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Lecture 11

# Lecture 11 - External Flow Flow over Bluff...

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External Flow: Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Dr. Srinath V. Ekkad

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Forward stagnation point Separation point V Wake D θ u (x) boundary layer CYLINDER in CROSS FLOW Photograph of flow past a circular cylinder. Visualization is by air bubbles in water. (From “An Album of Fluid Motion” by Milton Van Dyke) Observations For Re D 2 x 10 5 , boundary layer transition from laminar to turbulent occurs. 1.Fluid loses momentum under adverse pressure gradient ( dP/dx > 0 ) and detaches, forming a wake. This is known as boundary layer separation. 2.Transition delays separation since turbulence has more momentum
Cylinder in Cross Flow (cont.) Separation occurs when the velocity gradient reduces to zero 0 / y du dy = and is accompanied by flow reversal and a downstream wake . Location of separation depends on boundary layer transition . Re D VD VD ρ μ ν =

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1 10. 100. 1000. 10000. 100000. ReD 1 10. 100. NuD Nu C D D m n s = Re Pr Pr Pr / 1 4 ( 29 [ ] Nu D D D = + + + 0 3 062 1 0 4 1 282 000 1 2 1 3 2 3 1 4 5 8 4 5 . . Re Pr . / Pr Re , / / / / / / Experimental Data Correlation for a Cylinder in Cross Flow Average Nu for cross flow of air (Pr=0.7) over cylinders Convection Correlations for a Cylinder in Cross Flow Property Evaluation Comments T except Pr s evaluated at T s Accounts for temperature dependent property variation.See table for C and m values. If Pr 10, n=0.37 If Pr>10, n=0.36 T f =(T s +T )/2 Recommended for Re D Pr > 0.2.
Cylinder in Cross Flow (cont.) Heat Transfer Considerations The Local Nusselt Number : How does the local Nusselt number vary with for ? θ 5 Re 2 10 D < x What conditions are associated with maxima and minima in the variation? How does the local Nusselt number vary with 5 for Re 2 10 ? D What conditions are associated with maxima and minima in the variation? The Average Nusselt Number ( 29 / : D Nu hD k o Churchill and Bernstein Correlation: ( 29 4 / 5 5/8 1/ 2 1/ 3 1/ 4 2 / 3 0.62Re Pr Re 0.3 1 282,000 1 0.4/ Pr D D D Nu = + + + Cylinders of Noncircular Cross Section: 1/ 3 Re Pr m D D Nu C = , Table 7.3 C m o

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Tube Banks Flow Across Tube Banks A common geometry for two-fluid heat exchangers . max S T V V S D T = - Aligned and Staggered Arrays : Aligned: Staggered: ( 29 ( 29 if 2 max S T V V S D S D D T S D T = - - - ( 29 ( 29 ( 29 if 2 max 2 S T V V S D S D D T S D D = - - - or,
Tube Banks (cont.) Flow Conditions : How do convection coefficients vary from row-to-row in an array? How do flow conditions differ between the two configurations? Why should an aligned array not be used for

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Lecture 11 - External Flow Flow over Bluff...

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