Special Issue "Teaching and Learning of Fluid Mechanics, Volume II"

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (10 March 2021).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Ashwin Vaidya
E-Mail Website
Guest Editor
Department of Mathematics, Montclair State University, Montclair, NJ 07043, USA
Interests: mathematical fluid mechanics; non-linear partial differential equations; hydrodynamic stability; non-Newtonian fluid mechanics; fluid–structure interaction; experimental fluid mechanics; philosophy of science
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Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the various ways of teaching and learning about fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding in the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. Our Special Issue is therefore devoted to this very theme. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. We invite all kinds of articles, including research on the pedagogical aspects of fluid mechanics, communications, discussions, essays, letters, short notes and tutorials at the undergraduate or graduate level. Articles on historical aspects of fluids, novel and interesting experiments or theoretical calculations which can convey complex ideas in creative ways are welcome. Research articles are not appropriate for this issue. However, research presented in a simple manner and contextualized within the framework of the fluid mechanics curriculum may be acceptable.

All articles will undergo a rigorous peer review process.

Prof. Dr. Ashwin Vaidya
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Flow visualization
  • Experimental studies
  • Computer simulations
  • Mathematical modeling
  • Fluid flow in the arts
  • History of fluids
  • Undergraduate education
  • Applications of fluids

Published Papers (12 papers)

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Editorial

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Editorial
Contributions to the Teaching and Learning of Fluid Mechanics
Fluids 2021, 6(8), 269; https://doi.org/10.3390/fluids6080269 - 30 Jul 2021
Viewed by 378
Abstract
This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject [...] Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)

Research

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Article
Open Water Flume for Fluid Mechanics Lab
Fluids 2021, 6(7), 242; https://doi.org/10.3390/fluids6070242 - 03 Jul 2021
Cited by 1 | Viewed by 481
Abstract
Open water flume tanks with closed-loop circulation driven by centrifugal pumps are essential for hydro experimentation in academic settings as well as research centers. The device is also attractive due to its versatility and easy-to-maintain characteristics. Nevertheless, commercial open flume systems can be [...] Read more.
Open water flume tanks with closed-loop circulation driven by centrifugal pumps are essential for hydro experimentation in academic settings as well as research centers. The device is also attractive due to its versatility and easy-to-maintain characteristics. Nevertheless, commercial open flume systems can be expensive and become less prioritized in engineering schools. This paper describes the design and fabrication of an affordable, medium-size water flume tank, suitable for education purposes. The central piece of the system is a transparent observation chamber where fluid experiments are typically conducted and observed. The expected maximum average water speed in the observation chamber of about 60 cm per second was achieved by the inclusion of a 3 hp centrifugal pump. The size and capacity of the current design were constrained by space limitation and available funds. The educational facility was assigned as a two-semester multi-disciplinary capstone senior design project incorporating students and faculty of mechanical, electrical, and computer engineering programs in our campus. The design process provides a training platform for skills in the area of Computer Aided Designs (CAD), Finite Element Analysis (FEA), Computational Fluid Dynamics (CFD), manufacturing, and experimentation. The multi-disciplinary project has contributed to the improvement of soft skills, such as time management, team working, and professional presentation, of the team members. The total material cost of the facility was less than USD 6000, which includes the pump and its variable frequency driver. The project was made possible due to the generous sponsor of the Vibration Institute. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
A CFD Tutorial in Julia: Introduction to Laminar Boundary-Layer Theory
Fluids 2021, 6(6), 207; https://doi.org/10.3390/fluids6060207 - 03 Jun 2021
Cited by 1 | Viewed by 1258
Abstract
Numerical simulations of laminar boundary-layer equations are used to investigate the origins of skin-friction drag, flow separation, and aerodynamic heating concepts in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. A boundary-layer is a thin layer of fluid near a solid surface, and viscous [...] Read more.
Numerical simulations of laminar boundary-layer equations are used to investigate the origins of skin-friction drag, flow separation, and aerodynamic heating concepts in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. A boundary-layer is a thin layer of fluid near a solid surface, and viscous effects dominate it. Students must understand the modeling of flow physics and implement numerical methods to conduct successful simulations. Writing computer codes to solve equations numerically is a critical part of the simulation process. Julia is a new programming language that is designed to combine performance and productivity. It is dynamic and fast. However, it is crucial to understand the capabilities of a new programming language before attempting to use it in a new project. In this paper, fundamental flow problems such as Blasius, Hiemenz, Homann, and Falkner-Skan flow equations are derived from scratch and numerically solved using the Julia language. We used the finite difference scheme to discretize the governing equations, employed the Thomas algorithm to solve the resulting linear system, and compared the results with the published data. In addition, we released the Julia codes in GitHub to shorten the learning curve for new users and discussed the advantages of Julia over other programming languages. We found that the Julia language has significant advantages in productivity over other coding languages. Interested readers may access the Julia codes on our GitHub page. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
On the Existence of Leray-Hopf Weak Solutions to the Navier-Stokes Equations
Fluids 2021, 6(1), 42; https://doi.org/10.3390/fluids6010042 - 13 Jan 2021
Cited by 2 | Viewed by 999
Abstract
We give a rather short and self-contained presentation of the global existence for Leray-Hopf weak solutions to the three dimensional incompressible Navier-Stokes equations, with constant density. We give a unified treatment in terms of the domains and the relative boundary conditions and in [...] Read more.
We give a rather short and self-contained presentation of the global existence for Leray-Hopf weak solutions to the three dimensional incompressible Navier-Stokes equations, with constant density. We give a unified treatment in terms of the domains and the relative boundary conditions and in terms of the approximation methods. More precisely, we consider the case of the whole space, the flat torus, and the case of a general bounded domain with a smooth boundary (the latter supplemented with homogeneous Dirichlet conditions). We consider as approximation schemes the Leray approximation method, the Faedo-Galerkin method, the semi-discretization in time and the approximation by adding a Smagorinsky-Ladyžhenskaya term. We mainly focus on developing a unified treatment especially in the compactness argument needed to show that approximations converge to the weak solutions. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
Article
Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey
Fluids 2021, 6(1), 16; https://doi.org/10.3390/fluids6010016 - 31 Dec 2020
Cited by 4 | Viewed by 654
Abstract
Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., [...] Read more.
Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
PyDA: A Hands-On Introduction to Dynamical Data Assimilation with Python
Fluids 2020, 5(4), 225; https://doi.org/10.3390/fluids5040225 - 29 Nov 2020
Cited by 4 | Viewed by 1965
Abstract
Dynamic data assimilation offers a suite of algorithms that merge measurement data with numerical simulations to predict accurate state trajectories. Meteorological centers rely heavily on data assimilation to achieve trustworthy weather forecast. With the advance in measurement systems, as well as the reduction [...] Read more.
Dynamic data assimilation offers a suite of algorithms that merge measurement data with numerical simulations to predict accurate state trajectories. Meteorological centers rely heavily on data assimilation to achieve trustworthy weather forecast. With the advance in measurement systems, as well as the reduction in sensor prices, data assimilation (DA) techniques are applicable to various fields, other than meteorology. However, beginners usually face hardships digesting the core ideas from the available sophisticated resources requiring a steep learning curve. In this tutorial, we lay out the mathematical principles behind DA with easy-to-follow Python module implementations so that this group of newcomers can quickly feel the essence of DA algorithms. We explore a series of common variational, and sequential techniques, and highlight major differences and potential extensions. We demonstrate the presented approaches using an array of fluid flow applications with varying levels of complexity. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
Large-Scale, Multidisciplinary Laboratory Teaching of Fluid Mechanics
Fluids 2020, 5(4), 206; https://doi.org/10.3390/fluids5040206 - 11 Nov 2020
Cited by 1 | Viewed by 505
Abstract
The nature of fluid mechanics makes experimentation an important part of a course taught on the subject. Presented here is the application of a novel, large-scale multidisciplinary model of practical education in a fluids engineering laboratory. The advantages of this approach include efficiencies [...] Read more.
The nature of fluid mechanics makes experimentation an important part of a course taught on the subject. Presented here is the application of a novel, large-scale multidisciplinary model of practical education in a fluids engineering laboratory. The advantages of this approach include efficiencies through the economy of scale leading to better pedagogy for students. The scale justifies dedicated academic resources to focus on developing laboratory classes and giving specific attention to designing activities that meet learning outcomes. Four examples of applying this approach to fluid mechanics experiments are discussed, illustrating tactics that have been developed and honed through many repeated instances of delivery. “The measurement lab” uses a flow measurement context to teach identifying and managing general experimental uncertainty. In this lab, new students, unfamiliar with fluid mechanics, are guided through a process to gain understanding that can be applied to all future experimental activities. The “pressure loss in pipes” lab discusses the advantage of and process for sharing equipment and teaching resources between multiple cohorts. Here, the provision for students is adapted for context, such as the degree program or year of study. The “weirs big and small” lab provides a methodology for teaching the power of dimensional analysis to mechanical engineers using a field of fluid mechanics that is outside their usual theoretical studies. Finally, the “spillway design” lab discusses mechanisms for delivering independent, open-ended student experiments at scale, without excessive staff resource requirements. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
Numerical Computations of Vortex Formation Length in Flow Past an Elliptical Cylinder
Fluids 2020, 5(3), 157; https://doi.org/10.3390/fluids5030157 - 10 Sep 2020
Cited by 1 | Viewed by 1113
Abstract
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations [...] Read more.
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the bifurcation of the Karman vortex from steady symmetric to the unsteady, asymmetric configuration. Additionally, relationships between the vortex length and aspect ratio are also explored. The work presented here is an example of a module that can be used in a project based learning course on computational fluid dynamics. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
Continuous Project-Based Learning in Fluid Mechanics and Hydraulic Engineering Subjects for Different Degrees
Fluids 2020, 5(2), 95; https://doi.org/10.3390/fluids5020095 - 15 Jun 2020
Cited by 2 | Viewed by 750
Abstract
Subjects related to fluid mechanics for hydraulic engineers ought to be delivered in interesting and active modes. New methods should be introduced to improve the learning students’ abilities in the different courses of the Bachelor’s and Master’s degree. Related to active learning methods, [...] Read more.
Subjects related to fluid mechanics for hydraulic engineers ought to be delivered in interesting and active modes. New methods should be introduced to improve the learning students’ abilities in the different courses of the Bachelor’s and Master’s degree. Related to active learning methods, a continuous project-based learning experience is described in this research. This manuscript shows the developed learning methodology, which was included on different levels at Universitat Politècnica de València. The main research goal is to show the active learning methods used to evaluate both skills competences (e.g., “Design and Project”) and specific competences of the students. The research shows a particular developed innovation teaching project, which was developed by lecturers and professors of the Hydraulic Engineering Department, since 2016. This project proposed coordination in different subjects that were taught in different courses of the Bachelor’s and Master’s degrees, in which 2200 students participated. This coordination improved the acquisition of the learning results, as well as the new teaching methods increased the student’s satisfaction index. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Article
A Swing of Beauty: Pendulums, Fluids, Forces, and Computers
Fluids 2020, 5(2), 48; https://doi.org/10.3390/fluids5020048 - 12 Apr 2020
Cited by 2 | Viewed by 1410
Abstract
While pendulums have been around for millennia and have even managed to swing their way into undergraduate curricula, they still offer a breadth of complex dynamics to which some has still yet to have been untapped. To probe into the dynamics, we developed [...] Read more.
While pendulums have been around for millennia and have even managed to swing their way into undergraduate curricula, they still offer a breadth of complex dynamics to which some has still yet to have been untapped. To probe into the dynamics, we developed a computational fluid dynamics (CFD) model of a pendulum using the open-source fluid-structure interaction (FSI) software, IB2d. Beyond analyzing the angular displacements, speeds, and forces attained from the FSI model alone, we compared its dynamics to the canonical damped pendulum ordinary differential equation (ODE) model that is familiar to students. We only observed qualitative agreement after a few oscillation cycles, suggesting that there is enhanced fluid drag during our setup’s initial swing, not captured by the ODE’s linearly-proportional-velocity damping term, which arises from the Stokes Drag Law. Moreover, we were also able to investigate what otherwise could not have been explored using the ODE model, that is, the fluid’s response to a swinging pendulum—the system’s underlying fluid dynamics. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Review

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Review
An Introduction of Droplet Impact Dynamics to Engineering Students
Fluids 2020, 5(3), 107; https://doi.org/10.3390/fluids5030107 - 02 Jul 2020
Cited by 8 | Viewed by 1557
Abstract
An intensive training course has been developed and implemented at the California State University Long Beach based on 8 years of experience in the multiphase flow area with the specific focus on droplet–solid interactions. Due to the rapid development of droplet-based equipment and [...] Read more.
An intensive training course has been developed and implemented at the California State University Long Beach based on 8 years of experience in the multiphase flow area with the specific focus on droplet–solid interactions. Due to the rapid development of droplet-based equipment and industrial techniques, numerous industries are concerned with understanding the behavior of droplet dynamics and the characteristics that govern them. The presence and ensuing characteristics of the droplet regimes (spreading, receding, rebounding, and splashing) are heavily dependent on droplet and surface conditions. The effect of surface temperature, surface wettability, impact velocity, droplet shape and volume on droplet impact dynamics, and heat transfer are discussed in this training paper. Droplet impacts on moving solid surfaces and the effects of normal and tangential velocities on droplet dynamics are other topics that are discussed here. Despite the vast amount of studies into the dynamics of droplet impact, there is still much more to be investigated as research has expanded into a myriad of different conditions. However, the current paper is intended as a practical training document and a source of basic information, therefore, the scope is kept sufficiently broad to be of interest to readers from different engineering disciplines. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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Other

Essay
Teaching and Learning Floating and Sinking: Didactic Transformation in a Density-Based Approach
Fluids 2021, 6(4), 158; https://doi.org/10.3390/fluids6040158 - 14 Apr 2021
Cited by 1 | Viewed by 559
Abstract
This essay synthesizes more than a decade of research, most of which has been published, on the teaching and learning of floating and sinking (FS) phenomena. The research is comprised of the iterative design, development, implementation and evaluation of a Teaching-Learning sequence (TLS) [...] Read more.
This essay synthesizes more than a decade of research, most of which has been published, on the teaching and learning of floating and sinking (FS) phenomena. The research is comprised of the iterative design, development, implementation and evaluation of a Teaching-Learning sequence (TLS) for the teaching and learning of density within FS phenomena. It was initiated within the frame of the European Community supported “Materials Science” project. Due to the many, different aspects of the project, each publication has focused on a particular part of the study (e.g., effectiveness and the iteration process). The didactic transformation for the teaching of FS phenomena is presented and discussed here. In doing so, it is essential to mention: (a) the students’ ideas as the main cause of the scientific knowledge transformation, (b) the scientific/reference knowledge, and (c) the knowledge to be taught and its limitations. Thus, we intend to describe and justify the didactic transformation process and briefly synthesize the published (from previous papers) and unpublished results to show its effectiveness. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)
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