Dynamics, Volume 4, Issue 2 (June 2024) – 14 articles

Fluidized beds are pivotal in the process industry and chemical engineering, with Computational Fluid Dynamics (CFD) playing a crucial role in their design and optimization. Challenges in CFD modeling stem from the scarcity or inconsistency of experimental data for validation, along with the uncertainties introduced by numerous parameters and assumptions across different CFD codes. This study navigates these complexities by comparing simulation results from the open-source MFIX and OpenFOAM, and the commercial ANSYS FLUENT, against experimental data. Utilizing a Eulerian–Eulerian framework and the kinetic theory of granular flow (KTGF), the investigation focuses on solid-phase properties through the classical drag laws of Gidaspow and Syamlal–O’Brien across varied parameters. Findings indicate that ANSYS Fluent, MFiX, and OpenFOAM can achieve reasonable agreement with experimental benchmarks, each showcasing distinct strengths and weaknesses. The study also emphasizes that both the Syamlal–O’Brien and Gidaspow drag models exhibit reasonable agreement with experimental benchmarks across the examined CFD codes, suggesting a moderated sensitivity to the choice of drag model. Moreover, analyses were also carried out for 2D and 3D simulations, revealing that the dimensional approach impacts the predictive accuracy to a certain extent, with both models adapting well to the complexities of each simulation environment. The study highlights the significant influence of restitution coefficients on bed expansion due to their effect on particle–particle collisions, with a value of 0.9 deemed optimal for balancing simulation accuracy and computational efficiency. Conversely, the specularity coefficient, impacting particle–wall interactions, exhibits a more subtle effect on bed dynamics. This finding emphasizes the critical role of carefully choosing these coefficients to effectively simulate the nuanced behaviors of fluidized beds. Full article

Organic Rankine Cycle (ORC)–based small-scale power plants are becoming a promising instrument in the recent drive to utilize renewable sources and reduce carbon emissions. But the effectiveness of such systems is limited by the low efficiency of gas expanders, which are the main part of an ORC system. Limaçon-based expansion machines with a fast inlet control valve have great prospects as they could potentially offer efficiencies over 50%. However, the lack of a highly reliable and significantly fast control valve is hindering its possible application. In this paper, a push–pull solenoid valve is optimized using a stochastic optimization technique to provide a fast response. The optimization yields about 56–58% improvement in overall valve response. A performance comparison of the initial and optimized valves applied to a limaçon expander thermodynamic model is also presented. Additionally, the sensitivity of the valve towards a changing inlet pressure and expander rotor velocity is analyzed to better understand the effectiveness of the valve and provide clues to overall performance improvement. Full article

High-pressure gas quenching is widely used in the metals industry during the heat treatment processing of steel specimens to improve their material properties. In a gas quenching process, a preheated austenised metal specimen is rapidly cooled with a gas such as nitrogen, helium, etc. The resulting microstructure relies on the temporal and spatial thermal history during the quenching. As a result, the corresponding material properties such as hardness are achieved. Challenges reside with the selection of the proper process parameters. This research focuses on the heat treatment of steel sample batches. The gas quenching process is fundamentally investigated in experiments and numerical simulations. Experiments are carried out to determine the heat transfer coefficient and the cooling curves as well as the local flow fields. Quenched samples are analyzed to derive the material hardness. CFD and FEM models numerically determine the conjugate heat transfer, flow behavior, cooling curve, and material hardness. In a novel approach, the experimental and simulation results are adopted to train artificial neural networks (ANNs), which allow us to predict the required process parameters for a targeted material property. The steels 42CrMo4 (1.7225) and 100Cr6 (1.3505) are investigated, nitrogen is the quenching gas, and geometries such as a disc, disc with a hole and ring are considered for batch series production. Full article

In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work. Full article

Thermo-vortices (bright spots, blobs, swirls) in cosmic fluids (planetary atmospheres, or even black hole accretion disks) are sometimes observed as clustered into quasi-symmetrical quasi-stationary groups but conceptualized in models as autonomous items. We demonstrate—using the (analytical) Sharp Boundaries Evolution Method and a generic model of a thermo-vorticial field in a rotating “thin” fluid layer in a spacetime that may be curved or flat—that these thermo-vortices may be not independent but represent interlinked parts of a single, coherent, multi-petal macro-structure. This alternative conceptualization may influence the designs of numerical models and image-reconstruction methods. Full article

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson’s correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R²), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures. Full article

A semilinear quadratic equation of the form $A_{ij}\left(x\right)u^{ij}=B_i(x,u)u^i+F(x,u)$ defines a metric $A_{ij}$; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities $B_i(x,u),F(x,u).$ From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric $A_{ij}$, while the second set serves as constraint equations, which select elements from the conformal algebra of $A_{ij}.$ Therefore, it is possible to determine the Lie point symmetries using a geometric approach based on the computation of the conformal Killing vectors of the metric $A_{ij}$. In the present article, the nonlinear Poisson equation ${\Delta }_{g}u-f\left(u\right)=0$ is studied. The metric defined by this equation is 1 + 2 decomposable along the gradient Killing vector ${\partial }_t$. It is a conformally flat metric, which admits 10 conformal Killing vectors. We determine the conformal Killing vectors of this metric using a general geometric method, which computes the conformal Killing vectors of a general $1+(n-1)$ decomposable metric in a systematic way. It is found that the nonlinear Poisson equation ${\Delta }_{g}u-f\left(u\right)=0$ admits Lie point symmetries only when $f\left(u\right)=ku$, and in this case, only the Killing vectors are admitted. It is shown that the Noether point symmetries coincide with the Lie point symmetries. This approach/method can be used to study the Lie point symmetries of more complex equations and with more degrees of freedom. Full article

The emergence of electric vehicles has brought new issues such as the problem of rolling element bearings (REBs) operating at high speeds. Losses due to these components in mechanical transmissions are a key issue and must therefore be taken into account right from the design stage of these systems. Among these losses, the one induced by the motion of rolling elements, known as drag loss, becomes predominant in high-speed REBs. Although an experimental approach is still possible, it is difficult to isolate this loss in order to study it properly. A numerical approach based on CFD is therefore a possible way forward, even if other issues arise. The aim of this article is to study the ability of such an approach to correctly estimate the drag coefficient associated with the motion of rolling elements. The influence of the numerical domain extension, the mesh refinement, the simplification of the ring shape, and the presence of the cage on the values of the drag coefficient is presented. While it seems possible to compromise on the calculation domain and mesh size, it appears that the other parameters must be taken into account as much as possible to obtain realistic results. Full article

Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction of lava flows, it is indispensable to elucidate them for accurate predictions of areas where lava strikes. At the first step of this study, lava was expressed using a molten metal with known physical properties. The computational results showed that levees and toe-like tips formed at the fringe of the molten metal flowing down on a slope, which appeared for actual lava flows as well. The dynamics of an overlapped structure formation were also simulated successfully; therein, molten metal flowed down, solidified, and changed the surface shape of the slope, and the second molten metal flowed over the changed surface shape. It was concluded that the computational model developed in this study using the SPH method is applicable for simulating and clarifying lava flow phenomena. Full article

This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions. Full article

For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches, length scale parameters have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modeling, as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established, there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion, system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach, it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically, it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior. Full article

This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create diverse natural and engineered surface textures, governed by probabilistic principles. The model’s formulation addresses key questions related to deposition initiation, nucleation point behaviour, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. A versatile algorithm, relying on six parameters and employing nested loops and Gaussian sampling, is developed. The algorithm’s efficacy is examined through extensive simulations, involving variations in nucleation scaling densities, aggregate scaling scenarios, spread factors, and diffusion rates. Surface statistics are computed for simulated deposits and analyzed using Fast Fourier Transform (FFT). The resulting database enables quantitative comparisons of surfaces generated with different parameters, where the database-derived parallel coordinates offer guidance for selecting optimal model parameters to achieve desired surface morphologies. The proposed approach is validated against urea-derived deposits, exhibiting statistical consistency and agreement with experimental observations. Overall, the model’s adaptable framework holds promise for understanding and predicting deposit growth on surfaces in diverse practical scenarios. Full article

The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability. Full article

Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially in process engineering, the majority of the proposed surrogate models address steady-state problems, while poor studies refer to dynamic simulation modeling. For this reason, using a response function-based approach, a crystallization unit case study was set up in order to derive a dynamic data-driven model for crystal growth whose characteristic differential parameters are derived via Response Surface Methodology. In particular, multiple independent variables were considered, and a well-established sampling technique was exploited for sample generation. Then, different sample sizes were tested and compared in terms of accuracy indicators. Finally, the domain partition strategy was exploited in order to show its relevant impact on the final model accuracy. In conclusion, the outcome of this study proved that the proposed procedure is a suitable methodology for dynamic system metamodeling, as it shows good compliance and relevant improvement in terms of computational time. In terms of future research perspectives, testing the proposed procedure on different systems and in other research fields would allow for greater improvement and would, eventually, extend its validity. Full article