A probability density function of liftoff velocities in mixed-size wind sand flux

Abstract

With the discrete element method (DEM), employing the diameter distribution of natural sands sampled from the Tengger Desert, a mixed-size sand bed was produced and the particle-bed collision was simulated in the mixed-size wind sand movement. In the simulation, the shear wind velocity, particle diameter, incident velocity and incident angle of the impact sand particle were given the same values as the experimental results. After the particle-bed collision, we collected all the initial velocities of rising sand particles, including the liftoff angular velocities, liftoff linear velocities and their horizontal and vertical components. By the statistical analysis on the velocity sample for each velocity component, its probability density functions were obtained, and they are the functions of the shear wind velocity. The liftoff velocities and their horizontal and vertical components are distributed as an exponential density function, while the angular velocities are distributed as a normal density function.wind sand flux, mixed-size particle diameter, liftoff velocity, probability density function (PDF), discrete element method (DEM) It is obvious that the liftoff velocities of sand particles with different diameters are of crucial importance for the prediction of wind sand flux. Therefore, a key issue in the research of wind erosion is to clarify the dynamical characteristic of sand particles lifting from the natural sand bed surface due to particle-bed collision [1] , that is, with a given wind shear velocity, to obtain the probability density function (PDF) of liftoff velocities of sand particles rising from the mixed-size sand bed.There have already been many studies on the PDF of liftoff velocities of sand particles since the mid and later 1980s, e.g., deducing from the experimental photographs of 100 glass grains' trajectories with diameters ranging from 0.35 mm to 0.71 mm. Anderson and Hallet [2] thought that the probability densities of liftoff velocities are subject to an exponential function or a Gamma function with regard to shear wind velocity; Willetts and Rice [3] had direct observations on particle-bed collisions with 100 spherical and planar sand particles using a cine-camera. The diameters of sand

Vertical distribution of wind–sand interaction forces in aeolian sand transport

“…In the present simulation, the particle angular velocity at the height of 1 mm can be considered as the lift-off angular velocity of the sand particle on the bed surface, and the probability density function of particle angular velocity at the height of 1 mm is consistent with the results of Zheng et al (2008).…”

“…With the discrete element method (DEM), Zheng et al (2008) found that the lift-off angular velocity of the sand particles lies between −1500 and 1100 rev/s, and the probability density function of the lift-off angular velocity distribution is a normal function. In the present simulation, the particle angular velocity at the height of 1 mm can be considered as the lift-off angular velocity of the sand particle on the bed surface, and the probability density function of particle angular velocity at the height of 1 mm is consistent with the results of Zheng et al (2008).…”

Analysis of the forces acting on the saltating particles in the coupled wind-sand-electricity fields

“…It is seen in Figure 4 that for * 0.5 u < m/s, the numerical results are very close to the value given by formula (17); while for * 0.6 u > m/s, the results are close to the value given by formula (16). Compared all the results in Figure 4, it is obvious that the sand transport rates calculated in the work agree well with those obtained from Bagnold's and Kawamura's empirical formulas in their respective effective regions, demonstrating that the model and the algorithm proposed in this work are correct and have a good efficiency in discussing the windblown sand movement.…”

“…These two empirical expressions are recognized to be very efficient [22][23][24] , and their respective effective regions are that the best accordance between the predictions of Kawamura's formula (17), in which K = 1.0, and the measurements of transport rate is only in the range of * 0.4 u < m/s; while for * 0.4 m/s 0.7 m/s, u < < Bagnold's formula (16) is more efficient; when the friction velocity increases continuously, all the predictions by formulas (16) and (17) are smaller than the experimental data.…”

“…Considering the random characteristic of the sand particles splashing off from the sand bed surface [17,18] , the initial velocity distribution function p(v 0 ), which conforms to Gamma distribution given by Anderson et al [10] , is used to describe the lift-off state of the sand particles ejecting from the sand bed when the saltation reaches the steady equilibrium. Here,…”