Turbulence frequency fluctuating

Given a stochastic model for the turbulence frequency, it is natural to enquire how fluctuations in co will affect the scalar dissipation rate (Anselmet and Antonia 1985 Antonia and Mi 1993 Anselmet et al. 1994). In order to address this question, Fox (1997) extended the SR model discussed in Section 4.6 to account for turbulence frequency fluctuations. The resulting model is called the Lagrangian spectral relaxation (LSR) model. The LSR model has essentially the same form as the SR model, but with all variables conditioned on the current and past values of the turbulence frequency [ /(. ),. v < r. In order to simplify the notation, this conditioning is denoted by ( , e.g.,... 

Pressure Fluctuation Turbulent pressure fluctuations which develop in the wake of a cylinder or are carried to the cylinder from upstream may provide a potential mechanism for tube vibration. The tubes respond to the portion of the energy spectrum that is close to their natural frequency. 

Sleiched278 has indicated that this expression is not valid for pipe flows. In pipe flows, droplet breakup is governed by surface tension forces, velocity fluctuations, pressure fluctuations, and steep velocity gradients. Sevik and Park 279 modified the hypothesis of Kolmogorov, 280 and Hinze, 270 and suggested that resonance may cause droplet breakup in turbulent flows if the characteristic turbulence frequency equals to the lowest or natural frequency mode of an... 

The algorithms discussed earlier for time averaging and local time stepping apply also to velocity, composition PDF codes. A detailed discussion on the effect of simulation parameters on spatial discretization and bias error can be found in Muradoglu et al. (2001). These authors apply a hybrid FV-PDF code for the joint PDF of velocity fluctuations, turbulence frequency, and composition to a piloted-jet flame, and show that the proposed correction algorithms virtually eliminate the bias error in mean quantities. The same code... 

The purpose of the time averaging after the volume averaging is to express averages of products in terms of products of averages and to account for turbulent fluctuations and high-frequency fluctuations [Soo, 1989]. The volume-time averaging is presented here in a similar way to that of the Reynolds analysis of single-phase turbulent flow. 

It since appears that the frequency and size of the turbulent velocity fluctuations are more compatible with phenomena on a molecular micron size scale In a mixing vessel. For example, in a publication Paul Treybal (4) shows the yield of a given reaction which had several alternate paths was determined by the RMS velocity fluctuations at the feed point. Paul used data from Schwartzberg Treybal (5) and Cutter to calculate RMS velocity at the feed point. 

Polymer drag reduction is also associated with the following turbulence observations The frequency of turbulent eddy bursts decreases as drag reduction increases the spacing between nondimensionalized fluid streaks increases as drag reduction increases high-frequency components of turbulent velocity fluctuations are attenuated while low-frequency ones are enhanced axial turbulence intensity maxima shift away from the wall radial and tangential turbulence intensities are reduced, turbulent shear stresses (Reynolds stresses) are reduced and so on. 

It is known that the structure of turbulence is altered by additives, particularly near the wall for example, the low speed streak spacing increases and the bursting frequency decreases. Moreover, velocity fluctuations in the mean flow direction become more violent, whereas the intensity of the fluctuations normal to the wall and the correlation between the two velocity fluctuations both decrease. With the help of additives the experimenter thus has a knob in hand with which he can control the structure of turbulence. In spite of this tool, it has still not been possible to better understanding of the mechanism of turbulence to the present date. On the contrary, drag reduction by additives poses additional problems. The measurement, for example, of turbulent velocity fluctuations is made much more difficult. Since the drag reduction phenomenon can only be observed when the wall shear stress measures at least about 7 N/m2 (46) measurements at small turbulent Reynolds numbers become almost impossible, and thus the region near the wall is practically inaccessible to anemometric measurements (either laser or hot film). It should therefore also prove very difficult to directly verify the existence of streamwise vortices in flows with polymer additives and thus answer the question posed by Willmarth and Bogar (42) as to whether the small-scale vortical structure near the wall is inhibited by polymer additives. 

The process of coalescence in water treating systems is more time-dependent than the process of dispersion. In a dispersion of two immiscible liquids, immediate coalescence seldom occurs when two droplets collide. If the droplet pair is exposed to turbulent pressure fluctuations, and the kinetic energy of the oscillations induced in the droplet pair is larger than the energy of adhesion between them, the contact will be broken before coalescence is completed. If the energy input into the system is too great, dispersion will occur, as discussed below. If there is no energy input, then the frequency of droplet colhsion, which is necessary to initiate coalescence, will be low, and coalescence will occur at a very low pace. 

Because of its small size and portabiHty, the hot-wire anemometer is ideally suited to measure gas velocities either continuously or on a troubleshooting basis in systems where excess pressure drop cannot be tolerated. Furnaces, smokestacks, electrostatic precipitators, and air ducts are typical areas of appHcation. Its fast response to velocity or temperature fluctuations in the surrounding gas makes it particularly useful in studying the turbulence characteristics and rapidity of mixing in gas streams. The constant current mode of operation has a wide frequency response and relatively lower noise level, provided a sufficiently small wire can be used. Where a more mgged wire is required, the constant temperature mode is employed because of its insensitivity to sensor heat capacity. In Hquids, hot-film sensors are employed instead of wires. The sensor consists of a thin metallic film mounted on the surface of a thermally and electrically insulated probe. 

With LES we get much more information than with traditional time-averaged turbulence models, since we are resolving most of the turbulence. In Fig. T1.15 the computed u velocity is shown as a function of time in two cells one cell is located in the wall jet (Fig.. 15a), and the other cell is in the middle of the room (Fig. ll.lSh). It is found the instantaneous fluctuations are very large. For example, in the region of the wall jet below the ceiling where the time-averaged velocity u)/l] ) is typically 0.5, the instantaneous velocity fluctuations are between 0.2 and 0.9. In the middle of the room, which is a low-velocity region, the variation of u is much slower, i.e., the frequency is lower. 

Usually this type of anemometer does not provide information on the flow direction. Vice versa, the. sensors are made as independent of the flow direction as possible—omnidirectional. This is an advantage for free-space ventilation measurements, as the flow direction varies constantly and a direction-sensitive anemometer would be difficult to use. Naturally, no sensor is fully omnidirectional, but satisfactory constructions are available. Due to the high sensor thermal inertia, this type of anemometer is unsuitable for high-frequency flow fluctuation measurement. They can be used to monitor low-frequency turbulence up to a given cut-off frequency, which depends on the dynamic properties of the instrument. 

Figure 7.2.5 provides a visualization of a localized extinction event in a turbulent jet flame, using a temporal sequence of OH planar LIF measurements. The OH-LIF measurements, combined with particle image velocimetry (PIV) reveal that a distinct vortex within the turbulent flow distorts and consequently breaks the OH front. These localized extinction events occur intermittently as the strength of the coupling between the turbulent flow and the flame chemistry fluctuates. The characteristics of the turbulent flame can be significantly altered as the frequency of these events increases. 

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 ... 

When electrically insulated strip or spot electrodes are embedded in a large electrode, and turbulent flow is fully developed, the steady mass-transfer rate gives information about the eddy diffusivity in the viscous sublayer very close to the electrode (see Section VI,C below). The fluctuating rate does not give information about velocity variations, and is markedly affected by the size of the electrode. The longitudinal, circumferential, and time scales of the mass-transfer fluctuations led Hanratty (H2) to postulate a surface renewal model with fixed time intervals based on the median energy frequency. 

A record of the axial velocity component vx for steady turbulent flow in a pipe would look like the trace shown in Figure 1.22. The trace exhibits rapid fluctuations about the mean value, which is determined by averaging the instantaneous velocity over a sufficiently long period of time. Figure 1.22 shows the case in which the mean velocity remains constant this is therefore known as steady turbulent flow. In unsteady turbulent flow, the mean value changes with time but it is still possible to define a mean value because, in practice, the mean will drift slowly compared with the frequency of the fluctuations. 

The hot-wire anemometer can, with suitable cahbration, accurately measure velocities from about 0.15 m/s (0.5 fl/s) to supersonic velocities and detect velocity fluctuations with frequencies up to 200,000 Hz. Eairly rugged, inexpensive units can be built for the measurement of mean velocities in the range of 0.15 to 30 m/s (about 0.5 to 100 ft/s). More elaborate, compensated units are commercially available for use in unsteady flow and turbulence measurements. In cahbrating a hotwire anemometer, it is preferable to use the same gas, temperature, and pressure as will be encountered in the intended apphcation. In this case the quantity I RJAt can be plotted against /v, where I = hot-wire current, = hot-wire resistance. At = difference between the wire temperature and the gas bulk temperature, and V = mean local velocity. A procedure is given by Wasan and Raid [Am. Inst. Chem. Eng. J., 17, 729-731 (1971)] for use when it is impractical to calibrate with the same gas composition or conditions of temperature and pressure. Andrews, Rradley, and Hundy [Int. J. Heat Mass Transfer, 15, 1765-1786 (1972)] give a cahbration correlation for measurement... 

The approach of representing the fluid and particle motion by their component frequencies is only valid if drag is a linear function of relative velocity and acceleration, i.e., if the particle Reynolds number is low. This is the reason for the restriction on small particles noted earlier. The terminal velocity of the particle relative to the fluid is superimposed on the turbulent fluctuations and is unaffected by turbulence if Re is low (see Chapter 11). 

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