Robyn
Specifier/Regulator
- May 6, 2002
- 2
I am trying to estimate the peak air demand, in cfm, of a 444 cid turbocharged diesel. It is my hope that I can come up with a reasonable estimation without verified temperature data. I am willing to make reasonable assumptions on temperature and barometric pressure, but am not sure how that enters into the equation to meet my desired goal, which is, to determine if a particular air filter/air box combination is capable of flowing the engines peak demand air while at maximum allowable restriction... which is say 25 inches of water. 25" H2O is chosen because it is consistent with standard filter restriction measurements in the medium and heavy diesel engine industry.
Some methods I have seen for estimating CFM are as follows:
CFM = [CID x RPM x VE] / [2 x 1728]
Where, due to my lack of "special symbol key" knowlege on a keyboard, I will consistently use
"x" as my symbol for multiplicaton, and
"/" as my symbol for division, or a ratio.
And where, although you likely know the acronyms, standard constants, and symbols better than I, you may want to see if I am using them appropriately, thus:
VE = Volumetric Efficiency
2 = 2 strokes per crank revolution (4 stroke engine)
1728 = conversion of cubic inches to cubic feet.
The question then becomes identifying a value for VE. Most writings that I have read thus far seem to agree that .85 is a reasonable value to use for a naturally aspirated (NA) engine. The NA VE numbers I found in reading materials ranged from a low of .80 to a high of .90. Most were .85 . However, VE numbers for turbocharged (TC) engines, and turbocharged intercooled (TCI) engines, varied widely! I read of TC VE numbers from 1.2 to 1.8, and TCI VE numbers from 1.4 to 2.3. The average TCI VE of all of the material thus far reviewed seems to be 1.7.
I should be more clear: by "reading" and "reviewing" and "materials," I am refering to texts on the subject, or websites found in searches. I am not refering to readings from instrumentation, or calculations made from instrumented readings.
Anyway, I first got lost because I saw no provision in the formula to account for boost pressure in a TC or TCI engine. I second got lost because ...how do I pick an appropriate TC or TCI VE? Not being an experienced in this, I looked for help, and not being entirely willing to sit on my hands, I continued to prod at the issue as follows:
I started trying to find definitions of VE, and found several... a positive displacement pump property. A percentage of clearance volume defined as a proportion related to the swept volume of the pistons. Even while the importance of air density, the mass of air, or finding a density ratio determined by a ratio of absolute inlet and outlet temperatures multiplied by the ratio of absolute inlet and outlet pressures still loomed in my head, I wondered something else: Since the SF-1020 flowbench machine I used a while back to compare various air filters and air boxes for this application is really only capable of measuring flow at a given restriction, I thought maybe I should try to eliminate the mass of air, or the density ratio, from the equation. Not sure if this was misstep number 1, 2, or 3, or a misstep at all.
Prying around, I tried to reduce finding the CFM of the subject motor by seeing how the actual flow (with and without boost) differed from the ideal flow potential dictated by the CID and my selected RPM of the engine. This would make the first equation above useful, even if for just a NA engine. If I found ideal airflow at a selected RPM for the 444 CID as a NA engine by first ignoring any VE factor, and then mulitiplied by the widely accepted NA VE of .85 to find an actual air flow, I might have something to multiply with when I determined a relative pressure ratio for the boosted TCI 444, provided I assumed that the NA version's pressure was atmospheric, and the temperatures were constant (or ignored). Now there has to be a mistake in that thinking somewhere... especially with the temperature because of the TC compression heat.
Still uncertain, but soldering on, I first picked a peak "running" rpm a little higher than the rated peak horsepower rpm supplied by the engine manufacturer, based on my awareness that many of the people who would be interested in this comparison of air filter flow are running chips that manipulate fuel tables, boost allowance, and other parameters that in the end yeild greater dyno tested power at higher rpms. Assuming intake, intercooler, and exhaust tracts have been modified and or optimized to handle the additional flow required to make use of the added fueling... the question then becomes if the air filter/box combination itself is capable of handling that peak flow demand.
Thus, from the first formula above:
[3,000 RPM x 444 CID] / [2 x 1728] = 385.42 CFM IDEAL Naturally Aspirated
385.42 x .85 = 327.60 CFM ACTUAL Naturally Aspirated
Where .85 is an accepted value for Volumetric Efficiency, and where Atomspheric Pressure is assumed to be 14.7.
When running at 3,000 RPM, boost is at 26 psiG. (chipped turbodiesel
To find the absolute pressure ratio, I did as follows:
[26 psig + 14.7] / 14.7 = 40.7/14.7 = 2.77
I then took the ACTUAL NA CFM of 327.60, and multiplied it by this absolute pressure ratio in the hopes of obtaining ACTUAL Turbocharged Intercooled CFM, or ACTUAL TCI CFM:
327.60 x 2.77 = 907.45 ACTUAL TCI CFM
My alarm bells began ringing, since this is a lot of air, but then I realize I've made no correction for temperature, and don't really know how to without more data. Unless I can make fair assumptions. Ambient outside air, or pre inlet air on a cold air induction is say 77 degrees F, underhood air on a warm air induction filter system is at say 145 degrees F, delta T between inlet and outlet of intercooler is say 150 degrees F, and I don't know how hot a compressor will heat up the air. I do have a working knowlege of various boost pressures at RPMs under loads, since I have a boost guage in my own truck with this particular engine. Of course, the boost reading doesn't distinguish heat induced pressure rise from compresser induced pressure rise, and I don't know if heat induced pressure rise in negligible or not, since the air is in constant motion, not captive.
But continuing anyway, if I take the Actual TCI CFM, and divide it by the Ideal NA CFM, I thought I might find a workable TCI VE that I could use in lieu of a NA VE... thus:
907.45 / 385.42 = 2.35
Definitely on the high end of the published VE ratios of TCI engines... or is it? If I found that an inlet to outlet temperature ratio, in degrees Rankine, proved to be, say, .8, then my TCI VE might move within a more commonly seen range of VEs that I found:
2.3 x .8 = 1.84 TCI VE, now with a SWAG absolute temperature ratio and the aforementioned psiA ratio taken into consideration.
At this point, I have to remind myself that all I am really after is knowing what the maximum amount of airflow the 444 CID TCI engine may require on peak demand. I'd like to plug in different RPMs and boost pressures, to recognize this airflow demand, and eliminate filter candidates tested on the flowbench in this manner.
According to one filter manufacturer,
A CAT 3126TA turbocharged diesel, at 439 CID, requires 564 CFM.
A DET 6-71TA turbocharged diesel, at 426 CID, requires 1,190 CFM.
A DET 6V-71TA turbocharged diesel, at 426 CID, requires 1,087 CFM.
A DET 7.6TA turbocharged diesel, at 464 CID, requires 1,240 CFM.
A DET 6466T turbocharged diesel, at 466 CID, requires 474 CFM.
While no RPM, Boost, or temperature data is provided, the ratings all came from the same source (the filter manufacture) and, the engines are all very near the same displacement, averaging out to be exactly 444 CID. Also, with one exception, the engines all came from the same manufacturer, Detroit Diesel. Yet notice the HUGE differences in rated air requirements, from a low of 474 to a high of 1,240 CFM.
So, I'm stumped.
Thanks for your interest, and I would mightily appreciate any help you can provide in determining air flow requirements of the 444 CID TCI engine for which appropriate air filter and air box solutions are sought. International has been entirely non-responsive in providing their own CFM data. Their data might not be relevant anyway, considering the large installed base of chips and exhaust modifications. Measurement of an actual truck is not possible with the equipment I have, and my session on the flow bench, evaluating several OE filters, several replacement filters, several OE airboxes, and several more high performance filters and boxes, is all the data I have. If I knew what the max airflow requirements were, I could eliminate some air filter and air box selections from further instrumented testing on a vehicle.
Also, I don't know if the A/R ratio and efficiency island/map of a turbo need to be considered? It may not be for the diesel engine that I am concerned with, but it may be if I am looking over the fence at all those other engines listed above in attempt to draw parallels of CFM flow for similar displacement turbocharged compression ignited motors?
And getting back to my math process, I don't know if I could reduce steps by canceling terms in the algebra and saying that
TCI VE = {[PSIG + ATMOSPHERE] / ATMOSPHERE} x NA VE
and or if, in addition, I could reasonable assume absolute temperature values and gain more accuracy by saying that
TCI VE = [ITA / OTA] x [BPA / ATA] x NA VE
Where:
TCI VE = Turbocharged Intercooled Volumetric Efficiency
ITA = Inlet Temperature Absolute
OTA = Outlet Temperature Absolute
BPA = Boost Pressure Absolute
ATA = Atmospheric Pressure Absolute
NA VE = Naturally Aspirated Volumetric Efficiency
If the above works, the only thing I wouldn't know what assume would be the OTA!!!
If ITA is ambient temperature in degrees Rankine, as measured on the dirty side of the filter, where shall I assume outlet temperature to be measured as it relates to determining CFM flow requirements of the engine?
I apologize for the "creative" acronyms and terms I used immediately above for some of the variables. Some of that is due to typing in this format, and some of that is due to lack of familiarity with other standardizes terms.
My biggest concern is that the entire thought process outlined above has drifted partially, or perhaps completely offbase. Thanks for any direction you can provide!
Some methods I have seen for estimating CFM are as follows:
CFM = [CID x RPM x VE] / [2 x 1728]
Where, due to my lack of "special symbol key" knowlege on a keyboard, I will consistently use
"x" as my symbol for multiplicaton, and
"/" as my symbol for division, or a ratio.
And where, although you likely know the acronyms, standard constants, and symbols better than I, you may want to see if I am using them appropriately, thus:
VE = Volumetric Efficiency
2 = 2 strokes per crank revolution (4 stroke engine)
1728 = conversion of cubic inches to cubic feet.
The question then becomes identifying a value for VE. Most writings that I have read thus far seem to agree that .85 is a reasonable value to use for a naturally aspirated (NA) engine. The NA VE numbers I found in reading materials ranged from a low of .80 to a high of .90. Most were .85 . However, VE numbers for turbocharged (TC) engines, and turbocharged intercooled (TCI) engines, varied widely! I read of TC VE numbers from 1.2 to 1.8, and TCI VE numbers from 1.4 to 2.3. The average TCI VE of all of the material thus far reviewed seems to be 1.7.
I should be more clear: by "reading" and "reviewing" and "materials," I am refering to texts on the subject, or websites found in searches. I am not refering to readings from instrumentation, or calculations made from instrumented readings.
Anyway, I first got lost because I saw no provision in the formula to account for boost pressure in a TC or TCI engine. I second got lost because ...how do I pick an appropriate TC or TCI VE? Not being an experienced in this, I looked for help, and not being entirely willing to sit on my hands, I continued to prod at the issue as follows:
I started trying to find definitions of VE, and found several... a positive displacement pump property. A percentage of clearance volume defined as a proportion related to the swept volume of the pistons. Even while the importance of air density, the mass of air, or finding a density ratio determined by a ratio of absolute inlet and outlet temperatures multiplied by the ratio of absolute inlet and outlet pressures still loomed in my head, I wondered something else: Since the SF-1020 flowbench machine I used a while back to compare various air filters and air boxes for this application is really only capable of measuring flow at a given restriction, I thought maybe I should try to eliminate the mass of air, or the density ratio, from the equation. Not sure if this was misstep number 1, 2, or 3, or a misstep at all.
Prying around, I tried to reduce finding the CFM of the subject motor by seeing how the actual flow (with and without boost) differed from the ideal flow potential dictated by the CID and my selected RPM of the engine. This would make the first equation above useful, even if for just a NA engine. If I found ideal airflow at a selected RPM for the 444 CID as a NA engine by first ignoring any VE factor, and then mulitiplied by the widely accepted NA VE of .85 to find an actual air flow, I might have something to multiply with when I determined a relative pressure ratio for the boosted TCI 444, provided I assumed that the NA version's pressure was atmospheric, and the temperatures were constant (or ignored). Now there has to be a mistake in that thinking somewhere... especially with the temperature because of the TC compression heat.
Still uncertain, but soldering on, I first picked a peak "running" rpm a little higher than the rated peak horsepower rpm supplied by the engine manufacturer, based on my awareness that many of the people who would be interested in this comparison of air filter flow are running chips that manipulate fuel tables, boost allowance, and other parameters that in the end yeild greater dyno tested power at higher rpms. Assuming intake, intercooler, and exhaust tracts have been modified and or optimized to handle the additional flow required to make use of the added fueling... the question then becomes if the air filter/box combination itself is capable of handling that peak flow demand.
Thus, from the first formula above:
[3,000 RPM x 444 CID] / [2 x 1728] = 385.42 CFM IDEAL Naturally Aspirated
385.42 x .85 = 327.60 CFM ACTUAL Naturally Aspirated
Where .85 is an accepted value for Volumetric Efficiency, and where Atomspheric Pressure is assumed to be 14.7.
When running at 3,000 RPM, boost is at 26 psiG. (chipped turbodiesel
To find the absolute pressure ratio, I did as follows:[26 psig + 14.7] / 14.7 = 40.7/14.7 = 2.77
I then took the ACTUAL NA CFM of 327.60, and multiplied it by this absolute pressure ratio in the hopes of obtaining ACTUAL Turbocharged Intercooled CFM, or ACTUAL TCI CFM:
327.60 x 2.77 = 907.45 ACTUAL TCI CFM
My alarm bells began ringing, since this is a lot of air, but then I realize I've made no correction for temperature, and don't really know how to without more data. Unless I can make fair assumptions. Ambient outside air, or pre inlet air on a cold air induction is say 77 degrees F, underhood air on a warm air induction filter system is at say 145 degrees F, delta T between inlet and outlet of intercooler is say 150 degrees F, and I don't know how hot a compressor will heat up the air. I do have a working knowlege of various boost pressures at RPMs under loads, since I have a boost guage in my own truck with this particular engine. Of course, the boost reading doesn't distinguish heat induced pressure rise from compresser induced pressure rise, and I don't know if heat induced pressure rise in negligible or not, since the air is in constant motion, not captive.
But continuing anyway, if I take the Actual TCI CFM, and divide it by the Ideal NA CFM, I thought I might find a workable TCI VE that I could use in lieu of a NA VE... thus:
907.45 / 385.42 = 2.35
Definitely on the high end of the published VE ratios of TCI engines... or is it? If I found that an inlet to outlet temperature ratio, in degrees Rankine, proved to be, say, .8, then my TCI VE might move within a more commonly seen range of VEs that I found:
2.3 x .8 = 1.84 TCI VE, now with a SWAG absolute temperature ratio and the aforementioned psiA ratio taken into consideration.
At this point, I have to remind myself that all I am really after is knowing what the maximum amount of airflow the 444 CID TCI engine may require on peak demand. I'd like to plug in different RPMs and boost pressures, to recognize this airflow demand, and eliminate filter candidates tested on the flowbench in this manner.
According to one filter manufacturer,
A CAT 3126TA turbocharged diesel, at 439 CID, requires 564 CFM.
A DET 6-71TA turbocharged diesel, at 426 CID, requires 1,190 CFM.
A DET 6V-71TA turbocharged diesel, at 426 CID, requires 1,087 CFM.
A DET 7.6TA turbocharged diesel, at 464 CID, requires 1,240 CFM.
A DET 6466T turbocharged diesel, at 466 CID, requires 474 CFM.
While no RPM, Boost, or temperature data is provided, the ratings all came from the same source (the filter manufacture) and, the engines are all very near the same displacement, averaging out to be exactly 444 CID. Also, with one exception, the engines all came from the same manufacturer, Detroit Diesel. Yet notice the HUGE differences in rated air requirements, from a low of 474 to a high of 1,240 CFM.
So, I'm stumped.
Thanks for your interest, and I would mightily appreciate any help you can provide in determining air flow requirements of the 444 CID TCI engine for which appropriate air filter and air box solutions are sought. International has been entirely non-responsive in providing their own CFM data. Their data might not be relevant anyway, considering the large installed base of chips and exhaust modifications. Measurement of an actual truck is not possible with the equipment I have, and my session on the flow bench, evaluating several OE filters, several replacement filters, several OE airboxes, and several more high performance filters and boxes, is all the data I have. If I knew what the max airflow requirements were, I could eliminate some air filter and air box selections from further instrumented testing on a vehicle.
Also, I don't know if the A/R ratio and efficiency island/map of a turbo need to be considered? It may not be for the diesel engine that I am concerned with, but it may be if I am looking over the fence at all those other engines listed above in attempt to draw parallels of CFM flow for similar displacement turbocharged compression ignited motors?
And getting back to my math process, I don't know if I could reduce steps by canceling terms in the algebra and saying that
TCI VE = {[PSIG + ATMOSPHERE] / ATMOSPHERE} x NA VE
and or if, in addition, I could reasonable assume absolute temperature values and gain more accuracy by saying that
TCI VE = [ITA / OTA] x [BPA / ATA] x NA VE
Where:
TCI VE = Turbocharged Intercooled Volumetric Efficiency
ITA = Inlet Temperature Absolute
OTA = Outlet Temperature Absolute
BPA = Boost Pressure Absolute
ATA = Atmospheric Pressure Absolute
NA VE = Naturally Aspirated Volumetric Efficiency
If the above works, the only thing I wouldn't know what assume would be the OTA!!!
If ITA is ambient temperature in degrees Rankine, as measured on the dirty side of the filter, where shall I assume outlet temperature to be measured as it relates to determining CFM flow requirements of the engine?
I apologize for the "creative" acronyms and terms I used immediately above for some of the variables. Some of that is due to typing in this format, and some of that is due to lack of familiarity with other standardizes terms.
My biggest concern is that the entire thought process outlined above has drifted partially, or perhaps completely offbase. Thanks for any direction you can provide!
