Design and Simulation of Two Stroke Engines

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Design and Simulation of Two-Stroke Engines column labeled "E or C" describes whether the flow encountered was at an expansion (E) or a contraction (C) in pipe area. Table 2.12.3 Output data from the calculations using the more complex theory No. 1 2 3 4 5 6 Pn 0.8850 0.9036 1.1227 1.1292 1.1371 1.0174 Pf2 1.0785 1.0746 1.3118 1.2886 1.2595 1.0487 mg/s 46.38 43.91 48.70 44.69 39.77 27.98 T02K 294.5 296.2 293.0 295.2 298.1 306.7 Theory Sec. 2.10 Sec. 2.12 Sec. 2.11 Sec. 2.12 Sec. 2.12 Sec. 2.12 For simple expansions, in test data sets 1 and 2, the constant pressure theory works remarkably well with an almost negligible error, i.e., less than 3% in mass flow rate terms. If the expansion has a realistic coefficient of discharge of 0.85 applied to it then that error on mass flow rate rises slightly from 2.65 to 2.8%. The magnitudes of the reflected pressure waves compare quite favorably in most circumstances. At a simple sudden contraction in test data sets 3 and 4, even with a coefficient discharge of 1.0 the mass flow rate error is significant at 8.2%, rising to 17.9% error when the quite logical Cd value of 0.7 is applied to the sudden contraction. The magnitudes of the reflected pressure waves are significantly different when emanating from the simple and the complex theories. When any form of restriction is placed in the pipe, i.e., in test data sets 5 and 6 for an expansion and a contraction, respectively, the constant pressure theory is simply not capable of providing any relevant information either for the magnitude of the reflected wave or for the mass flow rates. The error is greater for expansions than contractions, which is the opposite of the situation when restrictions in the pipe are not present. Note the significant entropy gains in tests 4-6. The constant pressure theory is seen to be reasonably accurate only for flow which encounters sudden expansions in the ducting. 2.13 An introduction to reflections of pressure waves at branches in a pipe The simple theoretical treatment for this situation was also suggested by Benson [2.4] and in precisely the same form as for the sudden area changes found in the previous section. A sketch of a typical branch is shown in Fig. 2.13. The sign convention for all of the branch theory presented here is that inward propagation of a pressure wave toward the branch will be regarded as "positive." Benson [2.4] postulates that the superposition pressure at the junction, at any instant of wave incidence and reflection, can be regarded as a constant. This is a straightforward extension of his thinking for the expansion and contractions given in Sec. 2.9. 114
Chapter 2 - Gas Flow through Two-Stroke Engines (b) at the junction faces Fig. 2.13 Unsteady flow at a three-way branch. The incident pressure waves are pn, pj2, and pj3 and the ensuing reflections are of pressures pri, pr2, and pr3. The superposition states are psi, pS2, and ps3. Therefore, the theoretical solution involves expansion of Eqs. 2.9.3 and 2.9.4 to deal with the superposition state and mass flow rate of the extra pipe 3 at the junction. Benson's criterion inherently assumes isentropic flow. Psl = Ps2 = Ps3 or Xji + Xri - 1 = XJ2 + Xr2 - 1 = Xj3 + Xr3 - 1 The net mass flow rate at the junction is zero: Ai(Xii - Xri) + A2(Xi2 - Xr2) + A3(Xi3 - Xr3) = 0 (2.13.1) (2.13.2) There are three equations to solve for the three unknowns, Xri, Xr2 and Xr3. It is presumed that in the course of any computation we know the values of all incident pressure waves from one calculation time step to another. 115
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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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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 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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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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