Onset of flow instability

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

Kays WM, Krawford ME (1993) Convective heat and mass transfer. McGraw-Hill, New York Kennedy JE, Roach GM, Dowling ME, Abdel-Khalik SI, Chiaasiaan SM, Jeter SM, Quershi ZH (2000) The onset of flow instability in uniformly heated horizontal micro-channels. Trans ASME J Heat Transfer 122 118-125... 

Peles el al. (2000) elaborated on a quasi-one-dimensional model of two-phase laminar flow in a heated capillary slot due to liquid evaporation from the meniscus. Subsequently this model was used for analysis of steady and unsteady flow in heated micro-channels (Peles et al. 2001 Yarin et al. 2002), as well as the study of the onset of flow instability in heated capillary flow (Hetsroni et al. 2004). 

Carey VP (1992) Liquid-vapour phase-change phenomena. Hemisphere, Washington, DC Collier SP (1981) Convective boiling and condensation. McGraw-Hill, New York Ha JM, Peterson GP (1998) Capillary performance of evaporation flow in micro grooves an analytical approach for very small tilt angles. ASME J Heat Transfer 120 452 57 Hetsroni G, Yarin LP, Pogrebnyak E (2004) Onset of flow instability in a heated capillary tube. Int J Multiphase Flow 30 1424-1449... 

The viscous contribution to the total entrance pressure loss is very small. [C. D. Han, Influence of the Die Entry Angle in the Entrance Pressure Drop, Recoverable Elastic Energy and Onset of Flow Instability in Polymer Melt Flow, AIChE. J., 17, 1480 (1970).]... 

In view of the fact that fluid elasticity develops as the curing reaction progresses (i.e., as the size of the molecules becomes larger due to polymerization) and that the fluid elasticity increases with shear rate, the deviation of the viscosity-cure time curve from the vertical line at t

flow instability due to fluid elasticity. 

Tordella [35] was probably the first to show HDPE and LDPE birefnngence patterns highly perturbed after the onset of flow instabilities. Discontinuities in the extinction bands and non stationary patterns were then observed, which was confirmed later by Vinogradov et al. [24] on polybutadienes or Oyanagi et al. [36] on HDPE and PS. Piau et al. [17] observed on polybutadiene slight pulsations at the die exit, correlated to the frequency of the sharkskin defect. 

For an aqueous or a viscous solution, the onset of flow instability can be characterized by the Reynolds number. Re, which measures the relative importance of inertial and viscous effects in a fluid flow. It can be defined as... 

The use of cone-and-plate rheometers for polymer melts is limited to relatively low shear rates by the onset of flow instabilities, typically occurring not far beyond the onset of shear-rate dependence for t](y) and the a iVi crossing point. A capillary rheometer is sketched in Fig. 3.22. Stable operation at much higher shear rates is possible, but usually t]o cannot be determined because of instrumental limitations at low shear rates. The steady-state viscosity, however, can be obtained from measurements of the volumetric flow rate, Q, and the pressure drop, AP = P — Po, Po being the ambient pressure. For long tubes (L/D 1), the following equation applies for Newtonian liquids ... 

There are many effects limiting DMA resolution. One is Brownian diffusion of the ions away from their mean trajectory. Another is the onset of flow instability, either... 

Hamidouche, T., Bousbia-salah, A., 2006. RELAP5/3.2 assessment against low pressure onset of flow instability in parallel heated cannels. Annals of Nuclear Energy 33, 510—520. 

The phenomenon of flow instability is a result of interaction between pressure drop and coolant flow in heated channels. For the heated channels, the pressure drop as a function of mass flow deviates from m -dependency at low flow rates and shows a minimum. Before the minimum, any decrease in the flow rate results in an increase of the pressure drop with the consequence of low local pressure and saturation temperature. The minimum in the pressure drop/mass flow kurve depends on flow characteristics and heat flux. The determination of critical heat flux at the onset of flow instability has been experimentally inverstigated by whittle and Forgan /6/ for the coolant chaimels conditions exiting in MTR. They measured the mass flow, exit temperature and pressure drop corresponding to minima in the pressure drop -vs- flow rate kurve for subcooled water flowing (upward and downward) in norrow heated channels (width 2.54 cm, thickness 0.14 to 0.32 cm, and length 40 to 61 cm) under the followong conditions ... 

Values of n suggested by different authors are ranging from 12 to 37. A value of n = 25 was determined as best fit for Whittle and Forgan data. For different values of n, R is plotted as a function of Ljj / in Fig. 2. Safety margin Sf to the onset of flow instability is defined as... 

The results of calculations show that the safety margin to flow intability represents the limiting parameter regarding safe design and operation. Accordingly, the minimum margin to onset of flow instability amoimts to 1.47. 

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