Search

• The technique bypasses technically challenging derivation of stochastic representative solutions underlying Monte Carlo solution of initial boundary value problems. • In contrast to MC solutions, the technique estimates non-problem-specific impulse-response functions, i.e., Green's functions, which can be used to solve IBVP's subject to an infinite array of boundary and internal forcing conditions. • A random walker swarm is launched from a chosen response (or impulse) point, well-developed RWboundary interaction models can be implemented, and a simple estimator is used to estimate the transition density - and corresponding Green's function - between the response/impulse point and the impulse/response point. • Deleterious depletion of RW's at absorbing Dirichlet boundaries is solved using a RW respawning algorithm, while spatial variance in estimated GF's, produced by our naĩve transition density estimator, is minimized using a simple area-averaging technique. • The proposed technique is tested against three problems having known Green's functions. • The paper is presented in recipe fashion, and is aimed at non-specialists. A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate, though high-accuracy GF's, within any geometry, the technique solves the central challenge in obtaining Green's function solutions. In contrast to Monte Carlo solutions of individual transport problems, subject to specific sets of conditions and forcing, the proposed technique produces approximate GF's that can be used: a) to obtain (infinite) sets of solutions, subject to any combination of (random and deterministic) boundary, initial, and internal forcing, b) as high fidelity direct models in inverse problems, and c) as high quality process models in thermal and mass transport design, optimization, and process control problems. The technique exploits an equivalence between the adjoint problem governing the transport problem Green's function, G (x , t | x ′ , t ′) , and the backward Kolmogorov problem governing the transition density, p (x , t | x ′ , t ′) , of the stochastic process used in Green's function construction. We address nonspecialists and report four contributions. First, a recipe is outlined for diagnosing when stochastic Green's function estimation can be used, and for subsequently estimating the transition density and associated Green's function. Second, a naive estimator for the transition density is proposed and tested. Third, Green's function estimation error produced by random walker absorption at Dirichlet boundaries is suppressed using a simple random walker splitting technique. Last, spatial discontinuity in estimated GF's, produced by the naive estimator, is suppressed using a simple area averaging method. The paper provides guidance on choosing key numerical parameters, and the technique is tested against two simple unsteady, linear heat conduction problems, and an unsteady groundwater dispersion problem, each having known, exact GF's. [ABSTRACT FROM AUTHOR]

Physical arguments and comparisons with published experimental data suggest that in simple liquids: (i) single-molecule-scale viscous forces are produced by temperature-dependent London dispersion forces, (ii) viscosity decay with increasing temperature reflects electron cloud compression and attendant suppression of electron screening, produced by increased nuclear agitation, and (iii) temperature-dependent self-diffusion is driven by a narrow band of phonon frequencies lying at the low-frequency end of the solid-state-like phonon spectrum. The results suggest that collision-induced electron cloud distortion plays a decisive role in single molecule dynamics: (i) electron cloud compression produces short-lived repulsive states and single molecule, self-diffusive hops, while (ii) shear-induced distortion generates viscosity and single-molecule-scale viscous drag. The results provide new insight into nonequilibrium molecular dynamics in nonpolar, nonmetallic liquids. [ABSTRACT FROM AUTHOR]

Abstract: Time average shock-induced boundary layer separation is investigated using scale analyses, analytical modeling, and experiments. While the study focuses on turbulent boundary layer separation in overexpanded rocket nozzles, many of the analyses presented apply to the broad family of free interaction, shock-separated flows in which the structure of the boundary layer–shock interaction zone is self-similar and independent of the shock generator. The scale analyses lead to two approximate expressions for the wall pressure ratio at separation; over a range of separation Mach numbers, both models provide reasonable predictions of observed separation pressure ratios. The second model, representing a refinement of the first, appears to provide a fairly general description of free interaction separation: the model approximately captures separation pressure ratios observed in supersonic flow over backward facing steps and in the case of overexpanded nozzle flow, provides predictions that are consistent with the free interaction model. Experiments are carried out in a sub-scale nozzle under overexpanded, cold-flow conditions. The principal observations are as follows: (i) For the range of separation Mach numbers investigated (), nominal separation line locations can be predicted with reasonable accuracy using the classical generalized quasi-one-dimensional compressible flow model and an appropriate separation criterion. (ii) Over the same range of overexpanded flow conditions, the time-average pressure rise over the shock interaction zone can be accurately fit by the free interaction model. [Copyright &y& Elsevier]

It is well known that the dynamic performance of a rocket or launch vehicle is enhanced when the length of the divergent section of its nozzle is reduced or the nozzle exit area ratio is increased. However, there exists a significant performance trade-off in such rocket nozzle designs due to the presence of random side loads under overexpanded nozzle operating conditions. Flow separation and the associated side-load phenomena have been extensively investigated over the past five decades; however, not much has been reported on the effect of side loads on the attitude dynamics of rocket or launch vehicle. This paper presents a quantitative investigation on the influence of in-nozzle random side loads on the attitude dynamics of a launch vehicle. The attitude dynamics of launch vehicle motion is captured using variable-mass control-volume formulation on a cylindrical rigid sounding rocket model. A novel physics-based stochastic model of nozzle side-load force is developed and embedded in the rigid-body model of rocket. The mathematical model, computational scheme, and results corresponding to side loading scenario are subsequently discussed. The results highlight the influence of in-nozzle random side loads on the roll, pitch, yaw, and translational dynamics of a rigid-body rocket model. [ABSTRACT FROM AUTHOR]

This article theoretically and experimentally characterizes direct contact, packed bed thermal gradient attenuators in which a fluid control stream, subject to broadband thermal disturbances, flows through a thermally attenuating packed bed medium. The theoretical model decomposes the device into three subsystems: an upper mixing volume, the packed bed, and a lower mixing volume. Analysis of the packed bed subsystem leads to a coupled system of equations that describe local heat transfer within the control stream and within individual spherical elements comprising the packed bed; the system of equations obtained has the same general form as that derived in an earlier investigation of tube-in-shell, noncontact thermal gradient attenuators [J. Heat Transfer 123, 796 (2001)]. Associated subsystem transfer functions are derived, and in analogy with observations reported in the earlier investigation, are shown to provide simple, unambiguous criteria for designing and optimizing packed bed attenuators. It is found that, for 52 different sets of experimental conditions, theoretical performance of the device matches experimental performance to within 2.5 dB root mean square, and that the device provides several orders of magnitude attenuation for flow rates on the order of 1 l/min and disturbance frequencies higher than approximately 10 mHz. The results of the present study and the earlier investigation together provide a useful basis for analyzing and designing large and small, contacting and noncontacting, thermal gradient attenuators. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents information on a study which analyzed a precision method for attenuating temperature variations in a high-throughput control fluid stream. Details on tube-bank attenuator subsystem; Accumulator and total transfer functions; Set-up and transfer function results; Attenuation of broadband thermal variations.

A simple device for simultaneously measuring two spatially separated contact forces is described. The device uses a monolithic dual-cantilever touch sensor driven by a piezoelectric PZT actuator. A phase-locking method allows measurement of resonant frequency shifts at constant phase, based on the strain response of a second attached PZT. Calibration and force measurement procedures are developed to extract applied contact forces from the dual-cantilever's coupled, nonlinear response. Based on a preliminary calibration, the present device exhibits maximum relative measurement error on the order of 6%. Procedures for reducing this error are described. [ABSTRACT FROM AUTHOR]