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Lecture- 9 External Flows

Fluid Mechanics: Fundamentals of Fluid Mechanics, 7th Edition, Bruce R. Munson. Theodore H. Okiishi . Alric P. Rothmayer John Wiley & Sons, Inc.l , 2013. Lecture- 9 External Flows. Lecture slides by Dhafeer M. AL- Shamkhi 2014-2015 Department of Automotive Technical Engineering.

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Lecture- 9 External Flows

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  1. Fluid Mechanics: Fundamentals of Fluid Mechanics, 7th Edition, Bruce R. Munson. Theodore H. Okiishi. Alric P. Rothmayer John Wiley & Sons, Inc.l, 2013 Lecture- 9External Flows Lecture slides by Dhafeer M. AL-Shamkhi 2014-2015 Department of Automotive Technical Engineering

  2. Learning Objectives • After completing this Lecture, you should be able to: • identify and discuss the features of external flow. • explain the fundamental characteristics of a boundary layer, including laminar, transitional, and turbulent regimes. • calculate boundary layer parameters for flow past a flat plate. • provide a description of boundary layer separation. • calculate the lift and drag forces for various objects.

  3. Outline • Review of Viscous Pipe Flow • Laminar Pipe Flow • Overviewof ExternalFlows • Turbulent Pipe Flow • BoundaryLayerCharacteristics • PressureGradientsEffects • Lift and Drag

  4. ViscousPipeFlow:Review Pipe flow versus Open-channel flow: PipeFlow: Open-ChannelFlow: •Pipe is not fullof fluids •Pressure gradient is constant •Gravity is the driving force i.e., flowdownaconcretespillway. •Pipeiscompletelyfilledwithfluid •Pressure gradients drive the flow •Gravity can also be important

  5. ViscousPipeFlow:Flow Regime Osborne Reynolds Experimentto show the three regimes Laminar, Transitional, orTurbulent: Laminar “Experiment”: Transitional Turbulent

  6. ViscousPipeFlow:Flow Regime If we measure the velocityat any given point with respectto time in the pipe: Re > 4000 Reynolds Number Dependency: 2100< Re< 4000 Re< 2100 Turbulence is characterized by random fluctuations. Transitionalflowsarerelativelysteady accompanied by occasionalburst. Laminar flow is relatively steady. Forlaminarflowthereisonlyflowdirection: For turbulent flow, there isa predominate flow direction, but there are randomcomponentsnormaltotheflowdirection:

  7. ViscousPipeFlow:Entrance and Fully Developed The entrance region ina pipe flow is quite complex (1)to (2): The fluid enters the pipe with nearly uniform flow. Theviscouseffectscreateaboundarylayerthatmerges. Whentheymergetheflowisfullydeveloped. Thereareestimatesfordeterminingtheentrancelengthforpipeflows: and

  8. External Flows:Overview If abodyisimmersedinaflow,wecallitanexternalflow. Externalflowsinvolvingairaretypicallytermedaerodynamics. Some important external flows include airplanes, motor vehicles,and flow aroundbuildings. Typical quantitiesof interest are lift anddragactingontheseobjects. Oftenflowmodelingisusedtodeterminetheflowfieldsinawindtunnelor watertank. “Lift/Drag”:

  9. External Flows:Overview Typesof External Flows: Two-Dimensional:infinitelylongandof constant cross-sectional size and shape. Axisymmetric: formedbyrotatingtheircross- sectionalshapeabouttheaxisofsymmetry. Three-Dimensional:mayormaynotpossessa lineofsymmetry. The bodies can be classified as streamlined or blunt. The flow characteristics depend strongly on the amountof streamlining present. Streamlined object typicallymovemoreeasilythroughafluid. “Shapes”:

  10. External Flows:Drag and Lift Pressure Distributions around an object(BluffBody)leadtoliftanddrag. Shear Stresses on the surface also leadto lift anddrag. Drag:AlignedwiththeFlow Pressure(Form)Drag+SkinFrictionDrag Lift:NormaltotheFlow projected wetted 9 area area

  11. External Flows:Friction and Pressure Coefficient τw = Friction Coefficient: Cf 1 ρU 2 Δ p 2 Applying Bernoulli Eq. u2 p−p = Pressure Coefficient:C = 0 C =1− U2 p p ρU2 1ρU2 2 Df Skin Friction Drag Coefficient: C = 1 D,f ρU 2 2 ×Awetted Dp C = Pressure Drag Coefficient: 1 D,p ρU 2 2 ×Aprojected TotalDragCoefficient:CD =CD,f +CD,p

  12. External Flows:Boundary Layers Development ofaBoundaryLayer: Particles get distorted in the boundary layer. Viscouseffectsareimportant “Transition”: Definitions: Boundary layer height:

  13. External Flows:Boundary Layers Local Reynolds Number: CriticalReynoldsNumber:

  14. External Flows:Boundary Layers DisplacementThickness: “Conservation ofMass” δ flowreduction=∫(U−u)dy=Uδ* 0 MomentumThickness: “Momentum Flux” δ lossofmomentumflux =∫ρu(U−u)dy=ρU2θ 0

  15. External Flows:Boundary Layers Drag onaFlat Plate: Integral Relationships bisthewidthoftheplate Note:

  16. External Flows:Laminar Boundary Layers Flow overaFlat Plate can be SolvedExactly: Blasius SolutionIn1908 H. Blasius (1883–1970),oneofPrandtl’sstudents Assumes Steady, 2D Laminar, high Re Flow with negligiblegravitationaleffects. From Boundary Layer Analysis: conservation ofmass: momentum conservation: pressureisuniformacrosstheboundary layer and is determined by the external flow. boundary conditions: at y=0: at y=δ: u=0, u=U, v=0, du/dy=o du/dy=constant, d2u/dy2=0

  17. External Flows:Laminar Boundary Layers After solving, the governing equations with similarity variable: Boundary Layer Height: Displacement Thickness: MomentumThickness: WallShearStress: CoefficientofFriction: Coefficientof Drag: 1 = ∫0 Cf,x dx L note: CD,f L 16

  18. External Flows:Laminar Boundary Layers If we use various velocity profilesthat match the boundary layer conditions ofavelocityprofile: 1 7

  19. External Flows: Transitional and Turbulent Boundary Layers TurbulentSpotsinTransitionalFlow Norealtheoriesfortransitional boundary layers. Turbulent boundary layers are very similartothoseinpipeflow,andwe can use someof those equations andtheories. 18

  20. Fully Developed Turbulent Flow:Overview Turbulent flow is the least understoodof all flow phenomena,yet is more likelyto occur than laminar flow, soweaddresswaysofdescribingtheflow. Transition from Laminarto Turbulent Flow ina Pipe:

  21. Fully Developed Turbulent Flow:Overview Oneseefluctuationorrandomnessonthemacroscopicscale. fluctuating mean Oneof the few ways we can describe turbulent flow is by describing it in termsof time-averaged means and fluctuatingparts.

  22. Fully Developed Turbulent Flow:Overview Nowconsider,thetimeaverageofthefluctuatingparts: The fluctuations are equally distributed on either sideof the average. Now, consider the averageof the squareof the fluctuations: TurbulenceIntensity: Indicationof the “gustiness”of the flow. inAtmosphere, In “good” wind tunnel 21

  23. Fully Developed Turbulent Flow:Overview Now,shearstress: for turbulent flow. TurbulentFlow: However, Laminar Flow: “Experiment”: Shearcomesfromeddymotion whichhaveamorerandommotion and transfer momentum. Shearrelatestorandommotion as particles glide smoothly past each other. For turbulent flow: Is the combinationof laminar and turbulent shear. If there are no fluctuations, the result goes backto the laminar case. The turbulent shear stresses 22 (Reynolds Stresses) are positive, thus turbulent flows have more shearstress.

  24. External Turbulent Flow:Velocity Profile The velocity profilefor turbulent flow is been obtainedthroughexperimental analysis, dimensional analysis, and semiempiricaltheoreticalefforts. 1/7PowerLaw Boundary Layer Height: Displacement Thickness: MomentumThickness: WallShearStress: 0.0592 CoefficientofFriction: Cf,x= Re15 x Coefficientof Drag:

  25. External Flows:Flow Past Objects FlatPlate Flow: LowReynolds Number: Re= 0.1 LargeBoundaryLayer MediumReynolds Number: Re= 10 LargeReynolds Number: Re= 105 Thin Boundary Layer

  26. External Flows:Flow Past Objects Symmetric Separation Wake

  27. External Flows: Drag on Immersed Objects If there were not viscouseffects acting on an object there would be no frictiondragnoranypressuredrag. Viscosity causes friction and separation which causes pressure drag. Friction Drag: the partof drag due directlyto the shearstress Pressure Drag/Form Drag: the partof drag due directlyto the pressure TheDragCoefficientishighlydependent on shape and the ReynoldsNumber: At the same Reynolds number, the above shapes have the same amountof drag.

  28. External Flows: Separation Inasituationwherepressureincreasesdown stream the fluid particles can move up against it by virtueof its kinetic energy. Insidetheboundarylayerthevelocityina layer could reduce so muchthat the kinetic energyof the fluid particlesis no longer adequateto move the particles against the pressure gradient. This leadsto flow reversal. Sincethefluidlayerhigherupstillhave energytomoverforwardarollingoffluid streamsoccurs,whichiscalled separation. “Separation”

  29. External Flows: Separation Separationstartswithzerovelocity gradientat the wall Flowreversaltakesplacebeyond separation point Adverse pressure gradient is necessary forseparation(dp/dx>0) There is no pressure changeafter separationSo, pressure in the separated region is constant. Fluid in turbulent boundary layer has appreciably more momentum than the flowofalaminarB.L.Thusaturbulent B.L can penetrate further into an adverse pressure gradient without separation. 28

  30. External Flows: Separation

  31. External Flows: Separation Streamlining reduces adverse pressure gradient beyond the maximum thicknessanddelaysseparation Fluid particles lose kinetic energy near separation point. So these are either removed by suction or higher energy Highenergyfluidisblownnearseparationpoint Rougheningsurfaceto force early transitionto turbulent boundary layer

  32. External Flows: Drag on Immersed cylinder at very small velocities (Re<0.5) thefluidstickstothecylinderall the way round and never separate from cylinder. This producesa streamline pattern similartothatofanidealfluid. asvelocityincreasesthe boundary layer breaks away and eddiesareformedbehind. Furtherincreasesinvelocity causetheeddiestoelongate. at Re numberof around 90 the vortices break away alternatively form the top andbottomofthecylinderproducingavortexstreet in the wake region called Karman vortex street. Note:in the laminar flow as Re number increases, the separation point moves 31 tofront.

  33. External Flows: Drag on Immersed cylinder as flow within the boundary later becomes turbulent, the pointof separation movesbackproducinganarrowwakesincefluidparticleshavemorekinetic energy (momentum) dueto the natureof the turbulent flow (eddies existence). the friction drag is higher in the turbulent flow, but since pressure drag dominates, the net result isa significant reduction in the total drag. 32

  34. External Flows: Drag on Immersed cylinder RoughnessEffect: roughball(et.Golfball) smooth ball WireRingEffect:

  35. External Flows: Drag on Immersed cylinder thefront to rear pressure difference is greaterfor laminar flow, thus grater drag.

  36. External Flows: Drag on Immersed Objects DragonaSmoothSphereandCylinder: atRe<0.5thedragcoefficientisatitshighestandismainlyduetoskinfriction. as boundary layer becomes turbulent,a pronounced drop in the drag coefficient isproduced. 35

  37. External Flows: LiftonImmersedObjects Mostallliftcomesfrompressureforcesandnotviscousforces. Mostliftgeneratingdevicesarenotsymmetrical. Lift can be generated by adjusting the angelof attackof the object. Lift and drag coefficientsof wings are dependent on angleof attack. At large anglesof attack, the boundary layer separates and the wing stalls. 36

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