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The Cremer Impedance: An Investigation of the Low Frequency Behavior
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Industrial Engineering and Management (ITM), Centres, Competence Center for Gas Exchange (CCGEx).ORCID iD: 0000-0002-8474-8563
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Industrial Engineering and Management (ITM), Centres, Competence Center for Gas Exchange (CCGEx).ORCID iD: 0000-0001-7898-8643
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The Cremer impedance, first proposed by Cremer (1953) and then extended by Tester (1973), is supposed to give the maximum propagation damping in an infinitely long waveguide. Previous works including a uniform grazing flow have shown negative resistance in the low frequency range for both circular and 2-D rectangular waveguides, i.e., implying an active boundary. In order to further analyze the low frequency behaviour of the Cremer impedance, especially the negative resistance, two investigations are conducted in the current work. First, the previously used Ingard-Myers boundary condition is replaced by the Brambley boundary condition with the introduction of a thin inviscid boundary layer, and results obtained with the two boundary conditions are compared to see the effect of a sheared flow. The frequency range where the two boundary conditions can be applied is also analyzed. Second, discussions regarding the validity of the low frequency result in both the up- and downstream directions from the perspective of mode-merging are presented. This analysis is further extended from the fundamental mode to higher order modes in the frequency range where they are ‘just cut-on’.

Keywords [en]
the Cremer impedance; low frequency range; negative resistance; boundary condition; mode-merging
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-251437OAI: oai:DiVA.org:kth-251437DiVA, id: diva2:1315625
Note

QC 20190520

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-20Bibliographically approved
In thesis
1. Optimal damping and slow sound in ducts
Open this publication in new window or tab >>Optimal damping and slow sound in ducts
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis is dedicated to expanding knowledge on two duct acoustic issues including: 1) the optimal damping of low frequency sound and 2) the development and application of ‘slow sound’.

To address the first issue, the ‘Cremer impedance’ proposed more than half a century ago has been revisited and further developed. The original motivation is to extend the concept from large duct applications, such as aero-engines, to low frequency applications including vehicle intake and exhaust or cooling and ventilation systems. This leads to the derivation of the ‘exact’ solution of the Cremer impedance for single-lined rectangular ducts valid in the low frequency range in the presence of a ‘plug’ flow. A substantial improvement in the low frequency damping is achieved with the exact solution and a measurement campaign is carried out to validate this.

However, for both circular and rectangular ducts (including single-lined and double-lined types) the exact solution of the Cremer impedance has a negative real part in the low frequency range. This indicates that an active boundary is required to provide the optimal damping. Two investigations on the negative resistance are conducted. First, the ‘plug’ flow is replaced by a sheared flow by changing the boundary condition in the optimization model. With this modification, the Cremer impedance is recalculated and the negative resistance is still found in most cases, demonstrating that the negative resistance is not necessarily an artefact of the boundary condition. Second, since the Cremer impedance is based on mode-merging, a mode-merging analysis is carried out. The merging result shows that the downstream results are always valid, but some of the upstream results in the low frequency range are invalid in the sense that unexpected mode pairs merge, and the corresponding damping is smaller than expected. This finding is true for both the fundamental mode and higher order modes.

Regarding the second issue, ‘slow sound’ or sound with a much reduced ‘phase velocity’ is investigated using a resonant periodic system in the low frequency range. This can be seen as an acoustic metamaterial where sound propagates at a much smaller-than-normal speed around its resonance frequency. Following a hydrodynamic particle agglomeration model, the slow sound is applied to manipulate the distribution of small particles in the vehicle exhaust system. Although in principle this acoustic agglomeration method can work, it will only be efficient if the wave damping in the metamaterial is kept small. 

Abstract [sv]

Denna avhandling har till syfte att öka kunskapen om akustiska problem i kanaler, inklusive: 1) optimal dämpning av lågfrekvent ljud och; 2) utveckling och tillämpning av ‘slow sound’.När det gäller det första problemet, har ‘Cremer-impedansen’, som föreslogs för mer än ett halvt sekel sedan studerats och vidareutvecklats. Detta möjliggör nya tillämpningar svarande mot lågfrekvent ljud som insugnings- och avgassystem för fordon samt ventilationssystem. En ‘exakt’ lösning av Cremer-impedansen för rektangulära kanaler med en ljuddämpande vägg giltig i lågfrekvensområdet har härletts. En väsentlig förbättring av lågfrekvent dämpning har uppnåtts med denna lösning vilket även validerats med mätningar.Emellertid har den exakta lösningen av Cremer-impedansen en negativ realdel (‘resistans’) i lågfrekvensområdet, vilket betyder att en aktiv väggbeklädnad är nödvändig för att åstadkomma optimal dämpning. Två undersökningar av den negativa resistansen har genomförts för att studera om dessa lösningar är realiserbara. I den första ändrades randvillkoret för att inkludera gränsskikt i strömningen. Resultatet visade att negativ resistans erhålls i de flesta fall även med det modifierade randvillkoret. I den andra studerades lösningens giltighet i det komplexa vågtalsplanet. Resultatet visade att lösningen nedströms alltid är giltig medan vissa lösningar uppströms i lågfrekvensområdet är ogiltiga. Detta resultat gäller i princip för alla vågor eller moder i en kanal.När det gäller det andra problemet undersöktes möjligheterna att skapa ‘slow sound’, dvs ljud som utbreder sig mycket långsammare än normalt, genom att utnyttja ett resonant periodiskt system i en kanal i lågfrekvensområdet. Detta kan ses som ett s.k. akustiskt metamaterial och kan nyttjas för att med hjälp av starka ljudvågor påverka små partiklar som tvingas att kollidera och bli större. En studie om denna metod för sammanslagning av partiklar (‘particle agglomeration’) kan nyttjas för avgasrening har genomförts. Metoden är teoretiskt möjlig men begränsad av att tekniken för att skapa ‘slow sound’ inte bara saktar ned ljudvågen utan även dämpar dess amplitud och därigenom minska ljudvågens påverkan på partiklar.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. p. 75
Series
TRITA-SCI-FOU ; 2019:22
National Category
Fluid Mechanics and Acoustics
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-251443 (URN)978-91-7873-176-3 (ISBN)
Public defence
2019-06-04, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC20190514

Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-14Bibliographically approved

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Zhang, ZheBodén, HansÅbom, Mats

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