Turbofan forced mixer-nozzle internal flowfield. Volume 3: A computer code for 3-D mixing in axisymmetric nozzles

A finite difference method is developed for making detailed predictions of three dimensional subsonic turbulent flow in turbofan lobe mixers. The governing equations are solved by a forward-marching solution procedure which corrects an inviscid potential flow solution for viscous and thermal effects, secondary flows, total pressure distortion and losses, internal flow blockage and pressure drop. Test calculations for a turbulent coaxial jet flow verify that the turbulence model performs satisfactorily for this relatively simple flow. Lobe mixer flows are presented for two geometries typical of current mixer design. These calculations included both hot and cold flow conditions, and both matched and mismatched Mach number and total pressure in the fan and turbine streams

Prediction of laminar and turbulent primary and secondary flows in strongly curved ducts

The analysis is based on a primary secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial value problem in space using an implicit forward marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The solution procedure is effective even with the extreme local mesh resolution which is necessary to solve near wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compared very favorably with available analytical and experimental results. The overall method appears very promising as an economical procedure for making detailed predictions of viscous primary and secondary flows in highly curved passages

Acceleration of protons at 32 Jovian radii in the outer magnetosphere of jupiter

During the inbound pass of Pioneer 10, a rapid ten-fold increase of the 0.2 to MeV proton flux was observed at 32 Jovian radii (R sub J). The total event lasted for 30 minutes and was made up of a number of superimposed individual events. At the time, the spacecraft was in the outer magnetosphere about 7 R sub J below the magnetic equator. Before and after the event, the proton flux was characteristic of the low flux level normally encountered between crossings of the magnetic equator. Flux changes at different energies were coherent within 1 minute; a time comparable to the time resolution of the data. The angular distributions were highly anisotropic with protons streaming towards Jupiter. A field-aligned dumbbell distribution was observed initially, and a pancake distribution just before the flux decayed to its pre-event value. The alpha particle flux changed as rapidly as the proton flux but peaked at different times. The energetic electron flux behaved differently; it increased gradually throughout the period

The application of S isotopes and S/Se ratios in determining ore-forming processes of magmatic Ni–Cu–PGE sulfide deposits: a cautionary case study from the northern Bushveld Complex

The application of S/Se ratios and S isotopes in the study of magmatic Ni–Cu–PGE sulfide deposits has long been used to trace the source of S and to constrain the role of crustal contamination in triggering sulfide saturation. However, both S/Se ratios and S isotopes are subject to syn- and post-magmatic processes that may alter their initial signatures. We present in situ mineral δ34S signatures and S/Se ratios combined with bulk S/Se ratios to investigate and assess their utility in constraining ore-forming processes and the source of S within magmatic sulfide deposits. Magmatic Ni–Cu–PGE sulfide mineralization in the Grasvally Norite–Pyroxenite–Anorthosite (GNPA) member, northern Bushveld Complex was used as a case study based on well-defined constraints of sulfide paragenesis and local S isotope signatures. A crustal δ34S component is evident in the most primary sulfide assemblage regardless of footwall lithology, and is inferred that the parental magma(s) of the GNPA member was crustally contaminated and sulfide saturated at the time of emplacement. However, S/Se ratios of both the primary and in particular secondary sulfide assemblages record values within or below the mantle range, rather than high crustal S/Se ratios. In addition, there is a wide range of S/Se ratio for each sulfide mineral within individual assemblages that is not necessarily consistent with the bulk ratio. The initial crustal S/Se ratio is interpreted to have been significantly modified by syn-magmatic lowering of S/Se ratio by sulfide dissolution, and post-magmatic lowering of the S/Se ratio from hydrothermal S-loss, which also increases the PGE tenor of the sulfides. Trace element signatures and variations in Th/Yb and Nb/Th ratios support both an early pre-emplacement contamination event as seen by the S isotopes and S/Se ratios, but also a second contamination event resulting from the interaction of the GNPA magma with the local footwall country rocks at the time of emplacement; though this did not add any additional S. We are able to present an integrated emplacement and contamination model for the northern limb of the Bushveld Complex. Although the multitude of processes that affect variations in the δ34S signature and in particular S/Se ratio may be problematic in interpreting ore genesis, they can reveal a wealth of additional detail on a number of processes involved in the genetic history of a Ni–Cu–PGE deposit in addition to crustal contamination. However, a prerequisite for being able to do this is to utilize other independent petrological and mineralogical techniques that provide constraints on both the timing and effect of various ore-forming and modifying processes. Utilizing both bulk and in situ methods in concert to determine the S/Se ratio allows for the assessment of multiple sulfide populations, the partitioning behaviour of Se during sulfide liquid fractionation and also the effects of low temperature fluid alteration. In comparison, S isotopes are relatively more robust and represent a more reliable indicator of the role of crustal S contamination. The addition of trace element data to the above makes for an incredibly powerful approach in assessing the role of crustal contamination in magmatic sulfide systems

Further development of a method for computing three-dimensional subsonic viscous flows in turbofan lobe mixers

Procedure for computing subsonic, turbulent flow in turbofan lobe mixers was extended to allow consideration of flow fields in which a swirl component of velocity may be present. Additional, an optional k-lambda turbulence model was added to the procedure. The method of specifying the initial flow field was also modified, allowing parametric specification or radial secondary flow velocities, and making it possible to consider initial flow fields which have significant inlet secondary flow vorticity. A series of example calculations was performed which demonstrate the various capabilities of the modified code. These calculations demonstrate the effects of initial secondary flows of various magnitudes, the effects of swirl, and the effects of turbulence model on the mixing process. The results of these calculations indicate that the initial secondary flows, presumed to be generated within the lobes, play a dominant role in the mixing process, and that the predicted results are relatively insensitive to the turbulence model used

Energetic protons in the Jovian magnetosphere

The time histories, angular distributions and energy spectra of energetic protons were measured over an energy range extending from 0.2 - 20 MeV for the four passes of Pioneers 10 and 11 through the Jovian magnetosphere. Azimuthal asymmetries appear to dominate with time variations also contributing to the very complex topology. On the inbound P-10 pass the expected corotation anisotropy was not observed in the outer magnetosphere supporting the probable existence of a planetary wind in this region. Near the dawn meredian particle streaming away from the planet begins at about 15 RJ. On both the P-10 inbound and P-11 outbound passes, there are regions where only partial corotation is achieved. In the mid-magnetosphere, field-aligned streaming away from the near-equatorial current sheet region is the most prominent feature. At mid-latitudes in the subsolar regime, the streaming pattern is more chaotic and its magnitude is smaller. Qualitative discussions are presented for a number of possible mechanisms which could produce this streaming

Energetic particles in the pre-dawn magnetotail of Jupiter

A detailed account is given of the energetic electron and proton populations as observed with Voyagers 1 and 2 during their passes through the dawn magnetotail of Jupiter. The region between 20 and 150 R sub J is dominated by a thin plasma sheet, where trapped energetic electron and proton fluxes reach their maximum. Proton spectra can be represented by an exponential in rigidity with a characteristic energy of approximately 50 keV. Proton anisotropies were consistent with corotation even at 100 R sub J. A major proton acceleration event as well as several cases of field aligned proton streaming were observed. The flux of 0.4 MeV protons decreases by three orders of magnitude between 30 and 90 R sub J and then remains relatively constant to the magnetopause. Fine structure in the data indicate longitudinal asymmetries with respect to the dipole orientation. Electron spectra in the magnetosheath and interplanetary space are modulated by the Jovian longitude relative to the subsolar point

Coupling Non-Gravitational Fields with Simplicial Spacetimes

The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of coupling source to the lattice in Regge calculus.Comment: 10 pages, no figures, Latex, fixed typos and minor corrections