Turbulent flow conditions

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Under turbulent flow conditions, the Sauter mean diameter from two static mixers can be obtained from the following ... 

M ass Transfer. Exhaust gas catalytic treatment depends on the efficient contact of the exhaust gas and the catalyst. During the initial seconds after start of the engine, hot gases from the exhaust valve of the engine pass through the exhaust manifold and encounter the catalytic converter. Turbulent flow conditions (Reynolds numbers above 2000) exist in response to the exhaust stroke of each cylinder (about 6 to 25 times per second) times the number of cylinders. However, laminar flow conditions are reached a short (- 0.6 cm) distance after entering the cell passages of the honeycomb (5,49—52). 

Figure 5-17. Power consumption by impeller type/dimensions for turbulent flow conditions. Knowing impeller type, diameter, speed and batch density connect RPM with diameter. The Intersection with A, connected to the density scale, makes an intersection on B. A line from this point to the impeller scale intersects the horsepower scale at the correct value. By permission, Quillen, C. S., Chem. Engr., June 1954, p. 177 [15].

The better mixing occurs under turbulent flow conditions. 

Figure 10-67B. Correlation of McAdams representing the condensing film coefficient on the outside of vertical tubes, integrated for the entire tube length. This represents the streamline transition and turbulent flow conditions for Prandtl numbers 1 and 5. Do not extrapolate Prandtl numbers, Pr beyond 5. (Used by permission Engineering Data Book II 1984, Wolverine Tube, Inc.)...

Donohue reports agreement of 36% in turbulent flow conditions. 

When it is necessary to estimate the pressure drop in a pipeline where turbulent flow conditions exist, the following formula will give an approximation ... 

Very rapid and highly localised pitting is sometimes observed on components exposed to very turbulent flow conditions leading to cavitation in the stream. In general, these conditions appear to induce corrosion rather than erosion on cast iron surfaces, in contradistinction to what usually happens with other metals, apparently because the erosive component of the liquid flow scours away corrosion-stifling films and allows the development of very active electrochemical cells on the exposed metal surfaces . 

Wire form measured elements tends to suffer corrosion fatigue close to the points where it enters the support. This is particularly true in turbulent-flow conditions, and strip-type elements are preferred in such cases. 

So far as possible, components that operate in highly turbulent-flow conditions should be designed with a view to eliminating cavitation and/or impingement erosion attack. 

The calculation of heat transfer film coefficients in an air-lift bioreactor is more complex, as small reactors may operate under laminar flow conditions whereas large-scale vessels operate under turbulent flow conditions. It has been found that under laminar flow conditions, the fermentation broths show non-Newtonian behaviour, so the heat transfer coefficient can be evaluated with a modified form of the equation known as the Graetz-Leveque equation 9... 

If a gas is pumped under turbulent flow conditions from a reservoir at a pressure P to a second reservoir at a higher pressure P2 through a uniform pipe of cross-sectional area A by means of a pump situated at the upstream end, the power required is ... 

To avoid gas-liquid mass transfer Hmitation, which would have a negative influence on productivity, in correctly operated bioreactors there are turbulent flow conditions with more or less pronounced turbulence, for which the Reynolds stress formula (Eq. (2)) can be used. Whereas, as a rule there is fully developed turbulent flow in technical apparatuses (see condition (6) and explanations in Sect. 8), this is frequently not the case in laboratory fermenters. Equations (3) and (4) are then only valid to a limited extent. 

Many results with model systems and also biological particle systems indicate that the stress in technical bioreactors, in which turbulent flow conditions exist, could not be simulated by model studies in small bioreactors, where no fully turbulent flow exists, and especially with laminar flow devices such as viscosimeters, tubes or channels. 

Fig. 9. Sustained damage in Morinda citrifolia [54,59] and Damns carota [57] suspensions, as a function of total energy expended under turbulent flow conditions in capillary [54], jet [59] and viscometric devices [57]...

GP 10] [R 18]The best HCN yield of 31% at a p-gauze platinum catalyst (70 ml h methane 70 ml h ammonia 500 ml h air 1 bar 963 °C) is much better than the performance of monoliths (Figure 3.49) having similar laminar flow conditions [2]. A coiled strip and a straight-channel monolith have yields of 4 and 16%, respectively. The micro-reactor performance is not much below the best yield gained in a monolith operated under turbulent-flow conditions (38%). 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

By comparison of Eqs. (13-19) and (13-20), it is evident that the permeability is identical to the term in brackets in Eq. (13-20), which shows how the permeability is related to the equivalent particle size and porosity of the medium. Since Eq. (13-20) applies only for laminar flow, it is evident that the permeability has no meaning under turbulent flow conditions. 

In comparison with the large amount of literature that is available on the deposition of particles from laminar fluid flows, literature on turbulent deposition is virtually non-existant [114]. It was mentioned that the trajectory and convective diffusion equations also apply when the fluid inertial effects are considered, including the case of turbulent flow conditions, provided one is able to express the fluid velocities explicitly as a function of position and time. 

Since turbulent fluctuations not only occur in the velocity (and pressure) field but also in species concentrations and temperature, the convection diffusion equations for heat and species transport under turbulent-flow conditions also comprise cross-correlation terms, obtained by properly averaging products of... 

In view of secondary nucleation in crystallizers, Ten Cate et al. (2004) were interested in finding out locally about the frequencies of particle collisions in a suspension under the action of the turbulence of the liquid. To this end, they performed a DNS of a particle suspension in a periodic box subject to forced turbulent-flow conditions. In their DNS, the flow field around and between the interacting and colliding particles is fully resolved, while the particles are allowed to rotate in response to the surrounding turbulent-flow field. 

DNS simulations delivering fully resolved transient fields of velocities and other variables in either a flow domain of limited size under laminar or very moderately turbulent flow conditions or in a periodic box with some prescribed turbulence level ... 

LES with some model of the SGS flow and transport phenomena, suited for reproducing—at the level of the grid cell size—rather detailed transient fields of velocities and other transport variables in full-scale process equipment operated under turbulent-flow conditions. 

Another approach is increasing throughput via a monolith analytical column. Vintiloiu et al. (2005) used a self-made RAM online SPE under turbulent flow conditions to measure rofecoxib, a cyclooxygenase-2 inhibitor, in rat plasma. They constructed a cartridge (0.76 x 50 mm) packed with LiChrosphere 60 RP-18 ADS particles (40 to 63 /an, Merck KgaA). The analytical column was a Chromolith Speed ROD (RP-18, 50 x 4.6 mm, Merck KgaA). The injection volume was... 

At high OC1- concentrations, high temperature and high turbulent flow conditions, reduction of the CIO- becomes important. 

Boundary Layer. There exists a quiescent boundary layer through which the organotin species must diffuse before being carried by the sea water flow past the surface of the coating. The boundary layer under laminar flow conditions and under turbulent flow conditions are quantitatively defined (9) the thickness of the layer (L) decreases as the fluid velocity increases. 

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