Computer Modelling of Engines
5.1 Structure of a computer model
The key elements of any computer program to model a two-stroke engine are:
(a) The physical geometry of the engine so that all of the port areas, the cylinder volume and the crankcase volume are known at any crankshaft angle during the rotation of the engine for several revolutions at a desired engine speed.
(b) The composition of a model of the unsteady gas flow in the inlet, transfer and exhaust ducts of the engine.
(c) The composition of a model of the thermodynamic and gas-dynamic behavior within the cylinder and in the crankcase of the engine while the ports are open, i.e., the open cycle period.
(d) The composition of a model of the thermodynamic behavior within the cylinder of the engine while the ports are closed, i.e., the closed cycle period.
(e) The composition of a model of the scavenge process so that the proportion of fresh charge which is retained within the cylinder can be predicted.
Almost all of the material related to the above five topics has already been described and discussed in the earlier chapters, and all that remains to be done is to reorient the reader to each subject in turn, bringing them together for the preparation of a major program to describe a complete engine.
5.1.1 Physical geometry required for an engine model
It will be recalled that a detailed description of this is carried out in Sects. 1.4.3- 6, which formed the subject of three programs, Progs. 1.1-1.3. The geometry required for this new program is even more detailed, requiring all that was needed for those earlier programs as well as the information presented in Figs. 5.1 and 5.2.
The complete list of geometrical data required for the program is given in Figs. 5.3 and 5.4 for the four engines which will be used as worked examples in this chapter.
Although they will be discussed more fully later in the chapter, the four engines
Fig. 5.1 Nomenclature for cylinder porting dimensions in computer engine models.
labelled in Fig. 5.3 as QUB400, SAW, HUSQ4, and 125GP, are a QUB 400 single- cylinder research engine, a chainsaw engine, the Husqvarna 250 MK4 motocross engine described even more completely in reference (3.7), and an archetypical 125 cc Grand Prix racing motorcycle engine, respectively.
Turning first to Fig. 5.3 and the first block of data listed, the values required there are the macroscopic data which can describe the cylinder, the position of the piston at any crank angle, and the clearance volumes in the cylinder and crankcase. As described in Sect. 1.4, the values required are for the cylinder bore, stroke, connecting rod length between bearing centers, the trapped compression ratio in the cylinder and the compression ratio in the crankcase. The exhaust pipe temperature is the reference temperature as detailed in Sect. 2.5.1.
The next four blocks of data are best discussed in conjunction with Figs. 5.1 and 5.2. Fig. 5.1 shows various sectioned views of a two-stroke engine cylinder where the areas and timings of the exhaust, transfer and inlet ports are controlled by the relevant upper and lower timing edges of the piston. The heights of the ports, either total or exposed at any instant, are a function of the engine geometry in the first block
^ .
o
Lt
DIA.1 .. /
N.I p
•
,
DIA.1 .. IA.2.
LEN.2
r
.
L
BOX VOLUME CC UNITS
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IA.2,.
(A) NOMENCLATURE FOR EXHAUST PIPES AND BOX FOR Prog.5.
* L P°1 >|« ^ . , ^ i P 2 3 ^ LP54 LP45 , | P g ^
u i O l
( B ) NOMENCLATURE FOR THE DIMENSIONS OF A TUNED PIPE FOR Prog.5.
Fig. 5.2 Nomenclature and dimensions of exhaust systems for the computer programs in Chapter 5.
of data and of the crankshaft angles at opening and fully open (see Sect. 1.4). To determine the port areas at any instant, the port width is required at any piston position during the cycle, and the request is made for data on "number of ports,"
"effective width of each port in the gas flow direction," and the "top" and "bottom"
corner radii of each port. The instantaneous area of any open port at any crankshaft position is required within the computer model to calculate the AK area ratio value from a port to a pipe (see Eq. 2.3.17, Fig. 2.6 and Fig. 6.1).
The effective port width of each port, WE, WT and WI in Fig. 5.1 for exhaust, transfer or inlet ports, requires some further explanation. For a cylinder which has more than one exhaust or inlet port, it is quite common to have those ports of equal effective width, but this is rarely the case for transfer ports. Fig. 3.38 provides a perfect example of this situation. In that illustration, the engine has three scavenge ports, the two side ports with an effective width of 28.6 mm and a rear port of 30 mm effective width; however, neither of these numbers took into account the upsweep angles, which were 5 and 55 degrees, respectively. The effective port area, as explained in that figure, is the exposed port height at any point multiplied by the cosine of the upsweep angle and the effective port width at that point. In this
Chapter 5 - Computer Modelling of Engines
DATA NAME BORE, mm STROKE,mm CON-ROD, mm ENGINE SPEED,rpm EXHAUST TEMP, 2C TRAPPEDCR CRANKCASECR
EXHAUST PORT OPENS, 2ATDC FULLY OPEN,£ATDC
NUMBER OF PORTS WIDTH EACH PORT, WE TOP RADIUS, RTE BOTTOM RADI US, RBE
TRANSFER PORT OPENS,SATDC FULLY OPEN,2ATDC
NUMBER OF PORTS WIDTH EACH PORT, WT TOP RADIUS, RTT
BOTTOM RADIUS, RBT SCAVENGING TYPE INLET PORT OPENS, SBTDC FULLY OPEN,2BTDC NUMBER OF PORTS WIDTH EACH PORT, WI TOP RADIUS, RTI BOTTOM RADIUS, RBI TRANSFER LENGTH.T TRANSFER AREA RATIO INLET LENGTH.I THROTTLE AREA RATIO CARBURETTER DIAMETER.1 COMBUSTION EFFICIENCY COMBUSTION PERIOD, deg AIR-TO-FUEL RATIO COMPRESSION INDEX, NC
EXPANSION INDEX, NE
QUB400 85.0 70.0 125.0 3 0 0 0 400
6.7 1.45 96
180 1 54.8 12
12 118 180 6 15.3 3 3 VARIOUS
60 0 1 45.0 6 6 90.0
1.35 2 0 0 . 0
1 & 0 . 2 5 34.0 0.85 60.0 13 1.25 1.35
SAW 56.0 41.0 73.0 7 5 0 0 400 7.5 1.4& 1.5
100 180 1 31.5 6
6 119 180 2 20.0 3
3 YAM1
74 26 1 30.5
3 3 60.0
1.20 75.0 0.75 24.0 0.85 50.0 13 1.25 1.35
HUSQ4 69.5 64.5 120.0 VARIOUS
550 7.0
1.5 90 180 1 42.0 8
8 120 180 5
15.4 3 3 YAM6 80
0 2 21.0 3 3 90.0
1.40 185.0 1.0 36.0 0.80 55.0 AS EXPT 1.25 1.35
125GP 54.0 54.0 105.0 11500 650 7.2
1.5 81 180
1 41.0 12 12 114 180 4 15.0 3
3 YAM1 98 0
1 35.0 10 10 60.0
1.40 150.0
1.0 36.0
0.80 50.0 12 1.25 1.35 Fig. 5.3 Cylinder and engine geometry used in the
computer programs in Chapter 5.
NAME OF DATA QUB400 ENGINE CHAINSAW ENGINE
LEN.1 DIA.1 LEN.2 DIA.2 BOX VOLUME, cc 200 38 200 38 10000 90 28 90 18 500 (A) EXHAUST BOX DIMENSIONS FOR ENGINES USED IN COMPUTER MODELS
NAME OF DATA HUSQVARNA MK4 125 GRAND PRIX NAME OF DATA HUSQVARNA MK4 125 GRAND PRIX
LP01 LP12 LP23 LP34 LP45 LP56 75 385 275 195 280 230 64 341 116 93 200 200 DEP1 DEP2 DEP3 DEP4 DEP5 DEP6 49 66 110 100 28 28 38 78 112 112 20 20 ( B ) TUNED EXHAUST PIPE DIMENSIONS FOR ENGINES USED IN COMPUTER MODELS
Fig. 5.4 Dimensions of exhaust systems for the computer programs in Chapter 5.
example, the programmer using Prog.5.1 or 5.2 would insert the data value for number of transfer ports as 3, and the effective port width as [2*28.6*cos(5
9)+30*cos(55
e)]/3, or 74.2/3, i.e., 24.7. By this somewhat convoluted logic, the programmer is saved from a multiplicity of data entries for each port, its width and upsweep angle; yet within the computer calculation at the appropriate crank angle the correct transfer port area is being calculated by the inclusion of the precise number of top and bottom corner radii. The logician will point out that each of the transfer ports mentioned might have differing top or bottom corner radii also!
The author's defense is that it would be a very rare engine in which this is the case for transfer ports, and it is unheard of for multiple exhaust or inlet ports. Further, as has already been mentioned, it is possible to specify a program to cater to every geometrical whim of the designer, but it would be at the expense of writing a rather pedantic book about that and little else!
5.1.2 Geometry relating to unsteady gas flow within the engine model
As outlined in Sect. 5.1(b), it is necessary to specify the lengths and areas of any pipe or duct, and the volumes of any "boxes" which are allied to the exhaust, transfer or inlet system. The exhaust systems to be used with the two engine models in Progs.5.1 and 5.2 are illustrated in Fig. 5.2. The transfer and inlet duct are shown in Fig. 5.1.
The exhaust system for Prog.5.1 is sketched in Fig. 5.2(a). It is a simple box type silencer, with parallel pipes of differing length and area at entry and exit to the box.
The engines which will be used in the illustration of this type of system are the QUB 400 unit and a chainsaw engine; the power unit data values appropriate to Fig. 5.2(a) are listed in Fig. 5.4(a). The silencer for the QUB 400 engine is a generously
Chapter 5 - Computer Modelling of Engines
proportioned device with the box volume twenty-five times larger than the cylinder swept volume, with an outlet pipe equal in area to the inlet pipe from the engine. On the other hand, the chainsaw engine, which has a swept volume of 101 cc, has a silencer volume which is only 500 cc, i.e., five times larger than the cylinder swept volume, and an exit pipe which is but 41 % of the pipe area at the inlet to that exhaust box. This is typical of such power units where bulk and weight are at a marketing premium.
The exhaust system for the high specific output engine types within Prog.5.2 is illustrated in Fig. 5.2(b), and the data values appropriate to the Husqvarna MK4 and 125 Grand Prix engines are listed in Fig. 5.4(b).
The data value needed for the transfer duct length is sketched in Fig. 5.1 as LENGTHT and that for the inlet tract as LENGTH.I. It is assumed that the trans- fer ducts are not tapered and that the area along the duct is decreed as a function of the total transfer port area at full opening at bdc. Hence, as will be seen in block five of the data in Fig. 5.3, the programmer is requested to decide on a data value for the area ratio of the transfer ports to the transfer duct, called TRANSFER AREA RATIO. Typical values for this factor range from 1.2 to 1.5.
For the inlet duct, the length, LENGTH.I, is that from the piston face to the throttle body or venturi of the carburetor, and the duct is assumed to be linearly tapered from the full inlet port area to the carburetor flow diameter, the value of which is also observed in the same block of data in Fig. 5.3. Not all inlet ducts are designed in this manner, but the methodology represented by the data format given is the one which most readily fits the majority of cases. In the opinion of the author it is the logical manner in which they should be designed, i.e., that the area change with length is a constant.
Within an actual program, e.g., in ProgList.5.1, the unsteady gas flow portion is to be observed:
(a) In Subroutine NINT, where each pipe is divided into distance meshes. The exhaust pipe mesh is set at 30 mm and the others are proportioned at a somewhat lower dimensional value which is related to the reference speed of sound in those cooler ducts or pipes, in order that the actual time interval of calculation is approximately equal at each time step in all gas flow ducts during the calculation cycle (see Sect. 2.4.1(b)).
(b) In Subroutine AREA, where the areas and change of area between meshes is determined for all pipes (see Sect. 2.4.1(d)).
(c) In Subroutine STAB, where the minimum time step, dZ, is determined (see Sect. 2.4.1(d)).
(d) In Subroutine PIPE, where the interpolation for the 9 and 6 values is carried out for each mesh point (see Sect. 2.4.1(d)).
(e) In Subroutine PORT, where the determination of the reflection behavior at
cylinder port boundaries and at pipe ends is carried out using the UFLO data bank
(see Sect. 2.4.1(c)).
The Basic Design of Two-Stroke Engines
5.1.3 The open cycle model within the computer programs