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DOE OSTI2021

Enhanced Data Efficiency Using Deep Neural Networks and Gaussian Processes for Aerodynamic Design Optimization

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models. Our methodology finds applications in the early stages of aerospace design. (C) 2021 Published by Elsevier Masson SAS.

Renganathan, S. Ashwin↗

NASA NTRS1999

Simulation of the Universal-Time Diurnal Variation of the Global Electric Circuit Charging Rate

A global lightning model that includes diurnal and annual lightning variation, and total flash density versus latitude for each major land and ocean, has been used as the basis for simulating the global electric circuit charging rate. A particular objective has been to reconcile the difference in amplitude ratios [AR=(max-min)/mean] between global lightning diurnal variation (AR approximately equals 0.8) and the diurnal variation of typical atmospheric potential gradient curves (AR approximately equals 0.35). A constraint on the simulation is that the annual mean charging current should be about 1000 A. The global lightning model shows that negative ground flashes can contribute, at most, about 10-15% of the required current. For the purpose of the charging rate simulation, it was assumed that each ground flash contributes 5 C to the charging process. It was necessary to assume that all electrified clouds contribute to charging by means other than lightning, that the total flash rate can serve as an indirect indicator of the rate of charge transfer, and that oceanic electrified clouds contribute to charging even though they are relatively inefficient in producing lightning. It was also found necessary to add a diurnally invariant charging current component. By trial and error it was found that charging rate diurnal variation curves could be produced with amplitude ratios and general shapes similar to those of the potential gradient diurnal variation curves measured over ocean and arctic regions during voyages of the Carnegie Institute research vessels. The comparisons were made for the northern winter (Nov.-Feb.), the equinox (Mar., Apr., Sept., Oct.), the northern summer (May-Aug.), and the whole year.

Mackerras, David↗

NASA NTRS1999

Simulation of the Universal-Time Diurnal Variation of the Global Electric Circuit Charging Rate

A global lightning model that includes diurnal and annual lightning variation, and total flash density versus latitude for each major land and ocean, has been used as the basis for simulating the global electric circuit charging rate. A particular objective has been to reconcile the difference in amplitude ratios [AR=(max-min)/mean] between global lightning diurnal variation (AR approx. = 0.8) and the diurnal variation of typical atmospheric potential gradient curves (AR approx. = 0.35). A constraint on the simulation is that the annual mean charging current should be about 1000 A. The global lightning model shows that negative ground flashes can contribute, at most, about 10-15% of the required current. For the purpose of the charging rate simulation, it was assumed that each ground flash contributes 5 C to the charging process. It was necessary to assume that all electrified clouds contribute to charging by means other than lightning, that the total flash rate can serve as an indirect indicator of the rate of charge transfer, and that oceanic electrified clouds contribute to charging even though they are relatively inefficient in producing lightning. It was also found necessary to add a diurnally invariant charging current component. By trial and error it was found that charging rate diurnal variation curves in Universal time (UT) could be produced with amplitude ratios and general shapes similar to those of the potential gradient diurnal variation curves measured over ocean and arctic regions during voyages of the Carnegie Institute research vessels.

Mackerras, D.↗

NASA NTRS2015

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

shape optimization↗

DOE OSTI2018

Leveraging continuous material averaging for inverse electromagnetic design

Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit-a process which typically requires that we compute the gradient of a figure of merit which describes device performance, potentially with respect to many design variables. In this paper, we introduce a new strategy based on smoothing abrupt material interfaces which enables us to efficiently compute these gradients with high accuracy irrespective of the resolution of the underlying simulation. This has advantages over previous approaches to shape and topology optimization in nanophotonics which are either prone to gradient errors or place important constraints on the shape of the device. As a demonstration of this new strategy, we optimize a non-adiabatic waveguide taper between a narrow and wide waveguide. Finally, this optimization leads to a non-intuitive design with a very low insertion loss of only 0.041 dB at 1550 nm.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Unexpected Diffusion Anisotropy of Carbon Dioxide in the Metal–Organic Framework Zn 2 (dobpdc)

Metal–organic frameworks are promising materials for energy-efficient gas separations, but little is known about the diffusion of adsorbates in materials featuring one-dimensional porosity at the nanoscale. An understanding of the interplay between framework structure and gas diffusion is crucial for the practical application of these materials as adsorbents or in mixed-matrix membranes, since the rate of gas diffusion within the adsorbent pores impacts the required size (and therefore cost) of the adsorbent column or membrane. In this paper, we investigate the diffusion of CO 2 within the pores of Zn 2 (dobpdc) (dobpdc 4– = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. The residual chemical shift anisotropy for pore-confined CO 2 allows PFG NMR measurements of self-diffusion in different crystallographic directions, and our analysis of the entire NMR line shape as a function of the applied field gradient provides a precise determination of the self-diffusion coefficients. In addition to observing CO 2 diffusion through the channels parallel to the crystallographic c axis (self-diffusion coefficient D ∥ = (5.8 ± 0.1) × 10 –9 m 2 s –1 at a pressure of 625 mbar CO 2 ), we unexpectedly find that CO 2 is also able to diffuse between the hexagonal channels in the crystallographic ab plane (D ⊥ = (1.9 ± 0.2) × 10 –10 m 2 s –1 ), despite the walls of these channels appearing impermeable by single-crystal X-ray crystallography and flexible lattice MD simulations. Finally, observation of such unexpected diffusion in the ab plane suggests the presence of defects that enable effective multidimensional CO 2 transport in a metal–organic framework with nominally one-dimensional porosity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Hydroforming of elliptical cavities

Activities of the past several years in developing the technique of forming seamless (weldless) cavity cells by hydroforming are summarized. An overview of the technique developed at DESY for the fabrication of single cells and multicells of the TESLA cavity shape is given and the major rf results are presented. The forming is performed by expanding a seamless tube with internal water pressure while simultaneously swaging it axially. Prior to the expansion the tube is necked at the iris area and at the ends. Tube radii and axial displacements are computer controlled during the forming process in accordance with results of finite element method simulations for necking and expansion using the experimentally obtained strain-stress relationship of tube material. In cooperation with industry different methods of niobium seamless tube production have been explored. The most appropriate and successful method is a combination of spinning or deep drawing with flow forming. Several single-cell niobium cavities of the 1.3 GHz TESLA shape were produced by hydroforming. They reached accelerating gradients E acc up to 35 MV/m after buffered chemical polishing (BCP) and up to 42 MV/m after electropolishing (EP). More recent work concentrated on fabrication and testing of multicell and nine-cell cavities. Several seamless two- and three-cell units were explored. Accelerating gradients E acc of 30–35 MV/m were measured after BCP and E acc up to 40 MV/m were reached after EP. Nine-cell niobium cavities combining three three-cell units were completed at the company E. Zanon. These cavities reached accelerating gradients of E acc = 30–35 MV/m. One cavity is successfully integrated in an XFEL cryomodule and is used in the operation of the FLASH linear accelerator at DESY. Additionally the fabrication of bimetallic single-cell and multicell NbCu cavities by hydroforming was successfully developed. Several NbCu clad single-cell and double-cell cavities of the TESLA shape have been fabricated. The clad seamless tubes were produced using hot bonding or explosive bonding and subsequent flow forming. The thicknesses of Nb and Cu layers in the tube wall are about 1 and 3 mm respectively. The rf performance of the best NbCu clad cavities is similar to that of bulk Nb cavities. The highest accelerating gradient achieved was 40 MV/m. The advantages and disadvantages of hydroformed cavities are discussed in this paper.

36 MATERIALS SCIENCE↗

DOE OSTI2020

FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.

42 ENGINEERING↗

DOE OSTI2018

Electron thermal confinement in a partially stochastic magnetic structure

Using a high-repetition-rate Thomson scattering diagnostic, we observe a peak in electron temperature $T_e$ coinciding with the location of a large magnetic island in the Madison Symmetric Torus. Magnetohydrodynamic modeling of this quasi-single helicity plasma indicates that smaller adjacent islands overlap with and destroy the large island flux surfaces. The estimated stochastic electron thermal conductivity (≈30 m 2 /s) is consistent with the conductivity inferred from the observed $T_e$ gradient and ohmic heating power. Island-shaped $T_e$ peaks can result from partially stochastic magnetic islands.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

First coupled GENE–XGC microturbulence simulations

Covering the core and the edge region of a tokamak, respectively, the two gyrokinetic turbulence codes Gyrokinetic Electromagnetic Numerical Experiment (GENE) and X-point Gyrokinetic Code (XGC) have been successfully coupled by exchanging three-dimensional charge density data needed to solve the gyrokinetic Poisson equation over the entire spatial domain. Certain challenges for the coupling procedure arise from the fact that the two codes employ completely different numerical methods. This includes, in particular, the necessity to introduce mapping procedures for the transfer of data between the unstructured triangular mesh of XGC and the logically rectangular grid (in a combination of real and Fourier space) used by GENE. Constraints on the coupling scheme are also imposed by the use of different time integrators. First, coupled simulations are presented. We have considered collisionless ion temperature gradient turbulence, in both circular and fully shaped plasmas. Coupled simulations successfully reproduce both GENE and XGC reference results, confirming the validity of the code coupling approach toward a whole device model. Here, many lessons learned in the present context, in particular, the need for a coupling procedure as flexible as possible, should be valuable to our and other efforts to couple different kinds of codes in pursuit of a more comprehensive description of complex real-world systems and will drive our further developments of a whole device model for fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1979

Large Eddy Simulation of turbulent shear flows

The conceptual foundation underlying Large Eddy Simulation (LES) is summarized, and the numerical methods developed for simulation of the time-developing turbulent mixing layer and turbulent plane Poiseuille flow are discussed. Computational results show that the average Reynolds stress profile nearly attains the equilibrium shape which balances the downstream mean pressure gradient in the regions away from the walls. In the vicinity of the walls, viscous stresses are shown to be significant; together with the Reynolds stresses, these stresses balance the mean pressure gradient. It is stressed that the subgrid scale contribution to the total Reynolds stress is significant only in the vicinity of the walls. The continued development of LES is urged.

Moin, P.↗

NASA NTRS1981

Development of an efficient procedure for calculating the aerodynamic effects of planform variation

Numerical procedures to compute gradients in aerodynamic loading due to planform shape changes using panel method codes were studied. Two procedures were investigated: one computed the aerodynamic perturbation directly; the other computed the aerodynamic loading on the perturbed planform and on the base planform and then differenced these values to obtain the perturbation in loading. It is indicated that computing the perturbed values directly can not be done satisfactorily without proper aerodynamic representation of the pressure singularity at the leading edge of a thin wing. For the alternative procedure, a technique was developed which saves most of the time-consuming computations from a panel method calculation for the base planform. Using this procedure the perturbed loading can be calculated in about one-tenth the time of that for the base solution.

Mercer, J. E.↗

NASA NTRS1983

The control of float zone interfaces by the use of selected boundary conditions

The main goal of the float zone crystal growth project of NASA's Materials Processing in Space Program is to thoroughly understand the molten zone/freezing crystal system and all the mechanisms that govern this system. The surface boundary conditions required to give flat float zone solid melt interfaces were studied and computed. The results provide float zone furnace designers with better methods for controlling solid melt interface shapes and for computing thermal profiles and gradients. Documentation and a user's guide were provided for the computer software.

Foster, L. M.↗

NASA NTRS1985

HPFTP flow diverter analysis

A computational fluid flow analysis on the flow diverter system under consideration for the Space Shuttle main engine high pressure fuel turbopump (SSME HPFTP) is proposed. A three dimensional viscous flow environment is computed to optimize the geometric configuration and location of the flow diverter system. The analysis consists of a fully turbulent cold flow calculation by Navier-Stokes equations and a Baldwin-Lomax turbulence model. The equations are numerically by a finite difference/element procedure. The results will provide the steady and unsteady pressure field and thermal environment required to assess the usefulness of the flow diverter system in deflecting the cold flow away from the hot turbine components. A geometry optimization study determines the best diverter shape and location to avoid larger thermal gradients on the rotor/stator components.

Spadley, L. W.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1989

Internally drained condenser for spacecraft thermal management

This paper presents the results obtained to date in a program to develop a high heat flux condenser for use in two-phase spacecraft thermal management loops. The objective is to obtain a several fold increase in condensation heat transfer coefficient over those which can be achieved with shear-controlled or capillary-wick condensers. The internally drained condenser relies on shaped fins to develop a capillary pressure gradient over the surface of the fins and drive the condensate toward narrow drainage grooves separating the fins. The condensate then flows through a drainage network embedded in the condenser walls. Heat transfer coefficients of up to 8 W/sq cm C were measured in steam, providing a heat transfer enhancement ratio greater than a factor of 8. In the paper the proof-of-concept experiments are described and simplified models to predict the performance of the internally drained condenser are presented.

Valenzuela, Javier A.↗

NASA NTRS1994

Techniques For Focusing In Zone Electrophoresis

In two techniques for focusing in zone electrophoresis, force of applied electrical field in each charged particle balanced by restoring force of electro-osmosis. Two techniques: velocity-gradient focusing (VGF), suitable for rectangular electrophoresis chambers; and field-gradient focusing (FGF), suitable for step-shaped electrophoresis chambers.

Sharnez, Rizwan↗

NASA NTRS2002

Controls on Martian Hydrothermal Systems: Application to Valley Network and Magnetic Anomaly Formation

Models of hydrothermal groundwater circulation can quantify limits to the role of hydrothermal activity in Martian crustal processes. We present here the results of numerical simulations of convection in a porous medium due to the presence of a hot intruded magma chamber. The parameter space includes magma chamber depth, volume, aspect ratio, and host rock permeability and porosity. A primary goal of the models is the computation of surface discharge. Discharge increases approximately linearly with chamber volume, decreases weakly with depth (at low geothermal gradients), and is maximized for equant-shaped chambers. Discharge increases linearly with permeability until limited by the energy available from the intrusion. Changes in the average porosity are balanced by changes in flow velocity and therefore have little effect. Water/rock ratios of approximately 0.1, obtained by other workers from models based on the mineralogy of the Shergotty meteorite, imply minimum permeabilities of 10(exp -16) sq m2 during hydrothermal alteration. If substantial vapor volumes are required for soil alteration, the permeability must exceed 10(exp -15) sq m. The principal application of our model is to test the viability of hydrothermal circulation as the primary process responsible for the broad spatial correlation of Martian valley networks with magnetic anomalies. For host rock permeabilities as low as 10(exp -17) sq m and intrusion volumes as low as 50 cu km, the total discharge due to intrusions building that part of the southern highlands crust associated with magnetic anomalies spans a comparable range as the inferred discharge from the overlying valley networks.

Harrison, Keith P.↗