Fluid mechanics critical flow

A critical aspect, especially in the design of cold-wall reactors is the fluid dynamics of the gas flow. Even though the pressure in the reactor is reduced, the gas density is still sufficient to apply conventional fluid mechanics to its flow. Fluid mechanics tells us that a gas flowing down a smooth tube will move without turbulence as long as the Reynolds number, R , is less than 2000. The Reynolds number in a tube is given by ... 

Barclay, F. J., T. J. Ledwidge, and G. C. Cornfield, 1969, Some Experiments on Sonic Velocity in Two-Phase Critical Flow, Symp. on Fluid Mechanics and Measurements in Two-Phase Flow Systems, Proc. Inst. Mech. Eng. 184(Part 3C) 185-194. (3)... 

Macbeth (M5) has recently written a detailed review on the subject of burn-out. The review contains a number of correlations for predicting the maximum heat flux before burn-out occurs. These correlations include a dependence upon the tube geometry, the fluid being heated, the liquid velocity, and numerous other properties, as well as the method of heating. Sil-vestri (S6) has reviewed the fluid mechanics and heat transfer of two-phase annular dispersed flows with particular emphasis on the critical heat flux that leads to burn-out. Silvestri has stated that phenomena responsible for burn-out, due to the formation of a vapor film between the wall and the liquid, are believed to be substantially different from phenomena causing burn-out due to the formation of dry spots that produce the liquid-deficient heat transfer region. It is known that the value of the liquid holdup at which dry spots first appear is dependent on the heat flux qmi. The correlations presented by Silvestri and Macbeth (S6, M5) can be used to estimate the burn-out conditions. 

From fluid mechanics, the critical depth occurs at the minimum specific energy. Thus, the previous equation may be differentiated for E with respect to y and equated to zero. Convert V in terms of the flow Q and cross-sectional area of flow A using the equation of continuity, then differentiate and equate to zero. This will produce... 

In fluid mechanics, the physical implication of a Reynolds number is the ratio of inertial forces (up) to viscous forces (ju/L). It is, therefore, used to illustrate the relative importance and dominance of these two types of forces for a given flow. Depending on the magnitude of the Reynolds number, the flow regimes can be classified as either laminar or turbulent flow. If a flow has a low Reynolds number, a laminar flow occurs, where viscous forces are dominant. The flow is therefore smooth. When the Reynolds number for a flow is greater than a critical value, the flow becomes turbulent flow and is dominated by inertial forces, resulting in random eddies, vortices and other flow fluctuations. Some of the examples are illustrated in Table 2.7. 

C. Unal, P. Sadasivan, and R. M. Nelson, On the Hot-Spot Controlled Critical Heat Flux Mechanism in Pool Boiling of Saturated Fluids, in Pool and External Flow Boiling, V. K. Dhir and A. E. Bergles eds., pp. 193-201, ASME, New York, 1992. 

These forces are very small compared with typical colloidal forces, which can be of the order of 1000-2000 pN in dilute electrolyte solutions. Figure 3 shows an example of colloidal forces calculated between a fine quartz particle and a sandstone grain. To be of the same order of magnitude as the colloidal forces, a superficial velocity of the order of 200 cm/h would be required in some reservoirs (23, 27). This is not to say that mechanically induced fines migration does not occur in some reservoirs at lower velocities. Critical flow velocities below which fines migration does not occur have been reported to span the range from about 14 to 900 cm/h (31). Recognizing that there will be exceptions, as a first approximation it may be appropriate to consider fine particle mobilization to be independent of fluid velocity and consider simply the influence of solution and interfacial chemistry on the colloidal forces. 

A model of explosive boiling making use of the idea of intensive homogeneous nucleation allows us not only to give a qualitative explanation to effects observed in two-phase nonequilibrium flows but also to make trustworthy quantitative evaluations (for example of critical flow rates throu short channels) which cannot be obtained with the aid of traditional schemes of heterogeneous media mechanics. The field of applicability of the model is outlined quite definitely. This model is a usefxil addition to all other models of fluid mechanics. 

Erosion corrosion is associated with a flow-induced mechanical removal of the protective surface film that results in subsequent corrosion rate increases via either electrochemical or chemical processes. It is often accepted that a critical fluid velocity must be exceeded for a given material. The mechanical damage by the impacting fluid imposes disruptive shear stresses or pressure variations on the material surface and/or the protective surface film. Erosion corrosion may be enhanced by particles (solids or gas bubbles) and impacted by multi-phase flows [29]. Increased flow stream velocities and increases of particle size, sharpness, density, and concentration increase the erosion corrosion rate. Increases in fluid viscosity, density, target material hardness, and/or pipe diameter tend to decrease the corrosion rate. The morphology of surfaces affected by erosion corrosion may be in the form of shallow pits or horseshoes or other local phenomena related to the flow direction. 

Hot-wire anemometers have traditionally been applied in the fields of experimental fluid mechanics and aerospace engineering. Despite the possibilities to measure real-time physical parameters such as temperature, velocity, flow rates, and shear stress, the spatial resolution is limited to the device dimension. The advent of MicroElectroMe-chanical system (MEMS) and nano-scale thermal sensors has revolutionized the spatial and temporal resolution critical to gain entry into micro-fluidics, micro-circulation, biomedical sciences, and cardiovascular medicine. These micro/nano devices are fabricated with the Semiconductor-... 

Elaskar, S.A. and Godoy L.A. An Application of Non-Newtonian Fluid Mechanics to Granular Flow Using a Critical State Concept. Powder Handling and Processing 10 (1998) 3, pp. 239-244. 

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