Design and Simulation of Two Stroke Engines

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£2 = Pi P2 I Pi J Chapter 4 - Combustion in Two-Stroke Engines m u2 x V ul m ul V u2) (A4.2.11) The volume of the unburned zone, VU2, is the only unknown in the above equation. Consequently, the volume of the burned zone is: Vb2 = V2-Vu2 (A4.2.12) and the temperatures in the two zones may be found using Eq. A4.2.10. This is arguably a more accurate solution for the single-zone theory described in Sec. 4.4.2. There, the average gas properties for the entire cylinder space are determined as in Eqs. A4.2.5-A4.2.7, but the individual properties of the trapped air and the burned gas are determined less realistically using the average cylinder temperature, Ti, instead of the zone temperatures, Tui and Tbi, employed here. In the example given below, it is clear that this will induce errors; while not negligible, they are small. The use of this theory within an engine simulation In Chapters 4-7, a chainsaw engine is frequently employed as a design example for a computer simulation. The data used here for the computation are given in Sec. 5.5.1 for the standard engine. The fuel employed in the simulation is unleaded gasoline with a stoichiometric air-to-fuel ratio of 14.3. The results of a computer simulation with air-to-fuel ratios of 12, 13, 14, 15 and 16, are shown in Fig. A4.2, on which are displayed the cylinder temperatures as predicted by this two-zone combustion model. The mean cylinder temperature, and the temperatures in the burned and unburned zones, are indicated on this figure around the tdc period. The rapid rise of temperature in the burned zone to nearly 2400°C is clearly visible, and this peaks at about 10° atdc. The mean cylinder temperature peaks at about 2000°C, but this occurs at some 30° atdc. The temperature in the unburned zone has a real peak at about 15° atdc, whereas the spike at 50° atdc indicates the engulfement of, and disappearance of, the unburned zone by the combustion process. The maximum burn zone temperatures recorded during the simulations are shown in Fig. A4.3, with the highest value shown to be at an AFR of 13, and not closer to the stoichiometric point, i.e., where X is unity. The formation of nitric oxide (NO) The formation of oxides of nitrogen is very, indeed exponentially, dependent on temperature. In Fig. A4.3, as captured from Fig. A4.2, the results of a simulation incorporating the two-zone burn model show the peak temperatures in both the burned and the unburned zones with respect to the same fueling changes. The burn zone temperature reaches a maximum before the stoichiometric air-to-fuel ratio. The unburned zone encounters its highest peak temperature at the richest air-fuel ratio. The Zeldovitch [4.39] approach to the computation of NO formation, as in Eq. A4.1.14, takes all of these factors into account. The profile of the calculated NO formation, shown in Fig. A4.4 with respect to air-fuel ratio, is quite conventional and correlates well with the 349
Design and Simulation of Two-Stroke Engines O Ol UJ DC 3 % DC UJ 0_ LU O Ol UJ DC 3 DC LU 0_ LU h- LU Z o N Z DC 3 CD 3000 2000 - 1000 - CHAINSAW ENGINE SIMULATION AT 9600 rpm AT AIR-TO-FUEL RATIOS FROM 12 TO 16 BURN ZONE \ AFR 12-14 \ UNBURNEDZONE 320 340 360 380 400 420 CRANKSHAFT ANGLE, degrees Fig. A4.2 Cylinder temperatures in a simple two-zone burn model 2400 2300 2200 - 2100 CHAINSAW ENGINE AT 9600 rpm maximum unbumed zone temperature A^l.O 11 12 —r 13 —r 14 —r~ 15 AIR-TO-FUEL RATIO maximum bum zone temperature —r - 16 17 870 860 - 850 -840 830 Fig. A4.3 The effect of fueling on peak temperatures in the two zones. measured data shown in the same figure. That the bsNO peaks after the AFR location of maximum bum zone temperature may be surprising. The reason is, while the maximum bum zone temperature is decreasing toward the stoichiometric air-to-fuel ratio, the oxygen concentration therein is rising; see Fig. A4.8. The measured data are recorded at the same engine speed and bum the same gasoline employed in the simulation; further correlation of this simulation with measured performance 350 O Ol LU cc 3 DC LU 0_ LU h- LU Z O N Q LU Z DC 3 m z 3 440
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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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Design and Simulation ofTwo-Stroke
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Design and Simulation ofTwo'Stroke
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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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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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^ s C£ Q 2^ E Q. Q_ z' o ISSI HCEM
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o > z~ Q w CO UJ w g x O z o z o m
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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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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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