Pressure Drop Across A Louvered-Fin Heat ExchangerAnthony DelRicciNathan GentitMatthew Zeld

Problem Statement

The pressure drop across an array of nozzles is known and is used to calculate the volumetric flow rate of air through a wind tunnel. With this calculated volumetric flow rate and known geometrical properties of the louvered-fin heat exchanger, the loss coefficients, friction factor, and ultimately, the pressure drop across the louvered-fin heat exchanger can be estimated.

Thermal Fluids Principle• Pressure drop across

heat exchanger• Friction factor• Entrance/exit losses• Fluid properties• Fluid velocity• Heat exchanger dimensions

• Fluid velocity• Volumetric flow rate• Heat exchanger dimensions

• Volumetric flow rate• Wind tunnel with

nozzle array (ASHRAE standard)• Expansion factor• Discharge coefficient

of nozzles• Pressure drop across

nozzles• Nozzle dimensions• Tunnel dimension• Fluid properties

THEORY

Determining Volumetric Flow Rate (ASHRAE Standards)

• (1)

Figure 1. Example inlet chamber setup for multiple nozzles in a chamber

Determining Volumetric Flow Rate (ASHRAE Standards)

• (2)• Expansion factor

• (3)• Nozzle throat pressure to nozzle entrance pressure ratio

• (4)• Nozzle throat diameter to wind tunnel diameter ratio

Determining Volumetric Flow Rate (ASHRAE Standards)

• (5)

• Discharge coefficient of each nozzle

• (6)• Reynolds number through the nozzle array

Determining Velocity Through the Heat Exchanger• Function of volumetric flow rate and heat exchanger

dimensions• (7)

• : free-flow area

Figure 2. Theory for calculating the velocity through the heat exchanger

Pressure Drop Across Heat Exchanger• Standard equation for pressure drop across a compact heat

exchanger• (8)

Entrance effect Flowacceleration

Corefriction

Exit effect

Figure 3. Schematic of pressure variation of flow through a heat exchanger

Pressure Drop Across Heat Exchanger• (9)• Exchanger flow stream mass velocity

• : Exchanger total heat transfer area• Fin and tube surface area in contact with flowing air

• : Exchanger free-flow area• Total frontal area minus frontal area of tubes and fins

• (10)• Contraction ratio (= projected frontal area)

Pressure Drop Across Heat Exchanger• and : Entrance and exit

loss coefficient• Contraction ratio• Reynolds number

• (11)• : louver pitch• : dynamic viscosity

• For exchangers with frequent fin interruptions, use R = ∞ curve.

Figure 4. Finding loss coefficients [1]

Pressure Drop Across Heat Exchanger• Friction factor correlation for many types of compact heat

exchangers by Chang and Wang.• “Can correlate 85% of the present friction data with 10%

uncertainty.”

• (12)• : total airside surface area to external tube surface area ratio• : louver surface area to total airside surface area ratio

EXPERIMENTALAPPARATUS

Experimental Apparatus

• Blower• Wind tunnel• Nozzle array

• Housing duct• Condenser (heat exchanger)• Differential pressure gages• 1 : before and after nozzle array• 2 : before heat exchanger and atm

Experimental Setup

Figure 5. Blower side of the test setup

Experimental Setup

Figure 6. Heat exchanger side of the test setup

Experimental Setup

Figure 7. Nozzle array

Experimental Setup

Figure 8. Heat exchanger inside of housing duct, facing direction of flow

Experimental Setup

Gage used to measure nozzle array

pressure drop

Pressure tap in front of heat

exchanger

Figure 9. Pressure gage setup

Figure 10. Pressure gage setup

Heat Exchanger Dimensions• Width = 715 mm• Height = 433 mm• Depth = 12 mm• Tube height = 1.40 mm• Tube spacing = 5.63 mm

Figure 11. Schematic of heat exchanger tubes and fins

Heat Exchanger Dimensions• Fin pitch = 89 fins/dm• Fin thickness = 0.06 mm• Louver pitch = 0.850 mm

• E = 6.298• El = 0.4182

Figure 12. Schematic of heat exchanger louvers

Heat Exchanger Dimensions

Figure 13. Louver profiles

Figure 14. Picture of fins and louvers

EXPERIMENTALPROCEDURE

Experimental Procedure

• 1. Connect duct to wind tunnel• 2. Turn blower on low power setting• 3. Record pressure drop across nozzle array• 4. Record pressure drop across heat exchanger• 5. Repeat for two more blower settings• (moderate and high)

• 6. Turn off blower• 7. The remainder of the experiment is data calculation

*Read safety guidelines before performing experiment.

DISCUSSION OF RESULTS

Experimental Data

Table 1. Experimental pressure drop data

Theoretical Calculations• Using highest blower speed as a sample

• Looking at the graph:

Theoretical Calculations• Using highest blower speed as a sample

• Repeat for all flow rates

Discussion of Results

Figure 15. Theoretical and experimental pressure drops across heat exchanger

Discussion of Results• Error lies within the friction factor correlation• “Can correlate 85% of the present friction data with 10% uncertainty.”

• Rearrange Eq. 8 to solve for friction factor necessary to match theoretical pressure drop

Discussion of Results• Friction factor: function of Reynolds number

Figure 16. Calculated friction factor and necessary friction factor versus Reynolds number

Discussion of Results• Curve-fit necessary friction factors• Keeping same equation form• Reynolds number exponent changes• Heat exchanger components stay constant• Leading coefficient changes

Uncertainties• Pressure gages (± 2%)• Nozzle array: carried out through all equations• Heat exchanger: on Figure 15 experimental data points

• Friction factor (± 10%)• Cited as uncertainty in source• Overall largest contributor to uncertainty

CONCLUSION

Conclusion• Found volumetric flow rate in a wind tunnel• Using nozzle array• ASHRAE Handbook standards

• Determine pressure drop across a heat exchanger• Use existing empirical calculations• Compare calculations to experimental results

• Difference between experiment and theory was large• Derived new empirical formula for friction factor

QUESTIONS?