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1. Steady Rayleigh–Bénard convection between stress-free boundaries

   https://doi.org/10.1017/jfm.2020.812  

   Wen, Baole; Goluskin, David; LeDuc, Matthew; Chini, Gregory P.; Doering, Charles R. (December 2020, Journal of Fluid Mechanics)

   null (Ed.)

   Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios $${\rm \pi} /5\leqslant \varGamma \leqslant 4{\rm \pi}$$ , where $$\varGamma$$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $$10^3\leqslant Ra\leqslant 10^{11}$$ , and four orders of magnitude in the Prandtl number, $$10^{-2}\leqslant Pr\leqslant 10^2$$ . At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $$Ra \rightarrow \infty$$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $$Ra^{1/3}$$ uniformly in $Pr$ . The prefactor of this scaling depends on $$\varGamma$$ and is largest at $$\varGamma \approx 1.9$$ . The Reynolds number $Re$ for large- $Ra$ rolls scales as $$Pr^{-1} Ra^{2/3}$$ with a prefactor that is largest at $$\varGamma \approx 4.5$$ . All of these large- $Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox ( Phys. Fluids , vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $$\varGamma$$ is smaller. 

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2. Ocean wave blocking by periodic surface rolls fortifies Arctic ice shelves

   https://doi.org/10.1017/jog.2023.58  

   Nekrasov, Peter; MacAyeal, Douglas R (August 2023, Journal of Glaciology)

   Abstract The Ward Hunt and Milne ice shelves are the present-day remnants of a much larger ice shelf that once fringed the coast of Ellesmere Island, Canada. These ice shelves possess a unique surface morphology consisting of wave-like rolls that run parallel to the shoreline. Setting aside the question of how these rolls originally developed, we consider the impact of this roll morphology on the stability of the ice shelf. In particular, we examine whether periodic variations in ice-shelf thickness and water depth implied by the rolls prevent the excitation of Lamb waves in the ice shelf. Using a hierarchy of numerical models, we find that there are band gaps in the flexural and extensional modes of the ice shelf, implying the existence of frequency ranges that lack wave motion. We show that an ice shelf with rolls is able to reflect waves in these frequency ranges that are incident upon its ice front, thereby mitigating undue stress and calving. We speculate that the roll morphology provides a “fitness” for survival that explains why rolls are observed in the oldest and thickest multiyear sea ice of the Arctic. 

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3. Optimizing the Rolling Process of Lightweight Materials

   https://doi.org/10.3390/cryst14070582  

   Rawles, Jessica; Fialkova, Svitlana; Hubbard, Kai; Xu, Zhigang; Hale, Christopher; Sankar, Jagannathan (July 2024, Crystals)

   Conventional rolling is a plastic deformation process that uses compression between two rolls to reduce material thickness and produce sheet/plane geometries. This deformation process modifies the material structure by generating texture, reducing the grain size, and strengthening the material. The rolling process can enhance the strength and hardness of lightweight materials while still preserving their inherent lightness. Lightweight metals like magnesium alloys tend to lack mechanical strength and hardness in load-bearing applications. The general rolling process is controlled by the thickness reduction, velocity of the rolls, and temperature. When held at a constant thickness reduction, each pass through the rolls introduces an increase in strain hardening, which could ultimately result in cracking, spallation, and other defects. This study is designed to optimize the rolling process by evaluating the effects of the strain rate, rather than the thickness reduction, as a process control parameter. 

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4. Assessing Wound Roll Quality using Measured Stiffness and Models

   Markum, R.; Good, J.K. (June 2019, Proceedings of the Fifteenth International Conference on Web Handling)

   For those concerned with roll quality it is difficult to suppress the urge to compress the outer surface of a wound roll with your thumb to sense how tightly the roll was wound and how large the internal pressures might be. If several rolls of a given web are wound at unique tensions a human could often arrange these rolls in order of ascending winding tension using their thumb test. The thumb senses the relative conforming deformation of the roll surface. A soft roll would deform more and have greater contact area with our thumb than a hard roll for a given load. The thumb test is most useful on softer rolls wound from nonwovens, tissues, some grades of paper and polymer films but less so on metal coils that deform little in comparison to our thumb. The physics define stiffness as the extent to which an object resists deformation in response to an applied force. This publication reports the results of research where the stiffness of the outer surface of a wound roll is used to characterize the internal residual stresses throughout the roll due to winding. Measurements of stiffness of the outer surface of wound rolls will be demonstrated using commercially available devices along with a proposed handheld device all having greater resolution than the thumb. These measurements will be coupled with models to allow the exploration of internal residual stresses in the wound roll that can be used to investigate winding defects and roll quality. 

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5. Efficient Three-Dimensional Model to Predict Time History of Structural Dynamics in Cold Rolling Mills

   https://doi.org/10.1115/1.4052703  

   Patel, Akash; Malik, Arif; Mathews, Ritin (July 2022, Journal of Manufacturing Science and Engineering)

   Abstract Introduced is a new physics-based three-dimensional (3D) mathematical model capable of efficiently predicting time histories of the nonlinear structural dynamics in cold rolling mills used to manufacture metal strips and sheets. The described model allows for the prediction of transient strip thickness profiles, contact force distributions, and roll-stack deformations due to dynamic disturbances. Formulation of the new 3D model is achieved through a combination of the highly efficient simplified-mixed finite element method with a Newmark-beta direct time integration approach to solve the system of differential equations that governs the motion of the roll-stack. In contrast to prior approaches to predict structural dynamics in cold rolling, the presented method abandons several simplifying assumptions and restrictions, including 1D or 2D linear lumped parameter analyses, vertical symmetry, continuous and constant contact between the rolls and strip, as well as the inability to model cluster-type mill configurations and accommodate typical profile/flatness control mechanisms used in industry. Following spatial and temporal convergence studies of the undamped step response, and validation of the damped step response, the new model is demonstrated for a 4-high mill equipped with both work-roll bending and work-roll crown, a 6-high mill with continuously variable crown (CVC) intermediate rolls, and finally a complex 20-high cluster mill. Solution times on a single computing processor for the damped 4-high and 20-high case studies are just 0.37 s and 3.38 s per time-step, respectively. 

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