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High Resolution Global NOx Sub-Model for Embedded System Application with Low Calibration Effort
(2020)
The starting point of the present work is a global model of NOx formation for stoichiometric and lean combustion of hydrocarbons developed on the basis of a single non-linear algebraic equation. The latter is the exact solution of a system of differential equations describing the main kinetic reaction schemes of NOx formation, because it’s been analytically derived. The NOx sub-model incorporates the well-established thermal (extended Zeldovich) and the N2O reaction paths, which are considered to be the most relevant NOx production paths under certain operating conditions in arbitrary engine application. Furthermore, the NOx sub-model proposed here relies on well-established and adopted mechanisms like the GRI-Mech 3.0 [25] and consequently requires no parameter adjustment.
The single equation NOx sub-model has been developed by the authors in a previous study [14] and shown satisfactory results when validated against test bench data of two different engines operated under stoichiometric and lean burn combustion conditions respectively. Therefore, there is a strong evidence, that its implementation on embedded systems for "in-situ" and "in memory" analysis of engine process data, or even its application as a virtual sensor, is of great importance. Unfortunately, the previous developed NOx sub-model requires a few seconds running time per engine cycle. This long running time makes the model though less attractive for a real-time application. In the current study the main goal is to drastically reduce the computational times without compromising robustness and accuracy. The require-ments for the time resolution on a dSpace Microautobox (MAB) is set to at least 1 kHz, meaning running times of the NOx sub-model of 1 ms per engine cycle, while its accuracy needs to be ensured at the levels of the detailed NOx sub-model as validated in [14].
The computationally most expensive steps have been identified and concern on the one hand the chemical equilibrium calculations based on the minimization of the free Gibbs energy and on the other hand the iterative solution method of the non-linear algebraic equation for the determination of the actual NOx concentration. Approaches for both steps have been developed and tested on the dSpace MAB II leading to an average computational time of 20 μs per point. Main focus of the present work is on the NOx sub-model and not the associated thermodynamic sub-models needed to describe the whole process. In order to cope with any uncertainties in NOx sub-model’s input parameters (p, T and mixture composition) only one calibration factor has been introduced and hence leads to low calibration effort. The final NOx sub-model results are compared to the detailed model and show a very good agreement.
High Resolution Global NOx Sub-Model for Embedded System Application with Low Calibration Effort
(2020)
The Interior Permanent Magnet Synchronous machine (IPMSM) conventional mathematical model is generally employed to investigate and simulate the IPMSM
control and drive system behaviour. However, magnetic nonlinearities and spatial harmonics have a substantial influence on the IPMSM electromagnetic behaviour and
performances. In order to simulate the IPMSM real electromagnetic behaviour, this paper describes an enhanced mathematical model that takes into account the
saturation, cross-coupling and spatial harmonics effects. This model has been implemented in Matlab®/Simulink environment where the electric and magnetic parameters are derived from FEA investigations and implemented by the use of lookup tables. The high fidelity of the proposed IPMSM Simulink model is validated by the results of the FEA investigations carried out.
A shorter product life cycle and therefore, reduced
project duration is the major success factor for machinery and
plant engineering today. One use case for Virtual Commission-
ing (VC) is the early software test without an existing plant.
The primary effort of VC lies in the manual creation of the
plant model. There are various simulation tools with different
advantages available. Selecting one tool has consequences for
the whole engineering process. The exchange of models across
different tools is not possible or discouraged by the respective
vendors due to various reasons. This paper describes a concept to
exchange behavior models via the table-based import interfaces
for an automated model generation within common simulation
tools. The concept utilizes an approach to exchange the behavior
of components using the vendor-neutral and standardized pro-
gramming language PLCopenXML containing all IEC 61131-3
programming languages. This removes the main obstacle for a
broader industrial application of VC, as it minimizes the manual
effort for creating and exchanging behavior models through the
use of standardized library elements and existing interfaces.
Upgrading hundreds of thousands of already available CPAP home therapy machines to function as BIPAP/Bilevel machines may help to mitigate the current global threat of a shortage of ventilators. The concept may help to prevent the scenario that soon potentially thousands of COVID-19 patients will not be able to receive the necessary and sometimes life-saving respiratory support. This solution could be made available in very short time, because it is purely software based.
The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we develop and prove an equation to calculate the maximum possible number of divisions by two for any given a Collatz sequence. Whenever this maximum is reached, a sequence leads to the result one, as conjectured by Lothar Collatz. Furthermore, we show how many divisions by two are required for a cycle of a specific length. The findings are valuable for further investigations and could form the basis for a comprehensive proof of the conjecture.
The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we formulate and prove several theorems on the occurrence of cycles and the termination of Collatz sequences. The findings are useful for further investigations and could form the basis for a comprehensive proof of the conjecture.
<div class="section abstract"<div class="htmlview paragraph"In this work a quasi-dimensional multi-zone combustion diagnostic tool for homogeneous charge Spark Ignition (SI) engines is analytically developed for the evaluation of heat release, flame propagation, combustion velocities as well as engine-out NOx and CO emissions, based on in-cylinder pressure data analysis. The tool can be used to assess the effects of fuel, design and operating parameters on the SI engine combustion and NOx and CO emissions formation processes.</div<div class="htmlview paragraph"Certain novel features are included in the presently developed combustion diagnostic tool. Firstly, combustion chambers of any shape and spark plug position can be considered due to an advanced model for the calculation of the geometric interaction between a spherically expanding flame and a general combustion chamber geometry. Also, the temperature stratification of the burned gas developed during the combustion phase, which has to be captured for the theoretically realistic estimation of the in-cylinder formation of pollutant emissions, is taken into account by a multi-zone thermodynamic treatment. According to this, multiple spherically allocated burned zones are sequentially generated at specified (user-defined) crank angle intervals, forming overlapping shells. Moreover, complex chemical equilibrium compositions are computed, which can include any user-defined mixture of species in the combustion products, using an advanced modular method based on the minimization of Gibbs energy. Furthermore, NOx and CO engine-out emissions are calculated based on novel in-cylinder formation models presented by the authors in the past. Specifically, NOx emissions are evaluated by a global algebraic NOx emissions formation model, accounting for both thermal and N<sub2</subO pathway NO formation, based on the calculation of the characteristic timescales of the relevant NO formation mechanisms. CO emissions are assessed using a new kinetics-based model, consisting of a single Ordinary Differential Equation (ODE) that can be analytically integrated. The CO emissions model is derived considering the dynamics of a representative pool of active radicals in post-flame gases and explicitly describes the CO oxidation quenching process.</div<div class="htmlview paragraph"The combustion diagnostic tool is applied to a lean burn gas engine at various engine speeds under full load conditions and constant lambda value. Various combustion and NOx and CO emissions related results are presented and discussed to illustrate the capabilities of the tool for combustion diagnosis, while at the same time calculated engine-out NOx and CO emissions are found to be in satisfactory agreement with measured ones.</div</div
In this work a quasi-dimensional multi-zone combustion diagnostic tool for homogeneous charge Spark Ignition (SI) engines is analytically developed for the evaluation of heat release, flame propagation, combustion velocities as well as engine-out NOx and CO emissions, based on in-cylinder pressure data analysis. The tool can be used to assess the effects of fuel, design and operating parameters on the SI engine combustion and NOx and CO emissions formation processes. "Certain novel features are included in the presently developed combustion diagnostic tool. Firstly, combustion chambers of any shape and spark plug position can be considered due to an advanced model for the calculation of the geometric interaction between a spherically expanding flame and a general combustion chamber geometry. Also, the temperature stratification of the burned gas developed during the combustion phase, which has to be captured for the theoretically realistic estimation of the in-cylinder formation of pollutant emissions, is taken into account by a multi-zone thermodynamic treatment. According to this, multiple spherically allocated burned zones are sequentially generated at specified (user-defined) crank angle intervals, forming overlapping shells. Moreover, complex chemical equilibrium compositions are computed, which can include any user-defined mixture of species in the combustion products, using an advanced modular method based on the minimization of Gibbs energy. Furthermore, NOx and CO engine-out emissions are calculated based on novel in-cylinder formation models presented by the authors in the past. Specifically, NOx emissions are evaluated by a global algebraic NOx emissions formation model, accounting for both thermal and subO pathway NO formation, based on the calculation of the characteristic timescales of the relevant NO formation mechanisms. CO emissions are assessed using a new kinetics-based model, consisting of a single Ordinary Differential Equation (ODE) that can be analytically integrated. The CO emissions model is derived considering the dynamics of a representative pool of active radicals in post-flame gases and explicitly describes the CO oxidation quenching process. "The combustion diagnostic tool is applied to a lean burn gas engine at various engine speeds under full load conditions and constant lambda value. Various combustion and NOx and CO emissions related results are presented and discussed to illustrate the capabilities of the tool for combustion diagnosis, while at the same time calculated engine-out NOx and CO emissions are found to be in satisfactory agreement with measured ones.
A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.