Can someone guide me how to formulate a multiple stage compressor in terms of intake air mass flow rate, specific work of each stage and other parameters. In this problem, I only have the available electricity to be used by the compressors and the compression ration of each stage which is constant and equal for all and just nothing else. Clearly, the problem has several dimensions to be considered such as the rotor speed, the air mass flow rate, the specific work of each stage and so on. There are some operational diagrams for some typical compressors, however, I need some operational diagrams that match my work (air compressors for high pressures (up to 100 bar) and high mass flow rates (up to 100 kg/s)). Can someone help me to find a good reference please?, really thanks.
Maybe it can help
http://www.slideshare.net/abhishekgawande/compressor-091215172405phpapp01
Thank you for the responses dears, however, as I explained before, at this stage, I strongly need an actual operational performance curve for a real multiple stage air compressor for high pressures and high mass flow rates. The compressor is clearly centrifugal type. Thanks
By the way, all the references for calculating the work of multiple stage compressors consider poly-tropic factor "n" as a known parameter while in my problem, according to the previous explanation provided, we don't have this parameter as well. How can we have this parameter? Any idea?, Just please don't mention simple thermodynamic correlations. Thank you so much.
If you have the isentropic efficiency of each stage, the pressure ratio for each stage, and the inlet air temperature and pressure the overall work for any mass flow rate and operating pressure can be readily calculated. Can you send over your specs?
Dear Zech, I don't wanna consider the compressor as an isentropic one. I'm gonna have a polytropic process.
you can use the pressure ratio to find each stage pressure, then use your polytropic to relationship with inlet properties to find the specific volume for each stage [(p1*v1)^n=(p2*v2)^n]. once you have these two independent intensive properties for each stage you can look up the specific enthalpy at each state (h has units of [kJ/kg]). you work for each stage of compression is (W=m_dot*(h2-h1)) where m_dot is you mass flow rate. Then all that's left is to add up the stage compression work values. Calculations like these can be done very quickly with the help of a computer program like EES. EES will also allow for a parametric study of the compressor work, and efficiency for various "n" and pressure ratio values.
Dear Ahmed
If I am right with your issue, you want to correlate the compressor work as a function of mass flow rate. This means you are looking for off design data. In this case you need the compressor performance map.
Well in your case you just have the compressor work (I do not know what is it, is it a single point data or you have compressor work as a function of mass flow rate?).
In your case, you might use scaled maps. What you need is, a general map as you may find in some references or software like GasTurb. Then scale this map with your design point data (You should change your data into a point on the performance curve). After scaling you will have your compressor estimated map in your hand. In any speed or any mass flow rate you can evaluate the pressure ratio or other performance data you need.
I hope this will be helpful for you.
Regards
Hasan
Again, we don't have any information about ploytropic coefficient of "n". We also don't know anything about the compressor physical characteristics such as dimensions. We just have the total inlet electricity available which is variable (from 0 up to 50 MW), pressure ratio (2.88 for each stage) and the number of stages (5).
Go and read Thermodynamics and Fluid Mechanics of Turbamachinery by S.L.Dixon
Ahmad, I have been in your situation before and I can tell you how I handled this calculation-but this approach will have its detractors. First, you should know the approach temperatures of your intercoolers, i.e., say 10 C above ambient. I will assume that your pressure ratio is 2.88 and balanced for all 5 stages. For the first stage, you calculate the isentropic discharge temperature (using absolute values) for the gas (air?). Then you apply the definition of isentropic efficiency (I typically use 75% for a heavy duty, double acting lubricated compressor). This gives you an actual discharge temperature which is higher than the isentropic calculation. Then the work for this stage will be Cp for air, multiplied by the difference between the actual discharge temperature and the inlet temperature. Then for the next 4 stages, the procedure will be the same except the inlet temperature for subsequent stages will be 10 C higher than ambient. Hence, the work for each of these next 4 stages will be the same, so you can simply multiply work for second stage by 4 and add to the work for the first stage. Then this sum of specific work will be multiplied by the mass flow rate to provide the total power required. Of course, you also have fan work for the intercoolers, pump work for compressor cylinder water cooling, and the gearbox work.
May I suggest you read S.L.Dixon Thermodynamics and Fluid Mechanics of Turbomachinery. If you know how to plot the process on the T-S chart thenj it will be easier for you to understand how to calculate the power in multostage compressor
You may also refer to: Paul C. Hanlon (Ed.), "Compressor Handbook", McGraw-Hill, 2001:
http://www.mhprofessional.com/product.php?isbn=0071414665
A minimum-work based optimization study of a generic three-stage compressor can be found, given as academic example, at: P. Benedek, A. László, "Les Bases Scientifiques du Génie Chimique', French transl.: S. Fuzessery, Dunod, Paris, 1972 (orig. ed.: "A Vegyészmérnöki Tudomány Alapjai", M. Könyvkiadó, Budapest, 1964), pp. 426-429.
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