Intake vs. exhaust gas flow amount question
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Intake vs. exhaust gas flow amount question
Recently I was on Dynomax's website, looking at different mufflers, and noticed that they had max flow ratings for their mufflers, which were rated in SCFM. So it got me wondering... if I calculate the CFM my engine flows, how does that equate to the exhaust gas flow? I can only assume that if I'm taking in, for example, 500 CFM of ambient air, then that should expand quite a bit, as it gets heated to exhaust gas temps and enters the downpipe. Obviously, the mass doesn't change (at least not by much, I would think), but the volume should, shouldn't it? Does anyone know how to calculate this?
l8r)
l8r)
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Found the answer to my question on another engineering forum, which also confirmed what I suspected:
l8r)
Originally Posted by SBBlue (Automotive) - 4 Oct 04 23:46
Okay, class. Excellent question, Jaded. Pay attention now, because this will be covered on the test.
Several assumptions: 1) This is a gas engine we are talking about, 2) it is a four-cycle gas engine, 3) Combustion will be stochiometric and complete, 4) the compression ratio is about 10:1, 5) the engine is throttled (no variable valve timing), 6) normal aspirated engine (no turbocharger), and 7) volumetric efficiency (the amount of air that makes it into the cylinder during the induction stroke) is 1.00 (actually it depends upon the RPM and intake manifold pressure, but work with me here.)
First, it should be intuitively obvious to the most casual observer that the amount of air that passes through the engine in will be equal to the engine displacement times the RPM divided by 2. For an engine of 3 liter displacement going at 3000 RPM, the amount of air pumped for minute will be 4500 liters.
That will approximately be the intake volume flow for an engine with the throttle wide open. If we assume that the throttle is only open 33%, the intake volume flow will still be 4500 liters, but the pressure will be one-third of an atmosphere. The equivalent mass of air will be the same as 1500 liters at one atm of pressure.
Neglecting the addition of the fuel mass, the mass of the exhaust gas will be the same as the mass of the intake gas. From the ideal gas law we know that the increase in volume of the exhaust gas will be proportional to the increase in absolute temperature. If we assume an intake temperature of 80 deg F, and an exhaust temperature of 1800 deg F (reasonable assumption, depends upon compression ratio), the absolute temperature will be 540 and 2260 deg Rankine, respectively. The volume increase will therefore be 2260/540, or 4.185.
For the hypothetical 3 liter engine running at 3000 RPM and full throttle, the exhaust gas volume will be about 4500*4.185, or 18,833 liters/min. At one third throttle the corresponding flow is 6277 liters/min. Since one cubic foot is equal to 28.3 liters, the respective CFM flows will be 665.4 and 221.8, respectively.
How about the contribution from combustion products? Assuming stoichometric combustion, there will be one pound of fuel burned for each 14.55 lbs of air. Air is 21% oxygen, so there is 3.05 lbs of oxygen available to burn each pound of gas.
A reasonable chemical approximation for gasoline is octane, which has a chemical of C8H18. The molecular weight is (12*8+18*1)= 114.
The combustion formula is C8H18 + 12.5 O2 ==> 8 CO2 + 9 H20. For each 114 grams of C8H18, there will be 12.5 moles of oxygen consumed, producing 8 moles of CO2 and 9 moles of H2O. For gas volume purposes, since equal moles of gas produce equal volume, the volume of exhaust gas replacing oxygen will be equal to 17/12.5 = 1.36.
The volume percentage of oxygen in air is about 21% (not exact, but work with me here). This volume will be removed, and replaced by exhaust gas with a "volume" of (21*1.36) = 28.56%. The resulting post combustion volume is (79% + 28.56% = 107.56%) of the pre- combustion volume -- assuming no temperature increase.
So what do we have? Combining the increase in volume from combustion reactions and thermal expansion, an engine with a 3 liter displacement running at 3000 rpm with the throttle wide open will have an exhaust volume (at 1800 deg F) of 665.4*1.0756 ~~ 715 cubic feet per minute. For the throttle one-third open, the exhaust flow will be 238.6 cfm.
I'm tired, so I may have made some calculation errors, but this should get you in the ball park for exhaust flow.
Several assumptions: 1) This is a gas engine we are talking about, 2) it is a four-cycle gas engine, 3) Combustion will be stochiometric and complete, 4) the compression ratio is about 10:1, 5) the engine is throttled (no variable valve timing), 6) normal aspirated engine (no turbocharger), and 7) volumetric efficiency (the amount of air that makes it into the cylinder during the induction stroke) is 1.00 (actually it depends upon the RPM and intake manifold pressure, but work with me here.)
First, it should be intuitively obvious to the most casual observer that the amount of air that passes through the engine in will be equal to the engine displacement times the RPM divided by 2. For an engine of 3 liter displacement going at 3000 RPM, the amount of air pumped for minute will be 4500 liters.
That will approximately be the intake volume flow for an engine with the throttle wide open. If we assume that the throttle is only open 33%, the intake volume flow will still be 4500 liters, but the pressure will be one-third of an atmosphere. The equivalent mass of air will be the same as 1500 liters at one atm of pressure.
Neglecting the addition of the fuel mass, the mass of the exhaust gas will be the same as the mass of the intake gas. From the ideal gas law we know that the increase in volume of the exhaust gas will be proportional to the increase in absolute temperature. If we assume an intake temperature of 80 deg F, and an exhaust temperature of 1800 deg F (reasonable assumption, depends upon compression ratio), the absolute temperature will be 540 and 2260 deg Rankine, respectively. The volume increase will therefore be 2260/540, or 4.185.
For the hypothetical 3 liter engine running at 3000 RPM and full throttle, the exhaust gas volume will be about 4500*4.185, or 18,833 liters/min. At one third throttle the corresponding flow is 6277 liters/min. Since one cubic foot is equal to 28.3 liters, the respective CFM flows will be 665.4 and 221.8, respectively.
How about the contribution from combustion products? Assuming stoichometric combustion, there will be one pound of fuel burned for each 14.55 lbs of air. Air is 21% oxygen, so there is 3.05 lbs of oxygen available to burn each pound of gas.
A reasonable chemical approximation for gasoline is octane, which has a chemical of C8H18. The molecular weight is (12*8+18*1)= 114.
The combustion formula is C8H18 + 12.5 O2 ==> 8 CO2 + 9 H20. For each 114 grams of C8H18, there will be 12.5 moles of oxygen consumed, producing 8 moles of CO2 and 9 moles of H2O. For gas volume purposes, since equal moles of gas produce equal volume, the volume of exhaust gas replacing oxygen will be equal to 17/12.5 = 1.36.
The volume percentage of oxygen in air is about 21% (not exact, but work with me here). This volume will be removed, and replaced by exhaust gas with a "volume" of (21*1.36) = 28.56%. The resulting post combustion volume is (79% + 28.56% = 107.56%) of the pre- combustion volume -- assuming no temperature increase.
So what do we have? Combining the increase in volume from combustion reactions and thermal expansion, an engine with a 3 liter displacement running at 3000 rpm with the throttle wide open will have an exhaust volume (at 1800 deg F) of 665.4*1.0756 ~~ 715 cubic feet per minute. For the throttle one-third open, the exhaust flow will be 238.6 cfm.
I'm tired, so I may have made some calculation errors, but this should get you in the ball park for exhaust flow.
Was the muffler tested at elevated temperatures or at ambient temps?
Because the frictiona losses depend on the viscosity of the fluid, which will change depending on density and temperature. Thus there is a pressure and temperature dependency on the frictional flow losses.
The point, the pressure loss may not be the same as what the chart tells you due to the fluid temperature having an impact on frictional flow losses.
Because the frictiona losses depend on the viscosity of the fluid, which will change depending on density and temperature. Thus there is a pressure and temperature dependency on the frictional flow losses.
The point, the pressure loss may not be the same as what the chart tells you due to the fluid temperature having an impact on frictional flow losses.
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^ Hey, finally a non-troller. 
I understand what you're saying. Fortunately for my purposes (seeing if a 700 scfm rated muffler would work) the calculation shows a resounding NO! As I contemplate the next iteration of my car, I will probably look at this more closely to make sure my exhaust is appropriately sized.
l8r)
I understand what you're saying. Fortunately for my purposes (seeing if a 700 scfm rated muffler would work) the calculation shows a resounding NO! As I contemplate the next iteration of my car, I will probably look at this more closely to make sure my exhaust is appropriately sized.
l8r)
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