Bernoulli and 350 ft/s, 146 cfm/in²
Here is the source of some of my confusion on this subject. In book after book and in video after video, the theoretical limits of 350 ft/s and 146 cfm/in² are used. Several months ago, in pitot tube probing the combustion chamber side of the intake valve (see picture below), I was getting local velocities of well over 350 ft/s. I thought, well, that's OK as long as the average velocity is below the limit of 350ft/s. Look at the sixteen pitot tube readings in pink. The average is 370 ft/s.
The answer is twofold. One reason is because of the venturi effect. Air is speeding up to get through the venturi created by the valve and valve seat. The other answer is because of the 28 in H2O pressure drop across the intact port. The 350 ft/s velocity limit is the limit at the density of air at the inlet of the port (14.696 psi). Because the air in the chamber is at a lower pressure (13.675 psi) than the air at the inlet to the port, the density in the chamber is lower. So, as air travels down the intake port, it's pressure is reducing and therefore its density is also reducing. Since the mass flow rate of air through the port cannot change, the velocity has to increase as the air gets closer to the chamber. So, even if the area of the intake port is constant, the velocity will be increasing as the air travels down the port.
One other confusing part of this pitot testing in the chamber was the average cfm/in² readings. These can be seen in blue. Again, the average number of 154 cfm/in² seems to violate the maximum theoretical value of 146. But again, the reason it's doing so is because of the venturi effect and the reduction in density associated with high air speeds. The 154 number would yield a discharge coefficient of 154/146=1.05 if the 146 is used as the theoretical maximum. It should not be possible to get discharge coefficients higher than 1, but it is common at low lifts. I believe the explanation has to do with scfm vs acfm. The 154 number is cfm at a lower density than the 146 number. If both numbers were converted to standard conditions (scfm), I believe that a discharge coefficient of greater than 1 could never be achieved.
Discharge coefficients are about as intimidating as shaping a short side radius. I think the reason is because of the complexities of scfm vs acfm and the difficulty of measuring the valve curtain area. More on that later.
Saw this in a porting group on fakebook and remembered this post along with the 146cfm reference. Thought it might be interesting to add. I found the part about how he describes the MSCA actually moving between the valve and the port runner during the first 70ish deg of crank rotation fascinating and informative with respect to flow dynamics and how this is caused by the valve curtain changing the overall path of the air fuel charge on its way into the cyl.
In my head this tells me something about how the point past the SSR really needs to be a consistent "cone" or "cone-like" shape on the way in.
The bigger reason I am sharing this is the common reference to 146cfm which you painstakingly derived. Below is another way it's derived and used to find the theoretical MCSA for an engine with specific characteristics. Seems like a very good way to find a starting point and not overshoot for an engine.
The other observation is it seems valve diameter selection is dependent or at least complimentary to knowing the required MCSA for a particular engine. Different valves will have different curtains at the various lift values and at some point this needs to overcome the MCSA of the actual port runner, or the valve curtain would be the effective MCSA throughout the cycle (or so it seams) . Of course those numbers happen to be right around the 2.02 + range which is obviously very familiar so it might be a coincidence, or it might not.
Anyway, I'm just doing thought experiments with zero practical knowledge so I am MORE than happy to be told I am interpreting things wrong and be corrected.
enjoy
CFM Demand & the Minimum Cross-Sectional Area
By Sean Burns
January 15, 2024
When it comes to engine development there are many areas that need to be optimised for a strong, efficient
and reliable engine. From the aspect of airflow we look at the induction system, cylinder head ports,
combustion chamber, valvetrain, pistons, and exhaust system. On the mechanical side we have the camshaft,
which is closely integrated with the valvetrain, connecting rods, and crankshaft. All of these systems need to
work in harmony to produce optimum performance. Today I would like to address the linear equations used
for the Minimum Cross Sectional Area (MCSA) within a cylinder head port and how it affects other dynamics
within the induction process.
Fundamentally, air is forced to move by creating a pressure differential within a system, air moves from a
high pressure area to a lower pressure area in an attempt to equalise those pressures. A pressure differential
in an engine is created in a few ways; the main mechanism that I will address is the piston descending down
the bore on the intake stroke. When the piston starts to accelerate from Top Dead Centre (TDC) down
towards Bottom Dead Centre (BDC) a pressure differential is created, by the expanding the volume within the
bore. In addition the pressure differential is increased due to the restriction in the intake
port/runner/induction system. The measurement of the pressure differential is dependent upon 3 factors,
the bore diameter, the speed of the piston at any given moment, and the size of the restrictions in the MCSA.
At the beginning of the intake stroke the piston is accelerating from zero feet per second (fps) to its
maximum piston speed at around 75 degrees after TDC. Then the piston starts to decelerate from that peak
speed to once again zero fps at BDC. The maximum speed of the piston is dependent on the stroke length,
rod/stroke ratio, rpm, and engine type. Throughout the travel of the piston in the bore we have a varying
restriction; the intake valve and port MCSA. The camshaft profile is also a big player in this process as it is the
actuator that controls intake valves movement and thus its restriction. The intake valve is already starting to
open even when the piston is at TDC, then the piston starts to descend and the intake valve “chases” it down
the bore. For a portion of time the valve curtain area, which is the combined area in between the valve seat
and the valve face is the MCSA. Once the valve approaches 1⁄4 of its diameter in lift, for example a 2” diameter
valve that will be 0.500” of lift, it shifts to the port as he curtain area will be the equivalent to the valve head
area itself. The exact transition depends on the actual size of the MCSA.
Now that the MCSA has transition to the port, it can be either the throat area just below the valve seat or
further up in the main runner of the port itself, these areas now dictate the pressure differential in relation to
the piston speed at that moment, What we also get as a result of this pressure differential is the maximum
airspeed within that MCSA, this is what we want to control at peak engine speed and peak piston speed
during that one cycle. It is well known that for most conventional cylinder heads that we modify we want to
keep the airspeed to a max in between 619fps (Mach 0.55) and 675fps (Mach 0.6) at standard temperature
and pressure (stp). These speeds are a realistic target to maintain stability within most ports, yet fast enough
to aid in inertia cylinder filling as the piston slows down towards BDC and continues with the piston return
back to TDC on the compression stroke, this inertia filling is the reason we can achieve higher than 100%
volumetric efficiency (VE) numbers. This is the naturally aspirated version of “forced induction”, increasing
the density of the intake charge within the cylinder.
The pressure differential that is needed to achieve those airspeeds is between 3.17psi & 3.77psi. To keep our
targets within that range at peak rpm we have to calculate the MCSA. I would like to cover some of the
equations that are used for working targets when sizing ports to suit an engines displacement and rpm peak.
2
CFM Demand Calculation
The common and widely used calculation to start with is a CFM demand. This calculation gives us a target
cfm number at 28” test pressure. This is achievable on the vast majority of flowbenches and is the industry
standard test pressure. We now have a starting number to work with for the MCSA.
Cubic capacity * peak rpm * (variable) / number of cylinders = CFM target at 28” test pressure
The variable is a number that is derived from 1.01055 / fps / 2 * VE
The common variable is 0.0009785, represented by:
1.01055 / 640 / 2 * 1.2394 = 0.0009785
1.01055psi equivalent to 28” water column test pressure
640fps is in between our 2 max airspeed ranges
2 is needed because the intake cycle is every second crank rotation
1.2394 is the VE as a decimal, which is 123.94%
These numbers are used as a base because 640fps is around the average of our target maximum port speeds
and 123.94% VE is used because that is approaching the limit for the majority of naturally aspirated (NA)
engines. Therefore 0.0009785 is seen as a “best case scenario” target for us to work from. Now because the
(variable) is variable we can use it to cross reference future results from dyno testing or even give us an idea
of what the VE or port speeds may be in certain situations, This is going a bit beyond the scope for now but I
will revisit this another time.
Let’s set up an example engine to do our calculations on, I am a mad Ford inline 6 fan so I will use the Ford
Australia 250 Xflow inline 6, we will target 6500rpm as our peak engine speed, with these details we can do
our first calculation, CFM demand.
250 X 6500 X 0.0009785 / 6 = 265cfm at 28” test pressure
We now have a target cfm number, the engine at 6500rpm wants approximately 265cfm at 28” test pressure
per intake port to achieve a max port speed of approximately 640fps at a VE of 123.94%
Using the 265cfm result we can go ahead and start looking at what size MCSA is required to support the flow
number, with a set pressure differential of 28”, at sea level (14.7psi) and 21°C, the maximum ammout of air
that can flow through 1” square of area is 146cfm. This is defined by the following calculations.
V2 = 2(Pt – Ps) / density
V2 is velocity squared in meters per second
Pt – Ps is the pressure differential in pascals 28” water column is 6967.497 pascals
Density is in Kg/M3
V2 = 2(6967.497) / 1.225
V2 = 11375.5053m/s
Square root of 11375.5053 is 106.656 V=106.656m/s
To find the CFM per square inch we use the velocity answer X by the area.
V is in feet per minute
A is feet squared
106.656m/s = 349.92fps = 20,995.2fpm
1 square inch = 0.006944 square feet
3
CFM = 20,995.2 X 0.006944
CFM =
145.79 per square inch at 28” pressure differential
So we can say with rounding to a whole number that 1 square inch can only flow 146cfm at a pressure
differential of 28” water column.
To work out what area is required to flow our cfm demand answer of 265cfm we simply divide that number
by 146.
265 /
146 = 1.815” squared at 100% efficiency.
Now this next statement is based off my personal preference, it is what I personally target for MCSA and
efficiency wise. I target a 95% efficiency through the area, so if I want to achieve that 265cfm through an area
at 95% efficiency, I take the 100% efficiency area and multiply it by 1.05
1.815 X 1.05 = 1.906” squared
This 1.906” squared is now my target MCSA to meet the cfm demand of the 250ci engine at 6500rpm, with
target peak airspeed of 640fps and 123.94% VE
One point I want to stress is that these are calculated targets to aid in sizing of the MCSA, they should be
used as approximations only, the important thing is to stick to the calculated areas as close as possible, do
not chasing that flow number, if the best you can do because of the port architecture is 92% efficiency
through that calculated area then it is what it is. I do not recommend increasing the MCSA to chase in my
example 265cfm. When you change the MCSA you change the peak rpm point that the airspeed will peak at.
For example, if you increased the MCSA the engine will generally peak later in the rpm range but will not
produce increased power because the cfm demand is not being met at that higher rpm point, so stick to a
plan when it comes to MCSA.
I hope this is of use in understanding the process I use, and those with their next project at hand to help
achieve positive results.