Parameterizations of Entrainment-Mixing Mechanisms and Their Effects on Cloud Droplet Spectral Width Based on Numerical Simulations
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54 ENVIRONMENTAL SCIENCES↗
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Improved solar models constructed with a formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations
We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.
Lydon, Thomas J.↗
Three-dimensional computation of mixing of transverse injector in a ducted supersonic airstream
Numerical solutions of the three-dimensional mass-averaged elliptic Navier-Stokes equations, including species transport, are obtained for nonreacting, turbulent, mixing flow fields for the case of transverse sonic injection of a secondary gas into a supersonic airstream through a circular orifice injector. Results are presented for flow through a constant area duct and through a duct with a rearward-facing step upstream of the injector. The equations are numerically integrated using MacCormack's explicit method and turbulence is included using the Baldwin-Lomax algebraic eddy viscosity model. In the species transport and energy equations, diffusion coefficients based on Fick's law and an assumption of unit Lewis number are applied. The computations were performed on a CDC-VPS-32 (extended version of Cyber-205) using a grid consisting of approximately 200,000 points. The computed results are compared with experimentally observed penetration and spreading boundaries for an injected gas at two dynamic pressure ratios. Three-dimensional flow field structures are dipicted in terms of static pressure, mass fractions of species and velocity vectors.
Uenishi, K.↗
Mixed precision s –step Lanczos and conjugate gradient algorithms
Compared to the classical Lanczos algorithm, the s-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a price; despite being mathematically equivalent, the s-step variant may behave quite differently in finite precision, potentially exhibiting greater loss of accuracy and slower convergence relative to the classical algorithm. It has previously been shown that the errors in the s-step version follow the same structure as the errors in the classical algorithm, but are amplified by a factor depending on the square of the condition number of the O(s)-dimensional Krylov bases computed in each outer loop. As the condition number of these s-step bases grows (in some cases very quickly) with s, this limits the s values that can be chosen and thus can limit the attainable performance. In this work, we show that if a select few computations in s-step Lanczos are performed in double the working precision, the error terms then depend only linearly on the conditioning of the s-step bases. This has the potential for drastically improving the numerical behavior of the algorithm with little impact on per-iteration performance. Our numerical experiments demonstrate the improved numerical behavior possible with the mixed precision approach, and also show that this improved behavior extends to mixed precision s-step CG. Here, we present preliminary performance results on NVIDIA V100 GPUs that show that the overhead of extra precision is minimal if one uses precisions implemented in hardware.
97 MATHEMATICS AND COMPUTING↗
On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. III - A numerical solution
The results of a numerical computation of the interactions between the horizontally periodic monochromatic component of a large-scale coherent structure and the fine-grained turbulence in a mixing layer are presented. In the numerical calculations, the appropriate dependent variable is one which comprises both the mean and the large-scale coherent structure. The dynamical equations obtained for such a total coherent structure quantity are identical to the unsteady equations for the mean quantities in the Reynolds sense, except that the fine-grained turbulent stresses are interpreted as being conditionally averaged. It is shown how three dimensional fine-grained turbulence can be produced indirectly from the two dimensional large-scale structure via the isotropizing process of the approximated pressure-strain correlation.
Gatski, T. B.↗
Turbulent Mixing of Multiphase Flow
Thus we conduct numerical simulations of multiphase fluids stirred by two-dimensional turbulence to assess the possibility of self-similar drop size distribution in turbulence. In our turbulence simulations, we also explore the non-diffusive limit, where molecular mobility for the interface is vanishing. Special care is needed to transport the non-diffusive interface. Numerically, we use the particle level set method to evolve the interface. Instead of using the usual methods to calculate the surface tension force from the level set function, we reconstruct the interface based on phase- field modeling, and calculate the continuum surface tension forcing from the reconstructed interface.
Young, Y.-N.↗
Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams
Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.
Noor, A. K.↗
Detailed characteristics of drop-laden mixing layers: LES predictions compared to DNS
Results have been compared from Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of a temporal mixing layer laden with evaporating drops, to assess the ability of LES to reproduce detailed characteristics of DNS.
large eddy simulation↗
A Priori Analysis of Subgrid-Scale Models for Large Eddy Simulations of Supercritical Binary-Species Mixing Layers
Models for large eddy simulation (LES) are assessed on a database obtained from direct numerical simulations (DNS) of supercritical binary-species temporal mixing layers. The analysis is performed at the DNS transitional states for heptane/nitrogen, oxygen/hydrogen and oxygen/helium mixing layers. The incorporation of simplifying assumptions that are validated on the DNS database leads to a set of LES equations that requires only models for the subgrid scale (SGS) fluxes, which arise from filtering the convective terms in the DNS equations. Constant-coefficient versions of three different models for the SGS fluxes are assessed and calibrated. The Smagorinsky SGS-flux model shows poor correlations with the SGS fluxes, while the Gradient and Similarity models have high correlations, as well as good quantitative agreement with the SGS fluxes when the calibrated coefficients are used.
turbulence↗
Transient cycling of nitrogen, organic carbon and oxygen within the free-flowing Columbia River corridor: Linking exposure time dependent biogeochemical reactions to river stage fluctuations (Final project report)
The objective of this project was to develop next-generation techniques for representing the transformations of complex reaction networks like those impacting transient river-corridors, then apply them to develop upscaling tools. The project contributed significantly to the development of Lagrangian “mass transfer particle tracking” (MTPT) tools that are the first numerical framework that explicitly separates mixing and spreading processes; a crucial distinction for accurate representations of reaction rates across scales. The MTPT approach uses an operator splitting scheme where physical transport processes are simulated using classical random walk methods and each particle is treated as a “container” that carries with it any number of chemical species. Mixing between particles is simulated using a colocation-probability based mass transfer kernel and reactions are evaluated on each particle after mixing. The method is stable, accurate, and also allows the explicit modeling of residence time distributions of the individual containers of mass. The MTPT scheme allowed us to explore several research questions related to reactive transport in river corridors and complex reaction networks. We found that it is possible to quantify the exposure time distributions (ETDs) of reactants and that this does suggest some pathways to upscaling. However, comparable approximations can be obtained using simplified (reduced dimensionality) MTPT simulations in less time with similar uncertainty, so development of extensive ETD-based methods was not productive. The major findings are that i) the MTPT schemes are robust and highly accurate across a range of arbitrarily complex reactions, ii) the methods can be efficiently parallelized and the parallel performance characteristics of MTPT are predictable, and iii) the MTPT tools allow simultaneous tracking of residence time. The development of these research tools into efficient software packages continues. The methods are already available to the community because open-source, working examples have been included with all publications.
54 ENVIRONMENTAL SCIENCES↗
Challenge Problem 1: Preliminary Results of the Direct Numerical Simulation of Transient Flows
This report presents the first direct numerical simulations (DNS) of transient mixed convection in an idealized downcomer-like channel (Challenge Problem 1, Phase II). Using the GPU-accelerated NekRS solver, we modeled a sudden decay in driving pressure, mimicking loss-of-flow events, and tracked the resulting evolution of Reynolds number, boundary-layer structure, turbulence statistics, and heat-transfer metrics. Key findings include the systematic thickening and eventual asymmetry of velocity and thermal boundary layers under buoyant deceleration; minimal “memory” lag in Reynolds shear stress and TKE profiles when sampled at matching Re, yet clear shifts of peak locations toward the cooled wall; overshoots in transient eddy-viscosity and eddy-diffusivity (and corresponding sub-unity turbulent Prandtl numbers) on the cooled side; and a pronounced transient Nusselt-number enhancement driven by wall-temperature inertia and residual eddy mixing. These effects combined to offer a temporary cooling margin above steady-state predictions during reactor LOF transients. Future work will extend this work to a more complex “Case II” geometry (90° turn + lower plenum) and generate multi-Re/Pr datasets for data-driven turbulence closures.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Transient analysis of a thermal storage unit involving a phase change material
The transient response of a single cell of a typical phase change material type thermal capacitor has been modeled using numerical conductive heat transfer techniques. The cell consists of a base plate, an insulated top, and two vertical walls (fins) forming a two-dimensional cavity filled with a phase change material. Both explicit and implicit numerical formulations are outlined. A mixed explicit-implicit scheme which treats the fin implicity while treating the phase change material explicitly is discussed. A band algorithmic scheme is used to reduce computer storage requirements for the implicit approach while retaining a relatively fine grid. All formulations are presented in dimensionless form thereby enabling application to geometrically similar problems. Typical parametric results are graphically presented for the case of melting with constant heat input to the base of the cell.
Griggs, E. I.↗
Homotopy Algorithm for Fixed Order Mixed H2/H(infinity) Design
Recent developments in the field of robust multivariable control have merged the theories of H-infinity and H-2 control. This mixed H-2/H-infinity compensator formulation allows design for nominal performance by H-2 norm minimization while guaranteeing robust stability to unstructured uncertainties by constraining the H-infinity norm. A key difficulty associated with mixed H-2/H-infinity compensation is compensator synthesis. A homotopy algorithm is presented for synthesis of fixed order mixed H-2/H-infinity compensators. Numerical results are presented for a four disk flexible structure to evaluate the efficiency of the algorithm.
Whorton, Mark↗
Numerical Simulations of a Lobed Fuel Injector
Numerical modeling of the nonreactive mixing processes associated with a lobed fuel injector in a coflowing air stream is presented. The lobed fuel injector is a device which generates strong streamwise vorticity, producing locally high strain rates which can enhance the molecular mixing of reactants while delaying ignition in a controlled manner. Vortex element modeling is used to simulate flow field evolution and fuel element mixing characteristics for this lobed fuel injector. Quantitative predictions for vorticity generation and qualitative results for streamwise rollup compare well qualitatively with recent experimental investigations of this flow field [Smith et al, Phys. Fluids 9, 667 (1997)]. Parametric studies of the effects of lobe amplitude-to-wavelength ratio, lobe angle, and lobe shape for given flow conditions suggest that geometrical features may be optimized to enhance mixing and control reaction processes.
Strickland, J. H.↗
The Water Budget of a Simulated Hurricane
The Pennsylvania State University-National Center for Atmospheric Research mesoscale model MM5 is used to simulate Hurricane Bonnie at high resolution (2-km spacing) in order to examine budgets of water vapor, cloud condensate, and precipitation. Virtually all budget terms are derived directly from the model (except for the effects of storm motion). The water vapor budget reveals that a majority of the condensation in the eyewall occurs in convective hot towers, while outside of the eyewall most of the condensation occurs in weaker updrafts, indicative of a larger role of stratiform precipitation processes. The ocean source of water vapor in the eyewall region is only a very small fraction of that transported inward in the boundary layer inflow or that condensed in the updrafts. In contrast, in the outer regions, the ocean vapor source is larger owing to the larger area, counters the drying effect of low-level subsidence, and enhances the moisture transported in toward the eyewall. In this mature storm, cloud condensate is consumed as rapidly as it is produced. Cloud water peaks at the top of the boundary layer and within the melting layer, where cooling from melting enhances condensation. Unlike in squall lines, in the hurricane, very little condensate produced in the eyewall convection is transported outward into the surrounding precipitation area. Most of the mass ejected outward is likely in the form of small snow particles that seed the outer regions and enhance in situ stratiform precipitation development through additional growth by vapor deposition and aggregation. We examine artificial source terms for cloud and precipitation mass associated with setting to zero negative mixing ratios that arise from numerical advection errors. Although small at any given point and time, the cumulative effect of these terms contributes an amount of mass equivalent to 13% of the total condensation and 15-20% of the precipitation. Thus, these terms must be accounted for to balance the model budgets and the results suggest the need for improved model numerics.
Braun, S.↗
Thermal Decomposition of an Impure (Roxbury) Siderite: Relevance to the Presence of Chemically Pure Magnetite Crystals in ALH84001 Carbonate Disks
The question of the origin of nanophase magnetite in Martian meteorite ALH84001 has been widely debated for nearly a decade. Golden et al. have reported producing nearly chemically pure magnetite from thermal decomposition of chemically impure siderite [(Fe, Mg, Mn)CO3]. This claim is significant for three reasons: first, it has been argued that chemically pure magnetite present in the carbonate disks in Martian meteorite ALH84001 could have formed by the thermal decomposition of the impure carbonate matrix in which they are embedded; second, the chemical purity of magnetite has been previously used to identify biogenic magnetite; and, third, previous studies of thermal decomposition of impure (Mg,Ca,Mn)-siderites, which have been investigated under a wide variety of conditions by numerous researchers, invariably yields a mixed metal oxide phase as the product and not chemically pure magnetite. The explanation for this observation is that these siderites all possess the same crystallographic structure (Calcite; R3c) so solid solutions between these carbonates are readily formed and can be viewed on an atomic scale as two chemically different but structurally similar lattices.
McKay, D.S.↗
Asymmetric effects in three-dimensional spatially-developing mixing layers
Three-dimensional structures in spatially developing mixing layers are examined using direct numerical simulations. The growth of streamwise vortices and their interaction with the main two-dimensional rollers as well as the effects of the observed hydrodynamic structures on asymmetric entrainment and mixing are studied. It is found that, at low Reynolds number, the streamwise vortices reduce the entrainment asymmetry of the two-dimensional flow. Passive scalar mixing is quantified by calculating the amount of combustion product produced by a fast chemical reaction. It is shown that the temporally developing case is easier to simulate, but contains an extra symmetry not present in spatially developing flows.
Buell, Jeffrey C.↗
CFD Assessment of Orifice Aspect Ratio and Mass Flow Ratio on Jet Mixing in Rectangular Ducts
Isothermal CFD analysis was performed on axially opposed rows of jets mixing with cross flow in a rectangular duct. Laterally, the jets' centerlines were aligned with each other on the top and bottom walls. The focus of this study was to characterize the effects of orifice aspect ratio and jet-to-mainstream mass flow ratio on jet penetration and mixing. Orifice aspect ratios (L/W) of 4-to-1, 2-to-1, and 1-to-1, along with circular holes, were parametrically analyzed. Likewise, jet-to-mainstream mass flow ratios (MR) of 2.0, 0.5, and 0.25 were systematically investigated. The jet-to-mainstream momentum-flux ratio (J) was maintained at 36 for all cases, and the orifice spacing-to-duct height (S/H) was varied until optimum mixing was attained for each configuration. The numerical results showed that orifice aspect ratio (and likewise orifice blockage) had little effect on jet penetration and mixing. Based on mixing characteristics alone, the 4-to-1 slot was comparable to the circular orifice. The 4-to-1 slot has a smaller jet wake which may be advantageous for reducing emissions. However, the axial length of a 4-to-1 slot may be prohibitively long for practical application, especially for MR of 2.0. The jet-to-mainstream mass flow ratio had a more significant effect on jet penetration and mixing. For a 4-to-1 aspect ratio orifice, the design correlating parameter for optimum mixing (C = (S/H)(sq. root J)) varied from 2.25 for a mass flow ratio of 2.0 to 1.5 for a mass flow ratio of 0.25.
Bain, D. B.↗