On the topology of three-dimensional steady flows of an ideal fluid

1966 ◽  
pp. 25-28
Author(s):  
Vladimir I. Arnold
Keyword(s):  
Ideal Fluid ◽  
Three Dimensional ◽  
Steady Flows

STEADY FLOWS OF VISCOUS COMPRESSIBLE FLUIDS IN EXTERIOR DOMAINS UNDER SMALL PERTURBATIONS OF GREAT POTENTIAL FORCES

1993 ◽  
Vol 03 (06) ◽  
pp. 725-757 ◽  
Author(s):  
ANTONÍN NOVOTNÝ
Keyword(s):  
Existence And Uniqueness ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Compressible Fluids ◽  
Steady Flows ◽  
Exterior Domains ◽  
Uniqueness Of Solutions ◽  
Small Perturbations ◽  
Zero Velocity ◽  
Potential Forces

We investigate the steady compressible flows in three-dimensional exterior domains, in R3 and [Formula: see text], under the action of small perturbations of large potential forces and zero velocity at infinity. We prove existence and uniqueness of solutions in L2-spaces, and study their regularity as well as the decay at infinity.

Inflammatory Response of Endothelial Cells to Wall Shear Stress in Three Dimensional Stenotic Models

2009 ◽  
Author(s):  
Leonie Rouleau ◽  
Joanna Rossi ◽  
Jean-Claude Tardif ◽  
Rosaire Mongrain ◽  
Richard L. Leask
Keyword(s):  
Endothelial Cells ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Three Dimensional ◽  
Realistic Model ◽  
In Vitro Models ◽  
Steady Flows ◽  
Wall Shear

Endothelial cells (ECs) are believed to respond differentially to hemodynamic forces in the vascular tree. Once atherosclerotic plaque has formed in a vessel, the obstruction creates complex spatial gradients in wall shear stress (WSS). In vitro models have used mostly unrealistic and simplified geometries, which cannot reproduce accurately physiological conditions. The objective of this study was to expose ECs to the complex WSS pattern created by an asymmetric stenosis. Endothelial cells were grown and exposed for different times to physiological steady flows in straight dynamic controls and in idealized asymmetric stenosis models. Cell morphology was noticeably different in the regions with spatial WSS gradients, being more randomly oriented and of cobblestone shape. Inflammatory molecule expression was also altered by exposure to shear and endothelial nitric oxide synthase (eNOS) was upregulated by its presence. A regional response in terms of inflammation was observed through confocal microscopy. This work provides a more realistic model to study endothelial cell response to spatial and temporal WSS gradients that are present in vivo and is an important advancement towards a better understanding of the mechanisms involved in coronary artery disease.

Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows

1999 ◽  
Vol 390 ◽  
pp. 25-43 ◽  
Author(s):  
H. LI ◽  
A. CHPOUN ◽  
G. BEN-DOR
Keyword(s):  
Shock Waves ◽  
Wave Reflection ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Experimental Investigations ◽  
Hysteresis Phenomenon ◽  
Steady Flows ◽  
Shock Wave Reflection ◽  
Asymmetric Shock ◽  
The One

The reflection of asymmetric shock waves in steady flows is studied both theoretically and experimentally. While the analytical model was two-dimensional, three-dimensional edge effects influenced the experiments. In addition to regular and Mach reflection wave configurations, an inverse-Mach reflection wave configuration, which has been observed so far only in unsteady flows (e.g. shock wave reflection over concave surfaces or over double wedges) has been recorded. A hysteresis phenomenon similar to the one that exists in the reflection of symmetric shock waves has been found to also exist in the reflection of asymmetric shock waves. The domains and transition boundaries of the various types of overall reflection wave configurations are analytically predicted.

scholarly journals Existence of Optimal Control for a Nonlinear-Viscous Fluid Model

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Evgenii S. Baranovskii ◽  
Mikhail A. Artemov
Keyword(s):  
Optimal Control ◽  
Fluid Model ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Surface Force ◽  
Steady Flows ◽  
Bounded Set ◽  
Viscous Fluid Model ◽  
Existence Of Optimal Control ◽  
Solid Walls

We consider the optimal control problem for a mathematical model describing steady flows of a nonlinear-viscous incompressible fluid in a bounded three-dimensional (or a two-dimensional) domain with impermeable solid walls. The control parameter is the surface force at a given part of the flow domain boundary. For a given bounded set of admissible controls, we construct generalized (weak) solutions that minimize a given cost functional.

An Experimental Study of Natural Convection Cooling of an Array of Heated Protrusions in a Vertical Channel in Water

1989 ◽  
Vol 111 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Y. Joshi ◽  
T. Willson ◽  
S. J. Hazard
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Power Dissipation ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Steady Flows ◽  
Transfer Rates ◽  
Fluid Velocities ◽  
Convection Cooling ◽  
Flow Visualizations

An experimental investigation of steady state and transient natural convection from a column of eight in-line rectangular heated protrusions in a vertical channel in water is presented. Flow visualizations and element surface temperature measurements were carried out for several power dissipation levels in the range of 0.2–1.5 W per component and channel spacings from 6.4 to 23 mm. The three-dimensional steady flows were visualized in two mutually perpendicular planes. Average component temperatures determined from the measurements on the five fluid exposed faces were used to obtain nondimensional heat transfer rates. Heat transfer data for all channel spacings except the smallest did not differ from the measurements for an isolated surface by more than 14 percent. For the smallest spacing, the component surface temperatures increased significantly due to a reduction in the fluid velocities. Measurements and flow visualizations during the transient indicated an initial diffusive transport period, followed by the evolution of convective effects. No overshoots in component temperatures were found. Steady transport responses with selectively powered components are also examined.

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