A Close Up on COMSOL Multiphysics for soil-sensor design
Ronald W. Gamache is the director of Research and Development with TransTech Systems, Inc. (www.transtechsys.com). The company offers a wide range of products for asphalt paving and has achieved a worldwide reputation for innovation across various levels of the roadbuilding industry. By using COMSOL Multiphysics they acquired new insights into their sensor technology. Here Mr. Gamache gives his team's review of COMSOL Multiphysics (then called FEMLAB).
Rectangular slices of soil were simulated using 1-in.-thick layers. But simulations revealed an irregular shape to the response field. So the soil geometry was modified using a Bezier curve tool to produce subdomains that precisely reflected the measured volume. This shortened run times.
The best way to describe improvements added by the software is to work through an engineering problem, such as a sensor redesign. Our company produces an asphalt sensor that measures to a depth of 4 in. We wanted to apply this sensor to measure soil to a 12-in. depth but needed to limit its diameter. The primary design parameters were the shape and configuration of the sensing plates and associated ground planes. As there is no closed form solution for the electric field for this configuration, we resorted to simulation with COMSOL Multiphysics.
The software lets users model in 1d, 2d, and 3d, but because the soil-sensor concept is symmetric, we used a 2d axisymmetric mode for the electrostatics applications. Two-dimension models minimize computation time and memory requirements, while still providing excellent insight into resultant field patterns.
For example, sensor components and solids are represented by simple rectangular regions. After model building, the software translates the solid objects into subdomains and boundaries to which users assign material properties and boundary conditions. Because the soil sensor consists of regions with different electromagnetic properties, such as conductivity and permittivity, they are placed into separate subdomains.
To assist postprocessing, users may further subdivide homogeneous subdomains at important locations. In the sensor model, soil is subdivided into horizontal slices to assess values of interest at specified depths. Boundary conditions are assigned by specifying external voltage and currents. Geometry boundaries must exist where boundary conditions will be applied. Boundary condition values are specified in a dialog box or defined externally in the Constants dialog box (in Options menu) and symbolically specified in Boundary Settings. The software assists by assigning sensible defaults for each boundary, such as field continuity for internal dielectric boundaries between domains.
To build an adaptive mesh, users need only pick Initialize Mesh. If the automatic process does not produce an acceptable mesh, several levels of semiautomatic and manual controls are available to govern all aspects of mesh generation. The solve step finds a continuous solution for the entire model. On a 2 GHz P4 processor with 1 Gbyte ram and running xp, the sensor model took 8 seconds to solve. The time to solution depends on the physics, model, and mesh complexity.
Ron Gamache of Trans Tech Systems, Inc. analyzing soil sensor data.
The software then presents a default solution plot. In this case, it was a surface plot of potential across the view plane. The software also superimposes an arrow plot of the electric field vector. Values that would determine depth include the capacitance in each measurement subdomain and contour lines of the resultant displacement vector. To measure depth, the software calculates the capacitance in each subdomain measured by the sensor.
A general formula for capacitance is:
where V = potential across the domain and We = energy density. The integral is computed using a postprocessing integration function over the subdomain. We arbitrarily define the measurement depth as the depth at which the integrated capacitance is equal to 99.5% of its final value. But the Subdomain Integration function only calculates total energy, so its value was exported into Matlab. At the Matlab command line, capacitance is calculated using the equation above.
Visualization plots illustrate the performance differences between design options. Moving the ground plane (below) increased the sensing depth.
One idea for increasing the measurement depth without increasing sensor diameter is to remove the ground plane on the current sensor for asphalt. We thought field lines from the transmitter that are diverted to the ground plane would then pass into the soil. But the COMSOL Multiphysics solution for the modified sensor model illustrated the opposite: the ground plane allowed deeper penetration, the opposite of what was expected. Results showed field lines flowing from transmitter to ground penetrating deeper than those flowing from transmitter to receiver. This unexpected result steered the design in a different direction. Relocating and spacing the ground plane increased the penetration depth. The end result was a 100% increase in measurement depth with only a 10% increase in sensor diameter. Lab tests of a prototype agreed with simulation results.
In the design process, a problem developed with a boundary condition on an internal electrode that let the software technical support team demonstrate their quick response. The electrode has a floating potential that depended upon external circuits and properties of the material being measured. So this potential could not be specified prior to solving. COMSOL's documentation and sample library did not provide a method to apply floating potentials. However, an e-mail describing the problem and a call to the regional technical representative produced a timely solution and explanation. An entry regarding the problem and solution was later placed on the COMSOL website so others can benefit from the experience.
COMSOL Multiphysics is an intuitive, easy-to-use tool that provides insight to the detailed workings of complex devices. We estimate the software paid for itself on the first project.