Predicting phase shift effects for vibrating fluid-conveying pipes due to Coriolis forces and fluid pulsation

Knowing the influence of fluid flow perturbations on the dynamic behavior of fluid-conveying pipes is of relevance, e.g., when exploiting flow-induced oscillations of pipes to determine the fluids mass flow or density, as done with Coriolis flow meters (CFM). This could be used in the attempts to improve accuracy, precision, and robustness of CFMs. A simple mathematical model of a fluid-conveying pipe is formulated and the effect of pulsating fluid flow is analyzed using a multiple time scaling perturbation analysis. The results are simple analytical predictions for the transverse pipe displacement and approximate axial shift in vibration phase. The analytical predictions are tested against pure numerical solution using representative examples, showing good agreement. Fluid pulsations are predicted not to influence CFM accuracy, since proper signal filtering is seen to allow the determination of the correct mean phase shift. Large amplitude motions, which could influence CFM robustness, do not appear to be induced by the investigated fluid pulsation. Pulsating fluid of the combination resonance type could, however, influence CFMs robustness, if induced pipe motions go unnoticed and uncontrolled during CFM operation by feedback control. The analytical predictions offer an immediate insight into how fluid pulsation affects phase shift, which is a quantity measured by CFMs to estimate the mass flow, and lead to hypotheses for more complex geometries, i.e. industrial CFMs. The validity of these hypotheses is suggested to be tested using laboratory experiments, or detailed computational models taking fluid-structure interaction into account.     

Perturbation-based prediction of vibration phase shift along fluid-conveying pipes due to Coriolis forces,nonuniformity, and nonlinearity

This paper investigates the influence of tread conicity variation on hunting dynamical changing features for railway vehicle. Nonlinear contact force between wheels and rail is estimated by Vermeulen–Johnson creep force law. And a piecewise linear function is employed to appropriate the collision between wheel flange and rail. Hunting asymmetrical motions are analyzed by lateral bifurcation behaviors between maximum and minimum of car body lateral displacement. The result shows that the critical speed decreases with the increase in tread conicity, while the speed gap between linear and nonlinear speeds is narrowing. Compared with wheelsets, lateral amplitudes of the bogies are vulnerable to the tread conicity and decrease gradually. Besides, more asymmetrical motions are put into consideration with regard to tread conicity variation. Similarly, one asymmetrical behavior with small amplitude difference originates from the same chaotic attractor at both sides. And small interactive amplitude jumps in two sides at chaotic or periodic occasions are revealed. Distinguishingly, the other new asymmetrical type is found at a certain tread conicity that amplitudes of the hunting motion in positive and reverse directions no longer coincide and go away in opposite directions when the tread conicity increases to a certain value. And this particular asymmetrical motion disappears with further growth of tread conicity.

     

Ueber die Trennung der Oxyde, welche aus einer freie Salzs?ure enthaltenden L?sung durch Schwefelwasserstoff nicht gef?llt werden

Ohne Zusammenfassung     

Das Atomgewicht des Aluminiums

Ohne Zusammenfassung     

Über die Auswertung der Quantenintegrale für den unsymmetrischen Kreisel

Ohne Zusammenfassung     

Studies on organophosphorus compounds XLVII preparation of thiated synthons of amides,lactams and imides by use of some new p,s-containing reagents

The thionation properties of 2,4-bismethylthio-1,3,2,4-dithiadiphosphetane 2,4-disulfide, $\text{1}$, 2,4-bis(4-phen-oxyphenyl)-1,3,2,4-dithiaphosphetan is that $\text{2}$, $\text{3}$ and thionate most amides and lactams In THF at room temperature (reaction time 5 min) to give the corresponding thionated compounds. Imides are easily thionated by $\text{2}$, $\text{3}$ and $\text{4}$ In DME at 60 °C. The reactions of $\text{1}$ with amides, imides and most lactams are run at 60°C to give good yields of the corresponding thionated compounds.