Solar UV Geometric Conversion Factors: Horizontal Plane to Cylinder Model†

Most solar UV measurements are relative to the horizontal plane. However, problems arise when one uses those UV measurements to perform risk or benefit assessments because they do not yield the actual doses people get while they are outdoors. To better estimate the UV doses people actually get while outdoors, scientists need geometric conversion factors (GCF) that change horizontal plane irradiances to average irradiances on the human body. Here we describe a simple geometric method that changes unweighted, erythemally weighted and previtamin D₃-weighted UV irradiances on the horizontal plane to full cylinder and semicylinder irradiances. Scientists can use the full cylinder model to represent the complete human body, while they can use the semicylinder model to represent the face, shoulders, tops of hands and feet. We present daily, monthly and seasonally calculated averages of the GCF for these cylinder models every 5° from 20 to 70°N so that scientists can now get realistic UV doses for people who are outdoors doing a variety of different activities. The GCF show that people actually get less than half their annual erythemally weighted, and consequently half their previtamin D₃-weighted, UV doses relative to the horizontal plane. Thus, scientists can now perform realistic UV risk and benefit assessments.     

Time-averaging strategies in the finite-volume/particle hybrid algorithm for the joint PDF equation of turbulent reactive flows

The influence of time-averaging on bias is investigated in the finite-volume/particle hybrid algorithm for the joint PDF equation for statistically-stationary turbulent reactive flows. It is found that the time-averaging of the mean fluctuating velocity (TAu) leads to the same variances of the fluctuating velocity before and after the velocity correction, whereas without TAu the estimates are different, and an additional numerical dissipation rate is introduced for the turbulent kinetic energy (TKE). When 100 particles per cell are used without TAu, a large bias error is found to be involved in the unconditional statistics of the statistically-stationary solutions of two tested turbulent flames, the Cabra H₂/N₂ lifted flame and the Sandia piloted flame E. The use of TAu reduces this bias dramatically for the same number of particles per cell. The conditional statistics in these flames, however, are hardly affected by TAu. To a large extent, the effect of the bias error on the unconditional statistics is similar to the effect of increasing the model constant C _{ω 1} in the stochastic turbulence frequency model.     

PDF calculations of piloted premixed jet flames

A series of piloted premixed jet flames with strong finite-rate chemistry effects is studied using the joint velocity-turbulence frequency-composition PDF method. The numerical accuracy of the calculations is demonstrated, and the calculations are compared to experimental data. It is found that all calculations show good agreement with the measurements of mean and rms mixture fraction fields, while the reaction progress is overpredicted to varying degrees depending on the jet velocity. In the calculations of the flame with the lowest jet velocity, the species and temperature show reasonable agreement with the measurements, with the exception of a small region near the centerline where products and temperature are overpredicted and fuel and oxidizer are underpredicted. In the calculations of the flame with the highest jet velocity, however, the overprediction of products and temperature and underprediction of fuel and oxidizer is far more severe. An extensive set of sensitivity studies on inlet boundary conditions, turbulence model constants, mixing models and constants, radiation treatment, and chemical mechanisms is conducted to show that any parameter variation offers little improvement from the base case. To shed light on these discrepancies, diagnostic calculations are performed in which the chemical reactions are artificially slowed. These diagnostic calculations serve to validate the experimental data and to quantify the amount by which the base case calculations overpredict reaction progress. Improved calculations of this flame are achieved only through artificially slowing down the chemical reaction by a factor of about 10. The mixing model behavior in this combustion regime is identified as a likely cause for the observed discrepancy in reaction progress.     

Small scales,many species and the manifold challenges of turbulent combustion

A major goal of combustion research is to develop accurate, tractable, predictive models for the phenomena occurring in combustion devices, which predominantly involve turbulent flows. With the focus on gas-phase, non-premixed flames, recent progress is reviewed, and the significant remaining challenges facing models of turbulent combustion are examined. The principal challenges are posed by the small scales, the many chemical species involved in hydrocarbon combustion, and the coupled processes of reaction and molecular diffusion in a turbulent flow field. These challenges, and how different modeling approaches face them, are examined from the viewpoint of low-dimensional manifolds in the high-dimensional space of chemical species. Most current approaches to modeling turbulent combustion can be categorized as flamelet-like or PDF-like. The former assume or imply that the compositions occurring in turbulent combustion lie on very-low-dimensional manifolds, and that the coupling between turbulent mixing and reaction can be parameterized by at most one or two variables. PDF-like models do not restrict compositions in this way, and they have proved successful in describing more challenging combustion regimes in which there is significant local extinction, or in which the turbulence significantly disrupts flamelet structures. Advances in diagnostics, the design of experiments, computational resources, and direct numerical simulations are all contributing to the continuing development of more accurate and general models of turbulent combustion.     

New cohomogeneity one metrics with Spin(7) holonomy

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by , is complete and non-singular on . The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S⁴, and are denoted by , and . The metrics on and occur in families with a non-trivial parameter. The metric on arises for a limiting value of this parameter, and locally this metric is the same as the one for . The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on . We construct the covariantly constant spinor and calibrating 4-form. We also obtain an L²-normalisable harmonic 4-form for the manifold, and two such 4-forms (of opposite dualities) for the manifold.     

Orientifolds and slumps in G2 and Spin(7) metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by , which are complete on a complex line bundle over . The principal orbits are S⁷, described as a triaxially squashed S³ bundle over S⁴. The behaviour in the S³ directions is similar to that in the Atiyah–Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S⁴. We then consider new G₂ metrics which we denote by , which are complete on an bundle over T^1,1, with principal orbits that are S³×S³. We study the metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S² cycles, and both carry magnetic charge with respect to the R–R vector field. We also discuss some four-dimensional hyper-Kähler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(∞) Toda equation, which can provide a way of studying their interior structure.     

Application of higher-order flux-limited methods in compositional simulation

A higher-order flux-limited finite-difference scheme has been implemented into a compositional simulator to discretize the convection terms of the component conservation equations and the relative permeability terms of the phase fluxes. Harten's total variation diminishing criteria are imposed directly to the finite-difference equations and the bounds of the flux limiters which are suitable for larger Courant numbers and nonuniform grid systems are obtained. A time-correction technique is applied to increase the time accuracy and improve the stability condition.The scheme has been tested for miscible and immiscible flow problems in one and two dimensions, and the results were compared with those using a third-order method without flux limiting and some available analytical solutions.