CYLINDER, VOLUME V
3.4 Computational fluid dynamics
In recent years a considerable volume of work has been published on the use of Computational Fluid Dynamics, or CFD, for the prediction of in-cylinder and duct flows in (four-stroke cycle) ic engines. Typical of such publications are those by Brandstatter(3.26), Gosman(3.27) and Diwakar(3.28).
At The Queen's University of Belfast, much experience has been gained from the use of a general-purpose CFD code called PHOENICS. The structure and guiding philosophy behind this theoretical package has been described by its originator, Spalding(3.29). PHOENICS is developed for the simulation of a wide variety of fluid flow processes. It can analyze steady or unsteady flow, laminar or turbulent flow, flow in one, two, or three dimensions, and single- or two-phase flow.
The turbulent flow is predicted by what is referred to as a k-epsilon model to estimate the effective viscosity of the fluid. The program divides the control volume of the calculated region into a large number of cells, and then applies the conserva- tion laws of mass, momentum and energy over each of these regions. The mathematical intricacies of the calculation have no place in this book, so the interested reader is referred to the publications of Spalding(3.29) or Gosman (3.27), and the references those papers contain.
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Fig. 3.19 Theoretically determined values of exhaust port charge purity.
A typical computational grid structure employed for an analysis of scavenging flow in a two-stroke engine is shown in Fig. 3.20. Sweeney(3.23) describes the operation of the program in some detail, so only those matters which are relevant to the current discussion will be dealt with here.
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Fig. 3.20 Computational grid structure for scavenging calculati on.
Chapter 3 - Scavenging the Two-Stroke Engine In the preceding sections, there has been a considerable volume of information presented regarding experimentally determined scavenging characteristics of engine cylinders on the single cycle gas scavenging rig. Consequently, at QUB it was considered important to use the PHOENICS CFD code to simulate those experi- ments and thereby determine the level of accuracy of such CFD calculations.
Further gas-dynamics software was written at QUB to inform the PHOENICS code as to the velocity and state conditions of the entering and exiting scavenged charge at all cylinder port boundaries. The flow entering the cylinder was assumed by Sweeney(3.23) to be "plug flow," i.e., the direction of flow of the scavenge air at any port through any calculation cell at the cylinder boundary was in the designed direction of the port. A later research paper by Smyth(3.17) shows this to be inaccurate, particularly for the main transfer ports in a loop scavenged design, and there is further discussion of that in Sect. 3.5.4.
CFD calculations use considerable computer time, and the larger the number of cells the longer is the calculation time. To be more precise, with the cell structure as shown in Fig. 3.20, and 60 time steps from transfer port opening to transfer port closing, the computer run time was 120 minutes on a VAX 11/785 mainframe computer. As one needs 7 individual calculations at particular values of scavenge ratio, SR, from about 0.3 to 1.5, to build up a total knowledge of the scavenging characteristic of a particular cylinder, that implies about 14 hours of computer run time.
A further technical presentation in this field, showing the use of CFD calcula- tions to predict the scavenging and compression phases of in-cylinder flow in a firing engine, has been presented by Ahmadi-Befrui(3.30). In that paper, the authors also used the assumption of plug flow for the exiting scavenge flow into the cylinder and pre-calculated the state-time conditions at all cylinder-port boundaries using an unsteady gas-dynamic calculation of the type described in Chapter 2 and shown in Chapter 5. Nevertheless, their calculation showed the effect on the in-cylinder flow behavior of a varying cylinder volume during the entire compression process up to the point of ignition.
However, the insight which can be gained from this calculation technique is so extensive, and the accuracy level is also so very impressive, there is every likelihood that it will become the standard design method for the optimization of scavenging flow in two-stroke engines in the years ahead.
Examples of the use of the calculation are given by Sweeney(3.23) and a precis of the findings is shown here in Figs. 3.21 -30. The examples selected as illustrations are modified Yamaha cylinders, nos. 14 and 12, the best and the worst of that group whose performance characteristics and scavenging behavior has already been discussed in Sect. 3.2.3.
A comparison of the measured and calculated SE-SR and TE-SR profiles are given in Figs. 3.29 and 3.30. It will be observed that the order of accuracy of the calculation, over the entire SR spectrum, is very high indeed. For those who may be familiar with the findings of Sweeney et al(3.23) it will be observed that the order of accuracy of correlation of the theoretical predictions with the experimental data is considerably better in Figs. 3.29 and 30 than it was in the original paper. The reason for this is that the measured data for the variance of the flow from the port
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Fig. 3.21 Yamaha cylinder No. 14 charge purity plots at 39° bbdc.
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Fig. 3.22 Yamaha cylinder No. 14 charge purity plots at 29° bbdc.
Fig. 3.23 Yamaha cylinder No. 14 charge purity plots at 9° bbdc.
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Fig. 3.25 Yamaha cylinder No. 12 charge purity plots at 39° bbdc.
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Fig. 3.26 Yamaha cylinder No. 12 charge purity plots at 29° bbdc.
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Fig. 3.27 Yamaha cylinder No. 12 charge purity plots at 9° bbdc.
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Fig. 3.28 Yamaha cylinder No. 12 charge purity plots at 29° abdc.
The Basic Design of Two-Stroke Engines
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Fig. 3.29 Comparison of experiment and CFD theory for Yamaha cylinder No. 14.
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