Turbulence stream

If this reaction were in a turbulent flow, excess oxidizer will be present due to the unmixedness of the fuel and oxygen in the turbulent stream. Hence, r will effectively be larger for a turbulent reaction than the molecular chemical constraint.)... 

When a fluid flows past a solid surface, the velocity of the fluid in contact with the wall is zero, as must be the case if the fluid is to be treated as a continuum. If the velocity at the solid boundary were not zero, the velocity gradient there would be infinite and by Newton s law of viscosity, equation 1.44, the shear stress would have to be infinite. If a turbulent stream of fluid flows past an isolated surface, such as an aircraft wing in a large wind tunnel, the velocity of the fluid is zero at the surface but rises with increasing distance from the surface and eventually approaches the velocity of the bulk of the stream. It is found that almost all the change in velocity occurs in a very thin layer of fluid adjacent to the solid surface ... 

Eddies are turbulent instabilities within a flow region (Fig. 2). These vortices might already be present in a turbulent stream or can be generated downstream by an object presenting an obstacle to the flow. The latter turbulence is known as Karman vortex streets. Eddies can contribute a considerable increase of mass transfer in the dissolution process under turbulent conditions and may occur in the GI tract as a result of short bursts of intense propagated motor activity and flow gushes. ... 

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... 

If the drop is exposed to a turbulent stream of air the diffusion coefficient in Eq. (5) must be modified by multiplication by the calculated correction factor [1 + h where the second term in the bracket... 

In the consideration of the statistical aspects of turbulence it was found to be of utility (B6, K4, Rl) to establish the correlation in time (B6) of the velocity vectors as a function of the distance between two points in the turbulent stream. The correlation coefficient is defined by... 

Figure 4 depicts the variation of the root-mean-square longitudinal fluctuation as a function of position in a floiving stream. These data were taken from the recent experimental investigation by Laufer (L3) and illustrate the complexity of behavior encountered in a steady, uniformly flowing turbulent stream. It is to be expected that fluctuations of temperature and composition are encountered in turbulent streams involving thermal or material transport. 

In predicting convective thermal transport to turbulent streams it has usually been sufficient to determine the corresponding thermal flux at the boundary for a specified area. Such methods have been refined by many workers and ably summarized by McAdams (Ml) and Jakob (Jl). 

In Eq. (32) the subscript 1 refers to the location of the transition between the boundary flow and the turbulent stream. It appears that these analytical considerations by Deissler represent improvements over his earlier approach (D2). For the boundary flow close to the wall the foregoing expressions are based on the assumption that the eddy properties may be evaluated from... 

Little detailed experimental information is available on the value of eddy transport properties under conditions of simultaneous thermal and material transport. If it is assumed that the Reynolds analogy is applicable, it follows that the eddy diffusivity and eddy conductivity are equal and independent of cross linking. Such an assumption is probably not true since it is to be expected that a substantial part of the eddy transport is associated with molecular transport particularly as the eddies become small in accordance with Kolmogoroff s (K10) principle. For this reason it is to be expected that temperature gradients in turbulent streams will influence to some extent the material transport in the same... 

Fig. 10.14 Chemical plume of red dye spreading in turbulent stream. Highlighted sensors from the array are positioned downstream from the nozzle at distances LI and L2. They are selected for correlation analysis...

Besides a three-way cock, other devices can also be used for mixing, for example a cone feeder with tangential reaction stream feed, a vessel equipped with disks rotating on their axes, a cylinder into which the initial components are fed turbulently, and various tubes for producing turbulent streams, etc. 

Continuous water irradiation by e-beam is conducted on a bench scale at the Austrian Research Center, Seibersdorf. A 500-keV, 25-mA ICT accelerator (Vivirad-Eligh Voltage Corp.) is used as the electron source [52]. A 3-mm horizontal layer of water is irradiated. Low penetration by the lower energy electrons produced by this smaller accelerator is compensated for by irradiating a turbulent water flow. Dose distribution in the turbulent stream is not uniform, but the overall volume of water treated to an average dose is increased. A schematic of the system is shown in Fig. 5. 

The micromixing state in an agitated vessel is connected with coalescence of bubbles. Coalescence occurs mainly in the stirrer zone, where the recirculated gas bubbles partially mix with fresh gas in the cavities. It also occurs to a lesser extent in the highly turbulent stream leaving the stirrer, but it is virtually absent in other parts of the vessel because the low kinetic energy of the bubbles cannot stretch out the liquid film between a pair of bubbles to reach the coalescence thickness. 

The fluid particle fragmentation phenomena in a highly turbulent flow are related to the fact that the velocity in a turbulent stream varies from one point to another (i.e., validated by two-point measurements [99]). Therefore, different dynamic normal stresses will be exerted at different points on the surface of the fluid particle. Under certain conditions, this will inevitably lead to deformation and breakage of the fluid particle. 

Although particulates that are predominantly clay mineral in content are important attenuators of UVR in turbulent streams and rivers, dissolved and particulate organic substances largely control the penetration of UV into most lakes and the sea. Hence, this discussion of the carbon cycle begins with a discussion of the interactions of U V with CDOM, with emphasis on the optical properties of aquatic ecosystems and penetration of solar UVR into the water (see also Chapters 3 and 6). 

Equation of mass and heat transfer. In mathematically describing transfer of a passive admixture in a turbulent stream, the admixture concentration and the fluid velocity components are represented as... 

Temperature profile. Let us discuss qualitative specific features of convective heat and mass transfer in turbulent flow past a flat plate. Experimental evidence indicates that several characteristic regions with different temperature profiles can be distinguished in the thermal boundary layer on a flat plate. At moderate Prandtl numbers (0.5 < Pr < 2.0), it can be assumed for rough estimates that the characteristic sizes of these regions are of the same order of magnitude as those of the wall layer and the core of the turbulent stream, see Section 1.7. 

The turbulent boundary layer model accounts for the transfer of a solute molecule A from a turbulent stream to a fixed surface. Eddy diffusion is rapid in the turbulent stream and molecular diffusion is relatively insignificant. It is supposed that the turbulence is damped out in the immediate vicinity of the surface. In the intermediate neighborhood between the turbulent stream and the fixed surface, it is supposed that transport is by both molecular and eddy diffusion which take place in parallel. The total rate of transfer (moles of A transferred per unit time per unit area) is given by an extended form of Fick s law... 

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