Mixing turbulent

mixing in liquids is achieved by several mechanisms which gradually reduce the size or scale of the fluid elements and then redistribute them in the bulk. If there are initially differences in concentration of a soluble material, uniformity is gradually achieved, and molecular diffusion becomes progressively more important as the element 

The net head H is primary output parameter for any turbomachine. Usually v and V2 are about the same, Z2 — 2 1 is a meter or so, and the net pump head is essentially equal to the change in pressure head  

The power draw (i.e., power transferred from the impeller to the fluid by the lift forces) will eventually dissipate to heat (through viscous dissipation in the fluid). 

According to the z-component of the linear momentum equation, the thrust force from the impeller blade is balanced by the pressure difference over the pump [83] (p 423)  

Introducing a proportionality factor, the Newton number Np), the following relation occurs  

This relation determining the dependence of power draw on fluid pumping is identical to the expression we found earlier using the torque analysis. This result should be expected as the mechanical energy balance is not independent of the momentum equations, they basically provide the same information. 

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The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

In turbulent mixing, the Hquid velocity at any point u can be considered the sum of an average velocity ul and a fluctuating (with time) velocity u ... 

The physical mass-transfer rate of o2one into water is affected by the gaseous o2one concentration, temperature, pressure, gas dispersion, turbulence, mixing, and composition of the solution, ie, pH, ionic strength, and the presence of reactive substances. Mass transfer of gaseous o2one into... 

Many organisms are exposed to some of the thermal, chemical, and physical stresses of entrainment by being mixed at the discharge with the heated water this is plume entrainment. The exact number exposed depends on the percentage of temperature decline at the discharge that is attributed to turbulent mixing rather than to radiative or evaporative cooling to the atmosphere. 

A thermal oxidizer is a chemical reactor in which the reaction is activated by heat and is characterized by a specific rate of reactant consumption. There are at least two chemical reactants, an oxidizing agent and a reducing agent. The rate of reaction is related both to the nature and to the concentration of reactants, and to the conditions of activation, ie, the temperature (activation), turbulence (mixing of reactants), and time of interaction. 

Neglecting flow nonuniformities, the contributions of molecular diffusion and turbulent mixing arising from stream sphtting and recombination around the sorbent particles can be considered additive [Langer et al., Int. ]. Heat and Mass Transfer, 21, 751 (1978)] thus, the axial dispersion coefficient is given by ... 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

TIME-DEPENDENT TURBULENT MIXING AND CHEMICAL REACTION IN STIRRED TANKS ... 

The model used here is a slightly modified version of the standard Fluent model [2]. Two possible reaetion rates are ealeulated, the kinetie reaetion rate Rj, and a seeond reaetion rate R that is eontrolled by the turbulent mixing. The kinetie reaetion rate for speeies i is ealeulated as ... 

The turbulent mixing limited reaetion rate for speeies i is ealeulated as ... 

Landi,s E, and A. H. Shapiro. 1951. The Turbulent Mixing of Coaxial Gas Jets. Heat Transfer and Fluid Mechanics Institute, Preprints and Papers. Stanford University Press, California. 

The turbulent mixing between the zones depends on the air distribution method and device. "" ... 

Skaret presents a general air and contaminant mass flow model for a space where the air volume, ventilation, filtration, and contaminant emission have been divided for both the zones and the turbulent mixing (diffusion) between the zones is included. A time-dependent behavior of the concentration in the zones with constant pollutant flow rate is presented. 

The key flow elements in the zoning strategy arc the supply air jets, plumes of the buoyancy sources, buoyant airflows along the surfaces, and turbulent mixing between the controlled and the uncontrolled zones, as in Fig. 8.32. These flow elements have significant influence on the effectiveness of the system. 

Supply air is evenly distributed into the controlled zone. The momentum of the jets is high enough to ensure the uniform conditions but also low enough to avoid mixing in the whole room— i.e., the turbulent mixing between the zones is low. This means that usually the number of inlet devices is high. 

The plume airflows (q ) are determined as described in Section 7.5. The turbulent mixing iqi,) between zones and the penetration of the plume airflows iq, h,n) through the supply airflow patterns must be determined specially for the air distribution method and devices used as well as the locations of plumes and supply air devices. 

The effect of the plume airflow rate and the turbulent mixing airflow rate through the zone boundary is presented in Fig. 8.35. The heat removal effectiveness and contaminant removal effectiveness are presented as functions of the relative airllow rate. 

Measured results of effectiveness and turbulent mixing are presented In literature by Bach (several air distribution methods) and Hagstrom et al. (mixing air distribution methods in zoning strategy).A typical example of an air distribution method and device in the zoning strategy is the so-called active displacement method, which is based on a nozzle duct device. ... 

The design of low hoods is much simpler, since the adverse effects of turbulent mixing and cross-drafts are much less important than for high hoods. Low hoods are much more likely to capture a high percentage of the heated air and contaminants than high hoods, so they should be used whenever possible. 

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. 

The type C hood performance is due to turbulent mixing within the hood, which is caused by an inappropriate hood design or by objects below the hood face. 

The fundamentals of erystallization and preeipitation are reviewed in the books of e.g. Sohnel and Garside (1992), Mersmann (2001), Mullin (2001) and Myerson (2001), respeetively, whilst Baldyga and Bourne (1999) provide a eomprehensive aeeount of turbulent mixing and eliemieal reaetions. 

Baldyga, J. and Bourne, J.R., 1984a. A fluid mechanical approach to turbulent mixing and chemical reaction. Part I Inadequacies of available methods. Chemical Engineering Communications, 28, 231-241. 

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