Bl concept
- 1. Fluid Mechanics - II External Incompressible Viscous Flow Boundary layer and Applications
- 4. Boundary Layer Thicknesses • Disturbance Thickness, δ Displacement Thickness, δ* Momentum Thickness, θ
- 5. Laminar Flat-Plate Boundary Layer: Exact Solution • Governing Equations
- 6. Laminar Flat-Plate Boundary Layer: Exact Solution • Boundary Conditions
- 7. Laminar Flat-Plate Boundary Layer: Exact Solution • Equations are Coupled, Nonlinear, Partial Differential Equations • Blasius Solution: – Transform to single, higher-order, nonlinear, ordinary differential equation
- 8. Laminar Flat-Plate Boundary Layer: Exact Solution • Results of Numerical Analysis
- 9. Momentum Integral Equation • Equation is used to estimate the boundary- layer thickness as a function of x: 1. Obtain a first approximation to the free stream velocity distribution, U(x). The pressure in the boundary layer is related to the freestream velocity, U(x), using the Bernoulli equation 2. Assume a reasonable velocity-profile shape inside the boundary layer 3. Derive an expression for τw using the results obtained from item 2
- 10. Use of the Momentum Equation for Flow with Zero Pressure Gradient • Simplify Momentum Integral Equation (Item 1) The Momentum Integral Equation becomes
- 11. Use of the Momentum Equation for Flow with Zero Pressure Gradient • Laminar Flow – Example: Assume a Polynomial Velocity Profile (Item 2) • The wall shear stress τw is then (Item 3)
- 12. Use of the Momentum Equation for Flow with Zero Pressure Gradient • Laminar Flow Results (Polynomial Velocity Profile) Compare to Exact (Blasius) results!
- 13. Use of the Momentum Equation for Flow with Zero Pressure Gradient • Turbulent Flow – Example: 1/7-Power Law Profile (Item 2)
- 14. Use of the Momentum Equation for Flow with Zero Pressure Gradient • Turbulent Flow Results (1/7-Power Law Profile)
- 15. Pressure Gradients in Boundary-Layer Flow
- 17. Drag • Pure Friction Drag: Flat Plate Parallel to the Flow • Pure Pressure Drag: Flat Plate Perpendicular to the Flow • Friction and Pressure Drag: Flow over a Sphere and Cylinder • Streamlining
- 18. Drag • Flow over a Flat Plate Parallel to the Flow: Friction Drag Boundary Layer can be 100% laminar, partly laminar and partly turbulent, or essentially 100% turbulent; hence several different drag coefficients are available
- 19. Drag • Flow over a Flat Plate Parallel to the Flow: Friction Drag (Continued) Laminar BL: Turbulent BL: … plus others for transitional flow
- 20. Drag • Flow over a Flat Plate Perpendicular to the Flow: Pressure Drag Drag coefficients are usually obtained empirically
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- 25. Drag • Flow over a Flat Plate Perpendicular to the Flow: Pressure Drag (Continued)
- 26. Drag • Flow over a Sphere and Cylinder: Friction and Pressure Drag on a Sphere
- 27. Drag • Flow over a Sphere and Cylinder: Friction and Pressure Drag (Continued) on Cylinder
- 28. 28 Note that the lift coefficient strongly depends on the rate of rotation, especially at low angular velocities. The effect of the rate of rotation on the drag coefficient is small. Roughness also affects the drag and lift coefficients. In a certain range of Reynolds number, roughness produces the desirable effect of increasing the lift coefficient while decreasing the drag coefficient. Therefore, golf balls with the right amount of roughness travel higher and farther than smooth balls for the same hit.
- 29. Streamlining • Used to Reduce Wake and hence Pressure Drag
- 30. Lift • Mostly applies to Airfoils Note: Based on planform area Ap
- 31. Lift • Examples: NACA 23015; NACA 662-215
- 33. Lift • Induced Drag (Continued) Reduction in Effective Angle of Attack: Finite Wing Drag Coefficient:
- 34. Lift • Induced Drag (Continued)