Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two'Stroke Engines
Also, contained within the solution of the First Law of Thermodynamics for outflow
from the cylinder to the throat, in Eq. 2.16.10, is a direct solution for the pressure ratio from
the cylinder to the throat. The combination of Eqs. 2.16.10 and 2.16.12 provides:
G5{(a0iX1) 2 -(a01Xt) 2 }-(a01Xt) 2 =0
Consequently, or
Pi
, NG35
y+ 1
(2.16.13)
The pressure ratio from the cylinder to the throat where the flow at the throat is choked,
i.e., where the Mach number at the throat is unity, is known as "the critical pressure ratio." Its
deduction is also to be found in many standard texts on thermodynamics or gas dynamics. It is
applicable only if the upstream particle velocity is considered to be zero. Consequently it is
not a universal "law" and its application must be used only where the thermodynamic assumptions
used in its creation are relevant. For example, it is not employed in either Sees.
2.12.1 or 2.17.1.
This simplifies the entire procedure because it gives a direct solution for two of the unknowns
and replaces two of the four equations employed above for the subsonic solution. It is
probably easier and more accurate from an arithmetic standpoint to eliminate the momentum
equation, use the continuity and the First Law of Eqs. 2.16.8 and 2.16.9, but it is more accurate
thermodynamically to retain it!
The acquisition of all related data for pressure, density, particle velocity and mass flow
rate at both superposition stations and at the throat follows directly from the solution of the
two polynomials for Xr2 and ao2-
2.16.2 Numerical examples of outflow from a cylinder
The application of the above theory is illustrated by the calculation of outflow from a
cylinder using the data given in Table 2.16.1. The nomenclature for the data is consistent with
the theory and the associated sketch in Fig. 2.17. The units of the data, if inconsistent with
strict SI units, is indicated in the several tables. The calculation output is shown in Tables
2.16.2 and 2.16.3.
Table 2.16.1 Input data to calculations of outflow from a cylinder
No.
1
2
3
4
5
Pi
5.0
5.0
1.8
1.8
1.8
1"! °C
1000
1000
500
500
500
ni
0.0
1.0
0.0
0.0
0.0
dt mm
3
3
25
25
25
133
d2 mm
30
30
30
30
30
cd
0.9
0.9
0.75
0.75
0.75
Pi2
1.0
1.0
1.0
1.1
0.9
n2
0.0
1.0
0.0
0.0
0.0