What are types of boundary Layer and how they are numerically modeled?
By
Dr. Sharad Pachpute
Introduction to Boundary Layer
 In fluid dynamic, boundary layer is an essential topic. Boundary layer is a geion around the body within it viscous forces are significant.
 A thin layer of fluid is 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 formed for external and internal flows
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


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
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
Buffer Layer

 both viscous and turbulent stress exist
 U^{+} = f(Y^{+})
 Requires very fine mesh to capture very steep gradient near the wall
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
 High mesh density in the normal direction of the wall is required for turbulent boundary layers as shown below
 To save computational cost for resolution of viscous sublayer, salable wall functions are used during turbulent simulation
CFD of Laminar Flow Over A Flat Plate
 For laminar flow over a flat plate, a two dimensional geometry considered for CFD simulation
Computational Domain
 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.
Governing Equation for 2D boundary Layer
Continuity:
Momentum equation:
Energy equation:
 The local heat transfer coefficient (HTC) can be expressed as:
Numerical Procedure in ANSYS FLUENT
 CFD simulations carried out using a commercial FVM solver ANSYS FLUENT
 In all simulations, flow was considered to be steady laminar and two dimenional flow
 Pressure based incompreesible solver
 Boudnary condition:
 Inlet velocity and fluid properties selected as per Reynols number for constant air properties ( Pr =0.7)
 For thermal boudnary, wall temperature and heat fluxes varied to study the effect of parameters
 Pressure Velocity Coupling – SIMPLE Algorithm
 Discretization Scheme: QUICK
 Convergence Criterio: 10^6
CFD Results for Laminar Boundary Layer Over a Flat Plate
Case study for constant Wall Temperature
 Boundary conditions are set 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
Thermal Boundary layer for Constant wall Temperature condition
Thermal Boundary layer for Constant wall Heat Flux condition
Comparison of Boundary layer for Constant Temperature and Heat Flux
 CFD results comparec at Re_{L}=10,000 and Pr=0.7
Boundary Layer for Internal Flow
Geometry for axis Symmetric Flow
 When fluid flows thought a pipe, a region of velocity gradient is formed neat the wall.
 Axissymmetric boundary is formed

Geometry for TwoDimensional Pipe Flow
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:
Velocity Boundary Layer for Internal Flow
a) Velocity Contours in laminar flow through the pipe at Re_{D}=100
(b) Velocity Vectors in laminar flow
C) Static Pressure
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
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
You tube Video for CFD Analysis of Thermal Boundary Layer
 Watch the video on applications and CFD analysis of thermal boundary : You tube Video for CFD of Boundary Layer
Conclusion
 Based on CFD results, momentum and thermal boundary have been studied for constant wall and heat flux boundary conditions
 Boundary layer does not change significantly for constant values of Reynolds number and Prandlts number
 CFD results compare well with Nusselt number values obtained analytically
 The Nusselt number ( non – dimensional temperature gradient) is higher for constant heat flux compared to that for constant temperature wall condition
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