Lesson 5.5: Boundary Layer Theory & Flow Separation

Boundary Layer Theory is essential for understanding fluid flow near surfaces, which is critical for aerodynamics, turbines, and pipe flow design. GATE and PSU exams often test boundary layer thickness, flow separation, and drag concepts.

🔹 1. Introduction

• Definition: Boundary layer is the thin layer of fluid near a solid surface where viscous effects are significant.

• Applications:

  • Flow over wings and turbine blades

  • Pressure drop in pipes and channels

  • Heat and mass transfer in engineering systems

• Key Concepts:

  1. No-slip condition: Fluid velocity at surface = 0

  2. Velocity profile: Varies from 0 at wall to free-stream velocity outside boundary layer

🔹 2. Types of Boundary Layers

1. Laminar Boundary Layer: Smooth flow, layers slide over each other, low Reynolds number

   • Thickness δ∼5xRex\delta \sim \frac{5 x}{\sqrt{Re_x}}δ∼Rex​​5x​

2. Turbulent Boundary Layer: Irregular flow, mixing of layers, high Reynolds number

   • Thickness thicker than laminar, higher momentum transfer

3. Transition: Region where laminar changes to turbulent

🔹 3. Boundary Layer Separation

• Definition: Flow detaches from surface when adverse pressure gradient overcomes momentum near wall

• Consequences:

  • Increase in drag

  • Loss of lift (airfoils)

  • Flow recirculation zones

• Example: Flow over cylinder at high Reynolds number → boundary layer separation at rear stagnation point

• Separation Criteria:

dudy=0at wall (velocity gradient zero)\frac{du}{dy} = 0 \quad \text{at wall (velocity gradient zero)}dydu​=0at wall (velocity gradient zero)

🔹 4. Drag and Skin Friction

• Skin Friction Drag: Due to viscous shear in boundary layer

• Pressure Drag / Form Drag: Due to separation and pressure difference

• Total Drag: D=Dskin+DpressureD = D_\text{skin} + D_\text{pressure}D=Dskin​+Dpressure​

• Example: Flat plate in airflow, calculate laminar boundary layer thickness at x = 1 m, ν = 1.5e-5 m²/s, U∞ = 10 m/s

δ=5νxU=51.5e−5∗110≈6.1mm\delta = 5 \sqrt{\frac{\nu x}{U}} = 5 \sqrt{\frac{1.5e-5*1}{10}} ≈ 6.1 mmδ=5Uνx​​=5101.5e−5∗1​​≈6.1mm

🔹 5. Solved Examples (PYQ Style)

Example 1 (GATE ME 2017):
Compute boundary layer thickness for flat plate, laminar flow, given ν and U∞.

Example 2 (PSU Exam):
Explain flow separation on an airfoil at high angle of attack and its effect on lift.

Example 3:
Determine Reynolds number at which laminar boundary layer transitions to turbulent on a flat plate.

🔹 6. Practice Exercises

1. Calculate laminar and turbulent boundary layer thickness at given distance.

2. Identify flow separation points for different pressure gradients.

3. Determine skin friction drag on flat plate using Blasius solution.

4. Explain adverse pressure gradient effects with examples.

5. Sketch velocity profiles for laminar, turbulent, and separated flows.

🔹 7. Summary

• Boundary Layer: Thin layer near surface, viscous effects important

• Laminar vs Turbulent: Smooth vs chaotic flow, thickness difference

• Flow Separation: Occurs due to adverse pressure gradient → increases drag

• Applications: Airfoils, turbines, pipelines, pumps, hydraulic machines