Adiabatic compression

  1. is equation T2=T1*(p2/p2)^((k-1/k)) correct to calculate air temperatute during compression from 1bar to 2bar in a radial compressor?

    and equation for temperature drop throug intercoller T3=T2-ICefficiency*(T2-ambient_air_temp). Is this equation really so simple, what about air density when we are at high altitudes we have less dense air to cool the IC.

    below is the link to java turbo calc, where aplication calculates the temperature after the compresion and after the IC (intercoller) - they also use compressor efficiency data in the calculation? What the compressor efficiency even is?

    http://www.turbofast.com.au/tfcalc.html
     
  2. jcsd
  3. FredGarvin

    FredGarvin 5,087
    Science Advisor

    What you are showing is known as the isentropic temperature ratio across the compressor. It is an ideal assumption that is the best you would ever hope to get.

    Understand that when you are talking about the performance of turbomachinery, especially air breathing devices, you are not talking about static properties, you are really looking at stagnation pressure and temperature.

    Compressor adiabatic efficiency is a ratio of the ideal amount of work required to compress the air to the actual amount of work required to compress the air. There are a lot of assumptions made in basic models that will allow easy calculations to be made (constant specific heats, ideal gas, etc...). The efficiency weeds those assumptions out and compares that to the real world.

    As far as the intercooler goes, that's just a heat exchanger. I can't say that the equation you give rings a bell, but I am not into heat transfer all that much day to day. I can't recall that equation. However, a lot of manufacturers will work out simple equations to use for sizing/specification purposes. That definitely looks like a very simplified expression. Perhaps someone else can chime in on that one.
     
  4. You see the formula you give (T2=T1*(p2/p2)^((k-1/k)) ) plus also T2 = T1[ 1+(P2/P1^(k-1/k) –1
    ηc
    The last formula accounts for efficiency of the compressor, which you get from the compressor map. You try to get the highest efficiency where it operates the most because all in efficiencies turns into heat (which is what T2 is). Note: All temperatures and pressures must be in absolute for the above formulas.

    As for the intercooler the formula I have is T3 = T2(1-ε ) + εT1
    Where ε (efficiency) = T2 – T3 / T2 – T1. This does not account for the pressure loss through the intercooler.
    Richard Stone Introduction to ICE.
    There are more formulas at the following sites:
    http://www.theturboforums.com/turbotech/main.htmhttp://www.theturboforums.com/turbotech/main.htm
    http://www.turbominivan.com/tech/turbo101.htm
    http://www.gnttype.org/techarea/turbo/intercooler.html
     
  5. for the IC efficiency one is for sure. If you want to calculate temperature drop you will need an IC map - where efficiency will be shown in corelation with air density and velocity. If there is a wind you get coolder than if there isn't same is probaby in a car while moving fast or slow - more air per second through heat exchanger and if you are driving on a mountain road where air is thiner one more negative factor for the IC efficiency.
     
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