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Every Jordan isomorphism of triangular n¡Ñn matrices over F with characteristic 2 is either a isomorphism or a antiisomorphism while n is 2. But it is not true for n ¡Ù 3.

Isothermal, incompressible jets of air issuing from sharp-edged isosceles triangular orifices with apex angles of 10°, 20°, 30°, 70° and 160° into still surrounding air, were used to study the effects of apex angle variation on flow development in the jets. Some measurements were made in two round jets issuing from a sharp-edged orifice and from a contoured nozzle. The mean streamwise centreline velocity decay, mass entrainment and spreading results show that the 160° jet, which originates from the orifice with the longest perimeter, has the highest mixing rate in the near flow field. The results also suggest that the 10° jet, which originates from the orifice with the second longest perimeter, has the highest mixing rate in the far field. The results demonstrate that all the triangular jets have higher mixing rates than the round jets, throughout the flow region investigated.

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This thesis reports on the structure of the flow inside a nozzle which produces a naturally oscillating jet flow. The nozzle consists of a short cylindrical chamber with a concentric triangular-inlet orifice at one end and a circular exit lip at the other end. This triangular-jet nozzle was developed from the “fluidic-precessing-jet” (FPJ) nozzle, which has a similar arrangement of components, but has a circular rather than a triangular inlet. For reliably oscillating flow, the FPJ nozzle should have an inlet-to-chamber expansion ratio of at least 5.0, a chamber lengthto- diameter ratio between 2.6 and 2.8, and an exit-lip height of about 0.1 chamber diameters. The triangular-jet nozzle produces a continuously and aperiodically oscillating jet flow which is different from the FPJ flow. The oscillation occurs at smaller inlet-to-chamber expansion ratios (2.1 ≲ D /de₁ ≲ 3.5) and over a wider range of chamber lengths (2.0 ≲ L /D ≲ 2.5). The initial spreading angle of the jet flow is smaller, but is still much larger than that of non-oscillating, axisymmetric turbulent-jet flows. In addition, the external “oscillating-triangular-jet” (OTJ) flow has preferred azimuthal directions which are aligned with the three corners of the orifice. The kinetic-energy-loss coefficient of the OTJ nozzle is much smaller than that of the FPJ nozzle because oscillation occurs at much smaller inlet-to-chamber expansion ratios. For a narrow range of length-to-diameter ratios (1.00 ≲ L/D ≲ 1.25), the triangular-inlet nozzle can also produce a non-oscillating or “stationary deflected triangular jet” (SDTJ) which reattaches asymmetrically to the inside surface of the cylindrical chamber. The SDTJ has a weak tendency to oscillate, which suggests that flow patterns required for self-excited oscillation are already present in the SDTJ flow. Surface-flow visualisation and surface-pressure measurements in the SDTJ nozzle have provided the location of critical points and bifurcation lines on the chamber wall, and from this the topology of the SDTJ flow is deduced. Some details of the flow such as a jet-reattachment node near the chamber exit and a strong swirl adjacent to the inlet orifice are known from previous studies of the FPJ flow, but there are many newly observed features. The most easily identified of these are two sink-focus separation points, one on each side of the reattachment node but closer to the inlet plane. The foci counter rotate and are of unequal size. Reverse flow through the exit plane of the chamber is attracted to the larger focus. The vortex core rising from each focus is entrained by the reattaching-jet (SDTJ) flow and is drawn out of the chamber. A backward-facing pressure probe placed in the OTJ “reattaching-flow” region of chamber wall can be used as a reliable detector of jet-flow oscillation. Cross-correlating the signal from this detector probe with simultaneous static-pressure measurements elsewhere on the chamber wall gives a conditionally-averaged pressure on the wall of the OTJ chamber. The OTJ wall-pressure distribution has the same features as the SDTJ surface-pressure distribution, but it has greater asymmetry about a mirror plane drawn through the chamber axis and the detector probe. An array of three backward-facing pressure probes has been used as an “event detector” for conditionally-sampled (PIV) measurements of non-axial velocity components in cross-sections of the OTJ nozzle. The event-detection scheme responds only to a preselected (counter-clockwise) direction of motion of the oscillating-jet flow. The streamline patterns constructed from the conditionally-sampled measurements confirm the presence of the jet-reattachment node, the swirl and the sink foci identified from the SDTJ surface-flow visualisation. The shear-layer interaction between the jet from the triangular orifice and the swirl (adjacent to the inlet plane) produces strong longitudinal vortices in the ensemble-averaged flow. The jet flow distributes these vortices through the length of the chamber. Vortex cores representing the vortices are reconstructed by tracking streamline foci from one PIV cross-section plane to another. The tracking process includes the connection and termination of vortex cores in a manner which is consistent with the Helmholtz vortex law. In this flow field, the vortex core produced by the swirl and the vortex core rising from the larger sink-focus vortex on the chamber wall are connected to form a loop. The extent to which this vortex loop is contained within the chamber determines whether or not the flow is oscillating. If only a small fraction (e.g. 8%) of the vortex circulation passes through the exit plane of the nozzle, the loop is trapped inside the chamber and the deflected jet oscillates. If the length of the chamber is halved, about 35% of vortex circulation escapes from the nozzle and the oscillation stops. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1353005 / Thesis (Ph.D.) - University of Adelaide, School of Mechanical Engineering, 2009

This thesis reports on the structure of the flow inside a nozzle which produces a naturally oscillating jet flow. The nozzle consists of a short cylindrical chamber with a concentric triangular-inlet orifice at one end and a circular exit lip at the other end. This triangular-jet nozzle was developed from the “fluidic-precessing-jet” (FPJ) nozzle, which has a similar arrangement of components, but has a circular rather than a triangular inlet. For reliably oscillating flow, the FPJ nozzle should have an inlet-to-chamber expansion ratio of at least 5.0, a chamber lengthto- diameter ratio between 2.6 and 2.8, and an exit-lip height of about 0.1 chamber diameters. The triangular-jet nozzle produces a continuously and aperiodically oscillating jet flow which is different from the FPJ flow. The oscillation occurs at smaller inlet-to-chamber expansion ratios (2.1 ≲ D /de₁ ≲ 3.5) and over a wider range of chamber lengths (2.0 ≲ L /D ≲ 2.5). The initial spreading angle of the jet flow is smaller, but is still much larger than that of non-oscillating, axisymmetric turbulent-jet flows. In addition, the external “oscillating-triangular-jet” (OTJ) flow has preferred azimuthal directions which are aligned with the three corners of the orifice. The kinetic-energy-loss coefficient of the OTJ nozzle is much smaller than that of the FPJ nozzle because oscillation occurs at much smaller inlet-to-chamber expansion ratios. For a narrow range of length-to-diameter ratios (1.00 ≲ L/D ≲ 1.25), the triangular-inlet nozzle can also produce a non-oscillating or “stationary deflected triangular jet” (SDTJ) which reattaches asymmetrically to the inside surface of the cylindrical chamber. The SDTJ has a weak tendency to oscillate, which suggests that flow patterns required for self-excited oscillation are already present in the SDTJ flow. Surface-flow visualisation and surface-pressure measurements in the SDTJ nozzle have provided the location of critical points and bifurcation lines on the chamber wall, and from this the topology of the SDTJ flow is deduced. Some details of the flow such as a jet-reattachment node near the chamber exit and a strong swirl adjacent to the inlet orifice are known from previous studies of the FPJ flow, but there are many newly observed features. The most easily identified of these are two sink-focus separation points, one on each side of the reattachment node but closer to the inlet plane. The foci counter rotate and are of unequal size. Reverse flow through the exit plane of the chamber is attracted to the larger focus. The vortex core rising from each focus is entrained by the reattaching-jet (SDTJ) flow and is drawn out of the chamber. A backward-facing pressure probe placed in the OTJ “reattaching-flow” region of chamber wall can be used as a reliable detector of jet-flow oscillation. Cross-correlating the signal from this detector probe with simultaneous static-pressure measurements elsewhere on the chamber wall gives a conditionally-averaged pressure on the wall of the OTJ chamber. The OTJ wall-pressure distribution has the same features as the SDTJ surface-pressure distribution, but it has greater asymmetry about a mirror plane drawn through the chamber axis and the detector probe. An array of three backward-facing pressure probes has been used as an “event detector” for conditionally-sampled (PIV) measurements of non-axial velocity components in cross-sections of the OTJ nozzle. The event-detection scheme responds only to a preselected (counter-clockwise) direction of motion of the oscillating-jet flow. The streamline patterns constructed from the conditionally-sampled measurements confirm the presence of the jet-reattachment node, the swirl and the sink foci identified from the SDTJ surface-flow visualisation. The shear-layer interaction between the jet from the triangular orifice and the swirl (adjacent to the inlet plane) produces strong longitudinal vortices in the ensemble-averaged flow. The jet flow distributes these vortices through the length of the chamber. Vortex cores representing the vortices are reconstructed by tracking streamline foci from one PIV cross-section plane to another. The tracking process includes the connection and termination of vortex cores in a manner which is consistent with the Helmholtz vortex law. In this flow field, the vortex core produced by the swirl and the vortex core rising from the larger sink-focus vortex on the chamber wall are connected to form a loop. The extent to which this vortex loop is contained within the chamber determines whether or not the flow is oscillating. If only a small fraction (e.g. 8%) of the vortex circulation passes through the exit plane of the nozzle, the loop is trapped inside the chamber and the deflected jet oscillates. If the length of the chamber is halved, about 35% of vortex circulation escapes from the nozzle and the oscillation stops. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1353005 / Thesis (Ph.D.) - University of Adelaide, School of Mechanical Engineering, 2009

This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.

Experimental study was conducted to investigate fluidelastic instability in finned tube bundles with normal and parallel triangular arrays. Three arrays of each geometry type were studied experimentally: two arrays with serrated, helically wound finned tubes of different fin densities, and a bare tube array with the same base diameter as the finned tubes. The finned tubes under consideration were commercial finned tubes typically used in the fossil and process industries. For the purpose of the present investigation, the concept of "effective diameter" of a finned tube, as used to predict the vortex shedding, was used to compare the finned tube results with the existing bare tube world data and some theoretical predictions for fluidelastic instability. The finned tube arrays in this study have the same tube pitch and have been scaled to have the same mass ratio and tuned to have the same natural frequency. A low speed wind tunnel, Betz micro manometer and HP 35670a dynamic signal analyzer were employed to conduct the experiments. Experimental results for the triangular arrays show that the fin's structure strongly influences the fluidelastic stability of finned tube bundles and the fin pitch is demonstrated to reduce the difference in the fluidelastic instability between the tube arrangements as the fin density increases. The results also suggest that there might be an optimum fin pitch value at which the threshold reduced velocity for a finned tube array is much higher than the one for its corresponding bare tube array, due to the influence of fin geometry. In the appendix, an analytical model produces a new correlation of critical reduced velocity against mass damping parameter to predict the fluidelastic instability of tube bundles. Its predictions are in reasonable agreement with the experimental data. Since negative damping is one of the mechanisms of fluidelastic instability of a tube array, "Lift effect" was applied to explain the negative damping in an inviscid flow. An experiment is suggested to test the relationship between the pitch flow velocity and a tube velocity dependent "lift effect". Accordingly, two duct structure designs are suggested which may alleviate the negative damping by using the energy of oncoming flow to reduce the "lift effect" on the tubes. / Thesis / Master of Applied Science (MASc)

The main focus of this thesis is to develop full parametric and semiparametric Bayesian inference for data arising from triangular distributions. A natural consequence of working with such distributions is it allows one to consider regression models where the response variable is now the mode of the data distribution. A new family of nonparametric prior distributions is developed for a certain class of convex densities of particular relevance to mode regressions. Triangular distributions arise in several contexts such as geosciences, econometrics, finance, health care management, sociology, reliability engineering, decision and risk analysis, etc. In many fields, experts, typically, have a reasonable idea about the range and most likely values that define a data distribution. Eliciting these quantities is thus, generally, easier than eliciting moments of other commonly known distributions. Using simulated and actual data, applications of triangular distributions, with and without mode regressions, in some of the aforementioned areas are tackled. / text