Efficient Covariance Intersection of Attitude Estimates Using a Local-Error Representation

Tether dynamics investigations for the Canadian OEDIPUS sounding rocket program

Stabilization of a Mach 5.92 Boundary Layer by Two-Dimensional Finite-Height Roughness

Beech 1900D flight test to characterize propeller noise on the fuselage exterior

The supersonic combustion flow field of two hydrocarbon fuels, ethylene and propane, is studied numerically. Both configurations have the feature of the existence of a generic rearward-facing step in the upper longitudinal wall. Sonic pilot ethylene and propane are injected at the step base parallel to the incoming supersonic air. The main ethylene and propane are injected from the upper wall normal to the incoming air with sonic speeds. The wedge, located downstream of the rearward-facing step in the ethylene case study, showed a good potential towards enhancing the fuel-air mixing in addition to helping initiating and stabilizing the main flame. Sweeping the step from both end sides, in the propane case study, enhances the fuel-air mixing in the far field domain. The 3-D version of Fluent CFD code is used in the present study. The results show typical features of such flow field. The current work is a step towards an ongoing research work aiming at examining the combustion characteristics of a variety of hydrocarbon fuels. The motivation for this is to study the feasibility of using both pure hydrocarbon fuels and mixtures of hydrogen and hydrocarbons in engines for Graduate Research Assistant, Department of Mechanical Engineering, Student Member AIAA. Eminent Professor/Scholar, Department of Mechanical Engineering, Associate Fellow AIAA. Associate Professor, Mechanical Engineering Technology Dept., Member ASME. the mid-speed range of the hypersonic flight.

An experimental and numerical investigation has been performed to study the evolution of shock waves undergoing a sudden expansion in one direction while restricted in the second. Experimental data are gathered and studied for shock waves undergoing the sudden 4:l area expansion in air for Mach numbers of 1.5 and 2.0. Detailed, time-accurate measurements of the shock wave and vortex core location as well as wall pressure data are presented. In addition, the evolving flow structure through the time-accurate flowfield imagery is also presented. The results of these experiments are compared to twodimensional numerical simulations specific to the Mach 1.5 and 2.0 initial conditions and geometry. The direct comparisons of the experimental work and numerical simulations provide insight into flowfield phenomena such as viscous dissipation and sh&&/vortex interaction. The data presented in this effort further elucidates key modeling questions by providing time-accurate flow visualization and pressure data of a two-dimensional shock wave undergoing a sudden expansion in a confined chamber. * Aerospace Engineer, Senior Member AIAA ’ Senior Principal Consultant, Associate Fellow AIAA ’ Research Engineer, Member AIAA ’ Professor & Department Chairman, Associate Fellow AIAA ‘I Associate Professor ’ Associate Professor, Senior Member AIAA ‘* Assistant Professor This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Background Gas dynamics of fast, transient characteristics includes issues such as shock wave reflections, vorticity production, shock-vortex interaction, energy exchange between shock and turbulence, and shock focusing (Chang and Kim, 1995). Figure 1 illustrates the sudden area expansion of a shock wave within a confined domain indicating these interesting fluid dynamic phenomena. These phenomena occur at time scales ranging from microseconds to milliseconds. This paper presents a focused look at sudden shock wave expansion within a confined chamber and the interaction of that shock wave with other fluid dynamic features. Both experimental and numerical tools have been adopted. Recent investigations of this type of gas dynamic flow, given by Jiang et al. (1997), present experimental and numerical simulations of a circular shock tube generated flow undergoing a sudden expansion. Figure 1 highlights the salient flow features of such a sudden expansion. Here it is seen that as the initial shock wave travels down the shock tube (Figure 1) it will undergo a sudden area expansion into a confined area (Figure lb-d), the flowfield gives rise to two important features. First, a “starting jet”, characterized by the formation of a vortex ring, Mach disk, and shear layer’ appear. Second, this precursor shock reflects off the confining walls of the expansion chamber and interacts with the starting jet flowfield. It is clearly seen in Figure 1 that this reflected shock splits once it interacts with the primary vortex ring, which gives rise to secondary shock waves. This shock/vortex/shear layer interaction is also shown in Figure 1. Here the reflected shock splits when it interacts with the primary vortex ring. It was also American Institute of Aeronautics and Astronautics (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. observed by Jiang et al. (1997) that once the reflected shock wave passes through the developing shear layer that the shear layer splits, it is moved into the jet flow, and it is convected downstream. This allows another shear layer to form from the jet exit forming another weaker vortex ring. This is referred to as shear layer splitting and is largely an inviscid phenomenon (Jiang et al., 1997) Another phenomenon noted by Jiang et al. (1997) is the shock/shear layer interactions. It is noted that a vortex ring in the shear layer induced a shock wave and the shock wave separated the vortex ring from the shear layer. This is most often noted in strongly expanded free jets. Due to the strong influence of vortex dynamics and compressibility, the turbulence structure can be fruitfully assessed via an evaluation of viscous dissipation.

An experimental study of the breakdown of leading-edge vortices on diamond, cropped, delta, and double delta wings during dynamic pitching

Nomenclature A general two dimensional flow solver is presented for internal or external compressible flow fields with or without embedded shocks. Options allow for the solution of the steady or unsteady Euler, thin layer or full Reynolds averaged Navier Stokes equations. A cell centered conservative finite volume technique is utilized with a constant artificial viscosity coefficient for inviscid flows and a variable artificial viscosity for viscous flows or a TVD option for strong shocks. The time stepping is done by a hybrid mult~-stage Runge-Kutta scheme. Acceleration of the solution is accomplished through local time stepping, enthalpy damping, and implicit residual averaging. Good agreement is found for comparison of the numerical method with exact analytical solutions and experimental data. a speed of sound e total energy h enthalpy J Jacobian matrix k thermal conductivity 1 mixing length p pressure Q physical flux <In normal velocity u,v velocity components t time x,y cartesian coordinates e coefficient or artificial dissipation y ratio of specific heats 1C von Karman constant e,17 transformed coordinates p density a,'T stress J.L viscosity coefficient n limited function 'Assistant Professor, Mechanical Engineering Department, Director Computational Fluid Dynamics Laboratory, Member AIAA ......Graduate Research Assistant, Student Member AIAA

Reacting flow calculations are stiff for time-stepping. Recently, Zhong derived three sets of semi-implicit Runge-Kutta(SIRK) methods for split ordinary differential equations in the form of u' = /(«) 4g(u), where the nonstiff term / is treated explicitly while the stiff term g is simultaneously treated implicitly. The purpose of this work is twofold: first, to simulate multidimensional detonation waves using the high-order Rosenbrock semi-implicit Runge-Kutta time-stepping scheme(SIRK-3C); secondly to quantitatively compare the performance of SIRK with the second-order timesplitting schemes in dealing with the hyperbolic conservation laws with stiff relaxation terms. In the simulation of two-dimensional detonations, a full set of elementary hydrogen-oxygen kinetics with nine species are linear-implicitly treated while the explicit discretization of the basic advection equations are achieved by the third-order ENO schemes. Several model problems of hyperbolic systems with stiff relaxation are considered in the comparison of the Time-Splitting and the SIRK-3C scheme. A set of low-storage SIRK(LSSIRK) schemes is derived and tested to be high-order accurate and strongly A-stable. The results show that high-order SIRK time-stepping methods are suitable for stiff reactive flow simulations like the multi-dimensional detonations. INTRODUCTION In the reactive flow field solutions and the combustion related problems, the existence of several nonequilibrium states impose additional difficulties in the solutions of the reactive Euler equations with stiff relaxation terms. Since the smallest time scale is introduced from the chemical reaction kinetics, the second-order time-splitting method of Strang^ allows an independent calculation of the stiff ODE for the source term via implicit methods in one step, and an explicit highorder convective calculation in the following time steps. By the main source of stiffness from the basic hyperbolic conservation laws, it can accomplish a •Graduate Student, Member AIAA 'Assistant Professor, Mechanical and Aerospace Engineering Department, Member AIAA Copyright ©1997 by American Institute of Aeronautics and Astronautics, Inc. AH rights reserved. robust and easy-to-implement computation of reactive flow of current interests. Despite the second-order in time accuracy and the robustness of these methods, there are two main difficulties with the stiffness which have been minimally handled. The spurious solutions are one of the often observed phenomena, which are stable and free of oscillations, and yet may be completely incorrect.'-' Some type of resolution technique is needed to treat this known difficulties.^'!] The degrading of the second-order time accuracy to the first-order is another and quite recent observation when there exist solutions with many small-scaled structures of high-degree of complication. Jin® has modified the Strang splitting into the secondorder time-splitting methods which preserve its highorder accuracy when the considered solutions are complicated. New third-order semi-implicit Rosenbrock type Runge-Kutta scheme, based on the original version of Zhong'---', is computationally efficient with the linearized source term integration, thus requiring no iterations during the implicit treatment of the stiff source term. Third-order ENO schemes discretize the convective fluxes such that both implicit and explicit terms are treated at each of the three Runge-Kutta stages. This high-order Runge-Kutta scheme(SIRK-3C) still possesses the typical under-resolved characteristics of unphysical spurious numerical results of the TimeSplitting method. However the reduction to lower order if the small relaxation time is not temporally wellresolved, is successfully removed. Multi-dimensional Detonations Detonation waves are multi-dimensional and unstable phenomenon in nature as demonstrated by the early experiments of Urtiew and Oppenheinv-'. Existence of the triple points'^, consisting of an incident shock, a reflecting shock and a Mach stem, is the main characteristic of the reacting region behind the propagating shock front, and these detaching triple points from the leading front further contributes to the rolling up of vortices of opposite strength. One distinctive feature of the instability process observed in experiments is the formation of regular cell structures as triple points collide as they come together in the incident shock and move away from each other in the newly formed Mach stem. Figure[13] depicts this process of triple point col-

The finite volume method is used to model radiative heat transfer in three-dimensional irregular geometries. Transparent and participating media are examined. These test cases indicate that the finite volume method is a viable radiation heat transfer solution procedures for three-dimensional enclosures. NOMENCLATURE a coefficient in the discretization equation b source term in the discretization equation Dc direction cosine integrated over An I actual intensity L total number of control angles n outward unit normal of control volume face ./V, Number of control volumes in / direction Ng, Nj Number of control angles in 6 and directions ex, ey, ez unit vectors in x, y and z directions q heat flux q* nondimensional incident intensities, q/0Tg s distance traveled by a beam S source function Sm modified source function T temperature x, y, z coordinate directions /3 extinction coefficient, K+ a f3m modified extinction coefficient M area of control volume faces Av volume of the control volume AH control angle 9 polar angle measured from e2 K absorption coefficient a scattering coefficient or Stefan-Boltzmann constant O scattering phase function azimuthal angle measured from ex f, 77, Y curvilinear coordinates Copyright 1996 by J. C. Chai. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. *Assistant Professor, Department of Mechanical Engineering, P. O. Box 5014, Cookeville, TN 38505, Member AIAA +Aerospace Engineer, Internal Fluid Mechanics Division & Ph.D. Candidate, Department of Mechanical Engineering: Presently: Research Engineer, Honeywell Technology Center, MN. Subscripts b blackbody E, W, N, S, east, west, north, south, rear and front R, F neighbors of P e, w, n, s, east, west, north, south, rear and front control r,f volume faces g gas P control volume P x, y, z coordinate directions £, 77, Y curvilinear coordinates Superscripts I, I' angular directions

W ITH the development of piezoceramic sensors and actuators of varying shapes and sizes for use in structural applications, the field of smart structures has emerged as an area of research of great importance [1]. The mechanical, thermal, and electrical behavior of piezoceramics has been studied extensively by physicists and material scientists [2–9]. The introduction of these materials in structural applications has created a necessity to review the traditional structural modeling and analysis. Under cyclic variation of the applied electric field, piezomaterials exhibit polarization-electric (P-E) field hysteretic losses, as shown in Fig. 1. The points indicated by the symbols Ps, Pr, and EC represent saturation polarization, remnant polarization, and the coercive electric field, respectively. The saturation polarization Ps corresponds to the value of maximum polarization, which shows negligible change with further increase in electric field. Remnant polarization Pr is the value of polarization when the electric field becomes zero. Coercive electric fieldEC corresponds to the points of zero polarization. The observed phenomenon is due to the delay in polarization switching with variation in electric field. P-E hysteresis effect leads to an interesting variation of strainwith respect to electric field ( E), and it is denoted as butterfly loop. The hysteresiswill be affected by various parameters such as temperature, amplitude of oscillating electric field, frequency of oscillation, and external mechanical preloading. The effect of the amplitude of the electric field on the hysteresis loop has been studied experimentally by Nalwa [2]. It is observed that the remnant polarization and coercive electric field are functions of amplitude of the electric field. With a decrease in amplitude of the electric field, there is a reduction in the values of maximum polarization, remnant polarization, and coercive electric field. Viehland and Chen [3] experimentally studied the effects of frequency of oscillation of the electric field on the hysteresis loop. From the experiments, it was observed that if the amplitude of the electric field is above the coercive electric field ECmax corresponding to the case with saturation polarization, then the dissipation energy increases with an increase in frequency, whereas if the amplitude of the electric field is belowECmax, then the dissipation energy increases with a decrease in frequency. The effect of mechanical preloading on hysteresis has been studied experimentally by Arndt et al. [4]. It is observed that when a compressive mechanical preloading is applied parallel to the electric field, the reduction in polarization is found to be higher than that corresponding to the case with mechanical loading applied perpendicular to the electrical field. With the application of compressive mechanical preloading, the remnant polarization and coercive field show a reduction in magnitude. Mathematical modeling of hysteresis was approached at two different levels: 1) at the microscopic level and 2) at the macroscopic level of the piezomaterial. The microscopic models of hysteresis can be categorized as 1) polarization switching based on the Eshelby inclusion model [10], 2) crystal-plasticity-based nonlinear switching models [11], 3) free-energy-based domain-switching model [12], and 4) dipole–dipole interaction models with threshold-switching energy given by the time-dependent Ginzburg–Landau model [13,14] or the Landau–Devonshire model [15,16]. Macroscopic models can be categorized as either empirical models or thermodynamically consistent models. Empirical models are based on either introducing an additional variable in the constitutive relations [17], by representing the P-E curve by a tanhyperbolic function [18], or by using the Presaich model [19,20]. Bassiouny et al. [21–24] developed a thermodynamic phenomenological model for capturing the electromechanical hysteresis effects based on the work-hardening plasticity model. A similar approach was followed by McMeeking and Landis [25] in modeling domain switching in ferroelectric materials. A model based on extended irreversible thermodynamics was proposed by Lu and Hanagud [26]. Presented as Paper 1743 at the 15-th AIAA/ASME/AHS Adaptive Structures Conference, Honolulu, HI, 23–26 April 2007; received 1 May 2007; accepted for publication 25 August 2007. Copyright © 2007 by V. L. Sateesh, C. S. Upadhyay, and C. Venkatesan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/08 $10.00 in correspondence with the CCC. ∗Graduate Student, Department of Aerospace Engineering. Student Member AIAA. Associate Professor, Department of Aerospace Engineering. Pandit Ramachandra Dwivedi Chair Professor, Department of Aerospace Engineering. Senior Member AIAA. AIAA JOURNAL Vol. 46, No. 1, January 2008

W ITH the development of piezoceramic sensors and actuators of varying shapes and sizes for use in structural applications, the field of smart structures has emerged as an area of research of great importance [1]. The mechanical, thermal, and electrical behavior of piezoceramics has been studied extensively by physicists and material scientists [2–9]. The introduction of these materials in structural applications has created a necessity to review the traditional structural modeling and analysis. Under cyclic variation of the applied electric field, piezomaterials exhibit polarization-electric (P-E) field hysteretic losses, as shown in Fig. 1. The points indicated by the symbols Ps, Pr, and EC represent saturation polarization, remnant polarization, and the coercive electric field, respectively. The saturation polarization Ps corresponds to the value of maximum polarization, which shows negligible change with further increase in electric field. Remnant polarization Pr is the value of polarization when the electric field becomes zero. Coercive electric fieldEC corresponds to the points of zero polarization. The observed phenomenon is due to the delay in polarization switching with variation in electric field. P-E hysteresis effect leads to an interesting variation of strainwith respect to electric field ( E), and it is denoted as butterfly loop. The hysteresiswill be affected by various parameters such as temperature, amplitude of oscillating electric field, frequency of oscillation, and external mechanical preloading. The effect of the amplitude of the electric field on the hysteresis loop has been studied experimentally by Nalwa [2]. It is observed that the remnant polarization and coercive electric field are functions of amplitude of the electric field. With a decrease in amplitude of the electric field, there is a reduction in the values of maximum polarization, remnant polarization, and coercive electric field. Viehland and Chen [3] experimentally studied the effects of frequency of oscillation of the electric field on the hysteresis loop. From the experiments, it was observed that if the amplitude of the electric field is above the coercive electric field ECmax corresponding to the case with saturation polarization, then the dissipation energy increases with an increase in frequency, whereas if the amplitude of the electric field is belowECmax, then the dissipation energy increases with a decrease in frequency. The effect of mechanical preloading on hysteresis has been studied experimentally by Arndt et al. [4]. It is observed that when a compressive mechanical preloading is applied parallel to the electric field, the reduction in polarization is found to be higher than that corresponding to the case with mechanical loading applied perpendicular to the electrical field. With the application of compressive mechanical preloading, the remnant polarization and coercive field show a reduction in magnitude. Mathematical modeling of hysteresis was approached at two different levels: 1) at the microscopic level and 2) at the macroscopic level of the piezomaterial. The microscopic models of hysteresis can be categorized as 1) polarization switching based on the Eshelby inclusion model [10], 2) crystal-plasticity-based nonlinear switching models [11], 3) free-energy-based domain-switching model [12], and 4) dipole–dipole interaction models with threshold-switching energy given by the time-dependent Ginzburg–Landau model [13,14] or the Landau–Devonshire model [15,16]. Macroscopic models can be categorized as either empirical models or thermodynamically consistent models. Empirical models are based on either introducing an additional variable in the constitutive relations [17], by representing the P-E curve by a tanhyperbolic function [18], or by using the Presaich model [19,20]. Bassiouny et al. [21–24] developed a thermodynamic phenomenological model for capturing the electromechanical hysteresis effects based on the work-hardening plasticity model. A similar approach was followed by McMeeking and Landis [25] in modeling domain switching in ferroelectric materials. A model based on extended irreversible thermodynamics was proposed by Lu and Hanagud [26]. Presented as Paper 1743 at the 15-th AIAA/ASME/AHS Adaptive Structures Conference, Honolulu, HI, 23–26 April 2007; received 1 May 2007; accepted for publication 25 August 2007. Copyright © 2007 by V. L. Sateesh, C. S. Upadhyay, and C. Venkatesan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/08 $10.00 in correspondence with the CCC. ∗Graduate Student, Department of Aerospace Engineering. Student Member AIAA. Associate Professor, Department of Aerospace Engineering. Pandit Ramachandra Dwivedi Chair Professor, Department of Aerospace Engineering. Senior Member AIAA. AIAA JOURNAL Vol. 46, No. 1, January 2008

Introduction A new entry guidance concept is developed for an unpowered lifting vehicle. The two-dimensional longitudinal plane entry guidance scheme used by the U.S. Space Shuttle Orbiter is extended to a threedimensional entry guidance scheme. The guidance task is posed as planning and tracking a reference trajectory. This paper concerns the design and analysis of the tracking law. In the new guidance scheme, the complete ground-track is planned as a function of energy and tracked by commanding both the angle of attack and angle of bank. This extension to the Shuttle entry guidance scheme is carried out within the theoretical framework of differential flatness and feedback linearization. Approximately flat outputs for the system dynamics are identified which are then used to construct a state-variable transformation which together with a static state feedback control transformation renders the system approximately input-output, as well as input-state linear. In the transformed state and control variables, the system dynamics can be represented by two approximately decoupled linear systems. A feedback tracking law is then designed by taking advantage of the linear structure of the system dynamics in the transformed coordinates. This tracking law is shown to achieve bounded tracking of the flat outputs. Simulation results indicate that, if provided with an appropriate reference trajectory, the tracking law guides the vehicle to within one nautical mile of the target in downrange and cross-range during the hypersonic entry phase. 'Graduate Student, Student Member AIAA. t Research Assistant, AIAA member, presently at The Aerospace Corporation, 2350 E. El Segundo Blvd., El Segundo, CA 90245. ^Associate Professor, Associate Fellow AIAA. § Copyright ©by Kenneth D. Mease, Published by AIAA with permission Current efforts to develop a reusable launch vehicle (RLV) and a space station crew return vehicle provide particular motivation for improving the entry guidance capability for a lifting unpowered vehicle. In this paper we develop a natural extension to the longitudinal entry guidance scheme used by the U.S. Space Shuttle Orbiter. The new entry guidance scheme follows from the property of differential flatness of a A controlled system is differentially flat if there exist output functions, termed flat outputs, equal in number to the control inputs, such that all the state and control functions can be determined from the output functions and their derivatives through purely algebraic relations. A differentially flat system offers the possibility of reduced-order trajectory planning in terms of the flat outputs. Moreover, the flat outputs often permit feedback linearization of the controlled system dynamics, i.e., they lead to state and control transformations that globally linearize the dynamics. Thus guidance law design and analysis may become greatly simplified for a differentially flat system. Following this paradigm, the guidance task is divided naturally into a trajectory planning subtask of determining the reference output functions consistent with a trajectory that meets all the guidance objectives, and a trajectory tracking subtask of determining the control commands to track the reference output functions. The longitudinal-plane entry guidance logic used for the Shuttle can be viewed as a product of the approach just described. Drag is the flat output used in trajectory planning and the magnitude of the bank angle is commanded to track the reference drag trajectory. The reference drag trajectory is planned as a function of velocity such that it achieves the desired down-range and satisfies the vehicle thermal, normal load and dynamic pressure constraints, as well as the controllability constraint imposed by the

As part of an effort to develop efficient hollow cathodes for the International Space Station and low power electric propulsion systems, the effects of orifice length-to-diameter aspect-ratio on the performance of 0.5 to 2 A hollow cathodes were examined to compare with previous experiments and a recently developed model. Cathodes were constructed with nominally identical orifice diameters and lengths that varied from 1 to 6 diameters. The performance of the cathodes was evaluated at the beginning of life and after at least 50 hours of operation. The data generally followed the trends predicted by the model with a few exceptions which appear to be related to the thermal environment of the cathode. Power consumption scaled with the orifice aspect-ratio, while the minimum spot mode flow rate was inversely related to the length-to-diameter ratio. At currents below 1.0 A, the cathode operation became more complex than that which is assumed in the orifice model; low operating temperature caused instabilities in several of the devices. Nomenclature AR = aspect-ratio of the orifice c = speed of light, 3 x 10 m/s h = Planck's Constant, 6.63 x 10' J-s k = Boltzmann's Constant, 1.38 x 10' J/K n = index of refraction T = temperature, K e = emissivity X = wavelength, m Introduction A parametric investigation has been conducted at the NASA Lewis Research Center in order to evaluate the effect of orifice aspect-ratio on the performance of low current hollow cathodes. The aspect-ratio is defined as the orifice length divided by its diameter. The NSTAR derivative ion thruster for the Deep Space 4 mission, the plasma contactor for the International Space Station, and the NASA Lewis 8 cm ion thruster program all have requirements for low flow rate, low power cathodes.' Experimental data' exist both to support and to refute the hypothesis that cathode performance is inversely proportional to the orifice aspect-ratio. A recent hollow cathode model developed by Mandell and Katz describes the physics leading to the conclusion that cathode performance scales inversely with orifice aspect-ratio. Ions entering a finite length orifice will undergo collisions as they traverse the channel. Ions lost to collisions with the walls must be balanced by ions created in the orifice in order to satisfy the condition of a quasineutral plasma at the exit of the orifice. As orifice aspect-ratio increases, the number of ionizations occurring increases, and the conductivity of the plasma in the orifice decreases. The energy transport within the orifice also varies inversely with the aspect-ratio, and modeling the orifice processes becomes increasingly important to making an accurate prediction about the performance of the cathode. The physical arguments for the importance of orifice aspect-ratio to cathode performance are sufficiently compelling to warrant a new evaluation of the experimentally observed effects, particularly when trying to minimize the power consumption during low current operation. This report summarizes the experimental findings concerning the impact of * Graduate Student Researcher, Student Member AIAA 1 Associate Professor, Senior Member AIAA * Research Engineer, Member AIAA Copyright © 1998 by Matthew T. Domonkos. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. 1 American Institute of Aeronautics and Astronautics orifice aspect-ratio on the power consumption of low current hollow cathodes. Although the current density in the orifice far exceeds that found anywhere else in a plasma contactor, ion thruster, or Hall thruster, previous modeling efforts' have ignored the effects of the orifice processes on the overall performance. Mandell and Katz have proposed a model which conserves both energy and ions necessary for quasineutrality. The model assumes the plasma properties at the entrance to the orifice are known. The ion loss to the walls of the orifice is balanced by electron-neutral collisional ionization. The Ohmic heating in the plasma is balanced by the ionization, radiative, and convective losses. With the orifice region taken as a control volume, the flux of ions incident at the entrance will either collide with the walls or be transmitted through the orifice. Since ion-wall collisions represent a loss in the energy balance, optimization of power consumption requires minimization of the orifice aspect-ratio. Typically in orificed hollow cathodes, the maximum required current determines the orifice diameter. While the theoretical picture indicates that orifice length should then be minimized, practical considerations force a finite length orifice. The machining and welding methods currently employed to fabricate the cathode tubes require a certain minimum overall thickness of the orifice plate. Rawlin and Kerslake9 were among the first investigators to observe the erosion of the orifice plates on hollow cathodes, and increasing the thickness of the orifice plate would, to first order, mitigate the problem of erosion. The goal of the investigation reported here was to provide experimental data for comparison with Mandell and Katz's5 model while meeting the practical considerations for cathode design. This paper presents the results of a parametric experimental investigation of the effects of the orifice aspect-ratio on the power consumption of 3.2 mm diameter orificed hollow cathodes. The experimental apparatus and techniques are described first. Next, the performance data are presented. The results are then analyzed with an emphasis on the performance, and the implications for cathode lifetime are also discussed. Finally, the major conclusions of this investigation are summarized. Experimental Apparatus Four 3.2 mm outer-diameter hollow cathodes with different orifice aspect-ratios were assembled as shown in Figure 1. The construction of the hollow cathodes closely followed the methods developed previously at the NASA Lewis Research Center.10-11 The orifice plates were machined on a lathe. Figure 2 illustrates the variation in the aspect-ratios for three of the cathodes tested. Although some dimensions of this schematic were exaggerated for clarity, the orifice plate dimensions, the cathode-keeper gap (Lck), and the keeper orifice diameter (dj are all drawn to scale. For convenience, the cathodes are referred to in this paper as AR1, AR3, and AR6 for the orifices with aspect-ratios of 1, 3, and 6, respectively. The fourth cathode had an orifice diameter forty percent smaller than the other cathodes and an aspect-ratio of approximately 3; it will be referred to as AR3' here. The orifice plates were electron beam welded to a refractory metal alloy tube with a 3.2 mm outer diameter. The electron emitter was a cylinder of sintered porous tungsten impregnated with 4BaOCaO-Al2O3 and was located at the downstream end of the tube. The emitter outer diameter was nominally 0.38 mm smaller than the inner diameter of the tube. Cathode Tube with Insert Propellant Isolator Keeper Thermocouple — Heater Electrical Stand-Offs Mounting Bracket a) Schematic for the Hollow Cathode Assemblies b) IPhotbgraph Figure 1 The Hollow Cathode Assembly Refractory metal electrical leads attached to the upstream end of the emitter were swaged into electrical contact the with cathode tube. This also fixed the position of the emitter within the cathode American Institute of Aeronautics and Astronautics tube. A sheathed heater was wound and friction fit to the end of the cathode tube. Metal foil was wrapped tightly around the outside of the heater to function as a radiation shield.

Collision Probability with Gaussian Mixture Orbit Uncertainty

The rise of the internet and the increasingly symbiotic relationship between designers and computers have both made information increasingly easy to acquire and have changed the way design is carried out. At the same time, the ease with which information can be gathered has created demand for faster, more flexible design processes. Today, geographically distributed designers can take part in a design by breaking the design process down into smaller, independent tasks. In this situation, both computers and fellow designers become the assets that are necessary to carry out the process of product realization. Each asset provides the lead designer with a service that could be based solely on the experience of other designers or on the software tools available for use over the Internet. The heterogeneous nature of these available assets brings into light a need for a systematic means of exchanging design information and knowledge. The question that arises is: “How can these assets be integrated and used in the design process?” In this paper, we present a framework for integrating various activities along the design time line. The framework is based on XML based standards for communication between various software services and achieving interoperability between them. Simple Object Access Protocol (SOAP) is used as an underlying mechanism for transferring messages between different assets. We also discuss the model used to deploy, search for, and manage the available services on the Internet. Lastly, we discuss the management of the information that is generated as a natural byproduct of the process of product realization. We present an example in which the use of the web-based framework and information management model is demonstrated by using them to integrate the distributed services that make up the Technology Identification, Evaluation, and Selection (TIES) method, a conceptual design exploration method that has already been demonstrated in the literature. We close the paper with discussion of what has been shown and look towards the future of this ongoing work, paying particular attention to its use in a future strategic design framework. 1. FRAME OF REFERENCE Today, industrial enterprises are found spread out all over the world. Companies are expanding their base of operations in a search for cheaper labor, materials, or land, or as a way of bringing manufacturing closer to the targeted market. As this trend continues into the foreseeable future, engineers may increasingly find themselves working on the realization of products that could be designed in one location, built in another, marketed to consumers in a third region, and supported or serviced by a group elsewhere. Given this vision of the future, it is not too much of a stretch to also imagine that the design teams in such enterprises might themselves be split up, with members of the teams distributed amongst the company’s many worldwide locations. While some newer technologies such as broadband internet and cellular phones have eased the barrier that distance creates to verbal and written communication between individual co-workers, there is still a great deal of work to be done in facilitating the meaningful sharing of engineering information and in facilitating or approximating the same sort of collaborative environment that exists when designers are working in the same location. * Graduate Research Assistant, AIAA Student Member § Graduate Research Assistant, AIAA Student Member ¶ Associate Professor # Senior Research Scientist, AIAA Senior Member ** Professor and Corresponding Author, AIAA Associate Fellow. Email: farrokh.mistree@me.gatech.edu. Phone: (404) 894-8412