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NASA NTRS1977

The separated turbulent boundary layer over a wavy wall

A study and application of the fourth order spline collocation procedure, numerical solution of boundary layer like differential equations, is presented. A simple inversion algorithm for the simultaneous solution of the resulting difference equations is given. Particular attention is focused on the boundary condition representation for the spline second derivative approximations. Solutions using the spline procedure, as well as the three point finite difference method, are presented for several model problems in order to assess and improve the spline numerical scheme. Application of the resulting algorithm to the incompressible laminar self similar boundary layer equations is presented.

Polak, A.↗

DOE OSTI2023

Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. In conclusion, the last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1961

Constant Density Approximations for the Flow Behind Axisymmetric Shock Waves

The incompressible rotational flow equations are used to obtain solutions for the flow behind axisymmetric shock waves with conic longitudinal sections. The nonlinear part of the term due to rotation is retained in the analysis. Numerical results for standoff distance and stagnation point velocity gradient are presented for the case in which the shock wave is a paraboloid, a sphere, or an oblate or prolate ellipsoid. A similarity parameter is proposed which correlates approximately the flow behind geometrically similar shock waves at different free-stream conditions.

Munson, Albert G.↗

NASA NTRS1979

An efficient algorithm for numerical airfoil optimization

A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.

Vanderplaats, G. N.↗

NASA NTRS1993

Computational reacting gas dynamics

In the study of high speed flows at high altitudes, such as that encountered by re-entry spacecrafts, the interaction of chemical reactions and other non-equilibrium processes in the flow field with the gas dynamics is crucial. Generally speaking, problems of this level of complexity must resort to numerical methods for solutions, using sophisticated computational fluid dynamics (CFD) codes. The difficulties introduced by reacting gas dynamics can be classified into three distinct headings: (1) the usually inadequate knowledge of the reaction rate coefficients in the non-equilibrium reaction system; (2) the vastly larger number of unknowns involved in the computation and the expected stiffness of the equations; and (3) the interpretation of the detailed reacting CFD numerical results. The research performed accepts the premise that reacting flows of practical interest in the future will in general be too complex or 'untractable' for traditional analytical developments. The power of modern computers must be exploited. However, instead of focusing solely on the construction of numerical solutions of full-model equations, attention is also directed to the 'derivation' of the simplified model from the given full-model. In other words, the present research aims to utilize computations to do tasks which have traditionally been done by skilled theoreticians: to reduce an originally complex full-model system into an approximate but otherwise equivalent simplified model system. The tacit assumption is that once the appropriate simplified model is derived, the interpretation of the detailed numerical reacting CFD numerical results will become much easier. The approach of the research is called computational singular perturbation (CSP).

Lam, S. H.↗

NASA NTRS1971

A numerical method for computing three dimensional viscous supersonic flow fields about slender bodies

A numerical method is presented for the calculation of steady, three-dimensional, viscous, compressible flow fields about slender bodies at angle of attack and at supersonic speeds. Approximations are introduced in modeling the flow in the longitudinal direction. Accordingly, the flow fields calculated with the program were computed with a model that permits viscous crossflow together with inviscid axial flow. An analysis of the errors introduced by such a treatment is presented. Numerical calculations were made and compared with experimental results for an ogive-cylinder and an airplane fuselage configuration. Generally, good agreement with experiment was obtained. However, boundary layer separation and body vortex positions differed from experimental locations on the ogive-cylinder, and the shock induced by the fuselage canopy was predicted at a slightly different location.

Walitt, L.↗

DOE OSTI2023

Toward DMC Accuracy Across Chemical Space with Scalable Δ-QML

In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. With O(N 3 ) scaling with the number of electrons N, DMC has the potential to be a reference method for larger systems that are not accessible to more traditional methods such as CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes the stepping stone in making the method a reference for larger systems. We show that when coupled with quantum machine learning (QML)-based surrogate methods, the computational burden can be alleviated such that quantum Monte Carlo (QMC) shows clear potential to undergird the formation of high-quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: the fixed-node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models. Numerical evidence presented includes converged DMC results for over 1000 small organic molecules with up to five heavy atoms used as amons and 50 medium-sized organic molecules with nine heavy atoms to validate the AQML predictions. Finally, numerical evidence collected for Δ-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2007

Investigation of MMOD Impact on STS-115 Shuttle Payload Bay Door Radiator

The Orbiter radiator system consists of eight individual 4.6 m x 3.2 m panels located with four on each payload bay door. Forward panels #1 and #2 are 2.3 cm thick while the aft panels #3 and #4 have a smaller overall thickness of 1.3 cm. The honeycomb radiator panels consist of 0.028 cm thick Aluminum 2024-T81 facesheets and Al5056-H39 cores. The face-sheets are topped with 0.005 in. (0.127 mm) silver-Teflon tape. The radiators are located on the inside of the shuttle payload bay doors, which are closed during ascent and reentry, limiting damage to the on-orbit portion of the mission. Post-flight inspections at the Kennedy Space Center (KSC) following the STS-115 mission revealed a large micrometeoroid/orbital debris (MMOD) impact near the hinge line on the #4 starboard payload bay door radiator panel. The features of this impact make it the largest ever recorded on an orbiter payload bay door radiator. The general location of the damage site and the adjacent radiator panels can be seen in Figure 2. Initial measurements of the defect indicated that the hole in the facesheet was 0.108 in. (2.74 mm) in diameter. Figure 3 shows an image of the front side damage. Subsequent observations revealed exit damage on the rear facesheet. Impact damage features on the rear facesheet included a 0.03 in. diameter hole (0.76 mm), a approx.0.05 in. tall bulge (approx.1.3 mm), and a larger approx.0.2 in. tall bulge (approx.5.1 mm) that exhibited a crack over 0.27 in. (6.8 mm) long. A large approx.1 in. (25 mm) diameter region of the honeycomb core was also damaged. Refer to Figure 4 for an image of the backside damage to the panel. No damage was found on thermal blankets or payload bay door structure under the radiator panel. Figure 5 shows the front facesheet with the thermal tape removed. Ultrasound examination indicated a maximum facesheet debond extent of approximately 1 in. (25 mm) from the entry hole. X-ray examinations revealed damage to an estimated 31 honeycomb cells with an extent of 0.85 in. x 1.1 in. (21.6 x 27.9 mm). Pieces of the radiator at and surrounding the impact site were recovered during the repair procedures at KSC. They included the thermal tape, front facesheet, honeycomb core, and rear facesheet. These articles were examined at JSC using a scanning electron microscope (SEM) with an energy dispersive x-ray spectrometer (EDS). Figure 6 shows SEM images of the entry hole in the facesheet. The asymmetric height of the lip may be attributed to projectile shape and impact angle. Numerous instances of a glass-fiber organic matrix composite were observed in the facesheet tape sample. The fibers were approximately 10 micrometers in diameter and variable lengths. EDS analysis indicated a composition of Mg, Ca, Al, Si, and O. Figures 7 and 8 present images of the fiber bundles, which were believed to be circuit board material based on similarity in fiber diameter, orientation, consistency, and composition. A test program was initiated in an attempt to simulate the observed damage to the radiator facesheet and honeycomb. Twelve test shots were performed using projectiles cut from a 1.6 mm thick fiberglass circuit board substrate panel. Results from test HITF07017, shown in figures 9 and 10, correlates with the observed impact features reasonably well. The test was performed at 4.14 km/sec with an impact angle of 45 degrees using a cylindrical projectile with a diameter and length of 1.25 mm. The fiberglass circuit board material had a density of 1.65 g/cu cm, giving a projectile mass of 2.53 mg. An analysis was performed using the Bumper code to estimate the probability of impact to the shuttle from a 1.25 mm diameter particle. Table 1 shows a 1.6% chance (impact odds = 1 in 62) of a 1.25 mm or larger MMOD impact on the radiators of the vehicle during a typical ISS mission. There is a 0.4% chance (impact odds = 1 in 260) that a 1.25 mm or larger MMOD particle would impact the RCC wing leading edge and nose cap during a typical miion. Figure 11 illustrates the vulnerable areas of the wing leading edge reinforced carbon-carbon (RCC), an area of the vehicle that is very sensitive to impact damage. The highlighted red, orange, yellow, and light green areas would be expected to experience critical damage if impacted by an OD particle such as the one that hit the RH4 radiator panel on STS-115.

Hyde, J.↗

NASA NTRS1989

Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.

Hariharan, S. I.↗

NASA NTRS1992

Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

Hariharan, S. I.↗

NASA NTRS1992

Direct numerical simulations of a spatially developing plane wake

In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Maekawa, Hiroshi↗

DOE OSTI2020

Medium-induced gluon radiation with full resummation of multiple scatterings for realistic parton-medium interactions

The new precision era of jet quenching observables at both RHIC and the LHC calls for an improved and more precise description of in-medium gluon emissions. The development of new theoretical tools and analytical calculations to tackle this challenge has been hampered by the inability to include the effects of multiple scatterings with the medium using a realistic model for the parton-medium interactions. In this paper, we show how the analytical expressions for the full in-medium spectrum, including the resummation of all multiple scatterings, can be written in a form where the numerical evaluation can be easily performed without the need of the usually employed harmonic or single hard approximations. We present the transverse momentum and energy-dependent medium- induced gluon emission distributions for known realistic interaction models to illustrate how our framework can be applied beyond the limited kinematic regions of previous calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

A variational multiscale immersed meshfree method for heterogeneous materials

Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Manipulation of self-organized multi-vortical states in active magnetic roller suspensions

Ensembles of active magnetic colloids demonstrate complex collective behavior and self-organization when driven out of equilibrium by external magnetic fields. The interplay between magnetic and hydrodynamic interactions often result in spontaneous self-assembly and the emergence of localized vortices in ensembles of ferromagnetic rollers. We report experimental and computational study of the self-organized multi-vortical state in ensembles of magnetic rollers under the imposed external confining potential realized by patterned substrates. We explore the behavior of the system on a substrate patterned with shallow wells ordered in a lattice with square symmetry and lattice spacing smaller than the wells’ diameter. Here we demonstrate, that ensembles of active magnetic rollers evolve in response to changes in the geometry of the confining lattice from a globally correlated state characterized by anti-ferromagnetic vortex ordering to a state with rapidly changing particle flows and self-organized vortical states with a lattice constant larger than one of the confining pattern. Our experimental observations are accompanied by numerical simulations based on phenomenological coarse grained particle dynamics coupled to Navier–Stokes hydrodynamics in shallow water approximation. The reported results provide insights into the collective behavior of active magnetic rollers under confinement and suggest strategies for the manipulation of collective dynamic states in active magnetic liquids.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Evaluation of Methods for Causal Discovery in Hydrometeorological Systems

Understanding causal relations is of utmost importance in hydrology and climate research for systems identification, prediction, and understanding systems behavior in a changing climate. Traditionally, researchers in hydrometeorology attempted to study causal questions by conducting controlled experiments using numerical models. This approach, however, in most cases of interest provides uncertain results because the models are approximate representation of the natural system. An alternative approach that has recently drawn significant attention in several fields is to infer causal relations from purely observational data. It possesses several traits to its utility particularly in hydrometeorology due to the rapid accumulation of in situ and remotely sensed data records. The first objective of this study is to present a brief description of four causal discovery methods (Granger causality, Transfer Entropy, graph-based algorithms, and Convergent Cross Mapping) with special emphasis on the assumptions on which they are built. Second, using synthetic data generated from a hydrological model, we assess their performance in retrieving causal information taking into account sensitivity to sample size and presence of noise. Last, we use causal analysis to examine and formulate hypotheses on causal drivers of evapotranspiration in a shrubland region during summer and winter seasons. An interpretation of the hypotheses based on canopy seasonal dynamics and evapotranspiration processes is presented. It is hoped that the results presented here can be useful in guiding researchers studying hydrometeorological systems as to which causal method is most appropriate to the characteristics of the system under study.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗

DOE OSTI2022

Spin dynamics and exchange interaction in orthoferrite TbFeO 3 with non-Kramers rare-earth ion

The low-temperature spin dynamics of the orthorhombic TbFeO 3 perovskite has been studied. It has been found that the inelastic neutron scattering (INS) spectrum of the investigated compound contains two modes corresponding to different sublattices. It is shown that the iron subsystem orders antiferromagnetically at T N =632 K and exhibits the high-energy magnon dispersion. The magnetic dynamics of this subsystem has been described within the linear spin wave theory and the in-plane and out-of-plane exchange anisotropy has been demonstrated. The approach proposed previously to describe the magnon dispersion in the TmFeO 3 compound has been used. Three levels of the nondispersive crystal electric field corresponding to Tb 3+ ions have been found in the energy region below 40 meV at about 17, 26, and 35 meV. The behavior of the magnetic correlation length of the terbium subsystem has been determined by studying the diffuse scattering at different temperatures. The evolution of this subsystem has been numerically described within the point charge model. In conclusion, it is shown that the numerical data agree satisfactorily with the experiment and with the general concept of the single-ion approximation applied to the rare-earth subsystem of orthorhombic perovskites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗