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Related Concept Videos

Applications of Integration to Find Hydrostatic Pressure01:30

Applications of Integration to Find Hydrostatic Pressure

Hydrostatic force is a fluid's total force at rest on a surface. For a horizontal surface submerged at a fixed depth, the pressure is constant and calculated as the product of fluid density, gravitational acceleration, and depth. In the case of a vertical dam wall submerged in water, this force is not evenly distributed due to the increasing pressure with depth. This variation arises from the cumulative weight of the water above each point. Integration is used to account for the continuous...
Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
Fluid Pressure over Curved Plate of Constant Width01:12

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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
Hydrostatic Pressure Force on a Curved Surface01:04

Hydrostatic Pressure Force on a Curved Surface

Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...
Euler's Equations of Motion01:28

Euler's Equations of Motion

In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
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Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.

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EVALUATION OF INTERFACIAL FLUID DYNAMICAL STRESSES USING THE IMMERSED BOUNDARY METHOD.

Harvey A R Williams1, Lisa J Fauci, Donald P Gaver

  • 1Perforating Research Schlumberger, 14910 Airline Road, Rosharon, TX 77583, USA.

Discrete and Continuous Dynamical Systems. Series B
|October 2, 2012
PubMed
Summary

This study evaluates interfacial stress calculations using the immersed boundary method (IBM). We found that specific techniques, like exclusion filtering, enable accurate stress approximations for complex fluid dynamics simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Fluid Mechanics

Background:

  • Accurate evaluation of interfacial stresses is crucial in fluid dynamics simulations.
  • The immersed boundary method (IBM) offers a flexible approach for handling complex geometries.
  • Standard IBM implementations face challenges in precisely calculating stresses due to approximations.

Purpose of the Study:

  • To investigate and validate methods for calculating interfacial stresses with the finite difference based, immersed boundary method (IBM).
  • To compare IBM stress calculations against the boundary element method (BEM) for accuracy.
  • To develop and present reliable techniques for stress evaluation in complex flow scenarios.

Main Methods:

  • Investigated three low Reynolds number model flows: Poiseuille channel flow, flow over a channel bump, and peristaltic pumping.
  • Employed analytical solutions for Poiseuille flow to guide stress evaluation.
  • Developed and applied an 'exclusion filtering' technique for accurate stress measurement in curved and complex boundaries.

Main Results:

  • Demonstrated that fluid stress (FS) calculations in IBM should be evaluated approximately one grid spacing inward from the immersed boundary for accuracy.
  • Presented a procedure for selecting representative interfacial stresses for curved boundaries.
  • The 'exclusion filtering' technique proved effective for accurate stress measurement in both steady and unsteady complex flows.

Conclusions:

  • The immersed boundary method (IBM), when combined with appropriate stress evaluation techniques, can provide reliable approximations of interfacial stresses.
  • The findings offer practical guidance for improving the accuracy of CFD simulations involving complex geometries and interfacial phenomena.