58:160 Intermediate Fluid Mechanics Bluff Body Professor Fred Stern Fall 2014

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Winifred Spencer
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. External flows such as flow around vehicles and structures, which are characterized by unbounded or partially bounded domains and flow field

1 Professor Fred Stern Fall 04 Chapter 7 Bluff Body Fluid flows are broadly categorized:. Internal flows such as ducts/pipes, turbomachinery, open channel/river, which are bounded by walls or fluid interfaces: Chapter 8.. External flows such as flow around vehicles and structures, which are characterized by unbounded or partially bounded domains and flow field decomposition into viscous and inviscid regions: Chapter 9. a. Boundary layer flow: high Reynolds number flow around streamlines bodies without flow separation. b. Bluff body flow: flow around bluff bodies with flow separation.

walls and development and spreading in an unbounded or partially bounded ambient domain: advanced

2 Professor Fred Stern Fall Free Shear flows such as jets, wakes, and mixing layers, which are also characterized by absence of walls and development and spreading in an unbounded or partially bounded ambient domain: advanced topic, which also uses boundary layer theory. Basic Considerations Drag is decomposed into form and skin-friction contributions: C D ρv S A ( p p ) n îda + τ S w C Dp C f t îda

3 Professor Fred Stern Fall 04 3 CL ( p p ) n ĵda ρv A S t << Cf > > C Dp streamlined body c t CDp > > C f bluff body c Streamlining: One way to reduce the drag reduce the flow separation reduce the pressure drag increase the surface area increase the friction drag Trade-off relationship between pressure drag and friction drag Trade-off relationship between pressure drag and friction drag Benefit of streamlining: reducing vibration and noise

4 Professor Fred Stern Fall 04 4 Drag of -D Bodies First consider a flat plate both parallel and normal to the flow C ρv S A ( p p ) n î 0 Dp C f ρv τ S A w t îda.33 / Re L.074 / 5 Re L laminar flow turbulent flow flow pattern where C p based on experimental data vortex wake typical of bluff body flow

5 Professor Fred Stern Fall 04 5 C Dp ( p p ) n îda S ρv A C p A da S using numerical integration of experimental data C f 0 For bluff body flow experimental data used for C D.

6 Professor Fred Stern Fall 04 6 In general, Drag f(v, L, ρ, µ, c, t, ε, T, etc.) from dimensional analysis c/l C D Drag t ε f Re, Ar,,, T, etc. ρ L L V A scale factor

7 Professor Fred Stern Fall 04 7 Potential Flow Solution: θ ψ sin r a r U U p V p ρ + ρ + r p U u u U p p C θ + ρ ( ) θ p sin 4 a r C surface pressure r u r u r ψ θ ψ θ

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17 Professor Fred Stern Fall 04 7 Effect of Compressibility on Drag: CD CD(Re, Ma) Ma U a speed of sound rate at which infinitesimal disturbances are propagated from their source into undisturbed medium Ma < Ma Ma > Ma >> subsonic transonic ( sonic flow) supersonic hypersonic < 0.3 flow is incompressible, i.e., ρ constant C D increases for Ma due to shock waves and wave drag Ma critical (sphere).6 Ma critical (slender bodies) For U > a: upstream flow is not warned of approaching disturbance which results in the formation of shock waves across which flow properties and streamlines change discontinuously

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Chapter 9 Flow over Immersed Bodies

57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 009 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,