Averaged Boundary Conditions Research Articles

Non-invasive fractional flow reserve estimation in coronary arteries using angiographic images

Coronary artery disease is the leading global cause of mortality and Fractional Flow Reserve (FFR) is widely regarded as the gold standard for assessing coronary artery stenosis severity. However, due to the limitations of invasive FFR measurements, there is a pressing need for a highly accurate virtual FFR calculation framework. Additionally, it’s essential to consider local haemodynamic factors such as time-averaged wall shear stress (TAWSS), which play a critical role in advancement of atherosclerosis. This study introduces an innovative FFR computation method that involves creating five patient-specific geometries from two-dimensional coronary angiography images and conducting numerical simulations using computational fluid dynamics with a three-element Windkessel model boundary condition at the outlet to predict haemodynamic distribution. Furthermore, four distinct boundary condition methodologies are applied to each geometry for comprehensive analysis. Several haemodynamic features, including velocity, pressure, TAWSS, and oscillatory shear index are investigated and compared for each case. Results show that models with average boundary conditions can predict FFR values accurately and observed errors between invasive FFR and virtual FFR are found to be less than 5%.

Analysis of two-dimensional planar gratings and metasurfaces in the quasi-static approximation

Currently, composite materials based on metal gratings with a period D much smaller than the wavelength l are widely used. With the use of such materials, it is possible to control the amplitude, phase and polarization of an electromagnetic wave, which opens wide possibilities for the creation of new types of antennas, radio-absorbing coatings, etc. This paper considers gratings of metallic strip or patches on the surface of a thin metal-backed dielectric slab to control the phase of the reflected wave. In the quasi-static approximation, the input impedance of such materials can be calculated using simple analytical formulas. This paper investigates the accuracy of the quasi-static approximation at different angles of incidence of the electromagnetic wave on two-dimensional gratings. Using the equivalent circuits method, analytical expressions for the input impedance of metasurfaces are obtained. The dispersion properties of composite materials “inductive or capacitive grating on the surface of a thin metal-backed dielectric slab” are investigated, and a technique for determining the resonant frequency, which corresponds to the maximum of the input impedance of the metasurface, is presented. The obtained results show that at any angle of incidence, it is possible to evaluate the condition of the quasi-static approximation applicability for two-dimensional gratings and for metasurfaces based on such gratings. If this condition is satisfied, that simple analytical expressions can be used to calculate the input impedance. The use of these expressions allows us to determine the frequency at which the input impedance reaches its maximum. It is established that for inductive and capacitive gratings the impedance boundary condition of M.A. Leontovich is equivalent to the averaged boundary condition of M.I. Kontorovich. It is obtained that for grating in free space, quasi-static approximation corresponds to the M.A. Leontovich impedance condition. The dispersion properties of composite materials “inductive or capacitive grating on a thin metal-backed dielectric slab” are investigated. It is shown that the phase transition of the reflection coefficient through zero occurs at maximum values of the input impedance. Using the considered method of equivalent circuits, the presented results can be easily generalized to any type of multilayer metasurfaces.

Influences of Lateral Boundary Forcings on the 2020 Extreme Meiyu in the Yangtze‐Huaihe River Valley

AbstractMeiyu occurs in Yangtze‐Huaihe River valley (YHRV) every summer. Its intensity, distribution, and intraseasonal variation are greatly influenced by atmospheric forcings from different directions, such as the monsoon southwesterlies from the south, the western Pacific subtropical high (WPSH) in the east, the atmospheric longwave activities in the north, the southwest vortex from the west, and so on. In this study, to explore the contributions of the atmospheric forcings from different directions to 2020 extreme Meiyu, Regional Climate Model version 4.6 (RegCM4.6) is employed. A series of sensitivity experiments are conducted with realistic or climatological averaged lateral boundary conditions. The results show that the monsoon westerlies from the south transport moisture and heat to YHRV, converge with the cold air brought by the frequent atmospheric longwave activities in the north, and result in this extreme Meiyu. The frequent cold air from the north can lift warm air, provide unstable conditions, and make the distribution of precipitation similar to the teleconnection pattern in East Asia. The stable WPSH in the east anchors the 2020 Meiyu rainband to the YHTV for a long time. In addition, the contributions of the atmospheric forcings from different directions to evolution of 2020 Meiyu change with time. Before 10 June, the WPSH in the east mainly contributes to the Meiyu evolution. From 11 June to 3 July, the combined effects of atmospheric forcings from the south and north are dominant. From 3 July to 10 July, the cold air from the north plays a major role.

In-situ evaluation of window-wall joint performance using numerical models and thermal images

Infrared thermography is an effective method for assessing the on-site thermal performance and heat exchange of structures. On-site infrared thermography was generally performed under the assumption of quasi-steady sate, which refers to the averaged boundary conditions; however, a description of the actual on-site dynamic conditions is necessary to increase the reproducibility of the assessment. This study, through simulation models, describes the infrared thermal images of the surrounding wall depending on the thermal performance at the joint between the window and wall, through which the thermal performance of the joint is estimated to quantify insulation defects or thermal bridge flaws. As incremental research to the previous chamber-based preliminary research, the main objective was to apply the assessment method to an on-site experiment and verify the reproducibility of the results. In the case of the distinct differentiation of the temperature distribution of the wall according to the material properties of the joint, the reproducibility of the assessed results was verified as values of the material properties of the joint of the physical model that represent the minimum error were the same, regardless of the period of assessments. Furthermore, the difference in the results from the physical model, in which the derived physical property values were applied, and the infrared thermography measurements were also within 5% and 20% (coefficient of variance of the root mean square error and normalized root mean squared error).

Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates

Functionally graded porous plates have been validated as remarkable lightweight structures with excellent mechanical characteristics and numerous applications. With inspiration from the high strength-to-volume ratio of triply periodic minimal surface (TPMS) structures, a new model of porous plates, which is called a functionally graded TPMS (FG-TPMS) plate, is investigated in this paper. Three TPMS architectures including Primitive (P), Gyroid (G), and wrapped package-graph (IWP) with different graded functions are presented. To predict the mechanical responses, a new fitting technique based on a two-phase piece-wise function is employed to evaluate the effective moduli of TPMS structures, including elastic modulus, shear modulus, and bulk modulus. In addition, this function corresponds to the cellular structure formulation in the context of relative density. The separated phases of the function are divided by the different deformation behaviours. Furthermore, another crucial mechanical property of porous structure, i.e, Poisson’s ratio, is also achieved by a similar fitting technique. To verify the mechanical characteristics of the FG-TPMS plate, the generalized displacement field is modelled by a seventh-order shear deformation theory (SeSDT). A NURBS-based isogeometric analysis (IGA) is then employed to capture the C1 continuity in approximations. Numerical examples regarding static, buckling, and free vibration analyses of FG-TPMS plates are illustrated to confirm the reliability and accuracy of the proposed approach. The influences of various porosity distributions, average relative densities, thickness-to-length ratios, aspect ratios, and boundary conditions on the plate responses are achieved. Consequently, these FG-TPMS structures can provide much higher stiffness than the same-weight isotropic plate. The greater stiffness-to-weight ratio of these porous plates compared to the full-weight isotropic ones should be considered the most remarkable feature. Thus, these complex porous structures have numerous practical applications because of these high ratios and their fabrication ability through additive manufacturing (AM) technology.

2-D Artificial Media With Forced Refraction

The propagation of guided waves along two identical metal gratings symmetrically lying on both sides of a dielectric substrate is studied. Earlier, investigation of the properties of such waves has been restricted to odd waves equivalent to waves in grounded dielectric substrate. Averaged boundary conditions for the fields at the grating were used to simplify the analysis. Even waves equivalent to waves in a substrate grounded by a perfect magnetic wall are in the focus of this paper. The dominant even wave is studied with help of electromagnetic HFSS simulation and averaged boundary conditions. Both methods demonstrate that the investigated structure in some frequency range has properties of a 2D media with forced refraction. The results have potential application for microwave and millimeter wave planar quasi-optical lens antennas.

Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions

This work, which can be considered as a small monograph, is devoted to the study of twoand three-dimensional boundary-value problems for eigenvalues of the Laplace operator with frequently alternating type of boundary conditions. The main goal is to construct asymptotic expansions of the eigenvalues and eigenfunctions of the considered problems. Asymptotic expansions are constructed on the basis of original combinations of asymptotic analysis methods: the method of matching asymptotic expansions, the boundary layer method and the multi-scale method. We perform the analysis of the coefficients of the formally constructed asymptotic series. For strictly periodic and locally periodic alternation of the boundary conditions, the described approach allows one to construct complete asymptotic expansions of the eigenvalues and eigenfunctions. In the case of nonperiodic alternation and the averaged third boundary condition, sufficiently weak conditions on the alternation structure are obtained, under which it is possible to construct the first corrections in the asymptotics for the eigenvalues and eigenfunctions. These conditions include in consideration a wide class of different cases of nonperiodic alternation. With further, very serious weakening of the conditions on the structure of alternation, it is possible to obtain two-sided estimates for the rate of convergence of the eigenvalues of the perturbed problem. It is shown that these estimates are unimprovable in order. For the corresponding eigenfunctions, we also obtain unimprovable in order estimates for the rate of convergence.

Characterization of Flow Dynamics in the Pulmonary Bifurcation of Patients With Repaired Tetralogy of Fallot: A Computational Approach.

The hemodynamic environment of the pulmonary bifurcation is of great importance for adult patients with repaired tetralogy of Fallot (rTOF) due to possible complications in the pulmonary valve and narrowing of the left pulmonary artery (LPA). The aim of this study was to computationally investigate the effect of geometrical variability and flow split on blood flow characteristics in the pulmonary trunk of patient-specific models. Data from a cohort of seven patients was used retrospectively and the pulmonary hemodynamics was investigated using averaged and MRI-derived patient-specific boundary conditions on the individualized models, as well as a statistical mean geometry. Geometrical analysis showed that curvature and tortuosity are higher in the LPA branch, compared to the right pulmonary artery (RPA), resulting in complex flow patterns in the LPA. The computational analysis also demonstrated high time-averaged wall shear stress (TAWSS) at the outer wall of the LPA and the wall of the RPA proximal to the junction. Similar TAWSS patterns were observed for averaged boundary conditions, except for a significantly modified flow split assigned at the outlets. Overall, this study enhances our understanding about the flow development in the pulmonary bifurcation of rTOF patients and associates some morphological characteristics with hemodynamic parameters, highlighting the importance of patient-specificity in the models. To confirm these findings, further studies are required with a bigger cohort of patients.

ORC Optimal Design through Clusterization for Waste Heat Recovery in Anaerobic Digestion Plants

Waste heat recovery (WHR) systems through organic rankine cycles (ORCs) in anaerobic digestion plants may improve cogeneration efficiency. Cogeneration unit power output, flue gas temperature, and mass flow rate are not constant during the day, and the thermal load requested by digesters shows seasonal variations. For this reason, a proper design of the ORC is required. In this study, a design methodology is proposed, based on the clustering of the boundary conditions expected during one year of operation and the anaerobic digestion plant operation. The design has to be a compromise between part-load operation and nominal power rating. In this study, the ORC design boundary conditions were partitioned into four representative clusters with a different population, and the centroid of each cluster was assumed as a potential representative boundary condition for the cycle design. Four different ORC designs, one for each cluster, were defined through an optimization problem that maximized the cycle net power output. ORC designs were compared to those resulting from the seasonal average boundary conditions. The comparison was made based on the ORC off-design performance. Part-load behavior was estimated by implementing a sliding-pressure control strategy and the annual production was therefore calculated. ORC off-design was studied through a detailed Aspen HYSYS simulation. Simulations showed that the power output of each design was directly connected to the cluster population. The design obtained from the most populated cluster generated 10% more energy than that from a system designed by taking into account only the year average conditions.

Validation of steady and unsteady CFD strategies in the design of axial compressors for gas turbine engines

Steady and unsteady CFD predictions of a state-of-the-art 11-stage axial compressor performances are compared with measurements and scrutinized to determine their ability to assist in the design phase. Unsteady calculations are capable of reproducing the measured stage loads and spanwise stagnation temperature and pressure profiles with good accuracy, while front-to-back stage loads predicted by the steady calculations deviate from measurements and result in an unrealistic early stall. Numerical experiments in design and off-design conditions suggest that unsteady effects change stage loads mostly through a deformation of the spanwise flow profiles, the primary driver of the compressor operability limits. Hence, single stage steady calculations, generally used in design iterations, are demonstrated to reproduce the single stage performance extracted from full multistage unsteady calculation by simply enforcing the time averaged inlet and exit spanwise profiles extracted from the multistage run. The proposed approach may reduce the computational effort in design loops by reducing the number of unsteady runs in favor of single stage steady runs with time averaged boundary conditions.

КОНСТРУКТИВНИЙ СИНТЕЗ БАГАТОШАРОВОЇ ПОЛЯРИЗАЦІЙНО-ГОЛОГРАФІЧНОЇ АНТЕНИ. РЕКОМЕНДАЦІЇ ЩОДО ВПРОВАДЖЕННЯ РЕЗУЛЬТАТІВ ДОСЛІДЖЕНЬ

The analysis of methods of synthesis of antennas on the basis of lattice structures is carried out. Electrodynamic model of multilayer polarization-holographic antenna (MPНA) is developed. A matrix method for determining the general coefficients is developed of reflection and passing of electromagnetic waves (EMW) through a banner of a MPНA for the transformation function of the primary electromagnetic field (EMF) created by the illuminator in to secondary EMF which is created by system a multilayer banner-irradiator. Determined coefficients of reflection of EMW through the banner of a MPНA by the method of averaged boundary conditions. The order of constructive synthesis of MPНA is developed and recommendations for the implementation of research results are proposed.

Metal-insulator transition in the ground state of the three-band Hubbard model at half filling

The three-band Hubbard model is a fundamental model for understanding properties of the Copper-Oxygen planes in cuprate superconductors. We use cutting-edge auxiliary-field quantum Monte Carlo (AFQMC) methods to investigate ground state properties of the model in the parent compound. Large supercells combined with twist averaged boundary conditions are studied to reliably reach the thermodynamic limit. Benchmark quality results are obtained on the magnetic correlations and charge gap. A key parameter of this model is the charge-transfer energy $\Delta$ between the Oxygen p and the Copper d orbitals, which appears to vary significantly across different families of cuprates and whose ab initio determination is subtle. We show that the system undergoes a quantum phase transition from an antiferromagnetic insulator to a paramagnetic metal as $\Delta$ is lowered to 3 eV.

Impact of Inflow Boundary Conditions on the Calculation of CT-Based FFR

Background: Calculation of fractional flow reserve (FFR) using computed tomography (CT)-based 3D anatomical models and computational fluid dynamics (CFD) has become a common method to non-invasively assess the functional severity of atherosclerotic narrowing in coronary arteries. We examined the impact of various inflow boundary conditions on computation of FFR to shed light on the requirements for inflow boundary conditions to ensure model representation. Methods: Three-dimensional anatomical models of coronary arteries for four patients with mild to severe stenosis were reconstructed from CT images. FFR and its commonly-used alternatives were derived using the models and CFD. A combination of four types of inflow boundary conditions (BC) was employed: pulsatile, steady, patient-specific and population average. Results: The maximum difference of FFR between pulsatile and steady inflow conditions was 0.02 (2.4%), approximately at a level similar to a reported uncertainty level of clinical FFR measurement (3–4%). The flow with steady BC appeared to represent well the diastolic phase of pulsatile flow, where FFR is measured. Though the difference between patient-specific and population average BCs affected the flow more, the maximum discrepancy of FFR was 0.07 (8.3%), despite the patient-specific inflow of one patient being nearly twice as the population average. Conclusions: In the patients investigated, the type of inflow boundary condition, especially flow pulsatility, does not have a significant impact on computed FFRs in narrowed coronary arteries.

On stress analysis of load for microperiodic composite half-plane with slant lamination

The paper deals with the plane problem of normal and tangential load for microperiodic composite with slant lamination. The boundary condition was considered as a normal and tangential load given on the surface of the composite half-plane. Microperiodic composite consisted of two components, differing in their Young’s modules. The homogenized model with microlocal parameters, which is presented by Woźniak (Int J Eng Sci 25:483–498, 1987. https://doi.org/10.1016/0020-7225(87)90102-9), Jędrysiak (Compos Struct 202:1253–1262, 2018. https://doi.org/10.1016/J.COMPSTRUCT.2018.05.155) was used to solve the considered problem. The problem was formulated and solved using the averaged boundary condition given by Perkowski et al. (Compos Sci Technol 67:2683–2690, 2007. https://doi.org/10.1016/J.COMPSCITECH.2007.02.013). The considered boundary value problem will be solved using the Fourier transform method. An analytical solution was obtained in a general form for any form of the function describing normal and tangential loads on the surface of a half-plane. An analytical solution was determined for the special cases of an elliptical, normal and tangential loads and for the special case of the concentrated force. The results are shown in the form of figures.

Characterization of salt deposit layer growth and prediction of cladding temperature of heated rod bundles under long-term seawater injection and pool boiling conditions

Seawater has been recognized as an alternative water source in severe accident countermeasures even before the TEPCO Fukushima Dai-ichi NPS accident. In this article, influences of deposit layers of salt precipitates on the early core degradation were investigated. A heated part of a fuel bundle was regarded as a major deposit site and numerical models for predicting growing geometry of deposit layers and resultant temperature responses of cladding were developed. These models have been validated based on precipitation tests employing 5 × 5 short length mockup bundles submerged in solutions of simple seawater and a mixture of seawater and boric acid. Growth and geometry of salt deposit layers were expressed as a product of the shape function and Matsuoka's kinetic law (Matsuoka, 1991) where the growth factor is expressed by the Arrhenius law. Model parameters of the kinetic law and the shape function were quantified based on digitized image data of deposit layers acquired in the abovementioned precipitation tests based on the X-Ray CT scan. Combining with the axial onedimensional two-phase flow model, the effective heat transfer coefficient of the cladding surface was evaluated taking into account growth of deposit layers and two-phase flow regimes. Finally, cladding temperature responses were evaluated based on the energy balance. Final geometry of salt deposit layers was digitized under a wide range of pool boiling conditions based on image data acquired in precipitation tests employing 5 × 5 short length mockup bundles. Based on these data, the shape function of each test case was reduced. It was confirmed that Matsuoka's kinetic law could predict a total mass increase of deposit layers with a good accuracy by specifying a constant in the Arrhenius law as nearly equivalent values for all test cases. From a comparison of measured and predicted surface temperatures at the exit of a heated length of the center rod, it can be interpreted that temperature increased gradually after the salt concentration reached the saturation point, then temperature began to increase steeply when a gap formed by neighboring rods was closed and isolated chimney flow paths surrounding the center heater rod were formed. Another important finding is that there was a certain margin of time until chimneys were formed after reaching the saturated salt concentration, which indicates feasibility of a practical fast running evaluation model based on decay heat, average salt concentration and boundary conditions that can be estimated to a certain degree of confidence level even under accident conditions.

Transient thermoelastic analysis of infinite plates with time-periodic heat transfer coefficient: Frequency response of thermal stress

ABSTRACTAn analytical method is presented for one-dimensional transient heat conduction and associated thermal stress problems of a layered infinite plate whose heat transfer coefficient (HTC) on one external boundary is an arbitrary function of time. A shifting function method and an orthogonal expansion technique are used to obtain analytical solutions to the problems. Using the solutions, the structural response to sinusoidal HTC oscillation is investigated in single and bilayered plates, the other boundary of which is kept at constant temperature. Numerical results demonstrate the effects of average HTC (measured by the Biot number) and mechanical boundary conditions on the frequency responses of temperature and thermal stress. It is found that the range of stress oscillation decreases with an increase in the frequency of HTC oscillation except for single-layered plates without surface tractions.

Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin-correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half filling, we employ the constrained path AFQMC approach to eliminate the exponential computational scaling from the sign problem. The constraint employs unrestricted Hartree-Fock trial wave functions with an effective interaction strength $U$, which is optimized self-consistently within AFQMC. Large supercells are studied, with twist averaged boundary conditions as needed, to reach the thermodynamic limit. We find that the nearest-neighbor spin correlation always increases with the interaction strength $U$, contrary to the finite-temperature behavior where a maximum is reached at a finite $U$ value. We also observe a change of sign in the next-nearest-neighbor spin correlation with increasing density, which is a consequence of the buildup of the long-range antiferromagnetic correlation. We expect the results presented in this paper to serve as a benchmark as lower temperatures are reached in ultracold atom experiments.

Numerical simulations of flow pattern and particle trajectories in feline aorta for hypertrophic cardiomyopathy heart conditions

ABSTRACTNumerical simulations of pulsatile flow in a feline aorta for hypertrophic cardiomyopathy (HCM) heart conditions are performed to predict flow details and to evaluate possible thrombus trajectory patterns. The study demonstrates that average flow rate boundary conditions (QBC) at artery outlets act as a resistance-type boundary condition for pulsatile flow. For simulations when the exact artery outflows are not known, specification of estimated values from physiological conditions is a plausible approach. This boundary condition is further improved using an iterative method (I-QBC) to accurately satisfy outflow conditions when expected outflow is known. The approach is validated against experimental data for the prediction of iliac artery flow and wall stresses in a human abdominal aorta. The feline aorta simulations including Lagrangian particle transport are performed on grids with up to 11M cells for a generalized feline aorta. It is found that LES on larger grids performs significantly better than URANS for the prediction of vortical structures. Simulations for both healthy and HCM conditions show similar flow patterns in the upper abdominal aorta. However, the HCM condition shows the presence of large recirculation regions in the thoracic aorta resulting in 50% lower flow through the iliac arteries and increased entrapment of fluid-borne particles near the trifurcation region compared to the healthy condition.

A multifilar helical antenna on a sphere and the limits of broadbandness

An antenna in form of a dense multifilar helix of thin metal ribbons on a spherical surface with lower order transverse-electric and transverse-magnetic modes is considered. Averaged boundary conditions taking into account the capacitances between the edges of ribbons are formulated. Formulas for calculating the angle of inclination of ribbons and the required inter-edge capacitance from a given resonance frequency and approximate ellipticity coefficient are obtained. The inclination of the axes of the polarization ellipse and an improved ellipticity coefficient are determined. The fractional bandwidth of the antenna is expressed via the improved limits of the fractional bandwidth of linearly polarized antennas. The limits of the fractional bandwidth of circularly polarized antennas are found. It is established that the maximum fractional bandwidth is reached if the ellipticity coefficient is slightly different from unity.

Surface waves generated by charged particle bunch moving along the edge of semi-infinite planar wire grid

Surface waves generated by a charged-particle bunch at the semi-infinite planar periodic wire structure are analyzed. It is supposed that the bunch moves parallel to the edge of the structure. The influence of the grid is described by the averaged boundary conditions. The analytical results are given for a general case, which takes into account the finite period and wires radius. It is shown that the surface waves excited by the bunch propagate along wires with the speed of light in vacuum. The number and the structure of these surface waves depend on relative location of the bunch path and the grid. One type of wave is always excited, but its magnitude decreases with distance from the bunch path to the structure edge. If the bunch projection falls on the half-plane occupied by wires, then additionally three surface waves are generated: two of them are equivalent to ones excited by the bunch moving along infinite wire grid and another one represents the surface wave reflected from the edge. The analysis of the surface waves shows that their structure allows for determination of the length of the bunch. Typical numerical results are presented.