This document describes a numerical study of raindrop impact on saturated soil. It presents simulations using the discrete phase method (DPM) to model soil particles and the volume of fluid (VOF) method to model water flow. The DPM models individual soil particles eroded by raindrop impact, while the VOF provides the flow field of the water phase. Simulations are conducted for raindrops of 2 mm and 4 mm in diameter, corresponding to terminal velocities of 2.36 m/s and 7.65 m/s. The results show soil particle splash occurring over 50 ms for both droplet sizes. While this initial study couples DPM and VOF, future work is needed to more precisely simulate

1. Raindrop Impact on Saturated Soil
Mohsen Cheraghi, D. A. Barry
Ecole polytechnique fédérale de Lausanne, Faculté de
l’environnement naturel, architectural et construit, Institut
d’ingénierie de l’environnement, Lausanne, Switzerland
mohsen.cheraghi@epfl.ch
andrew.barry@epfl.ch
9th OpenFOAM® Workshop
23-26 June 2014 in Zagreb, Croatia

2. Contents
Introduction
Problem Definition
Numerical Parameters
Simulation
Results
Conclusions
1/14

3. Introduction
Water Erosion
http://www.montcalm.org/media/planningeduc/tn_raindrp.jpg http://intechweb.wordpress.com/2011/11/30/
soil-erosion-raising-awareness-on-current-environmental-issues/
http://www.geo.uu.nl/landdegradation/Fieldwork.htm
Splash Erosion Rill Erosion Gully Erosion
2/14

4. Problem Definition
Dd = 2 mm
Dd = 4 mm
Vt = 2.36 ms-1
Terminal Velocity of Raindrop (Vt)
Vt = 7.65 ms-1
3/14

5. Numerical Parameters
Discrete phase method
Particle size: 1 mm
Cohesion force: 0
youngsModulus 40e6;
poissonsRatio 0.35;
Drag model:
ErgunWenYuDrag
Collesion Model:
pairSpringSliderDashpotCoeffs
{
useEquivalentSize no;
alpha 0.02;
b 1.5;
mu 0.10;
cohesionEnergyDensity 0.0;
collisionResolutionSteps 12;
};
Wall Model:
wallSpringSliderDashpotCoeffs
{
useEquivalentSize no;
collisionResolutionSteps 12;
youngsModulus 1e8;
poissonsRatio 0.23;
alpha 0.01;
b 1.5;
mu 0.09;
cohesionEnergyDensity 0;
};
4/14

6. Numerical Parameters
Volume of Fluid method
phases
(
water
{
transportModel Newtonian;
nu nu [ 0 2 -1 0 0 0 0 ] 1e-06;
rho rho [ 1 -3 0 0 0 0 0 ] 1000;
}
air
{
transportModel Newtonian;
nu nu [ 0 2 -1 0 0 0 0 ] 1.48e-05;
rho rho [ 1 -3 0 0 0 0 0 ] 1;
}
);
Sigma ( surface tension)
(
(air water) 0.07197
);
5/14

7. Simulation: outline
+
Velocity profile of section A
is implemented as a boundary
condition on surface B
A B
VOF DPM
6/14

8. Velocity profile along cross section A
A
3.5 cm
Simulation: VOF
7/14

9. Simulation: VOF
V(x, t) = V0(x) f(t)
V0 (x) = Velocity Profile at the moment of collision
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 0.01 0.02 0.03 0.04 0.05
V0
x (m)
V0 (x)
8/14

10. Simulation: VOF
V(x, t) = V0(x) f(t)
V0 (x): Velocity Profile at collision instant
-0.15
-0.1
-0.05
0
0.05
0.1
0 0.01 0.02 0.03 0.04 0.05
V(ms-1)
x (m)
V0 (x)
V (x)
V0max (x)
Vmax (x)
-10
0
10
20
30
40
50
0 0.01 0.02 0.03 0.04 0.05 0.06
Vmax/V0max
t (s) 9/14

11. Simulation: VOF
V(x,t) = f(t)V0(x)
-10
0
10
20
30
40
50
0 0.01 0.02 0.03 0.04 0.05 0.06
Vmax/V0max
t (s)
f(t) = -366443498336t6 + 63529957792t5
- 4342637831t4 + 150446928t3
-2829761t2 + 25048t – 23
R² = 0.999
f(t) = -305662395148t6 + 52347905525t5
3496475928t4 + 114043721t3
- 1846164t2 + 12209t + 13
R² = 0.986
-60
-40
-20
0
20
40
60
80
0 0.01 0.02 0.03 0.04 0.05 0.06
Vmax/V0max
t (s)
2-mm Droplet:
4-mm Droplet:
10/14

12. Results
 Droplet size: 2 mm (Vt = 2.36 ms-1)
 Particle size: 1 mm
*Simulation for 50 ms splash
11/14
t = 0.00
t = 50 ms

13. Results
 Droplet size: 4 mm (Vt = 7.65 ms-1)
 Particle size: 1 mm
*Simulation is for 50 ms splash
12/14
t = 0.00
t = 50 ms

14. Conclusions:
 DPM method is able to simulate dense particles with the
ErgunWenYu drag model
 Simulation of random droplets (as in rainfall) demands
coupling of the DPM and VOF solvers
 This simulation was not verified or validated and a more precise
VOF and LES simulation is needed in the future
13/14

15. Thank You
Questions?