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Data for Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid
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Mandre, Shreyas (2020) Data for Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid. [Dataset]
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_zip.png) |
Archive (ZIP) (Zip archive)
data.zip - Published Version Available under License Creative Commons Attribution 4.0. Download (8Gb) |
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Archive (ZIP) (Zip archive)
code-archive.zip - Published Version Available under License Creative Commons Attribution 4.0. Download (15Kb) |
Abstract
The dataset contains the solution of the mathematical problem presented in "Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid".
We determine the globally minimum time T needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined computationally using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a ‘spectral condition’ to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed ∝t1/4 and comes to rest with speed ∝(T−t)1/4 as a function of time t. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping.
| Item Type: | Dataset | ||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Type of Data: | Computational Data | ||||||
| Library of Congress Subject Headings (LCSH): | Fluid mechanics, Kinematics, Aerodynamics, Mathematical optimization | ||||||
| Publisher: | University of Warwick, Department of Mathematics | ||||||
| Official Date: | December 2020 | ||||||
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| Status: | Not Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Media of Output (format): | .hdf5, .c, .h, .py | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Copyright Holders: | University of Warwick | ||||||
| Description: | Data record consists of two zip archives, 'data' containing the raw data and 'code-archive' containing the code associated with the computationally generated dataset. |
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| Date of first compliant deposit: | 4 January 2021 | ||||||
| Date of first compliant Open Access: | 12 January 2021 | ||||||
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