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DOE OSTI2020

Numerical Simulations of Orographic Convection across Multiple Gray Zones

Idealized simulations are used to determine the sensitivity of moist orographic convection to horizontal grid spacing Δ h . In simulated mechanically (MECH) and thermally (THERM) forced convection over an isolated ridge, Δ h is varied systematically over both the deep-convection (Δ h ~ 10 –1 km) and turbulence (Δ h ~ 1 km–100 m) gray zones. To aid physical interpretation, a new parcel-based bulk entrainment/detrainment diagnosis for horizontally heterogeneous flows is developed. Within the deep-convection gray zone, the Δ h sensitivity is dominated by differences in parameterized versus explicit convection; the former initiates convection too far upstream of the ridge (MECH) and too early in the diurnal heating cycle (THERM). These errors stem in part from a large underprediction of parameterized entrainment and detrainment. Within the turbulence gray zone, sensitivities to Δh arise from the representation of both subcloud- and cloud-layer turbulence. As Δ h is decreased, MECH exhibits stronger cloud-layer entrainment to enhance the convective mass flux M co , while THERM exhibits stronger detrainment to suppress Mco and delay convection initiation. The latter is reinforced by increased subcloud turbulence at smaller Δ h , which leads to drying and diffusion of the central updraft responsible for initiating moist convection. Numerical convergence to a robust solution occurs only in THERM, which develops a fully turbulent flow with a resolved inertial subrange (for Δ h ≤ 250 m). In MECH, by contrast, turbulent transition occurs within the orographic cloud, the details of which depend on both physical location and Δ h .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state: A localized artificial diffusivity method to simulate compressible multiphase flows using the stiffened gas equation of state

The development of numerical approaches to perform direct numerical simulations of compressible multiphase flows has been an active field of research for several years. Proper treatment of fluid interfaces is crucial as important physics occur in this infinitesimally small region. Furthermore, the compressibility of the fluid requires proper treatment of discontinuities. Artificial diffusivity is among a number of methods widely used for compressible flows. This study develops a general form of consistent artificial diffusion fluxes and extends the localized artificial diffusivity method for high-order central schemes to solve multiphase flows with an interface-capturing method. These fluxes ensure an oscillation-free interface for pressure, velocity, and temperature without employing a sharpening technique. Moreover, the high-order representation of all scales in the flow helps capture the wide range of instabilities inherent in these flows. The goal is to develop an approach capable of performing high-fidelity simulations supported by physics-driven validation. lastly, this is achieved by solving the five-equation model with the stiffened-gas equation of state using the proposed method for multicomponent and multiphase flows on a variety of 1D and 2D problems.

42 ENGINEERING↗

NASA NTRS1991

Variations of the cosmic-ray flux with time

The physical foundations of the modulation of the galactic cosmic ray flux by the sun are reviewed and related to heliospheric structure and dynamics. The basic physical effects - diffusion, convection, adiabatic cooling and drifts - are evaluated and shown to be all important. The results of numerical models are briefly presented and compared with observations. Present-day modulation is shown to reflect the combination of diffusion-convection effects and drift effects. The Maunder minimum is conjectured to be a period when a quiet sun and smooth solar wind resulted in the dominance of drift effects.

Jokipii, J. R.↗

DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

NASA NTRS1997

Binary Oscillatory Crossflow Electrophoresis

Electrophoresis has long been recognized as an effective analytic technique for the separation of proteins and other charged species, however attempts at scaling up to accommodate commercial volumes have met with limited success. In this report we describe a novel electrophoretic separation technique - Binary Oscillatory Crossflow Electrophoresis (BOCE). Numerical simulations indicate that the technique has the potential for preparative scale throughputs with high resolution, while simultaneously avoiding many problems common to conventional electrophoresis. The technique utilizes the interaction of an oscillatory electric field and a transverse oscillatory shear flow to create an active binary filter for the separation of charged protein species. An oscillatory electric field is applied across the narrow gap of a rectangular channel inducing a periodic motion of charged protein species. The amplitude of this motion depends on the dimensionless electrophoretic mobility, alpha = E(sub o)mu/(omega)d, where E(sub o) is the amplitude of the electric field oscillations, mu is the dimensional mobility, omega is the angular frequency of oscillation and d is the channel gap width. An oscillatory shear flow is induced along the length of the channel resulting in the separation of species with different mobilities. We present a model that predicts the oscillatory behavior of charged species and allows estimation of both the magnitude of the induced convective velocity and the effective diffusivity as a function of a in infinitely long channels. Numerical results indicate that in addition to the mobility dependence, the steady state behavior of solute species may be strongly affected by oscillating fluid into and out of the active electric field region at the ends of the cell. The effect is most pronounced using time dependent shear flows of the same frequency (cos((omega)t)) flow mode) as the electric field oscillations. Under such conditions, experiments indicate that solute is drawn into the cell from reservoirs at both ends of the cell leading to a large mass build up. As a consequence, any initially induced mass flux will vanish after short times. This effect was not captured by the infinite channel model and hence numerical and experimental results deviated significantly. The revised model including finite cell lengths and reservoir volumes allowed quantitative predictions of the time history of the concentration profile throughout the system. This latter model accurately describes the fluxes observed for both oscillatory flow modes in experiments using single protein species. Based on the results obtained from research funded under NASA grant NAG-8-1080.S, we conclude that binary separations are not possible using purely oscillatory flow modes because of end effects associated with the cos((omega)t) mode. Our research shows, however, that a combination of cos(2(omega)t) and steady flow should lead to efficient separation free of end effects. This possibility is currently under investigation.

Molloy, Richard F.↗

NASA NTRS1987

Short efficient ejector systems

A research program was conducted to improve the performance of low pressure ratio ejector systems. The results show that short, efficient ejectors operating at nearly ideal performance are possible through the use of forced mixer lobes. Forced mixer lobes generate large scale axial vorticity which results in rapid mixing and improved diffuser performance. Ejector testing was conducted using both an ejector wind tunnel. Numerous mixer lobe variations were tested to develop lobe design guidelines. The improved performance of mixer-ejectors is presented over a range of operating conditions. Results of mixer lobe angle, penetration, and alignment are presented. Lobe angles of up to 25 deg, coupled with diffuser wall angles over 20 deg, operate without separation, allowing efficient, short ejector systems. Both warm and cold flow test results are presented. Temperature similarity expressions previously developed are further formulated and verified.

Presz, Walter M., Jr.↗

NASA NTRS1974

Seasonal and magnetic storm related changes in the thermosphere induced by eddy mixing

The possibility of explaining the seasonal and magnetic storm related changes in the thermosphere and the ionosphere through variation in eddy diffusion coefficient in the lower thermosphere is investigated theoretically by obtaining simultaneous numerical solutions of the relevant continuity, momentum, and energy balance equations in a self-consistent manner. It is shown that various important features of thermospheric seasonal behavior, including the winter helium bulge phenomenon, can be explained by assuming effective reduction in the winter-time eddy diffusion coefficient by about one order of magnitude. Storm related changes in the thermal structure and composition are seen to arise by assuming a downward shift of turbulence. Physical implications and relative significance of variation in thermospheric turbulence and large scale inter-hemispheric circulation are briefly discussed.

Sinha, A. K.↗

DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

NASA NTRS1975

Diffusion effects on the line intensities of He I and He II in the solar transition region

A heuristic treatment of diffusion in the solar chromosphere-corona transition region is developed. It is shown that diffusion becomes increasingly important with steeper temperature gradients, in active and quiet regions relative to coronal holes, and with increasing excitation potential. Numerical calculations are made for the resonance lines of He I and He II and show that diffusion can enhance these lines. Thus the helium lines may appear relatively weak in coronal holes due to a weakening of the enhancement mechanism. Most transition region lines will be less affected by diffusion than He I or He II.

Shine, R.↗

DOE OSTI2017

Analysis of a Wave-Powered, Reverse-Osmosis System and Its Economic Availability in the United States: Preprint

A wave energy converter (WEC) system has the potential to convert the wave energy resource directly into the high-pressure flow that is needed by the desalination system to permeate saltwater through the reverse-osmosis membrane to generate clean water. In this study, a wave-to-water numerical model was developed to investigate the potential use of a wave-powered desalination system (WPDS) for water production in the United States. The model was developed by coupling a time-domain radiation-and-diffraction-method-based numerical tool (WEC-Sim) for predicting the hydrodynamic performance of WECs with a solution-diffusion model that was used to simulate the reverse-osmosis process. To evaluate the feasibility of the WPDS, the wave-to-water numerical model was applied to simulate a desalination system that used an oscillating surge WEC device to pump seawater through the system. The annual water production was estimated based on the wave resource at a reference site on the coast of northern California to investigate the potential cost of water in that area, where the cost of water and electricity is high compared to other regions. In the scenario evaluated, for a 100-unit utility-scale electricity-producing array, the estimated levelized cost of energy for these WECs is about 3-6 times the U.S.'s current, unsubsidized electricity rates. However, with clean water as an end product and by directly producing pressurized water with WECs, rather than electricity as an intermediary, it is presently only 12 percent greater than typical water cost in California. This study suggests that a WEC array that produces water may be a viable, near-term solution to the nation's water supply, and the niche application of the WPDS may also provide developers with new opportunities to further develop technologies that benefit both the electric and drinking water markets.

16 TIDAL AND WAVE POWER↗

DOE OSTI2018

Structural and dynamic basis of substrate permissiveness in hydroxycinnamoyltransferase (HCT)

Substrate permissiveness has long been regarded as the raw materials for the evolution of new enzymatic functions. In land plants, hydroxycinnamoyltransferase (HCT) is an essential enzyme of the phenylpropanoid metabolism. Although essential enzymes are normally associated with high substrate specificity, HCT can utilize a variety of non-native substrates. To examine the structural and dynamic basis of substrate permissiveness in this enzyme, we report the crystal structure of HCT from Selaginella moellendorffii and molecular dynamics (MD) simulations performed on five orthologous HCTs from several major lineages of land plants. Through altogether 17-μs MD simulations, we demonstrate the prevalent swing motion of an arginine handle on a submicrosecond timescale across all five HCTs, which plays a key role in native substrate recognition by these intrinsically promiscuous enzymes. Our simulations further reveal how a non-native substrate of HCT engages a binding site different from that of the native substrate and diffuses to reach the catalytic center and its co-substrate. By numerically solving the Smoluchowski equation, we show that the presence of such an alternative binding site, even when it is distant from the catalytic center, always increases the reaction rate of a given substrate. However, this increase is only significant for enzyme-substrate reactions heavily influenced by diffusion. In these cases, binding non-native substrates ‘off-center’ provides an effective rationale to develop substrate permissiveness while maintaining the native functions of promiscuous enzymes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Comparing the MELCOR Aerosol Deposition Model with Exact Analytical Solutions

Exact analytical solutions are presented for the evolution of the aerosol particle mass density function in a control volume for particle deposition due to gravitational settling, thermophoresis, and diffusion. The solutions are for arbitrary initial mass density functions and are applied for an initial lognormal density function. Integration of these solutions provides the suspended mass in the control volume as a function of time. These solutions serve as an exact benchmark to assess the accuracy of numerical methods. For the numerical algorithm used in MELCOR, excellent agreement is obtained for gravitational settling, diffusive deposition, and thermophoretic deposition for the suspended aerosol mass. In all cases, the default number of discrete particle size bins of 10 is shown to converge, with hardly any advantage to using 20 size bins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1986

Numerical simulation of electrophoresis separation processes

A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.

Ganjoo, D. K.↗

NASA NTRS1990

Relaxation of the loss-cone by quasi-linear diffusion of the electron-cyclotron maser instability in the solar corona

A self-consistent numeric two-dimensional code using kinetic-wave particle equations has been developed and applied to the maser dynamics of the solar corona. Time histories generated by the code reveal details of the evolution of the linear phase, the saturation and subsequent relaxation of the loss cone. Quantitative values are obtained for the saturation time, the amount of the converted free energy, the critical wave energy level for onset of maser diffusion, the velocity and pitch angle range of the resonant particles, and the relative importance of the different magnetoionic modes and harmonics. A wide range of initial conditions is covered by varying the loss-cone distribution and the ambient cold plasma parameters.

Aschwanden, Markus J.↗

NASA NTRS1973

Preliminary numerical analysis of improved gas chromatograph model

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Woodrow, P. T.↗

NASA NTRS1974

Thermodynamics and kinetics of reactions in protective coating systems

Investigations of fluoride activated packs with Al:Ni ratios greater than 50 a/o prove that the specimen surface is not in equilibrium with the pack at high Al:Ni ratios but that an activity gradient exists between pack and specimen. Therefore, gaseous diffusion and possibly surface reactions play a role in determining the overall rate of Al deposition in such packs. Noticeable differences in coating behavior have been obtained in packs activated with chloride and iodide, and it appears that poorest results are obtained with iodides, better with chlorides, and best with fluorides. A numerical method has been perfected for calculating rates of solid-state diffusion controlled coating formation, allowing for the variation of diffusivity with composition in the NiAl phase. Layer growth rates can now be accurately predicted from a knowledge of the surface and substrate compositions. Furthermore, the correct diffusion profiles are obtained by this method. These differ substantially from the profile obtained when the diffusivity is assumed constant.

Gupta, B.↗

DOE OSTI2026

Capturing the fractocohesive length scale in elastomers through a statistical mechanics-based gradient enhanced damage model

Here, this study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.

36 MATERIALS SCIENCE↗

NASA NTRS1987

Vortex-scalar element calculations of a diffusion flame stabilized on a plane mixing layer

The vortex-scalar element method, a scheme which utilizes vortex elements to discretize the region of high vorticity and scalar elements to represent species or temperature fields, is utilized in the numerical simulations of a two-dimensional reacting mixing layer. Computations are performed for a diffusion flame at high Reynolds and Peclet numbers without resorting to turbulence models. In the nonreacting flow, the mean and fluctuation profiles of a conserved scalar show good agreement with experimental measurements. Results for the reacting flow indicate that for temperature independent kinetics, the chemical reaction begins immediately downstream of the splitter plate where mixing starts. Results for the reacting flow with Arrhenius kinetics show an ignition delay, which depends on reactant temperature, before significant chemical reaction occurs. Harmonic forcing changes the structure of the layer, and concomitantly the rates of mixing and reaction, in accordance with experimental results. Strong stretch within the braids in the nonequilibrium kinetics case causes local flame quenching due to the temperature drop associated with the large convective fluxes.

Ghoniem, Ahmed F.↗