Velocity fluctuations

Cup anemometers have shaped cups mounted on the spokes of a wheel. The cups, under the action of the fluid forces, spin in a horizontal plane about a vertical shaft mounted in bearings. Vane or propeller types use a multibladed rotor, the axis of which is parallel to the flow direction as the rotating member. Both designs are commonly used for wind speed measurement or similar appHcations such as the velocity in ventilation ducts. Because of inertia, anemometers are most accurate under steady conditions. Velocity fluctuations cause readings that are too high. 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

Turbulent flow, by means of the chaotic eddy motion associated with velocity fluctuation, is conducive to rapid mixing and, therefore, is the preferred flow regime for mixing. Laminar mixing is carried out when high viscosity makes turbulent flow impractical. 

Turbulent velocity fluctuations ultimately dissipate their kinetic energy through viscous effects. MacroscopicaUy, this energy dissipation requires pressure drop, or velocity decrease. The ener dissipation rate per unit mass is usually denoted . For steady ffow in a pipe, the average energy dissipation rate per unit mass is given by... 

When the continmty equation and the Navier-Stokes equations for incompressible flow are time averaged, equations for the time-averaged velocities and pressures are obtained which appear identical to the original equations (6-18 through 6-28), except for the appearance of additional terms in the Navier-Stokes equations. Called Reynolds stress terms, they result from the nonlinear effects of momentum transport by the velocity fluctuations. In each i-component (i = X, y, z) Navier-Stokes equation, the following additional terms appear on the right-hand side ... 

The Reynolds stresses are nonzero because the velocity fluctuations in different coordinate directions are correlated so that in general is nonzero. 

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

The effect of pulsating flow on pitot-tube accuracy is treated by Ower et al., op. cit., pp. 310-312. For sinusoidal velocity fluctuations, the ratio of indicated velocity to actual mean velocity is given by the factor /l + AV2, where X is the velocity excursion as a fraction of the mean velocity. Thus, the indicated velocity would be about 6 percent high for velocity fluctuations of 50 percent, and pulsations greater than 20 percent should be damped to avoid errors greater than 1 percent. Tne error increases as the frequency of flow oscillations approaches the natural frequency of the pitot tube and the density of the measuring fluid approaches the density of the process fluid [see Horlock and Daneshyar, y. Mech. Eng. Sci, 15, 144-152 (1973)]. 

The ] atio of the I rns velocity fluctuation to the avei age velocity in the irnpelle] zone is about 50 pei cent with many open irnpellei s. If the ] rns velocity fluctuation is divided bv the avei age velocity iji the I est of the vessel, howevei the I atio is on the oi dei of 5 pei cent. This is also the level of I rns velocity fluctuation to the mean velocity in pipeline flow, Thei e ai e phenomena in rnici o-scale mixing that can occiu in mixing tanks that do not occiu in pipeline I eactoi s, Whethei this is good or bad depends upon the process requirements,... 

All tliJ ee irnpellei s ai e calculated foi the same irnpelle] flow and the same diarnete]. The A310 (Fig, 18-2) di aws the least powei and has the least velocity fluctuations. This gives the lowest rnici o-scale tiu bu-lence and slieai I ate, The A2()() (Fig, 18-3) shows inci eased velocity... 

Micro-scale variables are involved when the particles, droplets, baffles, or fluid chimps are on the order of 100 [Lm or less. In this case, the critical parameters usually are power per unit volume, distribution of power per unit volume between the impeller and the rest of the tanh, rms velocity fluctuation, energy spectra, dissipation length, the smallest micro-scale eddy size for the particular power level, and viscosity of the fluid. 

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. 

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. 

The step change is close to the situation where the sensor is suddenly moved from one place to another having a different state of the measured quantity. The exponential change could, for example, be the temperature change of a heating coil or some other first-order system. Finally, the velocity fluctuations of room air can be approximated with a sine or cosine function. 

A hot-wire anemometer, working in the CT mode, is capable of measuring rapid velocity fluctuations. This is an advantage in the measurement of flow turbulence and is also the main area of application for the hot-wire anemometer. It is an instrument mainly for scientific purposes. 

The complete LDA system includes the appropriate transmission and detection optoelectronics, traverse mechanisms, computer-controlled signal processing, and a data acquisition and evaluation system. The LDA equipment is a powerful tool for the measurement of flow velocity and velocity fluctuation, as well as the local concentration of particles or droplets transported in the airflow. 

The neglect of a low turbulence effect and a laminar flow is not justified in regions close to solid surfaces where the turbulent velocity fluctuations... 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

In streamline flow, E is very small and approaches zero, so that xj p determines the shear stress. In turbulent flow, E is negligible at the wall and increases very rapidly with distance from the wall. LAUFER(7), using very small hot-wire anemometers, measured the velocity fluctuations and gave a valuable account of the structure of turbulent flow. In the operations of mass, heat, and momentum transfer, the transfer has to be effected through the laminar layer near the wall, and it is here that the greatest resistance to transfer lies. 

In general, conventional theory has been tested for flow in micro-channels by comparing the experimental and theoretical data on pressure drop as a function of flow rate. During the last few years, better methods have been used for measurement of the mean velocity, as well as rms of the velocity fluctuations (Maynes and Webb 2002 Sharp and Adrian 2004). 

Sharp, Adrian (2004) Smooth 50-247 1,800- 2,200 Friction factor, centerline velocity, rms of centerline velocity fluctuations... 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

In the laminar region the rms of streamwise velocity fluctuations was expected to be zero (Sharp et al. 2001). Figure 3.10 shows that the first evidence of transition, in the form of an abrupt increase in the rms, occurs at 1,800 < Re < 2,200, in full agreement with the flow resistance data. There was no evidence of transition below these values. Thus, the behavior of the flow in micro-tubes, at least down to a 50 pm diameter, shows no perceptible differences with the macro-scale flow. 

Thus, the measurements of integral flow characteristics, as well as mean velocity and rms of velocity fluctuations testify to the fact that the critical Reynolds number is the same as Rccr in the macroscopic Poiseuille flow. Some decrease in the critical Reynolds number down to Re 1,500— 1,700, reported by the second group above, may be due to energy dissipation. The energy dissipation leads to an increase in fluid temperature. As a result, the viscosity would increase in gas and decrease in liquid. Accordingly, in both cases the Reynolds number based on the inlet flow viscosity differs from that based on local viscosity at a given point in the micro-channel. 

Under certain conditions the energy dissipation may lead to an oscillatory regime of laminar flow in micro-channels. The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of viscous energy dissipation on flow parameters. The oscillatory flow regime occurs in micro-channels at Reynolds numbers less than Recr- In this case the existence of velocity fluctuations does not indicate change from laminar to turbulent flow. 

Longitudinal component of velocity rms velocity fluctuation Slip velocity Friction velocity... 

We estimate the effect of the velocity fluctuations on the capillary pressure, using the Hoffman-Voinov-Tanner law which is valid at 9d < 135° and Ca < 0 (0.1)... 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

This system produces a steady laminar flow with a flat velocity profile at the burner exit for mean flow velocities up to 5m/s. Velocity fluctuations at the burner outlet are reduced to low levels as v /v< 0.01 on the central axis for free jet injection conditions. The burner is fed with a mixture of methane and air. Experiments-described in what follows are carried out at fixed equivalence ratios. Flow perturbations are produced by the loudspeaker driven by an amplifier, which is fed by a sinusoidal signal s)mthesizer. Velocity perturbations measured by laser doppler velocimetry (LDV) on the burner symmetry axis above the nozzle exit plane are also purely sinusoidal and their spectral... 

It is not possible to obtain exactly identical flow conditions for the configurations explored. The level of velocity fluctuation at the burner outlet also differs in the various cases. This level was adjusted to get an acceptable signal-to-noise ratio. In the results presented here, the specific heat ratio was taken as equal to y= 1.4, the sound speed Cq = 343 m/s corresponds to a room temperature T = 293 K. The air density is taken equal to = 1.205 kg/m. Laminar burning velocities are... 

In fact, the clearly posed problem of the final state of an unstable laminar flame is a limiting case of turbulent flame for vanishing initial turbulence of the oncoming flow, but the general case, for any initial velocity fluctuations, is clearly of great interest in practical devices such as spark-ignited engines, turbojet, or gas turbine combustion chambers. 

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