Daeil Aqua Co., Ltd. ---- Manufacturer of Industrial & HVAC Cooling Towers

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It is very convenient to use the below tool in calculating NTU.

Download the example file(exe2_4.zip)

Example 2-5. Compare NTU at the same given conditions as above example 2-4 excepting L/G = 1.2540.

(Solution)

Download the example file(exe2_5.zip)
(This file covers the examples of 2-6 & 2-7.)

The NTU at L/G = 1.2540 is smaller than NTU at L/G = 1.6492 under the same design conditions. What the L/G is reduced to 1.2540 from 1.6492 under the same water flow rate means that the air mass is increased. In other word, the decrease of L/G for the same water flow rate means the decrease of enthalpy in the air side and a value of 1 / (hw - ha) is consequently decreased. Also, the exit enthalpy per pound dry air is decreased and the temperature of exit air is reduced.

In the actual cooling tower, what the water is evenly distributed on the entire top of fill is very rare. If the temperature is measured onto the top of drift eliminator, the temperature at the area where the water is smaller than other locations is always lower than the water is larger. This is because the air at the area where the water is small can go easily up due to less pressure drop with the water loading.

Example 2-6. Compare NTU at the same given conditions as above example 2-4 excepting that the ambient wet bulb temperature has been changed to 81.0oF from 80.0oF.

(Solution)

WATER SIDE

AIR SIDE

ENTH DIFF.

Descriptions

tw (oF)

hw (But/Lb)

Description

ha (Btu/Lb)

1/(hw-ha)

tw1 + 0.1 x R

90.50

56.6478

ha1 + 0.1 x L/G x R

47.2587

0.1065

tw1 + 0.4 x R

95.00

63.3426

ha1 + 0.4 x L/G x R

54.6800

0.1154

tw1 + 0.6 x R

98.00

68.2591

ha1 + 0.6 x L/G x R

59.6276

0.1159

tw1 + 0.9 x R

102.50

76.4013

ha1 + 0.9 x L/G x R

67.0489

0.1069

Sum of 1 / (hw - ha)

0.4447

Total Tower Demand (NTU) = Cooling Range x Sum of 1 / (hw - ha)

1.6677

Through this example, the higher ambient wet bulb temperature (approach is smaller), the larger NTU. That is, the enthalpy driving force (hw - ha) is reduced as the ambient wet bulb temperature is increased. This means that less driving force requires more heat transfer area or more air. (Sometimes, NTU calls "Degree of Difficulty".)

Example 2-7. Compare NTU at the same given conditions as above example 2-4 excepting that the entering water temperature has been changed to 101.0oF from 104oF.

(Solution)

WATER SIDE

AIR SIDE

ENTH DIFF.

Descriptions

tw (oF)

hw (But/Lb)

Description

ha (Btu/Lb)

1/(hw-ha)

tw1 + 0.1 x R

90.20

56.2283

ha1 + 0.1 x L/G x R

45.6697

0.0947

tw1 + 0.4 x R

93.80

61.4808

ha1 + 0.4 x L/G x R

51.6068

0.1013

tw1 + 0.6 x R

96.20

65.2631

ha1 + 0.6 x L/G x R

55.5648

0.1031

tw1 + 0.9 x R

99.80

71.4001

ha1 + 0.9 x L/G x R

61.5019

0.1010

Sum of 1 / (hw - ha)

0.4001

Total Tower Demand (NTU) = Cooling Range x Sum of 1 / (hw - ha)

1.2004

This example presents that the smaller range under the same approach, the smaller NTU.

COMPARISON TABLE

Descriptions

Exe. 2-4

Exe. 2-5

Exe. 2-6

Exe. 2-7

Range (oF)

15.0

15.0

15.0

12.0

Approach(oF)

9.0

9.0

8.0

9.0

Wet Bulb Temp.(oF)

80.0

80.0

81.0

80.0

L/G Ratio

1.6492

1.2540

1.6492

1.6492

KaV/L

1.4866

1.1677

1.6677

1.2004

Driving Force (BTU/Lb)

10.1031

13.0670

9.0089

10.0073

Order of Cooling Difficulty

2nd

4th

1st

3rd