A novel numerical implementation of electrochemical-thermal battery model for electrified powertrains with conserved spherical diffusion and high efficiency

The performance of batteries in electrified powertrain systems is highly influenced by mass diffusion and electrochemistry which are often ignored in the simulation of these systems due to the lack of a conserved, efficient, and integrable battery model. Therefore, this work numerically implements an electrochemical-thermal battery model with conserved numerical schemes and efficient numerical methods which include Jacobian-based and Jacobian-Free Newton Krylov (JFNK) solvers. The performance of the developed model is evaluated by simulating measurements of a LiFePO 4 battery under constant discharge rates and Urban Dynamometer Driving Schedule (UDDS), as well as by a detailed comparison with existing battery models. The comparison highlights two features of our model: (a) negligible mass imbalances in the spherical diffusion modelling, which are five orders of magnitude smaller than those from a recent battery model in the literature; (b) efficient modelling of real-world driving cycles with the computational time two orders of magnitude shorter than that of the literature model. These advanced features indicate that our model can be applied in both fundamental electrochemical-thermal studies of lithium-ion battery and detailed simulations of electrified powertrains as an accurate and efficient sub-model.</p

Pneumatic drying of cassava starch: Numerical analysis and guidelines for the design of efficient small-scale dryers

In a number of tropical countries, the expansion of cassava processing is tied to the development of small-scale, energy-efficient pneumatic dryers used to dry flour and starch. To facilitate this development, in this study a model of the pneumatic drying of starch particles was developed, to be fitted to measurements taken from large cassava processing factories. After that, numerical simulations were performed to analyze the effects of geometry and operating conditions on the energy efficiency and pipe length required to dry the product. The results clarified the influence of processing capacity, air inlet conditions, and starch particle size, emphasizing that air velocity as well as the dilution of the starch should be minimized. In light of the findings described here, we offer guidelines for the design of efficient small-capacity flash dryers

Analysis of finite difference discretization schemes for diffusion in spheres with variable diffusivity

Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally dependent diffusivity, (III) spatially dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly defined, temporally and spatially dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position