Physics Commons^™

U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli

Department of Computer Science Faculty Publications

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data …

Patch-Wise Training With Convolutional Neural Networks To Synthetically Upscale Cfd Simulations, John P. Romano, Alec C. Brodeur, Oktay Baysal

Mechanical & Aerospace Engineering Faculty Publications

This paper expands the authors’ prior work[1], which focuses on developing a convolutional neural network (CNN) model capable of mapping time-averaged, unsteady Reynold’s-averaged Navier-Stokes (URANS) simulations to higher resolution results informed by time-averaged detached eddy simulations (DES). The authors present improvements over the prior CNN autoencoder model that result from hyperparameter optimization, increased data set augmentation through the adoption of a patch-wise training approach, and the predictions of primitive variables rather than vorticity magnitude. The training of the CNN model developed in this study uses the same URANS and DES simulations of a transonic flow around several NACA 4-digit airfoils …

Microfluidic Study Of The Electrocoalescence Of Aqueous Droplets In Crude Oil, Thomas Leary, Mohsen Yeganeh, Charles Maldarelli

Publications and Research

In electrocoalescence, an electric field is applied to a dispersion of conducting water droplets in a poorly conducting oil to force the droplets to merge in the direction of the field. Electrocoalescence is used in petroleum refining to separate water from crude oil and in droplet-based microfluidics to combine droplets of water in oil and to break emulsions. Using a microfluidic design to generate a two-dimensional (2D) emulsion, we demonstrate that electrocoalescence in an opaque crude oil can be visualized with optical microscopy and studied on an individual droplet basis in a chamber whose height is small enough to make …

Attainment Of Rigorous Thermodynamic Consistency And Surface Tension In Single-Component Pseudopotential Lattice Boltzmann Models Via A Customized Equation Of State, Cheng Peng, Luis F. Ayala, Zhicheng Wang, Orlando M. Ayala

Engineering Technology Faculty Publications

The lack of thermodynamic consistency is a well-recognized problem in the single-component pseudopotential lattice Boltzmann models which prevents them from replicating accurate liquid and vapor phase densities; i.e., current models remain unable to exactly match coexisting density values predicted by the associated thermodynamic model. Most of the previous efforts had attempted to solve this problem by introducing tuning parameters, whose determination required empirical trial and error until acceptable thermodynamic consistency was achieved. In this study, we show that the problem can be alternatively solved by properly designing customized equations of state (EOSs) that replace any cubic EOS of choice during …

Fluted Films, Nathan B. Spiers, Mohammad M. Mansoor, Jesse Belden, Randy Craig Hurd, Zhao Pan, Tadd T. Truscott

Mechanical and Aerospace Engineering Faculty Publications

This paper is associated with a poster winner of a 2017 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.P0030

The Role Of Surface Vorticity During Unsteady Separation, Matthew Scott Melius, Karen Mulleners, Raul Bayoan Cal

Mechanical and Materials Engineering Faculty Publications and Presentations

Unsteady flow separation in rotationally augmented flow fields plays a significant role in a variety of fundamental flows. Through the use of time-resolved particle image velocimetry, vorticity accumulation and vortex shedding during unsteady separation over a three-dimensional airfoil are examined. The results of the study describe the critical role of surface vorticity accumulation during unsteady separation and reattachment. Through evaluation of the unsteady characteristics of the shear layer, it is demonstrated that the buildup and shedding of surface vorticity directly influence the dynamic changes of the separation point location. The quantitative characterization of surface vorticity and shear layer stability enables …

Fluid-Dynamic Models Of Geophysical Waves, Alan Compelli

Doctoral

Geophysical waves are waves that are found naturally in the Earth's atmosphere and oceans. Internal waves, that is waves that act as an interface between uids of dierent density, are examples of geophysical waves. A uid system with a at bottom, at surface and internal wave is initially considered. The system has a depth-dependent current which mimics a typical ocean set-up and, as it is based on the surface of the rotating Earth, incorporates Coriolis forces. Using well established uid dynamic techniques, the total energy is calculated and used to determine the dynamics of the system using a procedure called …

Puddle Jumping: Spontaneous Ejection Of Large Liquid Droplets From Hydrophobic Surfaces During Drop Tower Tests, Babek Attari, Mark M. Weislogel, Andrew Paul Wollman, Yongkang Chen, Trevor Snyder

Mechanical and Materials Engineering Faculty Publications and Presentations

Large droplets and puddles jump spontaneously from sufficiently hydrophobicsurfaces during routine drop tower tests. The simple low-cost passive mechanism can in turn be used as an experimental device to investigate dynamic droplet phenomena for drops up to 104 times larger than their normal terrestrial counterparts. We provide and/or confirm quick and qualitative design guides for such “drop shooters” as employed in drop tower tests including relationships to predict droplet ejection durations and velocities as functions of drop volume, surface texture, surface contour, wettability pattern, and fluid properties including contact angle. The latter is determined via profile image comparisons with numerical …

More Investigations In Capillary Fluidics Using A Drop Tower, Andrew Paul Wollman, Mark M. Weislogel, Brentley M. Wiles, Donald Pettit, Trevor Snyder

Mechanical and Materials Engineering Faculty Publications and Presentations

A variety of contemplative demonstrations concerning intermediate-to-large length scale capillary fluidic phenomena were made possible by the brief weightless environment of a drop tower (Wollman and Weislogel in Exp Fluids 54(4):1, 2013). In that work, capillarity-driven flows leading to unique spontaneous droplet ejections, bubble ingestions, and multiphase flows were introduced and discussed. Such efforts are continued herein. The spontaneous droplet ejection phenomena (auto-ejection) is reviewed and demonstrated on earth as well as aboard the International Space Station. This technique is then applied to novel low-g droplet combustion where soot tube structures are created in the wakes of burning drops. …

Complex Capillary Fluidic Phenomena For Passive Control Of Liquids In Low-Gravity Environments, Logan Torres

Undergraduate Research & Mentoring Program

In an effort to further apply the recent results of puddle jumping research, we seek to expand the oblique droplet impact studies of others by exploiting large liquid droplets in the near weightless environment of a drop tower. By using the spontaneous puddle jump mechanism, droplets of volumes 1 mL ≤ V ≤ 3 mL with corresponding Weber numbers of We ≈ 1 are impinged on surfaces inclined in the range 40° ≤ α ≤ 80° (measured from the horizontal plane). Impact surface wetting characteristics exhibit static contact angles θstatic = 165 ± 5°. All impacts result in complete rebound. …

A Unified And Preserved Dirichlet Boundary Treatment For The Cell-Centered Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura A. Schaefer

Publications

A new boundary treatment is proposed for the finite volume discrete Boltzmann method (FVDBM) that can be used for accurate simulations of curved boundaries and complicated flow conditions. First, a brief review of different boundary treatments for the general Boltzmann simulations is made in order to primarily explain what type of boundary treatment will be developed in this paper for the cell-centered FVDBM. After that, the new boundary treatment along with the cell-centered FVDBM model is developed in detail. Next, the proposed boundary treatment is applied to a series of numerical tests with a detailed discussion of its qualitative and …

Dynamics Of Skirting Droplets, Caleb Akers, Jacob Hale

Annual Student Research Poster Session

No abstract provided.

A Mean Curvature Model For Capillary Flows In Asymmetric Containers And Conduits, Yongkang Chen, Noël Tavan, Mark M. Weislogel

Mechanical and Materials Engineering Faculty Publications and Presentations

Capillarity-driven flows resulting from critical geometric wetting criterion are observed to yield significant shifts of the bulk fluid from one side of the container to the other during "zero gravity" experiments. For wetting fluids, such bulk shift flows consist of advancing and receding menisci sometimes separated by secondary capillary flows such as rivulet-like flows along gaps. Here we study the mean curvature of an advancing meniscus in hopes of approximating a critical boundary condition for fluid dynamics solutions. It is found that the bulk shift flows behave as if the bulk menisci are either “connected” or "disconnected." For the connected …

Compound Capillary Rise, Mark M. Weislogel

Mechanical and Materials Engineering Faculty Publications and Presentations

Irregular conduits, complex surfaces, and porous media often manifest more than one geometric wetting condition for spontaneous capillary flows. As a result, different regions of the flow exhibit different rates of flow, all the while sharing common dynamical capillary pressure boundary conditions. The classic problem of sudden capillary rise in tubes with interior corners is revisited from this perspective and solved numerically in the self-similar visco-capillary limit à laLucas–Washburn. Useful closed-form analytical solutions are obtained in asymptotic limits appropriate for many practical flows in conduits containing one or more interior corner. The critically wetted corners imbibe fluid away from …

Unitary Qubit Lattice Gas Representation Of 2d And 3d Quantum Turbulence, George Vahala, Bo Zhang, Jeffrey Yepez, Linda L. Vahala, Min Soe

Electrical & Computer Engineering Faculty Publications

No abstract provided.

Nonlinear Ordinary Differential Equations In Fluid Dynamics, John D. Ramshaw

Physics Faculty Publications and Presentations

The equivalence between nonlinear ordinary differential equations (ODEs) and linear partial differential equations (PDEs) was recently revisited by Smith, who used the equivalence to transform the ODEs of Newtonian dynamics into equivalent PDEs, from which analytical solutions to several simple dynamical problems were derived. We show how this equivalence can be used to derive a variety of exact solutions to the PDEs describing advection in fluid dynamics in terms of solutions to the equivalent ODEs for the trajectories of Lagrangian fluid particles. The PDEs that we consider describe the time evolution of non-diffusive scalars, conserved densities, and Lagrangian surfaces advected …

Whispering-Gallery Acoustic Sensing: Characterization Of Mesoscopic Films And Scanning Probe Microscopy Applications, Andres H. La Rosa, Nan Li, Rodolfo Fernandez, Xiaohua Wang, Richard Nordstrom, S. K. Padigi

Physics Faculty Publications and Presentations

Full understanding of the physics underlying the striking changes in viscoelasticity, relaxation time, and phase transitions that mesoscopic fluid-like films undergo at solid-liquid interfaces, or under confinement between two sliding solid boundaries, constitutes one of the major challenges in condensed matter physics. Their role in the imaging process of solid substrates by scanning probe microscopy (SPM) is also currently controversial. Aiming at improving the reliability and versatility of instrumentation dedicated to characterize mesoscopic films, a noninvasive whispering-gallery acoustic sensing (WGAS) technique is introduced; its application as feedback control in SPM is also demonstrated. To illustrate its working principle and potential …

Gravity Effects On Capillary Flows In Sharp Corners, Enrique Ramé, Mark M. Weislogel

Mechanical and Materials Engineering Faculty Publications and Presentations

We analyze the effect of gravity on capillary flows in sharp corners. We consider gravity perpendicular and parallel to the channel axis. We analyze both steady and unsteady flows. In the steady analysis the main result is a closed form expression for the flow rate as a function of the two gravity components. Good agreement with steady experiments is offered as support of the model. The unsteady analysis is restricted to “small” values of the two gravity parameters and is accomplished using a similarity formulation. The similarity coefficients of the gravity corrections are fully determined by the coefficients of the …

Space Research Projects For The International Space Station, Kyle Hodgson

Posters

Space Italian Dressing Experimental Setup (SIDES) examines the dynamics of fluid segregation between fluids of differing densities. While in space the fluids will not undergo buoyant or convective forces, thus isolating the affects of separation due to density and molecular forces. The experiment will serve as an outreach experiment in addition to gleaning scientific data; mixtures are a topic of study in the 5th grade curriculum.

The objective of International Paper Airplanes in Space (IPAS) is to excite children about space research by giving them a chance to take part in it. IPAS includes collecting paper airplanes made by elementary-school …

Drag Reduction In Turbulent Flows Over Micropatterned Superhydrophobic Surfaces, Robert J. Daniello

Masters Theses 1911 - February 2014

Periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide drag reduction in the laminar flow regime, have been demonstrated capable of reducing drag in the turbulent flow regime as well. Superhydrophobic surfaces contain micro or nanoscale hydrophobic features which can support a shear-free air-water interface between peaks in the surface topology. Particle image velocimetry and pressure drop measurements were used to observe significant slip velocities, shear stress, and pressure drop reductions corresponding to skin friction drag reductions approaching 50%. At a given Reynolds number, drag reduction was found to increase with increasing feature size and spacing, as in …

Generalized Helmholtz-Kirchhoff Model For Two-Dimensional Distributed Vortex Motion, Raymond J. Nagem, Guido Sandri, David Uminsky, C. Eugene Wayne

Mathematics

The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite functions and of the centers of vorticity concentrations. We prove the convergence of this expansion and show that in the zero viscosity and zero core size limit we formally recover the Helmholtz-Kirchhoff model for the evolution of point vortices. The present expansion systematically incorporates the effects of both viscosity and finite vortex core size. We also show that a low-order truncation of our expansion leads to the …

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …

Dynamical Evolution Of Volume Fractions In Multipressure Multiphase Flow Models, C. H. Chang, John D. Ramshaw

Physics Faculty Publications and Presentations

Compared to single-pressure models, multipressure multiphase flow models require additional closure relations to determine the individual pressures of the different phases. These relations are often taken to be evolution equations for the volume fractions. We present a rigorous theoretical framework for constructing such equations for compressible multiphase mixtures in terms of submodels for the relative volumetric expansion rates ∆Ei of the phases. These quantities are essentially the rates at which the phases dynamically expand or contract in response to pressure differences, and represent the general tendency of the volume fractions to relax toward values that produce local pressure equilibrium. We …

Hydrodynamic And Magnetohydrodynamic Computations Inside A Rotating Sphere, P. D. Mininni, D. C. Montgomery, L. Turner

Dartmouth Scholarship

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar–Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest …

Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …

Capillary-Driven Flows Along Rounded Interior Corners, Yongkang Chen, Mark M. Weislogel, Cory L. Nardin

Mechanical and Materials Engineering Faculty Publications and Presentations

The problem of low-gravity isothermal capillary flow along interior corners that are rounded is revisited analytically in this work. By careful selection of geometric length scales and through the introduction of a new geometric scaling parameter Tc, the Navier–Stokes equation is reduced to a convenient∼O(1) form for both analytic and numeric solutions for all values of corner half-angle α and corner roundedness ratio λ for perfectly wetting fluids. The scaling and analysis of the problem captures much of the intricate geometric dependence of the viscous resistance and significantly reduces the reliance on numerical data compared with several previous solution methods …

Viscoelastic Flow In Rotating Curved Pipes, Yitung Chen, Huajun Chen, Jinsuo Zhang, Benzhao Zhang

Mechanical Engineering Faculty Research

Fully developed viscoelastic flows in rotating curved pipes with circular cross section are investigated theoretically and numerically employing the Oldroyd-B fluid model. Based on Dean’s approximation, a perturbation solution up to the secondary order is obtained. The governing equations are also solved numerically by the finite volume method. The theoretical and numerical solutions agree with each other very well. The results indicate that the rotation, as well as the curvature and elasticity, plays an important role in affecting the friction factor, the secondary flow pattern and intensity. The co-rotation enhances effects of curvature and elasticity on the secondary flow. For …

Low Magnetic Prandtl Number Dynamos With Helical Forcing, Pablo D. Mininni, David C. Montgomery

Dartmouth Scholarship

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from ∼0.3 to ∼0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity …

The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …