## January 28, 2008

### Cooling Tower: Performance calculation - II

This is in continuation of my previous post on this topic. In this part, I will explain the calculation of NTU for cooling towers, yes NTU which is very important & is similar to NTU in absorption towers.

It helps in indentifying the performance, capacity & effciiency of your cooling tower. In next part of this post I will explain How to use these calculations for mesurement of efficiencies, prediction for new conditions etc.

Now we will see the NTU calculation & efficiency of tower, use of NTU method for predictions etc.

Step-1
First consider the cooling water exit temperature ‘twex’ in column A in excel sheet so i.e. 35°C in this case. All the data is given in Part-I...So Check it First.

Put h’ in column B which is the enthalpy of saturated air at twex and can be calculated by the equation

h’=9.446443x10-13x(twex^8)-1.433603766x10-10x(twex^7)+5.39506924*10-9(twex ^6)+3.02962638*10-7(twex^5)-0.0000272854755*(B7^4)+0.00096596975*(B7^3)-0.005340108*(B7^2)+0.458708485*B7+2.219286635

Put tawet in column C starting with actual wet bulb temperature of entering air, which is 30°C in this case.

Put w as absolute humidity at tawet in column D that is calculated from the same formula as shown in Part-I of this post.

Put hcal as humidity at tawet using the formula given above for h’ in column E.

Put ha as humidity at actual wet bulb temperature of entering air, which is 30°C in this case. Yes, that means initially in the first row of calculation sheet hcal & ha will be same. This is in column F.

Now put calculation of difference of h’ – ha in column G.

Step-2
In first row G will be automatically zero.
Now in second row consider the twex 2 = (Twin – Twex)/19 + twex 1
i.e. twex 2 = (44 – 35 ) / 19 + 35
= 0.474 + 35 = 35.474°C

Copy this formula in column A for next 19 rows. This gives you incremental evaluation of tower step by step along the total tower height from 35° at exit at bottom to 44° at inlet at the top.

Copy h’ formula in column B for the same no of rows.

Step-3
Now put any assumed figure for tawet in column C, w in column D, hcal in column E.

Now calculation for ha will change which will come from actual L/G ratio of tower calculated in Part-I.

Use the following formula for ha in second row onwards.

ha 2 = ha1 + L/G * (twex 2 - twex 1) + (w 2 – w 1) / 1000 * twex 1
= ha1 + 1.715 * (35.474 – 35.00) + (w 2 – w 1) / 1000 * 35.0

Based on other figures it will vary.

Now since you have assumed tawet, hcal will be different from ha. Put this difference in next column G.

Now either change tawet manually to make the difference Zero in column G or use goal seek from excel. This will give you tawet, which is supposed to be the actual wet bulb temperature of air exiting from the tower at the top finally.

This will complete first part of NTU calculation after completing all the rows.

Step-4
Now in next column i.e. H; put (h’ – ha) value which is Column B – Column F and copy it down till the last row.

Put reciprocal of column H in column I. This will give you 1/ (h’ – ha) value and copy it down till the last row.

Now in next column J, leave first row blank & start from second row where you should put average of first & second row in column I. This will give you average of 1 / (h’ – ha) for first & second value. Copy this formula also down till the end of rows.

Step-5
Now in column K, put NTUL as calculated below (From second row as column J starts from second row).

NTUL = Column J x (twex 2 - twex 1)
= Column J x (35.474 – 35.0)

Copy this formula in all rows.

In column L, put progressive summation of NTUL calculated in column K i.e. in each row of column L, use previous row of column L + same row of column K.

This value at the end of last row will give your towers total NTU for liquid side.

Step-6
Repeat all calculations in next two columns for NTUG similar to Step-5 above and find out final value of gas transfer units. The only difference is to use the following formula to calculate NTUG in column M.

NTUG = Column J x (ha 2 - ha 1) ha is in column F.

Use progressive sum again in column N.

Now I will give you guidelines on using these calculations for prediction of performance, prediction of new conditions, calculation of existing system and how to improve it in the next part of this post.

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farabard said...

Dear sir
We are Farabard Company located at Shiraz/south of Iran. Farabard is one of the designer and constructor of wet counter flow concrete cooling towers.
We studied your performance calculation about cooling towers (NTU calculation). Your method is very good but there are some ambiguities for us. We invite you to come Iran and hope that you clear these ambiguities for us. Also we will be spent you all of your travel expenditures (include: air ticket, hotel, …).
Your prompt action will be appreciated.
Best Regard
info@farabard.ir
+987116294813
+987116266067

farabard said...

dear sir
Im sepideh samghani.I study mechanics engineering in shiraz university.I work as a trainee in farabard company for 2 mounths.I have studied your performance calculation of cooling tower and I have some question about it. could you please help me to understand them.
these are my quastion ...
1-how did you calculate the enthalpy content of moist air inlet,based on %saturation?
2-how did you calculate the amount of evaporated water?
your quick response is highly appreciated.

Best Regards
e_mail:info@farabard.ir
tel:+98-711-6294813
fax:+98-711-6266067

profmaster said...

1. First I used empirical equation which is already given in the post to find out the enthalpy of completely dry air and completely wet air at given dry bulb temp. Now by diff you have vapor enthalpy which can be added to dry air enthalpy after multiplying by %Saturation. So you have wet air enthalpy.

2. It is found by trial & error method based on enthalpy condition of air at inlet & exit.

I prefer only Email ocntact which you can do thru comments on this post.

TheServant said...

Hi profmaster,
I am confused with some of the wording here.
At the end of Step 1 you say make h'-ha in column G, and that that is "automatically zero" in step 2. I don't think it is, do you mean hcal-ha as you suggest in Step 3?

Also, I am unclear about what to put in tawet column (Step 3) where you say any assumed figure? Does it vary for the number of rows?

Finally, the number you use is 19, and I have forgotten, is that equivalent to column height you refer to with that number?

profmaster said...

Oops Yes dear,
You got it right. It is hcal-ha Not h'-ha in Column G.

No Tawet is any assumed figure at different intervals to make the balance by trial & error. So initially U assume it & then make difference in G column zero by varying it. That is your final tawet figure.

19 is a no based on my assumtion of 0.5° interval steps for 35 to 44°C. You can increase it for better results but this is generally sufficient. So if U use 0.1° interval U need 91 rows.

Anonymous said...

Hi Profmaster,
I am refrigeration engineer and I tray to optimize an cooling tower as you suggested. But with this equation if 99.9% is ok it is not good as you know 100% is good.So can you send me a general(or an example will be better) excel sheet with what you propose here?

profmaster said...

If you are an engineer then first thing you should understand that no engineering calculation is 100% accurate, they are not even 99.9% correct. Almost all corelations are 95-99% accurate & therefore design margins are always considered.

Regarding sheet I need to know your own efforts first in this direction.

Balaji said...

Dear Sir,

I was checking on cooling tower efficiency and found your useful 2 part calculations. However you have mentioned you will explain how to use these calculations to measure efficiency. But I am not able to find the post. Kindly help me with the link to that post. Thank you.

Anonymous said...

Dear Sir,

I got the task to design a cooling tower in detail, can these calculation performance help me plzzzzzz

antony said...

Sir please post the third part of the calculation soon sir.I have to finish my project work with this sir.

Darien said...

Sorry but I dont really understand Step 1 "Put hcal as humidity at tawet using the formula given for h' in column E". Is it the formula for hcal is the same for h' ?? but h' is enthalpy and hcal is humidity. Please advice. Thanks

profmaster said...

Dear Darien
The formula for h' is already given (Long formula mentioned in the post also). In that column h; is calculated at twex which means temperature of water at exit condition.

Now for hcal use tawet in place of twex in the same formula. tawet means wet air temperature.

I hope this clears. h is enthalpy & not humidity.

Meera mideen said...

Sorry to say that iam seeking for cooling tower to privide the polythene recycling unit

ABR Cooling Towers said...

FRP cooling towers - review our product catalog of cooling towers, which includes bottle shape cooling towers, FRP square cooling towers, rectangular towers etc.

Anonymous said...

The information is very useful for me. Thanks for your useful information.
http://www.classikcoolingtowers.com

Anonymous said...

When is next blog is expected. I am eagerly waiting for the next blog, where performance interpretation will be discussed

Anonymous said...

We want to use the humidified air for some industrial application.plz help us out. thanking u in anticipation

hardik gandhi said...

hello profmaster..
where is excel sheet. "twex" ??

dev said...

Dear Sir,
I'm a HVAC Design Engineer,now doing cooling tower thermal calculation for IDCT concrete cooling tower. do u have any excel calculation sheet?
Are you using Kelley's black hand book for L/G calculation.