The Basic Design of Two-Stroke Engines 100
300 320 340 360 380 400 420
CRANKSHAFT ANGLE, d e g r e e s
Fig. 4.5 Mass fraction burned in QUB LS400 engine at WOT and 3000 rpm
440All of the symbols and notation are exactly as used in Chapter 1. The gasoline fuel used has a lower calorific value of 43 MJ/kg. For the actual example quoted for the QUB LS400 unit, insertion of the experimental data into Eq. 4.2.15 reveals:
Heat available in fuel, J
=0.602*43*10
6*(0.435/1000/3600)*(6.28*10
5)*(397.2*10'
6)
=780.23 J
The heat released from the fuel as recorded on the heat release diagram for that engine, Fig. 4.4, is the total area under the heat release curve. This is calculated from Fig. 4.4 as 662.6 J. Consequently, the combustion efficiency of this engine at that particular test point is:
BE=662.6/780.23
=0.849
Chapter 4 - Combustion in Two-Stroke Engines 4.3 Modelling the combustion process theoretically
For the engine designer who wishes to predict the performance characteristics of the engine, it is clear that the theory already given in Chapter 2 on unsteady gas flow and in Chapter 3 on scavenging permits the preparation of a computer model which will predict the thermodynamic and gas-dynamic behavior of an engine at any throttle opening and any rotational speed. All of this theory pertains to the open cycle, from exhaust port opening to exhaust port closing. The remaining part of the computer analysis which is required must cover the closed cycle period, when the compression, combustion and expansion phases take place. The discussion on modelling the compression and expansion phases is in Chapter 5, as is the implementation of a model for the combustion process. However, it is pertinent in this chapter on combustion to point out the various possibilities which exist for formulating such a model. There are three main methods which are possible and each of these will be discussed in turn:
(a) a heat release model
(b) a one-dimensional flame propagation model (c) a three-dimensional combustion model
4.3.1 A heat release model of engine combustionOne of the simplest models of engine combustion is to use the heat release analysis presented in Sect. 4.2.2, in reverse. In particular, Eq. 4.2.12 would become a vehicle for the prediction of the pressure, P2, at the conclusion of any incremental step in crankshaft angle, if all of the other parameters were known as input data. This relies upon the assumption of data values for such factors as the combustion efficiency and the polytropic exponents during compression and expansion. At the same time, a profile has to be assumed for the heat release during the combustion phase as well as a delay period before that heat release commences.
At The Queen's University of Belfast, the use of heat release models has been used for many years, since their original publication on the subject(4.9) to the latest at the time of writing(4.10), some ten years later. That it is still found to be effective is evident from the accuracy of correlation between measurement and calculation of engine performance characteristics described in those publications.
The heat release characteristics of homogeneously charged spark-ignition two- stroke engines have been found to be remarkably similar, which is not too surprising as virtually all of the engines have rather similar combustion chambers. Such would not be the case for four-stroke cycle engines, where the combustion chamber shape is dictated by the poppet valve mechanisms involved. A uniflow two-stroke engine of the type illustrated in Fig. 1.5 would conform more to a four-stroke combustion model than one for a two-stroke engine.
Furthermore, the profile of the heat release rate as a function of crank angle is known not to be heavily dependent on load, or IMEP. Naturally, the peak value of heat release rate is dependent on load, but the profile would not appear to be so.
Therefore, the experimentally determined heat release rate curve shown in Fig.
4.4, typical of many which have been observed, can be postulated as a potential
theoretical model of combustion. Such a model is extracted from the experimental
data and displayed in Fig. 4.6. The heat release period is Pe, with a rise time of P-/3 equally distributed about tdc. The delay period is approximately P°/6, but it must be remembered that the optimum ignition timing for any engine is one which will start the process so that the ensuing cylinder pressure rise is distributed about tdc to give the highest IMEP. Therefore, in modelling terms, the ignition timing and the delay period fall into the category of second-order importance, as it is the phasing and duration of the heat release profile about tdc which will ensure the highest IMEP by a theoretical calculation. While this method makes it unnecessary, the delay period can be predicted theoretically (4.13). The selection of the period P is by far the most important criterion and it is the author's experience that this is rarely less than 45s, nor greater than 65°, irrespective of speed and load (IMEP). It will be noted that the heat release profile has a "tail" of magnitude Pe/3, falling to zero from one sixth of the maximum value of heat release.
The total area of the profile in Fig. 4.6 is (14/36)*HM*PS, where HM is the maximum rate of heat release. The actual value of HM in Fig. 4.4 is 28.8 J/deg and the period, P°, is 60°. The area under the model profile in Fig. 4.6, if that same peak
t
nksh*
O 9 *
u 1-
<
en
ELEASE HEAT R i
MAXIMUM VALUE HM
MAXIMUM VALUE 6
ZERO
, _., , _... —*- 102
P2 6
102 P2 6
TOTAL HEAT RELEASED
= 1 4 * H M * P 2 / 3 6
LX
202 P2 3
i
/
202 P2 3
i
^ P 2
1 '
300 320 340 360 380 400 CRANKSHAFT ANGLE, degrees
420 440
Fig. 4.6 Possible model of heat release rate for theoretical calculations.
value is maintained, is 672 J, which corresponds well with the measured value of 662.6 J. For a theoretical total heat release of 662.6 J, one would predict from the model a HM value of 28.4 J/deg.
One of the simplifying assumptions in the use of a heat release model for combustion is that the prediction of the heat loss to the cylinder walls and coolant is encapsulated in the selection of the polytropic exponents for the compression and expansion processes. This may be regarded by some as an unnecessary simplifica- tion, perhaps even an inaccurate one. However, as all models of heat transfer are more or less based on empirical forms, the use of experimentally determined polytropic exponents could actually be regarded as a more realistic assumption.
This is particularly true for the two-stroke engine, where so many engine types are similar in construction. The modeller, in the absence of better experimental evi- dence from a particular engine, could have some confidence in using polytropic indices of 1.25 and 1.35 for the compression and expansion phases, respectively, and 1.38 for the numerical value of g in Eq. 4.2.12, together with a value between 0.85-0.9 for the combustion efficiency, BE.
The difficult nature of heat transfer calculations in ic engines is best illustrated by the proliferation of "empirical equations" in the literature, all bearing prestigious names, such as those attributed to Eichelberg, Woschni, or Annand, to mention but three. This will be more evident in the ensuing discussion on flame propagation models of combustion.
4.3.2 A one-dimensional model of flame propagation
One of the simplest models of this type was proposed by Blizard(4.2) and is of the eddy entrainment type. The model was used by Douglas(4.13) at QUB and so some experience was gained of the use of such models(5.13), by comparison with the simpler heat release model discussed in the previous section. The model is based on the propagation of a flame as shown in Fig. 4.1, and as already discussed in Sect.
4.1.1. The model assumes that the flame front entrains the cylinder mass at a velocity which is controlled by the in-cy Under turbulence. The mass is burned at a rate which is a function of both the laminar flame speed, LFV, and the turbulence velocity, TV.
The assumptions made in this model are:
(a) The flame velocity, FV, is:
FV=LFV+TV (4.3.1) (b) The flame forms a portion of a sphere centered on the spark plug.
(c) The thermodynamic state of the unburned mass which has been entrained is identical to that fresh charge which is not yet entrained.
(d) The heat loss from the combustion chamber is to be predicted by convection and radiation heat transfer equations based on the relative surface areas and thermodynamic states of burned and unburned gases.
(e) The mass fraction of entrained gas which is burned, MEB, at any given time, t, after its entrainment is to be estimated by an exponential relationship of the form:
MEB=e(-'/F' (4.3.2)
where F=L/LFV and L is the turbulence micro-scale.
Clearly, a principal contributor to the turbulence present is squish velocity, of which there will be further discussion in Sect. 4.4. The theoretical procedure progresses by the use of complex empirical equations for the various values of laminar and turbulent flame speed, all of which are determined from fundamental experiments in engines or combustion bombs (4.1) (4.4) (4.5).
For spark ignition engines the heat transfer from the chamber during this combustion process is based upon Annand's work(4.15) (4.16) (4.17). For diesel engines, it should be added that the heat transfer equation by Woschni(4.18) is usually regarded as being more effective for such theoretical calculations. Typical of the heat transfer theory proposed by Annand is his expression for the Nusselt number, leading to a conventional derivation for the convection heat transfer coefficient, HC:
Nu=a*Re07 (4.3.3)
where, a=0.26 for a two-stroke engine, or, a=0.49 for a four-stroke engine.
Annand also considers the radiation heat transfer coefficient, HR, to be given by:
HR=4.25*109*(T4-TW4)/(T-TW) (4.3.4)
However, the value of HR is many orders of magnitude less than HC, to the point where it may be neglected for two-stroke cycle engine calculations.
It is clear from this brief description of a turbulent flame propagation model that it is much more complex than the heat release model posed in Sect. 4.3.1. As the physical geometry of the clearance volume must be specified precisely, and all of the chemistry of the reaction process followed, the calculation will require much more computer time. By using this theoretical approach, the use of empirically de- termined coefficients and correctors has increased greatly over the earlier proposal of a simple heat release model to simulate the combustion process. It is very questionable if the overall accuracy of the calculation, for example, in terms of IMEP, has been much improved over the simpler model. There is no doubt that valuable understanding will be gained, in that the user obtains data from the computer calculation on such important factors as the proportions of the ensuing exhaust gas emissions and the flame duration. This type of calculation is much more logical when applied in three-dimensional form and allied to a CFD calculation for the gas behavior throughout the cylinder. This is discussed briefly in the next section.
Chapter 4 - Combustion in Two-Stroke Engines 4.3.3 Three-dimensional combustion model
From the previous comments it is clearly necessary that reliance on empirically determined factors for heat transfer and turbulence behavior, which refer to the combustion chamber as a whole, will have to be exchanged for a more microscopic examination of the entire system if calculation accuracy is to be enhanced. This is possible by the use of a combustion model in conjunction with a computational fluid dynamics model of the gas flow behavior within the chamber. Computational fluid dynamics, or CFD, was introduced to the reader in Chapter 3, where it was shown to be a powerful tool to illuminate the understanding of scavenge flow within the cylinder.
That the technology is moving towards providing the microscopic in-cylinder gas-dynamic and thermodynamic information is seen in the paper by Ahmadi- Befrui(4.21). Fig. 4.7 is taken directly from that paper and it shows the in-cylinder velocities, but the calculation holds all of the thermodynamic properties of the charge as well, at a point just before ignition. This means that the prediction of heat transfer effects at each time step in the calculation will take place at the individual calculation mesh level, rather than by empiricism for the chamber as a whole, as was the case in the preceding sections. For example, should any one surface or side of the combustion bowl be hotter than another, the calculation will predict the heat transfer in this microscopic manner giving new values and directions for the motion of the cylinder charge; this will affect the resulting combustion behavior.
This calculation can be extended to include the chemistry of the subsequent combustion process. Examples of this have been published by Amsden et al(4.20) and Fig. 4.8 is an example of their theoretical predictions for a direct injection,
REFERENCE VECTOR
8S.3 N/S
K*33
Figure 12(a)
K = 23 K = U
Figure 4.7 CFD calculations of velocities in the combustion chamber prior to ignition.
The Basic Design of Two-Stroke Engines
stratified charge, spark-ignition engine. Fig. 4.8 illustrates a section through the combustion bowl, the flat-topped piston and cylinder head. Reading across from top to bottom, at 28
sbtdc, the figure shows the spray droplets, gas particle velocity vectors, isotherms, turbulent kinetic energy contours, equivalence ratio contours, and the octane mass fraction contours. The paper(4.20) goes on to show the ensuing combustion of the charge. This form of combustion calculation is preferred over any of those models previously discussed, as the combustion process is now being theoretically examined at the correct level. However much computer time such calculations require, they will become the normal design practice in the future, for computers are increasingly becoming more powerful yet more compact and relatively inexpensive.
4.4 Squish behavior in two-stroke engines
It has already been stated in Sect. 4.1.4 that detonation is an undesirable feature of ic engine combustion, particularly when the designer attempts to operate the engine at a compression ratio which is too high. As described in Sect. 1.5.8, the highest thermal efficiency is to be obtained at the highest possible compression ratio. Any technique which will assist the engine to run reliably at a high compres- sion ratio on a given fuel must be studied thoroughly and, if possible, designed into the engine and experimentally tested. Squish action, easily obtained in the unclut- tered cylinder head area of a conventional two-stroke engine, is one such technique.
Aphotograph of squish action, visually enhanced by smoke in a motored QUB type deflector piston engine, is shown in Plate 4.3.
c
ig. 4.8 Detailed calculation of gasoline combustion in a fuel-injected SI engine.
Plate 4.3 The vigorous squish action in a QUB type cross scavenged engine at the end of the compression stroke.
4.4.1 A simple theoretical analysis of squish velocity
From technical papers such as that given by Ahmadi-Befrui et al(4.21), it is clear
that the use of a CFD model permits the accurate calculation of squish velocity
characteristics within the cylinder. An example of this is seen in Fig. 4.7, a CFD
calculation result by Ahmadi-Befrui et al(4.21) for in-cylinder velocities at the point
of ignition at 20
<Jbtdc. This insight into the squish action is excellent, but it is a
calculation method which is unlikely to be in common use by the majority of
designers, at least for some time to come. Because a CFD calculation uses much
time on even the fastest of super-computers, the designer needs a more basic
program for everyday use. Indeed, to save both super-computer and designer time,
the CFD user will always need some simpler guidance tool to narrow down to a final
design before employing the fewest possible runs of the CFD package. An
analytical approach is presented below which is intended to fulfill that need. This
is particularly helpful, principally because the conventional two-stroke engine has
a simple cylinder head, so the designer can conceive of an almost infinite variety of
combustion chamber shapes. This is obvious from an examination of some of the
more basic shapes shown in Fig. 4.10.
The Basic Design of Two-Stroke Engines
There have been several attempts to produce a simple analysis of squish velocity, often with theory which is more empirically based than fundamentally thermodynamic. One of the useful papers which has been widely quoted in this area is that by Fitzgeorge(4.22). Experimental measurements of such phenomena are becoming more authoritative with the advent of instrumentation such as laser doppler anemometry, and the paper by Fansler(4.23) is an excellent example of what is possible by this accurate and non-intrusive measurement technique.
However, the following theoretical procedure is one which is quite justifiable in thermodynamic terms, yet is remarkably simple.
Figs. 4.2 and 4.9 represent a compression process inducing a squished flow between the piston and the cylinder head. The process commences at trapping, i.e., exhaust port closure. From Sect. 1.5.6, the value of trapped mass, Mtr, is known and is based upon an assumed value for the trapped charge pressure and temperature, Ptr and Ttr. At this juncture, the mass will be evenly distributed between the volume subtended by the squish band, VStr, and the volume subtended by the bowl, VBtr.
The actual values of VS1 and VB1 at any particular piston position, as shown in Fig.
4.9, are a matter of geometry based on the parameters illustrated in Fig. 4.2. From such input parameters as squish area ratio, S AR, the values of squish area, AS, bowl area, AB, and bowl diameter, DB, are calculated from Eq. 4.2.1.
For a particular piston position, as shown in Fig. 4.9, the values of thermody- namic state and volumes are known before an incremental piston movement takes place.
ON COMPRESSION STROKE
Fig. 4.9 Simple theoretical model of squish behavior.
Chapter 4 - Combustion in Two-Stroke Engines