International Journal of Automotive Technology, Vol 12, No 4, pp 469−474 (2011) DOI 10.1007/s12239−011−0055−3 Copyright © 2011 KSAE 1229−9138/2011/059−01 INFLUENTIAL FACTORS FOR HLA PUMP UP IN A ROLLER FINGER FOLLOWER ENGINE M CHOI* and K MIN School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea (Received April 2010; Revised September 2010) ABSTRACT−In an HLA (hydraulic lash adjuster) piston engine, “pump up” can occur when a valve is opened by the HLA when it should be closed HLA pump up is more frequently encountered with exhaust valves than with intake valves When HLA pump up in occurs in the exhaust valve, exhaust gas from the exhaust manifold enters the cylinder on the intake stroke, and fresh air-fuel mixture exits through the exhaust manifold on the compression stroke and is burned in the catalyst, causing partial burning, misfire, catalyst melting and power drop HLA pump up occurs when the force on the valve from the HLA is higher than the force on the HLA from the valve HLA pump up is related to design parameters, such as oil pressure, rocker ratio, spring load, spring surge, and both intake and exhaust valve timing In this study, valve lift and load on a roller finger follower were measured at varying engine firing conditions to evaluate HLA pump up The results indicated that effective measures to reduce HLA pump up include a higher rocker ratio, a lower oil supply pressure to the HLA, a higher spring installation load and a lower spring surge KEY WORDS : Engine, Combustion, Emission, Valve, HLA, Spring INTRODUCTION Therefore, the main concern in addressing HLA pump up is to minimize power loss and negative effects on other functional devices This study of HLA pump up was done with a Hyundai Tau V8 4.6L engine (see Figure 1) The cam and general specifications of the Tau engine are described in Tables and 2, respectively The types of valve trains used in internal combustion engines are classified according to the method of valve operation: by cam, such as a direct acting type, by roller rocker arm type and by roller finger follower (RFF) It is very important to select the correct valve type in an engine because the valving greatly determines basic engine characteristics, such as cost, volume, and friction Depending on the type of valve train, the amount of friction of may differ by up to 30% (Heywood, 1988) Every engine manufacturer has a preference for one type of valve train Nissan uses a direct acting type, Honda a rocker arm, BMW a roller finger follower, and Toyota a direct acting type However, in recent years, Toyota has been changing from direct acting valves to roller finger followers to reduce friction The roles of valves in engine are air aspiration and sealing The hydraulic lash adjuster (HLA) is an effective device for adjusting valve gap If the HLA becomes “pumped up” on the exhaust valve, exhaust gas can enter the cylinder on the intake stroke and fuel mixture is lost through the exhaust manifold on the compression stroke, resulting in partial burning, misfire and possible catalyst melting HLA pump up is not only caused by the HLA itself but due to overall engine conditions such as rocker ratio, oil pressure, valve spring surge (Eaton, 1946), intake valve timing and back pressure MECHANISM OF HLA PUMP UP Valve opening with HLA pump up is illustrated in Figure The HLA is pumped up, and the valve is opened in the cam base circle To keep the valves closed in the cam base circle, the forces on the valves in the closing direction must be higher than the forces in the opening direction (Choi, Han, 2006) The forces on the exhaust valve in the closing direction in the cam base circle are valve spring force and *Corresponding author e-mail: ms_choi@hyundai.com Figure Hyundai 4.6L V8 Tau engine 469 470 M CHOI and K MIN Table Cam specifications of the Tau engine (Lee and Kim, 2008) Valve lift Exhaust 10.0 mm 9.8 mm o 246oCA 246 CA Valve duration Ramp height (Opening/Closing) Intake 0.05 mm/0.15 mm 0.05 mm/0.15 mm Fullness 56.0% 56.3% Table General specifications of the Tau engine Engine name Tau 4.6 Type V8 Displacement 4,627 cc Bore x Stroke 92 mm×87 mm Valves Firing order DOHC 32 1-2-7-8-4-5-6-3 Compression ratio 10.4 Compression chamber Fuel injection Emission regulation Figure Force components on a valve Pent roof Port injection ULEV-II, USA Valve angle 23o/23o Valve diameter (In/Ex) Φ38 mm/Φ32 mm Rated power (6,500 rpm, RON 96) 380 PS (280 kW) Max torque (3,500 rpm, RON 96) 46.0 kgfm (451 Nm) pressure in the combustion chamber in the induction, compression, and expansion strokes Conversely, the forces on the exhaust valve in the opening direction are the pressure of the exhaust manifold, acting on back of the exhaust valve, the cylinder pressure on the induction stroke, spring force reduced by spring surge and the HLA lifting force due to oil pressure If the force on the HLA is less than the force from the HLA, then the HLA pumps up Figure HLA pump up and valve lift The forces acting on the valve are shown in Figure The force balance for the HLA is described by Equation (1): Force balance on HLA Fin_HLA = FPS + Fop (1) Fon_HLA= (FS– FSS–FBP–FV -Fbounce)×(RR –1) (2) Condition for HLA pump up Fon_HLA < Fin_HLA (3) Fin_HLA Fps Fop Fon_HLA FS FSS FBP Fcyl RR : Internal force from HLA : Force of plunger spring : Force due to oil pressure : Force on HLA : Spring force : Force from spring surge : Force from back-pressure acting on valve : Force from cylinder pressure acting on valve : Rocker ratio 2.1 HLA Pump Up and Valve Lift Signal and Load on RFF Signal To better understand HLA pump up, valve lift was measured with a gap sensor, as shown in Figure 4, and the load on the RFF was measured with a strain gauge, as shown in Figure (Bota et al., 2009) The gap sensor was installed above the spring retainer with a 0.5 mm gap as the valve is closed (see Figure 4), and Figure Gap sensor installation above valve retainer INFLUENTIAL FACTORS FOR HLA PUMP UP IN A ROLLER FINGER FOLLOWER ENGINE Figure Strain gauge on RFF However, the exhaust valve lift signal reached a minimum on the compression and expansion strokes, as the gap between the valve and the gap sensor was reduced due to the reduced pressure in the combustion chamber acting on the valve With HLA pump up conditions (Figure 7), the exhaust valve lift on the intake stroke was approximately 200 µm; due to HLA, the exhaust valve was open when it should have been closed The load signal on the RFF, shown at the top of Figure 8, showed a normal pattern without HLA pump up As HLA pump up increased, the load signal between EVC (exhaust valve closed) and EVO (exhaust valve open) was increased When the valve was closed, the pressure variance in the combustion chamber was shown as the load signal on the RFF The amount of load on the RFF from the valve during the expansion stroke is proportional to the amount of HLA pump up, as shown in Figure Figure PV diagram with or without HLA pump up the strain gauge was installed on the RFF to measure cam load (see Figure 5) (Schwarz et al., 2009) In normal engine conditions, without HLA pump up, the compression pressure and combustion pressure are high In contrast, in abnormal engine conditions with HLA pump up, the exhaust valve is not closed during the compression stroke and the compression pressure is thus lower than in normal conditions, as shown in Figure The low peak pressure in abnormal conditions seems to be the result of partial burning or misfire (see Figure 6) Without HLA pump up, as shown in Figure 7, the exhaust valve lift signal on the intake stroke is unchanged Figure Valve lift signal with or without HLA pump up 471 Figure Load signals on RFF and HLA pump up 472 M CHOI and K MIN TEST RESULTS 3.1 HLA Pump Up on the Exhaust Valve The load on the RFF is closely related to the pressure in the combustion chamber HLA pump up on the exhaust valve occurs ahead of that on the intake valve (Choi et al., 2007) As the intake valve was closed on the compression stroke, pressure in the combustion chamber acted on the intake valve in the valve closing direction Conversely, as the exhaust valve was closed during the induction stroke, the pressure in the combustion chamber was lower than the atmospheric pressure, and the back pressure acted on the exhaust valve in the valve opening direction The forces on the intake valve in the closing direction were higher than those on the exhaust valve The forces on the intake and exhaust valves were calculated at 6,000 rpm in a wide-open test condition, as shown in Figure The force difference between Fcyl_IVC and Fcyl_EVC was 214.9 [N] Fcyl_IVC = (2.5-1)/10×362×3.14/4 = 152.6 [N] (Intake) Fcyl_EVC={(0.9-1)/10×322-(1.7-1)/10×(322-62)}×π/4 = -62.3 [N] (Exhaust) Diameter of intake / exhaust valve: 36 mm /32 mm Dia of valve stem = mm At the same engine conditions, the load signal on the RFF during exhaust and intake differed, as shown in Figure Figure 11 Load signal on exhaust valve with and without HLA pump up at rocker ratios of 1.8 and 2.17 10 The load at EVO was much higher than at IVO HLA pump up occurred on the exhaust side but did not occur on the intake side 3.2 Rocker Ratio and HLA Pump Up The rocker ratio (RR) of the RFF is related to HLA pump up by Equation (2) The force on the HLA with an RR of 2.17 is 1.46 times higher than with an RR of 1.8 Although there was no HLA pump up with an RR of 2.17 RFF at 6,500 rpm (Otsubo et al., 2004), there was HLA pump up with an RR of 1.8 RFF at 6,000 rpm as Figure 11 Thus, a higher rocker ratio created a higher load acting on the bearing in the RFF Therefore, the use of a higher RR is an effective way to reduce HLA pump up, but the durability of the bearing in the RFF must also be considered 3.3 Oil Pressure in HLA and HLA Pump Up Oil pressure in the HLA is the origin of HLA pump up The upward force on the HLA (Koshimizu et al., 2004) can be calculated from Equation (4) F = Oil pressure × Cross-sectional area of HLA (4) Ex.) F = (3.5-1) [bar]×105[N/m2] × π × (10/2/1,000)2 = 19.6[N] Figure Pressure in the combustion chamber (WOT 6,000 RPM) HLA pump up occurred at an oil pressure of 4.3 [bar] To reduce the oil pressure, a relief valve was installed at the entrance of the oil gallery in the engine head Oil pressure was reduced from 4.3 [bar] to 3.0 [bar] by the relief valve The upward force was correspondingly decreased by 13 [N] as calculated by Equation (4), and HLA pump up disappeared, as shown in Figure 12 3.4 Spring Surge and HLA Pump Up To better understand the correlation between spring load and HLA pump up, spring load was measured with a strain Figure 10 Load signals on the RFF during intake and exhaust Figure 12 HLA pump up with oil pressure INFLUENTIAL FACTORS FOR HLA PUMP UP IN A ROLLER FINGER FOLLOWER ENGINE 473 Figure 13 Strain gauge on spring Table Specifications of test springs and test results Test sample #1 #2 #3 Figure 15 Spring surge @ 6000 RPM 6,400 rpm 6,400 rpm Springs with unequal pitches on either end, i.e., smaller wire diameters, show less spring surge There was very small spring surge with a diameter of Φ3.3, as shown in Figures 15 and 16 The result of the analysis for the design factor of spring surge show that the spring active coil mass was linearly correlated with spring surge, as shown in Figures 15, 16, and 17 Among the springs with unequal pitches at each end (NE2), only #1 (Φ3.3) showed no HLA pump up, and it had the lowest rate of spring load change With a similar gauge installed on the upper part of the spring, as shown in Figure 13, with a 100 µm wire-to-wire gap when the spring was compressed with maximum valve lift Table lists the specifications of the test springs and the test results When spring sample #1 was in the engine, there was no HLA pump up (bottom of Figure 14), but there was HLA pump up with spring samples #2, and #3, even with similar maximum spring load Spring load signals from the strain gauge showed a sine wave during the valve closing period When the valve was closed, the amplitude of the sine wave was at the maximum and then gradually reduced, as shown in Figure 15 For this test, springs with unequal pitches at either end were used Figure 16 Amplitude of spring surge and ratio of spring load change Spring shape Cylinder Cylinder Cylinder Pitch NE2* NE2* NE2* Wire size [mm] Φ3.3 Φ3.4 Φ3.5 300/600 310/634 313/608 7.8 7.72 34 (44) 37 (47) F1/F2[N] Number of turns Spring mass (+ retainer)[g] 33 (43) Engine speed of HLA pump up Non *NE2 = Unequal pitches at each end Rate of spring load change = (MAXdynamic-MINdynamic) ÷ (5) (MAXstatic - MINstatic) Figure 14 HLA pump up with different springs Figure 17 Correlation between mass of spring active coil and rate of spring maximum load change 474 M CHOI and K MIN spring load, sample #2 and sample #3 experienced HLA pump up whereas sample #1 did not CONCLUSIONS HLA pump up is one of the most undesirable phenomena in engine operation When HLA pumps up an exhaust valve, fresh air fuel mixture is lost and is burned in the catalyst As a result of HLA pump up, the catalyst can be melted and engine power is reduced The main results are summarized as follows: (1) HLA pump up in an exhaust valve occurs ahead of that in an intake valve because the forces on the intake valve in the closing direction are higher than those for the exhaust valve (2) HLA pump up occurs at a low rocker ratio, but a higher rocker ratio places a higher load on the swing arm, which is related to bearing axle pitting Therefore, in selecting a rocker ratio not only HLA pump up but also engine durability must be considered (3) Oil pressure to the HLA is one of the main sources of HLA pump up Without sufficient oil pressure for HLA, there could be no HLA pump up Therefore, oil pressure for the HLA should be managed to within a certain range (4) The amplitude of spring surge and rate of spring load change are linearly correlated with the mass of the spring active coil Lower mass in the active coil results in less spring surge In cylindrical springs with unequal pitches at each end, the spring with the lowest surge amplitude showed no HLA pump up ACKNOWLEDGEMENT−Test data for this paper was from Tau engine development in HMC Till the Tau engine was mass produced, lots of problems in valve train were occurred I was very appreciated with Mr Kyu Bong Han who had been worked for valve train of Tau engine and poured his all energies to cure the troubles And I was very appreciated with Douglas Nielsen in Eaton who cooperated with us and tried to his best to find root causes for troubles and solutions Finally I appreciated with all the engineers who worked for Tau engine in HMC and in Eaton REFERENCES Bota, J., Kumagai, T., Fujimura, T., Takayama, S and Hatamura, K (2009) Comparison of MBD simulation with measurements for roller-finger-follower with HLA valve train system behavior in higher engine speed Conf JSAE, JSAE 20095248 Choi, M S., Han, K B., Kim, H I., Oh, D Y and W T Kim (2007) Mechanical parameters for durability and HLA pump up in Tau engine Conf Hyundai-Kia Motors EN 01-07, 2007EN0108 Heywood, J B (1988) Internal Combustion Engine Fundamentals McGraw-Hill Int Edn 737−739 Koshimizu, T., Kikuoka, S., Hibino, Y., Otsubo, M and Ishikawa, S (2004) Development of high response hydraulic lash adjuster Conf JSAE, JSAE 20045667 Lee, S and Kim, W (2008?) Development of a new high performance 4.6 liter V-8 HMC Tau engine FISITA 2008, F2008-06-085 Otsubo, M., Saito, T and Hibino, Y (2004) Analysis method for high-speed performance of valve train with HLA Conf JSAE, JSAE 20045615 Schwarz, D., Bach, M and Fuoss, K (2009) Valvetrain investigation on fired engines Porsche Engineering Services, MTZ 06I2009, 70, 36−41 International Journal of Automotive Technology, Vol 12, No 4, pp 475−487 (2011) DOI 10.1007/s12239−011−0056−2 Copyright © 2011 KSAE 1229−9138/2011/059−02 EFFECT OF ENGINE EXHAUST GAS MODULATION ON THE COLD START EMISSIONS T SHAMIM* Department of Mechanical Engineering, The University of Michigan – Dearborn, Dearborn, MI 48128-2406, USA (Received June 2010: Revised 20 January 2011) ABSTRACT−This paper presents a computational investigation of the effect of engine exhaust gas modulations on the performance of an automotive catalytic converter during cold starts The objective is to assess if the modulations can result in faster catalyst light-off conditions and thus reduce cold-start emissions The study employs a single-channel based, onedimensional, non-adiabatic model The modulations are generated by forcing the variations in exhaust gases air-fuel ratio and gas compositions The results show that the imposed modulations cause a significant departure in the catalyst behavior from its steady behavior, and modulations have both favorable and harmful effects on pollutant conversion during the cold-starts The operating conditions and the modulating parameters have substantial influence on catalyst behavior KEY WORDS : Engine emissions, Engine exhaust after-treatment, Dynamic behavior, Numerical simulations NOMENCLATURE Cgj Csj cpg cps Dh Dj Ga DHk hg h∞ kmj L Nu Pr Rk Re Sc Sext t T∞ Tg Ts vg Xinlet Xoutlet z ε : void volume fraction, dimensionless ρg ρs : thermal conductivity of gas, J/m·s·K : thermal conductivity of substrate, J/(m·s·K) : gas density, kg/m3 : substrate density, kg/m3 λg λs : gas phase concentration of species j, mol/m3 : surface concentration of species j, mol/m3 : specific heat of gas, J/(kg·K) : specific heat of substrate, J/(kg·K) : hydraulic diameter, m : diffusion coefficient of species j, m2/s : geometric surface area, m2/m3 : heat of reaction of species k, J/mol : heat transfer coefficient between flow and substrate, J/(m2·s·K) : heat transfer coefficient between substrate and atmosphere, J/(m2·s·K) : mass transfer coefficient for species j, m/s : catalyst length, m : Nusselt number, dimensionless : Prandtl number, dimensionless : reaction rate of kth reaction, mol/(m2·s) : Reynolds number, dimensionless : Schmidt number, dimensionless : external surface to volume area ratio, m2/m3 : time, s : ambient temperature, K : gas temperature, K : substrate temperature, K gas flow velocity, m/s species concentration at the catalyst inlet, mol/m3 species concentration at the catalyst outlet, mol/m3 : coordinate along catalyst axis, m INTRODUCTION The progress in catalyst technology has resulted in highly efficient catalytic converters, which can easily meet the emission regulations However, since a catalytic converter remains essentially ineffective until it reaches the light-off temperature, the main challenge in meeting the progressively stringent emission regulations is the control of cold-start emissions This may require either lowering the light-off temperature or shortening the time taken by the catalytic converter in reaching the light-off temperature during a cold start This objective has led to the development of several fast light-off techniques (FLTs) These techniques may be classified as passive and active depending on the need of additional energy sources Passive techniques are focused on achieving fast light-off by optimization of the exhaust system design that includes the modification of catalytic converter design to improve heat transfer and/or change in the converter position relative to the engine, and the use of close-coupled catalyst (Lee et al., 2002; Persoons et al., 2004) and hydrocarbon traps (Noda et al., 1997; Yamamoto et al., 2002) These methods generally have less fuel penalty Active techniques, on the other hand, are based on providing the additional energy to raise exhaust system temperature during cold starts They generally require preheating of the catalytic converters *Corresponding author e-mail: shamim@umich.edu 475 476 T SHAMIM The external energy may be provided by using various means, such as electrically and chemically preheating the catalyst (Socha and Thompson, 1992; Pulkrabek and Shaver, 1993; Akcayol and Cinar, 2005), use of burner (Oeser et al., 1994) or exhaust gas ignition with secondary air injection (Ma et al., 1992; Cho and Kim, 2005) These methods usually need auxiliary devices and are relatively expensive Many past studies have shown that the catalyst conversion performance can be significantly influenced by the transient nature of the engine exhaust gases entering the catalyst (Herz, 1981, 1987; Silveston, 1995 and 1996; Shamim and Medisetty, 2003; Shamim, 2005) The effects of variations in exhaust gas air-fuel ratio and composition have been shown to alter the catalyst pollutant conversion performance (Silveston, 1996; Shamim and Medisetty, 2003; Shamim, 2005) Particularly, at temperatures below light-off values, the exhaust gas composition modulation has been found to result in a significant rate enhancement for CO oxidation over catalyst (Cutlip, 1979; AbdulKareem et al., 1980; Schlatter and Mitchell, 1980; Taylor and Sinkevitch, 1983; Cho and West, 1986; Zhou et al., 1986) Cho (1988) found higher conversions for all three pollutants by feed composition modulation around a timeaverage stoichiometric point below the reaction light-off temperature This trend reverses above the reaction light-off temperatures Koc`í et al (2004) reported the reduction in the light-off temperature and the increase in the HC and NO conversions by the forced modulation of oxygen concentration The difference in the catalyst behavior at temperature below and above the light-off value was explained by Lie et al (1993) on the basis of the coverage of catalyst site with CO for a catalyst with only CO oxidation They postulated that an increase in the time average conversion is possible only if the surface is almost completely covered with CO at steady state Therefore, a positive effect of cycling is to be expected only below the light-off temperature since such a situation only occurs at low temperatures Silveston (1996) also found modulations to be beneficial for cold start conditions but not for warm-up conditions In summary, the findings of the past studies indicate a positive effect of modulations on the catalyst pollutant conversion performance during cold start conditions Most of the past studies were laboratory-based and employed catalyst bed reactors However, there are differences between laboratory-based catalyst and the automotive three-way catalytic converter For example, many laboratory-based catalysts have smaller volume and are single channel and adiabatic reactors Whereas, the automotive three-way catalytic converters have larger volume, hundreds of channels and different heat transfer environment Furthermore, the composition of the sample gas passing through the laboratory-based reactor may be different from the engine exhaust gas passing through the automotive three-way catalytic converter under realistic driving conditions Owing to these differences, the results of past studies may not be accurately extrapolated to predict the influence of modulations on the cold-start performance of an actual automotive three-way catalytic converter during driving conditions The present study is motivated by realizing such an existing gap in the literature This study employs a mathematical model to investigate the influence of exhaust gas modulations on the catalyst performance during cold-start The catalyst considered is multi-channel and non-adiabatic, similar to those used in automotive applications However, the transient conditions considered in the study are not real driving conditions, which involve coupling effects of variations in exhaust flow, composition and temperature In this study, the transients are simulated by considering the catalyst subjected to temporal modulation in air-fuel ratio (A/F) and exhaust gas composition To isolate the effect of individual modulating parameters, the current simulations were performed by isolating and decoupling the effects of modulations in A/F and individual exhaust gas species The A/F was modulated through variations in oxygen concentrations while keeping the exhaust gas composition of CO, HC, and NO constant The exhaust gas composition was modulated by individually varying the concentrations of CO, HC and NO, while keeping the A/F constant through appropriate variations in the oxygen concentration MATHEMATICAL FORMULATION The governing equations were developed by considering the conservation of mass, energy and chemical species Using the assumptions listed elsewhere (Shamim et al., 2002), the governing conservation equations for a typical single channel may be written as follows: Gas phase energy equation: ∂T ∂t ∂T ∂z ρg cpg⎛⎝ ε g + vg g⎞⎠ = –hg Ga( Tg – Ts ) (1) Gas phase species equations (for species: CO, NO, NH3, O2, C3H6, H2 and C3H8): j ∂C j j j ⎛ ε ∂C g g⎞ ⎝ ∂t + vg ∂z ⎠ = –km Ga ( Cg – Cs ) j (2) Surface energy equation: ∂T ∂2 T ( – ε )ρs cps -s = ( – ε)λs 2-s + hgGa ( Tg – Ts ) – h∞Sext ( Ts – T∞ ) ∂t ∂z nreaction + Ga ∑ (3) n Rk( Ts, C1s , …, Cs specise ) ∆Hk k=1 Surface species equations (for species: CO, NO, NH3, O2, C3H6, H2 and C3H8): n ∂Cj ( – ε ) s = kmj Ga( Cjg – Cjs ) – GaRj ( Ts, C1s , …, Cs species ) ∂t (4) EFFECT OF ENGINE EXHAUST GAS MODULATION ON THE COLD START EMISSIONS The conservation equation for the surface oxygen storage mechanism is represented by Equation (4) excluding the convective mass transport term The heat and mass transfer coefficients (hg and kmj ) in the above equations are calculated from Nuλ hg = g Dh (5) ShD kmj = -j Dh (6) Values of Nu and Sh numbers are obtained from the following forms of correlations with Re, Pr and Sc numbers: L Nu = c⎛⎝ Re Pr -⎞⎠ z n L and Sh = c⎛⎝ Re Sc -⎞⎠ z (7) n (8) The values of constants c and n used in this study were based on proprietary information (Shamim, 2003) The chemical reactions and the corresponding kinetic data used in the present study were similar to those used in our past study (Shamim et al., 2002) The governing equations were discretized by using a non-uniform grid and employing the control volume approach with the central implicit difference scheme in the spatial direction A standard tridiagonal matrix algorithm with an iterative successive line under relaxation method was used to solve the finite difference equations The spatial node size ranging from 0.1693 mm to 19.32 mm and the time step of 0.001 second were employed The grid insensitivity of results was ensured by performing a sensitivity study Details of the solution procedure are described elsewhere (Shamim et al., 2002) 477 the exhaust composition of CO, HC and NO concentrations unchanged The exhaust composition was modulated by individually varying the concentrations of CO, HC and NO, while keeping the A/F constant During these oscillations, other inlet conditions remained unchanged 3.1 Effect of Modulation in Air-Fuel Ratio The effect of A/F modulation on the catalyst performance during cold starts was investigated by considering a steady state catalyst subjected to sinusoidal modulation in A/F at different exhaust temperatures Figure shows the results of the imposed modulation near stoichiometric conditions During the simulations, the A/F, initially set at 14.7, is varied sinusoidally with a frequency of Hz and amplitude of 5% During the cold-start, the near stoichiometric conditions (A/F = 14.7) in the catalyst can be achieved by injecting additional air in the exhaust prior to the catalyst inlet since the exhaust has low A/F value under these conditions The modulating A/F ranges between 13.97 and 15.43, and the catalyst undergoes a transition between rich and lean operating conditions during each modulation time period The catalyst responds to A/F modulation with different amplitudes at different exhaust temperatures The results show that the catalyst conversion performance of all three species responds to the imposed A/F modulation The response amplitude increases with an increase of exhaust temperature, which is expected since the catalyst is operating in the kinetically controlled regime The response is generally smooth and periodic The CO conversion exhibits a stronger influence of the imposed modulation and the RESULTS AND DISCUSSION The numerical model was validated by comparing with the experimental measurements as reported elsewhere (Shamim et al., 2002) The validation results showed the suitability of the model in simulating the transient performance of catalyst The catalyst used for the present study was palladium-based and had a length of cm, cross-sectional area of 86.0254 cm2, cell density of 62 cells/cm2, and wall thickness of 0.1905 mm The gas mass flow rate was 1.417×10-2 kg/s with 4.7184×10-5 kg/s CO, 8.0727×10-6 kg/s total HC, and 2.0363×10-6 kg/s NO, and the stoichiometric value of A/F was 14.51 Five feed gas temperatures were investigated: 100oC, 150oC, 200oC, 250oC, and 300oC The low feed gas temperature were selected to investigate the effect of exhaust gas modulations on the catalyst conversion performance during cold starts The exhaust gas modulations were simulated by sinusoidal and independent variations of A/F and exhaust gas composition The A/F was varied by changing the oxygen concentration and keeping Figure Catalyst response to sinusoidal modulations in A/ F for different exhaust gas temperatures near stoichiometric operating conditions (mean A/F = 14.7, frequency = Hz, amplitude = 5%) 616 C Y LIU, K J JIANG and Y ZHANG Rochon, P (1987) Magnetic brake: Simple theory and experiment Am J Phys 55, 6, 500−503 Yi, F Y., He, R., Liu, C Y and He, J Q (2004) 3-D finite element analysis of eddy current retarder J Traffic and Transportation Engineering 4, 2, 30−35 (in Chinese) International Journal of Automotive Technology, Vol 12, No 4, pp 617−630 (2011) DOI 10.1007/s12239−011−0072−2 Copyright © 2011 KSAE 1229−9138/2011/059−18 OPTIMAL DESIGN OF THE EXHAUST SYSTEM LAYOUT TO SUPPRESS THE DISCHARGE NOISE FROM AN IDLING ENGINE J.-G IH1)*, C.-Y CHOI1), T.-K KIM1), S.-H JANG2) and H.-J KIM3) 1) Center for Noise and Vibration Control (NoViC), Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea 2) Korea Railroad Research Institute, Wolam-dong, Uiwang-si, Gyeonggi 437-757, Korea 3) R&D Center, Faurecia Exhaust Systems Korea, Hwaseong-si, Gyeonggi 445-944, Korea (Received 17 June 2010; Revised 21 February 2011) ABSTRACT−At the idle engine speed, the exhaust discharge noise is influenced by resonances in the whole system, which is composed of connecting pipes and silencers This pipe resonance radiates a high level of low frequency discharge noise, which is dominated by the low order harmonics of the engine firing frequency This low frequency noise deteriorates the vehicle’s interior noise level and quality The following study attempted to optimize the layout of an exhaust system to minimize low frequency noise by changing the position of silencers and the lengths of inlet and outlet pipes in each silencer After modeling the exhaust system using four-pole parameters, the acoustical performance of the system was evaluated using the system insertion loss In the optimization, the virtual attenuation coefficient, which corresponds to the amount of attenuation coefficient required for the silencers, was calculated to find a minimum value for the layout The simulated annealing method, which is also known as finding an optimal, was employed in searching for the optimized exhaust layout Test examples of two cases, for two and six design variables, were used When the number of design variables was two, the positions of the center and rear silencers were considered When the number of design variables was six, the positions of the two silencers and the lengths of the inlet and outlet pipes were considered Three typical layouts for the exhaust system of each case were designed, including the given system and an optimal system By comparing the predicted and measured discharge noise level, it was confirmed that the optimized exhaust layout has a higher noise reduction than the other layout designs KEY WORDS : Exhaust system, Idle noise, Discharge noise, Silencer, Optimal layout design INTRODUCTION controlling this noise is difficult Recently, fuel economy has one of the main concerns for many auto makers An appropriate design of an intake or an exhaust system of an engine can lead to fuel savings Design efforts for such fuel efficient exhaust systems were made after the second oil shock in the late 1970s with low backpressure systems (Kleinhenz and Schmeichel, 1982) Moreover, in the early 21st century, an engine with a low idle speed has been attempted in addition to the low backpressure exhaust designs Reducing the idle noise is important because it results in a very low frequency tonal noise Then, the exhaust discharge noise will be severely affected by the acoustical resonance of various lengthy exhaust pipes rather than by the reactive actions of the silencers Accordingly, the optimal determination of exhaust pipe lengths related to the position of silencers is important in developing a low exhaust noise during idle conditions The length of pipe composing the total exhaust system includes the lengths of the extended inlet and outlet pipes, which are for multipurpose use, into the connected silencers Automotive intake and exhaust system engineers are familiar with the concept of the ‘tuned’ pipe system for Most of the engine exhaust noise in a car is due to the discharge noise from the tail pipe opening and the shell noise Discharge noise mainly consists of harmonics of the engine firing frequency and tonal components due to resonance from internal connecting pipes and silencers Therefore, the magnitude of the main spectral components of the discharge noise is greatly affected by the total or segmental lengths of the pipe elements of an exhaust system In this regard, the lengths of the exhaust system elements should be carefully considered in designing for low-discharge noise Particularly for the idle condition, the major cause of the vehicle noise is often ascribed to the exhaust discharge noise Idle noise is highest when the transmission gear is in the drive position or when the air conditioner is turned on In commercial use, it not always acceptable when this low frequency noise is audible from the vehicle interior, and thus noise control measures are required However, because of its low frequency characteristics, *Corresponding author e-mail: J.G.Ih@kaist.ac.kr 617 618 J.-G IH et al good air ventilation or for scavenging the emission gas (Smith, 1962) This concept expresses that the length of the total pipe system should be tuned to reinforce the negative pressure at the exhaust valve port to aid the combustion gas emission Along this tuned pipe, the rarefaction component of the reflected wave from the tailpipe opening travels in a backward direction to meet the exhaust valve port Whereas, in the intake system, the total pipe length should be set to match the intake valve port with the antinode of the reflected wave velocity from the orifice opening, thus aiding the fresh air entering the engine cylinder Accordingly, the length of the total exhaust or intake system should be tuned to be a half wavelength or to be its integer multiple at the target firing frequency, e.g., at an engine speed having a maximum torque Further, the pipe lengths in the manifolds should be adjusted to prevent the mutual interaction among cylinders Although the principle is simple, as aforementioned, fine tuning the intake or exhaust piping systems is possible only by using the numerical techniques of a nonlinear acoustic theory such as the shock tube theory The method of characteristics (Benson et al., 1964) and the finite difference method (Ospring et al., 1976) have been used in such a scenario The important parameters are the magnitude and phase of the instantaneously varying pressures The mean pressures, such as backpressure, are not as significant These numerical techniques have many input parameters in the engine operation, and the modeling of the complicated silencer can be difficult However, for the minimum sound discharge from the exhaust system with two silencers, the length of the front pipe lF, upstream from the front silencer, should be given as an odd multiple of the quarter wavelength, i.e., lF = (2m+1)λ/4 Here, λ is the wavelength of the firing frequency, and m denotes the integer implying the harmonic order The lengths of center pipe and tail pipe are determined in a similar manner to the front pipe length One can find that the two principles for ‘tuned’ and ‘detuned’ exhaust or intake systems are contradictory, which should be accounted for in order to alleviate the negative effect from each different design principle (Eriksson, 1982) It is noted that the foregoing principles not have much meaning because the wavelength will be changed with the engine rotational speed In addition, the resonances of the exhaust piping system cannot be avoided within the engine operation speed range, so the silencers should be appropriately positioned to adjust the resonance frequencies Consequently, one needs a simple and meaningful performance index to evaluate the noise reduction effectiveness of the exhaust system layout with many possible silencer positions changes Figure shows a typical configuration of the exhaust system, which consists of pipes and silencers To determine the optimal positions of the exhaust silencers for reducing the low frequency noise, a new performance index called the virtual attenuation coefficient was defined (Suyama and Hirata, 1979) The attenuation constant was adopted because one cannot neglect its effect Figure Typical exhaust system configuration (courtesy of Faurecia Exhaust Systems Korea) on the acoustic characteristics of resonant frequency ranges in a tube system The resonance is the major factor in the low frequencies for a lengthy pipe system such as the exhaust system However, Suyama and Hirata neglected the influence of source and radiation To overcome this limitation, a method using the simplified insertion loss, which was mentioned by Suyama and Hirata (Suyama and Hirata, 1979), was suggested in previous work (Ih et al., 2000) The latter also employed the virtual attenuation coefficient considering the ideal source impedance, radiation impedance, and gas temperature distribution The position of a silencer was obtained by fixing the position of the other silencer and not changing the positions of two silencers simultaneously This processes involves testing one factor at a time, which is not acceptable in the viewpoint of the design of experiment In this study, to find an optimal exhaust system layout, optimization techniques, known as robust methods in detecting the global optimal value, were employed for calculating the optimal geometric parameters in a robust fashion As a test example, an exhaust system with two simple expansion chambers was chosen In this example, the positions of the silencers were determined in an optimal manner for a given total length, and the computational performances of optimization methods were compared Three design layouts including the optimal design sample were experimentally tested to validate the method and the prediction result After confirming the applicability and precision of the present optimization technique, a practical exhaust system with two expansion chambers including the extended inlet and outlet pipes (and thus with six design parameters) was also used It was observed that the optimally designed layout was superior in reducing the low frequency noise during an idle condition compared with the non-optimal designs BACKGROUND THEORY 2.1 Transfer Matrix of a Pipe It is assumed that the plane wave only propagates in the pipe because very low frequencies, i.e., those lower than 100 Hz, are considered for the engine speed of less than 1000 RPM of a 4-cylinder engine A uniform flow with a mean flow velocity profile over the cross section is assumed It is also assumed that the walls are non-yielding and that the gas medium is the homogeneous air, which follows the adiabatic condition Idealized sources are OPTIMAL DESIGN OF THE EXHAUST SYSTEM LAYOUT TO SUPPRESS THE DISCHARGE NOISE considered, and the sound propagation is linear The transfer matrix of a straight pipe with a linear temperature gradient and flow rate is given by the relationship between the upstream and downstream pressure P and the volume velocity U as (Peat, 1988): P1 = AB P2 , U1 CD U2 T 2jM A = e–jMΓl ⎛⎝ + r⎞⎠ cos Γl – jTr ⎛⎝ ⎞⎠ sin ( Γl ) , 2kml (1) 619 of the total transfer matrix without silencing elements Here, Zr denotes the radiation impedance and Zs the source impedance When the parametric data during the optimization process are changed several times, the calculation of IL is not efficient because a repeated calculation of the same denominator is required To avoid such an unnecessary repetitive calculation, the following “system insertion loss (ILs)” can be defined: (2a) ILs = 20log 10 AZr + B + CZs Zr + DZs (4) ρ0C-0⎞ –jMΓl e B = ⎛⎝ -E, S ⎠ (2b) It is noted that the discharge sound level from the tail pipe is given by (Prasad and Crocker, 1981): S C = ⎛⎝ -⎞⎠ e–jMΓlE , ρ0 C0 (2c) Lp = 201og10Q – 201og10 AZr + B + CZr Zs + DZs , 2jM 3T D = e–jMΓl ⎛⎝ + -r⎞⎠ cos Γl – jTr⎛⎝ ⎞⎠ sin ( Γl ) , 2km l (2d) in which the ILs is used Here, R is the reflection coefficient from the tail pipe opening, r is the distance from tail pipe E = –2Tr M cos Γl + j [ + Tr ( + 2jM ⁄ kml ) ] sin ( Γl) , (2e) αcl T1 – T-2 , Tr = -Γ = km – j T1 + T2 – M2 (2f) 2.2 Insertion Loss of the System Insertion loss (IL or LIL), which is the difference in sound levels before and after incorporating a silencer in the duct system, is prevalently used in the design of silencing systems because the characteristics of source, silencing system, and radiation can be taken into account Sometimes, transmission loss, TL, is used for describing the acoustic performance of an acoustic element or system, but it is used for describing the sound power reduction capacity of an element, rather than for describing the actual interaction effect between pipes, source and radiation Therefore, TL is not an adequate performance index for this study, which deals with the pipe resonance and antiresonance due to coupling IL can be calculated using the total transfer matrix of the silencing system as (Munjal, 1987): LIL = 20log 10 AZr + B + CZs Zr + DZs , A'Zr + B' + C'Zs Zr + D'Zs (3) where A, B, C, and D are four-pole parameters of the total transfer matrix with silencing elements, A’, B’, C’, and D’ 1⁄2 + M ) – ( – M ) R S-0⎞ (usu 0.5 m), Q = ⎛⎝ ( ⎠ × Ps Zr , and Ps is + R2 4πr2 Here, T1 and T2 are the inlet and outlet temperature, respectively, of the straight pipe, km is the wave number, S is the cross sectional area, ρ0 is the density, C0 is the sound speed, M is the Mach number, l is the length of the pipe, and αcl, Γ denote the visco-thermal attenuation coefficient and the propagation constant, respectively (Pierce, 1981) It is well known that the total transfer matrix of the exhaust system can be obtained by multiplying the transfer matrices of all serially connected exhaust system components in a successive manner (5) 2 the source strength Eq (5) can be written as ILs = α-Lp, in which α( = 20log ( Q ⁄ Ps ) ) is a constant provided that the difference in mean flow velocity before and after the insertion of a silencing element is not meaningfully large and the source impedance does not change with the load change Source impedance, Zs, is required in Equation (4), which should be determined in the actual exhaust system from operating the engine This means that Zs has different characteristics for different engines Because the purpose of this study is to find an optimal exhaust layout in the early design stage, the constant volume velocity source (Zs = ∞) is used, although the other idealized sources may be adopted Then, ILs is given by: ILs = 20log 10 CZr + D (6) 2.3 Desired Acoustic Performance When a silencer is placed in a position other than the initial position, ILs will have a different value This value is a function of the frequency ILs has a different value because the resonance condition changes with the change in pipe lengths connecting the silencer element A new acoustic performance index is needed to easily estimate the efficiency by changing the position of silencers for a given total system length The virtual attenuation coefficient, δ, suggested by Suyama and Hirata (Suyama and Hirata, 1979), is defined as the amount of attenuation for a silencer required to reduce the radiated noise to less than the target noise level ILs will have a negative value in the case of the acoustical resonance in the whole system The application of a silencer at a position in the exhaust system allows one to supplement the negative ILs value, which corresponds to the required amount of δ for a silencer at this position, to 620 J.-G IH et al escape from the negative ILs This means that the contribution of a silencer in supplementing the negative ILs value can be made small if the effect of the acoustical resonance is small For the sound reduction efficiency of a silencer, a small δ value of a silencer at a certain position means that only a very simple and economical silencer can be used to satisfy the required amount of sound reduction at low frequencies The required amount of δ to obtain the lownoise level at a predetermined range of low frequencies can be obtained from the following necessary condition as: all[ ILs ( f ) ] ≥ T* , (7) where T* denotes the target ILs Because the difference between T* and ILs at the resonance frequency is largest out of all frequencies in the range of interest, the required attenuation of silencer, i.e., δ value, will be mostly be determined by the ILs value at resonance frequency If T* is too small or too large compared with the ILs value that can be calculated for all possible positions of the silencer, the calculation of δ requires a significant amount of time To set T* for an exhaust system composed of two silencers, one silencer position is varied to obtain the ILsmin value, which is the minimum ILs at each position, while the other silencer is fixed at a position Among all of the ILsmin values obtained in such an iterative manner, the maximum value is set as T* 2.4 Search Method Because the problem involves several of the lowest order resonances of the total pipe or partial pipe elements, there would be several very sharp peaks and troughs in the object function within the frequency range of interest Furthermore, a multivariable system will be the general situation in the optimal design of the positions and lengths in an exhaust system Therefore, it is expected that searching for the global optimal parametric values will be problematic because of the local optimal values Thus, the searching technique should be carefully chosen to avoid pitfalls of local minima in the virtual attenuation coefficient There are many search techniques for the optimal values including steepest descent, conjugate gradient, golden section search, stochastic search, and so forth Although the selection of a search method for the global optimum value was not the main topic of this study, it is important for the result The shape and nature of the objective function within the constraints are meaningful pieces of information In this study, the objective function would have several deep valley minima due to the system resonances, and these will be the obstacle in finding the minimum as mentioned above The basic character of the problem associated with the objective function is identical for two-variable problems and other multi-variable problems provided that the valleys, minima of virtual attenuation coefficient, are formed by the resonances Stochastic search methods are relatively simple in concept and have superb capability in numerical searching for the optimum value Among them, in particular, the simulated annealing algorithm (SA) and the genetic algorithm (GA) are known as the combinatorial search technique that does not require the continuity or the differentiability of associated cost or constraint function, which are beneficial in finding the optimum solution Simulated annealing (SA) is an iterative stochastic search technique that simulates the thermodynamic annealing process for a metal to obtain the lowest energy level (Laarhoven and Aarts, 1987; Metropolis et al., 1987) In SA, there are usually two basic iterative loops, an inner loop of Metropolis criterion and an outer loop of temperature reduction The genetic algorithm is a searchstrategy process that uses natural selection and evolution (Belegundu and Chandrupatla, 1999; Yeh et al., 2004) During the GA optimization process, trial solution set is chosen and “evolves” toward an optimal solution for which the initial population is built up by randomization The detailed discussion can be found in various references In this paper, two search techniques were employed initially, but only the SA technique was used in the further study after comparing their performances The test result was given in Sec 3.3.2 An investigation of the efficiency and applicability of the two search algorithms was performed, testing for the optimization of an exhaust system with two silencers under the given total length An exhaustive search result was also compared check the optimal solution As a result, two search methods achieved the same optimal solution as indicated by the exhaustive (or brutal) search method, but the SA algorithm result revealed that it is advantageous in calculation time by approximately 40% compared with the GA method In this work, the SA search method was adopted for all simulations OPTIMIZED LAYOUT FOR A SIMPLE TEST EXAMPLE: TWO VARIABLES As the resulting SPL spectra indicate, the objective function would have deep valley minima due to system resonances, and these will be the obstacles in finding the true minimum Although the practical target is the optimal layout for a multi-variable exhaust system, the basic character of the objective function is identical to the two-variable problem, provided that the valleys, minima of virtual attenuation coefficient, are formed by the resonances To this end, the performance of the two statistical optimization methods was compared with that of the exhaustive search calculation 3.1 Input Data Condition On the basis of the foregoing theoretical strategy, we tried to optimize an exhaust system consisting of two silencers to minimize the discharge noise at low frequencies in the engine idle condition Figure shows the schematic of the test system, in which the total length of the exhaust piping OPTIMAL DESIGN OF THE EXHAUST SYSTEM LAYOUT TO SUPPRESS THE DISCHARGE NOISE 621 Table Dimensional data of the initial exhaust system considered in the test calculations Part name Figure Schematic drawing of the exhaust layout and the design variables Li indicates the length of each ith pipe In the optimization, two design variables (XC, XR) were the positions of silencers, in which the lengths of silencers and the total length, Lt, were fixed The numbers on the pipe indicate the positions of four sensors for the gas temperature measurement All length dimensions are in m system, as well as the lengths of the silencers, is fixed The lengths of the front, the intermediate (or sometimes called the combination of center and kick-up pipes), and the tail pipe are denoted as L1, L2, and L3, respectively The position of the center and the rear silencer is denoted as XC and XR, respectively The front pipe length does not include the lengths of the manifold, the small front resonator, and the catalytic converter, although they were included in the calculation as constant lengths The dimensions of the exhaust system elements are as given in Table 1, and the main pipe diameter was 0.05 m The two silencers were simple expansion chambers without any internal extended pipes, and the secondary sound radiation due to flow generated noise and shell vibration was neglected A 4-cylinder, 2-liter, gasoline engine was chosen as the test engine operating at 660 RPM in the idling condition Sound levels at harmonics of engine firing frequency (designated as E2) were of concern, in particular for E2-E6 components or at frequencies lower than 66 Hz Here, E(2n) signifies the 2n-th order harmonic of the fundamental frequency due to the crankshaft rotation The average flow velocity and the temperature of the air medium, which were measured at typical positions along the pipe system as indicated in Fig 2, were also considered The measurement was conducted with a given layout of the exhaust system with a standard arrangement of silencers in which L1=0.1 m and L2=1.36 m Although the gas temperature and the flow velocity would be changed by the variation of the silencer positions and/or pipe lengths, it was assumed that the change amount and the effect on the acoustic performance would be small for such a simple piping system Thus, without this assumption, which would be useful in the early stage design of exhaust systems, it is not possible to calculate the virtual attenuation coefficient for each set of silencer settings Gas temperatures measured at four tap positions were 214, 172, 110, and 61oC, respectively, in the downstream direction Gas temperatures at other positions between positions #1 and #4 were estimated by the linear interpolation The flow Dimension Length (m) Diameter (m) Front pipe 0.10 0.050 Centre silencer Intermediate pipe 0.375 0.140 1.36 0.050 Rear silencer 0.580 0.178 Tail pipe 0.10 0.050 velocity was calculated from the measured mass flow rate of 0.0269 kg/s Then, for the aforementioned standard layout, the flow Mach numbers were calculated as 0.04, 0.005, and 0.003 for the main pipes, the center silencer, and the rear silencer, respectively The positions of the silencers were restrictively given as 0.395m ≤ XR ≤ 1.877m and 0.1m ≤ XC ≤ 1.511m Moreover, considering the length of center silencer, the rear silencer position should be limited as XR ≥ (XC+0.385) in m These three inequalities were used as the constraints during the optimization This study on the optimal layout for the exhaust system was suggested by an exhaust system maker, which was initially requested from a passenger car manufacturer The initial intention was to find a global optimal set of silencer positions regardless of the underbody shape design, which is usually, in the current practice of body design, carried out before the silencer positioning Thus, the purpose was to obtain the maximum silencing of low frequency noise with a maximum degree of freedom in the silencer setting while sacrificing the practicality This is the reason why the constraints in this study look somewhat impractical The center muffler can reach to the exhaust port without considering the manifold, and the rear silencer can be positioned next to the center silencer that is attached to the exhaust port For the system insertion loss calculation, the information on the source impedance and the radiation impedance at the tailpipe opening is required The radiation impedance was calculated using an empirical formula (Panicker and Munjal, 1982) that is a function of frequency, pipe radius, gas temperature, and Mach number of mean flow The source impedance of an engine exhaust or intake system can be measured using the indirect or direct method (Jang and Ih, 2000; Ih et al., 2009) It is usually difficult to obtain the source impedance spectrum in the early design stage of a vehicle because the engine is sometimes not yet available In such circumstances, ideal source models can be used for the rough computation, although the optimized result would be somewhat changed if the actual measured source impedance is adopted in the calculation Three ideal sources can be used in the acoustic modeling of the linear source in the intake or exhaust system: constant volume velocity source, constant pressure source, and anechoic 622 J.-G IH et al source (Munjal, 1987; Beranek, 1954) As discussed in the previous works (Fukuda, 1963; Callow and Peat, 1988), any of these three ideal source models not fit to the actual source characteristics in general, but one of them can be regarded as being similar to the actual source for a particular fluid machine and operating condition (Callow and Peat, 1988; Prasad and Crocker, 1983) Sometimes, the nonlinear and time-varying nature of the actual source are important (Ih and Peat, 2002; Albertson and Boden, 2006), which adds complexity to the problem In the early design stage of a vehicle, it is unlikely that any complicated information on the source would be beneficial to the layout design that involves the simple pipes and chambers and approximate gas conditions Therefore, idealized source models were only employed in this study 3.2 Mathematical Formulation for Optimization Mathematical formulation of objective functions and constraints are needed for optimizing the two variables of XR and XC The objective function was the virtual attenuation coefficient δ as a function of the two design variables, influenced by the frequency range of interest, flow velocity and temperature of the gas medium Design constraints were given, such that the length of each pipe is larger than 0.01 m, the position of center silencer should be ahead of the position of rear silencer, and the design tolerance as mentioned in Sec 3.1 is applicable Mathematical formulation of this optimization problem is as follows: minmize δ = F( XR, XC, f, M, T) , XC, XR change 3.3 Predicted Optimal Layout and Comparison of Search Methods 3.3.1 Comparison of ideal source models As discussed in Sec 3.1, because the measured source impedance was not available, three idealized models were employed for describing the in-duct source: constant velocity, constant pressure, and anechoic source The insertion loss, the system insertion loss or the virtual attenuation coefficient for a layout of the exhaust system will be calculated differently for each source model Figure is the result of a calculated virtual attenuation coefficient changing the source impedance models for two simulation conditions: Fixed XC at 0.02 m and varying XR and fixed XR at 1.8 m and varying XC Note that the fixed position of each silencer corresponds to the position of each silencer at the initially given layout Although the overall trend in two cases is different, it is clear that the constant pressure source exhibits the worst results, from which one cannot differentiate the superiority or inferiority of a set of silencer positions from the other set In this study, we adopted the constant volume velocity source in the necessary calculations because of the large variation in the δ value with the change of silencer positions It is interesting to find a monotonically increasing trend of δ value by (8) subject to 0.01≤ XC ≤1.511;0.395 ≤ XRm ≤ 1.877;XR ≥ (XC +0.385) (9) Here, f denotes the interested frequency (Hz), M is the average flow Mach number at each part, and T is the gas temperature (K) The search was performed with a spatial resolution of 0.01 m in length This search spatial resolution was related to the frequency resolution ∆f for investigating the change of pipe resonance due to the change in the length lp of the pipe by δlp as follows (Davies, 1996): nC 1 ∆f = ⎛⎝ - – ⎞⎠ lp lp + δlp (10) In this study, a unit frequency change of ∆f =1 Hz was employed At the idle engine speed of 660 RPM, the average speed of sound was about 400 m/s considering the average gas temperature The lowest resonance was taken, i.e., n=1, along with the engine frequencies of interest until the third harmonic of the firing frequency A lower the resonance frequency as the longer the pipe length, lp was taken as the longest possible length of the main pipe except that the pipe length was occupied by silencers, that is lp =1.4 m Then, one can calculate δlp = 0.0098 m, which is approximately equal to 0.01 m and is not a very significant Figure Calculated δ value at 660 RPM for three ideal source models; , constant pressure source; , constant volume velocity source; , anechoic source (a) Fixed XC at 0.02 m, varying XR; (b) fixed XR at 1.8 m, varying XC XR, XC are in m OPTIMAL DESIGN OF THE EXHAUST SYSTEM LAYOUT TO SUPPRESS THE DISCHARGE NOISE positioning the rear silencer to the tail pipe side, regardless of the adopted source model as can be seen in Figure 3(a) 3.3.2 Comparison of optimization methods As explained in Sec 2.4, two combinatorial search techniques, SA and GA, which are known to be effective in finding the optimum value, were employed in testing the ability to find a solution and the efficiency in calculation time For the purpose of comparison, an exhaustive search, also known as the brutal force search, was also conducted because it can be easily performed for a relatively simple problem with two design variables In this exhaustive search, every possible set of positions of center and rear silencers was tested with a spatial resolution of 0.01 m Table presents a comparison of simulation results using the simulated annealing (SA), the genetic algorithm (GA), and the exhaustive search One can see that the simulations were converged into the same optimal result in all three methods The exhaustive search was the slowest of all of the methods in finding the solution, but SA seems to be more efficient in the view point of calculation time than GA 3.3.3 Comparison of predicted acoustical performances for three typical layouts The search results summarized in Table present the optimal layout of the exhaust system with given lengths and diameters of total pipe and silencers In Table 3, three layouts obtained from the two-parameter design attempts are shown with rough sketches for demonstrating the validity of the present optimal design method Each of the layouts has a different δ value, and they each represent three representative design cases: ‘G1’ denotes the optimized layout as shown in Table 2, which is expected to have the best acoustical performance at low frequencies of interest, and ‘C1’ is the initially given layout from the silencer manufacturer It was noticed that the current layout for the silencer setting was expected to have the largest δ value of all possible positions Thus, the layout C1 can be Table Comparison of three search methods for finding the optimal silencer setting positions having the minimum δ value Optimization methods Parameters SA GA Number of function calls 2600 2900 Total computing time (min) 13 Minimum 0.11 Length of front pipe, L1 0.05 (m) Exhaustive search - 21 30 0.11 0.11 considered as one of the worst design layouts, which is expected to have a poor reduction of the low frequency discharge noise For this reason, one of the layouts was selected, which is expected to discharge a mediocre noise level among all layouts, and was designated as ‘M1’ As mentioned previously, the layout C1 is a standard setting of silencers, which was somehow used for an actual system in a car manufacturer after their own tuning by an empirical way or by running a nonlinear commercial design code The whole exhaust system is composed of three partial pipes and two cavities: a front pipe, an intermediate pipe, a tail pipe, a center silencer, and a rear silencer In the lumped parameter modeling, a tube with two open ends can be modeled as an inertia element with a mass of M = ρ0le/πa2, and a cavity can be modeled as a compliance element with a stiffness of s =ρ0C02/V, where le is the equivalent length of a pipe, a is the radius of a pipe, and V is the volume of a cavity If the pipe with open ends is concerned as this exhaust system pipes connected to the expansion chambers, the equivalent length of a pipe having a physical length l is given by using the end correction value, ∆l, as le = l + ∆l1 + ∆l2, where ∆l1 and ∆l2 are end correction values at two ends of a pipe The end correction ∆l is 0.85a for the flanged end, 0.61a for the unflanged end, and for the closed end Because the front pipe can be modeled as a pipe with one end closed and the other open, it can be regarded as a spring in the lumped parameter model Consequently, one can model a silencing system composed of three-pipe and two-cavity systems in tandem as follows (Beranek, 1954): Mint Mtailω4-(Mtail sfc + (Mint + Mtail)srr)ω2 + sfc srr = (11) Here, a parameter with a subscript ‘int’ means the property of the intermediate pipe, ‘tail’ the property of the tail pipe, ‘fc’ the combined property of the front pipe and the center silencer, and ‘rr’ the property of the rear silencer If Equation (11) is solved, two natural frequencies are obtained Table lists the lowest two natural frequencies calculated from Equation (11) for the three layouts in Table The lumped parameter model is valid when the involved Table Three design layouts and d values after the twoparameter optimization: ‘G1’ denotes the optimized layout, ‘C1’ the initially given layout, which is incidentally expected to have a poor noise reduction, ‘M1’ is the layout which is expected to discharge a mediocre noise level between G1 and C1 layouts Case δ Length of eaceh pipe L1 (m) L2 (m) L3 (m) 0.05 0.05 0.05 0.07 1.34 0.174 G1 M1 0.110 0.174 0.174 0.674 0.10 1.10 0.36 Length of tail pipe, L3 (m) 1.336 1.336 1.336 C1 1.380 0.10 1.36 0.10 Length of intermediate pipe, L2 (m) 623 Scheme of layout 624 J.-G IH et al Table Lowest two resonance frequencies calculated from the lumped parameter model and the transfer matrix method a continuous system model The limit frequency for a 5% error in the lumped parameter model was based on the average gas temperature of the corresponding pipe Calculated resonance frequencies Length Limit of 2nd, fr2 (Hz) Cases longest frEquation 1st, fr1 (Hz) for 5% element error (Hz) ContinuLumped Continu(m) ous Lumped ous G1 1.34 (L3) 36 17 17 90 117 M1 1.10 (L2) 42 26 26 48 49 C1 1.36 (L2) 35 29 29 66 68 Table Comparison of predicted discharge noise levels of three lowest firing harmonics of E2, E4, E6 components radiated from three layouts in Table Sound level (dB) Layout Order (frEquation in Hz) G1 M1 C1 E2 (22) 123 132 127 E4 (44) 113 134 129 E6 (66) 114 117 136 Overall, E2~E6 123.9 136.2 137.2 Figure Predicted sound level spectra for three layouts in Table 3: , G1; , M1; , C1 G1 is lower than 20 Hz, thus inaudible, and its level is the smallest of all of the peaks As previously mentioned, if any of the system resonances coincide with the engine firing frequency or one of its harmonics, a large response is expected In Fig 4, engine firing orders are also indicated to compare with the frequency The layouts C1 and M1 have resonances close to the major firing harmonics Table compares the predicted sound level discharge noise for the three lowest firing harmonics of E2, E4, E6 components radiated from three layouts A large difference in sound level is observed between optimally designed and nonoptimally designed layouts The acoustical performance predicted for C1 and M1 layouts are approximately the same in Table 5, although the calculated δ value has some notable differences as shown in Table Here, the comparison of backpressure data is not of interest because the backpressures would be approximately the same because of the straight-through line-up of pipes and silencers for the same total length without changing the internal structure of the silencers duct length is far smaller than a wavelength It is known that conditions of le < λ/8, for a tube, and le < λ/7, for a volume, should be met for a valid application, for less than a 5% error, of the lumped parameter model (Beranek, 1954) The first resonance frequencies in Table satisfy this condition, that is 36, 42, 35 Hz for G1, M1, and C1 layouts, respectively Figure shows the predicted sound level spectra and backpressure for the three layouts specified in Table Below 130 Hz, there are two peaks for each layout, which correspond to the lowest two resonances of the system composed of three partial pipes and two cavities It should be noted that the primary peak frequency of each layout is very similar to the first resonance frequency in Table 4, which reveals that the two peaks for each layout are actually the resonant peaks The difference in frequencies is due to the difference in the modeling method, i.e., the lumped parameter model vs the continuous system model from using the transfer matrix The primary peak of the discharge noise from the layout 3.3.4 Effect of pipe length on resonance frequencies Acoustic characteristics of an automotive silencing system at very low frequencies are affected greatly from the proximity of low order firing frequencies and lowest resonances of the system In particular, the first and the second resonance frequencies are important, which are affected from the length of pipes in the system The effect of the length of each elemental pipe upon the change of acoustical resonances was studied with fixed lengths of silencers as a preliminary study for the optimization Each pipe was changed to four different lengths while fixing the other pipe and silencer lengths: 0.1, 0.5, 0.9, and 1.3 m Diameters of all components and lengths of the silencers are the same as in Table 1, but the lengths of the pipes were initially set as L1 = 0.076 m (front pipe), L2 = 1.36 m (intermediate pipe), and L3 = 0.5 m (tail pipe), in which only two pipe lengths were fixed when the third pipe length was changed Considering Table 1, the simulations varying of the pipe lengths resulted in the change of the total pipe lengths, but the changing range for each pipe was the same Figure shows the change of resonance frequencies OPTIMAL DESIGN OF THE EXHAUST SYSTEM LAYOUT TO SUPPRESS THE DISCHARGE NOISE 625 the first resonance frequency far smaller than the E2 component, viz., the lowest engine firing order, and a short intermediate pipe length to make the second resonance frequency higher than the E6 component, viz., the highest engine firing order of concern in this study The tailpipe contribution to the overall discharge level was discussed by Fukuda (Fukuda, 1963), and it was observed in the design of a S-shape tailpipe in many cars although the sensitivity of the first pipe resonance to the change of tailpipe length was not explicitly mentioned OPTIMIZATION FOR A PRACTICAL EXAMPLE WITH SIX VARIABLES Figure Effect of pipe length on the resonance frequencies of the exhaust system below 90 Hz: (a) change of front pipe length, L1, (b) change of intermediate pipe length, L4, and (c) change of tailpipe length, L7 Each pipe was changed in four different lengths while fixing the lengths and diameters of other pipes and silencers: , Li=0.1 m; , Li=0.5 m; , Li=0.9 m; , Li=1.3 m (i=1, 4, 7) when the pipe lengths were varied in four steps as mentioned above By increasing the front pipe length, the first resonance frequency decreases by 0.25 Hz for a 0.1 m increase in length, and the second resonance frequency decreases by Hz for a 0.1 m length increase By lengthening the intermediate pipe, the first resonance frequency decreases by 0.5 Hz for a 0.1 m increase in length, while the second resonance frequency decreases in a significant amount The first resonance frequency decreases significantly as the length of the tailpipe increases In summary, the first resonance frequency is most sensitive to the change of the tailpipe length, and the second resonance frequency is affected greatly from the intermediate pipe length This behavior can be explained by solving the lumped parameter frequency equation, i.e., Equation (11) From these simple simulations, the general direction in the design of the optimal system layout can be determined The optimal layout has a long tailpipe to make In Sec 3, a very simple design condition in terms of the number of optimization variables was tested The purpose of the previous test example was to compare geometric variables and the performance of the optimized layout with those determined from the exhaustive search and the non-optimal worst case selection in an empirical manner It was discovered that both searching algorithms yield the identical converged search result, which is exactly the same as the exhaustive search result or the true global minimum This finding reveals that the search techniques are adequate for this kind of problem, because the basic nature of the complexity of the objective function is actually the same for the six-variable case In this section, we deal with a more complicated example for checking the practical applicability of the proposed optimization technique The SA technique was adopted as the main search algorithm considering its search speed 4.1 Input Data Condition Figure shows the schematic drawing of the test exhaust system, at which the total length of the exhaust piping system is fixed (Lt=2.515 m), and the lengths of the silencers (LFRT=0.375 m, LRR=0.580 m), which are basically the same as the total and silencer lengths in Fig and Table The length of front, intermediate, and tail pipe is denoted as L1, L4, and L7, respectively The position of the center and the rear silencer is denoted as XC and XR, respectively The length of extended inlet and outlet within the center silencer is denoted as L2 and L3, respectively Figure Schematic of the exhaust layout and the design variables Li indicates the length of each ith pipe and XC and XR are positions of center and rear silencers, respectively Six design variables (XC, XR, L2, L3, L5, and L6) were the target for optimization In the optimization, the lengths of silencers, LCM and LRM and the total length, Lt, were fixed 626 J.-G IH et al Moreover, the length of the extended inlet and outlet within the rear silencer is denoted as L5 and L6, respectively These results are indicated in Figure Again, the idle operating condition at 660 RPM for a 4cylinder test engine was of concern and discharge sound levels at three harmonics of engine firing frequency were of concern, i.e., E2, E4, E6 components The average flow velocity and the temperature of the air medium were assumed to be similar in the former two-parameter case Possible positions of silencers were restrictively given by an exhaust system maker as 0.01m ≤ XC ≤ 1.51m, 0.395m ≤ XR ≤ 1.877m, and XR ≥ (XC+0.385) in m Other constraining conditions imposed on the design were the lengths of the extended pipes within the silencers L2 and L3 should be less than the length of the center silencer, which was designed as a fully perforated resonator having a concentric or staggered inlet/outlet Each of L5 and L6 should be less than the twofold length of the rear silencer, which was designed as an expansion chamber allowing flow-reversal extended pipes This is the standard configuration of the exhaust system The design constraints, which look impractical for the available space in the underbody of a car, were suggested by an exhaust system maker to see what the maximum attainable noise reduction in the low frequency range was without considering the car body layout 4.2 Formulation for the Optimization Mathematical formulation of the objective function and constraints are needed to optimize the following six variables: XR, XC, L2, L3, L5, and L6 The objective function was the virtual attenuation coefficient δ as a function of the two design variables, influenced by the frequency range of interest, flow velocity and temperature of the gas medium Design constraints were given, such that the length of each pipe is larger than 0.01 m, the position of center silencer should be ahead of the position of rear silencer, and the design tolerance as mentioned in Sec 3.1 is applicable Mathematical formulation of this optimization problem was set as follows: minmize δ = F( XR, XC, L2, L3, L5, L6, f, M, T ) , (12) limited to occurring only once Therefore, the diameter or major axis of the cross section of the rear silencer should be larger than four times the diameter of internal pipe 4.3 Predicted Optimal Layout As suggested in Sec 3.3.1, a constant volume velocity source was assumed as the source model in the calculation The spatial resolution of searching for the optimal layout was 0.01 m The dimensional data of the initial exhaust system adopted as the starting values in the calculations were as listed in Table Table presents a list of computational and geometric data after finishing the SA search for an optimal exhaust system layout Similar to the previous test case with two design variables, the system settings of the other two layouts, one was the current or initial layout and the other the layout with a large δ value, were selected for comparison Table shows the three layouts representing the best (G2), mediocre (C2), and worst (P2) design for reducing the low frequency discharge noise, as determined from the calculated δ values Moreover, the lengths of the front pipe, the pipe, and the tail pipe for three layouts are given with rough sketches of the silencer setting viewed from the outside Figure depicts the drawings of internal structures and their dimensions of center and rear silencers for three layouts As briefly mentioned above, ‘G2’ denotes the optimized layout according to the smallest δ value, which is expected to have the best acoustical performance at the low frequencies of interest Layout ‘C2’ is the initial given layout from the silencer manufacturer Different from the preceding two-variable case, C2 was expected to have a mediocre level in low frequency noise reduction We selected one more layout for the comparison purpose: ‘P2’ Table Computational and dimensional data of the optimized layout of the exhaust system as shown in Fig An SA search algorithm was employed in the optimization Parameters in the optimization Minimum virtual attenuation coefficient, δ Optimized value 0.102 FR, XC, L2,L3,L5,L6 Elapsed time 30 subject to Total number of function calls 21075 Length of front pipe, L1 (m) 0.10 Length of intermediate pipe, L4 (m) 1.360 (13b) Length of tail pipe, L7 (m) 0.10 (13c) Length of extended inlet pipe in center silencer, L2 (m) 0.26 Length of extended outlet pipe in center silencer, L3 (m) 0.036 Length of extended inlet pipe in rear silencer, L5 (m) 0.495 Length of extended outlet pipe in rear silencer, L6 (m) 0.506 0.01≤ XC ≤1.511;0.39 ≤ XR ≤1.877; XR ≥ (XC+0.385); (13a) ≤ L2