Erbman's Engine Emporium, Part II

Russ Erb

Originally published January 1994

Erbman's Engine Emporium, Part I
Volumetric Efficiency
Induction System Effects
Exhaust System Effects
Summary
References
Erbman's Engine Emporium, Part III
Erbman's Engine Emporium, Part IV

In this installment, we will look at the dynamics of how air (or the fuel/air mixture, if you prefer) flows through an reciprocating engine, and how this affects the speeds for maximum torque and maximum horsepower.

The first step to understanding this is to realize that, for these purposes, a reciprocating engine cannot be analyzed statically. It must be looked at dynamically. So what does that mean? Here is the Otto cycle described from a static analysis:

  1. With the piston at top dead center (TDC), the intake valve opens.
  2. The piston moves down to bottom dead center (BDC), drawing the fuel/air charge into the cylinder. The intake valve closes.
  3. The piston moves up to TDC, compressing the fuel/air charge.
  4. A spark ignites the fuel/air charge, which burns and expands, driving the piston down to BDC.
  5. The exhaust valve opens, and the piston moves up to TDC, pushing out the exhaust gases.
  6. The exhaust valve closes.
  7. Repeat.

As it turns out, none of these things happens exactly when the piston is at TDC or BDC. Valve openings and sparks are timed either ahead of or behind the dead center positions to take maximum advantage of the dynamics of the flow.

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Volumetric Efficiency

An important concept to understanding the variations in power and torque is the volumetric efficiency, which depends on the current engine speed. Volumetric efficiency is defined as the ratio of the amount (mass or volume, depending on who you talk to) of fuel/air mixture drawn into a cylinder on the intake stroke to the maximum amount of fuel/air mixture that could be drawn into the cylinder at the intake density. Alternatively, "Volumetric efficiency is the ratio of the volume of fresh charge taken in during the suction stroke to the full piston displacement. The volume of the charge is taken at atmospheric pressure." (Ref 1) You can think of this as how much less is the amount of fuel/air charge in the cylinder compared to the maximum that could be there. Of course, the more fuel/air charge in the cylinder, the greater the force will be on the piston during the power stroke. This is how throttling reduces an engines power output. The throttle valve reduces the pressure in the manifold, such that the change in pressure caused by the piston's downward movement is less, thus drawing in less fuel/air charge. For the purposes of this discussion, for finding the maximum torque and maximum horsepower speeds, the throttle will be assumed to be wide open.

So it would seem that the way to get the maximum torque out of an engine would be to get the maximum amount of fuel/air charge into the cylinder. The maximum fuel/air charge will create the maximum pressure on the piston, which would create the maximum torque at the propeller shaft. This is true, but under what conditions does this occur?

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Induction System Effects

Two real world effects determine how much fuel/air charge gets into the cylinder. The first effect is that air is compressible. The second effect is the dynamics (acceleration/deceleration) of the air. The compressibility of the air becomes a factor when the air enters the intake port around the intake valve. The intake port/valve forms a constriction, much like the throat of a nozzle. Because air is compressible, it can only be pushed through a constriction so fast. Regardless of how much pressure you apply, the maximum velocity possible through the throat of a nozzle is a velocity equal to the speed of sound (Mach=1.0).

The same effect happens at the intake valve. "For convenience, the ratio of the typical velocity to the intake sonic velocity is called the inlet Mach index. From the science of fluid mechanics we know that the controlling velocity in a compressible flow system is usually the intake valve opening." (Ref 2) For a given cylinder and valve design, the inlet Mach index is proportional to the piston speed. This seems reasonable, that the fuel/air charge flows in faster when the piston moves down faster. Of course, at some point the constriction of the valve opening starts to limit this. When the inlet Mach index exceeds 0.5 (intake velocity equal to half the speed of sound), the volumetric efficiency falls rapidly with increasing speed. Therefore, engines typically are designed such that the inlet Mach index does not exceed 0.5 at the highest rated speed. (Ref 2)

The effect of this constriction shows up as a pressure drop through the intake valve. So why don't we just open the intake valve further? Because when the valve is lifted a distance equal to 1/4 its diameter, the area of a cylinder around the valve (that the fuel/air charge passes through, not the engine cylinder) is equal to the area of the valve face and intake port (ignoring the valve stem). See Figure 1. Mathematically, the area of the cylinder is (2 (PI) r)(d/4). Since d = 2r, this evaluates to (PI)r2, which is the area of the intake port. Experimentally, the amount of additional flow through the intake port increases very slowly as the lift of the valve increases beyond 1/4 of the valve diameter.

Valve Lift

Figure 1. Valve Lift

Because of the dynamics of the fuel/air charge, the intake valve normally closes at some time after the piston passes bottom dead center. As the piston moves down, it draws the fuel/air charge into the cylinder. This movement builds up momentum in the intake manifold. When the piston reaches bottom dead center, the fuel/air charge is still flowing into the cylinder as a result of this residual momentum. Thus, at the speed desired for maximum torque, the intake valve closing is timed to correspond with the velocity of the fuel/air charge through the intake port dropping to zero. This closing will occur at some time after the piston has started the compression stroke, and will result in the maximum amount of fuel/air charge being drawn into the cylinder. This maximizes the volumetric efficiency, and maximizes the torque delivered to the shaft (ignoring friction effects). The angle of the crankshaft at the time the intake valve closes is called the intake valve closing angle.

So what effects does this later valve closing have at other speeds? At low speeds, the momentum built up in the intake manifold will be small, such that part of the fuel/air charge will be pushed back into the intake manifold as the piston starts up prior to the intake valve closing. At speeds above the speed for maximum torque, the constriction of intake valve opening will cause a pressure loss which will reduce the amount of fuel/air charge entering the cylinder. In either case, the amount of fuel/air charge in the cylinder is reduced, and thus the torque is reduced.

The design of the intake manifold also affects the amount of momentum built up in the flow of the fuel/air charge. The momentum of the fuel/air charge is the sum of the effect of standing waves built up from previous intake strokes (remember any tube will have a resonant frequency, just like you hear blowing over the top of a coke bottle) and the effect of the transient wave caused by the current intake stroke. While the standing waves contribute to the overall effect, there are no sudden changes in the volumetric efficiency when the RPM of the engine is an even multiple of the natural frequency of the intake manifold.

Long, skinny intake manifold pipes give high volumetric efficiencies at low piston speeds because high momentum (lots of velocity) is built up in the pipe during the intake stroke. At high piston speeds, the small diameter of the pipe causes a constriction and the volumetric efficiency falls.

So why don't we use long, fat intake manifold pipes to avoid the constriction? Fat pipes show a maximum volumetric efficiency at intermediate piston speeds. However, at high piston speeds, the larger mass of the fuel/air charge in the fat manifold is slow to accelerate, and thus the volumetric efficiency falls off.

As the manifold pipes get shorter, the maximum gain in volumetric efficiency over having no intake manifold at all decreases. However, the gain you do get with shorter pipes happens over a greater range of piston speeds. (Ref 2) Basically, it comes down to the intake manifold should be designed according to the engine requirements. If you need high torque at slow piston speeds, use long, skinny intake pipes. For high torque at intermediate piston speeds, use long, fat intake pipes. For high torque over a wide range of piston speeds (i.e. a flat torque curve), use shorter intake pipes.

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Exhaust System Effects

Part of getting a large fuel/air charge into the cylinder (high volumetric efficiency) has to do with getting the combustion products of the previous cycle out of the cylinder. At first thought, it would seem that simply making the exhaust valve bigger would help get the combustion products out. As it turns out, the exhaust valve can be as small as 50% the size of the intake valve without affecting the volumetric efficiency over the usual range of inlet Mach indices. Normally, though, exhaust valves are at least 60% the size of the intake valve. (Ref 2) While I did not find this in print anywhere, this effect may arise because the combustion products are "pushed" out of the exhaust port by the piston, while the fuel/air charge is "sucked" in the intake port, pushed only by the manifold pressure.

To enhance the removal of the combustion products, the intake valve is opened prior to the end of the exhaust stroke. Since both valves are open at this point, this is referred to as valve overlap. If the pressure in the intake manifold is greater than the pressure in the exhaust manifold, the inrushing fuel/air charge will help scavenge the remaining combustion products in the cylinder as the piston reaches top dead center by pushing them out the exhaust port. While some of the fuel/air charge may go out the exhaust port, the engine designer tries to design the timing such that the exhaust valve closes just as the last of the combustion products leave the exhaust port. An additional benefit of valve overlap is that the intake valve is essentially fully open at the start of the intake stroke, thus reducing the pressure loss through the intake port during the intake stroke. (Ref 2) The angle that the crankshaft turns between the intake valve opening and the exhaust valve closing is called the valve overlap angle.

Of course, scavenging does not occur at all speeds. At low speeds, the throttle valve reduces the pressure in the intake manifold, such that the intake manifold pressure is less than the exhaust manifold pressure. In this case, a small portion of the combustion products enter the intake manifold, to be pulled back into the cylinder on the intake stroke. Additionally, the combustion products in the space above the piston at top dead center are not scavenged. Even so, at low power settings this is not a problem.

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Summary

In general, we have seen that the torque, and thus the horsepower produced by an engine depends on the amount of air that can be pumped through the engine. The more fuel/air charge drawn into the cylinder, the higher the volumetric efficiency. The higher the volumetric efficiency, the higher the torque. The biggest factor affecting the volumetric efficiency is the valve timing, specifically the valve overlap angle and the intake valve closing angle. Volumetric efficiency can also be improved by the intake manifold design. Since the camshaft used determines the valve timing, changing the camshaft will change the shape of the torque curve, and thus the horsepower curve. This is echoed by C. Hall "Skip" Jones in his article in Sport Aviation. (Ref 3)

Next month we'll talk about other factors affecting engine performance, including fuel injection, stroke/bore ratio, compression ratio, spark timing, and supercharging.

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References

1. V.L. Maleev, Internal-Combustion Engines: Theory and Design, 2nd ed. (New York: McGraw-Hill Book Company, Inc., 1945).

2. Charles Taylor, The Internal Combustion Engine in Theory and Practice, 2nd ed. (Cambridge: The M.I.T. Press, 1966), I.

3. C. Hall "Skip" Jones, "Converting Auto Engines For Aircraft Applications," Sport Aviation, April 1993.

Erbman's Engine Emporium, Part I

Erbman's Engine Emporium, Part III

Erbman's Engine Emporium, Part IV

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Revised -- 22 February 1997