5.1.7) The value of CGtl is the superposition particle velocity at the first mesh point in
Chapter 5 Computer Modelling of Engines A similar situation would exist for the calculation of the instantaneous value of
delivery ratio, DRt, although this is normally computed at the inlet port boundary to the crankcase:
DRt= S[AMF*At/Mdr] (5.1.9) Naturally, in any accurate calculation by a computer engine model, these mass
flow rates should be identical when summed over a complete cycle at any of the cylinder or crankcase boundaries. Consequently, the value of SRt and DRt at the conclusion of a computed engine cycle are the net levels of scavenge ratio and delivery ratio for the engine on that cycle.
However, both of these computations of fresh charge flow are for mass flow, while Chapter 3 teaches that the scavenging behavior will be a function of the volume flow at any instant by comparison with a reference volume. In the case of the single cycle rig described in Sect. 3.2.3, this is indisputably the swept volume, for the experiment is conducted at constant volume, with that volume set equal to the swept volume of the test cylinder in question. Therefore, the first logical approach to estimate scavenge ratio by volume, SRv, would be to sum the increments of AVF as a function of the instantaneous cylinder volume at that crank angle:
SRv=X[AVF/VCl] (5.1.10) However, the volume which exits the transfer duct is that calculated at properties
of the first mesh position in the transfer duct, and this fresh charge will clearly occupy a larger volume upon entering the cylinder which is at a lower pressure and lower density. Therefore, Eq. 5.1.10 must be modified to take this into account, which is rather difficult mathematically. In reality, as the fresh charge enters in a stratified manner, it will not immediately assume the density of the cylinder charge at that time step. Therefore, there is little point in following slavishly the dictates of the information for cylinder properties which would be provided by Subroutine BOX at that juncture. The only property which would be instantaneously common to both the "cold" fresh charge which entered and the "hot" cylinder charge in situ is the cylinder pressure. Thus, it would be logical to estimate that the fresh charge volume entering the cylinder would expand by the ratio of the transfer duct pressure (superposition, at that first mesh) to the cylinder pressure. Hence, the first logical assumption for an expansion ratio, EXPAND, for this entering fresh charge would be:
EXPAND=Ptl/PCl (5.1.11) The ensuing modification to Eq. 5.1.10 is then given by:
SRv=I[EXPAND*AVF/VCl] (5.1.12)
The Basic Design of Two-Stroke Engines
There is some evidence from correlation with known experimental data at QUB(1.22)(3.13) that this gives values of SRv, and consequently SE information to the combustion model, which are somewhat low. It has been found by some experience that a better value for the correction coefficient EXPAND is given by a density ratio proportioned as follows between the densities in the cylinder and the transfer duct:
EXPAND=Dtl/(0.6*Dtl+0.4*DCl) (5.1.13) Using Eq. 5.1.12, the computer calculation has available the SRv data as a
function of both time and crank angle, so it is quite logical to use the previously determined experimental data for any of the cylinders tested in Chapter 3 to determine the scavenging efficiency, SE. This can be applied either at the conclu- sion of the entire process at trapping, or during its progress from transfer port opening to transfer port closing. The value of scavenging efficiency at any instant during the scavenge process, SE, based on the SRv value at the same juncture, would be, from Eq. 3.3.4:
SE=l-e(M*SRv+c> (5.1.14)
In Prog.5.1 and 5.2, the reader will find this set of equations in the subroutine TRPORTOPEN. Both of the models for EXPAND are programmed there, so the user can select which of the two versions of EXPAND are most suitable for the design problems undertaken. All of the program examples presented within this chapter are computed using the version of EXPAND presented in Eq. 5.1.11. In a Utopia, the proper course of action would be to halt the unsteady gas-dynamic program at each calculation increment and side-step to a full CFD program of the type discussed in Sect. 3.4. At this stage of development of the microcomputer, the designer does not have the time to wait during the three or four hour intermission while this accurate scavenging calculation takes place. Perhaps during the next half decade, when computers will get faster exponentially, this will become a viable cal- culation option. In the interim, the simplistic model of scavenging discussed above will have to suffice for unsteady gas-dynamic engine models.
At the data input stage, the user is requested to name which of the scavenging systems described in Fig. 3.14 is to be employed in the subsequent calculation. The name in question is that used in the left-hand column of Fig. 3.14 and the character string is recognized by the program which translates it internally into the numerical values of the appropriate slope, M, and intercept, C, for that type of scavenging system.
To cope with any backflow which may occur into the transfer ducts towards the end of the blowdown phase, the computer calculation is instructed to sum all transfer duct flow and no computation of DRt, SRt or SRv will take place until the net transfer duct outflow has returned to zero. This would indicate that all exhaust gas backflow has been returned to the cylinder so that true scavenging of fresh charge can then commence.
At the trapping point at exhaust port closure, the mass of fuel trapped is determined from the scavenging efficiency and the cylinder mass at that juncture, Mtr. As discussed in Sect. 1.5.2, there is a fundamental difference between the purity of a trapped charge and the scavenging efficiency. In this form of engine modelling, the only option open to the programmer is to consider that they are identical, i.e., all of the oxygen in the cylinder is consumed by the previous combustion process. Thus, from Eq. 1.5.11, the mass of air and fuel trapped, Mtas and Mtf, is computed by:
Mtas=Mtr*SE (5.1.15) Mtf=Mtas/TAF (5.1.16) The values of trapping and charging efficiency are determined by applying Eqs.
1.5.13 and 1.5.14 directly.
From the last two equations (referring back to Sect. 1.5), it is assumed there is no air remaining in the cylinder exhaust gas from combustion during a previous cycle, i.e., the Mar value of Eq. 1.5.8. In other words, the value of scavenging efficiency being employed theoretically is also the charge purity.
5.1.6 Deducing the overall performance characteristics
The procedures used in the engine models presented in this chapter are as described in a paper by Blair(4.9) and in Sects. 1.5 and 1.6 of this text. The indicated work in the cylinder and the crankcase is assessed by the cyclic summation of the PdV term at each time step in the calculation. This permits the direct calculation of indicated mean effective pressure, IMEP, and the pumping mean effective pressure in the crankcase, PMEP. As discussed in Sect. 1.6.1, it implies that a separate term must be produced for the friction loss, FMEP, in order to predict the resulting brake mean effective pressure, BMEP (see Eq. 1.6.9). The expression for friction work employed in Progs.5.1 and 5.2 are for friction losses in an engine whose power output is being measured directly at the crankshaft. In the equation below, it is seen as being linearly related to piston speed(1.3)(5.12):
FMEP=100*ST*RPM (5.1.17) The cyclic deduction of specific fuel consumption characteristics follows
directly from the knowledge of the fuel mass trapped and the power which is calculated as being produced. The theory used to obtain this information is presented in Sects. 1.5.10 and 1.6.1.
5.2 Using Prog.5.1, "ENGINE MODEL No.l"
This engine model has the simple box type of exhaust silencer illustrated in Fig.
5.2(a). The basic data for the engine and its porting is listed in Fig. 5.3 and illustrated in Fig. 5.1. It should be noted that the program runs much faster in the compiled mode. Upon activating the compiled program, it will request the user to insert the data in blocks, exactly as in Fig. 5.3, or as an entire file of data previously stored.
Before the program will run, the user is asked to check the data on the computer screen to ensure its accuracy in thought or insertion. The result of running such a program for various sets of data, i.e., the QUB400 engine or the SAW engine, is demonstrated below, for many basic design principles are to be found in the ensuing output data from the computer calculation.
Apart from the normal output in the form of a printout of the required perform- ance characteristics of the engine represented by the data input, the computer screen depicts the events as they occur during the calculation, as shown in Fig. 5.9. The screen will show the dynamic variations of cylinder, crankcase and exhaust port pressure ratio during the open cycle from exhaust port opening to closure. To prevent programming problems, the maximum cylinder pressure ratio plotted during the open cycle is 2.0 atm. The screen will then be cleared and a second picture will appear showing the events for the remainder of the cycle for the crankcase and inlet port pressure ratio. On this same diagram is presented the cylinder pressure ratio and the delivery ratio as it progresses. The cylinder pressure ratio is plotted at 1/40 of the scale of the crankcase and inlet pressures and its 1.0 atm level is at the base of the diagram; in other words, each tick on the left-hand scale represents 4 atm for the cylinder pressure diagram. The pressure ratio scale for crankcase and inlet port pressure is at the left and delivery ratio at the right. The top and bottom halves of Fig. 5.9 show the encapsulation of the computer screen during the fifth engine cycle. The print underneath each picture appears at bdc or tdc on each cycle as the calculation proceeds, so the designer has progressive information on the net effect of the dynamic events on the computer screen upon the engine performance characteristics.
5.2.1 The analysis of the data for the QUB 400 engine at full throttle The exhaust system for the QUB 400 single-cylinder research engine has a short ppe of 200 mm to a generously proportioned silencer box which poses little restriction to the exhaust flow. This is evident in Fig. 5.9, where a suction reflection from the open pipe end into the exhaust box arrives back at the exhaust port and assists with the scavenging of the cylinder. A further compound reflection of that af pears around bdc as a compression wave and this opposes the scavenging flow to acertain extent.
This can be examined further in Figs. 5.10 and 5.11 where the calculation has been indexed for the instantaneous values of scavenge ratio, by either mass or vtlume, and of scavenging efficiency, which results from the use of Eq. 5.1.14
\Wthin the program. In Fig. 5.10, scavenge ratio by volume, SRv, and scavenging efficiency, SE, are plotted as a function of crank angle from transfer port opening
^closing. It can be seen that there is backflow from the cylinder during the first 10 degrees of opening, as both SRv and SE are zero at that juncture. That this would oacur could also have been deduced from Fig. 5.9, for the cylinder pressure is higher tfetn the crankcase pressure in this period. The effectiveness of the suction reflection iitassisting scavenge flow is observed in Fig. 5.10, for the scavenge ratio by volume rkes rapidly before bdc and has reached unity by bdc. As the final value is 1.15, with surne backflow occurring towards the end of the scavenge period, it is seen that the
2.0 P A T M
1.5
1 0 EP0
CRANK-ANGLE from EXHAUST PORT OPENING to EXHAUST PORT CL0S ENGINE SPEED, rpm= 3000 DELIVERY RATI0-0.854
POWER, kW= 12.2 BSFC,kg/kWh=0.464 BMEP, bar= 6.14 IMEP, bar= 6.72 PMEP, bar= 0.38 FMEP, bar= 0.21 PEAK CYLINDER PRESS., bar= 35.8 and TEMP., K=2891. atdeg.ATDC=1
1.5 P.
A T M
NG
6.2
1.0
0.7
CRANK-ANGLE from EXHAUST PORT CLOSING to EXHAUST PORT OPENING SCAVENGING EFF =0.818 TRAPPING EFF.=0.504 CHARGING EFF.=0.430 SCAV. RATI0(mass)=0.874 SCAV. RATIO(voO=1.1 34 EX. FLOW RATI0=0.876
Fig. 5.9 Predicted performance characteristics of the QUB 400 engine at full throttle.
The Basic Design of Two-Stroke Engines
majority of the scavenge flow enters the cylinder before bdc. From the viewpoint of retaining fresh charge within the cylinder, this early supply of air and fuel into the cylinder is not an optimum procedure, for it gives the longest possible time for the fresh charge to mix with the cylinder contents and escape through the exhaust port. Fig. 5.10 shows a plot of the individual characteristics for three of the different scavenge types calculated, namely SCRE, YAM6 and CD. It will be recalled that these refer to "very good" and "poor" loop scavenging and to deflector piston cross scavenging, respectively. Although the SRv characteristic is virtually common for all three scavenging types, the ensuing SE behavior is dissimilar, for this is controlled by Eq. 5.1.14 . The employment of the scavenge model provides the closed cycle model with the appropriate information on the purity of the cylinder charge. Within the program, as described in Sect. 5.1, this will translate into varying levels of trapped air and fuel mass, with this latter value leading to a prediction of the heat to be released for combustion. The end effect of the differing scavenge behavior produces the ensuing performance characteristics for the various types of scavenging.
0 50 100 150 DEGREE CRANK ANGLE FROM TRANSFER PORT OPENING