An Experimental Study of Eddy Diffusivities and Eddy Viscosities for Cases of Anisotropic and Non-Homogeneous Turbulence in Suspension Flow

Citation

Whatley, Gary Eugene (1982) An Experimental Study of Eddy Diffusivities and Eddy Viscosities for Cases of Anisotropic and Non-Homogeneous Turbulence in Suspension Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/entr-8p75. https://resolver.caltech.edu/CaltechETD:etd-09122006-091243

Abstract

An experimental study on the motion of small particles, about 120 microns in size, in turbulent pipe flow was completed. The goal of the study was to determine the effects of the anistropic, non-homogeneous turbulence generated by the pipe wall on the motion and diffusion of the particles. Measurements of the mean and rms velocities in the r, θ, and z directions were made on flows with Reynolds numbers of 8,400, 12,500, 16,700 and 20,900 for both the continuous and disperse phases. Values of eddy diffusivities for the particles and eddy viscosities for the continuous phase were determined.

Experimental data were obtained for the continuous phase (de-ionized water) in order to characterize the four flows used. All velocity measurements on the water were made at axial positions in the flow channel where the flows were fully developed. Mean velocities in the z direction were found to be well represented by the equation u⁺ = 4.0 + 2.9 ln y⁺ over the range from y⁺ = 50 to 550 where u⁺ is a dimensionless velocity, V/(τ_o/ρ)^1/2 and y⁺ a dimensionless length, y⁺ = (y/ν)(τ_o/ρ)^1/2. The buffer region in the flow was found to extend out to y⁺ = 50. The kinematic eddy viscosity, ν_e, for each flow-rate was calculated from the velocity data. The maximum values for ν_e were 0.22, 0.33, 0.43, and 0.47 cm²/sec for the flows at R_e = 8,400, 12,500, 16,700 and 20,900, respectively. The maximum values of ν_e were found to occur at r/r_o = 0.63 for all four flows. The rms velocities of the water for the r, θ, and z directions were measured across the flow channel. The measurements of the z component of the rms velocities at the center of the pipe were compared with measurements of other investigators. Figure 4.23 shows the values of (v'_z²)^1/2/U_℄ where U_℄ is the mean velocity on the channel centerline, measured by invasive methods are smaller than those measured non-invasively.

Mean velocity measurements of the PVC particles showed that the velocity profiles of the particles did not develop as quickly as the velocity profiles of the fluid phase. Experimentally measured rms velocities of the particles in the r, θ, and z directions were obtained at several radial positions across the channel. Other investigators have measured rms velocities of particles at the center of the channel or have calculated them from diffusion data which yields average rms velocities.

In the experiments performed in the study the values of the axial rms velocities of the particles were found to be smaller than the same values for the liquid. The r and θ components for the particles did not exhibit constant relationships with the water as did the z component. The radial diffusion of the PVC particles outward from a point source was found to be inhibited after an initial diffusion distance. The eddy-diffusion coefficients for the initial zone of diffusion were 0.31, 0.48, 0.66, and 0.72 cm²/sec, respectively for the four different Reynolds numbers. Values of the turbulent Schmidt numbers calculated over the same region of flow were 0.45, 0.42, 0.47, and 0.74 respectively. The eddy-diffusion coefficients determined for the region of flow in which the inhibition occurred were respectively found to be 0.13, 0.17, 0.22, and 0.25 cm²/sec. The corresponding values for the turbulent Schmidt numbers calculated with the diffusion coefficients from the region of inhibited spread were 1.39, 1.54, 1.54, and 1.56.

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