Different industrial applications involve the modeling of flow through porous material, like water filtration, catalyst beds, packing, etc.
Darcy-Forchheimer law can be used on the Porous media to characterize the pressure drop:
Where S is a source term added to the Navier-Stokes equations. This term is composed of a viscous loss term and an inertial loss term, creating a pressure drop that is proportional to the velocity and velocity squared, respectively.
The constants D and F have physical meaning and could be calculated based on permeability and Ergun’s coefficient, but in this work they have been determined by curve fitting of the pressure/velocity curves of the porous material.
This image shows streamlines passing trough the filling material and drift eliminator of a cooling tower:
The simulation has been performed at Idra Simulation on a 3.7 millions elements mesh.
From Design to Prototype using Topology Optimization
Topology optimization determines the distribution of material most suitable to a given objective. It is primarily used to produce a fundamental basis for the engineers at the conceptual design stage, or to generate ideas for new alternatives.
In order to express the distribution of materials in topology optimization, density variables of the finite elements created for analysis are used. The element density of 1 represents a part that requires the element, while 0 represents a part that does not require the element. Unlike parametric optimization, the only design variable is the element’s density. As such, the user does not specify separate design variables but composes an optimization problem using only the combinations of objective functions and constraints.
Like any optimization problem, Topology optimizationincludes the following fundamental elements:
Objective: In this problem, the objective is to minimized the static compliance (a function of element density expressed in the form of global deformation energy):
f : Load vector
u : Global & element displacement vectors
K: Global & element stiffness matrices
Design variables: Volume fraction (the n_nodes density values which determine whether material is present (1) or absent (0))
Geometric constraints: the initial unoptimized geometry:
Design evaluator: the linear elasticity solver of MidasNFX, that calculates deformation energy based on specified loads and boundary conditions.
Since we are looking for general guidelines of an optimal design (in practice, we should say “better design”), the next step consists of modifying the original CAD geometry to remove material when it’s not needed:
Topology optimization often leads to complicated organic-like products that cannot be manufactured using traditional processes (which is not necessarily the case here). Additive manufacturing, like 3D printing, is sometimes more adapted for this kind of design. Here, a printed version of the optimized part is produced.
A simple model, with a lot of added value! For this project, Midas NFX has been used to control the thickness of the thermocline (the layer of fluid where the temperature changes rapidly).
The container is initially filled with warm water, and the inlet of cold water progressively replace it. The shape of the diffusers and the flow rate are adjusted to keep the thickness of the thermocline under a critical value.
This short film presents an original application of HPC, namely Agent-based social simulation applied to prehistoric life:
The video is produced by the BSC Scientific Visualization Team. This center is also developing Alya (see this previous post about Alya), a multi-physics code designed to run efficiently in supercomputers.
The harmonic analysis can be performed directly in the physical space, or by the modal superposition method – which could be useful for large problems (superposition of modes of the full structure or a series of sub-structures).
The macro commande DYNA_VIBRA gathers many of the dynamic options under a single command, e.g.:
Fusion 360: professional CAE software for 20€/month
As mentioned in this blog some weeks ago, CAD is moving on the cloud. A “new” player in this market is Autodesk’s Fusion 360. It would be difficult to describe all the features of this revolutionary tool here, so visit this link. If you are not convinced yet, see:
Not enough? They have a big active user community, a good technical support and you can write scripts with an API:
You may or may not like Autodesk’s decision to stop selling perpetual licenses, but you have to admit that 20 €/month for Fusion 360 is a good price. Yes, I said 20€.
A last important detail for FEA user: you can do “direct modeling” on imported parts. But I let this for another post…
For all those reasons, Idra Simulation decided to adopt it. This option is more flexible than the expensive licenses of SolidWorks, Creo and cie (their maintenance fees alone are more expensive than Fusion 360); and the few active open-source CAD projects are not yet ready for the industry.