Topology optimization of internal partitions in a

Authors: GangWon Jang Jin Woo Lee

Publish Date: 2016/12/16

Volume: 55, Issue: 6, Pages: 2181-2196

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Abstract

A topologyoptimizationbased design method for a flowreversing chamber muffler is suggested to maximize the transmission loss value at a target frequency considering flow power dissipation Rigid partitions for high noise reduction should be carefully placed inside the muffler to avoid extreme flow power dissipation due to a 180° change in flow direction from an inlet to an outlet The optimal flow path for minimum flow power dissipation is well known to change depending on the Reynolds number which is a function of the inlet flow velocity To optimize the partition layout with an optimal flow path in an expansion chamber at a given Reynolds number a flowreversing chamber muffler design problem is formulated by topology optimization The formulated topology optimization problem is implemented using the finite element method with a gradientbased optimization algorithm and is solved for various design conditions such as the target frequencies rigid partition volumes Reynolds numbers nondesign domain settings and allowed amounts of flow power dissipation The effectiveness of our suggested approach is verified by comparing the optimized partition layouts obtained by the suggested method and previous methodsThis research was supported by the Basic Science Research Program through the National Research Foundation of Korea NRF funded by the Ministry of Education No 2013R1A1A2010158 and funded by the Ministry of Science ICT and Future Planning NRF2014R1A2A1A10051263 This work also was supported by the National Research Foundation of Korea NRF Grant No 2014M3A6B3063711 Global Frontier RD Program on Center for Wave Energy Control based on Metamaterials funded by the Korean Ministry of Science ICT and Future Planning MSIP contracted through IAMD at Seoul National UniversityTo maximize the transmission loss value at a target frequency equations in 1 2 and 5 were solved for Model A in Fig 1a where the nondesign domain for fluid passage should be defined because the flow power dissipation was not considered Optimal topologies depending on the partition volume ratio β target frequency f t and width of the nondesign domain l 3 were examined The acoustic attenuation performance of the optimization results was compared with that of the nominal muffler which does not have any partition insideFigure 12 illustrates four optimal topologies obtained for different partition volume ratios a β = 002 b β = 006 c β = 010 and d β = 014 Since the acoustic space where the acoustic wave does not transmit but stays was decreased relatively if extremely large amount of partitions was used the formulated problem was solved for small values of β The target frequency of f t  = 1000 Hz and the nondesign domain width of l 3 = d 1 were used to obtain the results In the optimal topologies the black area refers to rigid partitions and the white area denotes the air fluid region To increase the transmission loss value at the target frequency the rigid partition was built up around the middle of the right end and the length of the partition increased as more volume was allowed for the rigid partition When the partition volume ratio increased above a certain value the left end of the partition was divided into two branches Figure 13 shows that the transmission loss values of the optimized mufflers at the target frequency were much larger than that of the nominal muffler 168 dB for β = 002 1330 dB for β = 006 5883 dB for β = 010 and 6375 dB for β = 014 compared with 001 dB for the nominal muffler β = 0Figure 14 compares the optimal topologies obtained at four different target frequencies for the same partition volume ratio β = 007 and nondesign domain width l 3 = d 1 a f t  = 800 Hz b f t  = 1000 Hz c f t  = 1200 Hz and d f t  = 1400 Hz The figures show that the optimal topologies were strongly affected by the target frequency The partitions in Fig 14a were vertically built up from the top and the bottom whereas those in the other topologies grew horizontally around the middle of the right wall In the results of Fig 14b ~ d the left ends of the horizontal partitions were stretched straight or divided into two branches depending on the target frequency The transmission loss value at the target frequencies increased dramatically in the optimal topologies a 299 dB from 320 dB nominal muffler at 800 Hz b 181 dB from 001 dB nominal muffler at 1000 Hz c 2954 dB from 005 dB nominal muffler at 1200 Hz and d 2265 dB from 914 dB nominal muffler at 1400 HzThe rigid partitions of the optimized topologies in Fig 14a were located on the left edge of the design domain Thus the location of the partitions might be affected by the width of the nondesign domain l 3 To investigate this effect the topology optimization problem was solved for four different values of l 3 at the same target frequency f t  = 800 Hz Fig 15 shows the optimized results a l 3 = d 1 b l 3 = 075d 1 c l 3 = 05d 1 and d l 3 = 025d 1 For a fair comparison the same volume of rigid partitions V o  ⋅ β in 2 was allowed in each optimization β was adjusted considering the volume V o of the design domain β = 004 for l 3 = d 1 β = 004 ⋅ 6/7 for l 3 = 075d 1 β = 004 ⋅ 6/8 for l 3 = 05d 1 and β = 004 ⋅ 6/9 for l 3 = 025d 1 Note that all partitions of the optimal topologies were located at the left edge of the design domain In Fig 15a ~ c the transmission loss value at the target frequency increased as the width of the nondesign domain decreased which was not the case in Fig 15d transmission loss values were a 901 dB b 1569 dB c 1590 dB and d 1269 dB This result indicates that the nondesign domain for fluid passage must be carefully selected before optimization in case that only the transmission loss is considered for optimization formulation and a gradientbased optimizer is used in solving the optimization problem In the gradientbased optimizations the optimum result is highly affected by design updates of early iterations so it is inferred that the sensitivities of design variables around the left end of the design domain are higher than those of other design variables during early iterations The nondesign domain in the expansion chamber is not required if the acoustical and fluidic performances of the muffler are simultaneously considered

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