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
 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 Sublayer, Buffer Layer , Turbulent Region
 Friction velocity is calculated using the wall shear stress and fluid density
U^{* }= friction velocity = sqrt (wall shear stress/density) , m/s
 Nondimensional distance and velocity are defined as :
Y^{+} = normal distance × U^{*}/kinematic viscosity
U^{+} = local velocity / friction velocity
 Nondimensional velocity is plotted with nondimensional distance
 Three main layers of turbulent region are formed as shown below
a) Viscous Sublayer

 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

 Resolution of turbulent Boundary Layer
 To save computational cost for resolution of viscous sublayer, scalable wall functions are used during turbulent simulation
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 methodbased solver, ANSYS FLUENT.
4.3 CFD Results for Laminar Boundary Layer Over a Flat Plate
Case 1: for Re_{L}=20,000, Pr=0.7, T_{in}=300 K, T_{w}=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 Re_{L}=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.
 Axissymmetric boundary is formed

TwoDimensional Pipe Flow
5.1 Governing Equations in Cylindrical Coordinates
 The governing equations for laminar flow in cylindrical coordinates system for axissymmetric problem are given below, in two dimensional cylindrical coordinates,
 all derivatives with respect to circumferential directions are zero.
Where x is the axial coordinate, r is the radial coordinate; 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 Re_{D}=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 d_{th} 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
 Nondimensional 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
 Nondimensional Temperature (NDT) profiles for constant wall temperature condition is given below
 After a certain nondimensional distance from the inlet, the nondimensional 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 Nondimensional Temperature (NDT) profiles
 As the Nusselt number is a measure of NDT gradient at the wall
 More nondimensional temperature (NDT) gradient is observed in the case of constant heat flux condition compared to that for constant temperature condition
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