Classification of instabilities in parallel two-phase flow

Boomkamp, P.A.M.

doi:10.1016/s0301-9322(97)00013-x

Cited by 16 publications

(24 citation statements)

References 49 publications

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“…Since the magnitude of the eigenfunction is arbitrary, we normalize the eigenfunction by its maximum absolute value. In the energy analysis, it is convenient to normalize each term with respect to the total kinetic energy 1 0 (|v r | 2 +|v θ | 2 +|v z | 2 ) rdr (Boomkamp & Miesen 1996;Govindarajan, L'vov & Procaccia 2001). For an unstable flow,Ė should be positive.…”

Section: Formulation Of the Stability Problemmentioning

confidence: 99%

Stability of miscible core–annular flows with viscosity stratification

et al. 2007

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The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

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Section: Formulation Of the Stability Problemmentioning

confidence: 99%

Stability of miscible core–annular flows with viscosity stratification

et al. 2007

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“…Alternatively, a growing disturbance may be due to increasing energy at the interface due to capillary forces or viscosity stratification or from a combination of the above sources. Examining the energy associated with each one may lead to identification of the predominant instability mechanism, see Hooper & Boyd (1983), Hu & Joseph (1989) and Boomkamp & Miesen (1997). Owing to the mapping, (3.15)-(3.16), the free boundary problem is transformed into an equivalent one with fixed boundaries and the effect of the interface is reflected by the many additional terms that arise in the governing equations due to the transformation.…”

Section: Energy Analysismentioning

confidence: 99%

“…Hu & Joseph (1989), in addition to performing linear stability analysis of twoand three-layered concentric fluids, calculated the energy associated with the various mechanisms and, thus, identified the driving mechanism that leads to instability, which in turn depends on the parameter values. This idea was employed earlier by Hooper & Boyd (1983) and later used to classify instabilities in a variety of flows by Boomkamp & Miesen (1997). Hu & Patankar (1995) studied the stability of CAF of water and oil in a circular pipe with respect to non-axisymmetric disturbances and Huang & Joseph (1995) studied the stability of eccentric core-annular flow.…”

Section: Introductionmentioning

confidence: 99%

Core–annular flow in a periodically constricted circular tube. Part 1. Steady-state, linear stability and energy analysis

Kouris

Tsamopoulos

2001

J. Fluid Mech.

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The concentric, two-phase flow of two immiscible fluids in a tube of sinusoidally varying cross-section is studied. This geometry is often used as a model to study the onset of different flow regimes in packed beds. Neglecting gravitational effects, the model equations depend on five dimensionless parameters: the Reynolds and Weber numbers, and the ratios of density, viscosity and volume of the two fluids. Two more dimensionless numbers describe the shape of the solid wall: the constriction ratio and the ratio of its maximum radius to its period. In addition to the effect of the Weber number, which depends on both the fluid and the flow, the effect of the Ohnesorge number J has been examined as it characterizes the fluid alone. The governing equations are approximated using the pseudo-spectral methodology while the Arnoldi algorithm has been implemented for computing the most critical eigenvalues that correspond to axisymmetric disturbances. Stationary solutions are obtained for a wide parameter range, which may exhibit flow recirculation at the expanding portion of the tube. Extensive calculations are made for the dependence of the neutral stability boundaries on the various parameters. In most cases where the steady solution becomes unstable it does so through a Hopf bifurcation. Exceptions to this are cases where the viscosity ratio is O(10−3) and, then, the most unstable eigenvalue remains real. Generally, steady core–annular flow in this geometry is more susceptible to instability than in a straight tube and, in similar ranges of the parameters, it may be generated by different mechanisms. Decreasing the thickness of the annular fluid, inverse Weber number or the Ohnesorge number or the density of the core fluid stabilizes the flow. For stability reasons, the viscosity ratio must remain strictly below unity and it has an optimum value that maximizes the range of allowed Reynolds numbers.

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“…Likewise, viscous dissipation has a negative contribution to the kinetic energy budget. Accordingly, for the non-isothermal system, each term in the mechanical and thermal energy balance (see (11) in Boomkamp & Miesen (1996) and (7.2)) should be evaluated for values of the physical parameters used in a relevant LSA (e.g. for the most unstable mode at or near a pseudo-steady state).…”

Section: Stability Competition Between Thermocapillarity and Gravitymentioning

confidence: 99%

“…How much of the contribution of what is promoting or suppressing the interfacial instability is attributed to each of the mechanisms, although it is obvious that the base flow field is the energy source for any disturbance? The answers can be found by using a disturbance energy analysis as summarized early on by Boomkamp & Miesen (1996). They developed a classification scheme for instabilities in parallel two-phase flows by proposing a general methodology based on mechanical energy balance for an isothermal system without introducing a thermal energy budget.…”

Section: Stability Competition Between Thermocapillarity and Gravitymentioning

confidence: 99%