# Supercharger - Isentropic charts - Pressure Ratio and temperature

1. Jul 29, 2014

### Billy22Bob

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 wont converge - it simply runs away out of control...

#### Attached Files:

• ###### IsentopicExampleCalc.jpg
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2. Jul 31, 2014

### Baluncore

Black text. Top centre of the page. Inlet temperature = 20 C

Also the flows are in m3 per minute, NOT m3 per hour.

Question 1.
17 kW is small compared to the additional power generated. If it is not, then you should specify a lower capacity supercharger.

Question 2.
Do not iterate again. The 17 kW comes from the engine.