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Exit Temperature Of Roots Type Blower

roots discharge temperature isentropic

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#1 Anshul Jain

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Posted 24 July 2014 - 06:45 AM

Hi,

 

can i get any help on how to calculate discharge temperature roots type blower?

 

i was going through some links found on Google but landed up with an amazing situation.

 

For isentropic compression 

 

T2= T1+T1((P2/P1)^(K-1/K))

 

Where T1, T2 are inlet and outlet temperature

P1,P2 are inlet and outlet pressure absolute

 

Assuming P1=1bar, P2=2 bar, T1=50 deg C (323 deg K), and k for air is 1.4

 

solving for T2, T2=120 deg C

 

which seems feasible.

 

The problem is assuming P1=1mbar, P2=100mbar, T1 remains the same the value of T2 comes to 931 deg C.

 

What is the mistake that i am doing?

 

i guess for low pressure or pressure below 1 atm this condition needs certain variables.

 

Thanks 



#2 Art Montemayor

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Posted 24 July 2014 - 07:54 AM

Anshul:

 

You must not be an engineer and much less a chemical engineer.  Otherwise, you would:

  • Know the adiabatic discharge equation you are using is wrong;
  • You must always specifically state WHAT pressure you are using – absolute of gauge

Are you in the vacuum range?

 

Look at the attached calculation (which you should have submitted) and see what the results show.  Key in your pressure inputs in the YELLOW cells and observe the results in RED.

 

Attached File  Adiabatic Discharge Temperature.xlsx   14.69KB   261 downloads



#3 Anshul Jain

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Posted 24 July 2014 - 09:50 AM

Hello sir,

Yup i am not a chemical engineer. I am working in vacuum range and all the pressure range i was referring are absolute readings.

I was concern about the discharge temp if you feed .001 bar and .1 bar in yellow fields .

Thanks and regards

#4 PingPong

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Posted 24 July 2014 - 01:27 PM

I don't think you can go from 0.001 barabs to 0.1 barabs in just one roots blower.

 

You probably will need multiple blowers in series with coolers in between, or each blower has a built-in cooling system.


Edited by PingPong, 25 July 2014 - 02:58 AM.


#5 Anshul Jain

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Posted 24 July 2014 - 08:46 PM

I have seen vacuum systems from various manufacturers like Busch, Edwards, leybold, and many more. They have a roots vacuum booster in series with a back up pump used to generate vacuum. Considering that the backup pump generate a vacuum of 100 mbar(abs) then roots vacuum booster further can boost the vacuum to 1 mbar(abs). In that case compression ratio of roots pump is 100 times, putting all these values in above mention equation shows unexpected results.

#6 breizh

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Posted 24 July 2014 - 11:09 PM

Probably good to read . You will see that 1 term was missing in your formula .

 

Breizh


Edited by breizh, 25 July 2014 - 07:08 AM.


#7 Anshul Jain

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Posted 25 July 2014 - 05:46 AM

While going through some link i found an useful information on thuthill website. but rather then getting an appropriate solution i got confused a little more. attached is the document for reference 

Attached Files



#8 Art Montemayor

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Posted 25 July 2014 - 09:19 AM

Anshul:

 

What you submit is well detailed in calculation.  However, you fail to tell us your source(s) for the equation and graph.

 

Please tell us exactly where you found this data and equation and who authored it.  That would make your basis credible.   We all have to furnish the source and basis for our equations or data.  Otherwise, little or no faith can be placed on the subsequent results.

 

By referring to the source of the equation, we can evaluate if basic thermodynamic theory is logically employed in deriving the product equation.



#9 Anshul Jain

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Posted 25 July 2014 - 12:53 PM

Mr. Montemayor,

Sir, the embedded equation that i refered in excel can also be found in the PDF document Mr. Breizh, and the chart i found is from a roots blower manufacturer's website (Tuthill pumps). I am guessing that the chart which i refered to is correct because they are in the business from decades. Also logically that embedded equation in excel fits for the cases where pressure is above atmosphere, refering to chart TRC is 1 for pressure above 1000 mbar and if we put TRC =1 and consider VOlumetric efficiency also 1, then the results from both equations generates the same result.

#10 PingPong

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Posted 25 July 2014 - 01:50 PM

While going through some link i found an useful information on thuthill website. but rather then getting an appropriate solution i got confused a little more. attached is the document for reference 

Cell B31 in your spreadsheet is wrong. A deltaT of 881 K is equal to a deltaT of 881 oC, not 608 oC.

For temperature difference you shall not deduct 273.15 degrees to convert from K to oC.

So T2 in cell B33 shall be 931 oC, which is what you already calculated in your very first message.

 

Adiabatic compression with a pressure ratio of 100 would indeed result in T2 = 931 oC, but surely the vendor will provide internal cooling if the roots blower has to deliver a high pressure ratio, as obviously that kind of extremely high temperature is not practical for any equipment.



#11 fseipel

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Posted 26 July 2014 - 04:48 PM

Have you considered downloading Tuthill's software for rotary lobe blower sizing?  http://www.specwarei...rt6/bx6demo.htm

 

In my opinion, 100:1 compression is unrealistic in one stage.  Roots blowers have maximum allowable differentials/outlet temperatures -- too hot and the rotors contact the casing due to thermal expansion, and it's game over.  Often they are set up to trip on either high DP or outlet temperature to prevent such equipment damage.

 

If you want 100:1 compression, consider at least two roots blowers in series.  For instance, I work at a plant with two roots blowers in series and then an LRVP backing pump.  This is used to re-refine waste crankcase oil and achieves an inlet pressure of only 500 microns.  In this case, the LRVP is oil sealed.  In your case, a rotary piston backing pump & two boosters in series will get you where you need to go, OR a rotary vane vacuum pump alone, because these backing pumps would give better vacuum than the LRVP option.  LRVP is quite attractive from a maintenance standpoint and/or if you have fouling, but gives relatively poor vacuum, even when oil-sealed.



#12 Anshul Jain

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Posted 26 July 2014 - 08:53 PM

Fseipel

I have seen Tuthill's vacuum boosters, they operate on differential pressure of 80mbar. It means a compression ratio of 80:1 can be achieved, however they generally operate at maximum of 10:1 ratio. And it is possible to achieve 100:1 compression ratio, the only limiting factor in roots pump is power.

#13 xavio

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Posted 29 September 2014 - 07:56 PM

Hello all,

 

I hope it's not too late to jump into this topic.

 

Below are the sources of Anshul's formula:

http://www.tuthillva...atalog/3291.pdf

http://books.google.... vacuum&f=false

 

I can't comment on its applicability or accuracy because I have never used it, but I am quite sure to say that it is more accurate than the adiabatic compression one.

 

Going back to Anshul's calculation, I think the assumed volumetric efficiency of 0.8 is grossly excessive with such high P2/P1.

Volumetric efficiency decays steeply with increasing P2/P1; in Anshul's case it could be far less than 0.5, thus creating huge temp. increase.

 

As a rule of thumb (told to me by SIHI), the pressure ratio of single roots blower is between 1~10, with 5 being the usual max. design value.

Additionally, the pressure difference (P2-P1) of the blower should not exceed 20~60mbar.

Higher ratio can be selected at very low inlet pressure, where mass flow is very low.

Even higher ratio can be selected if roots blower is designed with internal cooling, which is much more expensive.

Above "rules" are meant to limit gas discharge temp. of each stage.

 

In my plant, two roots blowers are used to create 1mbarA final pressure against 35mbarA of backing pump inlet pressure.

Roughly, it is 10:1 in the first stage, and 3:1 in the second stage.

 

So, the P2/P1=100 mentioned by Anshul is simply impossible to attain with only one roots blower.

I anticipate that vendor will propose at least 3 stages of blowers.

 

Thanks.

 

xavio






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