Hear is the last word on flow
Air Flow Dynamics
When considering the airflow dynamics of a filtration induction system, the ideal objectives of the system must be defined. When relating to optimizing engine performance, the primary objective for the filtration induction system is to deliver total air pressure to the intake manifold as close to atmospheric pressure as possible. This objective holds regardless if the engine is naturally aspirated, turbo charged or supercharged. In the latter two forced air induction systems, the forced induction mechanism is fed by the same atmospheric pressure (about 14.7 PSI at sea level) that supplies air to the naturally aspirated engine. Restrictions to airflow will hamper the performance of the forced induction system in the same manner as a naturally aspirated engine. For the same displacement engine, a forced induction system puts a greater demand on the induction system because of the larger volumetric flow rates that are demanded by the power adder. Thus, forced induction systems demand higher capacities out of an induction system than does a naturally aspirated of the same displacement.
Every component that is used to control or perform some function in the induction system will contribute some restriction to the airflow. The goal is to choose materials, shapes, sizes and designs that will minimize the restrictions, regardless of how large or small the restrictions. Some of the induction system aspects that affect these restrictions are diameter of air ducting, surface conditions of the air ducting, bends in the air ducting, filtration elements and any obstructions placed in the intake system. Optimizing each aspect of the induction design will give rise to an optimal induction system.
To fully understand the principles of the airflow dynamics, we need to utilize the relationship that exists between changing air stream velocity, the static pressure of any point in the intake duct and frictional energy losses. All of these terms are defined in the relationship given by the extended Bernoulli equation:
With respect to an intake duct system on an engine, the changes in height of the air stream is negligible and no shaft work is being done. Therefore, these terms can be dropped to leave us with the following equation that describes airflow mechanics in the intake duct.
What this equation tells us is changes in the energy of the air stream is made up of changes in kinetic energy in the form of air velocity, changes in potential energy in the form of static pressure and lost energy to friction. All energy given up to friction limits the air stream velocity and the static pressure. Thus, keeping the frictional losses to an absolute minimum will benefit the engine.
With respect to duct diameters, the intake track should start out as large as feasible and gradually reduce down in size to match the inlet flange diameter of the throttle body or mass air flow (MAF) meter, which ever comes first. The diameter of any portion of the intake track determines the air velocity at that point for any given airflow rate. The calculation of these air velocities will be shown later. Higher air velocities lead to greater pressure losses due to larger friction losses. Decreasing the duct diameters gradually, and thus gradually increasing air velocities up to the throttle body/MAF, tends to minimize energy losses. Changing the intake diameters from larger to small and back to larger should be avoided. These erratic changes induce undue turbulence and unnecessary pressure losses due to lost energy to friction, compression and expansion.
To appreciate how much influence the duct diameter has on the friction losses, we can calculate the difference in friction between two different duct sizes. The calculation of the friction loss is given by the following Fanning equation for steady flow in uniform circular pipes under isothermal (i.e. constant temperature) conditions:
For example, if the difference in friction losses were calculated for using 3-inch inside diameter (ID) duct verses 4-inch ID duct, all of the parameters in the Fanning equation remain the same except for the friction factor and diameter. The friction factor is a function of the Reynolds Number (Re) for the system and the duct surface conditions, where the Reynolds Number has the following definition:
If we assume a constant bulk flow rate of 300 cubic feet per minute between the two duct sizes, which is a fairly good approximation for the calculations involved, then the 3 inch duct has an Re = 14.9x10^4 and the 4 inch duct has an Re = 7.46x10^4. When you apply these changes in the Reynolds number to the estimation of the friction factors, you will find the friction factor changes from 0.0042 for the 3 inch duct to 0.0048 with the 4 inch duct. These friction factor values come from a friction factor vs. Reynolds number chart that can be found in any good fluid dynamics reference book.
It should be noted that the velocity of the air in the 3 inch duct is ~102 ft/sec and the velocity in the 4 inch duct is ~57 ft/sec when flowing 300 cubic feet per minute. These velocities are calculated using the following simple relationship.
For 3" Duct: u = 300/( 3.14159(3/12)2/4)/60 = 101.8 ft/sec @ 300 ft3/min
For 4" Duct: u = 300/( 3.14159(4/12)2/4)/60 = 57.3 ft/sec @ 300 ft3/min
The act of increasing the air velocity is not desirable when it does not contribute to the harmonic tuning of the intake pulses in the intake manifold. Since the intake duct is ahead of the throttle body and MAF sensor, these harmonics do not come into play. Therefore, increasing the air velocity unduly increases energy losses to friction. The faster air travels the more friction losses grow and reduce the potential of the intake system. In performance engine configurations, engine builders rely on what are called velocity stacks to gradually increase the air velocity to the speed the air has in the throttle body or carburetor. These velocity stacks are funnel shaped intake ducts that start out with a larger diameter and gradually neck down to a smaller diameter that matches the throttle body or carburetor inlet flange diameter.
If we are interested in calculating the percent change in the friction when going from a smooth surface 4 inch duct to a smooth surface 3 inch duct, we can use the Fanning friction equation given above and derive the following:
Putting in the numbers for the friction factors and the diameters for the 3 inch and 4 inch ducts we arrive at the following:
What this means is going from a 4 inch duct to a 3 inch ID duct increases the friction losses by ~2.7 times. Thus, it is not hard to see that a 4 inch duct is preferable over a 3 inch duct by reducing friction losses as well as lowering the air velocity by nearly half.
Another design consideration that strongly influences the airflow dynamics is bends in the intake duct. Any time the airflow is forced to change directions, additional flow resistance is encountered. In typical flow dynamic calculations, the resistance contributed to the system by bends is determined by calculating the equivalent length of straight pipe that represents the bend's friction. For example, if a 3 inch duct has a 6 inch straight section, a 90° bend with a 3 inch centerline radius followed by another 6 inch section, then the contribution of the 90° bend could be considered as adding a calculated amount of straight pipe in place of the bend. (See illustration below.) Thus, the entire piping can be treated as a straight pipe. This makes overall piping friction calculations easier because once you know how much equivalent straight pipe in the system, the overall fiction of the piping is easily calculated by the Fanning friction equation given above.
Another simple way to look at this equivalent length of straight pipe substitution of a bend is realizing how long the effective length of the intake duct would be if it were completely straight and had the same flow restriction as with the bend.
Calculating the equivalent length (Le) of straight pipe substitution of a bend is rather simple. The flow dynamic relationship between bends and straight pipe has been empirically documented by the A.S.M.E. in the following chart.
If a 90° bend is designed into the intake duct, then the following can be estimated as shown in the following table. In these examples, 3" and 4 " ID pipes are given. For these pipe sizes, the centerline radius of close 90° elbows are typically equivalent to the diameter of the pipe.
These calculations illustrate the addition of a single 90° bend in a 3-inch or 4-inch duct is the same as adding 48 inches or 64 inches of straight duct respectively in its place. When compared to the rather short length desired for the intake duct, adding a single bend has a dramatic affect on increasing the intake's resistance to airflow. For bends other than 90°, they can be estimated by multiplying the 90° bend resistance by a percentage factor. For a 45° bend, the total friction loss is about 65% of the 90° bend's resistance. For a 180° bend, the total friction loss is about 140% of the 90° bend's resistance.
From the above table, one might conclude that the 48 inch equivalent length given by a 3 inch ID pipe would provide less friction than the 64 inch equivalent length for a 4 inch ID pipe. However, one must now determine the friction that is produced by these two pipe sizes before making such a judgment. As shown earlier, the 3 inch pipe has 2.69 times more friction than a 4 inch pipe. If you calculate the equivalent length of 4 inch ID pipe that would have the same friction as the 90° bend in a 3 inch ID pipe, then you would need to multiply the 48 inch equivalent length by 2.69. This result tells us the 90° bend in a 3 inch pipe is equivalent to 119 inches of 4 inch ID straight pipe. Thus, having bends and smaller pipe diameter is detrimental towards producing good flow characteristics in an induction system.
Another factor influencing the resistance to airflow is the intake duct surface roughness. As the interior surface of the duct becomes rougher, the surface creates turbulence, vortexes and possibly eddies in the air stream. The mechanical energy needed to form these aberrations in the air stream must come from the air itself. This removal of energy comes from the reduction of air pressure, per Bernoulli's extended equation. While estimating the friction loss due to various intake duct surface conditions could be estimated, it should suffice to say that the minimal friction loss is achieved with smooth intake duct surfaces. Therefore, the intake duct inside surface design/specification goal is a smooth surface. The accordion duct types that are common with OEM intake ducts meet the flexing needs of the intake duct. However, they are far removed from the optimal intake duct design. To counteract the air stream disturbances created by the folds in the accordion ducts, many OEM intake designs will have a laminar flow screen installed in the intake track to stabilize the air velocity profile in the intake air stream prior to the MAF sensor. This screen in turn adds further airflow resistance, which is not good. If the intake duct is designed to provide a uniform air velocity profile without needing such a device, then the laminar flow screen is not needed and the airflow resistance introduced by the screen can be avoided. Therefore, another intake design goal is to provide a uniform air velocity profile to the MAF sensor.
Another aspect of the induction system to consider is the dynamics of the air entering the intake system. This refers to the total air pressure available in the vicinity of the intake duct entrance or the air filter element, which ever applies. If the airflow that is supplying air to the intake duct entrance or the air filter element is restricted in some manner, then these restrictions must be accounted for in determining the overall induction system airflow capabilities. The optimal induction designs will have air freely flowing from outside the vehicle into the air intake and at a low velocity with the highest static pressure possible. Preferably, the static pressure surrounding the air filter element should be equal to atmospheric. If it is any less, then optimal performance can not be achieved.
Other considerations must be given to where the induction system is drawing air from, with respect to static pressure. Because the vehicle is designed to be in motion, the airflow dynamics surrounding the vehicle and the influence it has on the induction system should not be ignored. As the vehicle builds speed, various low-pressure zones and high-pressure zones are created around the vehicle. A good induction system will take advantage of these high-pressure zones and use the pressure available to feed the induction system. If done properly, the inlet to the induction system can be at pressure levels above ambient atmospheric pressure. This type of artificial boosting of the air pressure is commonly referred to as a "Ram Air" effect. This effect is based again on Bernoulli's equation. In this situation, the relative velocity of the air striking the front of the vehicle must slow down to approximately zero when entering the large volume air box. The energy from the air velocity changing must result in increasing the static pressure. If the air velocity is very low in the air box, then the friction losses can be considered negligible. Thus, the extended Bernoulli's equation given above can be rewritten as follows:
This relationship means the change in air pressure is directly proportional to the square of the change in air velocity. Since we are near atmospheric pressures, the Ideal Gas Law can apply. If we assume constant air density for the small changes in air pressure, then the relationship above can be written as:
Plotting this relationship with the appropriate constants and values derives the following chart.
From this chart, it can be easily seen that allowing the air box to become pressurized with dynamic air pressure can be very beneficial towards optimizing the induction system. This Ram Air effect grows with vehicle speed and becomes significant to above ~80 mph. This effect can only be taken advantage of when the inlet to the air box is open to the frontal area of the vehicle. If the air box or intake area is exposed to the sides or the undercarriage area of the vehicle, positive air pressures may not be available. Worse yet, some areas surrounding the vehicle can actually have lower air pressures because of the same relationship is working in reverse. This would mean that the air box is drawing air from regions of low pressure that exist at some point around the vehicle. Caution should always be exercised when selecting the area surrounding the vehicle that will feed air to the air box. Actual pressure measurements will ensure the best possible location is found and the benefits are realized.
I left the math out, You get the idea. Now dont you Buffman.