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Cooling Tower Fundamentals

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COOLING TOWERS FOR INDUSTRIAL AND HVAC APPLICATIONS: SAMPLE COOLING TOWER PROBLEM STATEMENT

Select replacement media to cool 1350 US GPM 95/85/78°F fitting the structure of an old crossflow-type cooling tower, as per catalog data.  HVAC is supposedly 450 chiller tons.

According to manufacturer catalog, louver side length L is 9' 4.5" or say about 9.5'. Approximate height B is 7' 9" or say 7.75'

Note: the vertical dimension closely agrees with the 7.5' fill height (ca. 2.29m) commonly used in vintage XF19060 graphs. However, it would seem that in order to compute the actual louver face area we would have to subtract about 1' basin depth - let it be for the moment.

Anyway, being a double-flow model we can approximate the louver face area as follows:

2 * 9' * 7' = 126 sq.ft. louver area

Kelly's handbook indicates that crossflow cooling towers are typically designed using 2,000 lb DRY air / hr per sq.ft. of louver area and anywhere in between the following bounds:

1,600 lb/hr per sq.ft. DRY AIR minimum

2,600 lb/hr per sq.ft. DRY AIR maximum

Using the calculated available louver face area, we can now get the following estimates for the various possible design values:

126 sq.ft. * 1,600 lb/hr sq.ft. = 201,600 lb/hr dry air (minimum)

126 sq.ft. * 2,000 lb/hr sq.ft. = 252,000 lb/hr dry air ("typical")

126 sq.ft. * 2,600 lb/hr sq.ft. = 327,600 lb/hr dry air (maximum)

Because we're aiming at order of magnitude performance estimate (there's specialized software now that does everything) let's disregard otherwise applicable entering air analysis and say settle for a ballpark specific volume of about 15 cu.ft./lb   We can approximate tentative air flows as follows:

126 sq.ft.*1,600 lb/hr sq.ft.*15 cu.ft./lb  / 60 = 201,600 * 15/60= 50,400 CFM (minimum)

126 sq.ft.*2,000 lb/hr sq.ft.* 15 cu.ft./lb / 60 = 252,000 * 15/60=  63,000 CFM ("typical")

126 sq.ft.*2,600 lb/hr sq.ft.* 15 cu.ft./lb / 60 = 327,600 * 15/60=  81,900 CFM (maximum)

Note: the last airflow value is under to the 94,645 CFM figure shown in the unit's catalog, [reportedly] rated to handle 1,350 US GPM (450 chiller tons) at 95/85/78°F.

Corresponding inlet air velocities would then be:

50,400 CFM / 126 sq.ft. = 400 fpm

63,000 CFM / 126 sq.ft. = 500 fpm

81,900 CFM / 126 sq.ft. = 650 fpm

Let's figure out L/G, the liquid to gas ratio.  First let's convert the published airflow  figure to lb/hr dry air, id est

94,645 CFM = 94,645 CFM * 60 min/hr / 15 cu.ft./lb = 378,580 lb/hr dry air

G' = 378,580 lb/hr dry air / 126. sq.ft. = ca. 3,005 lb/hr dry air per sq.ft.

Let's now convert the water flow, i.e. 1 ,350 US GPM, to suitable mass units as follows:

1,350 US GPM = 1,350 * 8.33 * 60 lb/hr water = 674,730 lb/hr water

Design L/G estimate turns out to be:

L/G =  674,730 lb/hr water /  378,580 lb/hr dry air = ca. 1.78

We are now bound to solve 95/t2/78°F using L/G = 1.78 in a crossflow configuration.  Using a  relatively involved KAY/L program calculator based on Kelly's guidelines (Gauss Seidel; dx= 0.297, dy = 0.165, L/G = dx/dy= 0.297/0,165= ca. 1.8 ) , we get the following matrix:  

KaY/L                                  dx 

            0.00   0.29   0.59  0.89 1.18  1.48  1.78  2.07  2.37  2.67  2.97

0.00     95.0   95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0
0.16     91.7  92.2  92.5  92.7  93.0  93.2  93.4  93.5  93.5   93.7  93.7
0.33     89.2  89.9  90.4  90.9  91.2  91.5  91.9  92.0  92.4   92.5  92.7
0.49     87.2  88.0  88.7  89.2  89.7  90.2  90.5  90.9  91.2   91.5  91.7
0.66     85.7  86.5  87.2  87.7  88.4  88.9  89.2  89.7  90.0   90.4  90.7
0.82     84.4  85.2  86.0  86.5  87.2  87.7  88.2  88.7  89.0   89.5  89.7
0.99     83.2  84.0  84.9  85.5  86.2  86.7  87.2  87.7  88.2   88.5  89.7
1.15     82.5  83.2  84.0  84.7  85.2  85.9  86.4  86.9  87.4   87.7  88.2
1.32     81.7  82.5  83.2  84.0  84.5  85.0  85.5  86.0  86.5   87.0  87.4
1.48     81.0  81.7  82.5  83.2  83.7  84.2 84.9  85.4   85.9   86.2  86.7
1.65    80.5  81.2  81.9  82.5  83.0  83.7 84.2  84.7   85.2   85.7  86.0

We find that required KaY/Ls "easily" approach ca. 1.65+ values even if we settle for ca. 86°F cold water.  Because of display figure rounding (plus rounding errors) let's rest the case as it were and rollback a little bit.  Even allowing for slight changes in L/G, we are talking about required KaY/Ls in the vicinity of 1.6+.  While we have only bold-faced diagonal elements (all correspond to desired L/G = dx / dy = ca. 1.8, e.g. 2.97/1.65= 1..8) all the rest can be used for as well. 

Let's now take a look at a classic crossflow fill media performance formula

KaY/L = .2454 * (G'^ 0.465) * (L^0.35) * Y/L´

where in our case, somewhat generously, we have

G' = 3,005 lb/hr per sq.ft. (as calculated earlier)

Y = ca. 7.5' (vertical dimension; fill stackable height)  

Let's work out L', i.e. crossflow water loading estimate (lb/hr water per sq.ft.).  Recalling involved  liquid mass:

1,350 US GPM = 1,350 US GPM * 8.33 * 60 = 674,730 lb/hr water

Checking out the vendor's published data we can roughly assume [crossflow] fill depth or air travel depth of be one fourth of what the catalog labels dimension A.

Thus an upper bound for air travel seems to be A / 4 = 18' / 4 = 4.5'.  Anyway let's just keep it 4' air travel fill depth.  Water will gravity fall over the following horizontal face area:

  2 sides * air travel depth * [XF] tower length = 2 * 4' * 9' = ca. 72 sq.ft

Hot water distribution basin water loading ends about about 1,350 US GPM/72 sq.ft. = 18.75 gpm/sq.ft. within published acceptable drift ranges.

L' =  674,730 lb/hr water / 72. sq.ft. = 9,372 lb/h per sq.ft.

We can now easily evaluate the previously given crossflow film fill formula 

KaY/L = .2454 * (G'^ 0.465) * (L^0.35) * Y/L´

for the following data set

G' = 3,005 lb/hr per sq.ft. (as calculated earlier)

Y = ca. 7' (vertical dimension; fill stackable height)  

L' =   9372 lb/h per sq.ft.

Straight forward evaluation produces 

KaY/L = .2454 * (3,005^ 0.465) * (9,372^0.35) * 7' / 9,372 = ca. 1.012!!! 

There's no way to attain catalog specs.  We could try to snag away using upper bound air flow (i.e. higher G's) or a little bit more vertical fill height but to no avail.  Simply redoing calcs for the corresponding data set, it can be likewise seen that the actual tower performance will be only 280 - 300 chiller tons for 95/85/78°F at 3 gpm/ton, or ca. two thirds the published thermal capacity. 

In-house crossflow tower KaY/L calculator produces the following matrix:

 

KaY/L                                  dx 

              0.00  0.15  0.31  0.46  0.62  0.78  0.93 1.09  1.24   1.40  1.56

0.00       95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0  95.0
0.13       92.4  92.5  92.7  92.9  93.0  93.0  93.2  93.4  93.4  93.5  93.5
0.26       90.2  90.5  90.9  91.0  91.2  91.5  91.7  91.9  92.0  92.2  92.2
0.39       88.5  88.9  89.2  89.5  89.7  90.0  90.2  90.5  90.7  91.0  91.2
0.52       87.0  87.5  87.7  88.2  88.5  88.7  89.0  89.4  89.5  89.9  90.0
0.65       85.7  86.2  86.5  87.0  87.4  87.7  88.0  88.2  88.5  88.9  89.0
0.78       84.7  85.2  85.5  86.0  86.4  86.7  87.0  87.4  87.7  88.0  88.2
0.09       83.7  84.2  84.7  85.0  85.5  85.7  86.2  86.5  86.7  87.0  87.4
1.04       83.0  83.5  83.9  84.2  84.7  85.0  85.4  85.7  86.0  86.4  86.7
1.17       82.4  82.7  83.2  83.5  84.0  84.4  84.7  85.0  85.4  85.7  86.0
1.30       81.7  82.2  82.5  83.0  83.4  83.7  84.0  84.4  85.0  85.0  85.2

L/G = dx / dy = 1.56 / 1.3 = 1.2.  We need fill to deliver a target KaY/L of about 1.30 or more.

900 US GPM = 900 US GPM * 8.33 * 60 = 449,820 lb/hr water

L' =  449,820 lb/hr water / 72. sq.ft. = 6,248 per sq.ft.

We can now easily evaluate the previously given crossflow film fill formula 

KaY/L = .2454 * (G'^ 0.465) * (L^0.35) * Y/L´

for the following data set

G' = 3,005 lb/hr per sq.ft. (as calculated earlier)

Y = ca. 7 - 7.5' (vertical dimension; fill stackable height)  

L' =   6,248 lb/h per sq.ft.

Straight forward crossflow film fill formula evaluation produces 

KaY/L = .2454 * (3,005^ 0.465) * (6,248^0.35) * 7.5' / 6,248 = ca. 1.31 

 

 

 

Need Some Help? answers@engineeringfundamentals.com - James C. Young Environmental - Balestie, Irwin & Balestie