External Flow: Flow over Bluff Objects (Cylinders, Sphere, Packed Beds) and Impinging Jets

The Cylinder in Cross Flow Conditions depend on special features of boundary layer development, including onset at a stagnation point and separation, as well as transition to turbulence. – Stagnation point: Location of zero velocity and maximum pressure. – Followed by boundary layer development under a favorable pressure gradient and hence acceleration of the free stream flow. – As the rear of the cylinder is approached, the pressure must begin to increase. Hence, there is a minimum in the pressure distribution, p(x), after which boundary layer development occurs under the influence of an adverse pressure gradient

– Separation occurs when the velocity gradient reduces to zero. and is accompanied by flow reversal and a downstream wake. – Location of separation depends on boundary layer transition.

– What features differentiate boundary development for the flat plate in parallel flow from that for flow over a cylinder? Force imposed by the flow is due to the combination of friction and form drag. The dimensionless form of the drag force is

Heat Transfer Considerations – The Local Nusselt Number: – How does the local Nusselt number vary with for ? What conditions are associated with maxima and minima in the variation? – How does the local Nusselt vary with What conditions are associated with maxima and minima in the variation? – The Average Nusselt Number – Churchill and Bernstein Correlation: – Cylinders of Noncircular Cross Section:

Flow Across Tube Banks A common geometry for two-fluid heat exchangers. Aligned and Staggered Arrays: Aligned: Staggered: or,

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 use for S T /S L < 0.7? Average Nusselt Number for an Isothermal Array: All properties are evaluated at except for Pr s.

Fluid Outlet Temperature (T o ) : What may be said about T o as Total Heat Rate: Pressure Drop:

The Sphere and Packed Beds Flow over a sphere – Boundary layer development is similar to that for flow over a cylinder, involving transition and separation. Gas Flow through a Packed Bed – Flow is characterized by tortuous paths through a bed of fixed particles. – Large surface area per unit volume renders configuration desirable for the transfer and storage of thermal energy. – –

– For a packed bed of spheres: – –

Problem: 7.78 Measurement of combustion gas temperature with a spherical thermocouple junction. SCHEMATIC: