Discrete Element Modeling (DEM) using Lagrangian Multiphase models has been applied to a multitude of industrial applications. With recent advances in the simulation of discrete particles and computing power, it is now being applied to the off-road vehicle sector.

Titus Sgro – Technical Marketing Engineer, CD-adapco

More powerful computing hardware has allowed automotive companies to expand upon their design simulations, reaching out from the “core” optimization areas of external aerodynamics and engine design to improve upon and perfect virtually every aspect of an automobile. One particular group of vehicles that has lagged behind traditionally but is now racing to catch up is off-road vehicles. This category includes, in addition to ATVs, massive industrial applications like farming equipment and construction vehicles as well as household items such as lawn mowers and snow blowers. Recent technological advances in the simulation world allow this machinery to be modeled using discrete elements to replicate small particles, bypassing approximations and guesswork and going straight to a high-fidelity examination of the true operating conditions of these vehicles.

While fluid flow has been a centerpiece of the Computer Aided Engineering (CAE) and Computational Fluid Dynamics (CFD) for decades, being able to predict the motion of individual particles has been an elusive utopia. The automotive sector has been the most demanding of these kinds of applications, seeking to understand and improve the complex processes going on within agricultural, construction and domestic vehicles. Agricultural and construction vehicles, (tractors, lawn mowers, front loaders, etc.) that are used to pick up and move enormous amounts of tiny particles, can be affected by airflow and motor mechanics, among many other physical mechanics. With recent advances in the simulation of discrete particles and computing power, engineers are finally able to use CAE to improve and optimize these vehicles by modeling each particle individually to create a much more faithful simulation of these complex machines.

Contaminant particles such as dust, as well as particulates that these objects are designed to work with, have previously been simulated in various methods as some form of fluid continuum. These particles include blades of grass (for a lawn mower), gravel and dirt (for construction equipment), and grain (for farming equipment). Simulating these particles as a fluid continuum creates imperfect results due to the simplification.

Applications of DEM

DEM using Lagrangian Multiphase has already been applied to a myriad of applications, from icing on airplane wings to mud and dirt simulation. Now this powerful technology is being applied to the off-road vehicle sector, including:
– Construction vehicles: dump trucks, excavators, and loaders
– Agricultural equipment: tractors and harvesters
– Domestic machinery: lawn mowers, snow blowers, and all-terrain vehicles
– Other areas of the Ground Transportation Industry: rain, mud, or snow modeling

A host of other industries have already begun using DEM, to simulate spray particles or atomizers – very common in the food industry, painting with aerosol cans or industrial applications for the automotive and aerospace industries – as well as the Life Sciences industry, investigating the dispersal of medication in a patient’s blood from a pill or in the lungs from an inhaler.

Two blade tractor lawn mower

The following example uses a dual bladed tractor lawn mower, with the blades positioned under the driver, as seen in Fig. 2. A plate protects the driver from the grass being propelled at them. The blades were set in their own region with a separate mesh and spun using CD-adapco STAR-CCM+’s Rigid Body Motion (RBM), which rotates the entire region around a set axis. Because of the limitations of RBM, CD-adapco recommends that during each time-step of the rotation, the spinning region should be turned by 1 degree at most so that the rotating cells do not become completely out of line with the stationary cells. In the simulation pictured, the two meter long blades are spinning at 1,500 revolutions per minute, which translates into a time-step of 1.11×10^-4s. The simulation was set at 20 inner iterations per time-step to ensure convergence. The particle injector field consisted of a 15×15 rectangular grid of injectors and each injector was set to inject 100 particles per second. The simulation ran for a bit over 0.5s of simulation time, meaning that almost 13,000 particles were injected.

Certain assumptions and approximations were used within the simulation. The most important assumption was that the tractor lawn mower did not actually move within the simulation. The wheel rotation, translation and creation of a real grass field for the lawn mower to drive over being beyond the reasonable scope of the simulation, the movement was simulated by having the grass particles constantly injected into the cutting areas. Since the full tractor body was not included in the simulation, it did not need to be meshed at all, allowing for finer refinement of the blades, protector plate, and air volume in the area of question. Another approximation was that the grass external to the plate was not physically present to impede the motion of the moving particles. Hence, an invisible barrier was setup around the perimeter of the plate to the ground to prevent the leakage of particles in areas besides the ejector. This barrier was set as a porous region, allowing the fluid (air) to flow freely but not allowing the particles to cross the barrier. The third major approximation was the shape of the grass particles. Every grass particle was modeled as a composite of spherical particles in a 1 cm long conical shape. The composite particle was forbidden from being broken. To keep it simple and inexpensive, only one particle model was used. Additionally, the particles were injected into the region already separated from the ground; the lawn mower blades were not involved in separating them from the injector in any way and only provide air motion.

Because of the small time-step (caused by the 1 degree rotation mentioned above), a detailed picture of the motion of the particles was created. This enabled the visualization of areas where clumping occurred, as well as areas that were affected by internal vortices. Every particle was permitted to exit only through the ejector (in all of the figures, the ejector is positioned on the left-hand side). The particles were modeled with drag and their density was set to a value such that each particle would be primarily affected by the motion caused by the spinning blades. As with the previous case study, the particles were colored with respect to their velocity magnitude. The benefit of this simulation was demonstrating that a complex physical simulation of a lawn mower can be accurately modeled, allowing for designers to see the movement of each individual blade of grass. This permits the designers to modify their design based on complexities too subtle to be seen with the naked eye, modifications which can significantly increase their efficiency by reducing fuel consumption and the time required to mow.

Lagrangian multiphase

The Lagrangian-Eulerian approach is based on “a statistical description of the dispersed phase in terms of a stochastic point process that is coupled with an Eulerian statistical representation of the carrier fluid phase.” In other words, the main fluid phase is solved as a continuum using the time -averaged Navier-Stokes equations. The second, discretized phase, involves either a second fluid dispersed in relatively small pockets (eg. bubbles or droplets) or small particulates of a solid that is mixed in with the liquid.

The Lagrangian Multiphase model makes use of DEM particles and simulates each particle individually as it is affected by the fluid domain and collisions with other particles and features within the simulation boundaries. This is the most faithful representation of particles possible within a fluid simulation, allowing for the examination of primary and secondary breakup models, as well as turbulent dispersion. However, as one can imagine, it also requires a lot of processor power, especially when the number of particles exceeds 105.