scholarly journals Comparing fluid mechanics models with experimental data

2003 ◽  
Vol 358 (1437) ◽  
pp. 1567-1576 ◽  
Author(s):  
G. R. Spedding
Keyword(s):  
Fluid Mechanics ◽  
Stokes Equations ◽  
Physical World ◽  
Experimental Models ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dimensionless Groups ◽  
Model Predictions ◽  
Provided Examples

The art of modelling the physical world lies in the appropriate simplification and abstraction of the complete problem. In fluid mechanics, the Navier–Stokes equations provide a model that is valid under most circumstances germane to animal locomotion, but the complexity of solutions provides strong incentive for the development of further, more simplified practical models. When the flow organizes itself so that all shearing motions are collected into localized patches, then various mathematical vortex models have been very successful in predicting and furthering the physical understanding of many flows, particularly in aerodynamics. Experimental models have the significant added convenience that the fluid mechanics can be generated by a real fluid, not a model, provided the appropriate dimensionless groups have similar values. Then, analogous problems can be encountered in making intelligible but independent descriptions of the experimental results. Finally, model predictions and experimental results may be compared if, and only if, numerical estimates of the likely variations in the tested quantities are provided. Examples from recent experimental measurements of wakes behind a fixed wing and behind a bird in free flight are used to illustrate these principles.

scholarly journals The inf-sup stability of the lowest order Taylor–Hood pair on affine anisotropic meshes

2019 ◽  
Vol 40 (4) ◽  
pp. 2377-2398
Author(s):  
Gabriel R Barrenechea ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Sufficient Conditions ◽  
Navier Stokes ◽  
Element Solution ◽  
Navier Stokes Equations ◽  
Anisotropic Meshes ◽  
Theoretical Results

Abstract Uniform inf-sup conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier–Stokes equations. In this work we prove a uniform inf-sup condition for the lowest-order Taylor–Hood pairs $\mathbb{Q}_2\times \mathbb{Q}_1$ and $\mathbb{P}_2\times \mathbb{P}_1$ on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalize Verfürth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

Perturbation Procedures for Nonlinear Viscous Flows

1983 ◽  
Vol 50 (2) ◽  
pp. 265-269
Author(s):  
D. Nixon
Keyword(s):  
Perturbation Theory ◽  
Shock Waves ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations

The perturbation theory for transonic flow is further developed for solutions of the Navier-Stokes equations in two dimensions or for experimental results. The strained coordinate technique is used to treat changes in location of any shock waves or large gradients.

Study of Flow and Thrust in Nozzle-Flapper Valves

1975 ◽  
Vol 97 (1) ◽  
pp. 39-50 ◽  
Author(s):  
S. Hayashi ◽  
T. Matsui ◽  
T. Ito
Keyword(s):  
Approximate Formula ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vena Contracta ◽  
Radial Gap ◽  
Good Agreement

The Navier-Stokes equations and the equation of continuity describing the flow in the flat-faced nozzle-flapper valve are numerically solved by the iterative relaxation method and the effect of the flow contraction (vena contracta) occurring in the radial gap in the valve is investigated. Furthermore, an approximate formula for the flow force acting on the flapper is derived on the basis of the numerical solutions. The formula for the flow force is in good agreement with experimental results.

scholarly journals Existence of Incompressible Vortex-Class Phenomena and Variational Formulation of Raleigh–Plesset Cavitation Dynamics

2021 ◽  
Vol 2 (3) ◽  
pp. 613-630
Author(s):  
Terry Moschandreou ◽  
Keith Afas
Keyword(s):  
Fluid Mechanics ◽  
Density Functional ◽  
Lagrangian Density ◽  
Stokes Equations ◽  
Closed Surface ◽  
Navier Stokes ◽  
The Novel ◽  
Navier Stokes Equations ◽  
Variational Framework ◽  
First Time

The following article extends a decomposition to the Navier–Stokes Equations (NSEs) demonstrated in earlier studies by corresponding author, in order to now demonstrate the existence of a vortex elliptical set inherent to the NSEs. These vortice elliptical sets are used to comment on the existence of solutions relative to the NSEs and to identify a potential manner of investigation into the classical Millennial Problem encompassed in Fefferman’s presentation. The article also presents the utilization of a recently developed versatile variational framework by both authors in order to study a related fluid-mechanics phenomena, namely the Raleigh–Plesset equations, which are ultimately obtained from the NSEs. The article develops, for the first time, a Lagrangian density functional for a closed surface which when minimized produced the Raleigh–Plesset equations. The article then proceeds with the demonstration that the Raleigh–Plesset equations may be obtained from thisenergy functional and identifies the energy dissipation predicted by the proposed Lagrangian density. The importance of the novel Raleigh–Plesset functional in the greater scheme of fluid mechanics is commented upon.

scholarly journals Application of Local Gauge Theories to Fluid Mechanics

2019 ◽  
Author(s):  
Thomas Merz
Keyword(s):  
Fluid Dynamics ◽  
Fluid Mechanics ◽  
Strain Rate ◽  
Gauge Theories ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Gauge Fields ◽  
Strain Rate Tensor ◽  
Hidden Symmetries ◽  
Navier Stokes Equations

The problem of fluid dynamics can be greatly simplified if, for every point in space, the strain-rate tensor is diagonalized. This tensor is introduced into the Navier-Stokes equations via material law and divergence of the stress tensor. This article shows that local SO(3)xU(1) gauge fields can be used to locally diagonalize the diffusion components of the strain-rate tensor. The gauge fields resulting from the connection can be interpreted as convection components of the flow, they show properties of quasiparticles and can be interpreted as elementary vortices. Thus, the proposed approach not only offers new insights for the solution and situative simplification of the Navier-Stokes equations, it also uncovers hidden symmetries within the flow convection, allowing - depending on boundary conditions - further interpretation.

Introductory Incompressible Fluid Mechanics

2021 ◽  
Author(s):  
Frank H. Berkshire ◽  
Simon J. A. Malham ◽  
J. Trevor Stuart
Keyword(s):  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Teaching Experience ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Science And Engineering ◽  
Navier Stokes Equations ◽  
Global Existence Of Solutions

This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum – only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.

scholarly journals Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Science ◽  
2020 ◽  
Vol 367 (6481) ◽  
pp. 1026-1030 ◽  
Author(s):  
Maziar Raissi ◽  
Alireza Yazdani ◽  
George Em Karniadakis
Keyword(s):  
Fluid Mechanics ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Quantitative Information ◽  
Navier Stokes ◽  
Observation Data ◽  
Navier Stokes Equations ◽  
Learning Framework ◽  
Pressure Fields ◽  
Potential Applications

For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in principle, described by the Navier-Stokes equations, extracting the velocity and pressure fields directly from the images is challenging. We addressed this problem by developing hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions. We demonstrate HFM for several physical and biomedical problems by extracting quantitative information for which direct measurements may not be possible. HFM is robust to low resolution and substantial noise in the observation data, which is important for potential applications.

scholarly journals Experiments and numerical modeling of baffle configuration effects on the performance of sedimentation tanks

2013 ◽  
Vol 40 (2) ◽  
pp. 140-150 ◽  
Author(s):  
A.M. Razmi ◽  
R. Bakhtyar ◽  
B. Firoozabadi ◽  
D.A. Barry
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laboratory Setup ◽  
Advection Diffusion Equation ◽  
Model Predictions ◽  
Empirical Function ◽  
Sedimentation Basins ◽  
Study Laboratory ◽  
Particle Laden Flow

The hydraulic efficiency of sedimentation basins is reduced by short-circuiting, circulation zones and bottom particle-laden jets. Baffles are used to improve the sediment tank performance. In this study, laboratory experiments were used to examine the hydrodynamics of several baffle configurations. An accompanying numerical analysis was performed based on the 2-D Reynolds-averaged Navier–Stokes equations along with the k-ε turbulence closure model. The numerical model was supplemented with the volume-of-fluid technique, and the advection–diffusion equation to simulate the dynamics of particle-laden flow. Model predictions compared well with the experimental data. An empirical function was constructed to indicate the location and amount of sediment collected in the tank. Hydraulic performance was determined for given baffle locations and heights. The results revealed that, for the laboratory setup, a baffle half way along its length decreases its performance, while a baffle much closer to its inlet and with height 25∼30% of water depth improves efficiency.

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