Model predictive energy management for plug-in hybrid electric vehicles considering optimal battery depth of discharge

When developing an energy management strategy (EMS) including a battery aging model for plug-in hybrid electric vehicles, the trade-off between the energy consumption cost (ECC) and the equivalent battery life loss cost (EBLLC) should be considered to minimize the total cost of both and improve the life cycle value. Unlike EMSs with a lower State of Charge (SOC) boundary value given in advance, this paper proposes a model predictive control of EMS based on an optimal battery depth of discharge (DOD) for a minimum sum of ECC and EBLLC. First, the optimal DOD is identified using Pontryagin's Minimum Principle and shooting method. Then a reference SOC is constructed with the optimal DOD, and a model predictive controller (MPC) in which the conflict between the ECC and EBLC is optimized in a moving horizon is implemented. The proposed EMS is examined by real-world driving cycles under different preview horizons, and the results indicate that MPCs with a battery aging model lower the total cost by 1.65%, 1.29% and 1.38%, respectively, for three preview horizons (5, 10 and 15 s) under a city bus route of about 70 km, compared to those unaware of battery aging. Meanwhile, global optimization algorithms like the dynamic programming and Pontryagin's Minimum Principle, as well as a rule-based method, are compared with the predictive controller, in terms of computational expense and accuracy

Development of a hydrodynamic model and the corresponding virtual software for dual-loop circulating fluidized beds

Dual-loop circulating fluidized bed (CFB) reactors have been widely applied in industry because of their good heat and mass transfer characteristics and continuous handling ability. However, the design of such reactors is notoriously difficult owing to the poor understanding of the underlying mechanisms, meaning it has been heavily based on empiricism and stepwise experiments. Modeling the gas-solid CFB system requires a quantitative description of the multiscale heterogeneity in the sub-reactors and the strong coupling between them. This article proposed a general method for modeling multiloop CFB systems by utilizing the energy minimization multiscale (EMMS) principle. A full-loop modeling scheme was implemented by using the EMMS model and/or its extension models to compute the hydrodynamic parameters of the sub-reactors, to achieve the mass conservation and pressure balance in each circulation loop. Based on the modularization strategy, corresponding interactive simulation software was further developed to facilitate the flexible creation and fast modeling of a customized multi-loop CFB reactor. This research can be expected to provide quantitative references for the design and scale-up of gas-solid CFB reactors and lay a solid foundation for the realization of virtual process engineering

A general EMMS drag model applicable for gas-solid turbulent beds and cocurrent downers

Eulerian-Eulerian models incorporated with the kinetic theory of granular flow were widely used in the simulation of gas-solid two-phase flow, while the effects of mesoscale structures such as particle clusters and gas bubbles could not be considered adequately if traditional homogeneous drag models were adopted in the coarse grid simulations. The energy minimization multiscale (EMMS) model has been proved to facilitate calculating a structure-dependent drag coefficient by considering particle clustering phenomena, which can be coupled with the two-fluid model (TFM) to improve the accuracy of coarse-grid simulation of gas-solid circulating fluidized beds. However, the original EMMS drag model cannot be further applied to the simulation of gas-solid fluidized beds with solids flow rate smaller than zero, e.g., turbulent fluidized beds and cocurrent downward flow, because the original cluster diameter correlation gives rise to a value smaller than single particle diameter or even negative value at extremely low solids fluxes or downward gas-solid flow. In this study, a new proposed cluster evolution equation is proposed by quantifying local clustering dynamics to replace the original cluster diameter correlation. The newly formulated EMMS drag model can be used to avoid a negative cluster diameter to be involved in calculating interphase drag force in the overall fluidization regime. The improved EMMS drag law is incorporated into the Eulerian-Eulerian model to simulate gas-solid turbulent fluidized beds and cocurrent downer reactors, since they both were widely used in many industrial processes. By analyzing local hydrodynamics as well as the axial and radial heterogeneous distributions in the two kinds of fluidized beds, it is clarified that the simulation using the improved EMMS drag model shows a better agreement with the experimental data than the computation using the homogeneous drag law. (C) 2019 Elsevier Ltd. All rights reserved

A CFD-PBM-EMMS integrated model applicable for heterogeneous gas-solid flow

Accurate prediction of the structure-dependent interphase drag coefficient in a computational cell is of importance for the simulation of heterogeneous gas-solid flow. However, the cluster diameter in the cell was usually correlated with macroscopic hydrodynamic parameters or simply approximated as a constant value, though there is a cluster size distribution (CSD) at the sub-grid scale. Based on the energy minimization multiscale (EMMS) model and the population balance model (PBM), a CFD-PBM-EMMS integrated model was proposed to account for the effect of CSD on the interphase drag within the computational grid in this article, in which the PBM was used to describe the spatio-temporal evolution of CSD by introducing an EMMS-based cluster growth rate model. The CFD-PBM-EMMS model was validated by the experiments in a pilot-scale circulating fluidized bed riser of Geldart A and/or B particles. Comparing with the two-fluid model using the EMMS drag or homogeneous drag law, the CFD-PBM-EMMS integrated model shows the best agreement with the experiments under various operating conditions. Much effort is being devoted to incorporating the coalescence and breakage kinetics of clusters to the PBM further to improve the simulation accuracy of the CFD-PBM-EMMS integrated model, especially for dense gas-solid flow

CFD-PBM simulation of gas?solid bubbling flow with structure-dependent drag coefficients

Bubble size distribution resulted from bubble coalescence and breakup has significant effects on the effective interphase drag in gas?solid bubbling fluidized beds, which was however not taken into account in previous coarse-grid simulations. In this study, the population balance model (PBM) was used to describe the dynamic evolution of gas bubbles in gas?solid bubbling fluidization, wherein the coalescence and breakup kernels were derived by considering the effects of bubble velocity difference, wake capture and bubble instability. An improved energy-minimization multi-scale (EMMS) bubbling model was developed to calculate the effective interphase drag in sub-grid scale. By incorporating both the PBM and the EMMS drag into an Eulerian continuum model, a CFD-PBM-EMMS coupled scheme was further proposed to predict the hydrodynamics of bubbling fluidized beds. The scheme was validated through comparison of simulated results with experimental data. The bed expansion characteristics and the lateral profiles of solids velocities were reasonably predicted at acceptable computational cost. Satisfactory agreement was also achieved between the measured and simulated bubble size distributions. The proposed sub-grid drag model and coupled simulation scheme can facilitate capturing the salient features of the hydrodynamics of gas?solid bubbling fluidized beds

Kinetic modelling and experimental validation of single large particle combustion of coal char

Understanding apparent kinetics of single large fuel particle combustion is of significance to the design and optimization of grate-firing and circulating fluidized bed boilers. Based on the concept of finite reaction zone approximation, a simple heterogeneous single particle model was formulated to consider the effects of external gas film, ash layer and chemical reaction simultaneously. To validate the proposed model and gain insight into the prevailing rate-controlling mechanism during the single particle combustion process at different combustion temperatures and particle sizes, the experiments on the combustion of coal char powder and single large char particles were carried out in a thermal gravimetric analyzer and a bench scale fixed-bed reactor, respectively. The intrinsic and apparent kinetics as well as the effective reacting zone thickness of single large particle combustion were quantified by combining theoretical analyses and experimental data. Both the bulk flow temperature and particle size have a remarkable influence on the global reactivity. The rate-controlling process was found to shift from the intrinsic chemical reaction to ash layer diffusion and return again to the intrinsic kinetics at the burnout stage. Particularly, an external effectiveness factor was defined as a function of conversion degree to better describe the ash diffusion effect on the apparent reactivity of large particles. The proposed model is physically general but simple enough to be incorporated into the computational fluid dynamic simulation of large-scale grate-firing and fluidized bed boilers

Steady-state modeling of axial heterogeneity in CFB risers based on one-dimensional EMMS model

Axial heterogeneity in circulating fluidized bed (CFB) risers is very important to the design of fluidized bed reactors, which is, however, still unable to be described in theory. Based on a successful description of local hydrodynamics in gas solid flow, the Energy-Minimization Multi-Scale (EMMS) theory further relates axial hydrodynamics with local and global stability conditions in the system, providing a theoretical way to account for the axial heterogeneity in CFB risers. This research reveals that the interaction between particle clusters and the dilute phase as well as the surrounding dense phase has a significant effect on their dynamical evolution. Similar to cluster diameter in the EMMS theory, number density of particle clusters serving as a comprehensive indicator to the heterogeneity in gas solid flow is constrained by both local and global stability conditions in the system. With the above cognition, a one-dimensional EMMS model is developed to perform steady-state modeling of the axial heterogeneity in CFB risers. The model successfully reproduces a complete transition zone and the parametric effects on it at the choking condition. The S-shaped axial voidage profile calculated by the one-dimensional EMMS model is in good agreement with the experimental results in gas solid fast fluidization. This research is not only the first step toward implementing the three-scale computation in virtual process engineering (VPE), but also of referential significance to industrial chemical process development. (C) 2013 Elsevier Ltd. All rights reserved

Kinetic modelling and experimental validation of single large particle combustion of coal char

Understanding apparent kinetics of single large fuel particle combustion is of significance to the design and optimization of grate-firing and circulating fluidized bed boilers. Based on the concept of finite reaction zone approximation, a simple heterogeneous single particle model was formulated to consider the effects of external gas film, ash layer and chemical reaction simultaneously. To validate the proposed model and gain insight into the prevailing rate-controlling mechanism during the single particle combustion process at different combustion temperatures and particle sizes, the experiments on the combustion of coal char powder and single large char particles were carried out in a thermal gravimetric analyzer and a bench scale fixed-bed reactor, respectively. The intrinsic and apparent kinetics as well as the effective reacting zone thickness of single large particle combustion were quantified by combining theoretical analyses and experimental data. Both the bulk flow temperature and particle size have a remarkable influence on the global reactivity. The rate-controlling process was found to shift from the intrinsic chemical reaction to ash layer diffusion and return again to the intrinsic kinetics at the burnout stage. Particularly, an external effectiveness factor was defined as a function of conversion degree to better describe the ash diffusion effect on the apparent reactivity of large particles. The proposed model is physically general but simple enough to be incorporated into the computational fluid dynamic simulation of large-scale grate-firing and fluidized bed boilers

Three-dimensional CFD simulation of tapered gas-solid risers by coupling the improved EMMS drag

Tapered gas-solid risers have been used in some industrial processes in order to adapt to the requirements of various reactions, but little attention was paid to these reactors in previous investigation. In this work, three-dimensional gas-solid flow in tapered-out and tapered-in risers was simulated by the two-fluid model using an improved structure-dependent drag based on the EMMS model. The EMMS model was solved at different axial levels to determine different correlations of heterogeneity index with voidage, which were then interpolated between these levels to improve the prediction of varying interphase drag in the tapered risers. Considering the axial variation of the EMMS drag, the simulation predicts much more reasonable flow dynamics in the tapered risers than those coupled with an average EMMS drag or homogeneous drag laws. The axial and radial heterogeneities as well as the parametric effects on the flow dynamics in the tapered risers were discussed in detail, so as to provide reference for the proper design of tapered gas-solid riser reactors. (C) 2019 Elsevier B.V. All rights reserved

Modeling the hydrodynamics of cocurrent gas-solid downers according to energy-minimization multi-scale theory

Cocurrent gas-solid downer reactors have many applications in industry because they possess the technological advantages of a lower pressure drop, shorter residence time, and less solid backmixing when compared with traditional circulating fluidized bed risers. By introducing the concept of particle clusters explicitly, a one-dimensional model with consideration of the interphase interactions between the fluid and particles at both microscale and mesoscale is formulated for concurrent downward gas-solid flow according to energy-minimization multi-scale (EMMS) theory. A unified stability condition is proposed for the differently developed sections of gas-solid flow according to the principle of the compromise in competition between dominant mechanisms. By optimizing the number density of particle clusters with respect to the stability condition, the formulated model can be numerically solved without introducing cluster-specific empirical correlations. The EMMS-based model predicts well the axial hydrodynamics of cocurrent gas-solid downers and is expected to have a wider range of applications than the existing cluster-based models. (C) 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese. Academy of Sciences. Published by Elsevier B.V. All rights reserved.</p