Expansion Chamber Design According to Blair

Introduction

All the information presented was taken from the book ‘Design and Simulation of Two Stroke Engines’ written by Dr. Gordon P. Blair, professor at Queens University Belfast, and published by the Society of Automotive Engineers. If you find this interesting, get this book.

Speed of Sound in a Gas (Sound Pressure Wave Velocity)

One of the main parameters involved in expansion chamber design is the speed of sound, this governs the speed of the pressure pulses that we use in the chamber.

Where:- T exc is Exhaust gas temperature in Celsius 273 added to T exc to convert to Kelvin R is 287 the Gas Constant of air in J/kgK g is 1.4 the Specific Heat Ratio of air a 0 is the speed of sound in m/s

Brake Mean Effective Pressure

BMEP is used in several of the expansion chamber design parameters, and is calculated as shown.

Where:- kW is engine power, kW (1bhp=746W) SVcc is swept volume, cc RPM is engine speed, rpm BMEP is in Bar

Average Exhaust Temperature

Now we must determine the exhaust gas temperature in Kelvin (k = C + 273.15). This is usually a function of the engine's BMEP.

Tuned Length of the Expansion Chamber

Blair’s formula assumes that the tuned length of the expansion chamber is from the face of the piston to the beginning of the stinger and is given by the formula below.

Where:- L t is tuned length, mm 83.3 = metric constant A 0 is speed of sound in m/s Q ep is exhaust duration, degrees

Effective Exhaust Diameter (EXD)

This is the diameter of a pipe whose area matches that of the exhaust port.

Where:- EXD is effective diameter, mm Width is port width, mm Height is port height, mm

Constants

The values for k ₁ and k ₂ are ranges depending on the type of engine (enduro, motorcross or road racing) and if broadly tuned or high specific output. k ₁ ranges from 1.05 for a high specific output road racing engine to 1.125 for a broadly tuned enduro engine. k ₂ ranges from 2.125 for a broadly tuned enduro to 3.25 for a high specific output road racing engine.

 
 

 

These constants have been interpolated from the following table.

 
 

Engine	BMEP, Bar	K 0	K 1	K 2
Enduro	8	0.7	1.125	2.25
Motocross	9-10	0.65
Grand Prix Racer	11+	0.6	1.05	3.25

Two Stage Diffuser Expansion Chamber Dimension Calculation

A diagram of a typical two-stage diffuser expansion chamber is shown above. Note that the length of the header pipe section LP01 includes the length of the exhaust port, i.e. LP01 is measured from the piston face.

Dimension Calculation Two Stage Diffuser

The following table gives the dimension for the two-stage diffuser expansion chamber section diameters.

D 1 = K 1 .EXD
D 3 = K 2 .EXD	D 4 = K 0 .EXD

The next table gives the dimensions for the two stage diffuser expansion chamber section lengths.

A diagram of a typical three-stage diffuser expansion chamber is shown above. Note that the length of the header pipe section LP01 includes the length of the exhaust port, i.e. LP01 is measured from the piston face.

Dimension Calculation Three Stage Diffuser

The following table gives the dimension for the three-stage diffuser expansion chamber section diameters.

D 1 = K 1 .EXD
D 4 = K 2 .EXD	D 5 = K 0 .EXD

Notice that two extra parameters are required for diameter calculation. These are given next.

Notice also that an extra coefficient has been introduced. This coefficient K_h is called the horn coefficient, with typical values between one and two. Small values of K_h are best suited to Grand Prix engines with narrow power bands, larger values are for wider more flexible engines.

The next table gives the dimensions for the three-stage diffuser expansion chamber section lengths.

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