# Relation between SFC vs RPM in diesel engine?

1. Apr 24, 2014

### suhas

What is the relation between sfc vs rpm in diesel engine and why does it happen like that ? what is relation between air flow vs rpm ??

2. Apr 24, 2014

### jack action

bsfc depends on the volumetric efficiency (VE), air density (ρatm), air-fuel ratio (AFR) and the Brake Mean Effective Pressure (BMEP):

bsfc = VE * ρatm / AFR / BMEP

BMEP depends on the Indicated Mean Effective Pressure (IMEP) and the Friction Mean Effective Pressure (FMEP):

BMEP = IMEP - FMEP

Finally, the FMEP is related to rpm, stroke (S) and IMEP in the following manner (C1 & C2 are some constants depending on engine design):

FMEP ≈ IMEP (C1 + C2 * S * rpm)

So the relation between bsfc and rpm is:

bsfc = VE * ρatm / AFR / IMEP / (1 - C1 - C2 * S * rpm)

air flow (Q) depends directly on VE, displacement (Vrev) and rpm. Assuming SI units:

Q = VE * Vrev * rpm / (2π)

source: http://hpwizard.com/engine.html

3. Apr 26, 2014

### suhas

can you explain this to me to this theoretically ??

4. Apr 26, 2014

### Ranger Mike

I should not post on this and I may regret this but....
Ok we will try it this way. I will use an internal combustion engine as that is what i am most familiar with.

The more rotation of the crankshaft per minute , the more fuel/air flow(BSFC) is required to feed the beast. It is that simple.

The IC is a big air pump. A series of pistons moving “up and down” in a cylinder causing the rotation of the crankshaft. Basic linear motion converted to rotary motion.

The piston moves when a fuel air mixture is compressed and ignited. Your question about BSFC I now re-phrase. What is relationship between air flow and RPM.

Nothing happens in the IC until the fuel air mixture is admitted to the cylinder is compressed and ignited at the proper time (with regard to the crankshaft rotation).
The more rotation of the crankshaft per minute , the more fuel/air flow(BSFC) is required to feed the beast. It is that simple.

Normal compression ratio is 9:1 where the volume of the cylinder is squeezed 9 times “ tighter “ than normal atmospheric conditions. My old Ford tractor has 6:1 compression ratio. Don’t get hung up on the CR.

Jack Action did a great job defining the relationship -
bsfc depends on the volumetric efficiency (VE), air density (ρatm), air-fuel ratio (AFR) and the Brake Mean Effective Pressure (BMEP):

fuel consumption depends on the engines ability to move the fuel air mixture (ρatm), (AFR) into the cylinder (VE) ,squeeze it , ignite it, force the piston to move linearly in a most efficient manner (BMEP) and expel the spent fuel air mixture while re-filling the cylinder (VE).

(VE) Volumetric efficiency in the internal combustion engine design refers to the efficiency with which the engine can move the charge into and out of the cylinders. Volumetric efficiency is a ratio (or percentage) of the quantity of air that is trapped by the cylinder during induction over the swept volume of the cylinder under static conditions. Volumetric Efficiency can be improved in a number of ways, most effectively this can be achieved by compressing the induction charge (forced induction) or by aggressive cam phasing in Normally Aspirated engines as seen in racing applications. In the case of forced induction Volumetric Efficiency can exceed 100%.

Air density (ρatm), typically I refer to normal aspirated engine but you can improve air density by forced induction like supercharging or turbocharging. The air-fuel ratio (AFR) is where your BSFC comes in as the ratio of fuel to air mixture is what drives the engine.

bsfc = VE * ρatm / AFR / BMEP

BMEP is the Brake Mean Effective Pressure. This is the Indicated Mean effective pressure calculated from in cylinder pressure, average in cylinder pressure over engine cycle (720° in a 4 stroke) after you subtract the al the parasitic drag of piston rings, piston to cylinder drag, rod and crank bearing friction, valve spring friction etc...which make up the Friction Mean Effective Pressure (FMEP).

Jack Action again puts it quite nicely..

FMEP is related to rpm, stroke (S) and IMEP in the following manner (C1 & C2 are some constants depending on engine design):

FMEP ≈ IMEP (C1 + C2 * S * rpm)

So the relation between bsfc and rpm is:

bsfc = VE * ρatm / AFR / IMEP / (1 - C1 - C2 * S * rpm)

5. Apr 26, 2014

### jack action

bsfc is the fuel flow needed (mass wise) per horsepower produced (mfuel / P). You put your engine on the dyno and you can measure the horsepower output. You could as well measure the amount of fuel used per unit of time.

But since the amount of fuel is directly linked to the amount of air (by a factor equal to AFR), we can also based it on the mass air flow needed (mfuel = mair/AFR). We can then relate it to volumetric air flow since air has a known (atmospheric) density (Vair = mair / ρatm).

But, we can also relate the power of the engine as the product of the BMEP and the volumetric airflow. The BMEP represents the force applied to the piston due to the combustion (minus some losses) and the volumetric air flow represents how often this force is applied.

Since the volumetric air flow is present in both the numerator and denominator, they cancel each other, giving us:

bsfc = VE * ρatm / AFR / BMEP

So, in theory, bsfc seems to be independent of the rpm.

But wait.

Remember that BMEP represents the force on the piston minus some losses? Well, one the important losses is the one due to the friction between all of the mechanical components (FMEP). And it has been shown that it is related to the mean piston speed, which is directly linked to the rpm.

This means that as the rpm increases, more power is needed to fight the friction (power that is not going to the crankshaft output). So, as the rpm increases, for the same amount of power produced at the crankshaft output, it takes more fuel because there is more friction to fight.

From the equation presented earlier, you can see that the rpm is in the denominator, which would suggest an inversely proportional relationship, but there is a minus sign in front of it. With common values, it can be shown that it is more of a linear relationship.

This is why we invented overdrive. We could drive a car at cruising speed on the highway and at a rpm of say 8000 rpm. But getting the same power output with the same engine at, say, 2000 rpm, we will probably get a 10-15% fuel economy, just because there is less engine friction to fight.

As for the air flow, as I said in my previous post, it is directly proportional to the rpm. Everything else being equal, if you double the rpm, you also double the air flow (but VE has a tendency to vary slightly with rpm).