Fluctuating component of velocity

The intensity of turbulence I is defined as the ratio of the mean value of the fluctuating component of velocity to the steady state velocity, For flow in the A-direction parallel to a surface this may be written as ... 

To examine the effect of turbulence on flames, and hence the mass consumption rate of the fuel mixture, it is best to first recall the tacit assumption that in laminar flames the flow conditions alter neither the chemical mechanism nor the associated chemical energy release rate. Now one must acknowledge that, in many flow configurations, there can be an interaction between the character of the flow and the reaction chemistry. When a flow becomes turbulent, there are fluctuating components of velocity, temperature, density, pressure, and concentration. The degree to which such components affect the chemical reactions, heat release rate, and flame structure in a combustion system depends upon the relative characteristic times associated with each of these individual parameters. In a general sense, if the characteristic time (r0) of the chemical reaction is much shorter than a characteristic time (rm) associated with the fluid-mechanical fluctuations, the chemistry is essentially unaffected by the flow field. But if the contra condition (rc > rm) is true, the fluid mechanics could influence the chemical reaction rate, energy release rates, and flame structure. 

Turbulent kinetic energy (TKE) Average kinetic energy associated with the fluctuating component of velocity in a fluid. 

Because of the random nature of the fluctuations, the time averages of the fluctuating components of velocity and pressure vanish when averaged over a time period fg of the order of a few seconds. Therefore... 

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

In an earlier phase of this work [9] the intensities of axial and circumferential components of velocity fluctuation were measured in the TC annulus, using Laser Doppler Velocimetry (LDV), for a wide range of cylinder rotation speeds. On average, the intensities of axial velocity fluctuations were found to be within 25% of the intensities of circumferential velocity fluctuations [9]. As in Ronney et al. [5], turbulence intensities were found to be nearly homogeneous along the axial direction and over most of the annulus width, and to be linearly proportional... 

A temporal mean is the mean of a fluctuating quantity over a time period, T. If the time period is sufficiently long, the temporal mean values are constant over time. Temporal means are often used in analyzing turbulent diffusion. For example, if u is the x-component of velocity and is a function of space and time, u = u x, y, z, t), in cartesian coordinates. Then the temporal mean velocity, u, would only be a function of X, y, and z ... 

Interactions of the particles with the fluctuating component of the gas velocity, which lead to particle turbulent diffusion and induce an exchange of the kinetic energy between the fluctuating components of the velocity of the two phases, which results in either damping the fluctuations of the gas velocity and enhancing fluctuations in particle velocity, or vice versa... 

The mean value of the fluctuation u must be zero over an extended period for steady flow conditions. There are also fluctuations in the y component of velocity, so we would write... 

For a unit area of the plane P-P, the instantaneous turbulent mass-transport rate across the plane is pv. Associated with this mass transport is a change in the x component of velocity u. The net momentum flux per unit area, in the x direction, represents the turbulent-shear stress at the plane P-P, or pv u When a turbulent lump moves upward (v > 0), it enters a region of higher u and is therefore likely to effect a slowing-down fluctuation in u , that is, u < 0. A similar argument can be made for v < 0, so that the average turbulent-shear stress will be given as... 

Fluctuating components of gas velocity are selected from a Gaussian distribution with variance derived from the local value of turbulent kinetic energy. Integration of the particle equation of motion yields the particle position at any given instant in time. 

The use of bold denotes that all quantities are vectors. The velocity V on the left-hand side is the instantaneous velocity, which is comprised of the sum of the mean velocity at the point (denoted by the overbar) and the fluctuating element of the velocity (denoted by the lowercase m). To permit the use of the Einstein summation convention, the component of the instantaneous velocity in direction i at a point is written as the sum of the mean and fluctuating components of the velocity in that direction. 

For multiphase flows perturbed by the presence of particles to obtain a turbulence like behavior the local instantaneous velocity of the continuous phase can for example be decomposed adopting the Reynolds averaging procedure (i.e., other methods including time-, volume-, ensemble-, and Favre averaging have been used as well) and expressed as Vg = Vg- - < v >g, where v(. is the fluctuating component of the continuous phase velocity. Introducing the peculiar velocity for the dispersed phase this relation can be re-arranged as ... 

Fig. 9. The best correspondence between the form of the two records is obtained when u is plotted with a 3-hr lag time. Work done on the water surface by the wind causes an increase in the level of the fluctuating component of the velocity near the bottom within a matter of hours even though the water is too deep to be directly affected by the wind (wind-...

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