Turbulent condition

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Dimensionless pumping number and blend time are independent of Reynolds number under fully turbulent conditions. The magnitude of concentration fluctuations from the final well-mixed value in batch mixing decays exponentially with time. 

Table 1. Relations Between Turbulent Conditions and the Weather.

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

The consequence of the second approach is that, if detonation of unconfined parts of a vapor cloud can be ruled out, the cloud s explosive potential is not primarily determined by the fuel-air mixture in itself, but instead by the nature of the fuel-release environment. The multienergy model is based on the concept that explosive combustion can develop only in an intensely turbulent mixture or in obstructed and/or partially confined areas of the cloud. Hence, a vapor cloud explosion is modeled as a number of subexplosions corresponding to the number of areas within the cloud which bum under intensely turbulent conditions. 

An important aspect of Clark s technology was that the oil being cracked, which flowed through the tubes and in a near vapor state, was maintained in a continually dynamic or turbulent condition. This meant that the coke particles which formed were prevented from... 

The basis for single-phase and some two-phase friction loss (pressure drop) for fluid flow follows the Darcy and Fanning concepts. The exact transition from laminar or dscous flow to the turbulent condition is variously identified as between a Reynolds number of 2000 and 4000. 

To recheck final design, the diameter of a single, pitched blade turbine, for turbulent conditions ... 

Dj = Diameter of single pitch blade turbine, under turbulent conditions, in,... 

As regards valves, diaphragm types are the most satisfactory but most valves have to withstand extremely turbulent conditions, and as with pumps, even the best designs need to be constructed of resistant materials, or be coated with a suitably durable material such as silastomer or neoprene. 

Ya.B. ZeFdovich, FizGoreniyaVzryva 7 (4), 463-76 (1971) CA 77, 64194 (1972) The influence of turbulence and nonturbulence is examined relative to a proplnt burning in a gas flow. Equations indicate exptl methods for determining the magnitudes of the thermal conductivity and viscosity under turbulent flow, and permit a study of thermal flow distribution and temps in a gas wherein an exothermic chem reaction occurs. Equations for non turbulent conditions can be used to calculate the distance from the surface of the proplnt to the zone of intense chem reaction and establish the relation of bulk burning rate to the vol reaction rate. 

If gas flows under turbulent conditions from a reservoir at a pressure P, through a horizontal nozzle, the velocity of flow M2. at the pressure Pi is given by ... 

For a fluid flowing under turbulent conditions in a pipe, = 0 and ... 

A reaction is to be carried out in an agitated vessel. Pilot scale tests have been carried out under fully turbulent conditions in a tank 0.6 m in diameter, fitted with baffles and provided with a flat-bladed turbine, and it has been found that satisfactory mixing is obtained at a rotor speed of 4 Hz when the power consumption is 0.15 kW and the Reynolds number 160,000. What should be the rotor speed in order to achieve the same degree of mixing if the linear scale of the equipment if increased by a factor of 6 and what will be the Reynolds number and the power consumption ... 

Whenever possible, streamline conditions of flow are avoided in heat exchangers because of the very low heat transfer coefficients which are obtained. With very viscous liquids, however, turbulent conditions can be produced only if a very high pressure drop across the plant is permissible. In the processing industries, streamline flow in heat exchangers is most commonly experienced with heavy oils and brines at low temperatures. Since the viscosity of these materials is critically dependent on temperature, the equations would not be expected to apply with a high degree of accuracy. 

Concentric tube heat exchangers are widely used because of their simplicity of construction and the ease with which additions may be made to increase the area. They also give turbulent conditions at low volumetric flowrates. 

It was shown in the previous chapter that when a fluid flows under turbulent conditions over a surface, the flow can conveniently be divided into three regions ... 

For hydrodynamically smooth pipes, through which fluid is flowing under turbulent conditions, the shear stress is given approximately by the Blasius equation ... 

For producing an oil-water emulsion, two portable three-bladed propeller mixers are available a 0.5 m diameter impeller rotating at 1 Hz and a 0.35 m impeller rotating at 2 Hz. Assuming turbulent conditions prevail, which unit will have the lower power consumption ... 

Capillary shear tests were performed on low density (50 g fresh weight 1" ) suspensions of M. citrifolia using the apparatus illustrated in Fig. 1. Under both laminar and turbulent conditions [54,120,121], the relative viability of the suspension, evaluated using the Evan s Blue dye exclusion technique, was found to fall with exposure time in the loop. Loss of viability is well described by a first-order model ... 

Fig. 2. Variation of specific death rate with average shear stress, under laminar and turbulent conditions, in the capillary flow loop apparatus [54,121]...

The power number becomes independent on mixing at turbulent conditions, which are achieved at Reynolds numbers greater than 20,000. Typical power numbers at high Reynolds number for some common stirrer types are shown in Table 5.4.22. 

The above expression is known as the free settling ratio of the two particles (minerals) under laminar conditions. In a similar way the ratio under turbulent conditions can be obtained from Newton s law as... 

Flow and recycle rates should not be high enough to cause excessive pumping costs or loss of hydraulic containment efficiency due to turbulent conditions, corrosion, flooding, or well blow out. 

In addition to the content of ion-exchangeable calcium, other factors must be considered when the rate of accumulation is in question. In order that the precipitates be retained in reaction vessels, it is necessary that they grow to a sufficient size to preclude elution. This condition is achieved in reactor configurations where residence time is relatively long. Alternatively, if turbulent conditions prevail, as in the H-Coal reactor, the precipitates may be abraded or not allowed to grow, so that retention would be inhibited, though their formation will not be prevented. 

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