head end to simulate acoustic oscillations of a traveling-wave motion in the combustion chamber. The amplitude of the pressure oscillation is 1.0 % of the mean pressure and the frequency is 1790 Hz, corresponding to the twice of the fundamental frequency of the chamber. Magnitude and phase of pressure and axial velocity fluctuations are influenced by the upstream reflecting wave from the nozzle wall. Axial velocity near surface region oscillates in phase advance manner with reference to the acoustic pressure. Large vorticity fluctuations are observed in near surface region. The mass-flow-rate at the nozzle exit periodically oscillates with a time delay compared to the imposed pressure oscillations at the head end

Applications of Various Methods of Analysis to Combustion Instabilities in Solid Propellant Rockets

Instabilities of motions in a combustion chamber are consequences of the coupled dynamics of combustion processes and of the flow in the chamber. The extreme complexities of the problem always require approximations of various sorts to make progress in understanding the mechanisms and behavior of combustion instabilities. This paper covers recent progress in the subject, mainly summarizing efforts in two areas: approximate analysis based on a form of Galerkin's method, particularly useful for understanding the global linear and nonlinear dynamics of combustion instabilities and numerical simulations intended to accommodate as fully as possible fundamental chemical processes in both the condensed and gaseous phases. One purpose of current work is to bring closer together these approaches to produce more comprehensive and detailed realistic results applicable to the interpretation of observations and for design of new rockets for both space and military applications. Particularly important are the goals of determining the connections between chemical composition and instabilities; and the influences of geometry on nonlinear behavior

Transient combustion responses of homogeneous propellants to acoustic oscillations in axisymmetric rocket motors

A numerical analysis of unsteady motions in solid rocket motors has been conducted. The formulation considers a 2-D axisymmetric combustion chamber and a choke nozzle, and treats the complete conservation equations accounting for turbulence closure and finiterate chemical kinetics in the gas phase and subsurface reactions. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. Results of the steady-state calculations indicate that the distributions of pressure in the motor and Mach number in the nozzle are one-dimensional along the axial direction. Vorticity contours show similar pattern to those of Mach number in the combustion chamber. The nozzle has an influence on the flow and temperature fields in the combustion chamber. A narrow pressure pulse is imposed at the head end to simulate unsteady acoustic oscillations in the combustion chamber. When the front of the pulse reaches near the nozzle throat, pressure near the nozzle throat increases and blocks the hot gas flow from passing through the nozzle throat. Self-generated oscillations have similar frequencies to those of standing waves of the combustion chamber. Large vorticity fluctuations are observed in near surface region. The luminous flame zone responds to low-frequency pressure wave rather than highfrequency one. Temperature fluctuations in the primary flame zone of the head end oscillates independently of the imposed pressure oscillations while temperature fluctuations in downstream region show pressure-dependent oscillations

Numerical study of acoustic oscillations and combustion instabilities in solid propellant rocket

A numerical analysis of unsteady motions in solid rocket motors has been conducted. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. A narrow pressure pulse is imposed at the head end to simulate unsteady acoustic oscillations in the combustion chamber. Pressure increases when the front of the pulse reaches near the nozzle area. Self-generated oscillations with frequency of standing wave propagates upstream in the combustion chamber. Investigation of transient response of gas-phase dynamics to traveling pressure wave and its effects on propellant combustion reveals several aspects: Combustion responses have a strong relationship with vorticity fluctuations in case of high turbulent intensity on the propellant surface. Temperature fluctuations of the propellant surface in the head end region seem to be very unstable and independent of the pressure wave. Surface temperature without turbulence effect looks more sensitive to temperature fluctuations in the primary flame zone. Stability of surface temperature is strongly related to turbulent intensity on the propellant surface

Numerical Analysis of Solid Rocket Motor Instabilities With AP Composite Propellants

A non-steady model for the combustion of ammonium perchlorate composite propellants has been developed in order to be incorporated into a comprehensive gasdynamics model of solid rocket motor flow fields. The model including the heterogeneous combustion and turbulence mechanisms is applied to nonlinear combustion instability analyses. This paper describes the essential mechanisms and features of the model and discusses the methodology of non-steady calculations of the combustion instabilities of solid rocket motors

Quasi-Local Energy Flux of Spacetime Perturbation

A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.Comment: 8 pages, added appendix, version to appear in Phys. Rev.

A Proposal for a Multi-Drive Heterogeneous Modular Pipe- Inspection Micro-Robot

This paper presents the architecture used to develop a micro-robot for narrow pipes inspection. Both the electromechanical design and the control scheme will be described. In pipe environments it is very useful to have a method to retrieve information of the state of the inside part of the pipes in order to detect damages, breaks and holes. Due to the di_erent types of pipes that exists, a modular approach with di_erent types of modules has been chosen in order to be able to adapt to the shape of the pipe and to chose the most appropriate gait. The micro-robot has been designed for narrow pipes, a _eld in which there are not many prototypes. The robot incorporates a camera module for visual inspection and several drive modules for locomotion and turn (helicoidal, inchworm, two degrees of freedom rotation). The control scheme is based on semi-distributed behavior control and is also described. A simulation environment is also presented for prototypes testing

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,

Electronic Structure of Electron-doped Sm1.86Ce0.14CuO4: Strong `Pseudo-Gap' Effects, Nodeless Gap and Signatures of Short Range Order

Angle resolved photoemission (ARPES) data from the electron doped cuprate superconductor Sm$_{1.86}$Ce$_{0.14}$CuO$_4$ shows a much stronger pseudo-gap or "hot-spot" effect than that observed in other optimally doped $n$-type cuprates. Importantly, these effects are strong enough to drive the zone-diagonal states below the chemical potential, implying that d-wave superconductivity in this compound would be of a novel "nodeless" gap variety. The gross features of the Fermi surface topology and low energy electronic structure are found to be well described by reconstruction of bands by a $\sqrt{2}\times\sqrt{2}$ order. Comparison of the ARPES and optical data from the $same$ sample shows that the pseudo-gap energy observed in optical data is consistent with the inter-band transition energy of the model, allowing us to have a unified picture of pseudo-gap effects. However, the high energy electronic structure is found to be inconsistent with such a scenario. We show that a number of these model inconsistencies can be resolved by considering a short range ordering or inhomogeneous state.Comment: 5 pages, 4 figure