Simple Boundary Conditions Research Articles

Boundary conditions in flutter simulations of subsonic, transonic and supersonic blade cascades

Simulations of blade flutter are highly sensitive to undesired wave reflections at inlet and outlet boundaries. A careful treatment of boundary conditions is required to prevent the generation of perturbations. This study is motivated by the need to perform flutter analysis of low-pressure steam turbine blades, for which supersonic inflow conditions may occur in the near-tip region. The exact steady non-reflecting boundary condition (NRBC), the spectral NRBC and a simple isentropic boundary condition are implemented in a time-marching flow solver and applied to turbomachinery flutter simulations covering a wide range of operating conditions. For the first time, the spectral NRBC is applied to a blade flutter simulation with a supersonic inlet and its performance is analysed and compared with other boundary condition formulations. It is shown that an effective non-reflective treatment in the design of the boundary condition is essential for an accurate aeroelastic prediction at all operating conditions, including the subsonic flow regime. The limitation of the exact steady NRBC to spatial modes causes it to perform poorly in some unsteady flow simulations, whereas the spectral NRBC achieves a satisfactory suppression of undesired wave reflections in all investigated cases.

Total capacity and LOS estimation of innovative and conventional roundabouts through macroscopic fundamental diagrams

Traffic congestion remains a significant problem, especially in urban areas. To avoid congestion phenomena, several measures can be adopted, including the construction of roundabouts and the control of the measures of effectiveness (MOEs) at intersections. This article compares different types of roundabouts by estimating the deterministic fundamental diagram (MFD) and using microscopic traffic simulations. The deduction of MFD for different roundabout types (single and double-lane, flower and turbo-roundabout) is based on reasonably simplified traffic and boundary conditions. MFDs are estimated through several OD traffic matrices, considering as outputs the values of the macroscopic traffic variable deduced in time intervals of 5 min and 1 h. The findings from this research, in terms of total capacity, travel times, and level of service (LOS) estimation, may be useful for traffic and highway engineers in many realistic applications to partially face congestion phenomena in urban areas. MFDs allow us to determine the best roundabout type based on the traffic demand and represent a parsimonious method for monitoring and controlling traditional and unconventional or smart roundabouts, even in the presence of connected and automated vehicles (CAVs).

Dynamic Recrystallization of Olivine During Simple Shear: Evolution of Microstructure and Crystallographic Preferred Orientation From Full‐Field Numerical Simulations

AbstractUpper mantle deformation is mainly controlled by the mechanical behavior of olivine. Crystallographic preferred orientations (CPOs) develop in olivine due to crystal‐plastic deformation during mantle flow, where the a‐axes of olivine polycrystalline aggregates are aligned with the flow direction. Therefore, the observed CPO in olivine‐rich rocks is used as an indicator of the mantle flow direction. Experimental data show that olivine rheology is strongly controlled by the microstructure. While the influence of plastic deformation is in general well characterized, the role of dynamic recrystallization during deformation is not totally understood, limiting our ability to interpret the deformation history of naturally deformed rocks. This contribution presents microdynamic numerical simulations of olivine polycrystalline aggregates with different iron content (i.e., fayalite content) with the aim of exploring the CPO and grain size response to dynamic recrystallization. We use a full‐field approach with an explicit simulation of viscoplastic deformation and dynamic recrystallization processes under simple shear boundary conditions up to high strain. The simulations show that the CPOs are similar and practically reach the same maximum regardless of the iron content. CPOs are characterized by a single cluster of a‐axis and two‐clusters of b‐axis, reveling a joint activity of the easy glide [100](010) and the moderate strength [100](010) slip systems. High‐strain domains of our models are consistent with experimental results, showing an A‐type fabric with double maxima, and where the CPO is aligned with the shear direction. The model provides a deeper understanding of the dynamic recrystallization influence on olivine CPOs resulting from plastic deformation.

Optimal Control Problem with Regular Mixed Constraints via Penalty Functions

AbstractBelow we derive necessary conditions of optimality for problems with mixed constraints (see Dmitruk in Control Cybern 38(4A):923–957, 2009) using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., De Pinho et al. in Optimization 71(11):3363–3381, 2022) and, more recently, to solve optimal control problems with pure state constraints (see De Pinho et al. in Syst Control Lett 188:105816, 2024). We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact. Based on our penalty functions approach we develop a numerical method admitting estimates for its parameters needed to achieve a given precision.

Necessary and sufficient conditions for avoiding Babuška’s paradox on simplicial meshes

Abstract It is shown that discretizations based on variational or weak formulations of the plate bending problem with simple support boundary conditions do not lead to the failure of convergence when polygonal domain approximations are used and the imposed boundary conditions are compatible with the nodal interpolation of the restriction of certain regular functions to approximating domains. It is further shown that this is optimal in the sense that a full realization of the boundary conditions leads to failure of convergence for conforming methods. The abstract conditions imply that standard nonconforming and discontinuous Galerkin methods converge correctly while conforming methods require a suitable relaxation of the boundary condition. The results are confirmed by numerical experiments.

Assessment of transient thermal stresses in gasketed plate heat exchangers

Thermal and mechanical stresses in stainless steel 316 L plates of gasketed plate heat exchangers (GPHEs) have been assessed with the aid of experiments. Stresses were indirectly determined with the aid of extensometers in critical plate areas. To the best of our knowledge, no experimental analysis of transient thermal loads on GPHE plates has been reported before. Experiments occurred with sudden and gradual heating processes with the aid of strain gauges. The former process implies that hot fluid enters the GPHE branch with the final target temperature, while the latter indicates that the hot fluid is progressively heated to the target temperature. Furthermore, combined mechanical and thermal stresses resulting from in-phase and out-of-phase loads are assessed in single and double operating conditions. Experiments were carried out with two plate thicknesses (0.5 and 0.7 mm). Stresses as obtained from experiments were compared to those provided by models containing simplified geometries and boundary conditions. Mechanical stresses promoted by the pressure difference between GPHE branches mostly affected the distribution area in single configuration. Thermal stresses at the porthole were higher than the ones found at the distribution zones, particularly for thicker plates. Besides, thermal stresses increased in double operation. Sudden heating processes with the system at rest promoted thermal peaking stress in a timescale of seconds, while the timescale to reach peak values by gradually heating the hot fluid is in the order of minutes. The most critical condition would be achieved at the porthole with in-phase loads and in double operation for the given settings.

Assessing the impact of surface water and groundwater interactions for regional-scale simulations of water table elevation

Groundwater flow models are increasingly considered for the regional scale simulation of hydraulic heads and water table elevation. In the most complete configuration, models explicitly simulate two-way interactions between surface water (SW) and groundwater (GW) to reproduce and forecast both SW and GW water levels. In most regional scale groundwater models, however, SW-GW interactions are represented by simplified boundary conditions that only allow one-way interaction from SW to GW, neglecting most of the dynamic exchange fluxes between SW and GW. To evaluate the potential consequences of such simplifications on the simulation of regional GW levels, we compare two models on a 36,900 km2 regional aquifer system in Southern Quebec. One model explicitly simulates both SW and GW flow with two-way SW-GW feedback and the other model only simulates GW flow with a surface boundary flux to represent a one-way interaction with the land surface. Both models are developed with the same numerical code to ensure that the only differences are the representation of SW water flow and SW-GW feedback. The one-way model simulates overall deeper water tables because it removes all exfiltrated groundwater from the system once it exits the subsurface, therefore not allowing exfiltrating groundwater to re-infiltrate. This effect is most pronounced in areas where the water table is close to the surface and for low-flow periods. The inclusion of two-way feedback also reduces the sensitivity of simulated GW levels to the magnitude of the hydraulic conductivity. This result highlights the need for additional data on other system states to improve the calibration of regional scale models that explicitly simulate two-way SW-GW interactions.

Dynamic response analysis of ship reef hard grounding

Abstract With the rapid growth of the world economy, the shipping industry has developed rapidly on a global scale, and the water traffic has become increasingly busy. Therefore, the risk of ship transportation has become bigger and bigger, and ship grounding and collision occupy about 50% of the total number of all accidents, among which the consequences of oil tanker grounding accidents are more serious, which not only jeopardize the safety of the personnel but also cause a large area of pollution to the sea. Therefore, it is particularly important to study the ship grounding and collision of oil tankers. Based on the nonlinear finite element software ABAQUS, a calculation model for oil tanker grounding is established, and simplified boundary conditions that can be used for grounding simulation analysis are determined. At the same time, material strain rate sensitivity and material hardening properties are considered. Based on the quasi-static tensile test data of Q235 steel used in ships, material parameters that meet the requirements of collision simulation calculation are calibrated and calculated. The dynamic response of hard grounding is analyzed from both external and internal mechanisms. The research results can provide a reference for improving the grounding collision performance of oil tankers.

Modeling the Transport of Solar Energetic Particles in a Corotating Interaction Region

We present a new three-dimensional (3D) magnetohydrodynamic (MHD) model and a new 3D energetic particle transport (EPT) model. The 3D MHD model numerically solves the ideal MHD equations using the relaxing total variation diminishing scheme. In the 3D MHD simulations, we use simple boundary conditions with a high-speed flow, and we can clearly identify a corotating interaction region (CIR) with the characteristics of forward shock and reverse shock. The 3D EPT model solves the Fokker–Planck transport equation for the solar energetic particles (SEPs) using backward stochastic processes, with the magnetic field and solar wind velocity field from MHD results. For comparison, the 3D EPT model results with Parker fields are also obtained. We investigate the transport of SEPs with particle sources and observers in different positions in MHD fields with a CIR, and we compare the results with those in the Parker fields. Our simulation results show that the compression region with local enhancement of the magnetic field, i.e., CIR, can act as a barrier to scatter energetic particles back, and particles can struggle to diffuse through the strong magnetic field regions. Usually, a normal anisotropy profile is commonly present in SEP simulation results with Parker fields, and it is also typically present in that with MHD fields. However, because of the compression region of the magnetic field, energetic particles may exhibit anomalous anisotropy. This result may be used to replicate the spacecraft observation phenomena of the anomalous anisotropy.

A simple boundary condition regularization strategy for image velocimetry-based pressure field reconstruction

A simple boundary condition regularization strategy for image velocimetry-based pressure field reconstruction

Crystallization kinetics during layer exchange of 28Si implanted Al films for fabrication of quantum computers: A theoretical model

We are investigating a novel enrichment process that could allow the use of industrial complementary metal–oxide–semiconductor implanters to manufacture “quantum grade” 28Si layers for use in quantum computers. Our implanted layer exchange enrichment process leverages conventional deposition-based layer exchange approaches but replaces a step of depositing a Si layer above an Al layer with a 28Si implant into the top of an Al layer. A subsequent anneal dissolves Si into Al beneath the implanted region where Si diffuses and either epitaxially grows onto the substrate or forms poly-crystals in the Al [Schneider and England, ACS Appl. Mater. Interfaces 15, 21609 (2023)]. We have developed a qualitative model using simple assumptions and boundary conditions to estimate characteristic times and rates of epitaxy or poly-crystallization for this novel layer exchange process. We have used the model to explain crystallization outcomes reported in this paper and previously. We find that the absence of an oxide boundary layer separating Si and Al allows Si diffusion to become established within the first second of all the anneals studied and that crystallization actually completes during the temperature ramp of most of the anneals. The rapid evolution of Si supersaturation in Al beneath the implanted layer explains the ratios of epitaxial growth to poly-crystallization observed after these anneals. We use this understanding to propose the implant layer exchange conditions that could produce the highest quality mono-crystalline quantum grade Si.

Analytical solution of forced vibration of rectangular plates with part through surface crack based on wave propagation method

An analytical wave propagation framework is developed in this study for steady state forced vibration of plates with part through surface cracks for the first time. Rectangular thin plates with partial-width and full-width cracks are considered. The analytical waves are obtained by solving the dual equations of the plate established considering the line–spring model (LSM) of crack. The dual equations formed here are characterized by simultaneously solving kinematic variables and their dual dynamic variables. Both conventional and refined LSMs are considered. Two ways are proposed to generate the system equation in wave space based on the relationships of wave propagation, wave reflection and wave scattering. Compared with the traditional methods, most of them can only give exact analytical solutions under the condition of opposite-side simply supported boundaries, the developed analysis framework can treat arbitrary combinations of simple boundary condition of the cracked plate. Comparisons of results of the proposed method with those from the literature and finite element method (FEM) validate the effectiveness of the proposed method. A series of parametric studies for investigating the effects of length, position and depth of crack on the forced response of cracked plate are also presented. The proposed framework are effective for predicting the forced responses and natural frequencies of thin plates with part-through surface cracks.

Optimal control problem with state constraints via penalty functions

In this paper, we derive necessary conditions of optimality for problems with state constraints using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al., 2022). Our aim is to provide a proof of the Maximum Principle that can be easily followed by those with basic knowledge of classical optimal control and elementary functional analysis. We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact.

From Domain Decomposition to Model Reduction for Large Nonlinear Structures

The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy.

Solution one-dimensional problems of heat conduction with convection using Poisson integral

There is the relevant problem of developing high-viscosity oil in the oil and gas industry. One of the ways increasing its production is the thermal method. It is necessary to combine hydrodynamic equations with the thermal conductivity equation for simulation of filtration processes. The resulting mathematical models are solved by using different numerical methods. The accuracy and convergence of such algorithms is rarely tested. One way to carry out this check is to simulate problems that can be solved analytically in particular cases. For example, Fourier series are used for simple boundary conditions. Another method is usage the Poisson integral. This method is more convenient for comparing results than the Fourier method, because with the same accuracy requires significantly less calculations. But the Poisson method requires knowledge of the initial condition over the entire space, and in real problems it is usually given in a limited area. In this paper we propose an algorithm for extending the initial conditions to the entire space. In this way, two heat conduction problems are solved taking into account convection using the Poisson integral. It is shown that the accuracy is comparable to the Fourier method, but with fewer calculations.

Effect of three-dimensional space on progressive collapse resistance of reinforced concrete frames under various column removal scenarios

In this study, high fidelity finite element (FE) model was adopted to investigate the progressive collapse resistance of reinforced concrete (RC) frame structures under various column removal scenarios. The validity of the numerical model was verified by comparing with the existing experimental results. Afterwards, to facilitate the research on possible simplified boundary conditions served for further various column removal scenarios, the effect of multi-span continuous beams was firstly evaluated and the simplified methods were compared. Then, the effect of various column removal scenarios addressing the three-dimensional effect on the progressive collapse resistance of RC frame structures with and without slab was systematically evaluated. The analysis results showed that the continuous span beams increased the internal compressive force of the beam section at compressive arch action (CAA) stage, which effectively improved the CAA strength of the substructure. For simple modeling, the use of horizontal constraints at the end of the beam could replace the continuous span beams. The presence of transverse beams and slab provided additional load transfer paths for collapse resistance. The compressive membrane action (CMA) and tensile membrane action (TMA) of the slab significantly improved the progressive collapse resistance of the substructure in the small and large deformation stages, respectively. The location of the removed column significantly affected the contribution ratio of transverse beams and slab to the progressive collapse resistance of the substructure, which was quantitatively evaluated for practical design.

Study via the finite element method of the behavior of deck joints in a bridge composed of precast concrete segments

AbstractThere is a demand for research to better understand the structural performance of segmental bridge joints. In this context, the main objective of this work is to present a 3D numerical modeling using the Finite Element Method (FEM) to physically simulate the behavior of concrete joints in a segmental concrete bridge. The analysis was conducted using the design of a real bridge, and the structure studied was the main span of the New Guaíba Bridge, located in Porto Alegre, RS, Brazil. The modeling was implemented using ANSYS software, version 21.2. The simulation considers a complete model of the span to provide a more realistic determination of the joint openings and the stress distributions in the elements. It is crucial to emphasize that the results obtained from the model do not reproduce the observed behavior of the studied bridge. The analysis considered only one span with simplified boundary conditions and higher loads than those typically adopted in usual design procedures.

The catastrophic break‐up of the ureilite parent body: Modeling constraints on the debris size

AbstractThe ureilite parent body (UPB) was, in all likelihood, completely broken apart when hit by another object early in its history and reassembled into daughter bodies. We here present a study tailored to constrain the dimensions of the impact debris produced in the catastrophic disruption. Using a customized Python code to simulate the thermal evolution of the UPB fragments, we compared the FeO profiles modeled for different depths within those fragments with those measured across the reduction rims in olivines of 12 different ureilites (n = 37). Our profile data were fitted to the theoretical cooling profiles determined with a transient thermal model. The results are coherent and consistent with earlier studies and, despite using simplified boundary conditions (fragments described as ideal spheres and maximum radiation), our data provide valuable context on possible cooling pathways of the UPB debris. In detail, we found that the average depths within the given fragments from which our samples of ureilites originated were limited to 0.3–0.4 ± 0.1 m, with only few exceptions (e.g., one highly reduced sample lacked suitable reduction profiles suggesting either a depth of origin of >2 m or shielding of this fragment from rapid cooling, e.g., due to hovering in the center of a relatively dense cloud of debris). In addition, we calculated that the cooling from 1473 to 1100 K of the average fragment at the depth of our samples took no more than 3–4 days, suggesting that the reassembly of the ureilite daughter bodies could have been a very fast process.

Research on precise and standardized numerical simulation strategy for vehicle aerodynamics

PurposeThe purpose of this study is to propose a precise and standardized strategy for numerically simulating vehicle aerodynamics.Design/methodology/approachError sources in computational fluid dynamics were analyzed. Additionally, controllable experiential and discretization errors, which significantly influence the calculated results, are expounded upon. Considering the airflow mechanism around a vehicle, the computational efficiency and accuracy of each solution strategy were compared and analyzed through numerous computational cases. Finally, the most suitable numerical strategy, including the turbulence model, simplified vehicle model, calculation domain, boundary conditions, grids and discretization scheme, was identified. Two simplified vehicle models were introduced, and relevant wind tunnel tests were performed to validate the selected strategy.FindingsErrors in vehicle computational aerodynamics mainly stem from the unreasonable simplification of the vehicle model, calculation domain, definite solution conditions, grid strategy and discretization schemes. Using the proposed standardized numerical strategy, the simulated steady and transient aerodynamic characteristics agreed well with the experimental results.Originality/valueBuilding upon the modified Low-Reynolds Number k-e model and Scale Adaptive Simulation model, to the best of the authors’ knowledge, a precise and standardized numerical simulation strategy for vehicle aerodynamics is proposed for the first time, which can be integrated into vehicle research and design.

A two-direction cross-iteration solution for in-plane vibrations of thin-walled composite plates with a simplified explicit vibration mechanical model

For the fine and high reliability design of advanced precision engineering structures, this work presents an analytically cross-iteration method for in-plane vibrations analysis of thin-walled composite plates, the single-layer and laminated structures both involved. The governing equations and corresponding boundary conditions are derived adopting Rayleigh’s principle, in which the governing partial differential equations are transferred into ordinary differential equations. The most important advantage of this method lies in the fact that the explicit eigenvalue equations and mode functions are obtained with only a series of four-by-four matrices by simplifying boundary conditions in the two-direction cross-iteration procedures. Accuracy of the present method is verified by comparison with the previous studies and the finite element method in natural characteristics solutions, and convergence analysis on the single-layer orthotropic plates and composite laminates reveals the high efficiency and stability. Finally, the effects of boundary conditions, ply orientation angles, stacking sequences, aspect ratios and stiffness ratios on the in-plane natural characteristics are investigated. The extensive results presented in this work for the first time can be taken as the benchmarks data compared with other methods.