The article describes various aspects of mathematical modeling of fluid flows, both in general and with reference to hydraulic machinery. The article reviews historical development of corresponding methods of mathematical modeling. Implementation of these aspects in modern commercial CFD software tools is described together with advantages and disadvantages of implemented methods. The conclusion is drawn concerning possibilities of computation of fluid flows nowadays.
The exact analytic solution is built for the plane flow of incompressible fluid through the wheel with profiles of blades approximating logarithmic spirals.
The acoustic modes of a rotating fluid-filled cavity can be used to determine the effective rotation rate of a fluid (since the resonant frequencies are modified by the flows). To be accurate, this method requires a prior knowledge of the acoustic modes in rotating fluids. Contrary to the Coriolis force, centrifugal gravity has received much less attention in the experimental context. Motivated by on-going experiments in rotating ellipsoids, we study how global rotation and buoyancy modify the acoustic modes of fluid-filled ellipsoids in isothermal (or isentropic) hydrostatic equilibrium. We g…
When a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating turbulent convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show t…
I examine contemporary work in fluids in motion to demonstrate strong connections between art, science and technology. In one burgeoning domain, falling liquid drops impacting solid substrates or pools it is valuable to compare how artists and scientists describe their goals and their use of high speed digital photography to capture and measure events. I also examine the use of devices beyond paint brushes to create pictures and views, including installations and projections from computer simulations. In particular, Ned Kahn whose installations in the public domain show various fluids in motio…
The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational and centrifugal forces on this converging flow. The focus is on the quasi-static spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. The collapse time, as it depends upon the initial hole size, is reported showing th…
Near the central engine, many astrophysical jets are expected to rotate about their axis. Further out they are expected to go through the processes of reconfinement and recollimation. In both these cases, the flow streams along a concave surface and hence, it is subject to the centrifugal force. It is well known that such flows may experience the Centrifugal Instability (CFI), to which there are many laboratory examples. The recent computer simulations of relativistic jets from Active Galactic Nuclei undergoing the process of reconfinement show that in such jets CFI may dominate over the Kelvi…
Elastohydrodynamic instability of a spinning elastic disk
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
In commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. We here provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. Its application to the accretion-disk problem is discussed. We numerically compare the new approach to the typical one in …
A coupling onset of the cyclone upward and rotation flows is experimentally demonstrated in a little bottle. The rotating flow provides a pressure increase in the outer part of the rotating flow by its centrifugal force. When a gradient of the fluid rotation appears along the rotation axis, the higher-pressure area is localized and pushes the fluid in a low pressure. Then the fluid staying in the central area of the rotation is pushed up along the rotation axis, and the upward wind is enhanced. In this coupling mechanism the rotation gradient is the key; the coupling of the rotation and the up…
The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Görtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various libration frequencies and Ekman numbers. The strongly nonlinear regime well above the insta…
A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterised by the Reynolds, Froude, Weber and Ekman numbers. The variation of the Ekman number ($Ek$), defined to be proportional of the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of $Ek$ values ($0 \leq Ek \leq 484$) in…
The present work focuses on the study of mixed convection of a purely viscous shear-thinning fluid in a horizontal annular eccentric duct. The inner and outer cylinders are heated with constant and uniform heat flux densities. The objective of this work is to study the effect of the variation of eccentricity, rheological behavior of the fluid as well as the thermodependency of the rheological parameters on the reorganization of the flow and thermal stratification caused by the buoyancy forces. At the entrance of the heating zone, the dynamic regime is assumed to be established and the temperat…
Politecnico di Torino（都灵理工大学）；Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；Roma Tre University（罗马三大）；Imperial College London（伦敦帝国学院）；Politecnico di Milano（米兰理工大学）；ONERA, Institut Polytechnique de Paris（法国航空发展局，巴黎理工学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Seoul National University（首尔国立大学）；Air Force Research Laboratory（空军研究实验室）；Université Marie et Louis Pasteur（玛丽和路易·巴斯德大学）；Delft University of Technology（代尔夫特理工大学）
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal variables are used. In addition to the previously known applications for shear flows with constant (including zero) vorticity, here a generalization is made to the case of potential flows in uniformly rotating coordinate systems, where centrifugal and Coriolis forces are added to the gravity force. A brief review is given of previous results obtained by this method…
In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a secondary flow in the meridian plane composed of two thin boundary layers along the disks separated by a non-viscous geostrophic core. Most numerical simulations have been performed using RANS and URANS modelling, and very few investigations have been performed using LES. This paper reports on quantitative comparisons of two high-order LES methods to predict a tu…
