Rms turbulent velocity

The length scale for describing the spatial variation of the pollutant species, L, is large when compared with the turbulent mean free path, /, a distance traveled by a particle in time Ti. Assuming the root-mean-square (rms) turbulent velocity of the particle is , this condition can be expressed as L > / = mJl. 

Fig. 7.12. Correlation of turbulent burning velocities. Broken curves show R,ILe, with R, (present notation) evaluated for the fully developed rms turbulent velocity, u equal to ul. Different combustion regimes are indicated, conditioned by the value of KLe. Redrawn...

As the engine speed increases, the locus of the flame condition during combustion moves to the right on Fig. 7.16, a consequence of the associated increase in rms turbulent velocity. This is accompanied by an increase in KLe and decline in combustion quality, as the combustion moves from the regime of the continuous laminar flame sheet to that of localized... 

A tube with obstacles can model some industrial explosions. A simple analysis indicates that there are two contributing factors involved in flame acceleration along a tube with obstacles. They are the character of the motion of the gas in front of the flame and the turbulence induced by the interaction of the motion of the gas in front of the flame with the boundary condition in the tube with obstacles. To study in detail the mechanism of flame acceleration by means of obstacles, explosion tests and measurements of the parameters of mean flow velocity and root mean squared (RMS) turbulent velocity were performed. The characteristics of methane-air and comstarch-air flame acceleration were investigated in a closed tube 0.19 m in diameter and 1,86 -m long filled with obstacles. The nonuniformity in the mean flow velocity and the RMS turbulent velocity across the tube with and without obstacles were measured in a substitutional tube in which the air free flow velocity ranged from 9 m/s to 177 m/s. Experimental results demonstrated that in the environment with obstacles flame acceleration caused by the nonuniformity of flow velocity is more efficient than that caused by the RMS turbulent velocity. 

The aims of the present paper are, first, to study the characteristics of cornstarch-air flame acceleration in environments with obstacles by means of a comparative method and, second, to measure the nonuniformity in the mean flow velocity and the rms turbulent velocity across the tube under the conditions with and without obstacles along the tube when the air flow velocities are in the range of 9 - 177 m/s. Finally, an examination of the role played by the mixture motion and turbulence in flame acceleration is carried out by means of a simple analysis. It demonstrates that in the obstacle environment the flame acceleration caused by the nonuniformity of mean flow velocity is more efficient than... 

A hot wire anemometer was used to record and analyze the mean flow and turbulence parameters. The system, shown in Fig. 2, was calibrated before each run. To determine the basic features of the flow field, measurements of the mean velocity and RMS turbulent velocity were carried out at three different cross sections (i.e., at sections 1,2, and 3) of a substitutional tube filled with obstacles for free flow velocities from 9 to 23 m/s and at one cross section (i.e., section 2) of the same tube for free flow velocities from 23 to 177 m/s as shown in Fig. 3. 

The measurements of the profiles of the flow velocity (U) and the RMS turbulent velocity (u ) performed in a substitutional tube with obstacles were carried out in the three cross sections at the free flow velocity region from 9 to 23 m/s (see Fig. 3). While the profiles measured in section 1 indicate the data of the flow velocity and RMS turbulent velocity in the tube without obstacles (see Fig. 8), the profiles measured in sections 2 and 3 indicate those data in the tube with obstacles (see Fig. 9). The measurements in section 3 were employed in the present study to indicate the data for the obstacles environment... 

The maximum values of mean flow velocity (Umax) at the tube axis, as well as the average value of flow velocity (U) and the RMS turbulent velocity (u ) at the cross sections, were obtained from the measured flow velocity and RMS turbulent velocity profiles. Table 2 shows the experimental data of the ratios of (Um - U)AJ and u /U, as well as the K values, which were measured in the tube with and without obstacles at the free flow velocity region from 9 m/s to 23 m/s. Experimental results showed that in the tube without obstacles the values of (Um - U)AJ and u AJ as well as the K values, have little change when the free flow velocities ranged from 9 m/s to 23 m/s. 

The measurements of the profiles of the flow velocity (U) and the RMS turbulent velocity (u ) performed in a substitutional tube with... 

Figure 10 shows the measured dimensionless velocity profiles (U/Umax) for the free flow velocity range of 23-177 m/s. Figure 11 shows the measured dimensionless RMS turbulent velocity profiles (u /u max) for the corresponding free flow velocities. Experimental results demonstrate that all of the profiles of flow velocity have a similar shape and that all of the profiles of RMS turbulent velocity have a similar shape. 

RMS Turbulent Velocity vs Radial Distance in Tube Without obstadce... 

Fig. 9 The profiles of flow velocity and RMS turbulent velocity measured at cross section 2 and 3 in the free flow velocity U = 9 m/s, 18.5 m/s, 23 m/s.

Fig. 11 The dimensionless RMS turbulent velocity vs radial distance from tube wall at section 3 for free flow velocities region from 23 m/s to 177 m/s.

The experimental measurements of the nonuniform flow velocity and the RMS turbulent velocity profiles in the tube environment with and without obstacles demonstrate that the values of two factors [(Um - U)/U and cu /U] and their summary (K) under the tube enviroment with obstacles are, at least, one order larger than those under the tube environment without obstacles (see Table 2). This indicates that obstacle environments create conditions more favorable for the flame acceleration. 

The averaging notions introduced above can be directly applied to define the average value of a velocity component, its instantaneous turbulent fluctuation, and the rms turbulent velocity in the ensemble-average sense ... 

We see hereinafter that the turbulent diffusion coefficient is also determined from the rms turbulent velocity Wnns and the integral scale f. It is also be observed, in other chapters of the second part, that the properties of turbulence are essentially described by the knowledge of the two quantities Wms and it ... 

The constant, called tnrbnlent diffusion coefficient, has the dimension of a diffusion coefficient (m -s ). It has the order of magnitnde of the product of the rms turbulent velocity by the integral scale of tnrbnlence." We write ... 

The rms turbulent velocity and the integral length scale are the two elementary variables that describe the mixing and transfer processes brought about by turbulence. In practice, Uims and t may vary in space (in the case of inhomogeneous tuibulence) and time (in the case of unsteady turbulence). Consequently, tools are needed to describe their evolution in time and space. The k-e model is the most widely used model that deals with this problem It is used in numerous computational fluid dynamics codes. 

Variables k and e are directly related to the rms turbulent velocity and to the integral scale. Variable k is the turbulent kinetic energy per unit mass, which is of the same order of magnitude as the squared rms turbulent velocity ... 

Evaluate the rms turbulent velocity in the three dye streaks, using the turbulent kinetic energy profile measirred by Laufer (1954) (Figure 8.6(b) of this chapter). 

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