Lecture on Fluid Dynamics and Boundary Layers

Introduction to Potential Flow Theory

• Streamlines around a flat plate and a cylinder in an inviscid fluid
• Real fluids exhibit different behaviors due to viscosity
• Boundary layers form along surfaces affecting flow dynamics

Effects of Viscosity

• Viscosity creates a drag force on objects like wings
• Viscous effects become pronounced with increased angles of attack
• Airfoil stall and recirculating flow formation

Boundary Layer Dynamics

• Importance of understanding boundary layers: causes, growth, response to pressure gradients, laminar vs turbulent layers
• Examination of flow over a flat plate for foundational understanding

Laminar Flow Characteristics

• Uniform and laminar flow visualized with hydrogen bubbles
• No vorticity in unobstructed flow
• Boundary layers exhibit lower velocities and vorticity near the plate
• Shearing and inertia forces are crucial in boundary layer motion

Boundary Layer Growth

• Thickness increases along the plate
• Viscosity transfers fluid deceleration
• No-slip boundary condition: velocity is zero at the plate
• Velocity profile and skin friction (shear stress) defined
• Velocity gradient decreases downstream, reducing wall shear stress

Vorticity and Boundary Layer Thickness

• Stokes' theorem: circulation and vorticity
• Vorticity distribution and diffusion explained
• Boundary layer thickness relates to vorticity diffusion

Reynolds Number and Flow Speed

• Relationship of boundary layer thickness and Reynolds number
• Increased flow speed reduces boundary layer thickness

Pressure Gradients and Flow

• Effects of favorable and unfavorable pressure gradients
  • Favorable: decreases boundary layer thickness, increases wall shear stress
  • Unfavorable: increases thickness, decreases wall shear stress, potential separation
• Separation point and recirculating flow

Turbulent Boundary Layers

• Transition from laminar to turbulent flow
• Tomien-Schlichting waves and streamwise vorticity
• Effects of trip rods on boundary layers

Turbulent vs Laminar Boundary Layers

• Turbulent layers withstand unfavorable pressure gradients better
• Higher wall shear stress in turbulent layers
• Momentum distribution differences

Applications on Airfoils and Diffusers

• Turbulent boundary layers prevent separation at high attack angles
• Vortex generators on wings enhance mixing, delaying separation

Conclusion

• Influence of cylinders on boundary layer flow
• Static pressure increase along stagnation streamline
• Effects of pressure gradient on boundary layer separation