Riassunto analitico
Lagrangian statistics of inhomogeneous turbulence are calculated from a direct numerical simulation of a pipe flow with Reb = 5300. The Lagrangian velocity of particles is obtained through a tricubic interpolation scheme which interpolates the Eulerian field at the particle instantaneous position, while the particle position is calculated by numerical integration performed with a fourth order Runge-Kutta method. To investigate the wall presence effect on statistics, particles were released in several positions with different wall-normal coordinates while, due to the pipe geometry both the tangential and the axial direction are statistically homogeneous, moreover the particles pool was enlarged by considering more realization to evaluate the statistics. The velocity autocorrelations were calculated to study the interaction between particles and turbulence coherent structures, moreover the conditional autocorrelations based on particles belonging to low speed streaks, high speed streaks and longitudinal vortices were also considered. Results showed a gradual increase of the correlations by moving away from the wall except from the central part of the tube where a decrease was observed, moreover the streamwise correlation appeared to persist for a longer time with respect to radial and tangential direction due to the presence of low and high speed streaks and vortices near the wall. Lagrangian integral timescale were derived from autocorrelations time integral, different upper limits were used to examine the results variability to different approximations. Particle dispersion was computed and confronted with Taylor’s theory, adding also the later results of Corrsin’s studies, revealing a good affinity with the theoretical predictions in the streamwise direction. Nevertheless, radial and tangential direction diverge from theory due to the inhomogeneity of the flow caused by the wall presence. Ultimately, the Lagrangian structure function for the velocity increment was calculated to observe the behaviour of the scaling exponent for the second order moment of velocity, besides the effects of turbulence intermittency were included in the evaluation in the exponents as well as the dependence to the wall distance.
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Abstract
Lagrangian statistics of inhomogeneous turbulence are calculated from a direct numerical simulation of a pipe flow with Reb = 5300. The Lagrangian velocity of particles is obtained through a tricubic interpolation scheme which interpolates the Eulerian field at the particle instantaneous position, while the particle position is calculated by numerical integration performed with a fourth order Runge-Kutta method. To investigate the wall presence effect on statistics, particles were released in several positions with different wall-normal coordinates while, due to the pipe geometry both the tangential and the axial direction are statistically homogeneous, moreover the particles pool was enlarged by considering more realization to evaluate the statistics. The velocity autocorrelations were calculated to study the interaction between particles and turbulence coherent structures, moreover the conditional autocorrelations based on particles belonging to low speed streaks, high speed streaks and longitudinal vortices were also considered. Results showed a gradual increase of the correlations by moving away from the wall except from the central part of the tube where a decrease was observed, moreover the streamwise correlation appeared to persist for a longer time with respect to radial and tangential direction due to the presence of low and high speed streaks and vortices near the wall. Lagrangian integral timescale were derived from autocorrelations time integral, different upper limits were used to examine the results variability to different approximations. Particle dispersion was computed and confronted with Taylor’s theory, adding also the later results of Corrsin’s studies, revealing a good affinity with the theoretical predictions in the streamwise direction. Nevertheless, radial and tangential direction diverge from theory due to the inhomogeneity of the flow caused by the wall presence. Ultimately, the Lagrangian structure function for the velocity increment was calculated to observe the behaviour of the scaling exponent for the second order moment of velocity, besides the effects of turbulence intermittency were included in the evaluation in the exponents as well as the dependence to the wall distance.
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