Fluid flow, instability

Although a simple extended fractional flow model, based on the Koval approach, is presented to describe laboratory viscous fingering experiments using polymer slugs, this does not imply that this can be carried over to the larger-scale simulation of fluid flow instabilities in polymer flooding in the... 

Discussion 4-9. Streamline tracing in 3D flows, 70 Discussion 4-10. Tracer movement in 3D reservoirs, 73 Fluid flow instabilities, 76 Problems and exercises, 78... 

The second example, shown in Figure 9, also illustrates some of the strange phenomena apparent when competitive crossover occurs in systems that exhibit flow instability or are close to a phase transition. The image shows the velocity profile obtained for a wormlike micelle solution sheared in the gap of a cone-and-plate rheometer, along with the resultant shear rate of the fluid. Flow instability phenomena have led to distinctive shear banding, in effect a first-order phase transition of the fluid maintained under non-equilibrium conditions. Microscopy has been able to provide unique insight in this emerging area of condensed-matter physics. 

Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Flow 28 1411-1435 Kennedy JE, Roach GM, Dowling ME, Abdel-Khalik SI, Ghiaasiaan 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... 

The forced fluid flow in heated micro-channels with a distinct evaporation front is considered. The effect of a number of dimensionless parameters such as the Peclet, Jacob numbers, and dimensionless heat flux, on the velocity, temperature and pressure within the liquid and vapor domains has been studied, and the parameters corresponding to the steady flow regime, as well as the domains of flow instability are delineated. An experiment was conducted and demonstrated that the flow in microchannels appear to have to distinct phase domains one for the liquid and the other for the vapor, with a short section of two-phase mixture between them. 

Thermally driven convective instabilities in fluid flow, and, more specifically, Rayleigh-B6nard instabilities are favorite working examples in the area of low-dimensional dynamics of distributed systems (see (14 and references therein). By appropriately choosing the cell dimensions (aspect ratio) we can either drive the system to temporal chaos while keeping it spatially coherent, or, alternatively, produce complex spatial patterns. 

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

The flow instability can best be understood by looking at a case with unidirectional flow (see Fig. 12.7). There will always be some nonuniformity between the sides. This will result in the flow front moving faster on one side of the core than it does on the other. The net force on the core from the resin will be higher on the side where the flow front has moved the farthest and as a result the core will be pushed away from this side. The displacement of the core will increase the permeability more and the flow front will move even farther ahead on the fast side, and so on. The process will reach an equilibrium when the reaction force from the reinforcement becomes large enough to balance the fluid pressure on the other side of the core. 

Because the role of convection is to transfer information in the direction of the flow, the derivative dV/dz must be approximated by a difference formula that uses information that is upstream of the flow. If the derivative is approximated as (Vj - Vj- )/dz when the velocity is negative, then the derivative communicates information ahead of the flow, which is physically unrealistic. Moreover, and importantly, such a downwind difference formula can cause severe numerical instabilities. From the point of view of a control volume, recall the origin of the convective terms in the substantial derivative. They represent the mass, momentum, or energy that is carried into or out of the control volume from the surrounding regions with the fluid flow. Thus the term must have a directional behavior that depends on the local fluid velocity. 

So far in this chapter we have looked into the viscous phenomena associated with the flow of polymer melts in capillaries. We now turn to the phenomena that are related to melt elasticity, namely (a) swelling of polymer melt extrudates (b) large pressure drops at the capillary entrance, compared to those encountered in the flow of Newtonian fluids and (c) capillary flow instabilities accompanied by extmdate defects, commonly referred to as melt fracture. ... 

F. N. Cogswell, Stretching Flow Instabilities at the Exits of Extrusion Dies, J. Non-Newt. Fluid Mech., 2, 37-47 (1977). 

This device is filled partially with working fluid. The flow instabilities inside of this device are produced due to the heat input in one part of it and heat output from the another part by heating multi-channels (H = 2mm, L = 5 mm) at one end and simultaneously cooling the other end thus resulting in pulsating fluid. This heat input and output stimulates a heat transfer, as a combination of sensible and latent heat portions. The flow instabilities are a superposition of various underlying effects. 

Figure 28 shows that the pressure drop of a conical bed reaches a maximum value at the initial fluidization point (GR)i, and it drops at higher fluid rates. Inherent in this drooping pressure-drop characteristic lies the instability of conical bed operation, especially with gas as the fluidizing medium, for as soon as fluid rate reaches (GR) , the decrease in pressure drop induces higher flow from a compressible medium. As the pressure expends itself, fluid flow drops to even lower values, only to permit reaccumulation of pressure because of reversion to the higher pressure-drop region of the system. 

These fluctuations maybe caused by rapid variations in pressure or velocity producing random vortices and flow instabilities within the fluid. A complete mathematical analysis of turbulent flow remains elusive due to the erratic nature of the flow. Often used to promote mixing or enhance transport to surfaces, turbulent flow has been studied using electrochemical techniques [i]. 

Azbel and Liapis (1983) analyzed gas/liquid systems with the assumption that the available energy at steady state is at a minimum. Reh (1971) mentioned the concept of the lowest resistance to fluid flow, and in a somewhat alternate way, the so-called minimum pressure drop was used by Nakamura and Capes (1973) in analyzing the annular structure in dilute transport risers. The instability of a uniform particle-fluid suspension was analyzed by introducing small disturbances into the system (Jackson, 1963 Grace and Tuot, 1979 Batchelar, 1988). 

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. 

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