Nonlinear gas oscillations in pipes. Part 1. Theory

Jiménez, Javier López

doi:10.1017/s0022112073001400

Cited by 47 publications

(13 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, as we will see in the following, the origin of the anomalous mode of oscillation has to be searched in a strong resonance of the excited wave with the eigenmodes of the rectangular container, which takes place for a particular value of the forcing frequency at which the associated mode becomes twodimensional. Similar resonances have been previously reported for a square cell (Jimenez, 1973).…”

Section: Introductionsupporting

confidence: 89%

“…Anomalous oscillations are characterized by subharmonic spatial and temporal response with respect to normal modes. The study and the understanding of anomalous modes could be important in the design of pipeline or channels, in order to prevent anomalous waves from perturbing the functioning of the circuits (Jimenez 1973;Hsu and Kennedy, 1971). It would be then interesting to study these anomalous surface waves in other geometrical and physical conditions.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Anomalous modes in Faraday instability

Guarino¹

2017

Sci. Res. Essays

View full text Add to dashboard Cite

This research presents an experimental study on the Faraday instability in one-dimensional cells filled with a mixture of water and glycerol, and for a range forcing frequency between 10 and 60 Hz. It showed that for a particular forcing frequency, whose value depends on the width of the cell, an anomalous surface oscillation arises, that appears as a large wavelength mode oscillating subharmonically with respect to the normal modes predicted by the linear stability analysis. Since all others studied forcing frequency, the observed modes are in agreement with the ones theoretically predicted.

show abstract

Section: Introductionsupporting

confidence: 89%

Section: Resultsmentioning

confidence: 99%

Anomalous modes in Faraday instability

Guarino¹

2017

Sci. Res. Essays

View full text Add to dashboard Cite

show abstract

“…Figure 4 shows that decrease in the internal diameter of the diaphragm 2Rin.f results in the increase of time of coagulation and sedimentation of aerosol, which reaches the maximum value in the case of the closed tube. This is due, firstly, to significant influence of the unsteady discharge of aerosol from the open end of the tube, and secondly, with the approach of the investigated excitation frequencies of aerosol in the open tube to its resonance frequency [17,18]. Note that time of coagulation and sedimentation of aerosol in the open tube with the diaphragm is longer than in the open tube without a diaphragm.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of nonlinear waves in the tubes filled with aerosol

2018

View full text Add to dashboard Cite

Abstract. The results of experimental investigations of nonlinear oscillations of finely dispersed aerosol in the tube with various geometry on the end in the shock-wave, the shock-free wave modes and in the mode of transition to shock waves near the resonance frequency are presented. The time dependences of the numerical concentration of the oscillating aerosol droplets are presented. The effect of the frequency and amplitude of the piston displacement and the influence of the diaphragm internal diameter on the time coagulation and sedimentation of aerosol were studied. An increase in the amplitude of the piston displacement in all modes results in acceleration of the process of coagulation and sedimentation of aerosol. The dependence of time of coagulation and sedimentation of aerosol on the excitation frequency was found to be of a nonmonotonic character with the minimum value upon the resonance frequency.

show abstract

“…. Whereas multimode response arises in the case of the closed tube , and in this case it is well known that periodic resonant solutions may involve shocks . Similarly, for open‐ended geometries, Seymour and Mortell found interesting array of resonant solutions and more recently Wang and Kassoy applied a multiple mode analysis to investigate an array of resonant behaviors for both open and closed configurations.…”

Section: Introductionmentioning

confidence: 99%

Resonances in Bounded Media

Amundsen

2017

Stud Appl Math

View full text Add to dashboard Cite

Resonant behavior in bounded domains and under the influence of weakly periodic forcing with magnitude M≪1 is studied for a general class of one‐dimensional nonlinear wave systems. The model encompasses and provides analogy to numerous physically motivated cases such as acoustic resonators. Through a generalized weakly nonlinear analysis the linear response and associated resonant spectrum may be determined. In the case where the spectrum is sufficiently noncommensurate a single mode response emerges with amplitude O(M13). Dependence upon detuning and dissipative effects follow immediately from the subsequent nonlinear balance. In the case where the spectrum is commensurate a multimodal response arises, leading to a coupled system of solvability conditions. The amplitude of the response depends in detail on the commensurate structure, O(M12) in the case where it is fully commensurate. This is in keeping with the well‐known dichotomy between responses for acoustic waves in open and closed tubes. Through continuous variation of the model system, the nature of the transition between these distinct regimes is then studied and through an appropriate modal truncation the connection is achieved. A numerical example is presented to further illustrate and corroborate the general analysis.

show abstract

Nonlinear gas oscillations in pipes. Part 1. Theory

Cited by 47 publications

References 13 publications

Anomalous modes in Faraday instability

Anomalous modes in Faraday instability

Dynamics of nonlinear waves in the tubes filled with aerosol

Resonances in Bounded Media

Contact Info

Product

Resources

About