Design and Simulation of Two Stroke Engines

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Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines short pipe in some designs. The usual practice is to employ a number of holes, Nh, each of area, Ah, or diameter, dh, if they are round holes for reasons of manufacturing simplicity. The volume of the resonant cavity is Vb where, if all cross-sections are circular: v A T rcLb(d3+2xt) 2 v b = A b L b : ( 8 - 5 - 6 ) According to Kato [8.18], the length, Lh, that is occupied by the holes should not exceed the pipe diameter, d3, otherwise the system should be theoretically treated as a diffusing silencer. The natural frequency of the side-resonant system, fsr, is given by Davis [8.4] as: fsr=^J^ (8.5.7) where Kh, the conductivity of the holes which are the opening, is calculated from: as: NhAh Kh - x,+0.8Ah < 8 - 5 ' 8 ' The attenuation or transmission loss in dB of this type of silencer, (3tr, is given by Davis where the term, Z, is found from: Ptr = 101og10(l + Z 2 ) (8.5.9) Z = V K h 2A f vb 3 f (8.5.10) When the applied noise frequency, f, is equal to the resonant frequency, fsr> the value of Z becomes infinite as does the resultant noise attenuation in Eq. 8.5.9. Clearly this is an impractical result, but it does give credence to the view that such a silencer has a considerable attenuation level in the region of the natural frequency of the side-resonant cavity and connecting passage. To help you use these acoustic equations for design purposes, a simple computer program is referenced in the Appendix Listing of Computer Programs as Prog.8.2, SIDE-RESONANT SILENCER. The attenuation equations programmed are those discussed above from Davis [8.4], Eqs. 8.5.6.-8.5.10. 561
Design and Simulation of Two-Stroke Engines To demonstrate the use of this computer design program, and to determine if the predictions emanating from it are of practical use to the designer of side-resonant elements within an exhaust muffler for a two-stroke engine, the geometrical and experimental data pertaining to SYSTEM 4 of Coates [8.3] are inserted as data and the calculation result is illustrated in Fig. 8.14. The information in that figure is the computer screen picture as seen by the user of Prog.8.2. The information displayed is the input data for, in this instance, SYSTEM 4 and you can check the methodology of data input from Fig. 8.2, and the output data which are the attenuation in dB over a frequency range up to 4 kHz. You may wonder about 10°C being the declared data value for exhaust temperature, but the simulation work of Coates was conducted by a rotor valve delivering very realistic exhaust pulses, but in very cold air! QUB is in Ulster and Ulster is not in the tropics. The calculated sound attenuation of SYSTEM 4, as seen in Fig. 8.14, shows a large peak of 50 dB transmission loss at 600 Hz, with further attenuation stretching to 2.5 kHz. If you examine the measured noise spectrum of SYSTEM 4 in Fig. 8.6, and compare it to the unsilenced SYSTEM 1 in Fig. 8.3, you can see that there is considerable attenuation produced by this side-resonant silencer at 500 Hz, although it is not as profound as 50 dB. Of even greater interest to the designer is the visibly strong attenuation of SYSTEM 4 stretching up to 10 kHz, which is not present in either of the diffusing silencer designs discussed in Sec. 8.5.1. Also note that the calculated attenuation stretches down to 100 Hz, i.e., below the DESIGN FOR A SIDE-RESONANT SILENCER NPUT DATA LB= 305 DSB= 76 DS3= 28.6 TH= 1.5 NH= 40 DSH= 3.18 T2C= 10 CALCULATION BY Prog.8.2 DATA FROM Coates/Blair SYSTEM 4 -I—I I I—r—i—|—1—i—I I I I—i—I—i—J—i—i—i—i—i—I I I— 2000 3000 4000 FREQUENCY, Hz Fig. 8.14 Calculation by Prog.8.2 for the silencing characteristics of SYSTEM 4. 562
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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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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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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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§ 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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o Q_ Ld < CD 15-, 10- Chapter 7 - R
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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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