CFD Modelling of Boundary Layer

What are types of boundary Layer and how they are numerically modeled?

By 

Dr. Sharad Pachpute

 

1. Introduction to Boundary Layer

  • A thin layer of fluid formed close to the solid surface where the gradient in velocity  or any scalar is significant. This thin region is called as boundary layer
  • A boundary layer can be there due to gradients in velocity, temperature and concentration or species
  • Depending on type of flow and geometry. The boundary layer is for external and internal flows

2.Types of boundary layer

  • Laminar boundary layers can be loosely classified according to their structure and the circumstances under which they are created
  • The thin shear layer which develops on an oscillating body is an example of a Stokes boundary layer,
  • Blasius boundary layer:
    • For a 2D laminar flow over a flat plate
    • Boundary layer over a flat plate is simplified with a function of similarity variable only

Objectives_template

  • Boundary Layer equations are given as below
  •  Falkner–Skan boundary layer
    • generalization of Blasius profile.
    • It is formed as a fluid has swirling motion and Coriolis effect (rather than convective inertia), balances viscous forces with  an Ekman layer forms
  • Laminar boundary layer:
    • It is formed near to leading edge of surface
    • Viscous forces are dominant
  • Turbulent boundary layer:
    • It is formed at a certain distance from the leading edge of surface
    • Inertia forces are dominant

3. Layers of Turbulent Boundary Layer

  • Turbulent boundary layer consists for three main layers formed in the direction normal to the wall: Viscous Sub-layer, Buffer Layer , Turbulent Region

Air boundary layer development on a flat plate. A laminar air boundary... | Download Scientific Diagram

Air boundary layer development on a flat plate. A laminar air boundary... | Download Scientific Diagram

  • Friction velocity is calculated using the wall shear stress and fluid density

U* = friction velocity = sqrt (wall shear stress/density) , m/s

  • Non-dimensional distance and velocity are defined as :

Y+ = normal distance × U*/kinematic viscosity

         U+ = local velocity / friction velocity

  1. Non-dimensional velocity is plotted with non-dimensional distance
  2. Three main layers of turbulent region are formed as shown below

a) Viscous Sub-layer

    • viscous stress is dominant
    • The plot shows a linear variation :   U+ =Y+    
    • Requires very fine mesh to capture very steep gradient close to the wall

b) Buffer Layer:

    • both viscous and turbulent  stress exist
    • U+ = f(Y+)
    • Requires very fine mesh to capture very steep gradient near the wall

c) Turbulent Region:

      • turbulent  stress is dominant
      • U+ = 1/k ln (Y+)+ B
      • Requires  course mesh to capture less gradient away from the wall

Boundary Layer, Y plus & Wall functions in Turbulent flows. : Skill Lync

  • Resolution of turbulent Boundary Layer

  • To save computational cost  for resolution of  viscous sub-layer, scalable wall functions are used during turbulent simulation

 

This offering is not approved or endorsed by OpenCFD Limited, the producer of the OpenFOAM software and owner of the OPENFOAM

 

4. Laminar Flow Over A Flat Plate

4.1 Governing Equation for 2D boundary Layer

Continuity:

Momentum equation:

Energy equation:

  • The local heat transfer coefficient (HTC) can be expressed as:

4.2 Computational Domain and Numerical Solution

  • Inlet specified with a constant velocity for Reynolds number of 10000 based on the length of flat plate
  • Outlet specified with a zero gradient
  • Governing equations of mass, momentum (Navier Stokes eqn.) and energy for laminar flow are solved using finite volume method-based solver, ANSYS FLUENT.

4.3 CFD Results for Laminar Boundary Layer Over a Flat Plate

Case 1: for ReL=20,000, Pr=0.7, Tin=300 K, Tw=350 K

  • U velocity profile

    

  • V velocity profile

   

 

 

 

Momentum Boundary Layer

   

Thermal Boundary Layer

4.4 Thermal Boundary layer for Constant wall Temperature condition

4.5 Thermal Boundary layer for Constant wall Heat Flux condition

4.6 Comparison of Constant Temperature and Heat Flux at ReL=10,000 and Pr=0.7

5.Boundary Layer for Internal Flow

  • When fluid flows thought a pipe, a region of velocity gradient is formed neat the wall.
  • Axis-symmetric boundary is formed

  • Two-Dimensional Pipe Flow

5.1 Governing Equations in Cylindrical Co-ordinates

  • The governing equations for laminar flow in cylindrical co-ordinates system for axis-symmetric problem are given below, in two dimensional cylindrical co-ordinates,
  • all derivatives with respect to circumferential directions are zero.

Where x is the axial coordinate, r is the radial co-ordinate; u and v are velocity components in z and r directions respectively.

Energy equation:

5.2 CFD Results

a) Velocity Contours in laminar flow through the pipe at ReD=100

(b) Velocity Vectors in laminar flow

 

C) Static Pressure

6. Convective Boundary Layer For Internal Flow

  • a thermal boundary layer develops when surface temperature is different from fluid temperature
  • The growth of dth depends on whether the flow is laminar or turbulent

Case (A): Laminar Internal Flow for Constant wall Heat Flux

  • Local Nusselt Number Variotion along the length of pipe is shown below.
  • Based on analytical solution, the Nusselt number is 4.36 for fully developed thermally flow. A same value is obtained usign numerical simulation for Laminar flow

 

 

  •  Temperature Distribution at Re=100, Pr=0.7

  • Velocity Vectors with T magnitude

  • Temperature Profile

  • Non-dimensional Temperature profiles

  • Local Nusselt number variation at constant heat flux condition 

 

  • After a certain distance from the inelt, the wall and mean tempetrature vary linaerly along the length of pipe
  • The following figure shows reslsts for a constant heat flux condition

Case (B): Laminar Internal Flow for Constant wall Temperature

  • The wall is maintained at constant temperature ( Ts = 350K) for laminar flow at Re=100 and Pr=0.7
  • Fluid temperature increases from inlet to outlet
  • Thermal boundary Layer

  • Temperature profiles

  • Non-dimensional Temperature (NDT) profiles for constant wall temperature condition is given below
  • After a certain non-dimensional distance from the inlet, the non-dimensional temperature remains constant

  • Axial Variation of wall and mean temperature at constant temperature condition is shown below
  • The mean temperature of fluid increases exponentially and the difference between wall and mean fluid temperature decreases from inlet to outlet

  • Local Nusselt number variation for laminar internal flow at constant wall temperature condition is given below
  • Based on analytical solution for lamiar internal flow at contant wall temperature , the Nusselt number is 3.66 for fully developed thermally flow. A similar value is obtained using the numerical simulation for Laminar flow

7. Comparison of the Non-dimensional Temperature (NDT) profiles

  • As the Nusselt number is a measure of NDT gradient at the wall
  • More non-dimensional temperature (NDT) gradient is observed in the case of constant heat flux condition compared to that for constant temperature condition

 

 

 

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