The increasing complexity of the now de facto advanced electric energy system demands design analyses employing a multitude of physical parameters.


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Multiphysics modeling of 3-D temperature streamlines around lithium-ion batteries provide battery designers indicators of the performance characteristics they can expect. Source: Comsol   

New technologies, new materials, and more sophisticated modeling systems have made lithium-ion (Li-ion)-based systems the battery of choice for many designers looking to implement high-energy advanced electric power systems. For these systems, Li-ion systems have replaced nickel-metal hydride systems. Li-ion systems gain their value from their inherently lighter weight than other energy-equivalent systems (a NiMH battery pack would weigh more than twice that of the equivalent Li-ion battery pack used in the Tesla Roadster), their comparatively higher open circuit voltages, no memory effects, lower self-discharge rates, and environmentally safer components. On the flip side, however, charging a Li-ion battery forms deposits inside the electrolyte that inhibits ion transport that over time reduces the cell’s capacity. High charge rates and elevated temperatures also can accelerate the cell’s capacity loss.

If overheated or overcharged, Li-ion batteries may experience a thermal runaway situation that can lead to cell rupture and even combustion. Thermal runaway is a very specific description of these events. Once started there is basically nothing that can be done to stop the thermal runaway event until it has consumed all of its fuel. Deep-discharges can also short-circuit the cell and result in unsafe recharging effects. But lithium-ion technology, construction, and basic materials are constantly evolving to improve their energy density, durability, cost, and safety aspects.

Thermal runaways
Safety has been one of the driving factors in the development and commercialization of Li-ion battery applications, with several high-profile situations focusing on the thermal runaways (chemical reactions) that are possible with these systems due to the large amount of internal heat that could be generated due to defects, damage, or contaminants. Overheating design case studies have included Li-ion battery packs for laptop computers, systems powering hybrid electric vehicles, and aircraft applications including the recent Li-ion batteries in the Boeing 787 aircraft.

To correct for these design situations, new battery anode and cathode designs have been incorporated with enhanced cell insulation systems, cooling systems, control systems, and housings. To quickly, efficiently, and safely design and develop new iterations of these increasing complex Li-ion battery systems and to see the effects of new materials and designs, battery designers employ software-based modeling systems such as Comsol’s Multiphysics system.

“The chemistry and transport properties of various battery systems are different, along with their structures and component geometries,” says Ed Fontes, chief technology officer at Comsol, Burlington, Mass. “This is reflected in a higher specific power and energy density in Li-ion systems compared to older systems. The high energy density may also lead to the release of large amounts of heat in the case of failure, such as accidental short-circuiting or due to poor thermal management causing thermal runaway. A lot of our users model thermal management and also study the mechanisms that may follow an accidental internal short-circuit. Such models involve a tight multiphysics coupling between electrochemistry, chemistry, heat transfer, and fluid flow.”

Materials’ characteristics are available for many battery chemistries in the Multiphysics Batteries and Fuel Cells Module. Almost all of the materials properties are non-linear. The chemical and electrochemical properties depend non-linearly on temperature. The electrochemical reactions are also non-linearly dependent on the electric potential in the ionic and electronic conductors in the cell. “On top of that, electric conductivity, thermal conductivity, and other properties have to be described as nonlinear functions of temperature and local composition,” says Fontes. “Properties used in our Multiphysics programs are therefore described as explicit functions or in additional implicit equations in the model.”

Modeling failures
Failures in Li-ion batteries are mostly associated with over-heating due to some particular effect. The modeling of this heat generation effect is complex. “Most of our models do not apply heat uniformly,” says Fontes. “Heat generation and temperature are treated with a space-dependent energy balance just like any other field in the model (i.e., electric, flow, concentrations). This means that models are able to accurately describe the effects of short circuiting.

“In a battery model, a small flaw in the separator causing a short circuit yields a large generation of heat, which is localized to this small region due to the high currents and resistive heating. Eventually localized chemical reactions described in the model may contribute with their heat of reaction, similar to combustion. The heat transfer equations, coupled to the electrical, electrochemical, and chemical heat sources, also describe the spreading of the heat due to temperature gradients in the battery. This accounts for the anisotropy in the structure of the battery. This model, then, can therefore simulate a localized failure, space-dependent heat transfer, and the consequences to the thermal management of a battery.”

Tatsuya Yamaue, a member in the Engineering Mechanics Div., of Kobelco Research Institute, Kobe, Japan, has modeled the thermal runaway of Li-ion batteries using Multiphysics software and successfully compared those results to the testing of actual systems in his laboratory. Kobelco is a contract testing and research firm that focuses on automotive, battery, iron and steel, semiconductor, and medical industries. He initially validated his thermal runaway models with results measured on actual devices with accelerating rate calorimeters. “We have since made various modifications of modeling heat generation in Li-ion batteries and thermal runaway situations in short-circuit testing, for example, voltage drop and discharge heat generation considering the structure of electrodes,” says Yamaue.

In addition to modeling thermal runaway situations, Yamaue has modeled charge and discharge cycles, ionic transport within the battery electrodes, and nanosimulations of electrode surface reactions. These models were created using Multiphysics software and several other applications relating to molecular dynamics and ab intio molecular dynamics.

“Multiphysics is a good platform for studying advanced technology batteries such as Li-ion systems, which requires the analysis of complex physical phenomena on different scales. This includes such studies as the modification of chemical reaction model formulae, the application of integral boundary conditions for current distribution analysis, and the analysis of different physical phenomena for each domain,” says Yamaue.

Li-ion battery modeling is a good application for Multiphysics software because the whole system consists of multiphysics applications. A Li-ion battery model is not just a CAD program utilizing structural mechanics and computational fluid dynamics (or thermal analysis) modules. A good battery model includes electrochemical reactions involving the transfer of electrons through current collectors and electrodes matrices. Materials balances also need to be calculated for the transport of chemical species through diffusion, migration, and convection to and from the electrode surfaces, as well as any possible chemical reactions that might occur in the electrolytic solution.

In one of his studies, Yamaue simulated a failure resulting from an internal short circuit in a Li-ion battery. Temperatures within the cell over a period of time during a thermal runaway event were shown on the model along with the isosurfaces of reacted ratios of the negative electrode at 20-W and 100-W heat sources from the short circuit. For several tens of seconds, a wide reaction zone was observed to move from the vicinity of the short circuit toward the end of the battery.

Automotive applications
“Multiphysics models in automotive applications are infinite in number,” says Comsol’s Fontes. “I don’t think that regulatory agencies have researched the modeling area to any large extent, especially compared to its future potential as a complement to physical testing.” Automotive manufacturers don’t really have much of a choice in terms of accepting or not accepting models and model results, according to Fontes. They have to keep themselves updated to the highest level possible.

“You can learn a lot more from an accurate Multiphysics model and such models can also be used over a much wider range of operating conditions, and conditions that more often resemble real operating conditions,” says Fontes. This leads to a better design and cost savings in the search for better products.

John Newman, the Charles Tobias Chair of Electrochemistry in the Dept. of Chemical Engineering at the University of California, Berkeley, published the first model for the Li-ion battery which has been accepted in the industry as an accurate generic model for quite a few different types of Li-ion batteries. Comsol includes this model and variations of this model in 1-D, 2-D, and 3-D versions. “If we look at batteries in general, we need to constantly follow the literature in order to include new battery types and battery chemistries, and modifications to old models,” says Fontes. Automotive companies usually request such new models as soon as they are published in the scientific literature. Software companies are quick to implement these new models and make them accessible for their users in interfaces that can be adapted to different geometries, operating conditions and materials properties.

Researchers at the University of Illinois, Urbana-Champaign, recently announced a new Li-ion battery design that is up to 2,000 times more powerful and recharges up to 1,000 times faster than current devices. These huge advances come from a new cathode and anode structure. Conventional Li-ion batteries have a solid, 2-D anode made of graphite and a cathode made of a lithium salt. The new Li-ion battery, however, has a porous 3-D anode and cathode. To create this new electrode structure, the UI researchers built up a structure of polystyrene on a glass substrate, electro-deposited nickel onto the polystyrene and then electro-deposited nickel-tin onto the anode and manganese dioxide onto the cathode. This results in porous electrodes with a massive surface area, allowing for more chemical reactions to take place in a given space and resulting in a massive boost to discharge speed, or power output, and charging. The initial prototypes are relatively small, with an energy density that is slightly lower than conventional systems, but with a 2,000 times greater power density.

Cooling situations
Researchers at the Fiat Research Center in Orbassano, Italy, also make use of Comsol’s Multiphysics software for managing the thermal loads generated in Li-ion battery packs used in their company’s electric and hybrid vehicles. For their designs, they chose to employ convection air cooling for the battery packs, while keeping the packs as small and as light as possible. If one cell out of 100 doesn’t work well due to problems with heat, it has a negative impact on the entire pack. Their design limit was to keep all cells within a 5 C maximum differential. With the Multiphysics model, the researchers were able to reduce the physical cooling channels between cells, thereby reducing overall space requirements, reducing the frame size, and increasing the ability to replace the battery pack. The researchers calculated that the model reduced their overall system design time by 70%, or a net reduction of 700 man-hr needed to design the battery pack.