1. 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

2. 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:

3. 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.

4. 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

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

6. Cylinder in Cross Flow (cont.)
Heat Convection Experiment

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

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

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

10. 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):

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

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

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

14. 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.

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

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

17. 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

18. 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:

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

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

21. 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.

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

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

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

25. Jets
Relative Nozzle Area:

26. 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: