98
Discharge of Exhaust Gases in Two-stroke Engines
By J. H. Weaving, Ph.D., B.Sc. (Eng.), Wh.Sc., A.M.I.Mech.E.*
The paper points out that the two-stroke engine still has a field of great importance, i.e. the compression-ignition engine, and that, although the two-stroke cycle has been known for so long, the
theory of the discharge of exhaust gases from the cylinder is still in doubt, and some of the generally
accepted assumptions have been challenged in recent years, in particular by Kadenacy.
A description is given of apparatus built at the Engineering Laboratories, University of Cambridge,
to simulate the discharge portion of the cycle only. This apparatus utilizes the gases nitrogen and
hydrogen under compression, these being respectively denser and less dense than exhaust gases.
Experiments were made to ascertain whether the older theories were valid, and to investigate the
claims of Kadenacy of supersonic discharge and resultant vacuum pressures in the cylinder. These
tests demonstrated that the older theories, based on the assumption of steady flow and Bernoulli’s
theory, were substantiated, provided that modifications were made to the index of expansion and the
coefficient of discharge.
Finally, a simplified system is derived for the calculation of the size of exhaust ports or valves, and
this system is applied to a practical case.
INTRODUCTION
Almost from the original conception of a practical internal combustion engine, a long struggle for supremacy has been waged
between the two- and four-stroke cycles; so far, the four-stroke
has had the best of it, with some notable exceptions in certain
fields such as motor ships and the Junkers aero-engine. However,
there is considerable indication that the two-stroke is now pushing itself to the fore.
The great restraint in the past has been the limited field of
usefulness for such an engine. The greater demand has been for
petrol carburettor engines, in which class the two-stroke cannot
hope to compete owing to the necessity of a large port overlap
for scavenging, which results in the inevitable short-circuiting
to exhaust of a definite proportion of the inlet charge, and hence
a considerable waste of fuel.
In the Diesel or compression-ignition field, however, where
injection is essential, the two-stroke has no such disadvantage,
and it is in this sphere in particular that its inherent advantage
of power/weight ratio is very desirable, as a compressionignition engine is essentially heavy; also, its even torque is no
mean advantage with regard to vibration smoothness. The
advent of petrol injection suggests a further field for the twostroke.
The ideal in two-stroke design is to get twice the power of a
four-stroke of the same capacity, but the problem is to get a high
brake mean effective pressure at high engine speeds without
using an excessive supercharger pressure, which is expensive in
fuel.
A typical example of modem practice will indicate the
difficulties. In General Motors two-stroke engines (Gas and Oil
Power 1945t)the valve timing is as follows :Exhaust opens 79 deg. before bottom dead centre.
Inlet opens
51 deg. before
,, JY Y,
Exhaust closes 51 deg. after
,, J J JY
Inlet closes
51 deg. after
,, JY ,,
The maximum governed speed is 2,000 r.p.m.
Thus there is a period of 130 crankshaft degrees or, at 2,000
r.p.m., about & second for exhausting, scavenging, and
recharging the cylinder. It is clear, therefore, that the port
areas must be designed with the greatest accuracy; the matter is
far more critical than with four-stroke designs and, in fact, is the
The MS. of this paper was originally received at the Institution on
15th May 1947, and in its revised form, as accepted by the Council
for publication, on 12th February 1948.
* Development Engineer, Austin Motor Company, Ltd., Birmingham.
t An alphabetical list of references is given in Appendix 11, p. 110.
key to n successfulengine. Each of these three processes (exhausting, scavenging, and recharging the cylinder) is quite complex,
but it is not proposed to deal with the latter two, as the theory
underlying them is not disputed.
Calculations giving formulae for port design have been made
by Bird (1923) and by Magg (1928); no experimental evidence,
however, was available to show that the assumptions made were
valid, and in recent years these assumptions have been challenged
by Kadenacy (1936) as inapplicable to the practical case. To
endeavdur to clarify the situation, and to establish equations for
the calculation of the port area required for the exhaust process,
the experiments to be described were carried out at the University
Engineering Laboratories, Cambridge.
The main assumption in Bird’s calculations is that the equations for continuous gaseous fluid flow from a source of high
pressure to a region of lower pressure, through an orifice or
nozzle, apply to this transient phenomenon lasting only about
second. It is by no means obvious that this period of time
is sufficient for such steady conditions to be set up, and the
checking of this was one of the main objects for which the
apparatus described below was designed. A second object of
investigation was to find out whether rapid discharge left a
vacuum pressure in the cylinder, as was alleged by Kadenacy.
EXPERIMENTS TO ASCERTAIN L A W S GOVERNING
D I S C H A R G E OF E X H A U S T GAS
Descl-iption of Apparatus. The main object was to reproduce,
as nearly as possible in a single-cycle apparatus in which accurate
measurements could be made, that part of the two-stroke cycle
during which the exhaust gas is being discharged. In an actual
engine it is diacult to obtain precision measurements of the low
pressures during this part of the cycle with an indicator that must
stand the stress of combustion temperatures and pressures; both
these factors were eliminated in the apparatus to be described.
This consists essentially of a cylinder containing a series of ports,
which may be opened and closed by means of a sleeve running
inside the cylinder. The cylinder is initially charged with a gas
at room temperature to a pressure of about that prevailing at
exhaust opening in an engine (60 lb. per sq. in. gauge), and the
ports are allowed to open and close.
Expansion from room temperature not only makes easier the
measurement of the pressure by means of an electronic indicator,
but also is almost a fundamental necessity for the establishment
of experimental proof for any theory; this is because present
technique will not enable the accurate measurement of the
instantaneous temperature of the gas in the cylinder of an engine
at the position of port opening, and thus the complete thermo-
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D I S C H A R G E O F E X H A U S T GASES I N T W O - S T R O K E E N G I N E S
99
The apparatus is used with its axis vertical and loading screw
dynamic state of the gas is unknown. In Carter’s (1946)paper,
where actual and theoretical pressure drops are plotted, a value downwards, the lower part being filled with oil. This reduces
must have been assumed for this temperature or density, so that the volume of the enclosed space for the gas, so that a large
the graph of pressure drop, though evidence, cannot be regarded ratio of port area to volume can be obtained while the springs
as substantiating the older theory or that of GifFen (1940), the are still kept within the cylinder, as any control of the sleeve
through a gland would reduce its speed considerably. But a more
results of the application of which are also plotted.
With this apparatus the initial and final states of the gas may important consideration-in fact the reason springs were used
be measured with static instruments. Thus the actual discharge in preference to a connecting rod and crank-is that with any
from the cylinder when the ports are opened and closed can be form of glanding there is a likelihood of leak which would
measured to a high order of accuracy, and when a pressure introduce a serious error difficult to estimate.
The use of oil provides other advantages; it allows the volume,
record of the expansion has been obtained, together with the
index of expansion, the complete state of the gas is known at all and hence the port area/volume ratio, to be easily varied. It
PRESSURE UNIT
8
I0
12 INCHES
POWER PACK AND VOLTAGE STABILIZER
ELECTRONIC PRESSURE INDICATOR
ARGE CYLINDE
MINATE PORTS
Fig. 1. Discharge Apparatus
Cross-section through cylinder, cross-section through ports, X-X, and general layout.
points in the cycle. I t is a further convenience that there is no
change in volume of the cylinder due to the movement of the
sleeve.
It may be objected that as the gas is at room temperature the
conditions are not similar to engine conditions. This, however,
is not important, as the question is one of fluid flow and not of
molecular diffusion, and thus density and not temperature is the
vital factor. Temperature only affects the viscosity-a second
order effect (Reynolds number being approximately 4 x 105)
which may be ignored. At room temperature hydrogen has a
density considerably less than exhaust gas at engine temperature,
and with its use conditions of an even more extreme nature than
in an actual engine may be obtained, as the discharge velocity is
almost double with t h i s gas.
The apparatus, which is shown in Fig. 1 and also in Fig. 2,
Plate 1, consists of a brass cylinder A in which runs a ground
steel sleeve B. Both the cylinder and the sleeve are provided with
a set of eight ports which coincide at a certain position of the
sleeve in the cylinder, and eight tension springs E actuate the
sleeve at high speed. The square-threaded shaft G serves two
purposes : to extend and vary the tension in the springs, and to
return the sleeve to its initial position at the top of the cylinder.
The sleeve is held in position at the top of the cylinder by two
catches H and may be released by a small angular movement of
shaft K through a gland from the outside.
I n order to bring the sleeve smoothly to rest, a stop is provided
in the form of a piece of bright-drawn Steel tube F which is
perforated with +inch diameter holes. End plates in this tube F
serve to hold, at one end, a piece of fibre packing D to prevent
damage to the working sleeve, and, at the other end, a base J to
buffer against four compression springs L to absorb the shock.
A considerablepart of the momentum of the sleeve is transferred
to the stop and the two move on together, being further retarded
by viscous drag, until they hit the buffer springs L.
eliminates the comparatively restricted volume at the lower end
of the apparatus and it also provides excellent damping to bring
the sleeve to rest.
Fig. 1, showing the sleeve in its initial position, conveys the
impression that the gas may be partially restricted; but as flow
only occurs while the ports are open, t h i s is the only position
of importance. When a volume of 1,000 cu. cm. is used (as in
most of the tests) the springs are almost completely submerged
in the oil, and the enclosed volume is practically free from any
obstructions.
Various accessories are fitted, including pressure gauge
(Bourdon type) in base N, mercury thermometer, and an
attachment for a mercury manometer in head C.
The rate at which the ports open and close, and hence their
time-area and the total time of opening, is obtained by photographing one of the ports with a special camera, consisting of a
drum holding highly sensitized recording paper and revolved at
1,500 r.p.m. precisely by a synchronous motor. The lens (a
telescope objective) is of long focal length in order that it may
be placed at a long distance (1 metre) from the ports, to avoid
interference or choking of the escaping gas (see Fig. 1).
The port is brightly illuminated by a slightly divergent beam
from a “Pointolite” arc-lamp and condenser system through
an opposite port, the lantern and both sets of ports being collinear
with the camera. Thus, with the ports fully open, an image of
one port is focused sharply on the sensitive paper; this image is
reduced in width to about inch by a mask immediatelyin front
of the paper. In operation, when the ports have opened, say,
& inch, a rectangular slit of the width of the mask and & inch
high is cast on the sensitive paper. After the ports have opened
,&s inch, a rectangular slit of the same width but pb inch high is
recorded, but in this time the paper on the revolving drum
camera has moved through a small angular distance, so a diagram
as shown in Fig. 3 is produced.
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+
100
DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
Rectangle CFBE is the instantaneous photographic record of
the port fully open, and therefore AB is the time of opening and
CD the time of closing. As FB is proportional to the total port
opening, then curve AF is the curve of opening of the port with
respect to time and, correspondingly, ED is that of closing. An
jl ljK/
A
B
E
Fig. 3. Shape of Port Timing Diagram
actual port timing photographic record is shown in Fig. 4,
Plate 1. It will be noticed from this record that the curves of
opening and closing are straight lines, i.e. the velocity of the
sleeve is constant over this period. This point is further
substantiated by the fact that the time of opening was approximately equal to the time of closing in most tests. A graph of port
area against time is thus as shown in Fig. 5.
Fig. 5. Relationship between Port Area and Time
In order to prevent a slow leakage of gas through the ports
when the cylinder is charged with compressed gas, a complete
closing is effected by two rubber-lined semi-circular wooden
shoes similar in appearance to external brake shoes; these are
hinged together on one side and are clamped round the ports
by means of a cam on the other side (see Fig. 2, Plate 1).
Arecord of the pressure in the cylinder was obtained by means
of an electronic indicator of the condenser type, in conjunction
with a cathode-ray oscilloscope. This was designed to record
static pressures as well as rapidly changing pressures, thus
enabling calibration lines to be put on a test record immediately
after discharge. Such a record is shown in Fig. 6, Plate 2, and
is described later; it will be noted that the port-timing diagram
is also photographed on the same sensitive paper. The total
length of this photographic record, and all subsequent ones,
represents second, being one revolution of the camera drum.
Method of Performing Tests. The discharge cylinder is first
filled with a thin oil, and gas (usuallynitrogen) from a compressed
gas cylinder is allowed to pass into the cylinder, displacing the oil
into a graduated flask through the cock M (Fig. 1) until the
required volume is displaced. The cock is then closed, and the
vessel charged with gas to a pressure a few lb. per sq. in. above
that from which it is proposed to release the gas. The usual pressure taken was 60 lb. per sq. in. gauge : this represents a typical
release pressure for a two-stroke compression-ignition engine.
The gas is then left for a few minutes to ensure that it has assumed
the temperature of the vessel. The port sealing device is removed
and the pressure slowly drops, owing to a slight leak through the
ports; this slow drop is indicated by the width of the top line
in Fig. 6, a typical test.
The sleeve is then released, the pressure being noted on a
Bourdon gauge. Immediately after the expansion the port sealing
device is replaced as a precautionary measure only, the leakage
being negligible at the low pressure which remains, and the
final pressure is read with a mercury manometer. The pressure
drop is clearly indicated on the diagram, on which a horizontal
time scale at &millisecond intervals has been drawn. The final
pressure in the cylinder after port closure is represented by the
penultimate dark line on the diagram; it is dark and somewhat
blurred because the drum holding the sensitivepaper has revolved
some 3,000 times with the oscilloscope spot stationary. Calibration lines are put on the diagram by recharging the cylinder to,
say, 50 lb. per sq. in., and opening the shutter on the revolving
drum camera for a short time, this being repeated at each of
the required pressures.
The discharge was violent, the noise being of almost explosive
character. The pressure in the cylinder dropped below the final
pressure owing to the expansion of the gas in the vessel causing
the temperature to drop below that of the walls. After port
closure, heat flowed into the gas, causing the pressure to rise to
the final steady pressure. This rise is clearly recorded in Fig. 7,
Plate 2, though the wavy line occurring some 2% second after
expansion is extraneous and is due to the sleeve hitting the stop.
It was realized that an experiment had inadvertently been
performed similar to the classical experiment of Clement and
Dksonnes for the determination of y (the ratio of specific heats),
but with a very different ratio of port area to volume of vessel.
This gives a simple and accurate method of finding the index
of expansion of the gas in the vessel by substitution in Clement
and DCsormes equation (for derivation see Partington and
Shilling 1924)
where po = release pressure, p , = minimum pressure, and
p z = final pressure.
Contrary to expectations, this expansion was found not to be
adiabatic, although the time of expansion was about & second,
and as this was assumed by both Bird and Magg it was the first
step in ascertaining the true value of n.
For this purpose, a thinner diaphragm was put in the condenser pressure unit to obtain more sensitive diagrams, such as
that shown in Fig. 7. With this sensitivity the oscilloscope spot
does not start to move until the pressure in the cylinder has
dropped to about 20 Ib. per sq. in. This is why, on the diagram,
the vertical line representing port opening is some 2 milliseconds before the point where the pressure appears to drop.
From a series of such tests the index of expansion n in the
cylinder was found to be considerably less than y, and a function
of the time of expansion. The lower curve in Fig. 8 shows this
-.
o
i
8
12
io
16
TIME-MILLISECONDS
24
28
ii
36
Fig. 8. Relationship between Index of Expansion and Time
relationship, which indicates that, though the period of expansion
was short, heat was flowing into the gas; this led to investigation
of the mode of heat transfer between the gas and the vessel. It is
clearly a case of forced convection, as the gas in the vessel is
scrubbing the walls with a velocity related to the velocity through
the ports,
In forced convections :Heat transfer = K(pVs)o*8xTAt (see Schack 1933) (2j
where p = density, V = velocity of flow, s = specific heat,
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DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
T = temperature difference between gas and walls, A = surface
area scrubbed, t = time of expansion, and K = a constant.
TOverify that heat transfer was the cause of the low values
of n, tests were performed as described above but with six of
the eight ports closed off. The velocity of flow V in the vessel
(not in the ports) was thus reduced without appreciably affecting
any of the other factors in equation (2). That this was effected,
in fact, is shown by the higher value of n consistently obtained,
as shown in Fig. 8. Substitution of estimated values in equation
(2) does not, however, produce a sufficient heat transfer to account
completely for the low value of n obtained.
Regrettably, there is an absence of experimental heat transfer
values for anything but low velocities of flow, and in this case
there are velocities varying from zero to that of sound in the
different parts of the vessel. Great care was therefore taken in
measuring the three pressures in equation ( 1 ) . With the advent
of internal-combustion turbines, no doubt more information on
heat transfer at high velocities will be forthcoming. Another
factor contributing to the low value of n is heat due to the
degeneration of energy by turbulence.
From expansion pv" = c in the cylinder :(6)
If M is the mass in the cylinder at any time t ,
As the pressure in the cylinder is above the critical,
Pl
Y
-.
(for derivation see Ewald, Poschl,
and Prandtl 1936)
(3)
Thus mass discharged per unit time
= q1p1A
(4)
where p = pressure in the cylinder, A = instantaneous port
area, p = density in the cylinder, p i = pressure at the orifice,
and p1 = density at the orifice.
Differentiation of equation (4) shows that discharge becomes
a maximum when the pressure ratio is given by
. . .
. . . . .. .
= 0.53 (for a diatomic gas)
.
=
P
=
--Y'l
2
=(TjY-l
y+l
Yfl
. .
(8)
Also
= KAplal (where K is the coefficient of discharge, and
al the velocity of sound)
The theory and its assumptions will now be considered,
together with the modification necessitated by the discovery of
the non-adiabatic expansion in the vessel.
The application of Bernculli's theorem gives the following
equation for the velocity of dischargc through the ports :I
2 - y
= P(&l
(i)(-)
dM
-dt
THEORY FOR GAS DISCHARGE
101
=
KA~Z
@+I)
1
= K A , / y p f ( T ) - 2 ? p 2(z)2n
p -
-dt
=
. . . . .
(9)
--dt
dM
dMxdp
dp
Whence, from equations (7) and (9),
and, by integration,
(5)
These equations (3) and (5) for the continuous discharge of a gas
from a receiver at a pressure p to a region of pressure p i , were
derived respectively by St. Venant and Wantzel in 1839 and
Reynolds in 1886. When equation (5) is substituted in equation
(3) a velocity of discharge equal to the velocity of sound is
obtained under the prevailing port conditions. When p , is atmospheric pressure, p is termed the critical pressure, for above this
value the velocity is acoustic. These equations assume adiabatic
expansion and that Bernoulli's theorem is valid. This expansion
is not the expansion of the gas in the vessel, but the expansion
from approximately the axis of the vessel to the port or orifice.
The envelope of this expansion is stagnant gas with the exception
of the port. edges (which in these tests were very thin). The time
of the expansion is also very short, the gas having to move only
some 3 inches with the velocity of sound, so that this expansion
can be expected to be adiabatic.
Both these assumptions have been accurately verified by
Stanton's (1926) experiments on continuous discharge, and
they will now be applied to the problem in question. The p is
no longer a steady receiver pressure but is the pressure in the
cylinder dropping in accordance with the law pvn = c.
The calculations may conveniently be divided into two stages,
the first for the expansion above the critical pressure and the
second for expansion below this pressure, when the velocity of
discharge drops from acoustic to zero.
First Stage: Above Critical Pressure.
The suffix 0 denotes initial conditions in cylinder,
1 denotes conditions in port, and
2 denotes conditions in cylinder at end of expansion,
being equal to or above critical conditions.
Symbols without suffixes denote conditions in cylinder at time t .
Second Stage: Below Critical Pressure
= K A p , J ~E
Y 1P
Y-i
From equations (7) and (12),
Whence
1--3n
where
c=
&--( )
g
7-1 Po fpo
2Y Po
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'(From equation (3), p1
now atmospheric
pressure.)
{ ~- ($IT>is
102
D I S C H A R G E OF E X H A U S T G A S E S I N T W O - S T R O K E E N G I N E S
If the variable is changed for convenience,
0
. . .
6
4
10
8
12
14
t 2 (TIME IN MILLISECONDS)
(13)
The problem is to verify experimentally equations (10)and (13).
Fig. 11. Test No. 312 : Discharge of Nitrogen
EXPERIMENTAL RESULTS
Equation (10)may be simplified to
KJAdt = C l p
--n-1
2n
+dl
. . . .
(14)
where c1 and dl are constants for any particular test and p 2
becomes the variable pressure in the cylinder denoted now as p.
The apparatus was designed so that the sleeve would have its
maximum velocity when m y open, and the tests described
earlier showed that the velocity was practically constant while
the ports were open.
t’ (TIME IN MILLISECONDS)
Fig. 13. Test No. 323 : Discharge of Hydrogen
0.57
,
1
no
Fig. 9. Test No. 237 : Discharge of Nitrogen
Thus, referring to Fig. 5, it is seen that for values of t < t l
L Vt2
JAdt = J‘LVtdt = 7
0
where L = circumferential port length, V = sleeve velocity, and
t I:time.
In equation (14)
n--
1
.
K t 2 = c p 2”+d
. . . . (15)
and so plotting t 2 against p - ( n - l ) P n should give a straight line.
This relationship has been plotted for test No. 237 (Fig. 6) and
is shown in Fig. 9, values of p being read off against the time
0
10
20
30
40
50
TIME IN MILLISECONDS)
60
70
TESTl6E
Fig. 14. Tests Nos. 268 and 270 : Discharge of Argon
Test Volume, ReNo. cu. cm. lease
pressure,
1b.qei
Final
pressure,
lb. per
Minimum time,
of
of retical
pres- second expan- graph slope
sure,
sion,
sq. m. lb. per
sq. m gauge sq. m.
I
gauge
gauge
--
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-I
DISCHARGE O F EXHAUST GASES
base of half-milliseconds marked on the photographic record;
this test had a slow sleeve speed. The slope of the line gives a
value of 0.83 for the coefficient of discharge K. The record
for a fast test is shown in Fig. 10, Plate 2, and the same relationship for this test is plotted in Fig. 11, giving a coefficient of 0.81.
In order to obtain these graphs, the appropriate value of n is
read off from Fig. 8.
These tests excellently substantiate the first stage of the theory
and the legitimacy of the assumptions, but an even more exacting
IN T W O - S T R O K E ENGINES
103
of the photographic record by a suitable adjustment of the
sensitivity of the indicator. A record for such a test is shown in
Fig. 7 (test No. 291) and the graph for it is plotted in Fig. 16.
In t h i s case the port is closing, and the function of time that
should give a linear relationship becomes r,t-(t2/4) (see Appendix I), where t l = time of opening, and t = time measured
from port opening (t>tJ. The coefficient of discharge for t h i s
test is 0.64.
It is considered that these results amply verify the theory,
though the coefficient of discharge is not constant. This point
will be considered later.
S I M P L I F I C A T I O N FOR D I S C H A R G E ABOVE C R I T I C A L
PRESSURE
t L (TIME
IN MILLISECONDS)
Fig. 15. Test No. 290 : Discharge of Nitrogen below Critical
Pressure
test is shown in Fig. 12, Plate 2 (test No. 323), which is for
hydrogen having an average discharge velocity of 3,700 ft. per
sec., approximately double that of exhaust gas under engine
conditions. The graph is plotted in Fig. 13.
The graphs for two final tests, in which argon was used, are
shown in Fig. 14; here the velocity of sound is varied by the
atomicity, argon having a value of y of 1.66.
It has been observed and verified that above the critical pressure the discharge occurs with the velocity of sound under port
conditions.
Velocity = a = d$T, where R = the gas constant, and
T = the absolute temperature in the port.
Owing to the expansion taking place in the cylinder, causing
the value of T i n the port to drop, as it is related by a constant
factor to the temperature in the cylinder, this velocity will not
be constant. It may be shown, however, that the decrcase in
velocity due to this expansion is only about 10 per cent, w d
only slight error will be introduced if it is assumed to be constant
and an average value is taken. This allows the following simplified
calculation :Symbols without suffixesdenote conditions in cylinderat time t .
The suffur 0 denotes initial conditions in cylinder,
1 denotes conditions in port,
2 denotes conditions in cylinder at end of expansion,
being equal to or above critical conditions, and
3 denotes fmal conditions in cylinder.
Then, in adiabatic flow between cylinder and port,
But above critical pressure (equation (5)),
Ti = TX- 2
Therefore
Velocity in the port is
Y+l
a1 =
z/m
Initially T = To, and finally at end of expansion T = T2,
where T, is derived as follows :In expansion in vessel according to law p u n = c,
"=(z)5. . . . .
Pz
(17)
-
Also, when ports are closed, gas heats up at constant volume
and p2v2/T2= p303/T3, wherev2 03 3: volume of cylinder,
and T3 = To= room temperature.
Therefore
t,t--'4
Fig. 16. Test No. 291 :Discharge of Nitrogen below Critical
Pressure
22--3
€32
T2
.
This gives the minimum temperature in the vessel and hence
the minimum and mean velocities from equation (16).
Below the critical pressure, calculations are more complicated.
Also
Equation (13) can only be integrated graphically, and this has
been done for a test (No. 290) in which the cylinder was charged
to a pressure a little below the critical, i.e. to 13 Ib. per sq. in.
Discharge is
gauge. The graph is shown in Fig. 15.
dM = -KalplAdt
It could have been objected that this was not a true comparison
1
with actual conditions, as release pressure was never so low as 13
= -Kalp(m
2 ) y- - l x Adt
lb. per sq. in. gauge. Further tests were made, therefore, from
a release pressure of 60 lb. per sq. in. gauge, and the part
of the expansion below the critical was made to occupy most where A = area at time t, and a1 = average velocity of sound.
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D I S C H A R G E O F EXHAUST GASES I N T W O - S T R O K E E N G I N E S
104
Hence dM = -KaliM
V
X
0.633 X Adt (where M = mass in the
cylinder at time t).
Thus equation (18) becomes
p, 0.633Kal At2
log, - =
x 2
P3
V
~~
. . . .
(19)
A few tests were made to obtain the index of expansion in
the vessel, the results being shown in Fig. 17; calculations are
given in Table 1 and the final results are plotted in Fig. 18,
T o verify this simple relationship, a series of tests made with
air have been taken. In these, the lowest pressure at the end of
expansion was kept above the critical by making the release
pressure high and keeping the time of port opening short.
Fig. 18. Discharge of Air above Critical Pressure to Find
Average Value of Coefficient of Discharge
0.7 x 10-3
Slope = ___ = 0.07. J A d t = 0.00824~
10 x 10-3
Fig. 17. Discharge of Air : Relationship between Index of
Exuansion and Time
Cylinder volume = 2,000 cu. cm. ;release pressure = 100 Ib. per sq.
in. gauge.
z, log @
In the apparatus under consideration, the mass of gas at the
end of expansion was, of course, the same as when the gas was
heated up again to room temperature, so that
Mo - Mo - POVO x A
M2
M3
To P3V3
= PO
- (as oo = 213, and
P3
To = T,)
Also, ]:'Adt = +At2,where t 2 = total time of port opening,
velocity being constant (see Fig. 5).
K =
P3
~1
X 0.633JAdl
= o.95.
= 0.0706 X0.07
0.633 X 0.00824
where it will be seen that the points lie quite well on a straight
line A passing through the origin. The slope of the line gives a
coefficient of discharge of 0.95. This lineality to a great extent
shows that the approximations involved in equation (18) are
justified. However, for test No. 305 a confirmation of the actual
value of the coefficient was made by calculating with the longer
method of equation (10); &is gave a value of 0.94 as compared
with one of 0.96 from equation (19). It will be observed that if
TABLE
1. DISCHARGE
OF AIR : TESTS
TO OBTAIN
COEPPICIENR
OF DISCHARGE
ABOVE CRITICAL
PREssm
__
Test No. Index
of expansion
n
Pressure,
Ib. per sq. in.
abs.
-
116.1
116.1
116.1
116.1
116.0
116.0
116.05
116.05
116.05
116.05
116.3
116.25
116.0
116.0
116.0
115.95
115.95
75.8
I
P3
75.9
47.75
75.6
60.0
58.6
45.35
50.55
35.15
cu. ft.
Log,
P3
-
Ql
Po
P3
x 103*
Total
time of
Port
qpenL"g?
Initial, At end
of exTo tansion
milllseconds
T2
-I
1
I
1
-log,
-
1.355
%:
1.475
67.0
1.735
77.7
44.6
42.65
Velocity, ft. per sec. Volume,
+p-i
Final,
-_
1.346
1.325
1.30
1.32
1*25
1.25
1.26
1.28
1.275
1.280
1.32
1.26
1.33
1.30
1.295
1.275
1.285
1.345
Temperature,
deg. C.abs.
TOIT,
-l
Initial,
Po
54
56
58
59
65
68
69
70
71
72
77
98
317
318
319
327
Ratio,
po/p3
1.50
2.60
2.72
1-535
2.44
1535
1.93
1.98
2.56
2.29
2.16
1.11
1.13
1.18
1.14
1.27
1.284
1.272
1.212
1.242
1.241
1.141
-~~
1.261
1.152
1.218
1.223
1.295
1.266
1.305
290
290
290
289.8
289
289
289
289
289
289
291
288
299
289
289
290
288
286
261
257
246
254
228
225
227
239
233
233
254
228
25 1
232
236
223
228
219
1,022
1,022
1'022
1,022
1,020
1,020
1,020
1,020
1,020
1,020
1,023
1,019
1,020
1,020
1,020
1,022
1,019
1,033
970
963
940
956
908
902
905
928
916
916
956
908
950
924
921
898
906
903
996
993
981
989
964
961
963
974
968
0.0706
0.071
0.071
0.0706
0.0712
0.0706
0.0706
0.0706
0.0706
989
964
985
972
971
960
963
968
0.0706
0.0706
0.0707
0.0706
0.0706
0.0706
0.0706
0.0706
968 o.oio6
0.3038
0.3888
0.586
0.4055
0.9555
1.001
0.9243
0.6907
0.7885
0.7724
0.4285
0.892
0.4285
0.6575
0.6831
0.940
08286
0.7701
0.305
0.394
0.564
0401
1.000
1.040
0.959
0.709
0.815
0.798
0.433
0.922
0.372
0.578
0.602
0.833
0.736
0.795
1
* The value log, has been decreased by a constant factor to allow for increased port area in all tests after No. 118.
a1
PS
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4.02
5.7
8.1
5.8
15.8
16.1
14.6
10.7
12.0
11-6
5.95
14.65
5.2
8.2
8.8
11.4
10.0
17.5
D I S C H A R G E O F EXHAUST GASES I N T W O - S T R O K E E N G I N E S
Fig. 2. Discharge Apparatus
Fig. 4. Port-Timing Photographic Record
[I.Mech.E., 19491
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Plate I
Plate 2
D I S C H A R G E OF EXHAUST GASES I N T W O - S T R O K E E N G I N E S
Fig. 6. Photographic Pressure Record for Discharge of Nitrogen
Test No. 237 : total time of port opening = 26 milliseconds; vertical divisions on expansion line at $-millisecond intervals ; cylinder
volume = 1,000 cu. cm.; release pressure = 61 lb. per sq. in. gauge.
Fig. 7. Photographic Pressure Record to Obtain Index of Expansion for Discharge of Nitrogen
Test No. 291 : light diaphragm used; time of expansion = 10.5 milliseconds; cylinder volume = 1,000 cu. cm. ;release pressure = 61 Ib.
per sq. in. gauge.
Fig. 10. Photographic Pressure Record for Discharge of Nitrogen
Test No. 312 : total time of port opening = 7.7 milliseconds; cylinder volume = 1,000 cu. cm. ; release pressure = 61 Ib. per sq. in. gauge.
Fig. 12. Photographic Pressure Record for Discharge of Hydrogen
Test No. 323: total time of port opening = 6 3 milliseconds; cylinder volume = 1,000 cu. cm.; release pressure = 61 Ib. per sq. in. gauge.
[I.Mech.E., 19491
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D I S C H A R G E OF E X H A U S T GASES I N T W O - S T R O K E E N G I N E S
Plate 3
Fig. 21. Pressure Record for Discharge of Nitrogen to Investigate Vacuum Pressures
Test No. 295 : total time of port opening = 9.2 milliseconds ;cylinder volume = 1,000 cu. cm. ; release pressure = 61 lb. per sq. in. gauge.
Fig. 22. Pressure Record for Discharge of Hydrogen to Investigate Vacuum Pressures
Test No. 296 : total time of port opening = 8.8 milliseconds; cylinder volume = 1,000 cu. cm. ;release pressure = 61 lb. per sq. in. gauge.
Fig. 23. Pressure Record for Discharge of Hydrogen to Investigate Effect of Exhaust Pipes
Test No. 339 : total time of port opening = 5.7 milliseconds ;cylinder volume = 1,000 cu. crn. ;release pressure = 61 lb. per sq. in. gauge.
Fig. 24. Pressure Record for Discharge of Air to Investigate Effect of Exhaust Pipes
Test No. 343: total time of port opening = 18 milliseconds; cylinder volume = 1,000 cu. crn.; release pressure = 61 lb. per sq. in. gauge.
[I.Mech.E., 19491
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D I S C H A R G E O F E X H A U S T GASES I N T W O - S T R O K E E N G I N E S
Plate 4
Fig. 26. Later Design of Discharge Apparatus
Fig. 27. Piessure Record and Valve Opening Diagram for Discharge of Nitrogen to Obtain Index of Expansion
Test No. 400 : cylinder volume = 1,000 cu. cm. ;release pressure = 61 lb. per sq. in. gauge.
Fig. 28. Pressure Record for Discharge of Nitrogen to Obtain Coefficient of Discharge
Test No. 402 : cylinder volume = 1,000 cu. cm. ;release pressure = 61 lb. per sq. in. gauge.
[I.Mech.E., 19491
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DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
105
the last four points in Fig. 18 are included, a smooth curve B fits contracta gets nearer the orifice. Stanton also found that the
the points better. This indicates that the coefficient of discharge K size of the vena contracta increased as the pressure ratio dein equation (18) is not constant, but decreases with increase of creases, thus providing an explanation for the increase in
coefficient. The reason for this increase in size of the coefficient
time of expansion; this will be considered in the next section.
It is considered that these results amply justify the simplifica- is, no doubt, due to the fact that with pressure ratios of less
than 0.5, the pressure in the jet is higher than the surrounding
tion, which is most useful in practical applications.
atmospheric pressure and the jet therefore tends to enlarge.
T H E C O E F F I C I E N T OF D I S C H A R G E
A very important factor in port design is the value given to the
coefficient of discharge. The values suggested by previous
investigators have varied from 0.6 (Bird 1923) to 0.8 (Magg
1928), and the value has not been settled. In the experiments
described, the coefficients vary from 0.64 below the critical
pressure, to 0.95 for tests conducted entirely above the critical
pressure.
Considerable light is thrown on this matter by the continuousflow experiments (made by discharging from one receiver to
another through a sharp-edged orifice) which were performed
many years ago by Zeuner (1887), and also by the much more
accurate tests by Stanton (1926). Zeuner’s coefficients and an
analysis of Stanton’s results (also for a sharp-edged orifice) are
shown in Fig. 19.
I
I
I
I
1
u
w b
e
L
Fig. 20. Stanton’s Measurements of Vma Contracts
Thin-lipped orifice bf 1.22 em. diameter.
po = pressure in reservoir; pr = atmospheric pressure.
0
0.2
0.4
PRESSURE
0.8
0.6
1.0
P
PO
RATIO.^
Fig. 19. Stanton’s Values for Coefficient of Discharge for
Various Pressure Ratios
o Actual discharge.
+ Theoretical discharge.
0 Variation of coefficient of discharge.
x Zeuner’s coefficient of discharge.
Curve A (Fig. 19) shows the relationship found by Stanton
between discharge and pressure ratio p , / p , (where po = pressure in cylinder, and p , = pressure in receiver); curve €3 shows
the theoretical discharge, taking a coefficient of discharge of
unity. Curve C, obtained by dividing the two ordinates, gives
the variation of this coefficient of discharge over the range. If
the one point at pressure ratio 0.9 is ignored, this being too high,
and a value of 0.6 is assumed for a pressure ratio of unity, which
is now an accepted value in gas flow measurement for small
pressure differences, a constant value of 0.86 from zero to a ratio
of 0.2 is obtained, falling off smoothly to 0.6 at unity.
Zeuner’s figures, curve D, show the same trend, but it would
appear from Stanton’s more accurate experiments that his values
are somewhat low. Stanton also performed tests to endeavour to
explain this increase in coefficient with pressure difference, his
method being to locate the venu contracta by means of a Pitot
search tube. Fig. 20 shows the results of his investigation.
The full curves (Fig. 20) represent the pressure measured along
the axis of the jet for various pressure ratios, and the dotted
curve the position of the theoretical pressure or vena contracta;
it will be noticed that as the pressure ratio decreases, the vena
The results of the experiments under review are, to a large
degree, in harmony with those of Stanton; below the critical
pressure, when the ratio of p l / p ois greater than 0.5, the values
are about 0.65 increasing to 0.95 as the ratio is reduced, and in
one or two cases of very high release pressure the values are
unity. In these cases the vena contractu probably coincided with
the orifice. In these tests the cylinder pressure was double that
of Stanton’s highest pressure, and, consequently, so also was
the pressure in the jet.
It is concluded that in a discharge over the whole range
from a high release pressure to atmospheric the coefficient varies
from 0.6 to unity, so that in practical calculations an average
value will have to be adopted.
VACUUM PRESSURES A N D EFFECT O F E X H A U S T - P I P E
RESONANCE
In the theory of the discharge considered, the discharge
velocity is that of sound until the pressure in the vessel has fallen
to the critical value; it then gradually decreases to zero as the
pressure in the vessel becomes equal to atmospheric. Consequently, there should be no residual velocity, and therefore no
momentum of the gas in the ports, as this would inevitably leave
a vacuum pressure in the vessel. In over two-hundred tests in
which pressure records were taken, only two very slight vacuum
pressures were recorded. Neither of these was repeatable, and
they were attributed to experimental error.
In order to confirm this point, two tests were made under the
same conditions as those in which these small vacuum pressures
had been observed, using a light diaphragm to obtain very great
sensitivity with the pressure indicator. The photographic records
of these two tests are shown in Figs. 21 and 22, Plate 3, for
nitrogen and hydrogen respectively. In both cases the pressure
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D I S C H A R G E O F E X H A U S T GASES I N T W O - S T R O K E E N G I N E S
falls smoothiy to atmospheric (or very near it), and thus the in which a long time of port opening was allowed, a vacuum as
velocity becomes zero at port closure. A vacuum calibration is large as 43 lb. per sq. in. was recorded (Fig. 24, Plate 3). The
recorded on the diagram showing that the indicator is quite horizontal lines in Fig. 24 represent pressures (from bottom to
top respectively)of - 10 and -5 inches of mercury, zero, and 2.6
capable of recording vacuum pressures.
Although there was no intention of making a complete and 5.9 lb. per sq. in. gauge. The final pressure, which was also
measured with a static gauge,
investigation of exhaust-pipe resonance-a subject in itself-it
- - showed that the calibration had
was realized that the apparatus was in fact very suitable for this not shifted.
A comDarison between. Figs. 21 and 24 shows the effect of
purpose, and it was decided to make one or two initial tests.
Two rectangular-sectionpipes, 3 feet in length and constructed the exha& pipe. The latter-causes the pressure line to sweep
of sheet metal, were fitted to the cylinder through the medium quite smoothly below atmospheric pressure instead of making
of a pair of wooden blocks, similar to those used for sealing its usual gradual tangential approach to the lowest pressure.
That a considerably larger mass of gas was removed from the
the ports (Fig. 2). The bore of these pipes increased from the
exhaust-port area at one end to four times this area at the cylinder is shown by comparison of the residual cylinder pressure
of 4 Ib. per sq. in. with that of 6 Ib. per sq. in. for a test of the
other.
The first test was made using air, but the time-area was same duration (18 milliseconds) for air without a pipe.
These vacuum pressures must be due to some exhaust-pipe
insufficient to reach atmospheric pressure. Hydrogen was then
used, and a vacuum pressure of 2 lb. per sq. in. was obtained effect, as they do not occur in the absence of the pipe. Fig. 24 also
(Fig. 23, Plate 3). Air was again tried, as an entirely different indicates that the pipe is resonating by the pressure wave that
gas with one-quarter the velocity, to show that the hydrogen test follows the minimum pressure, this in turn being followed by a
was not an exceptional resonant phenomenon, and in this case, slight vacuum. However, the matter is by no means as simple as
the familiar organ pipe resonance; each phenomenon would have
to be calculated with regard to the prevailing conditions, which
are somewhat complicated.
106
FURTHER EXPERIMENTS O N COEFFICIENT OF DISCHARGE
-A
The value of unity for the coefficient of discharge of a sharpedged orifice may cause some surprise, although, as shown, it
is supported by a reasonable explanation backed by independent
experimental evidence. This coefficient would contain any errors
in the assumptions of the theory, which are mainly based on the
prevalence of the velocity of sound. This issue being important,
it was thought desirable to obtain further verification, and, at
the suggestion of Mr. A. L. Bird, similar experiments were made
with an orifice having a known coefficient of discharge. An apparatus was designed to have a coefficient equal to unity; if the
theory applied to the sharp-edged apparatus were used, a
coefficient of about 1-5 or more might be expected, which would
be a very obvious demonstration of erroneous assumptions in
the theory of equations (10) and (13).
The apparatus, which is shown in Fig. 25 and Fig. 26, Plate 4,
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DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
consists essentially of a cylinder A and valve B of a shape carefully designed to give good gas flow. The actuating mechanism
for the valve consists of pairs of toggles C loaded by four tension
springs D.
The release mechanism E supports the pivot F, which may
be pulled out, by means of lever not shown, to allow the crosshead to move under the action of the four springs. This lifts
the valve to its maximum position, and closes it again as the
toggles reach the final position on the right of the valve axis.
The spring G and bar H, pivoted between friction disks, act
as decelerators for the spring mechanism, thus reducing seating
shock.
The timing device J is essentially a small hole, & inch in
diameter, drilled in a light bar screwed to a flat on the valve
stem. This hole is illuminated throughout its travel by means of
a “Pointolite” lamp and condenser system as in the earlier apparatus. A lens focuses the spot on the drum of a revolving drum
camera arranged to give a magnification of approximately two;
metal screens (not shown) cut off any stray light.
The typical time-lift record in Fig. 27, Plate 4, shows that
the valve slightly overshoots the maximum lift given by the
toggles and represented on the diagram by the top horizontal
line, but this is immaterial as the timing device is on the valve
itself. Secondly, there is a small amount of.valve bounce, but
this also does not affect the accuracy of the results, as it 1s
included in the relationship between total time and area of
opening.
The same electronic condenser indicator was used as in the
earlier apparatus, the pressure element being screwed into the
cylinder and cover, and the diaphragm being almost flush with
the inside surface of the cover to avoid a velocity head at this
sition of measurement. In this connexion, the recent dis2 a rge apparatus of Schweitzer, Van Overbeke, and Manson
(1946) is open to criticism, since, in the case where the largest
orifice was used, it was possible to have velocities near the
indicator approaching that of sound, which velocity would make
the measured static pressure something like 14 lb. per sq. in.
less than the total pressure due to static and velocity heads.
VALUE O F C O E F F I C I E N T OF D I S C H A R G E W I T H LATER
APPARATUS
The apparatus was made with interchangeable cylinders, and
in the followingtests a cylinder 4 inches in diameter and 6inches
long was used, the gas employed being nitrogen.
The first test (Fig. 27) was made with a light diaphragm in
the indicator for the sole purpose of obtaining the value of the
107
index of expansion, a value of 1.27 being obtained. A similar
test was then performed with a thicker diaphragm (Fig. 28,
Plate 4).
For calculation of the results the port time-area is required,
but the photographic record gives only the valve lift. Fig. 29
gives the relationship between valve lift and throat area; from
this and the test record, the graph in Fig. 30 was plotted to give
7
2
TIME-MILLISECONI:
Fig. 30. Time-Area Relationship for Test No. 402
3
3 x l,ooot
Slope = F~
;therefore A = 5.5
the required time-area. As this relationship was almost linear,
an average straight line was assumed. It will be noted that only
the discharge above the critical pressure is being considered, and,
in this test, this occurs before the valve has reached its maximum
lift.
The results of these tests are shown in Fig. 31 j as before, the
t’
(TIME IN MILLISECONDS)
Fig. 31. Test No. 402 : Discharge of Nitrogen with Later
Apparatus
VALVE LIFT-INCH
Fig. 29. Relationship between Valve Lift and Throat Area
0.067
Slope = 30 x 10-6 = 2,230
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DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
I08
relationship of t 2 and p-(”-l)lzn gives a good straight line.
Surprisingly, however, the slope of the line gave a coefficient
of discharge of only 0.75. This result confirms substantially that
the high values obtained with the old apparatus were not
erroneous.
Calculations for these tests are as follows :n-1
n = 1.27 and -= 0.1062
2n
From Fig. 30,
-’
G
Z
t inch-second units.
From equation (lo),
n-1
-__
3,000 X 0.27 X 1.405 X 99.4 X 32 X 288
11 x 2 x 0.035 x 1-73x 0.582 x 144
Theoretical slope = 2,980K and actual slope = 2,230;
therefore
K = 0.75
Another test was made with the pressure in the cylinder kept
entirely above the critical, so that equation (18) was applicable;
a value of 0.74 was obtained for the coefficient of discharge.
It was.thought possible that this low coefficient might be due
to the throat’s not running full, and a modification to the approach
was made by using a cylinder of large diameter and slightly
modified seating as in Fig. 32. The result (test No. 419, in which
p
2 n = K
The conspicuous difference between the sharp-edged sleeve
apparatus and the later apparatus is the much larger surface
area of “nozzle” in the latter. This surface area is scrubbed by
an average velocity approaching the acoustic velocity, and therefore (see equation ( 2 ) ) there is a far larger relative heat transfer
to the gas as it flows through the port. This will be further
increased by heat generated by any turbulence set up in the
port.
Mass discharge
= apV (where V = velocity of flow)
1
= a- x 1/T (above the critical pressure)
T
1
= u2/T
and thus, if the temperature at the port is generally higher than
assumed, the discharge will be correspondingly less.
Calculations show that temperature rise will not give a complete explanation of the problem, but this, coupled with the
effect of possible turbulence reducing the coefficient of contraction, is considered to be the true reason for these low values.
There is, however, great need for research into heat transfer for
flow of sonic velocity and its effect on the coefficient of discharge,
which could far more conveniently be performed by continuous
flow experiments.
Finally, it is pointed out that these tests give the sleeve-valve
engine added merit in relation to the discharge coefficient.
A P P L I C A T I O N O F T H E O R Y T O P R A C T I C A L CASE
In making this application, there are two points of major
importance to bear in mind. First, the temperature of the
cylinder gases at the point of exhaust opening is no longer
known and cannot easily be measured, and secondly, the index
of expansion of the gases in the cylinder during the period of the
exhaust discharge is unknown. It is therefore emphasized that
likely values will be assumed, which it is hoped to verify in the
future when the opportunity arises.
The expansion under consideration will be assumed to be
from the release pressure of 74.7 lb. per sq. in. abs., to 17.7 Ib.
per sq. in. abs. (a common scavenging pressure), and the initial
temperature at discharge has been taken as 1,230 deg. C.abs.*
The gas will be mainly nitrogen with some carbon dioxide,
oxygen, and steam, will have a temperature higher than the
walls of the cylinder, and will be losing heat. The latter will be
partly, but by no means completely, compensated for by
heat generated in the gas through turbulence. A value of n
greater than y can be expected, and a value of 1.5 has therefore
been assumed. The expansion from the vessel to the port will
be adiabatic for reasons already considered, and at this temperature will be taken as 1.375.
Consider a single-cylinder engine of the following dimensions :Bore = 3%inches; stroke = 49 inches; piston area = 813
sq. in.; cylinder volume = 36.2 cu. in.; compression ratlo
= 20 to 1 ; exhaust ports open 50 deg. before bottom dead
centre (0.62 inch high) ;connecting rod to crank ratio = 4 to 1.
It is required to find J A d t for the complete discharge of
exhaust gases. This wiIl be calculated in two stages-above and
below the critical pressure, using the simplified method for the
former.
q=y
Fig. 32. Discharge Apparatus with Modified Valve Approach
Above CnXcaZ Pressure. This stage is applicable to a pressure
range from 74.7 to 27.5 lb. per sq. in.
From equation (18), making a correction for y = 1.375,
M o 0.626Ka
log, - = --J-/dt
V
. . . . (20)
M 2
K = 0.75) showed that there was precisely no improvement in
the coefficient ;this indicated that the reason had not yet been
located.
It was observed earlier in the paper that the index of expansion in the vessel was, surprisingly, lower than y, indicating a
considerable heat transfer due to forced convection, and it is
considered that the same factor is reducing the coefficient here.
where Mo= initial mass, M2= mass at critical pressure, and
‘u = mean cylinder volume = volume when exhaust opens for
first approximation.
* This figure has been calculated from the known mass of gas in
the cylinder, using a value of R calculated from the specific heat of
the constituents of the exhaust gas at the elevated temperature of the
gases.
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D I S C H A R G E O F EXHAUST GASES I N T W O - S T R O K E E N G I N E S
109
Initially, the temperature TOof the gases at release is 1,230
deg. C. abs.
Final temperature at critical pressure is T2, where, from
equation (17),
Therefore
T2= 881 deg. C. abs.
From equation (16), gas velocity through port at temperature Tois
d
g
= 2,100 ft. per sec. (where R = 97)
Gas velocity at temperature Tz is
/B
= 1,780 ft. per sec.
Mean velocity a = 1,940 ft. per sec.
1MoInitial mass
Also
M2
Mass at critical pressure
-
1-n
= p_o x
$2
p)"
(from equation (17))
P2
1
-
= (2*72)1'5= 1.95
From equation (20), assuming a poppet exhaust valve with
Coefficient of discharge of 0.7,
0.626 X 0.7 X 1,940 X 1,728
log, 1.95 =
33.1 X 144
therefore
JAdt = 0.00217 inch-second units.
This gives the required JAdt to a fair degree of accuracy.
When the corresponding crank angle is ascertained, a correction
can be made for the mean cylinder volume 'u, which will be
increased by half the piston movement. Assuming this angle to
be 10 deg., which is equivalent to an increase in volume o f 0.89
cu. in.,
average volume = 33.99 cu.in.
then
JAdt = 0.00233 inch-second units.
and
Below Critical Pressure. This stage applies to a pressure
range from 2 7 5 to 17.7 lb. per sq. in., or a ratio of p l / p from
0.53 to 0.83.
The cylindet volume at 27.5 lb. per sq. in. (assumed to
correspond to 40 deg. before bottom dead centre) is 34.88 cu. in.
In equation (13) the somewhat complicated integral depends
upon n and can only be integrated graphically. The value of the
integral is very insensitive to change in n, however, as shown by
the three curves in Fig. 33, and thus the curve of the integral of
the function for various values of p l / p (Fig. 34), taking n = 1.4,
may be used without correction for all practical purposes,
irrespective of the actual value of n.
1.
Thus
J
p
I
("1)
Fig. 33. Variation off
with Change of PI
for Various
P
P
Indices of Expansion
CONCLUSIONS
I n the design of the two-stroke engine, the simplified equation
(18) for discharge above the critical pressure may be used with
the discharge coefficient of 0.95 if the exhaust ports are sharpedged and short. This coefficient would, however, have to be
reduced to 0.75 in most practical cases if a large nozzle area were
exposed, and to about 0.7 for a standard poppet valve owing to
its greater contraction coefficient.
Below the critical pressure, equation (13)-which has to be
integrated graphically (values of this integral for all practical
cases are given in Fig. 34)-is applicable, but a coefficient of 0.65
must be used for a sharp-edged orifice and 0.7 for a standard
poppet valve.
1 a77
053
From equation (13),
JAdt =
0.375
74.7 0.5
x 97 x 32 x 1,230(-)3'0
17 7
X 1.77
whence
JAdt = 0*00117
and, correcting for a further 10 deg. assumed movement,
35.6
JAdt = 0.00117 X- 0.0012 inch-second units
34.88 giving total JAdt, for the complete exhaust scavenging process,
= 0.0035 inch-second units.
RATIO
PI
P
Fig. 34, Integration for Expansion below Critical Pressure
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DISCHARGE OF EXHAUST GASES I N TWO-STROKE E N G I N E S
110
It is considered that it is now proved, experimentally as well
as theoretically, that the “velocity of sound” theory adequately
explains the process of exhaust discharge, and may be applied
with confidence in exhaust-port design. This, however, does not
in any way vitiate a wave theory of the type suggested by
Professor GSen (1940); his theory only concerns the velocity
of approach to the port, and, as he points out, has only a small
effect on the actual discharge. The present application of
Bernoulli’s equation is taken from the axis of the vessel, where
there is no velocity.
= K f g ) from
. equation (13), where K
is the coefficient of discharge.
Of the curve Of
Thus the
the coefficient of discharge.
(
ttl-$
‘7
against f
(“b)
-
A P P E N D I X I1
REFERENCES
BIRD,A. L. 1923 “Oil Engines”, pp. 100-102 (Methuen and
The author wishes to acknowledge the help, by valuable
Company, Ltd., London).
suggestions, of Mr. A. L. Bird, M.A., M.I.Mech.E., Hopkinson CARTER,
H. D. 1946 Proc. I.Mech.E., vol. 154, p. 386, “The
Loop Scavenge Diesel Engine”.
Lecturer in Thermodynamics, University of Cambridge, and
and PRANDTL,
L. 1936 “The
the kindness of Professor Sir Charles Inglis, O.B.E., MA., EWALD, P. P., P~scHL,TH.,
Physics of Solids and Fluids”, 2nd edition, p. 353, “The
LL.D., Hon. M.I.Mech.E., F.R.S., and Professor J. F. Baker,
Flow of Liquids and Gases-Part 3” (Blackie and Son,
O.B.E., Sc.D., D.Sc., M.A., for placing at his disposal the
facilities of the engineering laboratories.
Ltd., London and Glasgow).
FISHENDEN,
M., and SAUNDERS,
0. A. 1932 “The Calculation
of Heat Transmission”, p. 151, equation 55 (His Majesty’s
Stationery Office, London).
APPENDIX I
Gas and Oil Power 1945, vol. 40, p. 257, “A Study in TwoStrokes”.
C A L C U L A T I O N OF P O R T TIME-AREA AFTER F U L L Y
G ~ NE., 1940 Engineering, vol. 150, p. 134, “Rapid DisOPEN POSITION
charge of Gas from a Vessel into the Atmosphere”.
From Fig. 5, port area (attime t > r l ) isA = LVrl~LV(r-tt,), KADENACY,
M., and ARMSTRONG-WHITWORTH
SECURITIES
COMwhere L is the length of the circumference and V IS the sleeve
PANY, LTD. 1936 British Patent No. 473684.
velocity.
MAGG, J. 1928 “Dieselmachinen-Grudlagen, Bauarten,
The following applies to port time-area from time t x > t l to
Probleme” (V.D .I .-Verlag ,Berlin).
any time t :PARTINGTON,
J. R., and SHILLING,W. G. 1924 “The Specific
Heat of Gases” (Ernest Berm, Ltd., London).
= kVrldrLV(r-rl)dt
SCHACK,
A. 1933 “Industrial Heat Transfer”, p. 108 (John
Wiley and Sons, New York). Translated by GOLDSCHMIDT, H., and PARTRIDGE,
E. P.
=LV[rl(t-rx)-T( t -t ,12 (rx -r 12
SCHWEITZER,
P. H., VAN OVERBEKE,
C. W., and -SON,
L.
t 2 tx2
1946
Trans.
A.S.M.E.,
vol.
68,
p.
729,
“Taking
the
whence $Adt = [2rrl-2tlt,--+-]LV
2 2
Mystery out of the Kadenacy System of Scavenging
t2
Diesel Engines”.
=2LV@tt,--q+c) where c is a constant, as tl STANTON,
T. E. 1926 Proc. Roy. SOC.,vol. 111, p. 306, “On
and tx are constants for
the Flow of Gases at High Speeds”.
any particular test.
ZEUNER,G. 1887 “Technische Thermoydynamik” (Leipzig).
ACKNOWLEDGEMENTS
l?dr
1:
+ T ,I
Lornrnunica tions
Dr. F. K. BANNISTER,
A.M.I.Mech.E., wrote that he was
particularly interested in the author’s reference to the Kadenacy
depression and to the effects of fitting an exhaust pipe to the
discharge cylinder. That such a pipe greatly enhanced the
probability of a depression in the cylinder following discharge
was clear from Figs. 21 to 24, although, as had been shown both
theoretically (Giffen 1940)* and experimentally (Bannister and
Mucklow 1948)t, a small transient depression was possible even
where no pipe was fitted. The latter effect, which necessitated
extremely rapid port opening, was due to wave action in the
cylinder, a phenomenon which, for the more moderate valve
speeds considered, the author had reasonably neglected in his
theoretical analysis.
Wave action in the exhaust pipe, however, was much more
pronounced and, even with slow port openings, could not so
readily be neglected. Cylinder depressions such as those of
Figs. 23 and 24 could, in fact, be attributed? entirely to the
influence of a returning wave of rarefaction produced by reflection, at the open pipe-end, of the outgoing pressure pulse
generated by the discharge.
* See list of references in Appendix I1 above.
t BANNISTER,
F. K., and M U ~ O W
.G., F. 1948 Proc. I.Mech.E.,
vol. 159, p. 269, “Wave Actlon Followmg Sudden Release of Compressed Gas from a Cylinder”.
On that account, he felt that sufficient emphasis had, perhaps,
not been given to the fact that the author’s results for the subsonic phase of discharge in an actual engine would not be valid
where the cylinder discharged directly into an exhaust pipe; If
a large expansion chamber were fitted close up against the
cylinder the assumption of a constant value of atmospheric for
the port pressure, embodied in equation (13), would be reasonable. Where the pipe length between port and expansion box
was appreciable, however, the pressure waves set up in the pipe
would cause a marked deviation of the port pressure from
atmospheric and would thus become an important factor in the
discharge process. During the subsonic phase of each exhaust
period the increase in port back-pressure due to wave generation would, in the earlier stages, diminish the flow through the
port. After a delay corresponding to the double journey of the
wave along the pipe, the reverse would obtain, the rarefaction
pulse reflected from the expansion chamber returning to cause
either an increased rate of cylinder pressure die-away or, if its
return were postponed beyond the completion of exhaust, a
more effective scavenge. Those effects, augmented under certain
circumstances by the residual waves from previous cycles, would
thus render the results of equation (13) liable to serious errors.
Similarly, with several cylinders exhausting to a common
manifold of moderate cross-section, the pressure pulse from one
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C O M M U N I C A T I O N S ON DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
cylinder would react directly on the discharge from another and,
as shown by Carter (1946)*, might even be of sufficient amplitude
to cause a reversal of flow in the port.
During the sonic phase, flow through the port would be
unaffected by exhaust pipe effects, though the latter would, in
general, result in either a curtailment or an extension of the
sonic period. A very moderate port depression of -3 Ib. per
sq. in. (gauge) would, for example, reduce the critical cylinder
pressure from 27-5 to 21.9 lb. per sq. in. (abs.).
Where exhaust pipe effects could be ignored, the author’s treatment would, of course, apply, though he himself found some
difficulty in following the procedure of p. 109, whereby the
approximate figure of 0.00217 sq. in. sec. for JAdt was corrected
to 0.00233 sq. in. sec. in order to allow for piston motion.
Allowing for the possibility of a slight numerical inaccuracy, it
appeared that the original value was merely multiplied by the
factor 33.99/33.1, i.e. (vo+v2)/2v0. If that were the correct
interpretation, then it would seem that a further effect of variation in v, considerably greater than that allowed for, had been
overlooked. The assumption that v 2 = voJ adopted for the
evaluation of M0/M2,could be discarded for the second approximation since v2 had then been estimated. Substitution of
v2 = 34.88 cu. in. gave a new value of Mo/M2 = 1.85 which,
replacing M0/M2 = 1.95, introduced a further correction factor
of log 1-85/1og 1-95, i.e. 0.922, by which, in addition to that of
1.027 used by the author, the approximate value of 0.00217
sq. in. sec. should, presumably, be multiplied.
It was of interest to examine the accuracy of the assumption
that, in the right-hand side of equation (20), the corrected value
of v could be taken as the arithmetic mean of vo and v 2 For a
cylinder of constant volume the term v in the above equation
could be taken outside the integration sign as shown, but for
a running engine its rightful place was as a variable in the
integrand. If the author’s notation were adopted and it were
assumed, as a reasonably typical case, that port area and
cylinder volume varied linearly with time during the relatively
short period of sonic discharge, then
v =: eto+at and A = pt
CL and /3 being constants. Thus, equation (20) became
111
end of the phase. The difference would, of course, be most
marked in high-speed engines where, owing to early exhaust
valve opening, the piston velocity was high at release.
Mr. R. S. BENSON(London) wrote that although the author
had neglected the exhaust pipe effect, at no time during the
experiments (except in two tests attributed to experimental
error) did the pressure in the cylinder fall below atmospheric
when on open exhaust. He believed that one of the earlier experimental engines operating on the Kadenacy system was run
without exhaust pipe or inlet pipe and consequent claims were
made for a “baUistic’’ theory; from the author’s work, those
claims did not appear to be substantiated.
Experiments carried out by the N.A.C.A. in America on the
coefficient of discharge for sleeve valve ports gave values from
0.7 for p,/po = 1, to 0.89 for p l / p o = 0.22, the trend of the
curve being similar to Fig. 19 though much flatter. It was also
shown that for different port openings the coefficientof discharge
did not vary appreciably. Those results were obtained from a
similar experimental arrangement as that used by the author,
air being the medium, and no piston being used.
Under actual engine conditions there might be some piston
effect as taken into account by Parker (1947)*, who had analysed
results from tests by Allcut (1927)t and obtained an average
value for the coefficient of discharge of 0.89 for 120-130 deg. C.
and 0.657 for 130-1375 deg. A.T.C.
Some work should be carried out to ascertain the value of
coefficient of discharge under engine conditions, as that was an
important factor in port design.
The author had applied equations (18) and (13) suitably
corrected to give JAdt for complete evacuation of the gas; that
did not appear to be correct, for equation (13) was derived on
the assumption that the gas expanded in the cylinder to scavenge
air pressure. There would still be gas in the cylinder, the mass of
which would be given by p2212 which in the normal way was
RT2
scavenged in the second part of the scavenge cycle. Equation (13)
therefore, would apply to the blowdown period, when the pressure was reduced to that of the scavenge air pressure or slightly
lower. That would give the JAdt for the exhaust lead.
In applying the formulae to the data given, the author
assumed that the exhaust timing would be similar to the inlet,
and hence that exhaust took place when the inlet ports were
open; in practice, that might cause reverse flow. Thus, it would
= :{t2-zloge
VO
(l+Z)}
appear that there were two methods of applying the formulae,
namely,
or, expanding the log term and neglecting fourth and higher
(a) Assume a crank position and exhaust valve or port
powers of the small quantity at2/vo,
opening and thence follow through the method with equation (18) first and thence equation (13), iinally determining
crank position for inlet port opening, or
(b) Start in the reverse direction from the position of inlet
port opening, first determine JAdt below critical pressure and
thence above critical pressure to give reduction of cylinder
pressure to scavenge pressure, and hence position of exhaust
pt2‘
and
Thus, since for the case considered
Adt = 2
port opening and exhaust lead. That would involve ushg
equation (13) first and then equation (18).
at2 = vp-00
The second method was preferable in cases of loop and UniMo 0.626Ka
flow scavenge with exhaust valves, although for opposed piston
log, - = -(1-)VO
e )VOl f l 0A d t
M2
engines a compromise might have to be reached.
or, with slight error
Equation (3)for the velocity of discharge through the ports
was given in absolute units, and that caused some confusion
in the application of the data. I n equation (13) the usual value
for R (53.3 or 97) should be multiplied by g (32 ft. per
sec.2), otherwise a considerable amount of dimensional analysis
If correctly interpreted, the author’s treatment, expressed was required to ascertain the units used; that also applied to
equation (16) for the speed of sound in ports.
algebraically, gave
It appeared that the value for po in equation (13) had been
substituted incorrectly as 87-4instead of 74.7 Ib. per sq. in. abs.
The range of pressures above the critical was from 74.7 to
27-5 Ib. per sq. in. hence from equation (5) the minimum presfrom which it would appear that some slight gain in accuracy sure in the throat would be 14.7 Ib. per sq. in. He therefore
would follow from taking, as the corrected volume in the right* P,G. 1947 Proc. I.Mech.E., vol. 157, p. 367, “Theoretical
hand side of equation (20), the volume when the exhaust valve Investigation into the Porting of a Two-cycle High Mean Effective
opened plus two-thirds of the volume increment, rather than Pressure Internal Combustion Engine”.
the simple arithmetic mean of the volumes at beginning and
t AUCVT, E. A. 1927 Proc. 1.Mech.E.’ vol. I, p. 519.
Jz
-
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112
C O M M U N I C A T I O N S ON DISCHARGE O F EXHAUST GASES I N TWO-STROKE ENGINES
assumed that the exhaust manifold pressure was 14.7 Ib. per
sq. in.; the value for p l would thus be 14.7 Ib. per sq. in. and
not 1 7 7 Ib. per sq. in. Perhaps the author would elucidate that
point. The example given was difficult to follow since recourse
had to be made to the basic theory in order to follow the calculation. Perhaps the author might set out the data and the equations
(13) and (18) in such a manner that they codld be applied
directly in practice.
0.142 per cent-rhen, since the expansion temperatures given
were consistently below freezing point, it seemed reasonable to
infer t4at latent heat both of evaporation and fusion would be
liberated. If that heat were reabsorbed at constant pressure by
the mixture as a whole, a temperature rise of about 4 deg. C .
above the adiabatic values of T2 could be accounted for in all the
air tests of Table 1. That correction could fully cover the
differences between the adiabatic and experimental values of
T2for tests 54 and 56, while contributing 40,30, and 18 per cent
to the differences for tests 58, 70, and 65 respectively. It would
be interesting to know whether the author was certain that the
minute water content presupposed in that correction was not
actually present.
The author had indicated that the pressure integral in
equation (13) was fairly insensitive to the value adopted for n,
and it might therefore be worth mentioning that, taking
n = y = 1.4, an analytical solution was possible. The integral
could then be rewritten with the indices as multiples of 1/7,
giving :-
Dr. B. N. COLE,B.Sc. (Eng.), Wh.Sc., G.I.Mech.E., wrote
that the part of the paper which dealt with the depression of the
index of expansion n below y, appeared somewhat controversial.
The author’s explanation of the phenomenon in terms of heat
transfer assisted by forced convection was undoubtedly
qualitatively consistent with the trend of the n versus time curves
shown in Figs. 8 and 17, but the following considerations
suggested that the heat transfer requirements were, quantitatively, inordinately high.
If a gas expanded according to the law per* = constant,
between the pressures po and p2, the charge, or cylinder, volume
being vo, the rate of heat reception by the full mass of charge
was given by :dH
y-nt
;i;;= ( 3 ) J
where the general volume v signified the volume to which the which by the substitution of x = (p/p1)1/7 could be transformed
whole of the initial charge would expand at a pressure p . It thus into :followed that the rate of heat reception by the fixed cylinder
volume, in which the mass was progressively decreasing during
discharge, would be :which, on integration, became :d H = VoY--”_p
dv
v y-1 J
which, upon integration, yielded the expression :The constant of integration A was found from the value of
x for the instant at which the discharge embarked upon the subH = (-)-(I-&)
Y - n POVO
I “ - ‘
y-1 nJ
Po
sonic range. In employing that solution, the factor - ( p o / p J 2n
From the data given in Table 1 for test 65, for example, the
heat reception could thus be estimated as 0.178 C.H.U., and occurring in the coefficient to the integral in equation (13) was
since the time of discharge was given as 15-8milliseconds, the left unaltered, inasmuch as the equality of n to y had been
corresponding mean rate of heat transfer could be deduced as assumed merely to assist in an approximate solution to the
integral itself.
11.2 C.H.U. per sec.
In that test the cylinder volume was approximately 2,000
eu. cm. which, in a two-stroke compression-ignition engine,
Dr. E. W. GEYER,B.Sc. (Glasgow), wrote that the author had
would be capable of producing approximately a full load stated, in his conclusions, that the coefficient of discharge would
brake horse-power of 30; experience suggested that jacket have to be reduced to 0.75 in most practical cases if a large
losses would be of equal order. Jacket losses provided an in- nozzle area were exposed. The following observations would, he
dependent criterion of heat transfer capacities, so that, under thought, explain that marked decrease in the coefficient and
normal running conditions, the author’s cylinder volume would also show that only under certain conditions might the steady
be called upon to impart approximately 30 x 550/1,400 = 11.8 flow theory be applicable to the discharge of gases from vessels
with no inflow.
C.H.U. per sec.
Hence the heat transfer requirements necessary to secure the
If at any instant t seconds after flow from a vessel commenced,
observed depression in the index of expansion, n, to 1,25 in the mass of gas contained in the vessel was M Ib., and the
test 65 were commensurate with the transfer capacities of an temperature was T, then in time 6t an element of mass 6M
equivalent engine cylinder under running conditions. That con- would escape into a region where the constant pressure p b was
clusion became even more difficult to understand when it was maintained. Both the mass remaining in the vessel (M-SM)
realized that the mean temperature difference across the liner and the escaped mass SM were assumed to have expanded
in the experiment cited was of the order of 30 deg. C., whereas isentropically but while the mass M-6M experienced only an
the mean difference under working conditions was likely to be elementary change in temperature ST’, the element 6M was
about twenty times that amount. The fact that, experimentally, subjected to a finite drop in temperature from T to Tb where
r-1
heat was flowing into the cylinder, whilst practically, heat was
flowing out, did not appear to be of appreciable influence. Thus, T b was equal to
The total internal energy given up
on the basis of equal temperature difference across the cylinder
walls, it seemed that the author’s heat transfer requirements was thus ( M - 6M)6E+ 8Mc,( T - Tb),i.e. MsE+EZM- Eb8M j
RTb8M
were far in excess of the capacities of a normal engine cylinder. externaI work amounting to pb6v
- -had, however,
J Pye* had quoted the value of 1.30 for n for the compression
curve of a high-swirl, sleeve-valve engine ;that value, obtained been performed so that the total ideal available energy was
with far wider pressure and temperature ranges, with a
MSE+E S M - E~+?)SM
deliberately high scrubbing-velocity, yet with a time of compression comparable with several of the author’s times of
= MSE+ESM-H$M
expansion, remained appreciably greater than many of the
= McUST+EGM-H~~M
author’s values.
and if there were no losses, that could be equated to the energy
However, if the author’s initial charges were saturated-for
the initial temperatures and pressures given for the air tests of acquired by the escaping element, i.e.
V2
Table 1, that would represent a vapour mass content of only
Mcv6T+E6M-HbSM = 5 S M
(21)
* BE,
D. R. “The Internal Combustion Engine” (Oxford Univerwhere V was the velocity of the issuing element.
sity Press).
-(-)
.($Iy.
(
..
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COMMUNICATIONS ON DISCHARGE O F EXHAUST GASES I N TWO-STROKE ENGINES 113
1
Professor L. J. KASTNER,
M.A., M.Sc., M.I.Mech.E., wrote
that some years ago a discussion+ had taken place on the true
CPT1u
since M = R T andP = (T‘‘’’ it fOllOWedthat M = 7explanation for the high performance attained by two-stroke
engines built to the designs of M. Kadenacy. In t h i s discussion
giving 6T = R ( y - ~ ~and~ by
, the substitution of 6T in oninion had been divided between the view that the high verf6rmance was due to the exhaust gases being discharged Gom the
CvT7-l
cylinder en masse through an exceptionally large exhaust orifice
and leaving a depression behind them, and the opposing view
equation (21) the following relationships were obtained :that the exhaust discharge was not “ballistic” in character, and
differed in no way from the normal discharge predictable by
orthodox theory, the high output of the engine being ascribed
to excellent porting arrangements aided by exhaust pipe tuning.
Experimental evidence was produced in support of each point
P
c, -cv
since-C = y andy-1 =
of view: the exponents of the ballistic discharge theory drew
cv ’
attention to the sustained high performance of the Kadenacy
Ty-1
engines over a considerable speed range and denied that engines
employing exhaust pipe scavenging could do so well; the
supporters of the more orthodox view sought evidence for the
existence of the ballistic discharge, and, not finding any, were
unable to credit its existence.
As a result of the author’s experiments some part of the
position taken up by the supporters of the ballistic discharge
theory had now been undermined. He was surprised that the
author had not referred to the experimental evidence which had
or
been produced in that earlier discussion, not only because much
Thus, the author was justified in assuming that, at any instant, of it was concerned with sudden discharges of the type
the velocity of the jet could be found from the isentropic heat investigated with his own apparatus, but also because some
drop between the instantaneous pressures existing in the diagrams shown at that time had also been obtained with a
cylinder and nozzle exit, but one important reservation had to cathode-ray oscillograph indicator and had given results not
be made. If the exit area were a large fraction of the cylinder area agreeing with those obtained in his tests. It might be that
then an appreciable amount of energy would have to be acquired electronic indicators could give equivocal results and much
by the contents of the vessel and equation (21) no longer applied. might depend upon precise calibration where a particular presThe distribution of velocity throughout the vessel was probably sure-sensitive element was concerned.
Although the author’s remarks regarding gas temperature
complex, but, in developing the theory of the Kadenacy system,
he had assumed that it varied uniformly from zero at the closed were appreciated and understood, he felt that the supporters
end of the cylinder to a maximum value V1 at the nozzle end, of the ballistic theory-among whose number he himself was
and that the velocity across any section, at right angles to the not to be included-could always point to the fact that the gas
cylinder axis, was uniform. The energy due to that system was in the discharge apparatus was initially at atmospheric temperature, and suggest that that might make some significant
then L z p A d x , where L was the length of the cylinder, A the difference. Where the existence or non-existence of an obscure
phenomenon was to be investigated, inferential reasoning, of the
employed by the author, was satisfactory to those already
cross-sectional area, and p the density at a distance x from the type
converted to a particular point of view, but was no substitute
closed end. If it were assumed that V = Bx and that p was the for a direct experimental approach with the closest possible
mean density of the cylinder contents, the integration gave
simulation of practical working conditions. Until the dif€icuIties
consequent on accurate measurements of instantaneous temperature had been to some extent overcome, the direct refutation
of the Kadenacy theory was, in his view, hardly possible.
where M , was the mass of air in the cylinder at time t .
The author’s results for the coefficient of discharge were most
The energy equation then became
interesting, and certainly appeared to be in harmony with
Stanton’s. The author might, perhaps, not be aware that similar
results had been obtained from tests on model poppet valves,
where high coefficients were found to apply to conditions of
Equation (22) was only approximate because the velocity small lift, the coefficient decreasing rapidly when the valve
variation both along the length of the cylinder and at right opened more fully.
angles to it was not known, but the expression indicated, in a
The paper described the results of one or two tests with an
general manner, the effect on the velocity of efflux. That was exhaust pipe fitted to the discharge ports of the apparatus, and
necessarily reduced, with a consequent increase in the time of the author had rightly observed that the matter was by no means
discharge or in an apparent decrease in the coefficient of as simple as the familiar organ pipe resonance. It was a subject
discharge.
of very considerable interest and complexity, on which a great
With reference to the author’s statement on p. 100 that deal of work had been done both in this country and on the
“contrary to expectations this expansion was found not to be Continent. For an investigation of pipe phenomena, a static
adiabatic” he pointed out that in an article he had written*, discharge apparatus might seem at first sight attractive, and it
the index of expansion had been given as considerably less than could give some useful results, but a proper study demanded the
1.4 in a practical case. It might reasonably be claimed that it use of an engine.
would be contrary to expectations to find that isentropic conNo reference appeared to have been made in the paper to the
ditions prevailed, since the isentropic temperature drop, corre- short interval between the instant of opening of the exhaust and
sponding to a pressure drop from 75 to 15 lb. per sq. in. would
t DAVIES,S. J. 1937 Engineering,vol. 143, pp. 685 and 715, “The
be of the order of 200 deg. F. and would thus necessitate a very Characteristics of Engines of Kadenacy Design”; 1940 (a)Engmnemng,
rapid flow of heat from the walls of the vessel. The same argu- vol. 149, p. 17, “Sudden Discharge of Air from a Pressure Vessel”,
ment applied to the expansion through the nozzle, and he found and (b) p. 515, “An Analysis of Certain Characteristics of a Kadenacy
it difficult to reconcile the author’s assumption that the flow in Engine”.
HENDERSON, J. B. 1939 Engineering, vol 148, p. 378, “Phenomena
the nozzle was isentropic while that in the vessel was nonof the Exhaust of Internal Combustion Engines”.
isentropic.
G.F.1939 Engineering, vol. 148,p. 187, “The Kadenacy
MUCKLOW,
* GEYER,E. W. 1939 The Engineer, vol. 168, p. 60, “Time of System of Scavenging”. Communications thereon, pp. 207,330,357,
421, 589; and 1940, vol. 149, pp. 19, 122,286,443, and 509.
Discharge of High Pressure Gases”.
9
-
-
-
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114
C O M M U N I C A T I O N S ON DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
the instant of opening of the inlet in a two-stroke engine..In
the author’s cxample, at maximum governed speed that interval
was just over two milliseconds, and afterwards both scavenging
and exhausting occurred. The author might be interested in the
discharge cylinders developed by List and Niedermeyei*, in
particular the design employing a positively controlled piston j
Niedermeyer considered that Lx speeds above 1,100 r.p.m. such
a refinement was indispensable. The author had rejected the
possibility of extending the use of his apparatus to an investigation of scavenging effects, and, in view of the intimate connexion
between scavenging and exhausting in the two-stroke engine,
that seemed regrettable.
was suddenly opened and equally suddenly closed after 0.845
milliseconds. Such a transient flow process could be analysed
by the method of characteristics. Fig. 35 represented a position
25.4
/%i
A-
--A
Dr. J. KBSTIN,A.M.I.Mech.E., and Mr. J. S. GLASS,
G.I.Mech.E., wrote that the paper tried to prove that the process
of expansion in the cylinder was polytropic, i.e. reversible with
an intensive exchange of heat between the gas and its surroundings.
The main assumption was that the equations for continuous
gaseous fluid flow‘from a source of high pressure to a region of
lower pressure, through an orifice or nozzle, applied to that
transient phenomenon which lasted only about ~ A f isecond. It
was very difficult to conclude from the data supplied in the
paper that that was the case owing to the fact that agreement
between experiment and calculation was based on two experimental magnitudes: the coefficient of discharge K, and the
polytropic exponent n. The values for either, given in the paper,
seemed open to doubt. They suggested that it would be necessary
to estimate the actual flow by a method in which the transient
character of the phenomenon was taken into account. Such an
estimate could be obtained with the aid of the method of characteristics (Courant and Friedrichs 1948, Meyer 1948, and Kestin
and Glass 1948)t.
The author’s argument, which was centred around the adoption of a polytropic exponent n smaller than y, seemed to be
open to criticism from two points of view. First, the assumption Numbers represent pressure, lb. per sq. in. (upper number) and
that the expansion of a gas particle inside the cylinder was velocity, ft. per sec. (lower number) corresponding to the state of the
polytropic implied that there was an intensive exchange of heat gas along the axis of the cylinder.
with the surroundings. That was improbable as evidenced by
the failure to establish a heat balance with the aid of heat diagram for that example. The values were of the same order as
transfer data. Secondly, the assumption implied that the process those in some of the author’s experiments, and the state of the
inside the cylinder was quasi-static and reversible, which meant gas could be assumed constant in each area bounded by characthat the high velocities acquired by the gas particles were teristics.
Fig. 35 indicated the change of state and velocity at each
neglected. Gas particles near the ports acquired kinetic energies
which were comparable with their internal energy, and owing to point with time, and the distribution of states and velocity at
friction and disturbances part of the kinetic energy would be each moment along the axis of flow. Consequently, the kinetic
continually transformed into heat. The irreversible transforma- energy of the residual gas could be estimated at the moment
tion of kinetic energy into heat was particularly pronounced when the cylinder was closed. The mass, pressure, and velocity
during a short interval of time immediately after the ports were distribution after the sudden closing, i.e. after 0.845 milliclosed. The state of motion, existing immediately before closing, seconds, was seen to be, from Fig. 35, as follows :subsided owing to the presence of viscous forces, and the internal
energy of the residual gas was thereby increased. Such an Mass, 10-5 lb. . 80 174 190 190 135 248 80 305 160/8
irreversible process superimposed on adiabatic and reversible
expansion caused the apparent index of expansion to decrease.
Pressure, lb. per
In a Clement-DCsormes experiment, conditions had to be
sq. in. .
created to minimize the influence of high particle velocities
inside the cylinder and irreversible energy conversion. In the Velocity, ft. per
sec.
. . 0 93 186 280 373 467 560 653 840 902
problem under examination those phenomena were an integral
part of the process, and could not be neglected.
In order to illustrate the method of obtaining an estimation If the gas then attained equilibrium under adiabatic conditions
of the apparent index of expansion n, they had considered, as an its temperature would be determined by :example, a vessel of volume 0.07 cu. ft., 6 inches long, at a
Zmi(cvT,+’t?;.2/2g)= M,c,T,
pressure of 116 lb. per sq. in., and an initial temperature of
522 deg. F. The mass of the gas, M , was then determined by where m was the mass of gas in a region; c,, the specific heat at
the equation of statepv = M R T . It was supposed that the vessel constant volume; T,the particle velocity; and the suffues
was perfectly insulated, and that at a certain instant one end i, r, and e referred to initial, residual, and equilibrium conditions
respectively.
* NIEDERMEYER,
E. 1936 Forschung V.D.I., vol. 7, p. 227.
The equilibrium pressure followed from the equation of state
LIST,H., and NIEDERMEYER,
E. 1937 Forschung‘ V.D.I., vol. 8,
pv = MRT. After a certain initial period, during which the
p. 265.
E. 1949 Maschinenbau und Warmewirtschaft, vol. 4, rarefaction wave initiated upon opening reached the fixed
NIEDERMEYER,
cylinder head, the pressure along the axis of Aow was almost
pp. 1 and 18.
t COURANT,
R., and FRIEDRICHS,
K. 0. 1948 “Supersonic Flow and uniform. However, the equilibrium pressure was higher than
Shock Waves” (Interscience Publishers, New York and London).
that prevailing in the cylinder immediately before closing. In
MEYER,
R. E. 1948 Quarterly Jl. Mechanics and Applied Mathe- the actual example,
matics, vol. 1, part 2, pp. 196-215.
p , = 31-5 lb. per sq. in.
J., and GLASS,
J. S. 1948Proc. I.Mech.E., vol. 159, pp. 292KESTIN,
Te = 378.2 deg. F.
294, Discussion on the Wave Action of Gases.
I 1 ! I 1 I 1 1 1
1
~
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j
1 1 I 1 I 1 I
C O M M U N I C A T I O N S ON DISCHARGE O F E X H A U S T G A S E S I N TWO-STROKE E N G I N E S
That process had been plotted for a unit mass of gas, in
Fig. 36.
As the expansion in the cylinder was isentropic, the states
would traverse the initial isentrope, but the work of expansion
would be partly used in ejecting the gas particles into the atmosphere and partly in increasing the kinetic energy of the gas
remaining in the cylinder. When the cover closed, the residual
I
115
After a longer time, the state of the gas would change from
e to X at constant volume, as in the ordinary CICment-D&omes
experiment.
In their example, they had obtained
p x = 43.5 Ib. per sq. in.
lnpo -We= 1.32
lnPo -&x
Those values gave only an estimation of the trend and could
not be taken as being numerically exact, because it was assumed
that only the kinetic energy of the residual gas was converted
into heat, the quantity of heat converted from the kinetic energy
of the particles which had left the cylinder having been neglected.
Some heat might also have been added to the gas from the
outside; its quantity should be of the order indicated by heat
transfer considerations, but in an actual engine the direction of
the flow of heat might be reversed. Those reasons would explain
the fact that their value of the index n was higher than that
measured by the author.
The rather surprising values for the coefficient of discharge,
K,were obtained from the author's values of n, and on the basis
of the assumption of a polytropic change, so that it was difficult
to forward any suggestions on that point.
and
n=
Mr. W. P. MANSFIELD,
BSc. (Eng.), A.M.I.Mech.E., wrote
6 that, since the findings of the investigation were dependent on
measurements taken from cylinder pressure diagrams, it was
desirable that there should be some evidence that the diagrams
were
accurate. Very little description of the indicator was given,
Fig. 36. Theoretical Exhaust Phenomena
but it was stated that the pressure unit was of the condenser
(a) Expansion curve.
(b) Rarefaction wave.
type and that the circuit employed was such that the equipment
recorded static pressures as well as rapidly changing pressures,
gas in the cylinder underwent an irreversible process, as a result thus enabling calibration lines to be added to a record imof which its state became uniform, but at a higher value of mediately after discharge. The assumption appeared to have
entropy, at the point e.
been made that the dynamic response corresponded exactly to
In an actual process, with viscosity present, the two processes the static response, namely, that a diagram ordinate produced
were combined, and the actual path would be similar to that by a given pressure applied constantly would be reproduced
shown in Fig. 37.
exactly when the same pressure was traversed during the course
of a rapid change. That was not necessarily the case : indeed, it
P
was difficult to arrange the diaphragm of a pressure unit in such
a manner that its deflexion for a given pressure should be
PI
independent of the rate of change of pressure.
In the development of condenser type pressure units which
were commercially available, it had been found necessary to
limit the diaphragm deflexion to a value of the order of one-tenth
of a thousandth of an inch and to pay special attention to the
design of the diaphragm seats and clamping arrangements, in
order to obtain satisfactory dynamic behaviour. Details of the
diaphragms employed by the author would be of interest.
Clamping arrangements of the type suggested by Fig. 1 had not
been found satisfactory.
The pressure records indicated that at least three types of
error were present in the indicating equipment. It was stated
that with the lighter diaphragm in use, the oscilloscope spot
did not start to move until the pressure in the cylinder had
fallen to 20 lb. per sq. in. gauge. Accordingly, an abrupt initial
movement of the spot would be expected, since, when the pressure had fallen to 20 lb. per sq. in. gauge, the rate of change of
pressure had a high value, which was decreasing, as shown by
the records obtained with the thicker diaphragm. The light
L
z'
diaphragm records, such as Fig. 7, indicated, however, that the
rate of change of pressure at 20 lb. per sq. in. gauge was low
Fig. 37. Actual Expansion Process
and subsequently increased. The existence of that defect, which
The entropy would increase all the time, and the pressure was apparently due to some lag in the response of the indicating
wauld fall along a line differing from an isentrope, the lowest equipment, cast doubt on the validity of the lower parts of those
pressure being of the order of that at point e. The shorter the records.
In another test, according to Fig. 12, the cylinder pressure
time of opening the less the line ae deviated from the isentrope.
By the application of equation (I), an apparent index of expan- fell from 60 to 10 lb. per sq. in. gauge in 3 milliseconds and
sion, smaller than y, and deviating from y further as the time then during the next 2 milliseconds oscillated between 5 and 10
of opening increased, in accordance with Fig. 8, could be found. lb. per sq. in. gauge. The diagram indicated that the oscillation
A larger open area would tend to cause larger velocities, hence occurred about a mean pressure of 7.5 lb. per sq. in. gauge which
the deviation would tend to be more marked with all the ports was maintained at a time when the cylinder was in communicaopen than with only two. That did not, however, justifv the tion with the atmosphere through ports which were well open,
assumption that the gas inside the cylinder expanded according as shown by the port area diagram. It was much more likely that
to the law pv" = constant. They concluded, subject to experi- an oscillation occurred about atmospheric pressure, and that the
indicator failed to respond to the full pressure drop immediately.
mental correction, that the index n changed with time.
a
b
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116
COMMUNICATIONS ON DISCHARGE O F EXHAUST GASES I N TWO-STROKE ENGINES
If that were so, the record indicated that the pressure fell during
the oscillation to 2 5 lb. per sq. in. below atmospheric pressure,
a depression of the order of those recorded by other investigators.
No reliance could be placed on such measurements in the present
case, however, in view of the third defect which was apparent.
The author stated that the wavy line which occurred on the
records some & second after the discharge was due to the sleeve
hitting the stop. An oscillation at a similar frequency occurred
on important parts of some of the records, notably Fig. 22, but
no explanation of those oscillations had been given. It appeared
likely that they were due to a smaller vibration occurring earlier,
and were therefore spurious.
As a means of recording minimum pressures, and hence also
of determining whether a sub-atmosphericpressure was reached,
the indicator did not compare favourably with the Sunbury
balanced disk valve unit used in the experiments described by
Davies (194Oa)*. In one test a steady depression of 4 lb. per sq. in.
was applied to the side of the disk remote from the cylinder, and
when the gases were discharged a movement of the disk across
to its farther seat was recorded by the osdlIograph. Only the
existence of a depression in the cylinder greater than 4 lb. per
sq. in. could have produced that result. It was regrettable that
such a simple and reliable device was not used in the present
investigation to check the minimum pressures indicated by the
condenser pressure unit and thus provide a dynamic calibration.
That would have greatly enhanced the value of the work.
Mr. R. W. STUARTMITCHELL,
A.M.I.Mech.E., and Mr.
FRANK
WALLACE,
M.Sc., wrote that they were particularly
interested in the work described, since they were making similar
tests and their results, so far obtained, conflicted with those of
the author. They were using the author’s electronic indicator in
a slightly modified form, and they had found that it gave good
service.
They had given much thought to analyses of the low values
obtained by the author for the index of expansion of the gases
in the cylinder, in an endeavour to find an explanation. The
measurement, from the diagram, of the minimum pressure in
the CICment and DCsormes experiment was immediately
suspect but examination showed t k t , in the case of the slowest
discharge of air, quoted in Table 1, an error of 4-7lb. per sq. in.
in 30.5 Ib. per sq. in. (both figures approximate) would be
necessary to bring the index to 1.4. Again, leakage of air, whilst
heating up at constant volume to the final pressure, might be
a source of error but the maximum leakage would have to take
place in the slower tests, where the minimum pressure was least
and that seemed improbable.
The author’s theoretical analysis for gas discharge was concise
for the special condition obtaining in his apparatus, where the
cylinder volume was constant during discharge. They would
criticize the placing of the coefficient of discharge K, outside
and not inside, the time-area integral. Since the shape of the
port opening, over the discharge period, varied from a thin slot
to an almost square one, considerable variation of K must be
expected and further, since some of the avmuge values obtained
were close to unity, the corresponding maximum values would
be in excess of that figure.
In their own experiments, a two-stroke opposed piston engine
liner was sealed at either end by its own pistons, both of which
were adjustable; one was used to provide different degrees of
port opening whilst the other varied the effective length, and
hence volume, of the cylinder for a given discharge. The
cylinder was charged with air to a known release pressure, and
a sudden discharge was effected by bursting a cellophane
membrane incorporated in the joint between the port ring and
the exhaust system. The pressure changes in the cylinder were
recorded on a drum camera by the author’s electronic indicator.
The coefficient of discharge was obtained by an analysis similar
to that presented in the paper but adiabatic conditions were
assumed throughout. The equation of discharge became (using
the author’s notation)
KAt =
2v
(r- 1
) r n
* See reference at foot of p.
113.
and since y = 1-4
which should be compared with equation (10) in the paper.
Fig. 38 showed the comparison graphically for a release pressure
of 60 lb. per sq. in. (gauge).
Fig. 38. Expansion Process for Different Values of n
A-n = y = 1.4.
D-n = 1-27.
B-n = 1-37.
E-n = 1.23.
C n = 1.33.
Preliminary results from the writers’ experiments were plotted
in Fig. 2 for a pressure drop from 60 to 40 lb. per sq. in. and
showed that the coefficient of discharge varied from unity, at
zero port opening, to approximately 0.74 for full opening. The
ports were rectangular (10 mm. x 35 mm.) and sharp edged. If
the author’s equation (10) had been used to evaluate K,values
exceeding unity would have resulted, particularly since the
higher values of K occurred for slow times of discharge. It
appeared that, for their own experiments, the assumption of
adiabatic cylinder expansion was justified.
Fig. 39. Coefficient of Discharge
The dotted line w
the law
e in Fig. 39 showed a curve representing
K = -Cd+l
height of instantaneous port opening
and
where was the ratio
height of full port opening
C was constant.
That would enable the time-area integral in equation (lo),
with K inside the integral sign, to be evaluated. The actual
curve shown was represented by :K = -0.26m2+ 1
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COMMUNICATIONS ON DISCHARGE OF EXHAUST GASES I N TWO-STROKE ENGINES
That equation applied to conditions corresponding to equation
(15) in the paper and gave
Hs
0.8’7
Adt = -At
2
where A was the area at time t .
The factor 0.87 corresponded to the author’s coefficient of
discharge. That figure was based on adiabatic expansion and
the use of an index of the order of 1.24 would bring it back to
near unity.
Some preliminary results obtained from their own tests were
plotted in Fig. 39; the curves of Kobtained with release pressures
of 70 and 50 lb. per sq. in. suggested that for a given fixed port
opening, the coefficient of discharge varied according to the
range of the pressure drop.
It was difficult to understand why the coefficient of discharge
for the tulip valve experiments was so low. The author mentioned the possibility of heat transfer from the valve seat, although
in the theory from which he obtained his results, the expansion
through the ports was assumed to be adiabatic. An analysis of
the problem, where the adiabatic condition was not fulfilled,
could be made for the first stage above the critical pressure
thus :Let n be the index of expansion in the cylinder; m, the
index of expansion from the cylinder to the port; V,the gas
velocity in the port, then :=y
V2
-33
117
conditions were assumed throughout the expansion, i.e. in the
cylinder and from the cylinder to the port, K would be reduced
from 0.75 to 0.675. Those values depended an the accurate
determination of the geometrical flow area and they thought
that might be a source of error.
In the practical example worked out in the paper they were
not in complete agreement with the use of the simplified formula
nor some of the assumptions made. Also, with the value of
y = 1.375, the critical pressure ratio would no longer be 0 5 3
but 0.5326. For the discharge below the critical pressure ratio
the author had assumed a constant back pressure which did not
conform with engine conditions where an exhaust pipe was
fitted.
Fig. 40 showed the type of pressure-time curve which they
obtained from their own discharge apparatus. The “stepped”
form of the discharge curve was in complete accord with wave
theory particularly that put forward by Bannister and Mucklow
(1948)*. The differences between the two diagrams were due
to Merent release pressures of 50 and 80 Ib. per sq. in. respectively and cylinder lengths of 8.841 and 5.913 inches respectively.
The distance AB was a measure of the time occupied by the
first stage of discharge, and the agreement between theory and
experiment was good. Considering the ratio time interval AB
for Fig. 40bltime interval AB for Fig. 40a, the theoretical value
was 1.48 whilst the measured value from the diagrams was 1.54.
The other steps in the discharge gave similar agreement.
Mr. D. J. RYLEY,B.Sc. (Eng.), A.M.I.Mech.E., wrote that
he thought the author was to be commended for the ingenuity
he had shown, especially in respect of the indicating equipment.
As the velocity at the port was sonic
It was debatable how far the results achieved enabled predictions to be made concerning port effects in actual engines as
2 - 2Pl
there were a number of serious differences between the author’s
The combination of those two equations would give a ratio discharge apparatus and the ports in the orthodox two-stroke
engine. The ports in actual engines were usually uncovered by
corresponding to the critical pressure ratio,
the piston and not by the coincidence of similar ports in the
moving sleeve; thus in the discharge apparatus the length of
m
1
port in the direction of gas flow was greater than in an engine.
m- 1
Also, the sleeve provided a different set of surrounding
- [K.,-a.l]
boundaries from the piston and it would affect the streamlines
of the gas approachingthe port, especially during partial opening.
An analysis similar to the author’s in the paper, would give :Furthermore, even when oil nearly submerged the tension
m+l
2v
f
.v
b-f/:
springs, in the author’s apparatus there was still a space below
the ports to be emptied which had no counterpart in a real
engine. More seriously, in all actual engines, there was an
annular belt surrounding the exhaust ports to convey the exhaust
r+l
l+y to the manifold, and the ports themselves sometimes had
which was similar to equation (10) with the term ( ~ ) ~ ( ‘ ‘ - l gases
)
curved axes, to facilitate the entrance for the gases. The inner
m+l
boundaries of such an annular space might also affect the conreplaced by 1+ 7 z(m-l). For an extreme case where ditions obtaining within the ports, especially during the subsonic part of the exhaust discharge when pressure variations
\
-m-ll
could be transmitted backwards from walls to ports.
m = 1.23, the nvo factors were 1.728 and 1.932 respectively.
The author’s decision to use springs instead of a connecting
Hence, for the same observed rate of discharge, the coefiicient rod and crank on account of the difficulty of glanding was rather
of discharge would be increased in the ratio of 1-12 for the non- an unfortunate one, since, if the moving sleeve had been placed
adiabatic conditions. The actual‘increase in the value of K was
from 0.75 to 0.839, a value which still seemed low. If adiabatic
* See reference at foot of p. 110.
Vz-m
($)
a-
,
’
I
-
41
71)
30
-
-0
b
n
Fig. 40. PressureTime Curves
(a) Release pressure 50 lb. per sq. in. Cylinder length 8.841 inches.
(b) Release pressure 80 lb. per sq. in. Cylinder length 5.913 inches.
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118
C O M M U N I C A T I O N S O N DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
on the outside, there would have been no need for glanding. If
a crank and connecting rod were used an unobstructed interior
would be gained and it would still be possible, by inversion of
the apparatus, to secure a varying internal volume by the use
of oil. Moreover, the ports could be placed at the end of the
cylinder thus simulating engine practice.
He felt that it was necessary to be conservative in deciding
the numerical values of discharge coefficients, excepting those
obtained by direct experiment. That coefficient was a function
of two groups of factors : mechanical and thermodynamic, the
first group relating to the physical size, shape, and disposition
of the ports, and the second to the properties of the fluid;
viscosity, Reynolds number, etc. Thus, for example, for the first
group it was well known that a small chamfer or radius on the
approach side of an orifice substantially affected the value of
the coefficient. For the ports on the author’s apparatus there
were probably a number of different values for the discharge
coefficient, corresponding to the different degrees of opening ;
the numerical values obtained for the exhaust operation were
in the nature of mean effective ones and depended, amongst
other things, upon the A-t characteristic of the ports. They
would be governed both by the magnitude of JAdt and also by
the manner in which that integral was composed. The variation
caused by the first effect could be explored by altering the spring
setting in the discharge apparatus, whereas the variation caused
by the latter effect was outside the scope of the apparatus.
If the sleeve were placed on the outside as previously suggested
and a crank and connecting rod mechanism were used, as shown
.
process of engine exhaust and that no mystical “ballistic”
velocities were involved, but he did not agree that vacuum
pressures were non-existent after a sudden discharge from the
cylinder. The author had only recorded vacuum pressures when
an exhaust pipe was attached to the cylinder, and in two other
instances that he had attributed to experimental error.
The application of Bernoulli’s theorem, which ignored gas
inertia, seemed inadequate to explain the transient vacuums
with or without an exhaust pipe. In the case of a sudden discEarge, depressions did occur, and their behaviour could be
predicted by the pressure wave theory.
The author had probably failed to observe vacuum pressure
in the cylinder because of the relative slowness with which the
exhaust ports had been opened. The total port area was only
approximately 23 per cent of the piston area, and even if the
ports were opened instantaneously the ensuing vacuum in the
cylinder (originally filled to 61 lb. per sq. in. gauge air) would
only be about 0.4 inch mercury, and that might have been too
small to record with a condenser type pressure element which
was difficult to calibrate accurately for small pressures. If the
port opening expressed as a percentage of piston area was plotted
against time in milliseconds, test No. 296 showed a rate of
opening slower than in the General Motors Model 71 engine,
and even the fast test No. 323 gave a slower rate of port opening
than the Fairbanks Morse, 8-inch bore, 10-inch stroke, 720
r.p.m., opposed-piston engine.
He had already pointed out (Schweitzer, Van Overbeke, and
Manson 1946)* that an obstacle to the full exploitation of the
Kadenacy effect was that exhaust ports or valves could not be
opened rapidly enough. The rates of opening employed in the
author’s apparatus were of the magnitude occurring 111 engines
but were far from the almost instantaneous openings he had
employed himself.
He found it hard to visualize that a sharp-edged orifice should
-give a hieher coefficient of discharge than a rounded orifice.
For discgarge measurements the &gle blowdown seemed to
have little advantage over the intermittent blowdown or steady
flow. In using the latter he had measured$ some 20 per cent
larger discharge by rounding the edges of an exhaust port.
Dr. J. H. WEAVING,
in reply, wrote that he agreed with
Dr. Bannister that the fitting of an exhaust pipe without a
receiver would make the calculations on pp. 108-109 inaccurate.
The consideration of a simple general application, assuming a
receiver giving a steady port pressure, was more appropriate than
in Fig. 41, the following theory became applicable :catering for the many variant applications when a resonant
x = r [ l - cosB+n-2/(n2sin28)]
exhaust system was fitted. The fitting of exhaust pipes to such
= r [ l - cos w t + n - d ( n 2 - cos2 4 3
an engine did not render invalid the application of equations (13)
If the height of the opening was W,the total circumferential and (18), but only altered the limits of integration, which in
length L, and the piston travelled a distance d before opening some cases would have to be taken as an average value.
He agreed that more accuracy could be obtained by applying
commenced,
Dr. Bannister’s further corrections, for the practical calculaW = r [ l - coswt+n--(nzcos2wt)l--d
of port areas.
a d A = WL = L{r[I- cos WZ+YZ- .\/(a’- ~ 0 ~ 2 w t ) l - d ) tion
He thanked Mr. Benson for pointing out a numerical error
and JAdt = LJ{r[l- cos u r + n - 2/(n2- cos2wt)J-d)dt
in the advance copy. That had been corrected in the PROCEEDINGS.
That integral could be evaluated readily for a specific case, It was correct that an exhaust manifold pressure of 14.7 lb. per
sq. in. was assumed, but it was further assumed that it was only
and the A-t characteristic was similar to that shown in Fig. 4 2
necessary to expand the cylinder contents to the scavenge
pressure, 17.7 lb. per sq. in. abs., before opening the inlet ports,
and that was, therefore, the JAdt required for exhaust lead. M r .
Benson might have been misled by another error in the engine
data in the advance copy where “Inlet ports open” should have
read “Exhaust ports open”.
Several contributors to the discussion had remarked on the
low value of n. Generally, the author was equally reluctant to
accept values of n less than y (see p. IOI), but that was forced on
~R.D.C.
1F.d
him by the consistency of experimental results. Although it
needed a considerable rate of heat transfer and energy converFig. 42. A-t Characteristic
sion in the cylinder, that occurrence seemed possible for reasons
The permanent value of the present paper was that it detailed later in the discussion. However, there seemed no
demonstrated incontestably the validity of Bernoulli’s theorem reason for altering the assumption of adiabatic expansion in the
port, which was supported by the experiments of others (Stanton
when applied to the exhaust process.
1926).
Professor P. H. SCHWEITZER, D.Eng. (Pennsylvania) wrote
* See list of references in Appendix 11, p. 110.
that he was in agreement with the author’s contention that
-f. SCHWEITZER,
P. H. 1949 “Scavengmg of Two-Stroke Cycle
conventional thermodynamic theory adequately explained the Diesel Engines” (Macmillan).
Fig. 41. Engine Mechanism
11. = n.
IA
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COMMUNICA‘TIONS ON DISCHARGE O F EXHAUST G A S E S I N TWO-STROKE E N G I N E S
3,000
n
$250
=
-
I
VOLTS
-
1,000 52
119
$250 VOLTS
TO SECOND UNIT
0
+4W VOLTS
I50,000Q
d
C
Fig. 43. Pressure Indicator Circuit
First unit, oscillator.
(b) Second unit, amplifier.
(a)
Dr. Cole suggested that water vapour might account for the
low values of n obtained, and that possibility had been considered. Test 291 was performed with air passed through a
copper-coil trap immersed in liquid air (a value of n = 1-26at
c = 10-5milliseconds was obtained (see Fig. 8)). Tests after
test 100 were performed with gases from gas cylinders at 120
atm. pressure, which, even if saturated at that pressure would be
negligibly wet when expanded to the condition used ih the test.
It was the discrepancy between the theoretical heat transfer and
that required by the low value of n that led the author to suggest
a second source of heat, namely, the degradation of kinetic
energy, partly in the form of transitional velocity, and partly
turbulence, to heat.
In his treatment of the problems in terms of energy equations
involving heat values, which could not readily be measured,
Dr. Geyer appeared to assume that the author had ignored two
important points, namely, that the gas remaining in the vessel
did not expand fully and, secondly, that energy was given to the
contents of the cylinder. If he would examine the mathematical
treatment he would observe that an elemental mass d M under
conditions of expansion p v n = c was equated to an equal
elemental mass being ejected with the discharge velocity; that
allowed for the first point. Secondly, the index n was an experimental one actually measured and would thus be affected by any
energy given to the gas in the vessel.
Dr. Kestin and Mr. Glass also made calculations to estimate
the heat value of kinetic energy remaining in the vessel. Those
were interesting, and although involving rather large assumptions, confirmed the author’s statement that the kinetic energy
helped to explain the low values of n which he agreed was a
purely empirical index, taking into account the conditions of the
experiment. It was not a reversible gas law.
He supplied further details of the pressure indicator as
requested by Mr. Mansfield; they had been omitted from the
(c) Third unit, combined amplifier and rectifying circuit.
( d ) Voltage stabilizer for supplying (a), (b), and (c).
paper for brevity. The circuit (Fig. 43) consisted of three
principal elements, the first unit (a) being a resistance stabilized
oscillator supplying a carrier frequency of 110 kilocycles. The
second unit was an amplifier stabilized by negative feed-back
supplying a tuned resonant circuit, the main condenser of which
was the pressure element. That was followed by (c) a combined
single-stage final amplifier and rectifying circuit. The whole
unit was supplied from a voltage stabilizer.
Each of Mr. Mansfield’s three statements of apparent inaccuracy were manifestly incorrect, as could be seen from a
study of the diagrams alone, and appeared to be made from
his anxiety to create a depression in the vessel. He (Dr. Weaving)
would therefore deal with the matter in detail: in connexion
with Fig. 7, his statement that “with this [high] sensitivity, the
oscilloscope spot does not start to move until the pressure has
dropped to 20 lb. per sq. in.”, required further elucidation for
those not familiar with resonant condenser inductance circuits.
He should have stated “does not start to move appreciably”.
Fig. 44 showed a typical resonant curve for such a circuit.
Thus, the indicator was limited for response to changes of
capacity represented by points from a to b and for approximate
linear response from points c to d. That latter position of the
resonance curve was used for actual pressure measure in all
tests. If the whole range of pressure was being explored, then
the sensitivity of the pressure element had to be reduced.
In Fig. 7, a light diagram was being obtained and point d
represented the condenser capacity at 20 Ib. per sq. in. so that
the drop from 61 lb. per sq. in. to 20 lb. per sq. in. was represented
by the portion bd on Fig. 44 and the effect in Fig. 7 was exactly
as would be expected. Mr. Mansfield’s statement that “Fig. 7
indicated, however, that the rate of change of pressure at
20 Ib. per sq. in. was low and subsequently increased” was
incorrect, and was made, presumably, because he mistook the
top (release pressure) line for 20 lb. per sq. in. line, whereas it
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120
C O M M U N I C A T I O N S O N DISCHARGE O F EXHAUST GASES I N TWO-STROKE E N G I N E S
was clearly marked 61 lb. per sq. in. in both the figure and in
the caption. The position for a 20 lb. per sq. in. line could be
roughly estimated, and it was then clear that the rate of change
of pressure was high at 20 lb. per sq. in and subsequently
decreased.
Mr. Mansfield had tried to derive a vacuum pressure of 2.5 Ib.
per sq. in. from Fig. 12. It.was peculiar that he should have
chosen a test made for the purpose of investigating the discharge
above the critical pressure (see Fig. 13) and consequently insensitive at low pressures, for that purpose. However, closer
inspection would show that the pressure line did not oscillate
about a mean of 7-5 lb. per sq. in. with the ports open, but
oscillated down a falling line to atmospheric at the position of
a
CAPACITY
(INCREASES WITH PRESSURE)
Fig. 44. Typical Resonant Curve
port closure. That was admittedly plainer on the original record
than in the reproduction. Had he taken a record of an identical
experiment (Fig. 22) with the indicator adjusted for low pressure recording, he would not have fallen into that error. In both
cases, it would be noted that the minimum pressure was atmospheric, though test 323 (Fig. 12) would not be admitted as
evidence.
He took exception to Mr. Mansfield‘s statement that no
reliance could be placed on certain pressure records, because of
the extraneous wave caused by the sleeve hitting the stop. He
did not make that statement without due consideration. From
the known maximum velocity of the sleeve, it was easy to estimate
approximately the time to hit the stop, which was of the order of
& sec. from the position of ports fully open, and it was clear
that the sleeve was not hitting the stop at port closure. The
gas vibration there was undoubtedly due to the rapid discharge
of hydrogen. He considered that the extraneous wave occurring
when light diaphragms were used was of little or no importance
as it occurred well after the ports had closed.
T o check the indicator for dynamic calibrations, several tests
were made, so that the ports remained open after expansion,
giving a dynamic diagram running tangentially into an atmospheric calibration line. Mr. Mansfield appeared to have ignored
the fact that the indicator that produced Fig. 22 also produced
Figs. 23 and 24, both indicating vacuum pressures.
He was interested in the discharge measurements that had
been made by Mitchell and WaIlace, but was not sure that they
were similar to those described in the paper, owing to the
method of port opening by bursting a cellophane membrane.
That condition did not obtain in practice, and would also render
equation (10) inapplicable as the latter was integrated for a steady
cylinder pressure drop, while it was clear from Fig. 40 that the
pressure drops in their tests were stepped due to the travel-back,
and reflection in the cylinder, of a sudden pressure drop, initiated
by the bursting diaphragm.
He agreed that theoretically the coefficient of discharge, K,
should be placed within the integral, but suggested that it would
be premature to decide what function of pressure ratio and port
opening was to be taken. It was first suggested that K was a
function of m, that is, K = 1-O~26m2, which was plotted in
Fig. 39, but also that it was a function of pressure ratio, as he
had found. If K were taken inside the integral, it must be a
function of m and pressure ratio. He considered it best, therefore, to leave it as an average value and note the effect of various
conditions upon it. For practical applications to engines, it was
profitable to take two average values, that is, above and below
the critical pressure, as in the worked example.
The omission of measurement of the value of n, the index of
expansion in the cylinder, made the value of K inferential only.
He agreed with Mr. Ryley that an external sleeve, as distinct
from an internal sleeve, had much to commend it from point
of view of obtaining a completely unobstructed interior. He had
virtually obtained that with his second apparatus described in
the paper, except that a poppet valve replaced the sleeve.
He agreed with Professor Schweitzer that if the gas in the
cylinder itself could be induced to resonate as an organ pipe by
a suaciently sudden opening, then inevitably transient vacuum
pressure would traverse the cylinder. That was supported by
the experiments of Mucklow and Bannister, and in the
theoretical treatment by Professor GifFen, as well as in
Schweitzer’s own experiments. He shared the professor’s doubts
that the rates of port opening in engines was sufficient to produce
such a wave effect. That also applied to his own apparatus, in
which he had tried to simulate closely engine conditions.
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