- #1
Billy22Bob
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I am trying to understand my superchargers isentropic chart.
For an example case where a supercharger outputs 10m3/hr but the engine only takes 6.57m3/hr in capacity, I get a volume ratio (VR) of 1.52 - easy...
I can then work out a pressure ratio by VR^k = 2.0^1.4 = 1.8
The theoretical temperature for such a PR is = [inlet Temperature K] x PR^0.2857 =
where 0.2875 is the result of (k-1)/k
note this is all independent of the supercharger...
Now we head to our supercharger isentropic chart.
It tells me for PR=1.8 and 10m3/hr input I should have an adiabatic efficiency of 65%
The formula to work out the actual temperature from the theoretical is;
OutletT = [TheorT-InletT]/Eff. + InletT using Kelvin
so
lets say for an inlet of 27oC = 300K
TheorT = [inlet Temperature K] x PR^0.2857 =355K (82C)
OutletT = [TheorT-InletT]/Eff. + InletT = [355-300]/65% + 300 = 385K = 111oC
And the chart tells me 100C - close.
note - there is no indication on the chart what inlet temp it uses.
Question 1 - Is the above approach sound?
Now the chart also tells me the Supercharger will be using 17kW of poer to execute this task - that it it will steal 17kW of power from the crank to hopefully produce enough increased power in the motor to compensate for this 17kW plus more...otherwise its a waste of time.
Question 2 - do I need to include some of this 17kW in the pressure ratio and iterate again?
After all - it is going to go in as temperature increase in the air stream (approx. 35% of it) and if this was a constant volume - it would increase the pressure and hence the PR...unfortunately if I do this - it won't converge - it simply runs away out of control...
For an example case where a supercharger outputs 10m3/hr but the engine only takes 6.57m3/hr in capacity, I get a volume ratio (VR) of 1.52 - easy...
I can then work out a pressure ratio by VR^k = 2.0^1.4 = 1.8
The theoretical temperature for such a PR is = [inlet Temperature K] x PR^0.2857 =
where 0.2875 is the result of (k-1)/k
note this is all independent of the supercharger...
Now we head to our supercharger isentropic chart.
It tells me for PR=1.8 and 10m3/hr input I should have an adiabatic efficiency of 65%
The formula to work out the actual temperature from the theoretical is;
OutletT = [TheorT-InletT]/Eff. + InletT using Kelvin
so
lets say for an inlet of 27oC = 300K
TheorT = [inlet Temperature K] x PR^0.2857 =355K (82C)
OutletT = [TheorT-InletT]/Eff. + InletT = [355-300]/65% + 300 = 385K = 111oC
And the chart tells me 100C - close.
note - there is no indication on the chart what inlet temp it uses.
Question 1 - Is the above approach sound?
Now the chart also tells me the Supercharger will be using 17kW of poer to execute this task - that it it will steal 17kW of power from the crank to hopefully produce enough increased power in the motor to compensate for this 17kW plus more...otherwise its a waste of time.
Question 2 - do I need to include some of this 17kW in the pressure ratio and iterate again?
After all - it is going to go in as temperature increase in the air stream (approx. 35% of it) and if this was a constant volume - it would increase the pressure and hence the PR...unfortunately if I do this - it won't converge - it simply runs away out of control...
