Chapter 7 Sections 7.4 through 7.8 External Flow: Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Chapter 7 Sections 7.4 through 7.8

Circular 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 fluid flows towards the rear of the cylinder, pressure increases. The boundary layer develops under the influence of an adverse pressure gradient:

Cylinder in Cross Flow (cont.) Separation occurs when the velocity gradient becomes zero followed by flow reversal and a wake downstream of the separation point.

Cylinder in Cross Flow (cont.) Location of separation depends on boundary layer transition. For Reynolds number > 200,000 on a smooth cylinder, the boundary becomes turbulent. Flow separation is delayed, and the wake is small then that when the boundary is laminar. Drag force on the cylinder is the sum of friction and form (pressure) drag Define drag coefficient: Where FD = Total drag force Af = Frontal area of cylinder = Diameter x Length

Cylinder in Cross Flow (cont.) Cylinder in Cross Flow: Experimental Drag Coefficient

Cylinder in Cross Flow (cont.) Heat Convection Experiment

Cylinder in Cross Flow (cont.) Local Heat Convection Coefficient: Experimental Results

Experimental Data for Average Nusselt Number Turbulent Flow Experimental Data for Average Nusselt Number

Cylinder in Cross Flow (cont.) Correlation of Average Nusselt Number: Churchill and Bernstein correlation for all ReD :

Spheres and Packed Beds Forced Convection on Sphere Flow characteristics similar to flow over cylinder. Drag coefficient lower than that of cylinder because of 3D relief effect (Fig. 7.8) Correlation of average Nusselt number (ms is the fluid viscosity at surface temperature):

Cylinder in Cross Flow (cont.) Cylinders of Noncircular Cross Section:

Flow Across Tube Banks Typical design for two-fluid heat exchangers.

Definition of Max. Velocity Tube Banks Definition of Max. Velocity Staggered: Aligned:

Tube Banks (cont.) Aligned Tube Bank: Flow behind first row is turbulent, causing convection coefficients to increase gradually in subsequent rows if there are sufficiently spacings. If the rows are too close (ST/SL < 0.7), each tube is confined in the wake of the one in front, and convection coefficient would decrease instead.

Tube Banks (cont.) Staggered Tube Bank: Heat convection is more evenly distributed, and therefore more effective then the aligned tube bank.

Zukauskas Correlation for an Isothermal Array: Tube Banks (cont.) Zukauskas Correlation for an Isothermal Array:

Prs is evaluated at surface temperature of the tubes Ts. Tube Banks (cont.) Pr is evaluated at average of inlet and outlet temperature of the cross flow. Prs is evaluated at surface temperature of the tubes Ts. Reynolds number for the flow across the tube bank is defined as: ReD,max = Vmax D/n

From an energy balance, it can be shown that the Tube Banks (cont.) From an energy balance, it can be shown that the inlet & outlet temperatures (Ti , To) of the flow is related by: (Challenge: Prove it!) N is the total number of tubes: Total Heat Convection Rate can also be shown as: As is the total surface area of the tubes: DTlm is called the “Log-Mean Temperature”: Correlation of Pressure Drop across the tube bank:

Correlation Factor & Friction Factor: Aligned Tube Bank Tube Banks (cont.) Correlation Factor & Friction Factor: Aligned Tube Bank

Correlation Factor & Friction Factor: Staggered Tube Bank Tube Banks (cont.) Correlation Factor & Friction Factor: Staggered Tube Bank

Spheres and Packed Beds Flow Through Packed Beds of Particles Large surface area per unit volume: desirable for the transfer and storage of thermal energy.

Spheres and Packed Beds (cont.) Correlation For a packed bed of spheres: jH is the Colburn j-factor: jH = St Pr2/3

Jets Jet Impingement Characterized by large convection coefficients and used for cooling and heating in numerous manufacturing, electronic and aeronautic applications.

Example of Multiple Jet Impingent Design: Slot Jet Array Jets Example of Multiple Jet Impingent Design: Slot Jet Array

Jets Relative Nozzle Area:

Typical Experimental Data of Local Nusselt number distribution: Jets Hydraulic diameter: Dh = 4 Area/Perimeter = D (round nozzle), Dh ~ 2W (slot nozzle) Typical Experimental Data of Local Nusselt number distribution: Average Nusselt number: