Viscosity single phase flow

Figure 6.35 shows dependence of the dimensionless initial liquid thickness of water and ethanol 5, on the boiling number Bo, where 5 = 5U/v, f/ is the mean velocity of single-phase flow in the micro-channel, and v is the kinematic viscosity of the... 

Calculate the friction factor in the normal way for single-phase flow but evaluating the Reynolds number using a mean viscosity, ji ... 

The "correlative" multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a "multilevel" approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

Me Effective turbulent viscosity in a single phase flow... 

By analogy to single-phase flow, under steady-state conditions, the flow rate of each fluid should be directly proportional to the applied pressure gradient and the cross-sectional area of the medium and inversely proportional to the fluid viscosity. Therefore, an equation analogous to equation 1 can be written for each fluid ... 

This term may be determined in various ways from experimental data. A frequently used method for single-phase flow (S4) is to differentiate an experimental velocity profile graphically, and to obtain the kinematic viscosity from the velocity gradient with basic relations [e.g., Eqs. (3-1) and (3-2)]. The currently available data for velocity profile do not appear accurate enough to yield as a function of radial position. As an alternative, Hills (H9) has assumed a relation between the local vt and the radial position ... 

Discussions in Chapter 2 may be referred to for explanations of the various symbols. It is straightforward to apply such conservation equations to single-phase flows. In the case of multiphase flows also, in principle, it is possible to use these equations with appropriate boundary conditions at the interface between different phases. In such cases, however, density, viscosity and all the other relevant properties will have to change abruptly at the location of the interface. These methods, which describe and track the time-dependent behavior of the interface itself, are called front tracking methods. Numerical solution of such a set of equations is extremely difficult and enormously computation intensive. The main difficulty arises from the interaction between the moving interface and the Eulerian grid employed to solve the flow field (more discussion about numerical solutions is given in Chapters 6 and 7). 

In order to approximate the effective viscosity /Ueff = p,m,t + Pm for the mixture flows, separate models are needed for the turbulent viscosity j and the mixture viscosity /x. The standard k-e model originally developed for singlephase flows has been used to compute the turbulent viscosity p,m,t in the majority of publications on numerical simulations of two-phase flows. Nevertheless, it is still an open question whether the approximate turbulence models which were originally developed for single-phase flow are appropriate for two-phase flow simulations [122]. 

The bulk viscosity is set to zero for the continuous gas phase, in line with what is common practice for single phase flows. 

Single-phase fluid flow in porous media is a well-studied case in the literature. It is important not only for its application, but the characterization of the porous medium itself is also dependent on the study of a single-phase flow. The parameters normally needed are porosity, areal porosity, tortuosity, and permeability. For flow of a constant viscosity Newtonian fluid in a rigid isotropic porous medium, the volume averaged equations can be reduced to the following the continuity equation,... 

The heat transfer rates in bubble columns are much higher than that anticipated from single phase flow considerations. This enhancement is ascribed solely to the bubble-induced turbulence and liquid circulation. Little work has been reported on heat transfer, both at wall and to/from immersed surfaces, in bubble columns employing non-Newtonian media. Nishikawa et al. reported the first set of data on the effect of shearthinning viscosity of CMC solutions on jacket and coil heat transfer coefficients [7]. They reconciled their results for Newtonian and power law liquids by introducing the notion of an effective viscosity estimated via Equation 3, provided the gas velocity was greater than 40 mm/s. For superficial gas velocity lower than this value, the effective shear rate varies as for coil heat transfer... 

A more rigorous viscous turbulent model of single-phase flow, based on a Prandtl mixing length theory was published by Bloor and Ingham. Like Rietema, these authors obtained theoretical velocity profiles, but they used variable radial velocity profiles calculated from a simple mathematical theory. The turbulent viscosity was then related to the rate of strain in the main flow and the distribution of eddy viscosity with radial distance at various levels in the cyclone was derived. 

An emulsion ccxisisting of 99.5% continuous organic phase with a density of 934 kgAn and a viscosity of 4.6 mPa.s at 20 C and 0.5% tap water. This low water content was chosen because initially all of the calculations were based on a single phase flow and this small amount of dispersed phase was assumed to be negligible. 

The two key properties in single-phase flow are the fluid density and the viscosity. The density is quite straightforward it is the mass per unit volume. In turbulent flow, pressure drop is directly proportional to density, so that the accuracy of the density is the accuracy of the pressure drop prediction. It is easy to get better than 1% accuracy on such values. Viscosity, on the other hand, is a more complex measurement. Low viscosity systems usually run in turbulent flow, where the viscosity has little or no effect on mixing or pressure drop. For low viscosity material the prime use of the viscosity is in calculating a Reynolds number to determine if the flow is laminar or turbulent. If turbulent, little accuracy is needed. An error in viscosity of a factor of 2 will have negligible effect. In laminar flow, however, the viscosity becomes all important and pressure drop is directly proportional to it, so that an accuracy of 10% or less is often required. For laminar processing a complete relation of stress versus strain or shear rate versus shear stress is required. See Chapter 4 for the means and type of data required. 

The value of the integral in Eq. 5.124 is analogous to a viscosity in the single-phase flow of a homogeneous fluid through a linear system. For this reason, this integral is defined as X, the average apparent viscosity. That is,... 

Fluid to be handled Identify the fluid to be handled is a process fluid or a utility fluid (such as steam, cooling water). Next identify it is single phase flow (vapor or liquid only), two phase flow, gravity flow, oratimy flow. Also check whether the fluid is Newtonian fluid or not. For Newtonian fluid, its viscosity is constant at fixed operating conditions (temperature and pressure). This chapter vvdit discuss line size for Newtonian fluid only. 

Per Eq. (15b) and Eq. (15c), the two phase mixture s density and viscosity are volume averages. Once they are known, we can calculate line pressure drop using the method outlined for single phase flow in section III. 1.2. 

In large tubes, as well as in tubes of a few millimeters in diameter, two-phase flow patterns are dominated in general by gravity with minor surface tension effects. In micro-channels with the diameter on the order of a few microns to a few hundred microns, two-phase flow is influenced mainly by surface tension, viscosity and inertia forces. The stratified flow patterns commonly encountered in single macro-channels were not observed in single micro-channels. 

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