Fuel Flow Calculations - Check My Math?

[RDY4WAR]

I'm missing something in this calculation somewhere.

It's said that going from gasoline to E98 (98% ethanol) is a 37.5% increase in fuel flow to maintain the same lambda. This is proven with datalogs repeatedly. However, let's say we have an engine consuming 50 lbs/min of air (~620 CFM) based on given VE and assuming perfect sea level air. E98 has a stoich air/fuel ratio of 9.01:1 while ethanol free gasoline is 14.7:1.

50 / 14.7 = 3.40 lbs/min of fuel with gasoline
50 / 9.01 = 5.55 lbs/min of fuel with E98

5.55 / 3.40 = 63.2% increase in fuel flow by weight

Even factoring in flow by volume with E98 at .790 SpG (6.59 lbs/gal) and gasoline at .745 SpG (6.21 lbs/gal)...

3.40 / 6.21 = 0.5475 gal/min
5.55 / 6.59 = 0.8422 gal/min

0.8422 / 0.5475 = 53.8% increase in fuel flow by volume

What am I missing here?

 

[wpod]

Does the alky vaporize like the gasoline? I don't know anything about using Alcohol other that is is different and oil seems to need to be changed at a different interval that Gasoline.

 

[RDY4WAR]

Does the alky vaporize like the gasoline? I don't know anything about using Alcohol other that is is different and oil seems to need to be changed at a different interval that Gasoline.

Ethanol vaporizes quicker and at a lower temperature than gasoline. It's how some drag racers on E85 and E98 can get away with no radiator as the alcohol does such a good job of cooling. I'm not sure how that effects the fuel flow requirements.

Boiling point
- Gasoline = 110°F - 420°F
- Ethanol = 174°F

Heat of vaporization
- Gasoline = 128 BTU/lb (795 BTU/gal)
- Ethanol = 364 BTU/lb (2,399 BTU/gal)

BTU Energy / Power Potential
- Gasoline = 18,500 BTU/lb - 114,885 BTU/gal - 62,900 BTU/min @ 50 lbs/min air flow
- Ethanol = 12,800 BTU/lb - 84,352 BTU/gal - 71,040 BTU/min @ 50 lbs/min air flow

 

[javacontour]

Where/what data shows the 37.5% increase. You show your math, but I don't see the case supporting what you are comparing against.

I'm not saying it's not true, just would like to see the case you are comparing against.

TIA

 

[RDY4WAR]

Where/what data shows the 37.5% increase. You show your math, but I don't see the case supporting what you are comparing against.

I'm not saying it's not true, just would like to see the case you are comparing against.

TIA

That's fair. I don't have the datalogs in front of me, but looking at logs of cars that I've seen and dealt with over the years, going from ethanol free gasoline to E85 required ~34% more fuel to achieve the same 1.0 lambda reading. Using E98 wanted 37.5% more fuel for 1.0 lambda. This was per wideband O2 reading.

 

[adams355]

That sounds about right, it is a large increase. Check here, I only work in metric.

E85 Injector Sizing

E85 has a different than "normal" size selection per application. Learn how to figure the size needed for your E85 application.

injector-rehab.com

 

[javacontour]

I wonder if this has to do with Ethanol bringing oxygen with it vs gasoline?

While the formulas are based on the weight of the fuel, I wonder if the mass of the Oxygen relative to the rest of the molecule is high enough to throw off that value.

1 Mol of Octane (C8H18) is 114.23g vs 1Mol of EtOH is 46.07 but nearly 1/3rd of the molar mass of EtOH is the oxygen molecule.

Expected vs Empirical values can be different.

Of course, then, wouldn't you need MORE fuel, not less since it's bringing O2 with it?

It's been too long since I've been in a chemistry class to work this out. But my gut feeling (and I still have an ample gut, more gut than brains) is that the mass of the Oxygen molecule in the Ethanol perturbs the strictly mass calculation somehow.

But I could be totally wrong.

 

[RDY4WAR]

That may be a factor. Looking at different fuels, their oxygen content, respective air/fuel ratio, and respective specific gravity.

Fuel -------- Oxygen % - Stoich AFR - Specific Gravity

Gasoline 0% 14.7:1 0.745
E10 3.5% 14.1:1 0.748
E85 29.6% 9.85:1 0.788
E98 34.1% 9.01:1 0.790
Acetone 27.6% 9.54:1 0.791
Methanol 49.8% 6.48:1 0.794
Nitromethane 52.1% 1.70:1 1.139

So there's somewhat of a trend with oxygen content and air/fuel ratio though it deviates some. Acetone, for example, has less oxygen content than E85, but has a lower air/fuel ratio. Nitromethane has similar oxygen content to methanol but a much lower air/fuel ratio.

Where does this all fit in?

 

[Belker]

RDY4WAR,

An alternate approach is to look at the ratios of the BTU’s per gallon for the various fuel types in order to get an estimate of what the relative flow rates would be in order to maintain constant lambda. The BTU estimates I am using below were taken (or estimated) from the Sunoco Racing Fuels webpage.

112,150 BTU’s per gallon for E0;
82,200 BTU’s per gallon for E85;
75,100 BTU’s per gallon for E98;
74,350 BTU‘s per gallons for E100 (estimated from above data).

Relative flow rates relative to E0 for constant lambda based on the BTU per gallon difference:
For E85: (E0 BTU‘s)/(E85 BTU’s)=112,150/82,200=136.4%;
For E98: (E0 BTU’s)/(E98 BTU’s)=112,150/75,100=149.3%;
For E100: (E0 BTU’s)/(E100 BTU’s)=112,150/74,350=150.8%.

I hope this helps.

 

[RDY4WAR]

RDY4WAR,

An alternate approach is to look at the ratios of the BTU’s per gallon for the various fuel types in order to get an estimate of what the relative flow rates would be in order to maintain constant lambda. The BTU estimates I am using below were taken (or estimated) from the Sunoco Racing Fuels webpage.

112,150 BTU’s per gallon for E0;
82,200 BTU’s per gallon for E85;
75,100 BTU’s per gallon for E98;
74,350 BTU‘s per gallons for E100 (estimated from above data).

Relative flow rates relative to E0 for constant lambda based on the BTU per gallon difference:
For E85: (E0 BTU‘s)/(E85 BTU’s)=112,150/82,200=136.4%;
For E98: (E0 BTU’s)/(E98 BTU’s)=112,150/75,100=149.3%;
For E100: (E0 BTU’s)/(E100 BTU’s)=112,150/74,350=150.8%.

I hope this helps.

Interesting. It certainly lines up much closer with what's seen in fuel trims. The relative power isn't the same as there's a 3-4% power gain naturally aspirated going from E0 to E85 and upwards of 10-12% with boost. However, a lot of that is likely due to intake cooling.

Another factor is fuel flow is measured in mass, not volume. Fuel injectors are rated in pounds per hour (lbs/hr) and air/fuel ratio is measured in pounds of air to pounds of fuel. Maybe comparing BTU/lb would be more accurate?

Let's look at other fuels as well.

Methanol = 56,800 BTU/gal

112,150 / 56,800 = 197.4%

That's about in line with people saying "double the fuel volume for methanol."

What about a GEM fuel? (gasoline, ethanol, and methanol blend) There's a blending ratio that is supposed to be rather close to the air/fuel ratio of E85.

37% gasoline
21% ethanol
42% methanol

(112,150 x 0.37) + (74,350 x 0.21) + (56,800 X 0.42) = 41,496 + 15,614 + 23,856 = 80,966 BTU/gal

112,150 / 80,966 = 138.5%

Is it really that simple?

Let's look at BTU/lb.

Gasoline = 18,500 BTU/lb
Ethanol = 12,800 BTU/lb
Methanol = 9,500 BTU/lb

(18,500 x 0.15) + (12,800 x 0.85) = 2,775 + 10,880 = 13,655 BTU/lb

18,500 / 13,655 = 135.5%

Alright, I'm officially geeking out now.

GEM blend by the pound!

(18,500 x 0.37) + (12,800 x 0.21) + (9,500 x 0.42) = 6,845 + 2,688 + 3,990 = 13,523 BTU/lb

18,500 / 13,523 = 136.8%

 

[adams355]

Up to 25% with boost and its mostly to do with octane (lots more timing advance available). The cooling is secondary in gains. E85.

 

[RDY4WAR]

...its mostly to do with octane (lots more timing advance available). The cooling is secondary in gains. E85.

Eh, I disagree. I helped with tuning a friend of mine's Trans Am several years ago when he switched from VP C16 to VP C85. It was a built LS1 with a Precision 7675 turbo making ~760 rwhp at ~24 psi on C16. Other than fuel system upgrades for the flow and adjusting fuel tables to maintain AFR, it was a A-B switch with no changes to timing. It picked up over 50 rwhp with C85 with the same timing. After several runs to dial in the fuel and spark tables, we ended up at 855 rwhp at the same boost pressure and faster spool.

C16
- RON = >120
- MON = 116
- R+M/2 = >118

C85
- RON = 106
- MON = 86.5
- R+M/2 = 96.3

So it's definitely not an octane thing. The theory I understand is that fuel detonation / pre-ignition is temperature based. With E85 cooling the intake charge so much, it keeps the air/fuel mixture out of that dangerous temperature range more easily allowing for more boost and timing and thus more power. While the octane of C85 is much lower than C16, the cylinder temperature at the time of ignition is also significantly lower.

I think the AFR supports this as well. C16 made the best power at .82 lambda while C85 made the best power at .74 lambda. More fuel supported more cooling and thus more power despite likely not completely burning the rich mixture.

 

[adams355]

You were comparing pump fuel to E98, not C16 to E85.

50rwhp with C85 isn't a significant jump at 7-800hp anyway. I have seen cars with 10 degree c coolant temp differences make up to 20rwhp changes on dyno. I did not say E85 has no cooling properties at all and you were running the same timing on the E85 which was on C16 anyway, which supports what I said.

At the end of the day we are saying the same thing the E85 has a higher 'real' RON rating due to cooling, however it is the amount of timing that can be added that is its benefit.

Also, there are large gains made on intercooled cars as well which have a lower intake charge to begin with. It is the extra oxygen in ethanol fuels which lowers the intake temps.