Modeling re-ignition and chuffing in solid rocket motors

A nonlinear model is developed to numerically simulate dynamic combustion inside a solid rocket motor chamber. Using this model, the phenomena of re-ignition and chuffing are investigated under low-L* conditions. The model consists of two separate submodels (coupled to each other), one for unsteady burning of propellant and the other for unsteady conservation of mass and energy within the chamber. The latter yields instantaneous pressure and temperature within the chamber. The instantaneous burning rate is calculated using a one-dimensional, nonlinear, transient gas-phase model previously developed by the authors. The results presented in this paper show that the model predicts not only the critical L*, but also the various regimes of L*-instabihty. Specifically, the results exhibit (1) amplifying pressure oscillations leading to extinction, and (2) re-ignition after a dormant period following extinction. The re-ignition could be observed only when a radiation heat flux (from the combustion chamber to the propellant surface) was included. Certain high-frequency oscillations, possibly due to intrinsic instability, are observed when the pressure overshoots during re-ignition. At very low values of initial L*, successive cycles of extinction/reignition displaying typical characteristics of chuffing are predicted. Variations of the chuffing frequency and the thickness of propellant burned off during a chuff with L* are found to be qualitatively the same as that reported from experimental observations.

Numerical modeling of heat and mass transfer in laser surface alloying: Non-equilibrium solidification effects

A transient macroscopic model is developed for studying heat and mass transfer in a single-pass laser surface alloying process, with particular emphasis on non-equilibrium solidification considerations. The solution for species concentration distribution requires suitable treatment of non-equilibrium mass transfer conditions. In this context, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modeled by Means of a number of macroscopically observable parameters related to the solidifying domain. The numerical model is so developed that the modifications on account of non-equilibrium solidification considerations can be conveniently implemented in existing numerical codes based on equilibrium solidification considerations.

Sandwich propellant combustion: Modeling and experimental comparison

This paper reports reacting fluid dynamics calculations for an ammonium percholrate binder sandwich and extracts experimentally observed features including surface profiles and maximum regression rates as a function of pressure and binder thickness. These studies have been carried out by solving the two-dimensional unsteady Navier-Stokes equations with energy and species conservation equations and a kinetic model of three reaction steps (ammonium perchlorate decomposition flame, primary diffusion flame, and final diffusion flame) in the gas phase. The unsteady two-dimensional conduction equation is solved in the condensed phase. The regressing surface is unsteady and two dimensional. Computations have been carried out for a binder thickness range of 25-125 mum and a pressure range of 1.4 to 6.9 MPa. Good comparisons at several levels of detail are used to demonstrate the need for condensed-phase two-dimensional unsteady conduction and three-step gas-phase reactions. The choice of kinetic and thermodynamic parameters is crucial to good comparison with experiments. The choice of activation energy parameters for ammonium percholrate combustion has been made with stability of combustion in addition to experimentally determined values reported in literature. The choice of gas-phase parameters for the diffusion flames are made considering that (a) primary diffusion flame affects the low-pressure behavior and (b) final diffusion flame affects high-pressure behavior. The predictions include the low-pressure deflagration limit of the sandwich apart from others noted above. Finally, this study demonstrates the possibility of making meaningful comparisons with experimental observations on sandwich propellant combustion.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.

The Borkar-Meyn theorem for asynchronous stochastic approximations

In this paper, we give a generalization of a result by Borkar and Meyn (2000) 1], on the stability and convergence of synchronous-update stochastic approximation algorithms, to the case of asynchronous stochastic approximations with delays. We then describe an interesting application of the result to asynchronous distributed temporal difference (TD) learning with function approximation and delays. (C) 2011 Elsevier B.V. All rights reserved.

Efficient statistical modeling for the compression of tree structured intermediate code

We propose a scheme for the compression of tree structured intermediate code consisting of a sequence of trees specified by a regular tree grammar. The scheme is based on arithmetic coding, and the model that works in conjunction with the coder is automatically generated from the syntactical specification of the tree language. Experiments on data sets consisting of intermediate code trees yield compression ratios ranging from 2.5 to 8, for file sizes ranging from 167 bytes to 1 megabyte.

Modeling reservoir irrigation in uncertain hydrologic environment

In a detailed model for reservoir irrigation taking into account the soil moisture dynamics in the root zone of the crops, the data set for reservoir inflow and rainfall in the command will usually be of sufficient length to enable their variations to be described by probability distributions. However, the potential evapotranspiration of the crop itself depends on the characteristics of the crop and the reference evaporation, the quantification of both being associated with a high degree of uncertainty. The main purpose of this paper is to propose a mathematical programming model to determine the annual relative yield of crops and to determine its reliability, for a single reservoir meant for irrigation of multiple crops, incorporating variations in inflow, rainfall in the command area, and crop consumptive use. The inflow to the reservoir and rainfall in the reservoir command area are treated as random variables, whereas potential evapotranspiration is modeled as a fuzzy set. The model's application is illustrated with reference to an existing single-reservoir system in Southern India.

Modeling the solubilities of fatty acids in supercritical carbon dioxide

A thermodynamic model was developed for modeling the solubilities of fatty acids in supercritical carbon dioxide. The model combines the Peng-Robinson equation of state (EOS) with the two parameter van der Waal's mixing rules. The model is applied to predict the solubilities of various fatty acids. The two adjustable interaction parameters in the model are found to vary linearly with the chain length of the fatty acids. Thus this model can be used to predict the solubilities of various fatty acids in supercritical carbon dioxide. (C) 2003 Elsevier Science B.V. All rights reserved.