Flow Inside a Cavity: A Comprehensive CFD Analysis Guide Example

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  • A fundamental CFD case study analyzing fluid flow inside a cavity using SIMPLE algorithm and second-order discretization schemes.
  • Problem features water flow with a moving top lid (U=1 m/s) and no-slip conditions on other walls.
  • Simulation implemented through MATLAB code, demonstrating practical application of Navier-Stokes equations and pressure-velocity coupling.
  • Study explores effects of under-relaxation factors, grid size, and various boundary conditions on flow patterns.
  • Results show formation of distinct vortices under different cavity dimensions and boundary conditions.
  • Case serves as an excellent example for understanding fundamental CFD concepts and numerical methods in fluid dynamics.
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Description

Flow Inside a Cavity: A Comprehensive Computational Fluid Dynamics Analysis Guide

Introduction to Cavity Flow Simulation

This tutorial demonstrates the numerical simulation of flow inside a cavity using the SIMPLE algorithm. The case study serves as a practical application of different discretization schemes in computational fluid dynamics.

Problem Setup and Boundary Conditions

Geometry and Mesh

– Cavity dimensions: LX × LY – Boundary conditions: * Top: Constant velocity (U) * Bottom, left, and right walls: No-slip condition – Fluid properties: Water (ρ = 1000 kg/m³, μ = 0.001 Pa·s)

Numerical Method

– Pressure-Velocity Coupling: SIMPLE algorithm – Discretization: Second-order central differencing scheme – Governing equations: 2D Navier-Stokes equations

Implementation Details

Key Components

1. Momentum Equations – X-direction momentum equation – Y-direction momentum equation – Pressure correction equation

  1. Solution Process
    • Initialization of variables
    • Iterative solving using SIMPLE algorithm
    • Convergence monitoring

Under-Relaxation Effects

– Impact on convergence rate – Stability considerations – Optimal values for different scenarios

Results and Analysis

Visualization

– Velocity vector plots – U-velocity contours – Convergence history

Case Studies

1. Standard cavity flow 2. Modified cavity dimensions 3. Different boundary conditions: – Symmetric top/bottom velocities – Opposing top/bottom velocities

Practical Applications and Insights

– Understanding vortex formation – Effect of geometry on flow patterns – Importance of boundary conditions – Real-world engineering applications

This case study demonstrates fundamental CFD concepts and provides practical insights into fluid behavior in confined spaces, essential for various engineering applications.

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