Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,027 records · Page 57

Towards an Enhanced Droplet Activation Scheme for Multi-Moment Bulk Microphysics Schemes

Initial droplet spectra produced upon activation impact the ensuing chain of microphysical processes andtherefore play a crucial role in cloud evolution. This work re-examines dependencies of newly formed clouddroplet size distribution (CDSD) characteristics on environmental and aerosol properties via parcel model simulationsthat serve as the basis for a multi-moment bulk microphysics droplet activation scheme suitable for acloud-resolving model (CRM). It is found that applying a fixed size threshold to define activated droplets versusemploying physical considerations can lead to erroneous activation and overly broad CDSDs for high aerosolconcentration and weak updraft conditions. Aerosol distributions characterized by larger median sizes and/orincreased solubility can result in greater activated droplet numbers, whereas impacts of these parameters onCDSD spectral width depend on both aerosol number concentration and updraft velocity. An expansion of theactivation scheme to include CDSD spectral width is proposed to aid efforts to extend high-order momentprediction to cloud droplet categories in CRMs as well as better represent variability in the activation process onthe cloud scale.simulations to investigate the regime dependence of the relative dispersion(d)1 of newly activated CDSDs, where d is the ratio of dropletradius standard deviation (σ) to the mean radius (r ). C16 demonstratedthat increasing Na resulted in increasing (decreasing) d values via reducedcondensational narrowing (spectral broadening) rates within theAL (UL) regime, with d values peaking in the TR regime. Their findingssuggest a similar regime dependence for d as R09 noted for Nc and helpexplain reportedly conflicting relationships between Na and CDSDspectral characteristics (cf. Hudson and Noble, 2014; Liu et al., 2014),although the applicability of these results within bulk microphysicalschemes was not addressed.Simulating aerosol-cloud interactions with CRMs employing bulkmicrophysics requires that the scheme minimally predict two CDSDparameters, namely mass and number concentrations, and represent thedroplet activation process. Various activation schemes aim to determineNc from aerosol and environmental properties and include analyticalexpressions (e.g., Abdul-Razzak et al., 1998; Morrison et al., 2005) aswell as lookup tables (LUTs) based on detailed parcel model calculations(e.g., Saleeby and Cotton, 2004, hereafter SC04; Segal and Khain,2006; Thompson and Eidhammer, 2014). Expressions to diagnose CDSDspectral width from Nc (Grabowski, 1998; Liu et al., 2006; Morrison andGrabowski, 2007) or cloud water content (Geoffroy et al., 2010) havealso been developed, although more robust methods to obtain CDSDspectral width upon activation are presently lacking. This latter point isrelevant for triple-moment (3 M) bulk microphysics that aim to predictdistribution spectral width alongside number and mass concentrations(e.g., Loftus et al., 2014; Milbrandt and Yau, 2005).The current work extends the findings of C16 to the current LUTbasedaerosol activation scheme used in the Regional AtmosphericModeling System (RAMS) (Cotton et al., 2003; SC04; Saleeby and vanden Heever, 2013, hereafter SvdH13) and additionally examinesaerosol size and solubility impacts on newly activated CDSD properties.Because early cloud development processes such as condensationalgrowth, evaporation, and droplet self-collection depend on and impactCDSD spectral width (Hudson and Yum, 1997; Seifert and Beheng 2001;Lu and Seinfeld, 2006; Igel and van den Heever, 2017), an expansion ofthe activation LUTs to include CDSD spectral width is proposed as apreliminary step for extending 3M prediction to CDSDs in CRMs forimproved simulations of aerosol-cloud interactions.2. MethodologyThe current RAMS two-moment microphysics module determinesthe fractional number of aerosol particles that activate to cloud dropletsfrom five-dimensional LUTs based on model predicted air temperature(T), w, Na, and the geometric median radius (rg) and soluble fraction (ε)of the aerosol size distribution (SvdH13). These LUTs are created offlineusing a one-dimensional Lagrangian adiabatic parcel model (Feingoldand Heymsfield, 1992; Heymsfield and Sabin, 1989; SC04) to simulateexplicit droplet activation and initial CDSD growth for a range of ambientatmospheric conditions [T, w] and binned lognormal aerosol sizedistributions given by= ⎡⎣ ⎢− ⎤⎦ ⎥N r Nr π σr rσ( )2 lnexp[ln( / )]2(ln )aggg22 (1)where r is the dry aerosol particle bin radius and σg is the geometricstandard deviation of the distribution. As the parcel model simulationsfocus on the activation process, other processes such as coalescence,sedimentation, and mixing are not considered. Details of the parcelmodel can be found in SC04 and SvdH13, and only a brief description isprovided here. At the onset of parcel model calculations, the initiallydry aerosol particles in all bins first deliquesce and reach theirequilibrium diameters in a sub-saturated environment based on theKöhler equation for solution droplets. The parcel is then lifted at a fixedupward velocity w, and particle growth by vapor diffusion, along withconcurrent changes in the ambient environment, are iteratively computedusing the Variable-coefficient Ordinary Differential Equation(VODE) solver (Brown et al., 1989). The time resolution of these calculationsis determined within the VODE solver, and the frequency atwhich the solver is called is controlled by a longer model time stepbased on fixed upward parcel displacement increments (Δz) at thespecified w (Δt=Δz/w). Model calculations proceed until the parcelreaches a height 50m beyond the level of maximum saturation ratio(Smax) or total parcel displacement exceeds 2 km. Upon model termination,Smax and the fractional number of aerosols (factv) resulting innewly formed cloud droplets, defined as particles having diameters of atleast 2 μm, are cataloged in the LUTs according to the specified T, w, Na,rg, and ε parameter values.A critical point regarding the creation of these LUTs is the use of afixed minimum diameter (Dmin) to define cloud droplets in the parcelmodel, which can produce erroneous CDSD characteristics, particularlywithin the UL regime. For aerosol distributions with large rg valuesunder low SS conditions, for example, deliquesced aerosols within thelarge tail of the distribution can exceed 2 μm in diameter yet remainunactivated as ‘haze’ particles (Levin and Cotton, 2009; McFigganset al., 2006). For this study, aerosol particles activate to cloud dropletsbased on the critical diameter Dcrit as a function of parcel supersaturationratio (Sr) as in R09:D = σ MS RTρ83 ln( ) critsol wr w (2)where σsol is the surface tension of a solution droplet, Mw and ρw are themolar mass and density of liquid water, respectively, and R is theuniversal gas constant. Additionally, at relatively large w values withinthe AL regime, Nc stabilizes shortly after reaching supersaturation.However, parcel ascent and condensational growth continue beyondthe level of Smax, potentially causing additional narrowing of the CDSD.In the current work, model calculations terminate upon reaching Smaxas changes in Nc are negligible with continued ascent (Peng et al., 2007;R09).Parcel model simulations are performed to examine the sensitivitiesof CDSD characteristics to w, Na, rg, and ε, with the ranges for theseparameters listed in Table 1. Aerosols are assumed to be a mix of solubleand insoluble material of equal density, specified by ε, where fullysoluble aerosols correspond to ammonium sulfate with hygroscopicityparameter κ=0.61 (Petters and Kreidenweis, 2007). FollowingSvdH13, aerosol geometric standard deviation is fixed at σg=1.8, andaerosol distributions (Eq. 1) are partitioned into 100 logarithmicallyspacedbins spanning a size range specific to each rg value. For all simulations,Δz=1 m, and initial values of relative humidity, air temperatureand pressure are set to RH=0.99, T=10 °C and p=900 hPa,respectively.

Loftus, Adrian M.↗

A comparison between implicit and hybrid methods for the calculation of steady and unsteady inlet flows

Numerical simulation of steady and unsteady transonic diffuser flows using two different computer codes are discussed and compared with experimental data. The codes solve the Reynolds-averaged, compressible, Navier-Stokes equations using various turbulence models. One of the codes has been applied extensively to diffuser flows and uses the hybrid method of MacCormack. This code is relatively inefficient numerically. The second code, which was developed more recently, is fully implicit and is relatively efficient numerically. Simulations of steady flows using the implicit code are shown to be in good agreement with simulations using the hybrid code. Both simulations are in good agreement with experimental results. Simulations of unsteady flows using the two codes are in good qualitative agreement with each other, although the quantitative agreement is not as good as in the steady flow cases. The implicit code is shown to be eight times faster than the hybrid code for unsteady flow calculations and up to 32 times faster for steady flow calculations. Results of calculations using alternative turbulence models are also discussed.

Coakley, T. J.↗

Model-based optimization strategies for direct hydrogenation of carbon dioxide to dimethyl ether

Here, this study discusses model-based optimization strategies for CO 2 hydrogenation to dimethyl ether (DME) over aCuZnZr (CZZ) and ferrite (FER) mixed catalyst system in a packed-bed reactor configuration. A two-dimensional axisymmetric, nonisothermal packed-bed reactor model was developed using COMSOL Multiphysics 6.2 software. The model solves two-dimensional (radial and axial) heat and mass transport equations in the packed-bed and integrates intraparticle diffusion and heat transfer in a 1D approach. This powerful feature differs from a traditional porous media approach and takes into account any heat and mass transfer limitations that may exist. Analysis shows that the heat transfer limitations are negligible, but strong internal mass transfer limitations were observed at 10 ≤ WHSV ≤ 90 h -1 on the FER catalyst and at 240 °C. The optimum catalyst composition (i.e., mixing ratio) varies depending on the operating regime. The FER catalyst weight in the mixture can be as low as 5 wt.%, but the ideal composition de-pends on the internal mass transfer limitation and its relationship with the operating regime (i.e., weight hourly space velocity, temperature). A catalyst composition of 80 wt.% CZZ and 20 wt.% FER was suggested; this composition can provide high CO 2 conversion and DME production rates at a wide range of temperatures and flow rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polyethylene in Dead-End Silica Nanopores: Forces and Mobility from Non-Equilibrium Statistical Mechanics and Exchange Spectroscopy Nuclear Magnetic Resonance

Billions of tons of plastic have been produced, and only a small fraction of this has been recycled. Tennakoon et al. [Nature Catalysis 3, 893 (2020)] developed a catalyst that repeatedly cleaves C 10 –C 30 hydrocarbons from the end of a polyethylene chain. The reaction occurs at a Pt nanoparticle at the base of a cylindrical silica mesopore with a diameter of 2 nm and a length of 110 nm. Portions of the polymer situated inside the pore can be differentiated from those outside using 13 C nuclear magnetic resonance (NMR), allowing the dynamics and extent of polymer threading to be monitored using two-dimensional (2D) exchange spectroscopy NMR. Here we construct a Fokker–Planck equation for the polymer dynamics by assuming a reptation diffusivity and a graduated adsorption free energy that depends linearly on the depth of polymer penetration in the pore. The solutions allow us to predict the intensities of the 2D NMR resonances as a function of time. We use the solutions to extract a polymer diffusivity at each temperature and estimate the per-segment desorption free energy, enthalpy, and entropy. Random and systematic errors are examined to test key assumptions in the theory and interpretation of the experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

The behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide-ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (w s ) in turbulence and its still water counterpart (w so ). This difference is explored here for a range of particle-to-fluid densities (1 – 10) and particle diameter to Kolmogorov micro-eddy sizes (0.1 – 10). Conventional models of particle fluxes that equate w s to w so result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why w s /w so is sub-unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought.

Geology↗

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

97 MATHEMATICS AND COMPUTING↗

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/$\mathrm{cm^3}$ to 16 g/$\mathrm{cm^3}$ and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. Here, we find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Theoretical model of vertical distributions of CO and CH4 in the mesosphere and upper stratosphere.

Carbon compounds (CO and CO2) and methane are added to an existing computer program (Shimazaki and Laird, 1970, 1972), which calculates diurnal variations in density distributions of pure oxygen compounds, hydrogen compounds, and nitrogen compounds. For the present model calculations, the original program was modified to calculate the steady-state profiles for all constituents, and then these solutions were used as the initial condition for solving the time-dependent equations. The effects of chemical reactions and vertical eddy diffusion transport on the CH4 and CO concentrations above 40 km, where one-dimensional treatment may not be too inappropriate, are discussed. Some of the 15 constituents included in the computer program interact with CO and CH4 chemically, and CH4 is more sensitive to the eddy diffusion coefficient than any other constituent. Therefore it is easier to determine the most appropriate profile of the eddy diffusion coefficient by comparing the model profile with the observations for CH4.

Shimazaki, T.↗

Electron precipitation in the postmidnight sector of the auroral zones

Measurements of the angular distributions and energy spectra of electron intensities within the energy range 50 eV to 15 keV with electrostatic analyzer arrays on board the low-altitude satellite Injun 5 are reported for the postmidnight sector of the auroral zones during the high-intensity events accompanying magnetic substorms. Precipitation features on closed terrestrial field lines well equatorward of the trapping boundary for electrons with energies greater than 45 keV are examined. Precipitation of low-energy electron intensities was characterized by isotropy for all pitch angles outside the atmospheric backscatter cone. The region of electron precipitation observed is associated with the diffuse aurora and with pulsating aurora in the postmidnight sector. Similar variations of the energetic electron intensities with energies above 45 keV were observed in the regions of fluctuating energy fluxes of low-energy electrons associated with auroral luminosity. The increases of energetic electron intensities were not coincident with those of the principal energy fluxes into the atmosphere, except when the average electron energy for the energy fluxes was unusually high, i.e., in the 10-keV range. Precipitation of electron intensities within these energy ranges is consistent with strong pitch angle diffusion of electron intensities near or at the magnetic equator by high-frequency wave turbulence, the effectiveness of which is modulated by perturbations attributable to micropulsations.

Frank, L. A.↗

Characteristics of the motions, turbulence intensity, diffusivity, flux of momentum and sensible heat in the upper atmosphere

Analyses of the meteorological rocket data obtained from an experiment conducted at 3-hour intervals at 8 western meridional rocket stations are presented. Large variations in the meridional wind contribute substantially to overall turbulence in the tropical stratosphere. The solar semidiurnal component of wind oscillations in the tropics was observed to be much higher than predicted by theory, often exceeding the magnitude of the diurnal amplitude throughout the stratosphere. The observed value of the solar diurnal amplitude in the stratosphere was in line with theoretical prediction. The solar terdiurnal amplitudes for temperature, meridional and zonal winds were non-negligible and must be considered in any harmonic analysis. Phase angle variation with height was rapid for all harmonics; however, there was general agreement between predicted and observed phase angles. Because of large changes in the mean winds in the mesosphere with season, harmonic determinations are difficult. There appear to be large zonal wind changes even within the same season as mentioned previously. Turbulence diffusivity in the upper stratosphere is greater near the equator than in the mid-latitudes.

Kao, S. K.↗

Determination of optimum sunlight concentration level in space for 3-5 cascade solar cells

Current-voltage curves were calculated for each cell in a cascade structure using a solar cell diode equation and superposition. Terms for the light generated current, diffusion current, space charge recombination current and series and shunt resistance are included. Individual current voltage curves are added in series with ohmic resistance losses for the cell interconnects to obtain the cascade cell performance. Temperature was varied with concentration, using several models, and ranged from 55 C at one Sun to between 80 and 200 C at 100 Suns. A variety of series resistance and internal resistances were used. Coefficients of the diffusion and recombination terms are strongly temperature dependent. The study indicates that maximum efficiency (30%) occurs in the 50 to 100X Sun concentration range, provided series resistance is below 0.015 ohm-sq cm and cell temperature is 80 C at 100 Suns.

Curtis, H. B.↗

Modelling of dimensional stability of fiber reinforced composite materials

Various methods of predicting the expansion and diffusion properties of composite laminates are reviewed. The prediction equations for continuous fiber composites can be applied to SMC composites as the effective fiber aspect ratio in the latter is large enough. The effect of hygrothermal expansion on the dimensional stability of composite laminates was demonstrated through the warping of unsymmetric graphite/epoxy laminates. The warping is very sensitive to the size of the panel, and to the moisture content which is in turn sensitive to the relative humidity in the environment. Thus, any long term creep test must be carried out in a humidity-controlled environment. Environmental effects in SMC composites and bulk polyester were studied under seven different environments. The SMC composites chosen are SMC-R25, SMC-R40, and SMC-R65.

Hahn, H. T.↗

The effect of convection upon charged particle transport in random magnetic fields

In a coordinate system moving with the plasma and random magnetic fields of a wind that blows with constant velocity in the direction of the guiding field, transport of energetic particles is described by a Boltzmann equation which is similar to the one that describes unconvected transport. Although this formulation is mathematically identical to that developed by Luhmann, which refers to the system where the guiding field is static, there are both practical and fundamental reasons to adopt the new approach. It leads to first-order approximate transport equations which are similar to those that apply in the absence of convection. However, these equations are more general than Parker's description of diffusion and convection, for they describe the coherent modes of transport that appear when the mean free path is large compared to the scale length for spatial variations of the guiding field, and they are valid for arbitrary wind velocity. The latter characteristic opens up new possibilities for analyzing particle transport in relativistic flows seen in some astronomical objects.

Earl, J. A.↗

The influence of gravity wave breaking on the general circulation of the middle atmosphere

The zonal mean solstice circulation of the global middle atmosphere is simulated using a semi-spectral numerical model. Radiative heating and cooling is computed by the algorithm of Wehrbein and Leovy. Mechanical dissipation is represented by the gravity wave breaking parameterization of Lindzen. An inertial adjustment parameterization is used to prevent the development of inertially unstable meridional shears near the equator. It is shown that gravity wave drag and diffusion in the mesosphere can account for the observed large departure from radiative equilibrium in both summer and winter. Experiments incorporating a forced stationary wavenumber 1 disturbance indicate that planetary wave EP flux convergences, although they may modify the mean flow profile significantly, cannot provide the major source of mechanical dissipation in the winter mesosphere. A simulated sudden warming is accompanied by an equally strong mesospheric cooling. This cooling is caused primarily by the relaxation of the polar mesosphere toward radiative equilibrium when the easterly mean winds in the polar stratosphere induced by the sudden warming reduce the transmission of gravity waves into the mesosphere.

Holton, J. R.↗

Numerical simulation and comparison with experiment for self-excited oscillations in a diffuser flow

This paper describes numerical simulations of self-excited oscillations in a two-dimensional transonic diffuser flow obtained by solving the Navier-Stokes equations with a two-equation turbulence model. Comparisons were made between the computational results and experimental data. For the mean flowfields, the agreement between computation and experiment is good for the wall pressures, shock location, and the separation and reattachment points. However, the thickness of the computed recirculation zone is about 50 percent of the measured thickness. For the fluctuating flowfields, a great deal of qualitative similarity exists between the computation and experiment; however, the predicted oscillation frequency is about 50 percent higher than the measured value. The formation of a succession of downstream-traveling counter-rotating vortices, as seen experimentally, is also vividly displayed in the numerical results.

Hsieh, T.↗

Effect of free stream turbulence on flow separation

An analysis is presented to study the influence of free stream turbulence on separation in the case of crossflow over a circular cylinder. An eddy diffusivity model has been formulated and the governing momentum equation has been solved numerically. A correlation parameter has been suggested to correlate the angle of separation. It has been found that the angle of separation increases with increasing free stream turbulence intensity.

Gorla, R. S. R.↗