Mathematical Models Of Fluid Dynamics Pdf

Mathematical Modeling of Two-Phase Flow

Free first page

Related Articles
Journal Most Downloaded

Abstract - Figures Preview

Abstract

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract ...Read More

Full Text HTML
Download PDF

Figures

Figure 1: Machine learning algorithms may be categorized into supervised, unsupervised, and semisupervised, depending on the extent and type of information available for the learning process. Abbrevia...

Figure 2: First example of learning and automation in experimental fluid mechanics: Rechenberg's (1964) experiments for optimally corrugated plates for drag reduction using the Galtonbrett (Galton boa...

Figure 3: The learning problem. A learning machine uses inputs from a sample generator and observations from a system to generate an approximation of its output. Figure based on an idea from Cherkassk...

Figure 4: Recurrent neural networks (RNNs) for time series predictions and the long short-term memory (LSTM) regularization. Abbreviations: , previous cell memory; , current cell memory; , previous ce...

Figure 5: PCA/POD (left) versus shallow autoencoders (center) and deep autoencoders (right). If the node activation functions in the shallow autoencoder are linear, then u and are matrices that minim...

Figure 6: Unsupervised learning example: merging of two vortices (top), proper orthogonal decomposition (POD) modes (middle), and respective modes from a linear autoencoder (bottom). Note that unlike ...

Figure 7: Comparison of standard neural network architecture (a) with modified neural network for identifying Galilean invariant Reynolds stress models (b). Abbreviations: , anisotropy tensor; , scala...

Figure 8: Deep reinforcement learning schematic (a) and application to the study of the collective motion of fish via the Navier–Stokes equations (b). Panel b adapted from Verma et al. (2018).

Abstract - Figures - Supplemental Materials Preview

Abstract

This review focuses on Leonardo da Vinci's work and thought related to fluid mechanics as it is presented in a lifetime of notebooks, letters, and artwork. It shows how Leonardo's remaining works offer a complicated picture of unfinished, scattered, and ...Read More

Full Text HTML
Download PDF

Supplemental Materials

Supplemental Appendix Read More

Figures

Figure 1: (a) Drawings of flumes (Codex Leicester, f. 9v). Image reprinted with permission of the licensor through PLSclear from Laurenza & Kemp (2019), copyright 2019 Oxford University Press. (b) Exp...

Figure 2: Sketch showing a mechanical measure of hydrostatic force (Codex Leicester, f. 6r). Image reprinted with permission of the licensor through PSclear from Laurenza & Kemp (2019), copyright 2019...

Figure 3: Sketch study for The Battle of Anghiari (circa 1503–1504). Pen and ink on paper, Gallerie dell'Accademia, Venice. Image reprinted with permission from World History Archive/Alamy Stock Photo...

Figure 5: One of Leonardo's series of deluge drawings. Royal Collection at Windsor (RCIN 912382). Image reprinted with permission of Royal Collection Trust, copyright 2020 Her Majesty Queen Elizabeth ...

Figure 6: Pipe flows showing a varying velocity gradient. Royal Collection at Windsor (RCIN 919117r). Images reprinted with permission of Royal Collection Trust, copyright 2020 Her Majesty Queen Eliza...

Figure 7: (a,b) Drawings of vortices in the aorta. Royal Collection at Windsor (a, RCIN 919117r; b, RCIN 919082r). (c) Sketch of a glass model of the base of the aorta (RCIN 919082r). (d) Particle ima...

Figure 8: Rising bubbles in water in (a) Codex Leicester (f. 25r) and (b) Paris Manuscript F (f. 37v). (c) Unsteady path of spheres. Panel a reprinted with permission of the licensor through PLSclear ...

Figure 9: (a) Sketch of a bearded man. Royal Collection at Windsor (RCIN 912553). (b) Zoomed-in crop of hair sketch in panel a. (c) Deluge drawing (RCIN 912380r). (d) Zoomed-in crop of turbulent flow ...

Figure 10: (a) Vitruvian Man (circa 1490). Gallerie dell'Accademia, Venice. (b) Length measurements of human subjects. Royal Collection at Windsor (RCIN 919132). (c) Male head in profile with proporti...

Figure 11: Logarithmic spirals. (a) Logarithmic spiral with growth factor 0.191 (Paris Manuscript E, f. 34v). (b) Golden spiral (Paris Manuscript G, f. 54v). (c) Golden spiral. Royal Collection at Win...

Figure 12: Sketches of a plunging water jet into a pool, with the resultant turbulent flow. (a) Royal Collection at Windsor (RCIN 912660v). (b) RCIN 912662. (c) Paris Manuscript F, f. 72r. Images repr...

Figure 13: Spiral eddy number density distribution, n(s), per eddy size, s, across 10 deluge drawings. The −1.7 power law slope is considerably less than the value of −2.3 expected for, e.g., random A...

Figure 14: (a) Ornithopter (Paris Manuscript B, f. 74v). (b) Rotorcraft (Paris Manuscript B, f. 83v). (c) Streamlined bodies (Codex Arundel, f. 54r). Images reprinted with permission from (a,b) RMN–Gr...

Figure 15: Hydraulic jumps (Codex Arundel, f. 167v). Images reprinted with permission from the British Museum.

Figure 16: (a) Vortices strong enough to carve cavities in rock (Codex Arundel, f. 29v). (b) Conservation of volume for a branching tree (Paris Manuscript M, f. 78v). Images reprinted with permission ...

Abstract - Figures Preview

Abstract

For an infectious disease such as the coronavirus disease 2019 (COVID-19) to spread, contact needs to be established between an infected host and a susceptible one. In a range of populations and infectious diseases, peer-to-peer contact modes involve ...Read More

Full Text HTML
Download PDF

Figures

Figure 1: (a) Gap in knowledge of infectious disease transmission at the intermediate (host-to-host) spatial scale. (b) The gap is framed from the lens of the underlying physiological/biophysical (gra...

Figure 2: Examples of fluid dynamic processes involved in (a) pathogen transfer in respiratory disease transmission (turbulent gas cloud emission), (b) foliar disease transmission (drop-on-leaf fluid–...

Figure 3: (a) Exhalations such as breathing, coughing, and sneezing release a turbulent puff cloud of hot and moist air containing suspended droplets trapped within it. The cloud and its payload can t...

Figure 4: Contrasting the isolated droplet emission picture of Wells (1934, 1955) with the recently developed turbulent gas cloud emission picture of exhalations (Bourouiba et al. 2014; Bourouiba 2016...

Figure 5: Fragmentation of mucosalivary fluid during a sneeze showing initial sheet formation and stretching (left); sheet piercing, resulting in sheet retraction in a rim, itself destabilizing into l...

Figure 6: (a) High-speed imaging of droplet trajectories emitted from a high-pressure flush of a typical hospital toilet, showing ballistic trajectories for larger droplets and meandering droplet susp...

Figure 7: (a) Once gently deposited as a drop on the surface of a young bubble, potassium permanganate mixes and forms lamellae that elongate and overlap in an ever-weakening stirring field. (b) A bub...

Figure 8: The competition between two bubble-thinning mechanisms important at different timescales. The earlier part of a bubble's life (blue regions) is dominated by thinning governed by drainage fro...

Figure 9: The shift in the physical picture for rain-induced disease transmission in plants, from the view of leaves coated by films (Fitt et al. 1989) to the dominant role of average wetting with ses...

Figure 10: Local, small, and rapid fragmentation processes shape the larger-scale pathogen footprint of contamination (Gilet & Bourouiba 2015). (a) Impact of a drop on a rigid surface with a sessile d...

Figure 11: Removal of pathogens from leaves where pathogen ejection is governed by fluid–structure interactions during rainfalls. (a) Crescent-moon fragmentation leading to the formation of a sheet ri...

Figure 12: Universality in unsteady fluid fragmentation. (a) Crescent-moon fragmentation from a drop-on-drop impact (Gilet & Bourouiba 2015). (b) Splash on a thin film. (c) Sheet expansion from impact...

Figure 13: Three unsteady fluid fragmentation processes: (a) drop-on-pole, (b) drop-on-edge, and (c) drop-on-film fragmentation for which (d) the rim thickness is governed by the local Bond number cri...

Figure 14: The important role of unsteadiness in shaping the droplet sizes and speeds from unsteady fluid sheet fragmentation. (a,d) Skewed overall probability density functions of droplet size, D = d...

Abstract - Figures - Supplemental Materials Preview

Abstract

Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow ...Read More

Full Text HTML
Download PDF

Supplemental Materials

Supplemental Appendix Read More

Figures

Figure 1: Dimensionless vortex size, xR/H2, as a function of Deborah number, De, for the 4:1 planar contraction flow of an Oldroyd-B fluid with a solvent viscosity ratio of under creeping flow condit...

Figure 2: Comparison between different numerical results for the flow past a cylinder in a channel. (a) Drag force coefficient, CD, as a function of Deborah number, . (b) Maximum dimensionless normal ...

Figure 3: Streamline patterns and contour plots of normalized first normal stress difference, , where D is the channel width and U is the average velocity in each channel, using the upper-convected Ma...