Turbulent motion model

This stochastic model is in fact one type of turbulent motion model. For the uni-vocity problem, we consider that a gas element can be influenced by any type of elementary process after its insertion into the MWPB at x = 0. The permanent velocity Wg, pushes the gas element outside the bed at x = H and through any of the elementary processes. The presented model can be completed by considering the different frequencies induced by passing from one elementary process to another ... 

Examination of Eq. (22) shows that the R, equations contain a pressure-strain-rate correlation term that vanishes in the contraction [Eq. (23)]. The effect of this term must therefore be to transfer energy conservatively between the three components Rn, R22, and R33, and it is generally believed that this transfer tends to produce isotropy in the turbulent motions. Modelings of this term should incorporate this feature. A plausible model of this term, supported somewhat by the data of Champagne et al. (C4) is... 

The blast resulting from the remaining unconfined and unobstructed parts of a cloud can be modeled by assuming a low initial strength. For extended and quiescent parts, assume minimum strength of 1. For more nonquiescent parts, which are in low-intensity turbulent motion, for instance, beeause of the momentum of a fuel release, assume a strength of 3. 

Dreybrodt W, Buhmann D. A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion. Chem Geol 1991 107-122. 

In addition to phase change and pyrolysis, mixing between fuel and oxidizer by turbulent motion and molecular diffusion is required to sustain continuous combustion. Turbulence and chemistry interaction is a key issue in virtually all practical combustion processes. The modeling and computational issues involved in these aspects have been covered well in the literature [15, 20-22]. An important factor in the selection of sub-models is computational tractability, which means that the differential or other equations needed to describe a submodel should not be so computationally intensive as to preclude their practical application in three-dimensional Navier-Stokes calculations. In virtually all practical flow field calculations, engineering approximations are required to make the computation tractable. 

A model of transfer within an oscillating droplet was proposed by Handlos and Baron (H3). They assumed that transfer within the drop was entirely by turbulent motion, random radial movement, superimposed upon toroidal circulation streamlines. No allowance was made for the variation of shape or... 

Third, turbulent transport is represented as a succession of simple laminar flows. If the boundary is a solid wall, then one considers that elements of liquid proceed short distances along the wall in laminar motion, after which they dissolve into the bulk and are replaced by other elements, and so on. The path length and initial velocity in the laminar motion are determined by dimensional scaling. For a liquid-fluid interface, a roll cell model is employed for turbulent motion as well as for interfacial turbulence. 

The transport equations for laminar motion can be formulated, in general, easily and difficulties may lie only in their solution. On the other hand, for turbulent motion the formulation of the basic equations for the time-averaged local quantities constitutes a major physical difficulty. In recent developments, one considers that turbulence (chaos) is predictable from the time-dependent transport equations. However, this point of view is beyond the scope of the present treatment. For the present, some simple procedures based on physical models and scaling will be employed to obtain useful results concerning turbulent heat or mass transfer. 

The point of view based on a physical model started with the 1935 paper of Higbie [30], While the main problem treated by Higbie was that of the mass transfer from a bubble to a liquid, it appears that he had recognized the utility of his representation for both packed beds and turbulent motion. The basic idea is that an element of liquid remains in contact with the other phase for a time A and during this time, absorption takes place in that element as in the unsteady diffusion in a semiinfinite solid. The mass transfer coefficient k should therefore depend on the diffusion coefficient D and on the time A. Dimensional analysis leads in this case to the expression... 

The mathematics of the wall boundary model slightly changes if the media on either side of the interface are different. As an example, consider the volatilization of a dissolved chemical into the well-mixed atmosphere from a shallow puddle of water in which advective and turbulent motion is completely suppressed. Another example is the transport between a solid phase and a turbulent water body. 

The first group of models ( eddy models) assumes that the liquid renewal is due to small-scale eddies of the turbulent field. These models are based on idealized eddy structures of turbulence in the bubble vicinity. Lamont and Scott [1] have assumed that the small scales of turbulent motion, which extend from the smallest viscous motions to the iner-... 

The dissipation term can be modeled by considering the work done against the drag force on a fluid lump as it moves with the turbulent motion [22]. Now, if a body has a characteristic size, R, and is moving with velocity, V, relative to a fluid,... 

The third level of combustion simulations is direct numerical simulations (DNS) where the full instantaneous Navier-Stokes equations are solved without any model for turbulent motions all turbulence scales are explicitly determined and their effects on combustion are captured. DNS would predict all time variations of temperature (Fig. 7.4) exactly like a high-resolution sensor would measure them in an experi-... 

Another approach that has promise for study of turbulence structure is the fluctuating velocity field (FVF) closure, adopted by Deardorff (D3). Using the analog of a MVF closure for turbulent motions of smaller scale than his computational mesh, Deardorff carried out a three-dimensional unsteady solution of Navier-Stokes equations, thereby calculating the structure of the larger-scale eddy motions. While it is likely that calculations of such complexity will remain beyond the reach of most for some time to come, results like Deardorff s should serve as guides for framing closure models. 

A large proportion of the models of Reynolds stress use an eddy viscosity hypothesis based on an analogy between molecular and turbulent motions. Accordingly, turbulent eddies are visualized as molecules, colliding and exchanging momentum and obeying laws similar to the kinetic theory of gases. This allows the description of Reynolds stresses ... 

Turbulent motions are irregular and seemingly unpredictable. This is the most spectacular characteristic which distinguishes turbulent flows from laminar flows. The first scientific study of turbulence, performed by Reynolds [126], relates to this difference. Reynolds did study flows through pipes of constant diameter and by using the method of color bands clearly established that there are two fundamentally different flow regimes, laminar and turbulent flows. Reynolds also determined the conditions under which transition took place. This is now described in terms of the critical Reynolds number. The Reynolds number used in modeling fluid flow is thus named after him. 

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