Turbulent Pipe Flow Laden With Solid Particles (original) (raw)
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Particle Response in a Turbulent Pipe Flow
In this work the behavior of heavy solid particles in a turbulent flow along a pipe is studied. The particle concentration is very small, so that the flow field is not affected by the particles. The particle density is much larger than the fluid density, and Basset and virtual mass forces are neglected. The velocity field of the fluid is obtained with DNS using a finite-difference method of fractional-step type and a semi-implicit (in the second order viscous derivatives) third order Runge-Kutta method. In axial and azimuthal directions the boundary conditions are supposed periodical which permits the use of fast Fourier transform in the discretized equations. The particles Lagrangian-path are obtained by using an implicit sixth/third order (Lobatto type) Runge-Kutta method with step size control. Particles are injected uniformly in several initial cross-sections at different radial and azimuthal positions, with the mean axial velocity of fluid. Due to periodicity imposed by DNS in the axial direction, when the particles reach the exit, they are re-injected at the entrance, and in this way they are circulating in the tube for an infinitely long time. After a large enough time, the statistical characteristics should become independent of initial conditions, and axially symmetrical. Results are obtained for two Stokes numbers. Comparison is made with results of Kulick and Li, although these are for a vertical channel. Expressions for fluid-particle difference of kinetic turbulent energy and for particle energy dissipation given in García & Crespo are confirmed in the core of the flow near the axis.
In the study of the turbulent pipe flow laden with solid spherical particles it has been observed a preferential migration of particles toward the wall of the pipe, and a little lower toward the core of the flow. The minimum of particle concentration is located approximately at 0.7 of the pipe radius. Including for higher Stokes number, it may appear an annular section of the pipe void of particles. This phenomenon obey the law: In average, particles have the tendency to migrate from regions where dissipation is lower than ν<w’.w’>, being w’ the fluctuation of the vorticity (Maxey,1987; Shaw,2003]. Turbulent flow within a circular pipe has been chosen to a moderate Reynolds number of 5600 so that the computacional requirements are relatively low. This flow, studied and documented in (Loulou et al.,1997), has been simulated again, but with a different numerical methods. The results have been validated comparatively. The method, selected by its rapidity in the execution, has been the finite differences of fractional-step with advance in time of third order Runge-Kutta type. This method is semi-implicit of second order in the viscous terms and explicit up-wind of fourth order in the convective terms. The simulations have been obtained with direct numerical simulation (DNS) over the exactly the same mesh of the mentioned reference with refinement of sizes that ranges from a tenth to unity of Kolmogorov scale. Both the influence of Stokes number and mass load are studied. Low Stokes number ranges over 0.043 – 0.578 and high Stokes number is of order of 4. Two-ways influence particle-fluid is considered. For low concentration of particles the modulation of turbulenece is negligible. For high concentration of particles with two different mass load ( =20%, 40%) the modulation of fluid turbulence is appreciable. Particle equations have been solved with a sixth order Runge-Kutta method and velocity field is found by four degree polynomial 3-D interpolation. Although the number of particles is some cases is high, they have been recirculated a certain number of times in the simulated piece of ten-radius pipe length in order to obtain the wished ensemble. The turbulent flow recirculates simultaneously with particles by the imposition of periodic conditions in the axial direction. The results are qualitatively compared with experimental (Kulick et al.,1994) and numerical (Li et al.,2001) data coming from turbulent channels flow. When the turbulent flow becomes statistically stationary the particles apparently do not migrate (in averages). This means that there is a mechanism of diffusion that counteract over the particles in order to maintain a static average concentration profile. A model of turbulent diffusion following the Fick law has been formulated. The coefficient of diffusivity has been calculated by fitting in all cases.
Analysis of the heat transfer coefficient in a turbulent particle pipe flow
International Journal of Heat and Mass Transfer, 1995
A Eulerian-Lagrangian mathematical model is used to predict the average heat transfer coefficient at the inner wall of a vertical pipe. Air flows within the pipe in a turbulent regime loaded with spherical glass particles of uniform size 70, 140 and 200 μm in diameter. The suspension flow is predicted by solving numerically the mass, momentum and energy equations for the continuous phase and the motion and energy equations for individual particles. The turbulence of the air flow is calculated by using a standard K-ε model and the dispersion of the particles is predicted by the Lagrangian stochastic deterministic model. The average heat transfer coefficient of the suspension is calculated for different Reynolds numbers, particle loading ratios and particle diameters. The results are compared with experimental data published in the literature.