Mean Flow Characteristics

Compared with the bubble characteristics, the information on the liquid flow characteristics specified by the axial and radial mean velocities, u and v, the root-mean-square values of the axial and radial turbulence components, m and the Reynolds shear stress u V, and higher correlations of turbulence components, such as the skewness and flatness factors, are limited except for a water-air system [8-12]. 

In general, precise measurements of the liquid flow characteristics in a molten metal bath at high temperatures are very difficult. At present, the mean velocity can be measured under limited conditions by using reaction probes [13-16] andKarman 

Iguchi and O. J. Ilegbusi, Modeling Multiphase Materials Processes Gas-Liquid Systems, DOI 10.1007/978-l-4419-7479-2 2, 

Numerical simulation techniques therefore have acted as a bridge between water models and actual processes [ 19,20], The aforementioned liquid flow characteristics in a molten metal bath agitated by gas injection were predicted numerically by using turbulence models, such as the A — e model, developed originally for single-phase flows [19,20], Numerical results thus obtained, however, have not received reliable experimental confirmation even for mercury and Wood s metal flows. 

In this section, a description is provided of the bubble and liquid flow characteristics measured in a molten Wood s metal bath stirred by bottomhelium gas injection. The aim is to provide experimental data for judging the adequacy of numerical results and to examine whether the results of liquid flow characteristics obtained for a water-air system are useful to predict molten metal flows. 

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The periodic phenomenon described above indicates that the entire channel acts like the area beneath a growing bubble, going through periodic drying and rewetting. The cycle was repetitive with venting of the elongated bubble. Such a behavior affects the mean flow characteristics that usually are measured at the manifolds. 

Mean flow characteristics of wall-jets for hydraulic engineering applications... 

The water flow within a rectangular duct is used for investigations on the effect of near wall injected polymer solution on development and cnaracte-ristics of boundary layer, comprising both bulk mean flow characteristics and turbulence structure. The author of the study had in mind possible... 

Kramer, T. J. Ph.D. Thesis, A Study of the Mean Flow Characteristics of Gas-Solid Suspensions Flowing in Vertical Tubes, University of Washington, Seattle, 1970. 

Effusion separator (or effusion enricher). An interface in which carrier gas is preferentially removed from the gas entering the mass spectrometer by effusive flow (e.g., through a porous tube or through a slit). This flow is usually molecular flow, such that the mean free path is much greater than the largest dimension of a traverse section of the channel. The flow characteristics are determined by collisions of the gas molecules with surfaces flow effects from molecular collisions are insignificant. 

Material-Flow Cbaracteristics Two important definitions of the flow characteristics of a storage vessel are mass flow, which means that all the material in the vessel moves whenever any is withdrawn (Fig. 21-17), and funnel flow, which occurs when only a portion of the material flows (usually in a channel or rathole in the center of the system) when any material is withdrawn (Fig. 21-18). Some typical mass-flow designs are shown in Fig. 21-19. 

Thus, the measurements of integral flow characteristics, as well as mean velocity and rms of velocity fluctuations testify to the fact that the critical Reynolds number is the same as Rccr in the macroscopic Poiseuille flow. Some decrease in the critical Reynolds number down to Re 1,500— 1,700, reported by the second group above, may be due to energy dissipation. The energy dissipation leads to an increase in fluid temperature. As a result, the viscosity would increase in gas and decrease in liquid. Accordingly, in both cases the Reynolds number based on the inlet flow viscosity differs from that based on local viscosity at a given point in the micro-channel. 

As distinct from the gelling properties of certain natural gums, usually exhibited by structural rigidity, viscosity is a thickening of the aqueous portion of a system by means of particle water absorption, and swelling of the colloid. From a practical angle, it manifests itself by the phenomena of thickening and reduced flow characteristics. 

In whichever approach, the common denominator of most operations in stirred vessels is the common notion that the rate e of dissipation of turbulent kinetic energy is a reliable measure for the effect of the turbulent-flow characteristics on the operations of interest such as carrying out chemical reactions, suspending solids, or dispersing bubbles. As this e may be conceived as a concentration of a passive tracer, i.e., in terms of W/kg rather than of m2/s3, the spatial variations in e may be calculated by means of a usual transport equation. 

Now it is important to stress that, whereas the laminar flame speed is a unique thermochemical property of a fuel-oxidizer mixture ratio, a turbulent flame speed is a function not only of the fuel-oxidizer mixture ratio, but also of the flow characteristics and experimental configuration. Thus, one encounters great difficulty in correlating the experimental data of various investigators. In a sense, there is no flame speed in a turbulent stream. Essentially, as a flow field is made turbulent for a given experimental configuration, the mass consumption rate (and hence the rate of energy release) of the fuel-oxidizer mixture increases. Therefore, some researchers have found it convenient to define a turbulent flame speed, S T as the mean mass flux per unit area (in a... 

Another method to measure pore size distribution is capillary flow porometry [202,203], in which a sample material is soaked with a low surface tension liquid that fills all its pores. Then, gas pressure is applied on one side of the sample in order to force the liquid out of the pores. At low pressures, the flow rate is close to zero however, as the pressure increases, the flow rate also increases and the amount of liquid inside fhe pores decreases. Thus, the flow rate is determined as a function of pressure and is then used to calculate the desired pore characteristics, such as pore size distribution, largest pore diameter, and mean flow pore diameter. 

The following discusses relevant aspects of flow characteristics in alpine regions, using the example of the European alpine region which in terms of data is well documented, and predicated on the classical mean water - high water - low water breakdown. 

According to [50], the lower border of the alpine-influenced catchments can be located (in Switzerland) at a mean altitude of around 1,500 m ASL. Above this altitude, flow characteristics are dictated by snow and glaciers (see below). Hence a comparison of runoff depths at the lower edge of the alpine region is shown in the second column of Table 2 the precipitation-related higher runoff on the south side of the Alps and the relative scarcity of runoff in inner-alpine zones is pronounced. Because of the varying gradients between the north and south side of the Alps, similar runoff depths can be assumed from mean altimdes of 2,500 m. 

Once the mathematical description of dispersion has been clarified, we are left with the task of quantifying the dispersion coefficient, Eiis. Obviously, Edh depends on the characteristics of the flow field, particularly on the velocity shear, dvx/dy and dvx /dz. As it turns out, the shear is directly related to the mean flow velocity vx. In addition, the probability that the water parcels change between different streamlines must also influence dispersion. This probability must be related to the turbulent diffusivity perpendicular to the flow, that is, to vertical and lateral diffusion. At this point it is essential to know whether the lateral and vertical extension of the system is finite or whether the flow is virtually unlimited. For the former (a situation typical for river flow), the dispersion coefficient is proportional to (vx )2 ... 

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