Design and Simulation of Two Stroke Engines

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Design and Simulation of Two-Stroke Engines an engine simulation value, i.e., the "actual" coefficient of discharge, Cda, is then determined as: u _ Aeff n At k eff - —— - C da -— " C da k (A2.3.4) A2 A2 v The algebraic solution to this iterative procedure (for it requires a solution for the several unknowns from an equal number of simultaneous polynomial equations) is not trivial. The number of unknowns depends on whether the flow regime is inflow or outflow, and it can be subsonic or sonic flow for either flow direction; the number of unknowns can vary from two to five, depending on the particular flow regime encountered. The iterative procedure is completed until a satisfactory error band has been achieved, usually 0.01% for any one unknown variable. Then, and only then, with the incorporation of the actual discharge coefficient, Cda,at the same cylinder-to-pipe pressure ratio, P, and geometric area ratios, k, into the simulation will the correct value of mass flow rate and pressure wave reflection and formation be found in the replay mode during an unsteady gas-dynamic and thermodynamic engine computer simulation. Apart from some discussion in a thesis by Bingham [2.64], I am unaware of this approach to the determination of the actual coefficient of discharge, Cda, being presented in the literature until recent times [5.25]. I have published a considerable volume of Cd data relating to both two- and four-stroke engines, but all of it is in the format of Cdi and all of it is in the traditional format whereby the ideal mass flow rate was determined by an isentropic analysis. Where the original measured data exist in a numeric format, that data can be re-examined and the required Cda determined. Where it does not, and the majority of it no longer exists as written records, then that which I have presented is well nigh useless for simulation purposes. Furthermore, it is the complete digitized map, such as in Fig. 2.27, that is needed for each and every pipe discontinuity to provide accurate simulation of unsteady gas flow through engines. Some measurements ofCj at the exhaust port of an engine In Figs. A2.4 to A2.7 are the measured discharge coefficients for both inflow and outflow at the exhaust port of a 125 cm 3 Grand Prix racing motorcycle engine, as shown in Fig. A2.3 [5.25]. These figures plot the discharge coefficients with respect to pressure ratio from the cylinder to the pipe, P, and for geometrical area ratios, k, of 0.127, 0.437, 0.716 and 0.824, respectively. On each figure is shown both the actual discharge coefficient, Cda, and the ideal coefficient, Cdi, as given by Eq. A2.3.3. It should be noted that any difference between these two numbers, if replayed back into an engine simulation at identical k and P values, will give precisely that ratio of mass flow rate difference. At a low area ratio, k, there is almost no difference between Cdi and Cda- The traditional analysis would be equally effective here. As the area ratio increases, and where the mass flow rate is, almost by definition, increasing, then the mass flow rate error through the application of a Cdi value also rises. The worst case is probably inflow at high area ratios, where it is seen to be 20%. 208
(A2.3.4) 0.84 - 0.83 - 0.82 - 0.81 - 0.80 - o — D — Cdi INFLOW Chapter 2 - Gas Flow through Two-Stroke Engines 0.79 - T 1 i • i • i • 0.5 0.6 0.7 0.8 0.9 1.0 1 2 3 P CYLINDER TO PIPE P CYLINDER TO PIPE Fig. A2.4 Coefficient of discharge variations for cylinder inflow and outflow. 0.68 0.66 i ' i • i • i 0.5 0.6 0.7 0.8 0.9 1.0 P CYLINDER TO PIPE i • i • i • i • i 1.0 1.21.4 1.6 1.8 2.0 2.2 P CYLINDER TO PIPE Fig. A2.5 Coefficients of discharge for port k=0.437'. 0.68 0.66 - O 0.64 0.62 T • r 0.60 0.7 0.8 0.9 1.0 P CYLINDER TO PIPE 1.0 1.1 1.2 1.3 P CYLINDER TO PIPE Fig. A2.6 Coefficients of discharge for port k=0.716. 209
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Design and Simulation of Two-Stroke
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A Second Mulled Toast When as a stu
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Acknowledgments As explained in the
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Table of Contents Nomenclature xv C
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Table of Contents 2.10.1 Flow at pi
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Table of Contents 3.5.3.1 The use o
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Table of Contents 6.1.3 The effect
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Nomenclature NAME SYMBOL UNIT (SI)
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speed of rotation speed of rotation
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attenuation or transmission loss wa
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Chapter 4 Combustion in Two-Stroke
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Chapter 4 - Combustion in Two-Strok
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a stratilpl o tions to ivior. If m
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CD 30 -, W 20 - LU CO iS _J LU OC 1
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181 also x3 = — = 0.905 x6 = 2.17
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to be cur .3.20) .3.21) .3.22) for
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3.23) com- :on is hhas has a /eng-
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stroke .3.29) mean me to 3land ssio
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a LU z: en 3 CO a LU z EC D m O ho
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CD 1.2 -i 1.0 - di „„ LU 0.8 cc
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CO —> 111" cc LU < LU _J LU CC £
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Combustion in compression-ignition
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stroke ari more often lseful lental
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lat the ssi ;tribu- ELEVATION VIEWS
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CYLINDER HEAD TYPE IS CENTRAL BORE,
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CO E 50 40 - O O _i Hi > I CO 30 Z)
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CURRENT INPUT DATA FOR 2-STROKE 'SP
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Cylin- PP £ Pa- tics of Paper Chap
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vfitro- ;titi >tants 1970. i(In- Ch
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£2 = Pi P2 I Pi J Chapter 4 - Comb
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CHAINSAW AT 9600 rpm. Chapter 4- Co
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LLI •z. O N -z. 0.21 -, 0.20 DC 0
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Chapter 7 Reduction of Fuel Consump
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Chapter 7 • Reduction of Fuel Con
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Chapter 7 - Reduction of Fuel Consu
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0.35 • 0.34 LU ° 0.33 - c 03 DC
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§ 2000
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y, ,6 Chapter 7 - Reduction of Fuel
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Chapter 7- Reduction of Fuel Consum
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INLET FOR r AIR AND FUEL Chapter 7
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Chapter 8 Reduction of Noise Emissi
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Chapter 8 • Reduction of Noise Em
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Chapter 8 - Reduction of Noise Emis
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• • / . • Appendix Listing of
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Active radical (AR) combustion and
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initial conditions, assumptions reg
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in two-stroke engine (schematic dia
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exhaust timing control valve, effec
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I Exhaust emissions/exhaust gas ana
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Exhaust systems (continued) untuned
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gas constant/universal gas constant
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in crankcase heat transfer analysis
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Mercury Marine air-assisted fuel in
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I PISTON POSITION (computer program
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Pressure wave reflection (in pipes)
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local acoustic velocity, 60 local M
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Roots blower in turbocharged/superc
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Scavenging (continued) scavenging e
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Simulation, engine See Computer mod
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temperature vs. crankshaft angle (c
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work per thermodynamic (Otto) cycle
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Design and Simulation of Two Stroke Engines

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