Fig. 2.7 has lines of constant AK expressed as
2.5 Illustration of unsteady gas flow into and out of a cylinder
2.5.1 Simulation of exhaust outflow with Prog.2.1, EXHAUST
For most of the simulations which are described the following common data values are used:
cylinder pressure, 1.7 bar; cylinder temperature, 500°C;
cylinder volume, 300 cc; cyclic speed, 6000 rev/min;
maximum port diameter, 22.4 mm; pipe diameter, 25 mm;
pipe length, 250 mm; total port opening period, 100s crank angle.
Any change of data value, from any of the numbers above, will be indicated in the text at that juncture.
As with the example given in Sect. 2.3.3, it is the cylinder temperature and the isentropic pressure ratio between the cylinder and the reference pressure which control the pipe reference temperature, Tref. It can be seen in Fig. 2.16 that this is predicted as 394aC.
The several effects which can be observed from the EXHAUST program will be discussed below.
(a) Calculation stopped on cycle number 1 at 21.49 crank angle
This is shown in Fig. 2.16. The calculation has been stopped at 21.4a crank angle, and the cylinder pressure is observed to have fallen, the port has commenced opening and an exhaust pulse has been created. The front of the exhaust pulse has reached the open end and an expansion wave reflection has been created. The superposition pressure along the pipe dips sharply towards the open end, for the criterion is that the superposition pressure ratio in the plane of the open end is unity (see Eq. 2.3.6).
The gas particles are being impelled towards the open end and further moved in that direction by the suction reflection. The cylinder mass has already dropped by 4.6%.
(b) Calculation stopped on cycle number 1 at 34.5° crank angle
This is shown in Fig. 2.17. At this point the cylinder pressure is still falling rapidly and the cylinder now contains 88.1% of its original contents after the passage of 34.5° crank angle at 6000 cycles per minute. The time which has passed is just (34.5*60)/(360*6000) seconds or 0.96 ms. The exhaust pulse is past its peak amplitude and the front of the suction reflection has just arrived at the exhaust port.
The suction reflection is due to get stronger at the exhaust port as the expansion wave deepens with time. The gas particle velocity is seen to be increasing towards the pipe
1 5
1 0
0.5
TOTAL PRESSURE RATIO ALONG PIPE
.NOTE FALLING PRESSURE ALONG PIPE y DUE TO SUPERPOSITION
1.5
GAS PARTICLE MACH NUMBER NOTE RISING MACK NO DUE TO 0 5 /SUPERPOSITION >" "
0.5 1.5 H
.0
X
OUTWARDS PULSE PRESSURE RATIO
\ EXHAUST PULSE PROFILE ALONG PIPE VIRTUALLY CONSTANT
INWARDS PULSE PRESSURE RATIO
SUCTION REFLECTION RETURNED / T O EXHAUST PORT
1.5
1.0
0 5
PORT OPENED FURTHER 0.5 -
CVLINDER PRESSURE AND PORT PRESSURE /CYLINDER PRESSURE STILL FALLING
EXHAUST PULSE PRESSURE PAST THE PEAK
\
+ -+-
360 deg CRANKANGLE
-+-
EXHAUST PORT DUE TO SHUT AT 1002 IN THIS PARTICULAR CALCULATION
CYCLE N0.= 1 CRANKANGLE= 34.5 CYLINDER MASS RATI0=0.8B1 EXHAUST TEMP.=394.
Fig. 2.17 The expansion wave reflection returns to the exhaust port to assist scavenging.
exit where the strong suction pulse is accelerating the flow. The exhaust pulse profile along the pipe is virtually constant, but the superposition pressure profile is seen to fall towards the open end. The exhaust port is still not yet fully open; that will occur in this calculation data set at 50s crank angle.
(c) Calculation stopped on cycle number 1 at 88.3° crank angle
This is shown in Fig. 2.18. The effect of the suction reflection is now evident.
The cylinder pressure has been dragged below the atmospheric pressure and the CMR value is 0.625. The cylinder has been emptied of 37.5% of the original mass contents. The port is due to shut in 11.7° crank angle, so the suction reflection peak at the exhaust port is being reflected off this partially closed end as another expansion wave. It can be seen being propagated outward and following on the tail of the original exhaust compression pulse. The gas particle velocity profile along the pipe is still outward.
TOTAL PRESSURE RATIO ALONG PIPE
SUPERPOSITION PRESSURE PROFILE
COMPOSED OF 'INWARDS' AND 'OUTWARDS' VALUES
0.5
I
GAS PARTICLE MACH NUMBERCYLINDER HAS EMPTIED 37.555 ORIGINAL MASS CONTENTS
0.5 / CTLIIU>t
OF ORIG
0.5
J X
•5H
\
OUTWARDS PULSE PRESSURE RATIO
FRONT OF SUCTION REFLECTION
TRAVELLING TOWARDS TAIL OF ORIGINAL THE OPEN PIPE E N D . EXHAUST PULSE
INWARDS PULSE PRESSURE RATIO
NOTE PEAK OF SUCTION REFLECTION AT PORT
EXHAUST PORT SHUTTING 0 . 5 .
CYLINDER PRESSURE AND PORT PRESSURE
OF ORIGINAL EXHAUST PULSE
CYLINDER PRESSURE REDUCED BELOW ATMOSPHERIC 3 6 0 d e a CR A N K A N G L E
Z ZL i
HAS NOW RETURNED AS A PEAK REFLECTION
CYCLE N0.= 1 CRANKANGLEr 68.3 CYLINDER MASS RATI0=0.625 EXHAUST TEMP.=394.
Fig. 2.18 Expansion wave reflection has pulled cylinder pressure below atmospheric pressure.
(d) Calculation stopped on cycle number 2 at 360s crank angle
This is shown in Fig. 2.20, for the pipe length of 250 mm, where the pressure crank-angle diagram has been extracted and plotted with others of differing pipe length, to be discussed later. To continue with the sequence for the 250 mm pipe length, it can be seen that the final CMR value of 0.62 was lower than at 88.3s in (c).
After the port has shut, the pressure wave is reflected to and fro between the open and closed ends of the pipe, changing its type from compression to expansion, or vice-versa, at each open ended reflection. Indeed, the pipe is traversed eight times by such reflections before the next cycle commences.The cylinder pressure remains constant at its "trapping" condition until the next cycle commences, when its mass contents and state conditions are "miraculously" restored mathematically.
Chapter 2 - Gas Flow Through Two-Stroke Engines (e) Effect of residual pressure waves on the exhaust process
The first cycle allowed the exhaust pulse to proceed into a pipe with no residual pressure waves present, i.e., the 9 and 6 values at the eight meshes in the pipe were all unity at the start of cycle number 1. This will not be the case at the start of cycle number 2, when all of the 3 and R values at the mesh points will have values other than unity. That this has an effect on the exhaust process can be observed in Fig.
2.19, for a calculation for a pipe length of 400 mm, all other data being common with the original data set. The first cycle leaves a residual compression wave at the exhaust port as it opens on the second cycle, and this changes the exhaust port pressure-crank angle history on cycle number 2. It is not a major change, but the CMR value is altered from 0.677 to 0.672 on cycle number 2 and to 0.671 on cycle number 3. Thus, all cycles after the second are more or less the same. In all subsequent calculations, to demonstrate the effects of changing various parameters, the results of the second cycle will be quoted and displayed.
1.5
1.0
0 5
l*PIPELENGTH=400 mml
CYLINDER PRESSURE AND PORT PRESSURE
THIS RESIDUAL REFLECTION COMBINES VITH _NEV EXHAUST PULSE
360 deg CRANKANGLE -t-
CYCLEN0.= 1 CRANKANGLE=358.5 CYLINDER MASS RATI0=0.677 EXHAUST TEMP.=394 1.5
NEY EXHAUST PULSE HAS
/DIFFERENT PROFILE CYLINDER PRESSURE AND PORT PRESSURE
THIS RESIDUAL REFLECTION IS IDENTICAL VITH THAT ON FIRST CYCLE
60 deg CRANKANGLE
NEV TRAPPED PRESSURE IS LOVER THAN ON FIRST CYCLE AS IS CYLINDER MASS CONTENTSv
CYCLE NO.=2 CRANKANGLE=359.7 CYLINDER MASS RATI0=0.672 EXHAUST TEMP.=394.
1 5 ' ^ CYLINDER PRESSURE AND PORT PRESSURE
/- 360 deg CRANKANGLE
THIRD CYCLE ALMOST IDENTICAL TO SECOND CYCLE
0.5-|
CYCLE N0.=3 CRANKANGLE=359.0 CYLINDER MASS RATI0=0.67 1 EXHAUST TEMP.=394.
Fig. 2.19 Three individual cycles of a calculation showing that residual effects are important.
(f) The effect of changing pipe length at the same cyclic speed
Fig. 2.20 illustrates the cylinder and pipe pressures for various pipe lengths from 150 to 400 mm, all other data values being common with the original data set. It will be observed that this has a marked effect on the cylinder mass ratio and on the pressure diagrams. The lowest CMR value is for a pipe length of 200 mm. This effect will also be seen in the value of trapping pressure, the lowest pressure giving the lowest CMR value. The number and amplitude of the residual reflections is also greatly influenced by pipe length. It will also be observed that the reflections decay in amplitude with each succeeding reflection. This is caused more from the reflection of an expansion wave at an open end of a plain pipe, where a contraction coefficient of 0.6 applies to the particle inflow, than it does from any friction effects
along the pipe. In fact, the friction factor, f, in the calculation is set at zero, as Blair and Goulburn(2.14) showed that a value between 0 and 0.004 would be applicable for smooth pipes. The reason for this is that the mathematical interpolation action within the program for the d and 8 values also gives an apparent diminution to the wave amplitude in a manner similar to a friction effect.
(g) Effect of cyclic speed on cylinder and pipe pressure-time histories This is demonstrated in Fig. 2.21 for the original data set, but with the cyclic speed varied from 2500 to 6000 cycles per minute. The effect is not dissimilar to changing pipe length at a common cyclic speed. For the pipe length of 250 mm, it can be seen that the cylinder is most effectively emptied at 5000 cycles per minute and the least effective speed is at 2500 cycles per minute. All of the pressure diagrams in Fig. 2.21 are for the second cycle of the calculation. The attenuation of the multiple reflections between the open and closed ends of the straight pipe is most evident at the lowest cyclic speed of 2500 cpm.
Perhaps more importantly, the reason for the poor cylinder emptying at the lower speeds is because a compression wave reflection arrives at the exhaust port and blocks it, gas-dynamically speaking. At 2500 cpm, the suction wave arrives too early, pulls the cylinder pressure below atmospheric pressure at about the peak port opening period, and the CMR value at that point is about 0.6. However, the ensuing reflection of that suction pulse as a compression wave at the open end is able to return and repack some of the cylinder mass contents. This is the first indication of anexhaust tuning action which would have a double benefit for a two-stroke engine.
At the higher speeds, the action of the exhaust pipe assists with cylinder emptying and the scavenge process, if one had taken place in this simulation. In this case, the continued extraction of any fresh charge of air and fuel would impair the value of mass trapped and the resulting BMEP attained, as discussed in Sect. 1.0. However, inthe 2500 cpm simulation, the suction pulse would arrive early, assist with cylinder emptying and the scavenge process, whereupon the subsequent blocking of the exhaust port by the later compression wave reflection would greatly assist the retention of any fresh charge of air and fuel within the cylinder. This action is known as"plugging" the exhaust port. Early racing two-stroke engines had short, straight, parallel exhaust pipes about 300 mm long for this very purpose.
360 deg
60 deg
360 deg
360 deg
360 deg
Fig. 2.20 Effect of pipe length on unsteady gas flow at the same cyclic speed.
In the 1930's the effects just discussed were advocated by Kadenacy, but without the benefit of knowledge of the behavior of pressure waves in the ducts of engines.
Kadenacy, who held patents(2.21) on tuned exhaust pipes and diffusers attached to engines, attributed the enhanced cylinder pressure drop to the kinetic energy of the
"outrushing gases extracting cylinder gas." It was Giffen(2.22), an Ulsterman, as were Kelvin and Reynolds, who showed in a classic paper in 1940 that the Kadenacy phenomenon was due to pressure wave action. In later years, the tuned expansion chamber was invented to enhance this effect, which will be discussed in detail in Chapters 5 and 6.
Fig. 2.21 Effect of cyclic speed on cylinder and exhaust pressure records.
(h) Effectiveness of cylinder emptying without an exhaust pipe
Yet another important question can be answered regarding the effectiveness of cylinder emptying: If the pipe were so long that there were no wave reflections, or so short that the discharge took place directly to the atmosphere, would the cylinder be more, or less, effectively emptied? With the computer program that question is easily answered by mathematically instructing the meshes that all 6 values are unity.
The result of this for the original data set is shown in brief for two cyclic speeds in Fig. 2.22 and in graphic form in Fig. 2.23.
Chapter 2 - Gas Flow Through Two-Stroke Engines
^CYLINDER
0.5 H
6 0 0 0 RPM
CVLINDER MASS R A T I 0 = 0 . 7 4 1 CYLINDER P, atm=1.1 1 3 6 0 deg -f
EXHAUST TEMP. 3C=394.
2 5 0 0 RPM
CYLINDER MASS RATICbO.688 CYLINDER P, a t m = 1 . 0 1 3 6 0 deg
•+• •+-
EXHAUST TEMP e c = 3 9 4 .
Fig. 2.22 Effect of cylinder blowdown into a pipe with no wave reflections.
0.8
|
| 0.7
<
V) V)
<
z
0.6 A5-
0.5
PIPE WITH NO VAVE REFLECTIONS
2 5 0 mm LONG PLAIN OPEN PIPE
-n- 2 5 0 M M PIPE -m- VERY LONG PIPE
1 1 1 1 • 1 1 - ~r
2000 3000 4000 5000 6000 EXHAUST CYCLE R A T E , CPM
7000
Fig. 2.23 Effect on cylinder mass of pressure waves in an exhaust pipe.
In Fig. 2.22, the second calculation cycle for both 6000 and 2500 cpm is shown.
As might be expected, the cylinder pressure decays more closely to atmospheric pressure at the lowest possible cyclic speed when there is the longest time available for outflow in each cycle. At 6000 cpm, the cylinder pressure ratio has fallen to 1.11 atm by exhaust closing, whereas it has fallen to 1.01 atm at 2500 cpm. The result of carrying out this calculation for the range of cyclic speeds used (2500 to 6000 cpm) and comparing it with the equivalent situation where the pressure waves are propagating in the 250 mm pipe (as shown in Fig. 2.21), is shown in Fig. 2.23 in a graphic format. Apart from the 2500 cpm situation previously discussed, the 250 mm pipe is substantially more effective as a means of emptying the cylinder than either a "zero length" pipe or a "very long pipe" where reflections could not return in time to influence the exhaust process.
(i) Effect of throttling the exit of an exhaust pipe
Although it might seem to be a means of decreasing the effectiveness of emptying a cylinder, throttling an exhaust pipe is exactly what is done by attaching a turbocharger to it. A preliminary discussion of that has already taken place in Sect.
1.2.4. Although the simulation by Prog.2.1 does not include the scavenging of the cylinder by the compressor, the effect on the restriction of the exhaust flow can be simulated by assigning throttling diameters at the very end of the pipe and replacing the normal boundary condition of outflow to atmosphere by one of inflow through a restricted "pipe entrance" to another cylinder at atmospheric pressure. The Prog.2.1, EXHAUST, does not have this facility built in, but the interested reader may care to alter the software to carry out this calculation, thereby creating a new program as a tutorial exercise. In the software ProgLists.2.2 and 2.3, the appropriate lines have been indicated by REMinder statements.
In Fig. 2.24 the results of altering the pipe exit diameter in stages from the original data value of 25 mm to 12.5 mm are shown. As in the original data set, all of the calculations are conducted at 6000 cpm. The top graph is the original data set solution and is identical to that given previously as the top graph in Fig. 2.21. As the pipe exit is progressively restricted to 12.5 mm diameter, it can be observed that the suction reflections are progressively eliminated until the pipe end reflection criteria is almost one of neutrality! At the smallest pipe exit diameter of 12.5 mm, the main suction reflection is replaced by one of compression which opposes outflow during the closing period of the exhaust port. Any further restriction would result in increasingly larger compression wave reflections. The smallest value used here, where the exit diameter is half the pipe diameter, or a pipe exit area ratio of 0.25, corresponds to the normally acceptable restriction area ratio of the nozzle ring of a turbocharger(2.23). It will be observed that the cylinder pressure would only fall to 1.2 atm with this pipe exit area ratio of 0.25. Consequently, if one wished to scavenge this cylinder with a turbo-blower, one would need a compressor with an air supply pressure ratio of at least 1.5 atm to force a reasonable quantity of air through it during any scavenge period. Having done so, however, the high back- pressure provided by the restriction due to the turbine nozzle ring would ensure a high trapped mass characteristic within the cylinder; this would lead directly to a high IMEP and power output.
Chapter 2 - Gas Flow Through Two-Stroke Engines
CYLINDER
250 MM LONG 025 PLAIN PIPE
CYLINDER MASS RATI0=0.620 CYLINDER P, atm=0.87 360 deg
250 MM LONG 025 PIPE WITH 0 2 0 EXIT
CYLINDER MASS RATI0=0.662 CYLINDER P, atm=0.95 360 deg
^
• ^ X X^>,
250 MM LONG 025 PIPE WITH 015 EXIT
CYLINDER MASS RATI0=0.740 CYLINDER P, atm=1.1 I 360 deg
250 MM LONG 025 PIPE WITH 012.5 EXIT
CYLINDER MASS RATI0=0.782 CYLINDER P, atrn= 1.20 360 deg 4-
Fig. 2.24 Effect of restricting the outlet of an exhaust pipe to the atmosphere.
2.5.2 Simulation of "crankcase" inflow with Prog.2.2, INDUCTION For the simulations which are described using Prog.2.2, INDUCTION, the following common data values are used:
cylinder pressure, 0.6 bar; cylinder temperature, 50SC;
cylinder volume, 500 cc; cyclic speed, 6000 rev/min;
maximum port diameter, 27 mm; pipe diameter, 30 mm;
pipe length, 250 mm; total port opening period, 180s crank angle;
pipe reference temperature, 25SC; pipe end is "bellmouth" type.
Any change of data value from any of the numbers above will be indicated in the following subsections of the text.
As with the inflow example given in Sect. 2.3.3, the pipe reference temperature, Tref, must be supplied as an input data value. This is normally the atmospheric temperature, To, or a value denoting some temperature drop into the pipe due to inflow from the atmosphere. It can also be a value representing some pipe wall heating effects, such as the case with a "hot-spot" in the intake manifold of a car engine; this latter effect is virtually incalculable(2.18) with any degree of confi- dence. In any event, the pipe reference pressure is clearly the atmospheric pressure, Po.
The Basic Design of Two-Stroke Engines
The several effects which can be observed from the INDUCTION program will be discussed below.
(a) Calculation stopped on cycle number 1 at 20.32 crank angle
In Fig. 2.25, the expansion wave created by the sub-atmospheric cylinder pressure is seen to be propagating towards the bellmouth end of the pipe to the atmosphere. The calculation has been stopped at an interesting point on the first cycle, for the front of the wave has not quite reached the open end. In the last two mesh points on the gas particle velocity diagram, the arrows indicating direction are still at the default undisturbed condition of zero velocity and pointing rightwards.
In the remainder of the pipe the particle velocity is observed to be accelerating towards the port. In the lower diagram of pressure against crank angle, the cylinder pressure is already rising from the starting pressure of 0.6 bar, and the creation of a suction pressure wave as a function of time is observed. As the wave has not yet reached the open end, there are no reflections thus far, so the "inward pulse pressure ratio" diagram is seen to register an undisturbed set of values. Hence the "superposi- tion pressure" diagram and the "outward pulse pressure ratio" diagram are identical.
1 5
1 0
« 0.5
I
TOTAL PRESSURE RATIO ALONG PIPE
SUPERPOSITION PRESSURE AND OUTWARDS PRESSURE PROFILE AS THERE IS NO INWARDS PULSE ON THIS FIRST CYCLE AT THIS POINT
GAS PARTICLE MACH NUMBER
-•—CYLINDER STARTS TO FILL WITH AIR PARTICLES MOVE INWARDS 'TOWARDS CYLINDER
0 5
WAVE NOT YET ARRIVED
1.0
0.5 1.5 -
OUTWARDS PULSE PRESSURE RATIO
FRONT OF SUCTION PULSE PROPAGATES TOWARDS OPEN END '
\
INWARDS PULSE PRESSURE RATIO
1.0
0.5
INTAKE PORT OPENING 0 . 5 J
CYLINDER PRESSURE AND PORT PRESSURE
^ T
360 deg CRANKANGLE
-+-
" SUCTION PULSE CREATED
"CYLINDER PRESSURE SUB-ATMOSPHERIC
CYCLE NO.= 1 CRANKANGLE= 20.3 CYLINDER MASS RATI0=0.547 CYLINDER P, atm=0.6 1
Fig. 2.25 Creation of an expansion wave in a pipe from a sub-atmospheric cylinder pressure.
(b) Calculation stopped on cycle number 1 at 40.1s crank angle
In Fig. 2.26, the calculation is stopped at a juncture where the front of the expansion wave reflection from the bellmouth open end is returning towards the cylinder port. It is a compression wave, as Sect. 2.3.2 would have predicted, and is colloquially referred to as a "ramming" wave. The effect is to increase the gas particle velocity in the pipe as a superposition of the inward compression and the outward expansion pressure waves. The result is the more rapid filling of the cylinder with air and this effect will be recorded by both cylinder pressure and the cylinder mass ratio, CMR.
1.5
0.5
I
TOTAL PRESSURE RATIO ALONG PIPE 1.5
1.0
GAS PARTICLE MACH NUMBER
COMPRESSION REFLECTION CARRIES 0 5 PARTICLES IN SAME DIRECTION AS ORIGINAL SUCTION PULSE \
0.5 1.5
OUTWARDS PULSE PRESSURE RATIO
INWARDS PULSE PRESSURE RATIO
/
FRONT OF COMPRESSION REFLECTION MOVES TOWARDS THE CYLINDER
1.0
0.5 -
\ PORT IS NOT YET WIDE OPEN 0 . 5 .
CYLINDER PRESSURE AND PORT PRESSURE
360 deg CRANKANGLE
CYLINDER PRESSURE RISES TOWARDS ATMOSPHERIC AS CYLINDER FILLS
CYCLE N0.= 1 CRANKANGLE; 40.1 CYLINDER MASS RATI0=0.575 CYLINDER P, atm=0.66 /
Fig. 2.26 Ramming reflection created at bellmouth open end enhances airflow to the cylinder.
(c) Calculation stopped on cycle number 1 at 90.5s crank angle
In Fig. 2.27, the calculation is stopped at a juncture where the port is virtually fully open and the ramming process is at its peak with this combination of pipe length at 250 mm and induction process cycling rate of 6000 cpm. The cylinder pressure has almost risen to the atmospheric value in the short space of 1/400 second, which is the highest it could ever rise in any steady flow process conducted over an "infinite" time period so that the cylinder and the atmospheric pressures are allowed to equalize. The suction pulse and the compression wave reflection fill the