Presentation on theme: "Flow Over Immersed Bodies"— Presentation transcript:
1 Flow Over Immersed Bodies Fluid Mechanics IIChapter 9Flow Over Immersed Bodies
2 Content Classification of External Viscous Flow Fluid Dynamic Forces: Lift and DragReynolds Number EffectBoundary Layer: Laminar and TurbulentFlow SeparationExperimental Drag DataAirfoil and Wing Characteristics
4 Reynolds Number Effect The Reynolds number, Re = U l/n , is the ratio between the inertial force and the viscous force.Low Re: Mostly viscous flowModerate Re: Partial viscous flow around bodyHigh Re: Viscous Boundary Layer near surface09_0409_04
5 09_05 Flow Past Cylinder Low Re: Mostly viscous flow Moderate Re: Partial viscous flow around body with separation and re-circulation flow in wakeHigh Re: Viscous Boundary Layer near surface till separation and wake09_0509_05
6 09_03 Surface Forces Pressure: Normal to surface Shear Stress: Tangent to surface09_03
7 Lift and DragThe sum of forces due to pressure distribution and skin friction (shear stress) is the resultant force on a 2-D object.This net force can be represented by its two components:Lift: Component normal to the flowDrag: Component in the flow direction09_0209_02
8 E_09_01 Example 9.1 (p. 329) Flow parallel to flat plate Skin Friction Drag only:D = lbf, L = 0Flow normal to flat plate:Pressure Drag onlyD = 55.6 lbf, L = 0Flow at an angle with plate:Both Lift and Drag are present.Drag consists of both pressure drag and skin friction drag.E_09_01
9 Boundary Layer Flow Along a Smooth Flat Plate 09_06Boundary Layer Flow Along a Smooth Flat PlateExperimental observation:At local Reynolds number (Rex = U x/n) around 5x105, transition from Laminar to Turbulent Boundary Layer Flow occurs. This Rex of 5x105 is known as the critical or transitional Reynolds number.
10 09_09Velocity ProfilesThe gradient (du/dy) of the turbulent velocity profile at the wall (y=0) is higher than that of the laminar velocity profile.Hence skin friction drag of turbulent boundary layer is higher than that of laminar one.
11 09_08Boundary layer thickness d (x): The location normal to surface at which the velocity reaches 0.99 of the velocity U in the inviscid free-stream. It increases in the x-direction along the plate.Displacement thickness d*(x): The distance normal to the surface that the streamline passing d(x) is displaced from its original distance (h) at the leading edge of the plate. Hence,d*(x) = d(x) – h09_08
12 Laminar Boundary Layer on Flat Plate Blasius SolutionMomentum Integral Method
13 Experimental Skin Friction Drag Data Curve fit formula for turbulent boundary layer (Re > 500,000):
14 of Flat Plate with Roughness Drag Coefficientof Flat Plate with RoughnessCurve fitting ofExperimental Data09_1009_10
15 Drag Coefficient of Flat Plate 09_01tblDrag Coefficient of Flat PlateEmpirical Formulas
16 Boundary Layer Flow Separation When flow separation occurs,there is also pressure drag.
17 Pressure (Form) Drag due to Flow Separation 100% Pressure DragTotal Profile Drag= Skin Friction Drag+ Form Drag
18 Development of velocity profile in the boundary layer on curved surface: Flow separation occurs when the gradient of the velocity profile at the wall is zero, forming a re-circulating wake downstream.09_1209_12Separation
19 Motor-controlled mechanism adjusts the model’s angle of attack. Wind Tunnel TestsForce transducer behind model senses lift, drag and pitching moment directly.Motor-controlled mechanism adjusts the model’s angle of attack.
20 09_15 Typical Experimental Data Notice the sudden drop at the transition Re of 5x105 (Point E)09_15
21 09_15For Re > 5x105, the boundary is turbulent, which has a fuller velocity profile.Flow separation is delayed, resulting in a smaller wake, and hence the pressure drag.
22 Adding surface roughness on circular and spherical shapes triggers turbulence at lower Re, and hence helps to reduce the drag coefficient09_18
24 Benefit of Streamlining Pressure drag is greatly reduced by preventing flow separation using a gradually tapering tail. Though skin friction increases with larger area, the total drag is much less. Hence streamlined bodies are made of smooth surfaces to reduce skin friction.These objects have approximately the same drag:09_14