Mechanical turbulent flow

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

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. 

Several texts are available for further reading on turbulent flow, including Tennekus and Lumley (ibid.), Hinze (Turbulence, McGraw-HiU, New York, 1975), Landau and Lifshitz (Fluid Mechanics, 2d ed.. Chap. 3, Pergamon, Oxford, 1987) and Panton (Jncompressible Flow, Wiley, New York, 1984). 

Visually, the sites resemble mechanically induced gouges or indentions in the tube wall. However, examinations of the microstructure at these sites revealed no distortion of the metal, which would certainly occur had the indentions been mechanically induced. The erosive character of the highly localized turbulent flow was the predominant aspect responsible for the metal loss, there being little or perhaps no contribution from corrosion of the metal. 

Davidson, L. Numerical simulation of turbulent flow in ventilated rooms. Ph.D. thcsi.s, Dept, of Applied Thermodynamics and Fluid Mechanics, Chalmers University of Technology, Goth enburg, 1989. 

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods e.g., SIMPLE (Patankar 1980) SOLA-ICE (Cloutman et al. 1976). 

X(( = Correlation parameter, dimensionless (tt refers to the turbulent-turbulent flow mechanism)... 

X = correlating parameter, dimensionless for turbulent-turbulent flow mechanism, Eigure Rf ... 

Power is defined for a well-agitated vessel with a mechanical stirrer then read power number for turbulent flow from Figure 6.6, Chapter 6 ... 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

Fig. 64. Possible molecular stretching mechanism between region A and B in turbulent flow (sketched according to Ref. [185])...

The mechanism of suspension is related to the type of flow pattern obtained. Suspended types of flow are usually attributable to dispersion of the particles by the action of the turbulent eddies in the fluid. In turbulent flow, the vertical component of the eddy velocity will lie between one-seventh and one-fifth of the forward velocity of the fluid and, if this is more than the terminal falling velocity of the particles, they will tend to be supported in the fluid. In practice it is found that this mechanism is not as effective as might be thought because there is a tendency for the particles to damp out the eddy currents. 

The wall superheat that corresponds to bubble formation in liquid flow can be estimated using an approach that is not connected to the mechanism of bubble formation. Such tentative estimation makes it possible to consider only the low level of wall superheat. According to Kays and Krawford (1993) the temperature distribution in turbulent flow and Pr 1 is... 

P. Clavin and F.A. Williams. Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. Journal of Fluid Mechanics, 116 251-282,1982. 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

Many experimental results have been published, which deal with shear stress in biological systems. Most of them use laminar flow systems such as viscosimeters, flow channels or flasks and very small agitated vessels which are not relevant to technical reactor systems with fully developed turbulent flow. On the other hand the geometric and technical parameters are often not sufficiently described. Therefore it is not possible to explain the complex mechanism of force in bioreactors only on the basis of existing results from biological systems. 

Cherry and Papoutsakis [33] refer to the exposure to the collision between microcarriers and influence of turbulent eddies. Three different flow regions were defined bulk turbulent flow, bulk laminar flow and boundary-layer flow. They postulate the primary mechanism coming from direct interactions between microcarriers and turbulent eddies. Microcarriers are small beads of several hundred micrometers diameter. Eddies of the size of the microcarrier or smaller may cause high shear stresses on the cells. The size of the smallest eddies can be estimated by the Kolmogorov length scale L, as given by... 

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