Turbulent degree, measure

Second, the cross-shore variation of the degree of sediment suspension is estimated using the experimental finding of Kobayashi et aZ. who showed that the turbulent velocities measured in the vicinity of the bottom were related to the energy dissipation rate due to bottom friction. Representing the magnitude of the instantaneous turbulent velocity by with D f = O.Sp/ftt/f in light of... 

Its first invariant A] is equal to zero by definition. The second and third invariants of this tensor arc A — atJaJt and A3 — atjajkakt, respectively. The range of physically allowed values of A2 and A3 is bounded and represented by the so-called Lumley triangle in the (A3, A2) plane (Lumley, 1978). The distanced = (Ay + Af) from the isotropic state, i.e., from the origin (A2 — 0, A3 — 0), is a measure of the degree of anisotropy. See also Escudie and Line (2006) for a more extensive discussion as to how to quantify and visualize how different from isotropic turbulence a stirred vessel is. 

The degree of local mixing in a RANS simulation is measured by the scalar variance (complete mixing (i.e., (j> — (j>) is uniform at the SGS) up to (4>max — (4>))((4>) — 4>min) where () is the mean concentration and max and r/>min are the maximum and minimum values, respectively. The rate of local mixing is controlled by the scalar dissipation rate (Fox, 2003). The scalar time scale analogous to the turbulence integral time scale is (Fox, 2003) as follows ... 

Second, due to the difficulty of accessing multiphase flows with laser-based flow diagnostics, there is very little experimental data available for validating multiphase turbulence models to the same degree as done in single-phase turbulent flows. For example, thanks to detailed experimental measurements of turbulence statistics, there are many cases for which the single-phase k- model is known to yield poor predictions. Nevertheless, in many CFD codes a multiphase k-e model is used to supply multiphase turbulence statistics that cannot be measured experimentally. Thus, even if a particular multiphase turbulent flow could be adequately described using an effective viscosity, in most cases it is impossible to know whether the multiphase turbulence model predicts reasonable values for... 

There are many ways of categorizing air quality models. One differentiation is between statistical and deterministic models. The structure of statistical models is based on the patterns that appear in the extensive measured data. The structure of deterministic models is based on mechanistic principles wherever possible. Most deterministic models contain some degree of empiricism. For example, few models, if any, use turbulent-diffiision formulations that are based on first principles, but rather use measured values of dispersion. The same is true in regard... 

When a low viscous solvent must be used in combination with a rather low molecular weight of the polymer, measurements are restricted to low /3-values, due to the discussed onset of turbulent flow. As in such a case the extinction angle % does not deviate very much from 45 degrees within the regime of laminar flow, it must be measured with a high absolute accuracy to furnish a reliable value for cos 2% or cot 2% [cf. eq. (3.42) or (3.44a)]. Measurements on a polydisperse sample become more reliable under such conditions due to the fact that cot 2 is increased by the polydispersity factor [eqs. (3.75a) and (3.83a)]. Examples for such a behaviour will be discussed in Section 3.8.3. 

The heat transfer to supercritical carbon dioxide was measured in horizontal, vertical and inclined tubes at constant wall temperature for turbulent flow at Re-numbers between 2300 and lxl 05. The influence of the variation of physical properties due to the vicinity of the critical point was examined, as well as the influence of the direction of flow. Therefore most of the measurements were conducted at pseudocritical points. At those supercritical points the behaviour of the physical properties is similar to the behaviour at the critical point, but to a lesser degree. At such points the heat capacity shows a maximum density, viscosity and heat conductivity are changing very fast. [1]... 

Brodkey [56] stated that only with the advent of the modem turbulence theory a deep understanding of micro-mixing processes and turbulent scalar transfer processes on a microscopic level was possible and that this theory enabled the definition of measurable mixing criteria. Knowledge of the turbulence parameter made it possible to estimate the degree of mixing. The parameters could be estimated from the geometry of the flow system and from simple empirical expressions. The... 

---