Numerical model for the fall speed of raindrops in a rainfall simulator

The impact velocity or kinetic energy of raindrops is an important factor when studying processes such as splash erosion and crusting. Often rainfall simulators are used to study these processes, but most rainfall simulators are not high enough for large raindrops accelerate to velocities close to their terminal velocity. A numerical model is developed to quantify the difference between the terminal velocity and the impact velocity of raindrops falling from a rainfall simulator of limited height. The model accounts for the development of turbulence in the flow around the drop by making friction a function of the particle Reynolds number. Distortion of the raindrops is expressed in terms of the dimensionless Weber number, which relates the hydrodynamic pressure perturbation (tends to distort the drop) to surface tension (tends to keep the drop spherical). The terminal velocities calculated with the model compare well with measured terminal velocities over a very wide range (diameters of 0.01 to 5.8 mm). The model results show that only drops smaller than 1 mm in diameter will attain 95% of their terminal velocity within 2 m falling distance. For drops larger than 1 mm in diameter the required distance increases rapidly (5.6 m distance for a 2 mm drop). Most harm is usually done by drops larger than 1 mm. Most rainfall simulators are not high enough for these drops to obtain their terminal velocity. The presented model can be used to evaluate the difference between the terminal velocity and the impact velocity of drops from a rainfall simulator.