On the use of Helmholtz resonators as sound attenuators

Summary In the present paper a nonlinear acoustic theory is proposed, to accurately describe the properties of a generalized type of Helmholtz resonators. The theory may be used as a layout tool to design sound attenuators for combustion facilities. The present investigation shows that, in addition to the nonlinear effects, the effects due to thermoacoustic boundary layers and the first frequency correction to the Helmholtz approximation should be taken into account, in order to predict the frequency-dependent attenuation properties of Helmholtz attenuators with the accuracy required by typical technical applications. A series of experiments is presented which is used to validate the theoretical predictions.

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Zusammenfassung In der vorliegenden Abhandlung wird eine nichtlineare akustische Theorie vorgeschlagen, mit der das Verhalten einer verallgemeinerten Art von Helmholtzresonatoren beschrieben werden kann. Die Theorie kann als Werkzeug zur Auslegung von Schalldämpfern für Verbrennungsanlagen benutzt werden. Die vorliegende Arbeit zeigt, dass neben den nichtlinearen Effekten auch die Einflüsse der thermoakustischen Grenzschichten und der ersten Frequenzkorrektur zur Helmholtzapproximation berücksichtigt werden müssen, damit die frequenzabhängigen Eigenschaften von Helmholtzdämpfern mit technisch ausreichender Genauigkeit beschrieben werden können. Mit einer Reihe von Experimenten werden die theoretischen Ergebnisse untermauert.

     

Quantitative determination of chloride by means of flow injection analysis with spectrophotometric detection in the UV/VIS range

Chloride is determined indirectly by Spectrophotometric flow injection analysis. Two systems are compared, both based on the principle of ion exchange of easily detectable anions versus chloride from suitable mercury salts. The first method is based on the exchange of chloride with chloranilate which is detected at 332 nm or at 306 nm in neutral or in acidic medium respectively. In the second case, chloride reacts with Hg(SCN)₂. The liberated thiocyanate forms a strongly coloured complex with Fe(III) in acidic solution with an absorption maximum at 460 nm. Both methods have a detection limit of about 5 mol Cl^–/l (175 ng/ml). In the case of the thiocyanate method, the relative standard deviation is about 2% (7 measurements) in the range of 5 to 150 mol/l and decreases significantly to a value of approximately 0.2% at higher concentrations; for the chloranilate method it is 10% for lower and about 1% for higher concentrations respectively.     

Stereoselektive Synthesen von (Z)-(10-Methoxy-4H-benzo[4,5]cyclohepta[1,2-b]thiophen-4-yliden)essigsäure

Stereoselective Syntheses of (Z)-(10-Methoxy-4H-benzo[4,5]cyclohepta[1,2-b]thiophen-4-ylidene)acetic Acid Two stereoselective syntheses for the antiinflammatory compound 1 ((Z)-isomer) are described. In the first approach (Strategy A, Scheme 1) the stereoselective synthesis of 1 was realized via the bicyclic compound 11 under thermodynamic conditions, followed by a thiophene annelation with retention of the double-bond geometry (Schemes 2–4). Optimized conditions were necessary to avoid (E/Z)-isomerization during annelation. In the second approach (Strategy B, Scheme 1), diastereoisomer 17b was obtained selectively from a mixture of the diastereoisomers 17b and 18b by combining thermodynamic epimerization and solubility differences (Scheme 5). Diastereoisomer 17b was converted into the tricyclic compound 23 using a novel thiophene annelation method which we described recently (Scheme 6). In a final step, a stereospecific ‘syn’-elimination transformed the sulfoxide 24 into the target compound 1 (Scheme 7). To avoid (E/Z)-isomerization, it was necessary to trap the sulfenic acid liberated during the reaction. The key reactions of both approaches are highly stereoselective (> 97:3).     

Assembly and Dissociation of Α-Cyclodextrin [2]Pseudorotaxanes with α,ω-Bis(N-(N,N′-dimethylethylenediamine)alkane Threads

A series of novel bischelate bridging ligands, CH₃NH(CH₂)₂N(CH₃)(CH₂) _n N(CH₃)(CH₂)₂NHCH₃ (n = 9, 10, 11, and 12) were synthesized as hydrochloride salts and characterized by elemental analyses, electrospray mass spectrometry, and ¹H and ¹³C NMR spectroscopy. These ligands form [2]pseudorotaxanes with α-cyclodextrin (α-CD) and the stability constants have been determined from ¹H NMR titrations in D₂O. The kinetics and mechanism of the assembly and dissociation of a [2]pseudorotaxane in which α-CD has been threaded by the CH₃NH₂(CH₂)₂N(CH₃)(CH₂)₁₂N(CH₃)(CH₂)₂NH₂CH ₃ ²⁺ ligand were determined in aqueous solution using ¹H NMR spectroscopy. A weak inclusion of the dimethylethylenediamine end group precedes the passage of the α-CD onto the hydrophobic dodecamethylene chain.