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Convergence speeding up in the calculation of the viscous flow about an airfoil
A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations.
Fabrication of organic-inorganic perovskite thin films for planar solar cells via pulsed laser deposition
We report on fabrication of organic-inorganic perovskite thin films using a hybrid method consisting of pulsed laser deposition (PLD) of lead iodide and spin-coating of methylammonium iodide. Smooth and highly crystalline CH{sub 3}NH{sub 3}PbI{sub 3} thin films have been fabricated on silicon and glass coated substrates with fluorine doped tin oxide using this PLD-based hybrid method. Planar perovskite solar cells with an inverted structure have been successfully fabricated using the perovskite films. Because of its versatility, the PLD-based hybrid fabrication method not only provides an easy and precise control of the thickness of the perovskite thin films, but also offers a straightforward platform for studying the potential feasibility in using other metal halides and organic salts for formation of the organic-inorganic perovskite structure.
NASA ACC High Energy Dynamic Impact Methodology and Outcomes
High fidelity analysis methods known as Progressive Damage Analysis (PDA) methods, capable of reliably predicting the onset and progression of damage in composite materials, are being developed for HEDI event simulation. Four state-of-the-art PDA methods are being investigated: LS-DYNA MAT162, LS-DYNA MAT261, Smooth-Particle Galerkin (SPG), and EMU Peridynamics. Validation of these PDA models aims to follow a building block approach, starting with coupon- and component-level development. As part of the overall effort, material characterization testing was performed to bridge gaps between existing experimental data and the material property inputs required to predict ballistic impact behavior at the component-level. The material models were updated with the results of the coupon-level testing and were then used to predict panel behavior and damage in ballistic impact events. To assess the accuracy of the PDA methods, these pre-test predictions were compared to the results of ballistic impact testing.
Heat transfer measurements from a NACA 0012 airfoil in flight and in the NASA Lewis icing research tunnel
Local heat transfer coefficients from a smooth and roughened NACA 0012 airfoil were measured using a steady state heat flux method. Heat transfer measurements on the specially constructed 0.533 meter chord airfoil were made both in flight on the NASA Lewis Twin Otter Research Aircraft and in the NASA Lewis Icing Research Tunnel (IRT). Roughness was obtained by the attachment of small, 2 mm diameter, hemispheres of uniform size to the airfoil surface in four distinct patterns. The flight data was taken for the smooth and roughened airfoil at various Reynolds numbers based on chord in the range of 1.24x10(exp 6) to 2.50x10(exp 6) and at various angles of attack up to 4 degrees. During these flight tests the free stream velocity turbulence intensity was found to be very low (less than 0.1 percent). The wind tunnel data was taken in the Reynolds number range of 1.20x10(exp 6) to 4.52x10(exp 6) and at angles of attack from -4 degrees to +8 degrees. The turbulence intensity in the IRT was 0.5 to 0.7 percent with the cloud making spray off. Results for both the flight and tunnel tests are presented as Frossling number based on chord versus position on the airfoil surface for various roughnesses and angle of attack. A table of power law curve fits of Nusselt number as a function of Reynolds number is also provided. The higher level of turbulence in the IRT versus flight had little effect on heat transfer for the lower Reynolds numbers but caused a moderate increase in heat transfer at the higher Reynolds numbers. Turning on the cloud making spray air in the IRT did not alter the heat transfer. Roughness generally increased the heat transfer by locally disturbing the boundary layer flow. Finally, the present data was not only compared with previous airfoil data where applicable, but also with leading edge cylinder and flat plate heat transfer values which are often used to estimate airfoil heat transfer in computer codes.
Advanced Validation Risk-Informed Approach for the Flooding Tool Based Upon Smooth Particle Hydrodynamics: Validation and Development Status of NEUTRINO
Risk-Informed validation is to focus advanced validation on high-priority and critical elements of the RISMC methods and tools that can best be addressed by this targeted approach to validation. Initial validation focus will be on the RISMC flooding analysis computer software based upon Smoothed Particle Hydrodynamics (SPH), NEUTRINO. The NEUTRINO code is a SPH-based CFD software adopted as one of the RISMC modeling tools for external hazards analysis. This document discusses the validation and development activities of NEUTRINO, especially in relation to its simulation capability for flooding hazards analysis. In order to draw meaningful conclusions from the discussion, we first analyzed the potential risks to nuclear power plants in flooding scenarios (e.g., hazard modes, industry/regulatory concerns, etc.). Then, an initial high-level PIRT was proposed to define the key phenomena relevant to the analysis of flooding hazards. Finally, based on the framework of this PIRT analysis, the validation and development efforts that have been conducted to date for NEUTRINO were discussed. This analysis helped to determine the sufficiency, efficiency, and adequacy of the current code development and validation efforts for NEUTRINO.
A Runge-Kutta discontinuous finite element method for high speed flows
A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.
Solar Cycle 24 and the Solar Dynamo
We will discuss the polar field precursor method for solar activity prediction, which predicts cycle 24 will be significantly lower than recent activity cycles, and some new ideas rejuvenating Babcock's shallow surface dynamo. The polar field precursor method is based on Babcock and Leighton's dynamo models wherein the polar field at solar minimum plays a major role in generating the next cycle's toroidal field and sunspots. Thus, by examining the polar fields of the Sun near solar minimum, a forecast for the next cycle's activity is obtained. With the current low value for the Sun's polar fields, this method predicts solar cycle 24 will be one of the lowest in recent times, with smoothed F10.7 radio flux values peaking near 135 plus or minus 35 (2 sigma), in the 2012-2013 timeframe (equivalent to smoothed Rz near 80 plus or minus 35 [2 sigma]). One may have to consider solar activity as far back as the early 20th century to find a cycle of comparable magnitude. We discuss unusual behavior in the Sun's polar fields that support this prediction. Normally, the solar precursor method is consistent with the geomagnetic precursor method, wherein geomagnetic variations are thought to be a good measure of the Sun's polar field strength. Because of the unusual polar field, the Earth does not appear to be currently bathed in the Sun's extended polar field (the interplanetary field), hence negating the primal cause behind the geomagnetic precursor technique. We also discuss how percolation may support Babcock's original shallow solar dynamo. In this process ephemeral regions from the solar magnetic carpet, guided by shallow surface fields, may collect to form pores and sunspots.
Optimization-based scatter estimation using primary modulation for computed tomography
Purpose: Scatter reduces the image quality in computed tomography (CT), but scatter correction remains a challenge. A previously proposed primary modulation method simultaneously obtains the primary and scatter in a single scan. However, separating the scatter and primary in primary modulation is challenging because it is an underdetermined problem. In this study, an optimization-based scatter estimation (OSE) algorithm is proposed to estimate and correct scatter. Methods: In the concept of primary modulation, the primary is modulated, but the scatter remains smooth by inserting a modulator between the x-ray source and the object. In the proposed algorithm, an objective function is designed for separating the scatter and primary. Prior knowledge is incorporated in the optimization-based framework to improve the accuracy of the estimation: (1) the primary is always positive; (2) the primary is locally smooth and the scatter is smooth; (3) the location of penumbra can be determined; and (4) the scatter-contaminated data provide knowledge about which part is smooth. Results: The simulation study shows that the edge-preserving weighting in OSE improves the estimation accuracy near the object boundary. Simulation study also demonstrates that OSE outperforms the two existing primary modulation algorithms for most regions of interest in terms of the CT number accuracy and noise. The proposed method was tested on a clinical cone beam CT, demonstrating that OSE corrects the scatter even when the modulator is not accurately registered. Conclusions: The proposed OSE algorithm improves the robustness and accuracy in scatter estimation and correction. This method is promising for scatter correction of various kinds of x-ray imaging modalities, such as x-ray radiography, cone beam CT, and the fourth-generation CT.
Deep kernel methods learn better: from cards to process optimization
Abstract The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards dataset and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The Jupyter Notebooks that encapsulate the complete analysis accompany the article.
Friction factor data for flat plate tests of smooth and honeycomb surfaces
Friction factors for honeycomb surfaces were measured with a flat plate tester. The flat plate test apparatus was described and a method was discussed for determining the friction factor experimentally. The friction factor model was developed for the flat plate test based on the Fanno Line Flow. The comparisons of the friction factor were plotted for smooth surfaces and six-honeycomb surfaces with three-clearances, 6.9 bar to 17.9 bar range of inlet pressures, and 5,000 to 100,000 range of the Reynolds number. The optimum geometries for the maximum friction factor were found as a function of cell width to cell depth and cell width to clearance ratios.
Friction-factor data for flat-plate tests of smooth and honeycomb surfaces
Friction factors for honeycomb surfaces were measured with a flat plate tester. The flat plate test apparatus was described and a method was discussed for determining the friction factor experimentally. The friction factor model was developed for the flat plate test based on the Fanno Line Flow. The comparisons of the friction factor were plotted for smooth surfaces and six-honeycomb surfaces with three-clearances, 6.9 bar to 17.9 bar range of inlet pressures, and 5,000 to 100,000 range of the Reynolds number. The optimum geometries for the maximum friction factor were found as a function of cell width to cell depth and cell width to clearance ratios.
Vortex methods for separated flows
The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.
A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows
Abstract Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized-reduced order model for the numerical simulation of convection-dominated flows of moderate Reynolds number. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier–Stokes equations, and diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method better reflects the dynamics of the benchmark results than the ensemble-POD scheme. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.
MPACVD growth of single crystalline diamond substrates with PCD rimless and expanding surfaces
Single crystal diamond (SCD) growth was performed in optimized pocket substrate holders at a high pressure (240 Torr) and a high power density (∼1000 W/cm3). In an effort to overcome the challenges of growing large area SCD substrates without a corresponding polycrystalline diamond (PCD) rim, a growth recipe using these pocket holders was developed. This growth recipe controls the substrate temperature (Ts) and the incident microwave power (Pinc) in a prescribed function of growth time. Through this process, the feasibility to enlarge the SCD substrate in situ, i.e., during the growth itself is shown. By allowing the temperature to increase from ∼980 °C to 1040 °C, then reducing the temperature, and then allowing it to drift up again, the deposition process alternates between the fast growth of the different crystal directions (i.e., 〈110〉, 〈111〉, and 〈100〉) and a slow growth to smoothen the top surface. This leads to an increased lateral SCD growth. The slow growth of the crystal faces in turn leads to a smooth and enlarged top surface. Certain strategies such as the termination of the growth process at the appropriate time are critical in obtaining flat and smooth SCD surfaces without the formation of any PCD rim. The SCD substrates grown via this method have been analyzed by optical and scanning electron microscopies. The lateral SCD surface area increased between 1.7 and 2 times greater than the initial seed surface area during one continuous run. The deposited SCDs have high growth rates of ∼30 μm/h resulting in smooth, flat and rimless substrates, hence indicating the improvement in the quality and morphology of the deposited substrates.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
First Experimental Test of the Ratio Method
The ratio is a new reaction observable suggested to extract accurately structure information on halo nuclei. It corresponds to the ratio of differential cross sections for scattering and breakup, which is predicted to remove the uncertainty related to the reaction dynamics. We present here the first experimental test of the method for the 11 Be + 12 C collision at E Lab = 20A MeV performed at Texas A&M University. Differential cross sections for scattering and inclusive one-neutron breakup have been measured with the new detector array BlueSTEAl. The ratio of cross sections is very smooth and independent of the projectile-target interaction, which demonstrates the validity of the ratio method. We extend our analysis to existing 11 Be + 208 Pb data, confirming that the method works well on any target.
A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.