Measurement and analysis of a small nozzle plume in vacuum

Pitot pressures and flow angles are measured in the plume of a nozzle flowing nitrogen and exhausting to a vacuum. Total pressures are measured with Pitot tubes sized for specific regions of the plume and flow angles measured with a conical probe. The measurement area for total pressure extends 480 mm (16 exit diameters) downstream of the nozzle exit plane and radially to 60 mm (1.9 exit diameters) off the plume axis. The measurement area for flow angle extends to 160 mm (5 exit diameters) downstream and radially to 60 mm. The measurements are compared to results from a numerical simulation of the flow that is based on kinetic theory and uses the direct-simulation Monte Carlo (DSMC) method. Comparisons of computed results from the DSMC method with measurements of flow angle display good agreement in the far-field of the plume and improve with increasing distance from the exit plane. Pitot pressures computed from the DSMC method are in reasonably good agreement with experimental results over the entire measurement area

Discussion quality diffuses in the digital public square

Studies of online social influence have demonstrated that friends have important effects on many types of behavior in a wide variety of settings. However, we know much less about how influence works among relative strangers in digital public squares, despite important conversations happening in such spaces. We present the results of a study on large public Facebook pages where we randomly used two different methods--most recent and social feedback--to order comments on posts. We find that the social feedback condition results in higher quality viewed comments and response comments. After measuring the average quality of comments written by users before the study, we find that social feedback has a positive effect on response quality for both low and high quality commenters. We draw on a theoretical framework of social norms to explain this empirical result. In order to examine the influence mechanism further, we measure the similarity between comments viewed and written during the study, finding that similarity increases for the highest quality contributors under the social feedback condition. This suggests that, in addition to norms, some individuals may respond with increased relevance to high-quality comments.Comment: 10 pages, 6 figures, 2 table

The effect of composition on the mechanism of stress-corrosion cracking of titanium alloys in nitrogen tetroxide, and aqueous and hot- salt environments Annual summary report, 1 May 1967 - 30 Apr. 1968

Stress corrosion data for titanium alloys in aqueous, hot salt, and nitrogen dioxide environment

Detailed modeling and analysis of spacecraft plume/ionosphere interactions in low Earth orbit

Detailed direct simulation Monte Carlo/particle‐in‐cell simulations involving the interaction of spacecraft thruster plumes with the rarefied ambient ionosphere are presented for steady thruster firings in low Earth orbit (LEO). A nominal mass flow rate is used to prescribe the rocket exit conditions of a neutral propellant species for use in the simulations. The charge exchange interactions of the steady plume with the rarefied ionosphere are modeled using a direct simulation Monte Carlo/particle‐in‐cell methodology, allowing for a detailed assessment of nonequilibrium collisional and plasma‐related phenomena relevant for these conditions. Results are presented for both ram‐ and wake‐flow configurations, in which the thrusters are firing into (ram) or in the direction of (wake) the free stream ionosphere flow in LEO. The influence of the Earth's magnetic field on the development of the ion plume is also examined for three different field strengths: two limiting cases in which B →0 and B → ∞ , and the LEO case in which B =0.5 Gs. The magnetic field is found to have a substantial impact on the resulting neutral and ion plumes, and the gyroscopic motion of the magnetized ions results in a broadening of the ion energy distribution functions. The magnetic field model also incorporates a cross‐field diffusion mechanism which is shown to increase the current density sampled far from the thruster. Key Points Particle‐based model for plume/ionosphere interactions Charge‐exchange reactions modeled using detailed DCS/TCS data B ‐field has a strong influence on the development of plumesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106930/1/jgra50833.pd

Spacecraft plume interactions with the magnetosphere plasma environment in geostationary Earth orbit

Particle‐based kinetic simulations of steady and unsteady hydrazine chemical rocket plumes are presented in a study of plume interactions with the ambient magnetosphere in geostationary Earth orbit. The hydrazine chemical rocket plume expands into a near‐vacuum plasma environment, requiring the use of a combined direct simulation Monte Carlo/particle‐in‐cell methodology for the rarefied plasma conditions. Detailed total and differential cross sections are employed to characterize the charge exchange reactions between the neutral hydrazine plume mixture and the ambient hydrogen ions, and ion production is also modeled for photoionization processes. These ionization processes lead to an increase in local plasma density surrounding the spacecraft owing to a partial ionization of the relatively high‐density hydrazine plume. Results from the steady plume simulations indicate that the formation of the hydrazine ion plume are driven by several competing mechanisms, including (1) local depletion and (2) replenishing of ambient H+ ions by charge exchange and thermal motion of 1 keV H+ from the ambient reservoir, respectively, and (3) photoionization processes. The self‐consistent electrostatic field forces and the geostationary magnetic field have only a small influence on the dynamics of the ion plume. The unsteady plume simulations show a variation in neutral and ion plume dissipation times consistent with the variation in relative diffusion rates of the chemical species, with full H2 dissipation (below the ambient number density levels) approximately 33 s after a 2 s thruster burn.Key PointsSpacecraft hydrazine plume interacts with GEO via charge exchange and photoionization processesMagnetized hydrazine ion plumes envelop spacecraft, and neutral plumes convect downstreamIon and neutral plume dissipation times longer and species‐dependentPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135463/1/jgra52433_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135463/2/jgra52433.pd

Solving rank-constrained semidefinite programs in exact arithmetic

We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active, this is a non-convex optimization problem, otherwise it is a semidefinite program. Both find numerous applications especially in systems control theory and combinatorial optimization, but even in more general contexts such as polynomial optimization or real algebra. While numerical algorithms exist for solving this problem, such as interior-point or Newton-like algorithms, in this paper we propose an approach based on symbolic computation. We design an exact algorithm for solving rank-constrained semidefinite programs, whose complexity is essentially quadratic on natural degree bounds associated to the given optimization problem: for subfamilies of the problem where the size of the feasible matrix is fixed, the complexity is polynomial in the number of variables. The algorithm works under assumptions on the input data: we prove that these assumptions are generically satisfied. We also implement it in Maple and discuss practical experiments.Comment: Published at ISSAC 2016. Extended version submitted to the Journal of Symbolic Computatio

Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time-protocols of the outer force exist under which the operation is reversible and the ideal value of efficiency is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures

Modeling of Stardust Entry at High Altitude, Part 2: Radiation Analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83561/1/AIAA-37357-833.pd

Analyses of the anode region of a Hall Thruster cahnnel

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77093/1/AIAA-2002-4107-729.pd

Plasma flow and plasma–wall transition in Hall thruster channel

In this paper a model of the quasineutral plasma and the transition between the plasma and the dielectric wall in a Hall thruster channel is developed. The plasma is considered using a two-dimensional hydrodynamic approximation while the sheath in front of the dielectric surface is considered to be one dimensional and collisionless. The dielectric wall effect is taken into account by introducing an effective coefficient of the secondary electron emission (SEE), s. In order to develop a self-consistent model, the boundary parameters at the sheath edge (ion velocity and electric field) are obtained from the two-dimensional plasma bulk model. In the considered condition, i.e., ion temperature much smaller than that of electrons and significant ion acceleration in the axial direction, the presheath scale length becomes comparable to the channel width so that the plasma channel becomes an effective presheath. It is found that the radial ion velocity component at the plasma–sheath interface varies along the thruster channel from about 0.5Cs0.5Cs (Cs(Cs is the Bohm velocity) near the anode up to the Bohm velocity near the exit plane dependent on the SEE coefficient. In addition, the secondary electron emission significantly affects the electron temperature distribution along the channel. For instance in the case of s = 0.95,s=0.95, the electron temperature peaks at about 16 eV, while in the case of s = 0.8s=0.8 it peaks at about 30 eV. The predicted electron temperature is close to that measured experimentally. The model predictions of the dependence of the current–voltage characteristic of the E×BE×B discharge on the SEE coefficient are found to be consistent with experiment. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70923/2/PHPAEN-8-12-5315-1.pd