# Engineering Acoustics/Sonic Supercharging of 2 Stroke Engines

## Sonic Supercharging of 2 Stroke Engines

This page of the Engineering Acoustics Wikibook discusses the merits and
design of Tuned Pipes for 2 Stroke Engines. For introductory material on
2 Stroke Engines please see the following links:

Wikipedia 2 Stroke
Engines

HowStuffWorks 2 Stroke
Engines

## Introduction

For a 2 stroke engine the tuned pipe is the section of the exhaust
system that begins at the exhaust port and ends at the end of the
converging section. A tuned pipe is made of between 3 and 4
characteristic sections depending on the desired effect. The figure
below depicts cross sections for 3 typical configurations of tuned pipes
as well as a straight pipe:

!Typical pipes

The purpose of straight and tuned pipes is to utilize the pressure waves
originating from the exhaust port to assist the breathing of the engine.
This is achieved by designing the pipe in such a way that positive and
negative reflected waves arrive back at the exhaust port at an instant
when a low or high pressure is desired. This is beneficial for two
stroke engines because unlike four stroke engines, they do not have
dedicated intake and exhaust strokes and valves.

The following picture labels the various elements of a two-stroke engine
which are referred to in this Wikibook page.

!Two-stroke engine
elements

Furthermore; abbreviations will help as well:

-   In order of accensding crank angle
    -   TDC - Top Dead Center, 0 deg
    -   EPO - Exhaust Port Open
    -   TPO - Transfer Port Open
    -   BDC - Bottom Dead Ceneter, 180 deg
    -   TPC - Transfer Port Close
    -   EPC - Exhaust Port Close

For introductory material on 2 Stroke Engines please see the following
links:

Wikipedia 2 Stroke
Engines

HowStuffWorks 2 Stroke
Engines

## Straight Pipe

The goal of a tuned straight pipe in this application is to use the
reflected negative pressure waves from the open end of the pipe to help
draw out the exhaust gases. By selecting the appropriate length of the
pipe, the reflected rarefaction wave arrives at the exhaust port just as
the transfer port opens thus assisting the flow of fresh mixture into
the cylinder, and exhaust gases out of the cylinder. The figure below
illustrates this action. In the figure, even though the piston has
reached bottom dead center (BDC), fresh mixture continues to enter the
cylinder because the rarefaction wave causes P2 to be smaller than P1. A
key point to note is that the velocity with which the pressure and
rarefaction waves travel down and up the exhaust pipe is for the most
part independent of the engine operating frequency (RPM). Due to this
fact, the conclusion must be made that for a given pipe length there is
an optimal RPM for which the waves will arrive producing the greatest
benefit for the breathing of the engine. At this optimal RPM, the engine
breathes significantly better and hence produces a noticeable increase
in output power. This effect is quantified by calculating the ratio of
fresh mixture to exhaust gases within the cylinder as the compression
stage begins at EPC. If the rarefaction wave is very large, it is
possible that fresh mixture is pulled into the exhaust pipe while both
transfer and exhaust ports are open. This phenomenon is known as short
circuiting the engine and produces undesired effects such as a decrease
in fuel economy and an increase in release of volatile organic
compounds. These negative effects can be mitigated by designing the
exhaust system such that either no fresh mixture is pulled into the
exhaust pipe (i.e. perfectly tuned straight pipe) or further utilizing
the exhaust pressure wave to inhibit short circuiting. For performance
two-stroke engines, the second solution is most often employed by means
of a tuned exhaust pipe known as a tune pipe.

!Schematic of two-stroke engine with straight
pipe

## Tune Pipe

With a converging-belly section-diverging type tune pipe the goal is to
have the diverging section create a returning rarefaction wave and the
converging section create a returning pressure wave. The belly section
acts as an appropriate time delay between the returning waves such that
the pressure wave arrives at the exhaust port after the transfer port
has closed. This pressure wave pushes the excess fresh mixture in the
exhaust pipe from a short circuit, back into the cylinder. Here the
short circuited fresh mixture is actually desired since this allows the
returning pressure wave to \"super charge\" the cylinder giving it more
fresh mixture than if the cylinder were filled at ambient pressure. This
is a similar result to turbo-charging or super-charging a four-stroke
engine. If the mixture contained within the cylinder before combustion
occurs were allowed to expand to ambient pressure, its volume would be
larger than the displacement of the engine. This phenomenon is
quantified as volumetric efficiency; it is calculated as the ratio of
the ambient pressure volume of the fresh charge, divided by the
displacement volume of the engine. The operation of a two-stroke engine
equipped with a properly tuned pipe is shown in the animation below, for
a step by step description of the process, please follow the link below
the animation.

There are exhaust manufacturers now that are mating up tuned pipes to
tuned (ported) engines to get the best possible \'supercharging effect\'
at given rpm\'s. In the past a tuned pipe would have been tested on a
stock engine but the length and shape of the pipe will differ on a
\'tuned\' engine because of the way it is able to rev higher .

Two-stroke engine
operation

## Tune Pipe Design Geometry

The most basic form of a tune pipe is shown in the figure below with
corresponding wave equations.

!geometry and equations for simple
pipe

This pipe consists of an expansion chamber which serves to create both
the returning rarefaction and pressure waves. From reference \[1\], we
know that wave speed in the pipe is effectively independent of engine
RPM and largely dependent on temperature of the gases in the pipe. This
means that a tune pipe with basic geometry operates optimally for only
one specific RPM, as the engine RPM deviates from this optimal value the
timing of the arrival of the returning waves is less optimal for the
volumetric efficiency. The relation between the volumetric efficiency
and the engine RPM is characterized qualitatively by the following
graph:

!Qualitative relation of volumetric efficiency to
RPM

Although the basic tune pipe performs the desired task of increasing the
volumetric efficiency, the narrow RPM band width for which increased
power is available reduces the practicality of the basic pipe since
engines are typically required to operate within a wide range of RPM.
One way to broaden the effective RPM band width of a pipe is to taper
the pipe at sections of increasing and decreasing cross section. To
understand how this works, we can represent a tapered section as many
small step increases/decreases in cross section. Each step will produce
transmitted and reflected waves in the same way as the basic geometry;
however, the overall effect is weaker waves with longer wave lengths
arriving back at the exhaust port. Although the waves have smaller peak
amplitudes, the effect on volumetric efficiency is greater due to the
longer interaction times of the waves with the cylinder and crankcase.
If the number of steps increased to n diverging steps and m converging
steps, the equations shown represent the plane waves as well as the
transmission and reflection factors for each change in cross section.

!geometry and equations for stepped
pipe

!reflection and transmission coefficients for
step

The graph below shows qualitatively how pressure at the exhaust port
varies with crank angle for both basic and tapered pipe geometry.

!qualitative different between EPP for basic and tapered
pipes

The important differences to notice in the graph are the relative
magnitudes and durations of the positive and negative pressure waves
arriving back at the exhaust port at TPO and EPC. In this graph, if we
pin down the waves with respect to time along the horizontal axis and
then we increase or decrease the RPM, the effect will be that the
positions of the port timing will no longer match up with the same
positions of the waves. This is due to the fact that, as mentioned
above, the wave speed is independent of RPM. In more detail if we
increase the RPM it would have the effect of shrinking the port timing
scale while keeping EPO in the same position. If we increase the RPM,
the port timing scale expands with EPO remaining in the same position.

Looking at things the other way around, if we change some aspects of the
pipe geometry we can see how they change wave propagation in the pipe
and hence operation of the pipe with respect to the engine.

-   Length of the pipe between the exhaust port and the diverging
    section (L1) - this length set by the difference in crank angle
    between EPO and TPO and the desired effective RPM range of the pipe.
    Making the section longer would fit a lower RPM range or a greater
    difference between the crank angle of EPO and TPO.
-   Length of the belly section - this length is set by the difference
    in crank angle between TPO and EPC and the desired effective RPM
    range of the engine. This length and L1 are interdependent since the
    crank angles are also interdependent, (e.g. EPC=(0-EPO)).
-   The angle of the diverging/converging sections - changing this angle
    from steep angled cone (interior angle \> 90 degrees) to a shallow
    angle cone (interior angle \< 90 degrees) has the effect of
    broadening out the wave length. This increases the effective band
    RPM band width of the pipe since there greater flexibility of crank
    angle for which an appropriate pressure will at the exhaust port.
    This also has the effect of decreasing the maximum attainable
    volumetric efficiency of the pipe since the peak pressure amplitude
    is diminished by spreading out the waves energy over a longer
    wavelength. Note that if the diameter of section L1 and the belly
    section are kept constant, changing the angle and changing the
    length of the diverging/converging section is geometrically the
    same.
-   The ratio of the cross section of section L1 and the belly section -
    the ratio is largely dependent on the desired angle and length of
    the diverging/converging sections and the minimum diameter desired
    to avoid impeding the flow of the exhaust gases.

## Further Investigation

For further investigate of the operation of two-stroke engines with
tuned exhaust pipes it is most appropriate to analyze actual test data.
For this we can go to the TFX website where they demonstrate their
testing and data analysis software, or read the paper referenced below
titled \"Exhaust Gas Flow Behavior in a Two-Stroke Engine.

For the class presentation I would like to do both given sufficient
time.

## References

1.  Exhaust Gas Flow Behavior in a Two-Stroke Engine; Y. Ikeda T.
    Takahashi, T. Ito, T. Nakajima; Kobe Univ.; SAE 1993
2.  Power Tuning - Two Stroke
    Engines
3.  2 STROKE WIZARD - Tuned Pipe Design
    Software
4.  Ian Williams Tuning MOTA Tune Pipe Design
    Software
5.  Les phénomènes d\'ondes dans les moteurs; M. Borel; Edition TECHNIP;
    2000
6.  Engineering Acoustics Course Notes; McGill University MECH 500; L.
    Mongeau; 2008
7.  Engineering Acoustics; L. Kinsler, A. Frey; 4th Edition; 2000
