Details

Autor(en) / Beteiligte

• McPhail, M.A.
• Oliver, J.M.
• Parker, R.
• Griffiths, I.M.

Titel

Extensional flow of a compressible viscous fluid

Ist Teil von

• Journal of fluid mechanics, 2023-12, Vol.977, Article A43

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We derive reduced models for extrusion problems where it is necessary to account for fluid compressibility. We consider the two-dimensional extensional flow of a compressible viscous fluid and discuss two specific applications: weakly compressible fluids and bubbly liquid–gas mixtures that behave as a single compressible fluid. The mathematical model we present consists of equations for conservation of mass, conservation of momentum and a closure relationship between the pressure and density. The most substantial differences between compressible extrusion problems is in the closure relationship. By integrating the conservation equations across the fluid cross-section and exploiting a slender aspect ratio, we derive reduced equations for conservation of mass and conservation of momentum in the direction of flow. The reduced system of equations relating cross-sectionally averaged quantities is closed by a relationship between the averaged pressure and density, which will differ substantially depending on the application. We demonstrate the utility of a reduced model for both the weakly compressible fluid and bubbly mixture applications; namely, in providing valuable quantitative insights without needing to solve a complicated free-boundary problem.