Power and torque calculations for 9 bar compressed air engine

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karan_s
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TL;DR
I have done some calculations to obtain power from the engine but don't think they are correct. Also need some help calculating torque at different rpms and air tank emptying time.
Hi, I posted a question a while ago which I have managed to do some more calculations for. I need a bit of help to see if they are correct. I am trying to obtain power and torque values at different rotational speeds of a single cylinder compressed air engine. The inlet pressure into the engine is a constant 9 bar and the air is discharged from the chamber as the piston reached BDC rather than a conventional cam valve design. My calculations below for power do no seem right compared to MATLAB and experimental results.

I have attached screenshot as it will not let me post equations into this.

I would like to get torque values at different rpms and also any formulas to calculate how quickly a air tank would empty at a specific rpm.

Much appreciate the help.
 
Attachments
  • Handwritten-style typed calculation sheet of compressed air engine cycle: V = πr²h, P1V1^k = P2V2^k, K = Cp/Cv with K = 1.4 for air, volumes v1 to v4 and pressures p2 to p4 computed from p1 = 9 bar, and work integral W = ∫p dv.
    Screen Shot 2019-05-01 at 20.18.21.png
    29.3 KB · Views: 567
  • Handwritten-style derivation of work done by a compressed air engine: integral of 1/v^k giving W = c[v^(-k+1)/(-k+1)] from 1 to 4, then c = 9 x 0.000056548^1.4 = 1.0177 x 10^-5, W = 0.00054155 J, and power p = W N/n for 500 to 2000 rpm, giving 0.270775, 0.54155, 0.812325 and 1.0831 kW.
    Screen Shot 2019-05-01 at 20.18.30.png
    25.2 KB · Views: 584

Discussion

What sort of engine do you have in mind? Is it a reciprocating machine employing a slider-crank mechanism or a continuous flow machine like an air turbine? You need to tell us more about what you are contemplating before much can be said about your calcs.
 
Dr.D said:
What sort of engine do you have in mind? Is it a reciprocating machine employing a slider-crank mechanism or a continuous flow machine like an air turbine? You need to tell us more about what you are contemplating before much can be said about your calcs.
It would like a reciprocating engine
 
You use of the constant k = 1.4 seems to imply an adiabatic expansion. In fact, it will be more nearly a polytropic expansion, k = 1.35 roughly.

The other problem I see is that you have assumed a very idealized cycle, with instantaneous fill and exhaust; this is not how it actually happens.
 

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