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At least 559 records · Page 31

Integral methods in the theory of the boundary layer

The application of the well-known basic principle of mechanics, the principle of Jourdain, to problems of the theory of the boundary layerleads tp an equation from which the equations of Von Karman, Leibenson, and Golubev are derived as special cases. The given equation may be employed in other integral methods. The present paper deals with the method of the variation of the thickness of the boundary layer. A number of new approximate formulas valuable in aerodynamic calculations for the fristion distribution are derived from this procedure. The method has been applied only to laminar boundary layers, but it seems probable that it may be generalized to include turbulent layers as well.

Loitsianskii, L G↗

A light weight regularization for wave function parameter gradients in quantum Monte Carlo

The parameter derivative of the expectation value of the energy, ∂E/∂p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve estimate of this derivative suffers from an infinite variance, which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator, which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias, which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of ∂E/∂p for a multi-Slater–Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater–Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of ∂E/∂p for VMC optimization techniques.

36 MATERIALS SCIENCE↗

Gaussian Process Modeling For Experimental Procedure Uncertainty

Many laboratory experiments generate data that are characterized by a form of uncertainty that differs from noise: experimental procedure uncertainty. The origin of this type of uncertainty is the difficulty in controlling a subset of experimental conditions in such a way that the experiment is perfectly reproducible within noise. In this report, we describe a Gaussian Process modeling-based method that accounts for experimental procedure uncertainty. The method accounts for variations in conditions from experiment to experiment that are independent between experiments, but correlated within each experiment, and incorporates the resulting uncertainty into predictions at future experimental settings. The method is discussed in the context of a specific chemistry application in which Raman scattering spectra are measured from three-component mixtures.

42 ENGINEERING↗

Corrosion Resistance of 309L Stainless Steel Claddings on Carbon Steel Produced with Wire-Fed Directed Energy Deposition

Additive manufacturing (AM) tools are capable of applying overlay austenitic stainless steel (SS) claddings to carbon steel components. The benefits of this approach over arc welding include a smaller heat-affected zone, residual stress reduction, and material savings. In particular, wire-directed energy deposition is a suitable technique because of its low material cost and high rate of production compared to other AM methods. However, metallurgical variations in composition, phase fraction, and microsegregation can potentially influence the corrosion behavior of such claddings. In this work, 309L SS is clad on carbon steel substrates and electrochemical methods are used to measure their general and pitting corrosion resistance in simulated marine environments (3.5 wt% NaCl solutions). Two-layer claddings are fabricated with four laser powers to understand the effects of bulk chemical composition, austenite/δ-ferrite phase fractions, and individual phase compositions on corrosion behavior. The two-layer claddings are compared to a single-layer cladding, wrought 304 SS, and the carbon steel substrate for a comprehensive assessment of corrosion performance. The two-layer claddings are remarkably resistant to general corrosion in the 3.5 wt% NaCl environment because of their high Cr content (21.6 wt% to 23.3 wt% Cr). The single-layer cladding exhibits localized corrosion at unmixed Fe-rich peninsulas that originate at the dissimilar metal boundary and protrude into the first cladding layer. All two-layer claddings possess higher pitting corrosion resistance than wrought 304 SS, demonstrating their effectiveness as a corrosion-resistant barrier. Here, the pitting corrosion resistance is superior for claddings made with lower laser powers, due to low dilution and greater δ-ferrite contents.

36 MATERIALS SCIENCE↗

Primal interface debonding formulation for finite strain isotropic plasticity

In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.

42 ENGINEERING↗

Grid adaption for bluff bodies

Methods of grid adaptation are reviewed and a method is developed with the capability of adaptation to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. Also the method was formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method and a movie was produced which shows simulataneously the transient behavior of the solution and the grid adaptation. The results are compared with the experimental and other numerical results.

Abolhassani, Jamshid S.↗

Grid adaption for hypersonic flow

The methods of grid adaption are reviewed and a method is developed with the capability of adaption to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. Also the method has been formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose body. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.

Abolhassani, Jamshid S.↗

Numerical solutions of three-dimensional Navier-Stokes equations for closed-bluff bodies

Methods of grid adaption are reviewed and a method is developed with the capability of adaption to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. The method has also been formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method and a movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption. The results are compared with the experimental and other numerical results.

Abolhassani, Jamshid S.↗

Topology and grid adaption for high-speed flow computations

This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.

Abolhassani, Jamshid S.↗

Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method

One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.

Blech, Richard A.↗

Stirling Analysis Comparison of Commercial Versus High-Order Methods

Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

Dyson, Rodger W.↗

Stirling Analysis Comparison of Commercial vs. High-Order Methods

Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/ proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's Compact scheme and Dyson s Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model although sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

Dyson, Rodger W.↗

Investigating the crust of neutron stars with neural-network quantum states

An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm −3 and 0.1 fm −3 , matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter.

Nuclear astrophysics↗

Dual-cone variational calculation of the two-electron reduced density matrix

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $\textit{N}$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. Further, we apply the method to computing the energies and properties of strongly correlated electrons—including atomic charges, electron densities, dipole moments, and orbital occupations—in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Floating Wind Farm Layout Optimization Considering Moorings and Seabed Variations

This paper presents a method for optimizing the layout of floating wind farms that accounts for realistic seabed variations and the consequent adjustments to the mooring systems required for different turbine positions. The mooring lines of floating wind farms create large spatial constraints that are depth-dependent, since mooring designs must adapt to variations in seabed conditions over the array area. We develop a layout optimization methodology that addresses this, adjusting mooring system designs based on the local seabed characteristics as the layout changes and using steady-state models for the wake effects and mooring lines. The approach includes design algorithms that adjust the anchor positions and line length to achieve the desired mooring line profile for different water depths, and a layout optimization framework that implements spatial constraints between the turbines, mooring lines, and lease area boundaries. Demonstrating the method on several cases shows the effect of the seabed and spatial-constraint factors, as well as their interactions, on the optimal array layout. This demonstration paves the way for scaling up the method, using more powerful optimization algorithms to handle larger farm sizes and situations with more intensely varied seabed conditions.

17 WIND ENERGY↗

The Localized Active Space Method with Unitary Selective Coupled Cluster

Here, we introduce a hybrid quantum-classical algorithm, the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. Derived from the localized active space unitary coupled cluster (LAS-UCCSD) method, LAS-USCCSD first performs a classical LASSCF calculation, then selectively identifies the most important parameters (cluster amplitudes used to build the multireference UCC ansatz) for restoring interfragment interaction energy using this reduced set of parameters with the variational quantum eigensolver method. We benchmark LAS-USCCSD against LAS-UCCSD by calculating the total energies of (H 2 ) 2 , (H 2 ) 4 , and trans-butadiene, and the magnetic coupling constant for a bimetallic compound [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ . For these systems, we find that LAS-USCCSD reduces the number of required parameters and thus the circuit depth by at least 1 order of magnitude, an aspect which is important for the practical implementation of multireference hybrid quantum-classical algorithms like LAS-UCCSD on near-term quantum computers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of the effects of manufacturing variations and materials on fatigue crack detection methods in gear teeth

The fatigue life of a gear tooth can be thought of as the sum of the number of cycles required to initiate a crack, N(sub i), plus the number of cycles required to propagate the crack to such a length that fracture occurs, N(sub p). The factors that govern crack initiation are thought to be related to localized stress or strain at a point, while propagation of a fatigue crack is a function of the crack tip parameters such as crack shape, stress state, and stress intensity factor. During a test there is no clear transition between initiation and propagation. The mechanisms of initiation and propagation are quite different and modeling them separately produces a higher degree of accuracy, but then the question that continually arises is 'what is a crack?' The total life prediction in a fracture mechanics model presently hinges on the assumption of an initial crack length, and this length can significantly affect the total life prediction. The size of the initial crack is generally taken to be in the range of 0.01 in. to 0.2 in. Several researchers have used various techniques to determine the beginning of the crack propagation stage. Barhorst showed the relationship between dynamic stiffness changes and crack propagation. Acoustic emissions, which are stress waves produced by the sudden movement of stressed materials, have also been successfully used to monitor the growth of cracks in tensile and fatigue specimens. The purpose of this research is to determine whether acoustic emissions can be used to define the beginning of crack propagation in a gear using a single-tooth bending fatigue test.

Wheitner, Jeffrey A.↗