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Fluctuations, turbulent

The quantity k is related to the intensity of the turbulent fluctuations in the three directions, k = 0.5 u u. Equation 41 is derived from the Navier-Stokes equations and relates the rate of change of k to the advective transport by the mean motion, turbulent transport by diffusion, generation by interaction of turbulent stresses and mean velocity gradients, and destmction by the dissipation S. One-equation models retain an algebraic length scale, which is dependent only on local parameters. The Kohnogorov-Prandtl model (21) is a one-dimensional model in which the eddy viscosity is given by... [Pg.102]

Measurement by Thermal Effects. When a fine wire heated electrically is exposed to a flowing gas, it is cooled and its resistance is changed. The hot-wire anemometer makes use of this principle to measure both the average velocity and the turbulent fluctuations in the flowing stream. The fluid velocity, L, is related to the current, /, and the resistances, R, of the wire at wire, and gas, g, temperatures via... [Pg.110]

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). [Pg.514]

The fundamental principle of Hquid disiategration Hes ia the balance between dismptive and cohesive forces. The common dismptive forces ia atomizer systems iaclude kinetic energy, turbulent fluctuation, pressure fluctuation, iaterface shearing, friction, and gravity. The cohesive forces within the Hquid are molecular bonding, viscosity, and surface tension. [Pg.329]

The manifestation of turbulent eddies is gustiness and is displayed in the fluctuations seen on a continuous record of wind or temperature. Figure 19-3 displays wind direction traces during (a) mechanical and (b) thermal turbulence. Fluctuations due to mechanical turbulence tend to be quite regular that is, eddies of nearly constant size are generated. The eddies generated by thermal turbulence are both larger and more variable in size than those due to mechanical turbulence. [Pg.294]

The probability density function of u is shown for four points in Fig. 11.16, two points in the wall jet and two points in the boundary layer close to the floor. For the points in the wall jet (Fig. 11.16<2) the probability (unction shows a preferred value of u showing that the flow has a well-defined mean velocity and that the velocity is fluctuating around this mean value. Close to the floor near the separation at x/H = I (Fig. 11.16f ) it is hard to find any preferred value of u, which shows that the flow is irregular and unstable with no well-defined mean velocity and large turbulent intensity. From Figs. 11.15 and 11.16 we can see that LES gives us information about the nature of the turbulent fluctuations that can be important for thermal comfort. This type of information is not available from traditional CFD using models. [Pg.1049]

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... [Pg.138]

Embedded in such models, in which variations were developed [12] are further detailed. The laminar burning velocity is expressed as a function of fuel type, fuel/ air ratio, level of exhaust gas recirculation, pressure, temperature, etc. Furthermore, submodels have been developed to describe the impact of engine speed, port-flow control systems, in-cylinder gross-flow motion (i.e., swirl, tumble, squish), and turbulent fluctuations u. Thus, with a wider knowledge base of the parametric impact of external variables, successful modeling of... [Pg.180]

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. [Pg.342]

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... [Pg.347]

In the velocity field of the determining eddies, which is characterized by the turbulent fluctuation velocity the particles experience a dynamic stress according to the Reynolds stress Eq. (2) ... [Pg.39]

In order to use Eqs. (3) and (4) or the data given in Fig. 1, for the calculation of maximum turbulent fluctuation velocity the maximum energy dissipation e , must be known. With fully developed turbulence and defined reactor geometry, this is a fixed value and directly proportional to the mean mass-related power input = P/pV, so that the ratio ,/ can be described as an exclusive function of reactor geometry. In the following, therefore details will be provided on the calculation of power P and where available the geometric function ,/ . [Pg.43]

The turbulent fluctuation frequency can be estimated by means of turbulent measurements. Mockel 124] found that the wave number k = 2Tlft/u in the interesting dissipation range is k>ko with the limiting value ko= (0.1. ..0.2)qL-From this becomes the frequency to ft> (0.016...0.032)u/qL. An important measure should be the related number of turbulent fluctuation z/zp which occur during the residence time of particles ti=Vi/qp inside the fictive impeller volume Vj at one circulation. It follows to ... [Pg.75]

Figure 5.135. Time-variant turbulent fluctuations of concentration about a mean value C, showing the fluctuation value C, ... Figure 5.135. Time-variant turbulent fluctuations of concentration about a mean value C, showing the fluctuation value C, ...
D Intermittent to dispersed bubble Turbulent fluctuations versus buoyancy forces... [Pg.160]

Chemical engineers, however, have to find practical ways for dealing with turbulent flows in flow devices of complex geometry. It is their job to exploit practical tools and find practical solutions, as spatial variations in turbulence properties usually are highly relevant to the operations carried out in their process equipment. Very often, the effects of turbulent fluctuations and their spatial variations on these operations are even crucial. The classical toolbox of chemical engineers falls short in dealing with these fluctuations and its effects. Computational Fluid Dynamics (CFD) techniques offer a promising alternative approach. [Pg.155]

The focus of RANS simulations is on the time-averaged flow behavior of turbulent flows. Yet, all turbulent eddies do contribute to redistributing momentum within the flow domain and by doing so make up the inherently transient character of a turbulent-flow field. In RANS, these effects of the full range of eddies are made visible via the so-called Reynolds decomposition of the NS equations (see, e.g., Tennekes and Lumley, 1972, or Rodi, 1984) of the flow variables into mean and fluctuating components. To this end, a clear distinction is required between the temporal and spatial scales of the mean flow on the one hand and those associated with the turbulent fluctuations on the other hand. [Pg.163]

In real life, the parcels or blobs are also subjected to the turbulent fluctuations not resolved in the simulation. Depending on the type of simulation (DNS, LES, or RANS), the wide range of eddies of the turbulent-fluid-flow field is not necessarily calculated completely. Parcels released in a LES flow field feel both the resolved part of the fluid motion and the unresolved SGS part that, at best, is known in statistical terms only. It is desirable that the forces exerted by the fluid flow on the particles are dominated by the known, resolved part of the flow field. This issue is discussed in greater detail in the next section in the context of tracking real particles. With a RANS simulation, the turbulent velocity fluctuations remaining unresolved completely, the effect of the turbulence on the tracks is to be mimicked by some stochastic model. As a result, particle tracking in a RANS context produces less realistic results than in an LES-based flow field. [Pg.166]

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... [Pg.166]

Of course, the role of the artificially introduced stochastics for mimicking the effect of all eddies in a RANS-based particle tracking is much more pronounced than that for mimicking the effect of just the SGS eddies in a LES-based tracking procedure. In addition, the random variations may suffer from lacking the spatial or temporal correlations the turbulent fluctuations exhibit in real life. In RANS-based simulations, these correlations are not contained in the steady spatial distributions of k and e and (if applicable) the Reynolds stresses from which a typical turbulent time scale such as k/s may be derived. One may try and cure the problem of missing the temporal coherence in the velocity fluctuations by picking a new random value for the fluid s velocity only after a certain period of time has lapsed. [Pg.168]

All these findings of disappointing quantitative agreement with experimental data stem from the inherent drawback of the RANS-approach that there is no clear distinction between the turbulent fluctuations modeled by the Reynolds stresses and (mesoscale) fluctuations. In LES, however, the distinction between resolved and unresolved turbulence is clear and relates to the cell size of the computational grid chosen. [Pg.191]

CFD models for turbulent multiphase reacting flows do not solve the laminar two-fluid balances (Eqs. 164 and 165) directly. First, Reynolds averaging is applied to eliminate the large-scale turbulent fluctuations. Using Eq. (164) as an example, we can apply Reynolds averaging to find (with pg constant)... [Pg.297]

As the fluid s velocity must be zero at the solid surface, the velocity fluctuations must be zero there. In the region very close to the solid boundary, ie the viscous sublayer, the velocity fluctuations are very small and the shear stress is almost entirely the viscous stress. Similarly, transport of heat and mass is due to molecular processes, the turbulent contribution being negligible. In contrast, in the outer part of the turbulent boundary layer turbulent fluctuations are dominant, as they are in the free stream outside the boundary layer. In the buffer or generation zone, turbulent and molecular processes are of comparable importance. [Pg.66]

In some practical processes, a high relative velocity may not exist and effects of turbulence on droplet breakup may become dominant. In such situations Kolmogorov, 280 and Hinze[27°l hypothesized that the turbulent fluctuations are responsible for droplet breakup, and the dynamic pressure forces of the turbulent motion determine the maximum stable droplet size. Using Clay s data, 2811 and assuming isotropic turbulence, an expression was derived for the critical Weber number 270 ... [Pg.176]

Under noncoalescing conditions, the size of gas bubbles in gas-liquid dispersions can be obtained by balancing the surface-tension forces with those due to turbulent fluctuations, which results in (C3, H3) ... [Pg.354]


See other pages where Fluctuations, turbulent is mentioned: [Pg.107]    [Pg.110]    [Pg.671]    [Pg.672]    [Pg.1177]    [Pg.1209]    [Pg.157]    [Pg.157]    [Pg.158]    [Pg.37]    [Pg.39]    [Pg.39]    [Pg.164]    [Pg.156]    [Pg.165]    [Pg.210]    [Pg.317]    [Pg.66]    [Pg.90]    [Pg.332]    [Pg.333]    [Pg.102]    [Pg.104]    [Pg.422]   
See also in sourсe #XX -- [ Pg.395 ]

See also in sourсe #XX -- [ Pg.446 ]




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Mean square fluctuation turbulence

Pseudo-turbulent fluctuations

Time-Smoothed Fluctuating Advective Turbulent Flux

Turbulence frequency fluctuating

Turbulent diffusivity fluctuations

Turbulent dissipation rate fluctuating

Turbulent velocity fluctuations

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