Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session L23: General Fluid Dynamics: Mathematical Methods |
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Chair: Tom Mullin, Oxford Room: 605 |
Monday, November 25, 2019 1:45PM - 1:58PM |
L23.00001: Force at the surface of a swirl in a fluid obeying the 3D-wave equation: closed form equations from our novel nonharmonic solutions to the wave equation in spherical coordinates. Hector Munera This writer discovered in the 1990s new nonharmonic closed solutions for the three-dimensional homogeneous classical wave equation (3D-HCWE) in spherical coordinates [1-3]. Here we report for the first time the force at the surface of a swirl formed in a classical fluid described by the 3D-HCWE. Force is obtained in closed form, and calculation does not require time consuming numerical methods. [1] Munera H A, Buritica D, Guzman O and Vallejo J I (1995) ``Non-conventional solutions for the travelling wave equation'' (in Spanish) \textit{Revista Colombiana de Fisica }(\textit{Colombian Journal of Physics}) \textbf{27} (1) 215-218. [2] Munera H A and Guzman O (1997) ``New explicit nonperiodic solutions of the homogeneous wave equation'' \textit{Found. Phys. Lett.} \textbf{10} (1) 31-41. [3] Munera H A (2000) ``New closed solutions in spherical coordinates for the three dimensional homogeneous wave equations'' (in Spanish) \textit{Momento} \textbf{20} 1-30. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L23.00002: An extension to the extended Beltrami solution method and solutions to the 3D Navier-Stokes equations Nolan Dyck, Anthony Straatman Recirculating flows, such as those seen in vortex separators, swirl combustion chambers, and Ranque-Hilsch vortex tubes can seldom be modelled analytically, and where exact solutions may be found, viscous effects are neglected. In this work we attempt to describe swirling motions, by extending the extended Beltrami solution method for the Navier-Stokes equations to describe 3D flows wherein the flow variables may be written as a function of two spatial co-ordinates. The new formulation emerges when auxiliary functions are added to the general Bragg-Hawethorne equations and reinserted into the governing equations. As is the case with the extended Beltrami approach, solutions are sought by guessing forms of the auxiliary functions, and attempting to solve the system of equations. Using this technique, we find many new solutions. Well known planar flows including Kovasznay flow and Wang's flow have been generalized to three-dimensions. A unique solution in plane polar co-ordinates has been found. A new 3D swirling flow solution which can be considered the angular analogue to Kovasznay flow is found which exhibits many realistic features observed in swirling flow applications. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L23.00003: Exact Solutions for Flows in Periodic Domains Peter Baddoo, Darren Crowdy In this work it is shown that recent advances in conformal geometry can be leveraged to obtain analytic solutions for flows in periodic domains. The solutions are constructed in a parametric circular domain and then conformally mapped to the periodic physical domain. By expressing the problem in terms of the transcendental Schottky--Klein prime function, the ensuing solutions are valid for domains of arbitrary connectivity, i.e. any number of objects per period window. Moreover, the conformal mapping to the desired physical domain may be constructed using a new periodic Schwarz--Christoffel formula. The mathematical analysis is valid for conformally invariant equations and is therefore applicable to a range of scenarios in fluid mechanics including potential flows, advection-diffusion problems and interfacial dynamics. Accordingly, the solutions find relevance in areas such as vortex dynamics, transport phenomena, turbomachinery flows, mesh generation and fractal growth. [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L23.00004: Comparison of Deep Learning strategies for flow field reconstruction from wall measurements Samir Beneddine This work explores deep learning reconstruction techniques to estimate the pressure field in the laminar wake of a bluff body from a few wall measurements. It aims at comparing two main strategies: a classical approach, where a neural network maps the input (the point-wise pressure measurements) to the target (the full pressure field) by minimizing the $L_2$-norm of the error between the output of the network and ground truth, a so-called decoupled approach, based on Generative Adversarial Networks. For the latter, a network is first trained to generate fields that are not distinguishable from actual pressure field obtained from a simulation. Then, given input measurements, it searches for the best match among all the possible field that it can generate. This generative strategy is a state-of-the-art approach for image inpainting, and it presents several strong advantages over the first method. For instance, it is totally flexible with respect to the input measurements: the same network can carry out the reconstruction no matter the location or the number of input sensors. Other interesting advantages will be detailed during the presentation, such as the ability of generative approaches to be used for temporal super-resolution. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L23.00005: Deep Learning Time-Dependent Hagen-Poiseuille Flow Nina Prakash, Wei Hu, Amir Barati Farimani Deep learning has emerged as a valuable tool for data-driven modeling of fluid flow systems. Rather than a traditional physics-based computational approach based on governing equations, deep learning can be used to derive models of flow systems directly from experimental or simulation data. In this work, we use Long Short Term Memory (LSTM) to learn the velocity profile development of Hagen-Poiseuille Flow in its time-dependent entry region. Given arbitrary boundary conditions including the pipe diameter, fluid properties, and axial pressure gradient, the network is able to predict the entry region velocity profiles as flow develops from rest with a mean squared error of less than 1{\%}. The model is trained solely on simulation data and thus is able to learn the behavior of the system with no knowledge of the physical mathematical model. This work contributes to a growing body of work on the application of machine learning to fluid modeling by proving the success of LSTM to model a time-dependent fluid flow system. The deep learning framework presented in this work has the potential to be successful for systems that involve complex geometries or turbulence that can make traditional approaches computationally inefficient and cumbersome, or for systems for which the underlying mathematical model is unknown. [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L23.00006: On the Advective-Diffusive Mass Transport of Gas Mixtures Alex Jarauta, Valentin Zingan, Peter Minev, Marc Secanell Mass transport of gas mixtures often occurs in a variety of engineering applications, such as fuel cells and cooling towers. Classic approaches such as the advection-diffusion equation are limited to binary mixtures and diluted species in a mixture. Also, these theories have been shown to be unable to reproduce several phenomena occurring in capillaries or small pores [1], such as osmotic diffusion (i.e., diffusion without a concentration gradient), reverse diffusion (i.e., diffusion in the direction of a positive concentration gradient), and diffusion barrier (i.e., no diffusion with a concentration gradient). The limitations of these classic models stem from the fact that only a mass-averaged velocity field is considered. In this work, a new multicomponent mass transport model was developed based on the work of Kerkhof and Geboers [1]. This model considered the velocity of each individual species, as well as an individual momentum equation. The Stefan tube diffusion experiment was used to compare our model to the advection-diffusion equation. Partial viscosities and gradients of species velocities were identified as key parameters to overcome the limitations of the advection-diffusion equation. References: [1] P.J.A.M. Kerkhof and M.A.M. Geboers, AIChE J., 51(1):79-12 [Preview Abstract] |
Monday, November 25, 2019 3:03PM - 3:16PM |
L23.00007: On the structure of distribution function in kinetic methods and its implications Lian-Ping Wang This theoretical talk will provide a derivation of the structure of the distribution functions in kinetic schemes such as the lattice Boltzmann method and the discrete unified gas kinetic scheme. Starting from the continuous Boltzmann equation with the BGK collision model and an external force field, the structure of the distribution functions, in terms of the macroscopic variables, is derived by using only the Chapman-Enskog expansion for continuum flows. The result can be used to understand why a source term in the kinetic equation can be designed to adjust fluid viscosity and thermal conductivity, {\it etc}. The structure of the discrete distribution functions used in the kinetic methods is then derived by proper transformation and the use of Gauss-Hermite quadrature. The result then provides a basic framework to discuss proper implementation of boundary condition in the kinetic methods. Previous boundary implementation methods will be examined under this framework and alternative boundary implementation methods will be explored. Possibility of using this approach to explore truncation errors in kinetic methods will also be discussed. [Preview Abstract] |
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