Mathematical modeling and analysis of operation of cylindric pyrolysis reactor with radial heating

The vector of development of solid-fuel energy is currently directed towards expanding the range of renewable fuels used. Along with the direct combustion of fuel, the processes of controlled thermal transformation of the raw biomass in an oxygen-free surrounding to obtain a new fuel based on it (liquid, solid, gaseous) are widely spread. A significant part of research in this sphere is related to the study of the formal kinetics of such processes, at the same time, the hardware design of the process is no less important, but less studied. Thus, development of mathematical models of pyrolysis equipment operation is relevant. A decisive difference approximation of these processes in the framework of an axisymmetric formulation of the problem is chosen as a mathematical basis for modeling physical and chemical transformations and transfer processes in the radial direction of a cylindrical pyrolysis reactor. The material constants of the processes are borrowed from the well-known literature references The authors studied the modes of reactor operation not covered by a full-scale experiment, using the previously proposed and verified one-dimensional mathematical model of a cylindrical pyrolysis reactor. The issues of the influence of the dimensionless kinetic function of the process (reaction model) on the thermal transformation of the material in the apparatus are considered. The significant influence of the chosen reaction model on the kinetic nature of the process is pointed out. The mutual influence of drying and pyrolysis the presence of which is due to the energy effects of the processes is considered. A significant spatial heterogeneity of the process is defined and the possibility of the existence of a non-trivial effect of advanced heating of the internal zones of the apparatus in comparison with the peripheral ones is specified. The paper shows that a computational experiment can help to detect non-trivial effects and identify the variability of the process implementation even within the framework of a single design and technological solution of the pyrolysis process. According to the authors, the results of the obtained numerical experiments indicate that mathematical modeling can be the basis of making technological solution. However, further research is also needed to determine reliably the material constants of the process.

High-temperature effect on the material constants and elastic moduli for solid rocks

Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures.

Automated Material Parameter Calibration for an Electric Motor Stator

For accurate prediction of E-motor noise and vibration performance at the design stage, it is important to model the E-Motor stator structural behavior with high fidelity. Orthotropic material properties have been widely used in practice to simulate laminated steel in the stator. In these models, material constants are calibrated to match natural frequencies of critical modes such as oval/triangle/square modes. Typically, identifying accurate material properties is a manual, time-consuming process, involving lots of trial and error. This study presents an automated workflow to calibrate the material properties for the stator with Ansys Mechanical and optiSLang. The developed workflow can track natural frequencies and corresponding mode shapes of critical modes, and adjust material constants automatically to find best material parameters for the given frequencies. It can rotate the mode shapes and find the orientation that gives best match to the measurements based on modal assurance criteria (MAC). This workflow has shown a good correlation between simulation and test in terms of natural frequencies and corresponding mode shapes for the stator of a switched reluctance motor (SRM). Such an automated workflow enables the fast, efficient material calibration process, therefore accurate electric powertrain NVH simulations.

A Global Optimization Method to Determine the Complex Material Constants of Piezoelectric Bars in the Length Thickness Extensional Mode

Optimization methods have been used to determine the elastic, piezoelectric, and dielectric constants of piezoelectric materials from admittance or impedance measurements. The optimal material constants minimize the difference between the modeled and measured admittance or impedance spectra. In this paper, a global optimization method is proposed to calculate the optimal material constants of piezoelectric bars in the length thickness extensional mode. The algorithm is applied to a soft PZT and a hard PZT and is shown to be robust.

Characterization of Hoek–Brown constant mi of quasi-isotropic intact rock using rigidity index approach

An accurate determination of Hoek–Brown constant mi is of great significance in the estimation of the failure criteria of brittle rock materials. So far, different approaches such as rigidity index method (R-index), uniaxial compressive strength-based method, and tensile strength-based method, and the combination of these two methods (combination based method) have been proposed to calculate the value of mi. This paper aims to thoroughly review the previously existing methods to calculate the value of mi and make comparison between the obtain results to propose the new material constants that provide the best fit with the experimental data. In order to fulfill this goal, a large number of data for different quasi-isotropic intact rock types from the literature were collected and statistically analyzed. Additionally, based on rock types, new material constants are introduced for igneous, sedimentary, and metamorphic rocks. The obtained results proves that for different rock groups (igneous, sedimentary, and metamorphic rocks), R-index method provides the best fit with the experimental data among the others, and it is also independent of rock type. Interestingly enough, there is significant differences in the predicted mi values using different methods, which is more probably due to the quantity and quality of data used in the statistical analysis.

Method and Verification for Material Calibration of the Chaboche Plasticity Model for Multiple Material Directions

The Chaboche model is a well-validated non-linear kinematic hardening material model. This material model, like many models, depends on a set of material constants that must be calibrated for it to match the experimental data. Due to the challenge of calibrating these constants, the Chaboche model is often disregarded. The challenge with calibrating the Chaboche constants is that the most reliable method for doing the calibration is a brute force approach, which tests thousands of combinations of constants. Different sampling techniques and optimization schemes can be used to select different combinations of these constants, but ultimately, they all rely on iteratively selecting values and running simulations for each selected set. In the experience of the authors, such brute force methods require roughly 2,500 combinations to be evaluated in order to have confidence that a reasonable solution is found. This process is not efficient. It is time-intensive and labor-intensive. It requires long simulation times, and it requires significant effort to develop the accompanying scripts and algorithms that are used to iterate through combinations of constants and to calculate agreement. A better, more automated method exists for calibrating the Chaboche material constants. In this paper, the authors describe a more efficient, automated method for calibrating Chaboche constants. The method is validated by using it to calibrate Chaboche constants for an IN792 single-crystal material and a CM247 directionally-solidified material. The calibration results using the automated approach were compared to calibration results obtained using a brute force approach. It was determined that the automated method achieves agreeable results that are equivalent to, or supersede, results obtained using the conventional brute force method. After validating the method for cases that only consider a single material orientation, the automated method was extended to multiple off-axis calibrations. The Chaboche model that is available in commercial software, such as ANSYS, will only accept a single set of Chaboche constants for a given temperature. There is no published method for calibrating Chaboche constants that considers multiple material orientations. Therefore, the approach outlined in this paper was extended to include multiple material orientations in a single calibration scheme. The authors concluded that the automated approach can be used to successfully, accurately, and efficiently calibrate multiple material directions. The approach is especially well-suited when off-axis calibration must be considered concomitantly with longitudinal calibration. Overall, the automated Chaboche calibration method yielded results that agreed well with experimental data. Thus, the method can be used with confidence to efficiently and accurately calibrate the Chaboche non-linear kinematic hardening material model.

A new type of S-N equation and its application to multiaxial fatigue life prediction

The S-N equation is one of the most important equations in fatigue model investigation. A majority of fatigue models, including multiaxial fatigue model and mean effect models, are established on the basis of the S-N equation. Obviously, an accuracy of the S-N equation is very important. Taking into account that the S-N equation is, in fact, an empirical one in which the material constants are determined by numerical fitting fatigue experimental data, in this paper, the S-N equation can be improved, by further processing these fatigue experimental data, to present a new type of S-N equation that is more accurate than the S-N equation. The new type of S-N equation is called a similar S-N equation in this paper. By using a large number of experimental data of metallic materials reported in literature, an accuracy of the similar S-N equation has been proven.