Non-reflecting 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.

Exploring the dynamic compression behavior of glass/epoxy composite through cutting-edge numerical modeling techniques

Experimental tests are essential for obtaining reliable results. However, fabricating specimens, conducting tests, and post-processing experimental data are both costly and time-consuming. A reliable numerical model that matches experimental results can help avoid these issues. Using commercial ABAQUS explicit finite element software, we have developed numerical models that accurately replicate experimental outcomes while significantly reducing computation time. In this paper, we examine mesh convergence to ensure the precision and reliability of our numerical models. We detail the progression from a full model (FM) to a reduced model with infinite elements (RM-WIE) and its quarter version (QM-WIE). For non-reflective boundary conditions in the Split Hopkinson Pressure Bar (SHPB) tests, we used CIN3D8 infinite elements in the RM-WIE and QM-WIE models. This approach yields substantial time savings without sacrificing accuracy, reducing computation time from over 22 minutes for the full model to 15 minutes for RM-WIE and 11 minutes for QM-WIE. Moreover, our validation efforts demonstrate a strong numerical-experimental correlation of SHPB global parameters for E-Glass/Epoxy composites across four distinct lay-up configurations: [0°]40, [±30°]20, [±45°]20, and [90°]40, with an error margin of less than 10 %. This validation not only highlights the effectiveness of our numerical models but also underscores their utility in expediting the design process of E-Glass/Epoxy composites, offering a reliable and cost-effective alternative to traditional experimental testing methodologies.

Impacts of the mechanical connectors on seismic performance of the restored masonry Plaka Bridge using experimental and numerical studies

The use of clamp and dowel materials in the arch of the masonry bridges holds pivotal significance in enhancing the seismic resilience of these structures, as these elements contribute crucially to the structural integrity and dynamic response of these venerable structures. For this reason, the seismic performance of the restored historic Plaka Bridge, originally constructed in 1866 in Arta, Greece, and later restored in 2015 after flooding, was investigated considering the dowels and clamps in the arch section of this study. A combination of experimental and numerical analyses was conducted and verified to understand the in-situ interface behavior of the arch stones. In the first phase of the study, the mechanical properties of the dowels and clamps were characterized by the experimental tests. Compression and tension tests were conducted on the stone samples containing dowel bars and clamps respectively to determine the mechanical properties, The experimental outcomes were subsequently validated through Three-Dimensional (3D) Finite Difference Models (FDM). It was obtained that the dowels and clamps represent the bi-linear material model at the interfaces. Finally, the idealized interface behavior was constructed with normal and tangential spring stiffness properties in 3D-FD Models. These springs successfully simulate the interface delamination failure of the stones in all directions. In the final phase of the study, a 3D-FD model of the Plaka Bridge was constructed employing the previously validated normal and tangential stiffness elements in the arch of the bridge. A free-field non-reflecting boundary condition was imposed on the base and lateral boundaries of the bridge model. Seismic analyses were conducted utilizing the significant seismic events including 2023 Kahramanmaraş earthquakes. The results revealed significant alterations in the structural behavior of the bridge under considered earthquakes. Furthermore, the displacements, principal stresses and tensile-compressive damages in the main arch significantly reduced with the adopted stiffness values. This study proposes the undeniably realistic and efficient implementation of interface material modeling for the mechanical connections as opposed to the traditionally assumed mortar properties in literature. Furthermore, the combined behavior of the dowel, clamp, and Khorasan mortar proposes non-linear interface material model to the existing literature by invalidating commonly assumed linear interface behavior in masonry structures.

Egg White and Eggshell Mortar Reinforcing a Masonry Stone Bridge: Experiments on Mortar and 3D Full-Scale Bridge Discrete Simulations

In this study, experimental and numerical investigations were conducted to examine the time-dependent creep and earthquake performance of the historical Plaka stone bridge, which was constructed in 1866 in Arta, Greece. During the original construction of the bridge in 1866, Khorasan mortar with an egg white additive was used between the stone elements. Furthermore, when the bridge underwent restoration in 2015, Khorasan mortar with an eggshell additive was employed between the stone elements. Consequently, two distinct 3D finite-difference models were developed for this study. In the first bridge model, egg white was used in the Khorasan mortar, replacing water at various proportions of 0%, 25%, 50%, 75%, and 100%. In contrast, for the second model, eggshell was incorporated into the Khorasan mixture at percentages of 25%, 50%, 75%, and 100%, relative to the lime amount. Subsequently, the mortars were subjected to curing periods of 1 day, 7 days, and 28 days, and their mechanical properties were determined through unconfined compression strength experiments. Taking into account the determined strengths of the mortars, the kn and ks stiffness values of the interface elements between the stone elements and Khorasan mortar were calculated. In the 3D model, each stone element was individually represented, resulting in a total of 1,849,274 stone elements being utilized. Non-reflecting boundary conditions were applied to the edge boundaries of the bridge model, and the Burger creep and Mohr–Coulomb material models was employed for time-dependent creep and seismic analyses, respectively. Subsequently, time-dependent creep analyses were conducted on the bridge, and seismic events that occurred in the region where the bridge was located were simulated to assess their impact. Based on the results of the time-dependent creep and seismic analyses, we observed that the use of 50% eggshell-mixed Khorasan mortar between the stone elements had a positive influence on the earthquake and creep behaviors of both restored and yet-to-be-restored historical bridges.

Theoretical analysis and numerical validation of the mechanisms controlling composition noise

A new definition of entropy fluctuation is provided in this paper, that allows properly separating entropy and mixture composition fluctuations. This decomposition into linearly independent variables prevents from overestimating compositional noise in indirect noise prediction. When considering quasi one-dimensional flow in nozzles, a new resulting system of linearized Euler equations is obtained. Two analytical solutions of this system of equations are investigated in this study, one dedicated to low-frequency perturbations and another one for all frequency perturbations. This new theory is then validated by comparing the model predictions with direct numerical simulation of nozzle flows in which composition fluctuations are pulsed. To do so, new Navier–Stokes characteristics boundary conditions to account for the new properly defined entropy wave are provided. Furthermore, non-reflecting inlet boundary conditions have been newly derived, relaxing on the axial mass-flow rate, static temperature and species mass fractions. Finally, a parametric study based on an air-kerosene (equivalent C10H20) mixture and an ideal framework shows that composition noise can reach a maximum of 10% of entropy noise for lean combustion and choked nozzle while for rich combustion, composition noise and entropy noise show comparable levels.

Determination of future creep and seismic behaviors of dams using 3D analyses validated by long-term levelling measurements

This study aims to assess the future structural performance of the Kozlu-Ulutan clay core rockfill (CCR) dam, one of the most significant water structures in the Black Sea region of Turkey, by utilizing 35 years of levelling measurements and 3D finite-difference analyses. Settlement measurements were obtained from five different points on the dam surface every 6 months. Subsequently, a three-dimensional (3D) model of the dam was created using the finite-difference method. Time-dependent creep analyses and seismic analyses were conducted sequentially, employing the Burger-Creep and Mohr–Coulomb material models, respectively. Non-reflecting boundary conditions were defined for the boundaries of the dam model. The 3D numerical analysis results were found to be highly compatible with the 35 years of levelling measurements. Additionally, the future seepage and settlement behaviors of the dam over a 100-year period (2023–2123) were analyzed, considering special time functions. Current and future seismic analyses were performed, taking into account the settlement results of the dam in 2023 and 2123. For seismic analyses, data from ten various earthquakes that occurred in Kahramanmaraş, Hatay, Malatya, and Gaziantep in Turkey in 2023 were utilized. The seismic analysis results provided significant information about the future seismic behavior of the Kozlu-Ulutan Dam, revealing notable differences between the current and future earthquake behaviors of the dam. Moreover, it was concluded that the clay core is the most crucial section concerning the current and future seismic behaviors of CCR dams. The study results emphasized the importance of continuous monitoring and periodic seismic evaluations for the safe operation of CCR dams.

A polynomial-correction Navier-Stokes characteristic boundary condition

In an effort to assess the efficacy of different non-reflecting boundary conditions (NRBCs) in high-order solvers, several NRBCs have been implemented in the context of the discontinuous Galerkin (DG) discretization. The methods considered are based on buffer zone techniques and boundary-imposed conditions. The former mainly utilizes the sponge layer (SL), the perfectly matched layer (PML) and the supersonic layer (SSL), while the latter uses a Riemann extrapolation (RE) technique and a novel polynomial-correction Navier-Stokes characteristic boundary condition (PC-NSCBC). The developed PC-NSCBC method reconstructs an explicit boundary state, instead of modifying the equations on the boundary or specifying ad hoc compatibility conditions on corners and edges. This property pairs well with a Riemann solver, as is typical in a DG method. Moreover, the boundary state can be assembled either from a one-dimensional perspective (NSCBC1D) or using partial knowledge of multi-dimensional effects (NSCBC3D).Four different benchmark problems are considered: a 1D linear acoustic pulse in a quiescent flow, a 2D non-linear pressure pulse in a quiescent flow, an isentropic vortex and a shear-flow vortex shedding instability. Results imply that mainly the PML performs better than most other approaches. This is especially true for acoustically-dominated flows. Alternatively, for flow conditions predominantly less acoustic in nature and strongly non-linear, instabilities in the PML may arise. The SL and SSL both suggest that a larger layer is required to deliver comparable results to the PML. The proposed (PC-)NSCBC methods demonstrate reasonable success with no instabilities reported, which is impressive given the comparatively less computational effort required. Partial inclusion of the transverse terms in the NSCBC3D noticeably enhances the output of the NSCBC1D, albeit further investigation is required to determine an optimal, universal expression for its transverse tuning coefficient.

Implementation of Non-Reflecting Boundary Conditions in the EFES Software Package for Solving Dynamic Contact Problems

Implementation of Non-Reflecting Boundary Conditions in the EFES Software Package for Solving Dynamic Contact Problems

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{2}$$\\end{document} Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests.

The mechanisms of jetting, vortex sheet, and vortex ring development in asymmetric bubble dynamics

Bubble dynamics near a rigid boundary at Reynolds numbers of O(10–100) exhibit significant viscous effect, associated with ultrasonic cavitation and cavitation damage. We study this phenomenon experimentally using high-speed photography of spark-generated bubble oscillation in silicone oils, whose viscosity is about three orders larger than water. Comparing to bubbles in water, bubble surfaces in silicone oil are more stable and thus more cycles of oscillations may be observed and studied. Additionally, we investigate this phenomenon numerically using the volume of fluid method. We propose a non-reflective boundary condition, reducing the computational domain's dimensions tenfold based on the far-field asymptotic behavior. This paper pays particular attention in the mechanism for the bubble jetting, the vortex sheet, and the vortex ring development. Initially, a stagnation point at the bubble center moves away from the wall owing to asymmetric bubble expansion, leaving the bubble around the moment the bubble reaches its maximum volume. During this process, a vortex sheet forms inside the bubble. As the vortex sheet approaches the bubble interface, it transfers momentum to the gas–liquid interface, influencing the flow near the bubble wall. The high-pressure zone at the stagnation point drives the distal bubble surface to collapse first and fastest subsequently. This asymmetric collapse generates circulation around the bubble's side cross section, leading to the development of a vortex ring within the bubble gas at the outer rim of the decaying vortex sheet. The vortex ring, with its core inside the bubble gas, functions like a bearing system in accelerating the jet.

Coupled dynamic and thermal simulation of airfoil flap movement in turbulent flow using the lattice Boltzmann method

The study introduces an innovative approach that combines dynamic and thermal lattice Boltzmann simulations utilizing the ghost fluid boundary detection method for enhanced flow stability during flapping oscillation. This novel methodology is applied to large-eddy simulations of a flapping airfoil, aiming to capture the complex dynamics of oscillatory vortices and their impact on aerodynamics, while also allowing control over aerodynamic responses through airfoil surface temperature modulation. The investigation involves integrating the ghost fluid method into the lattice Boltzmann framework, synchronized with each time step to accurately model both the airfoil's oscillatory and boundary-induced movements. The advancement of specific fluid domain nodes due to boundary motion is managed using a recharging and force imposition scheme, estimating energy, and density function distributions on these nodes. Variations in lift and drag coefficients resulting from dynamic viscosity changes and thermal effects are observed due to airfoil surface temperature adjustments. A nonreflecting boundary condition is introduced to regulate flow velocity upper and lower near the domain boundary, facilitating smooth flow transfer from the boundary to the oscillating airfoil flow and minimizing transverse interference. Changes in energy exchange lead to delayed boundary layer separation, suggesting enhanced performance with reduced airfoil temperature. It is shown that decreasing the airfoil temperature by 100 K compared to the fluid temperature reduces the drag coefficient by 34% and increases the lift coefficient by 14%, while with an increase in 100°, the drag coefficient increases by 14.9% and the lift coefficient decreases by 4%. The proposed approach offers computational simplicity, concise solvable equations, and high accuracy, eliminating the need for mesh size adjustments when simulating different Reynolds numbers. Additionally, its ability to accommodate heat transfer-induced alterations within the aerodynamic context is highlighted. Comparative analysis with the finite volume method validates its effectiveness, demonstrating potential applications for controlling aerodynamic coefficients through controlled thermal interventions. In conclusion, the study presents a comprehensive methodology that integrates dynamic and thermal lattice Boltzmann simulations with the ghost fluid boundary detection method for enhanced flow stability during flapping oscillation. The insights gained contribute to a deeper understanding of complex aerodynamic phenomena, with implications for aerospace and fluid dynamics research, where accurate prediction and control of airfoil behavior are crucial. In summary, this study offers a groundbreaking strategy that seamlessly integrates dynamic and thermal lattice Boltzmann simulations, leveraging the ghost fluid boundary detection method for enhanced stability in flapping oscillatory motion. The outcomes contribute to a deeper understanding of intricate aerodynamic phenomena, thus holding promise for broader applications in aerospace and fluid dynamics research.

Boundary effects on wave trains in the Exner model of sedimental transport

In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca in Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes. PhD thesis, Universit‘a degli Studi di Palermo, Palermo, (2022) and Major Revision, (2023)). The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantees better stability properties than explicit ones, still at a lower cost than fully implicit schemes. We show the effect of spurious reflected waves generated at the outflow edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.

Impact of the injector lateral offset on the dynamics of a lean premixed flame and the thermoacoustic stability of a burner

The response of a laminar lean premixed flame to excitations based on its position in the combustion chamber and the stability of a burner are numerically investigated. A finite-volume large-eddy simulation method is used to solve the compressible Navier-Stokes equations and a combined G-equation progress variable approach is used to model the flame. Various injector positions in the combustion chamber are investigated in a computational setup with an acoustically non-reflecting outflow boundary condition to analyze the impact on the response of the flame to an external excitation. Due to the changes in the flow field the shape of the flames depends on the displacement offset of the injector. Consequently, the instantaneous, local distribution of the heat release rate fluctuations which is caused by wrinkles on the flame surface is determined by the position of the injector. The heat release rate fluctuations are the dominant source of sound in the investigated configurations. Due to the discrepancies in the local heat release rate fluctuations the flame response to an excitation depends on the lateral offset of the injector. The overall trend of the integrated heat release is the same in most configurations, however, the phase is significantly altered. Since the phase angle of the response of the flame to an excitation determines the stability of a burner, self-excited instabilities can be avoided by adjusting the position of the injector. This is demonstrated using a modified computational domain with an acoustically reflecting outflow boundary condition, which causes the burner to have an acoustic quarter-wave eigenmode. Based on the results of the previous analysis of the flame responses, two injector positions in the combustion chamber are chosen such that the response of the flames is mutually phase-shifted by approximately π. Therefore, it is expected that one of the configurations will lead to a stable burner while the other one exhibits a self-excited instability. The results show that the injector position determines the stability of the burner configuration for the investigated flames.

Finite Element Modelling of a Flow-Acoustic Coupling in Unbounded Domains

One of the main issues of design process of HVAC systems and ventilation ducts in particular is correct modelling of coupling of the flow field and acoustic field of the air flowing in such systems. Such a coupling can be modelled in many ways, one of them is using linearised Euler equations (LEE). In this paper, the method of solving these equations using finite element method and open source tools is decribed. Equations were transformed into functional and solved using Python language and FEniCS software. The non-reflective boundary condition called buffer layer was also implemented into equations, which allowed modelling of unbounded domains. The issue, influence of flow on wave propagation, could be adressed using LEE equations, as they take non-uniform mean flow into account. The developed tool was verified and results of simulations were compared with analytical solutions, both in one- and two-dimensional cases. The obtained numerical results are very consistent with analytical ones. Furthermore, this paper describes the use of the developed tool for analysing a more complex model. Acoustic wave propagation for the backward-facing step in the presence of flow calculated using Navier-Stokes equations was studied.

Assessing 3D Seismic Plastic Damages of Arch Dams Considering Optimum Mesh Spaces Based on FOS Analyses and 2023 Kahramanmaraş, Hatay, Malatya, and Gaziantep Earthquakes in Turkey

In this paper, the three-dimensional (3D) seismic plastic damage performance of the Ermenek Arch Dam (220 m), which was built in Karaman, Turkey, in 2009, is investigated by including different gallery spaces. 3D modeling of the dam is performed using the finite-difference method, and four various gallery spaces are added to the dam model considering their original oval geometries. WIPP-Drucker (WD) material model is utilized for the dam’s concrete material in creep and seismic damage analyses. Moreover, the Mohr–Coulomb material model is utilized for the foundation. Quiet nonreflecting and free-field boundary conditions are taken into account in the earthquake analyses, and reflecting (fix) boundary condition is used in the factor of safety (FOS) analyses in order to minimize the reflection of earthquake waves at the boundaries. First, the FOS analyses of the Ermenek Dam are performed considering the WD material model, and the optimum mesh space is determined according to FOS analyses. Then, 3D earthquake analyses are performed for 10 important strong ground motions that occurred in Kahramanmaraş, Hatay, Malatya, and Gaziantep in 2023. As a result of the FOS analyses, it is suggested that the mesh length of arch dams should not be chosen randomly while performing the earthquake analyses, and the FOS analyses of arch dams should be carried out using the WD material model before choosing the mesh space. Besides, it is concluded that selected ground motions for seismic analyses have created significant plastic damage around the galleries of the Ermenek Arch Dam, and gallery spaces are of great importance for the seismic plastic damage behavior of arch dams.

Assessing Seismic Crack Performance of Diyarbakır Çüngüş Masonry Stone Bridge Considering 2023 Kahramanmaraş, Hatay, Malatya, Gaziantep Earthquakes

Examination of the creep behavior of historical buildings and interpretation of seismic failures in historical buildings are of great importance for the safety and future of these important structures. In this study, time-dependent settlement and three-dimensional (3D) seismic analyzes of a historical stone bridge are investigated using the 3D discrete element modeling technique. For the settlement and seismic analyses, the historical single-span Çüngüş bridge which was built in the 18th century in Diyarbakır-Turkey by Ottoman Empire is used. Since Diyarbakır is in a dangerous zone according to the Turkey seismic map, the examination of this structure is very critical for the history of Turkey. The 3D model of the bridge is created using the FLAC3D program based on the finite difference method and all the stone elements in the historical bridge are modeled separately as blocks. Special interaction elements are defined between the discretely modeled stones. For settlement creep analyses, the Burger-creep material model, which was not used for the creep behavior of historical buildings in the past, is utilized. Firstly, the 500-year long-term creep behavior of the bridge is examined by considering the fix boundary condition and full reservoir condition. According to the creep analyses, it is seen that the most deformation and failure section of the bridge is the arch section. Then, for the seismic analyses of the bridge, free-field and quiet non-reflecting boundary conditions are defined in the model. Furthermore, hysteresis damping coefficients are taken into account in seismic analyzes with the help of special fish functions. 10 various earthquakes are considered for seismic analyses. According to the earthquake analyses, the earthquake behavior of the Çüngüş historical bridge is assessed by considering the full reservoir condition and it is understood that 2023 Kahramanmaraş, Hatay, Malatya, Gaziantep earthquakes significantly changed the seismic safety behavior of Çüngüş single-span historical bridge.

Numerical Modeling and Geometry Enhancement of a Reactive Silencer

Internal combustion engines and blowers frequently utilize silencers to reduce exhaust noise. In the current paper, the transmission loss of reactive silencers is predicted using the plane wave decomposition method and a three-dimensional (3-D) time-domain computational fluid dynamics (CFD) approach. A mass-flow-inlet boundary condition is first used to perform a steady flow computation, which serves as an initial condition for the two subsequent unsteady flow computations. At the model's inlet, an impulse (acoustic excitation) is placed over the constant mass flow to perform the first unstable flow computation. Once the impulse has fully propagated into the silencer, the non-reflecting boundary condition (NRBC) is then added. For the scenario without acoustic excitation at the inlet, a second unsteady flow computation is performed. During the two transient computations, the time histories of the pressure and velocity at the upstream measuring points as well as the history of the pressures at the downstream measuring point are recorded. The related acoustic quantities show variations between the two unsteady flow computational findings. As a result, the transmitted sound pressure signal is just the sound pressure downstream, while the incident sound pressure signal is obtained by utilizing plane wave decomposition upstream. The transmission loss (TL) of the silencer is then calculated after the Fast Fourier Transform (FFT) converts the two sound pressure signals from the time domain to the frequency domain. The numerical calculations and the reported data are in good agreement for the published results, in addition to geometry enhancement by increasing number of holes in the cross section for muffler.

Harmonic Method for Simulating Unsteady Multispool Interactions

Abstract Modern civil jet engines arrange components on spools with different rotational speeds in order to improve compressor stall margin, overall engine performance, etc. The unsteady interactions among these components can be significant and should be considered at an early design stage if possible. Unsteady Reynolds-averaged Navier–Stokes (URANS) is a common approach to simulate these unsteady effects, but the disparity in time scales in a multispool simulation can lead to expensive URANS simulations. Harmonic methods are effective and efficient approaches to simulate unsteady interactions among turbomachinery components, but their applications to multispool simulations remain a challenge. The objective of this paper is to address this challenge. This paper extends the Favre-averaged non-linear harmonic method to simulate multispool turbomachinery components using a unified bladerow interface which transfers disturbances through bladerows with arbitrary blade counts at any rotational speed. The regularization of non-reflective boundary condition is described for certain circumferential wave number of the zero-frequency mode. The capability of the proposed approach is demonstrated by simulating the transfer of hot streaks through full 3D high- and intermediate-pressure turbines in a three-shaft engine. The temperature distributions from the harmonic method show good agreement with direct unsteady simulation in terms of the mean flow and the instantaneous flow. The radial migration of the hot streaks towards the hub are captured very well by the proposed harmonic method. The required wall-clock time of the harmonic method is roughly 240 times smaller than the whole annulus URANS simulation. This demonstrates that the proposed method can be an efficient design tool to trace hot streaks in multispool turbines at the early design stage.

The influence of boundary conditions on nonlinear time domain site response analysis using LS-DYNA

The dynamic response of nuclear power plants and other critical infrastructure under seismic conditions is a major issue, and the earthquake-resistant capacity design of such facilities and their interior equipment should be based on prediction of dynamic response. Therefore, field geological investigations and corresponding site response analyses facilitate the evaluation of seismic site effects for the entire construction process, including site selection and detailed design. During site response analysis, soil parameters are usually obtained from laboratory tests using specimens retrieved from boreholes or from empirical equations. Conventional site response analysis software assumes horizontal layering in a 1D soil model, though the actual conditions of underground stratification are far more complicated. Some research efforts have undertaken 3D site response and soil-structure interaction analysis using LS-DYNA; however, the influence of different boundary conditions in these studies has been rarely discussed. The research reported on in this paper utilized LS-DYNA to perform nonlinear time-domain site response analysis and evaluated the difference between 1D and 3D model results. The results of both 1D and 3D site response analyses conducted using LS-DYNA were comparable to those of traditional approaches using a constrained boundary. The 3D models that adopt a non-reflective boundary condition can be affected by energy attenuation near the model boundary, causing a significant difference in the results. We suggest that the constructed model should have an area of at least 600 m × 600 m (plan view) to ensure accuracy in a 200 m × 200 m area in the center of the 3D simulation model using non-reflecting boundary conditions. Furthermore, four soil profile from real sites have been verified that the suggestion is also applicable in multilayered scenario.

CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries

Abstract In this paper, we present a numerical method based on the coupling between a Curved Virtual Element Method (CVEM) and a Boundary Element Method (BEM) for the simulation of wave fields scattered by obstacles immersed in homogeneous infinite media. In particular, we consider the 2D time-domain damped wave equation, endowed with a Dirichlet condition on the boundary (sound-soft scattering). To reduce the infinite domain to a finite computational one, we introduce an artificial boundary on which we impose a Boundary Integral Non-Reflecting Boundary Condition (BI-NRBC). We apply a CVEM combined with the Crank–Nicolson time integrator in the interior domain, and we discretize the BI-NRBC by a convolution quadrature formula in time and a collocation method in space. We present some numerical results to test the performance of the proposed approach and to highlight its effectiveness, especially when obstacles with complex geometries are considered.