2 Overview Non-Uniform Flow Boundary Layer Concepts Viscous Drag Pressure Gradients: Separation and WakesPressure DragShear and Pressure ForcesVortex Shedding
3 Non-Uniform FlowIn pipes and channels the velocity distribution was uniform (beyond a few pipe diameters or hydraulic radii from the entrance or any flow disturbance)In external flows the boundary layer is always growing and the flow is non-uniform
4 Boundary Layer Concepts Two flow regimesLaminar boundary layerTurbulent boundary layerwith laminar sub-layerCalculations ofboundary layer thicknessShear (as a function of location on the surface)Drag (by integrating the shear over the entire surface)
5 Flat Plate: Parallel to Flow UUUboundary layer thicknessUyxshearWhy is shear maximum at the leading edge of the plate?is maximum
6 Flat Plate Drag Coefficients 1 x 10-35 x 10-42 x 10-41 x 10-45 x 10-52 x 10-51 x 10-55 x 10-62 x 10-61 x 10-6
7 Separation and Wakes Separation often occurs at sharp corners fluid can’t accelerate to go around a sharp cornerVelocities in the Wake are ______ (relative to the free stream velocity)Pressure in the Wake is relatively ________ (determined by the pressure in the adjacent flow)smallconstant
9 Drag of Blunt Bodies and Streamlined Bodies Drag dominated by viscous drag, the body is __________.Drag dominated by pressure drag, the body is _______.Whether the flow is viscous-drag dominated or pressure-drag dominated depends entirely on the shape of the body.streamlinedbluffBicycle page at Princeton
10 Drag Coefficient on a Sphere 1000100Stokes LawDrag Coefficient1010.10.1110102103104105106107Reynolds Number
11 Shear and Pressure Forces: Horizontal and Vertical Components dragParallel to the approach velocityliftNormal to the approach velocityp < p0negative pressureA defined as projected area _______ to force!Unormalliftqdragp > p0 positive pressure
12 Shear and Pressure Forces Shear forcesviscous drag, frictional drag, or skin frictioncaused by shear between the fluid and the solid surfacefunction of ___________and ______of objectPressure forcespressure drag or form dragcaused by _____________from the bodyfunction of area normal to the flowsurface arealengthflow separation
13 Example: Beetle Power Cd = 0.38 Height = 1.511 m Width = 1.724 m Length = mGround clearance = 15 cm?85 kW at 5200 rpmWhere does separation occur?Calculate the power required to overcome drag at 60 mph and 120 mph.Is the new beetle streamlined?
14 Solution: Power a New Beetle at 60 mph P = 8.8 kW at 60 mphP = 70 kW at 120 mph
15 Drag on a Golf BallDRAG ON A GOLF BALL comes mainly from pressure drag. The only practical way of reducing pressure drag is to design the ball so that the point of separation moves back further on the ball. The golf ball's dimples increase the turbulence in the boundary layer, increase the _______ of the boundary layer, and delay the onset of separation. The effect is plotted in the chart, which shows that for Reynolds numbers achievable by hitting the ball with a club, the coefficient of drag is much lower for the dimpled ball.inertiaWhy not use this for aircraft or cars?
16 Effect of Turbulence Levels on Drag Flow over a sphere: (a) Reynolds number = 15,000; (b) Reynolds number = 30,000, with trip wire.Causes boundary layer to become turbulentPoint of separation
18 Spinning SpheresWhat happens to the separation points if we start spinning the sphere?LIFT!
19 Vortex SheddingVortices are shed alternately from each side of a cylinderThe separation point and thus the resultant drag force oscillateDimensionless frequency of shedding given by Strouhal number SS is approximately 0.2 over a wide range of Reynolds numbers ( ,000,000)