Eigenspectra and mode coalescence of temporal instability in two-phase channel flow

Abstract

The stability of two immiscible fluids with different densities and viscosities is examined for channel flow. A multi-domain Chebyshev collocation spectral method is used for solving the coupled Orr-Sommerfeld stability equations for the entire spectrum of eigenvalues and associated eigenfunctions. Numerical solution of the eigenvalue problem is obtained with the QZ eigenvalue solver and is validated with analytical results derived in the long and short wave limits. A parametric study is carried out to investigate the spectral characteristics and eigenfunction structures related to the shear and interfacial modes of instability. The interactions and mode switching between the two instability modes are investigated. Under certain conditions, the two modes are found to become unstable simultaneously. Mode coalescence can occur in either the stable or the unstable part of the spectrum. In general, the eigenfunction of the most dangerous mode is observed to vary sharply in the neighborhood of the interface and the critical points. C 2015 AIP Publishing LLC.

Waves and instabilities in high quality adiabatic flow in microgap channels

“…In the liquid layer, however, the Reynolds numbers are substantially lower and a fully developed flow is expected. Moreover, a recent study by Kaffel and Riaz (2015) indicates that the eigenvectors of the unstable interfacial modes are generally localized in the neighborhood of the interface where the local Reynolds numbers are sufficiently low when the film thickness is small. Hence, close to the interface, the fully developed velocity profile may represent a reasonable approximation in both layers.…”

“…This approach is well suited for non-periodic domains and also allows the solution to converge at an exponential rate. It has been used effectively in the past for similar problems (Kaffel and Renardy, 2010;Kaffel and Renardy, 2011;Kaffel and Riaz, 2015). For a more detailed description of the method, see Trefethen (2000), Boyd (2000) and Peyret (2002).…”

“…The stability characteristics for such cases thus appear to be correlated more with the flow behavior in the vicinity of the interface, indicating a dominance of the interfacial mode of instability. Kaffel and Riaz (2015) have recently investigated this mode of instability in more detail. The shear mode of instability, on the other hand, is expected to play a bigger role for larger values of , corresponding to values of greater than those considered in this study.…”

Stability of stratified two-phase flows in inclined channels

“…Indeed, since the classical work of Yih (1967), where long-wave two-dimensional analysis was presented, the stability of stratified flow in the two-plate geometry has been extensively studied in the literature (e.g. Hooper and Boyd, 1983, Yiantsios and Higgins, 1988, Charru and Fabre, 1994, Ó Náraigh et al, 2014, Kaffel and Riaz, 2015. Most of the studies addressed horizontal flow driven by an imposed pressure gradient (see Barmak et al, 2016 and references therein), where the gravity-driven multiple solutions do not exist.…”

Non-modal stability analysis of stratified two-phase channel flows

“…Linear stability of stratified two-phase flows in horizontal and inclined channels was studied by Yih(1967), Hooper and Boyd (1983), Yiantsios and Higgins (1988), Charru and Fabre (1994), Tilley et al (1994), Ó Náraigh et al (2014), Kaffel and Riaz (2015), and others. Recently, this problem was addressed more rigorously with reference to the prediction of the operational region corresponding to stable stratified-smooth flow on flow pattern maps (Barmak et al, 2016a, b).…”