5.1.7) The value of CGtl is the superposition particle velocity at the first mesh point in
Chapter 5 Computer Modelling of Engines
5.3.1 Analysis of data for a Husqvarna motorcycle engine using Prog.5.2 In a previous paper(3.7), Blair and Ashe presented experimental and theoretical
Plate 5.1 The QUB 500 single-cylinder 68 bhp engine with the expansion chamber exhaust slung underneath the motorcycle (photo by Rowland White).
represented by Prog.5.2 is the result of many years of theoretical research allied to experimentation with high specific output engines. Although Prog.5.2 does not contain induction system variations to handle disc valve or reed valve induction systems, the program permits the designer to model all of the engine porting and exhaust geometry of a high-performance engine. There will be discussion in a later chapter on the design of racing engines and the interpretation of calculated data from a power unit with piston controlled induction for the design of reed valves and disc valves. It has been amply demonstrated by Blair et al(5.9) and Fleck et al(4.10)( 1.13) that engine modelling can incorporate reed valve induction, and predict both the reed valve motion and the delivery ratio. The incorporation of disc valve induction into a computer program like Prog.5.2 is quite straightforward, as can be observed from the relevant design discussions in Chapter 6.
It is rather interesting to consider that in Sect. 5.2.3, dealing with the chainsaw type of engine, adverse comment is passed on the debilitating effect on engine performance posed by a restrictive exhaust system. Here, if one interprets the data in a simple fashion for the expansion chamber proposed in Fig. 5.4(b) for the 125 Grand Prix engine, the exhaust pipe at the exhaust port has a diameter of 38 mm and an outlet diameter to the atmosphere of just 20 mm. There are those who would logically consider that to be "restrictive"! The following discussion will reveal that this area restriction at outlet is vital to the attainment of a high specific power output.
Before commencing to discuss the behavior of expansion chamber exhaust systems, it is important to describe the format of the computer screen output from
Chapter 5 - Computer Modelling of Engines Prog.5.2. The program will produce line-print output of all input data and calcula- tion output, including all of the screen graphs. The latter is the principal output of the analysis and is the basis of Figs. 5.17-5.20 regarding the Husqvarna MK4 engine.
Taking Fig. 5.17 as an example of the screen output from Prog.5.2 while it is running, the x-axis is the crankshaft angle commencing at exhaust port opening, EO, for one complete cycle; exhaust port closure is marked as EC. The other timing events are for the transfer port, i.e., opening and closing is TO and TC, respectively, and for the inlet port, i.e., opening and closing is 10 and IC, respectively. The markers for top and bottom dead center are self-explanatory as TDC and BDC. The diagram on the computer screen is refreshed at the conclusion of each cycle. There are two sets of pressure ratio-time histories being written simultaneously. The top one with its scale at the left is for cylinder pressure, exhaust pipe pressure (that value next to the exhaust port), and crankcase pressure. To prevent a programming problem, the maximum cylinder pressure plotted is at 2.0 atm. The bottom set, with its scale of pressure ratio at the right, is for the crankcase pressure and for the inlet pipe pressure in the pipe next to the intake port. Unlike Prog.5.1, the cylinder pressure diagram during combustion does not appear, because the major interest is in the tuning effect of the exhaust system and its control over engine power and torque. This latter information is presented at the base of the diagram at bdc on each cycle, as seen in Fig. 5.17 for the fifth engine cycle in that example. There, the information includes the peak cycle maximum pressure, temperature and crank angle location and includes that for SE, TE, and CE on each cycle as for Prog.5.1.
5.3.1 Analysis of data for a Husqvarna motorcycle engine using Prog.5.2
The Basic Design of Two-Stroke Engines
CRANK-ANGLE from EXHAUST PORT OPENING f o r one cycle
2.0 J | I I I I I
i i i i l l I I L 0 5
EO TO BDC TC EC 10 TDC IC EO ENGINE SPEED, r p m = 4 0 0 0 DELIVERY R A T I 0 = 0 . 6 5 2
POWER, kW= 9.0 B S F C , k g / k W h = 0 . 4 6 1 BMEP, bar= 5 . 5 4 IMEP, b a r = 6 . 1 2 PMEP, b a r = 0 . 3 2 FMEP, bar= 0.26
SEFF=0.818 T E F F = 0 . 7 0 7 CEFFrO.465 PEAK CYLINDER PRESS, bar= 3 8 . 0 and T E M P , K = 2 4 4 9 . a t deg.ATDC=14.9
Fig. 5.17 Predicted performance characteristics of the Husqvarna MK4 engine at 4000 rpm.
exhaust system provides a strong suction action throughout the scavenge period, with the crankcase pressure pulled down to the atmospheric line by the end of the scavenge period at transfer port closure. The next action of the exhaust system is to give a positive compression wave at the exhaust port in the period before the piston closes that port physically. Thus all of the fresh charge supplied to the cylinder, and retained in it up to a point at or about transfer port closure, is now gas-dynamically kept inside the cylinder by this "plugging" exhaust pressure pulse. Indeed, as the exhaust port pressure is actually briefly above the cylinder pressure in this period, some of the fresh charge which had been lost to the exhaust pipe during scavenging is "stuffed" back into the cylinder. From whence comes these useful pressure reflec- tions?
The suction reflection at the exhaust port is caused by the exhaust pulse travelling through the diffuser section in Fig. 5.2(b), indicated by lengths LP12 and LP23. As Eq. 2.4.19 would predict from the positive DF/F terms within it, the continual area increase with length sends back a series of 6 reflections as expansion waves to the
CRANK-ANGLE f r o m EXHAUST PORT OPENING f o r one c y c l e
I I I I I I I I l_ (J S
EO TO BDC TC EC 10 TDC IC EO ENGINE SPEED, rpmr: 5 5 0 0 DELIVERY R A T I 0 = 1.067
POWER, kW= 19.7 B S F C , k g / k W h = 0 . 4 5 8 BMEP, bar= 8.78 IMEP, bar= 9 . 6 4 PMEP, bar= 0.50 FMEP, bar= 0.35
SEFF=0.918 TEFF=0.602 CEFF=0.632 PEAK CYLINDER PRESS, bar= 5 5 . 3 and T E M P , K = 2 9 7 5 a t deg.ATDC=14.4
Fig. 5.18 Predicted performance characteristics of the Husqvarna MK4 engine at 5500 rpm.
engine, i.e., at a sub-atmospheric pressure. The reflection process in the diffuser is rather like having a continuous series of small sudden area expansions like those in Sect. 2.3.4(a). The use of a diffuser is a more efficient method of reflecting pressure wave energy than that obtained by conducting it completely at one physical location, such as at a sudden enlargement in a pipe or at an open end to the atmosphere.
The "plugging" pulse is a compression wave reflection which emanates from the
onward progression of the original exhaust pulse into the nozzle portion of the pipe
indicated by length LP45 in Fig. 5.2(b). Here, Eq. 2.4.19 would dictate that the
negative values of DF/F for each mesh in that section would produce 6 reflections
which are above unity, i.e., compression waves which are greater than the atmos-
pheric pressure. The process, like that in the diffuser, is efficient because it is spread
over the length of the nozzle section. The pipe outlet diameter can then be quite
restrictive so as to attain the strongest plugging pressure characteristic. The
compression pressure wave reflection will reflect to and fro between the exhaust
port and the nozzle during the closed cycle period, however, the expansion chamber
must empty in good time before the advent of yet another exhaust pulse. Thus, the
design criterion for tail pipe diameter is that which will give the strongest plugging
The Basic Design of Two-Stroke Engines
CRANK-ANGLE f r o m EXHAUST PORT OPENING f o r [^CYLINDER
one c y c l e
EO TO BDC TC EC 10 ENGINE SPEED, r p m = 6 5 0 0 DELIVERY RATIO:
POWER, kW=20.6 B S F C , k g / k W h = 0 . 5 1 9 IMEP, bar= 8 . 6 4 PMEP, bar= 0.46
SEFF=0.902 TEFF=0.555 PEAK CYLINDER PRESS., bar= 5 0 . 2 and TEMP., K=
TDC IC EO 1.036
BMEP, bar= 7.76 FMEP, bar= 0.42 CEFF=0.566
2 9 5 1 . at deg.ATDC=15.
Fig. 5.19 Predicted performance characteristics of the Husqvarna MK4 engine at 6500 rpm.
reflection while not allowing the chamber pressure to rise to a level which would seriously deteriorate the strength of the suction reflection behavior in the diffuser in succeeding cycles(2.17).
(b) The effect of the exhaust dynamics on charge trapping
The trapping pressure ratios in the cylinder in Figs. 5.17-5.20 are 1.3,1.7,1.6 and 1.35 atm. These trapping pressures are closely related to the BMEP which is produced. As discussed in Sect. 1.5.6, the principal control of trapped mass is by trapping pressure. By contrast, the QUB 400 engine in Fig. 5.9 is seen to trap at 1.25 atm without the benefit of a tuned exhaust system and by piston action only. The quality of the scavenging process also plays a part in this behavior, as it affects the fresh charge retention characteristics up to the point of any exhaust port plugging by the pressure waves in an expansion chamber type of exhaust system.
Of general interest is the level of specific fuel consumption from this engine with a tuned exhaust pipe. The trapping efficiency is 0.555 and the BSFC is 0.519 kg/
kWh even though the air-fuel ratio is quite rich at 11.17(3.7). The QUB 400 engine with an untuned exhaust, but a better scavenging system, has a trapping efficiency of 0.511 and a BSFC of 0.462 kg/kWh with an air-fuel ratio set quite lean at 13. This contrast reveals the obvious potential to produce good power and efficiency
Chapter 5 - Computer Modelling of Engines
CRANK-ANGLE f r o m EXHAUST PORT OPENING f o r one c y c l e
E0 TO BDC TC EC 10 TDC IC E0 ENGINE SPEED, r p m = 8 0 0 0 DELIVERY R A T I O N . 8 1 0
POWER, kW= 18.4 B S F C , k g / k W h = 0 . 5 4 1 BMEP, bar= 5.65 IMEP, bar= 6.53 PMEP, b a r r 0 . 3 6 FMEP, bar= 0 . 5 2
SEFF=0.843 TEFF=0.505 CEFF=0.424 PEAK CYLINDER PRESS.,ber= 3 9 . 0 and TEMP., K = 2 8 4 8 . a t deg.ATDC=14.2