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At least 73 records · Page 4

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Science & Technology - Other Topics↗

Neutron Electric Dipole Moments with Clover Fermions

We present preliminary results for the contributions to the neutron EDM arising from the QCD θ-term, the Weinberg three-gluon and the quark chromo-EDM operators from our ongoing lattice calculations using clover valence quarks on the MILC HISQ lattices. We use the gradient-flow technique to smooth the lattices and renormalize the gluonic operators, and use the Schwinger source method to incorporate the quark chromo-EDM interactions in the quark propagator. For the QCD θ-term and the Weinberg three-gluon operator, we report results in the gradient-flow scheme from 8 ensembles at four lattice spacings and three pion masses, including 2 physical pion mass ensembles. For the quark chromo-EDM, unrenormalized results are presented at two lattice spacings, a=0.12 and 0.09 fm, and two pion masses, M π =310 MeV and 220 MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-frequency sound propagation in a spatially varying mean flow

An equation for acoustic ray paths in a spatially varying mean flow was examined to determine some of the characteristics of the flow gradient effects on sound propagation. In a potential flow, the acoustic rays are deflected in the direction of increasing mean flow, and the gradient of the mean flow speed is the dominant factor causing the ray deflection. In contrast, in a sheared mean flow, the vorticity is the dominant factor in deflection of the acoustic rays.

Cho, Y. C.↗

High-frequency sound propagation in a spatially varying mean flow

An equation for acoustic ray paths in a spatially varying mean flow has been examined to determine some of the characteristics of the flow gradient effects on sound propagation. In a potential flow the acoustic rays are deflected in the direction of increasing mean flow, and the gradient of the mean flow speed is the dominant factor causing the ray deflection. In contrast, in a sheared mean flow, the vorticity is the dominant factor in deflection of the acoustic rays.

Cho, Y. C.↗

Scale setting of SU⁡(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence

We set the scale of SU⁡(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A novel nonperturbative renormalization scheme for local operators

The gradient flow exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization). It can be used to describe real-space Wilsonian renormalization group transformations and determine the corresponding beta function. We propose a new nonperturbative renormalization scheme for local composite fermionic operators that uses the gradient flow and is amenable to lattice QCD calculations. We present preliminary nonperturbative results for the running of quark bilinear operators in this scheme and outline the calculation of perturbative matching to the MS-bar scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗

Effectiveness of Micro-Blowing Technique in Adverse Pressure Gradients

The impact of the micro-blowing technique (MBT) on the skin friction and total drag of a strut in a turbulent, strong adverse-pressure-gradient flow is assessed experimentally over a range of subsonic Mach numbers (0.3 less than M less than 0.7) and reduced blowing fractions (0 less than or equal to 2F/C (sub f,o) less than or equal to 1.75). The MBT-treated strut is situated along the centerline of a symmetric 2-D diffuser with a static pressure rise coefficient of 0.6. In agreement with presented theory and earlier experiments in zero-pressure-gradient flows, the effusion of blowing air reduces skin friction significantly (e.g., by 60% at reduced blowing fractions near 1.75). The total drag of the treated strut with blowing is significantly lower than that of the treated strut in the limit of zero-blowing; further, the total drag is reduced below that of the baseline (solid-plate) strut, provided that the reduced blowing fractions are sufficiently high. The micro-blowing air is, however, deficient in streamwise momentum and the blowing leads to increased boundary-layer and wake thicknesses and shape factors. Diffuser performance metrics and wake surveys are used to discuss the impact of various levels of micro-blowing on the aerodynamic blockage and loss.

Welch, Gerard E.↗

Reynolds number influences in aeronautics

Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical portion of the problem.

Bushnell, Dennis M.↗

A review of turbulence measurements in compressible flow

A survey of turbulence measurements in compressible flows is presented. The majority of turbulence measurements at super- and hypersonic speeds were made for the zero pressure gradient, turbulent boundary layer. It was found that the nondimensional turbulent stress terms for the zero pressure gradient flow appear to agree closely with equivalent incompressible measurements in the outer part of the boundary layer. The stress terms were nondimensionalized by the wall value of shear stress and plotted versus the distance from the wall, nondimensionalized by the boundary-layer thickness. Indirect evaluation of the total shear stress distribution from mean velocity measurements for both super- and hypersonic flows (zero pressure gradient, two-dimensional flows) indicate a near universal distribution. These total shear stress curves also agree very closely with measured incompressible shear stress distributions. Recent laser anemometer measurements of the turbulent Reynolds shear stress (puv), reported by Johnson and Rose for a Mach number 2.9 flow, are in reasonable agreement with the expected total shear stress curve over the outer 60% of the boundary layer.

Sandborn, V. A.↗

The Blunt Plate In Hypersonic Flow

The sonic-wedge characteristics method has been used to obtain the shock shapes and surface pressure distributions on several blunt two-dimensional shapes in a hypersonic stream for several values of the ratio of specific heats. These shapes include the blunt slab at angle of attack and power profiles of the form yb = a)P, where 0 les than m less than 1, Yb and x are coordinates of the body surface, and a is a constant. These numerical results have been compared with the results of blast-wave theory, and methods of predicting the pressure distributions and shock shapes are proposed in each case. The effects of a free-stream conical-flow gradient on the pressure distribution on a blunt slab in hypersonic flow were investigated by the sonic-wedge characteristics method and were found to be sizable in many cases. Procedures which are satisfactory for reducing pressure data obtained in conical flows with small gradients are presented.

Baradell, Donald L.↗

Study of effect of PWR cold leg temperature gradient on reactor core condition

Effects of temperature and flow gradients in Westinghouse designed three-loop Pressurized Water Reactor (PWR) cold legs, the piping between the main coolant pump and the reactor vessel, were evaluated using Computational Fluid Dynamics (CFD) code STAR CCM+ and coupled neutronic and thermal-hydraulic (T/H) code system VERA. In the parametric study, several symmetric and asymmetric temperature gradients that were significantly larger than those observed from plant measurements were applied to the cold leg inlets for comparison with the base case without any temperature gradient. A CFD model using the STAR-CCM+ code was developed for a portion of the RCS region between the Reactor Coolant Pump (RCP) and the core inlet based on previously validated modeling approach. The CFD simulation results were processed for the temperature and flow rate distributions at the core inlet as input to the VERA calculations. The VERA code system consists of COBRA-TF (CTF) for thermal-hydraulics, MPACT for reactor physics and neutron transport, and ORIGEN for isotopic depletion. The VERA model was for depletion calculations of a high-burnup loading pattern with the reactor core in pin-by-pin and subchannel resolution. The results of the study indicate that the postulated temperature gradients within the PWR cold legs do not result in any significant changes in the core inlet temperature distributions and the core power distributions during the reactor operation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Refinement Of Hexahedral Cells In Euler Flow Computations

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Melton, John E.↗

On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system

We present a convergence analysis of an unconditionally energy-stable first-order semi-discrete numerical scheme designed for a hydrodynamic Q-tensor model, the so-called Beris-Edwards system, based on the Invariant Energy Quadratization Method (IEQ). The model consists of the Navier–Stokes equations for the fluid flow, coupled to the Q-tensor gradient flow describing the liquid crystal molecule alignment. By using the Invariant Energy Quadratization Method, we obtain a linearly implicit scheme, accelerating the computational speed. However, this introduces an auxiliary variable to replace the bulk potential energy and it is a priori unclear whether the reformulated system is equivalent to the Beris-Edward system. In this work, we prove stability properties of the scheme and show its convergence to a weak solution of the coupled liquid crystal system. We also demonstrate the equivalence of the reformulated and original systems in the weak sense.

Weber, Franziska↗

Critical examination of two-equation turbulence closure models

Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.

Chambers, T. L.↗