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Related Concept Videos

Couette Flow01:22

Couette Flow

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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Basic Equation for Pressure Field01:13

Basic Equation for Pressure Field

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The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...
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Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Phase Diagram01:19

Phase Diagram

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Color-gradient-based phase-field equation for multiphase flow.

Reza Haghani1, Hamidreza Erfani1, James E McClure2

  • 1PoreLab, Department of Geoscience and Petroleum, Norwegian University of Science and Technology (NTNU), 7031 Trondheim, Norway.

Physical Review. E
|April 18, 2024
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Summary
This summary is machine-generated.

This study introduces a new phase-field model to accurately simulate density-contrast fluids, overcoming limitations of the color-gradient method. The novel approach ensures fluid invariance and enhances simulations of complex fluid flows.

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Area of Science:

  • Computational Fluid Dynamics
  • Multiphase Flow Modeling
  • Phase-Field Methods

Background:

  • The color-gradient (CG) method exhibits limitations in handling fluids with significant density differences, specifically lacking fluid invariance.
  • Accurate simulation of incompressible, immiscible two-fluid flows with high density and viscosity contrasts is crucial in various scientific and engineering fields.

Purpose of the Study:

  • To address the shortcomings of the CG method for density-contrast fluids by proposing a novel phase-field interface-capturing model.
  • To develop a robust computational framework for simulating binary fluid flows with substantial property variations.

Main Methods:

  • Nondimensionalization of the CG method to derive a new phase-field formulation.
  • Implementation of a lattice Boltzmann method solver coupled with a hydrodynamic solver for binary fluid flow.
  • Utilizing separate distribution functions for the phase-field formulation and Navier-Stokes equations.

Main Results:

  • The proposed phase-field model successfully captures interfaces advected by flow velocity, avoiding issues with individual fluid speeds of sound.
  • A binary fluid flow package capable of handling high density and viscosity contrasts was developed and validated.
  • Numerical tests demonstrated good agreement with analytical and numerical solutions, confirming model accuracy and stability.

Conclusions:

  • The novel phase-field model provides a fluid-invariant and stable approach for simulating density-contrast fluids, outperforming the traditional CG method.
  • The developed lattice Boltzmann-based solver offers a reliable tool for complex multiphase flow simulations.