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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Spatial modes in one-dimensional models for capillary jets.

J Guerrero1, H González2, F J García3

  • 1Department of Chemistry and Physics, Georgia Regents University, 1120 15th Street, SCI W3005, Augusta, Georgia 30912, USA.

Physical Review. E
|April 15, 2016
PubMed
Summary
This summary is machine-generated.

This study clarifies how one-dimensional (1D) models approximate axisymmetric capillary jet behavior, validating their use by comparing them to exact three-dimensional (3D) models. The findings help refine stability analyses for capillary jets.

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Area of Science:

  • Fluid Dynamics
  • Mathematical Modeling
  • Surface Physics

Background:

  • One-dimensional (1D) models simplify axisymmetric capillary jet analysis, approximating axial velocity profiles as uniform or parabolic.
  • Previous spatial stability analyses using 1D models led to misinterpretations regarding the yielded modes.
  • Existing three-dimensional (3D) analyses of axisymmetric spatial modes provide a basis for relating 1D and 3D models.

Purpose of the Study:

  • To relate spatial modes from 1D capillary jet models to their exact 3D counterparts.
  • To establish criteria for validating 1D models in capillary jet stability analysis.
  • To investigate the influence of axial-velocity profiles and surface stresses on 1D model outcomes.

Main Methods:

  • Analysis of the surface stimulation problem using normal and tangential stresses to perturb the jet.
  • Application of Green's function for spatially local, time-harmonic stimulation to derive a general formalism.
  • Comparison of 1D model results with classical 3D results for absolute instability conditions and unstable mode amplitudes.

Main Results:

  • The smallness of the wave number associated with each mode serves as a criterion to validate 1D approaches.
  • Proposed axial-velocity profiles (planar or parabolic) significantly influence the outcomes of different 1D models.
  • Comparison with 3D results validates the physical relevance of the derived 1D spatial modes.

Conclusions:

  • The study provides a framework for relating simplified 1D capillary jet models to exact 3D solutions.
  • Validation criteria are established based on wave number analysis, clarifying previous misinterpretations.
  • The findings enhance the understanding and application of 1D models for analyzing capillary jet instabilities, including various surface stresses.