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An Analysis of Hiemenz Flow

An Analysis of Hiemenz Flow. E. Kaufman and E. Gutierrez-Miravete Department of Engineering and Science Rensselaer at Hartford. OBJECTIVE. To solve a simple flow field for which an exact solution is available using COMSOL & FLUENT HIEMENZ FLOW Planar Laminar Viscous Incompressible

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An Analysis of Hiemenz Flow

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  1. An Analysis of Hiemenz Flow E. Kaufman and E. Gutierrez-Miravete Department of Engineering and Science Rensselaer at Hartford

  2. OBJECTIVE • To solve a simple flow field for which an exact solution is available using COMSOL & FLUENT • HIEMENZ FLOW • Planar • Laminar • Viscous • Incompressible • Close to a stagnation point

  3. Viscous Inviscid BACKGROUND • Exact Solution Exists for Hiemenz Flow • Viscous Solution is Derived from the Inviscid Solution

  4. HIEMENZ SOLUTION • Substitute into 2D Incompressible Navier-Stokes Equations • Similarity Solution Yields Hiemenz Equation • Boundary Conditions • Solve Using Shooting Method

  5. Inviscid and Viscous Hiemenz Flow: Velocity Velocity Profiles Flow Direction Symmetry Line Wall

  6. Inviscid and Viscous Hiemenz Flow: Pressure Pressure Contours Flow Direction Wall

  7. Inviscid and Viscous Hiemenz Flow: Temperature • Inviscid heat flux at the wall is ~ 2X Viscous

  8. Inlet (0,6) (6,6) Exit Symmetry Wall: T=1000 (0,0) (6,0) COMSOL & FLUENT: Case Study - Inputs • Compare Analytical Solution to Computational Results • Set up Dimensional Problem for Easy Comparison Material Properties Inlet Velocity:(u, v) = (x, 5.3521) Inlet Temperature: T=100 • Density = 1 kg/m3 • Viscosity = 1 kg/ms • Conductivity = 1 W/moC Flow Field Scale Factor • a = 1 s-1 Similarity Factors • η = y/1 • ϕ = f/1 Boundary Conditions • Consistent with analytical solution at boundaries • Assume stagnation pressure of 100 Pascals Computational Domain • 6 meters by 6 meters

  9. COMSOL & FLUENT: Case Study - Results COMSOL Mesh COMSOL Velocity COMSOL Pressure Field FLUENT Mesh FLUENT Velocity FLUENT Pressure Field

  10. Inlet Flow Direction Wall COMSOL & FLUENT: Case Study – Results Static Pressure Along Symmetry Plane

  11. COMSOL & FLUENT: Case Study – Results Temperature COMSOL Temperature Distribution FLUENT Temperature Distribution

  12. CONCLUSIONS • Both COMSOL and FLUENT have been shown to reliably reproduce the flow field • Velocities, Pressures and Temperatures match the analytical predictions closely • Selection of appropriate boundary conditions and adequate domain size are critical to accurately predict flow field

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