Shape optimization of stirring rods for mixing binary fluids
Abstract Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint lo...
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| Published in | IMA journal of applied mathematics Vol. 85; no. 5; pp. 762 - 789 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford University Press
01.10.2020
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| Online Access | Get full text |
| ISSN | 0272-4960 1464-3634 |
| DOI | 10.1093/imamat/hxaa012 |
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| Abstract | Abstract
Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier–Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilize a Fourier-based approach for parameterizing and optimizing the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimization space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency. |
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| AbstractList | Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier–Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilize a Fourier-based approach for parameterizing and optimizing the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimization space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency. Abstract Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier–Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilize a Fourier-based approach for parameterizing and optimizing the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimization space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency. |
| Author | Schmid, Peter J Eggl, Maximilian F |
| Author_xml | – sequence: 1 givenname: Maximilian F surname: Eggl fullname: Eggl, Maximilian F email: meggl@princeton.edu organization: Department of Mathematics, Imperial College London, London SW7 2AZ, UK – sequence: 2 givenname: Peter J surname: Schmid fullname: Schmid, Peter J organization: Department of Mathematics, Imperial College London, London SW7 2AZ, UK |
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| CitedBy_id | crossref_primary_10_1017_jfm_2020_448 crossref_primary_10_1103_PhysRevFluids_7_073904 crossref_primary_10_1177_09544089221143892 crossref_primary_10_1016_j_jcp_2020_110033 crossref_primary_10_1088_1361_6420_acdd8e |
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| Keywords | penalization Fourier-based shape parameterization optimization mixing adjoint method |
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Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing... Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing... |
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