Continuous Boundary Conditions Research Articles

Light Interaction with Cluster Chiral Nanostructures by High-Order Bessel Beam

Interactions between cluster chiral nanoparticles and a high-order Bessel beam (HOBB) with arbitrary illuminations are investigated. The generalized Lorenz–Mie theory (GLMT) is applied to derive the expansions of HOBB. Based on the additional theorem, multiple scattering results of cluster chiral nanoparticles are obtained by taking into account the tangential continuous boundary conditions. The present theory and codes proved to be effective when confronted with the simulations obtained from the Computer Simulation Technology (CST) software. Numerical results concerning the effects of beam order, beam conical angle, incident angles, beam polarization state, the chirality, and the material loss on the scattering of various types of aggregated chiral particles are displayed in detail, including the linearly chiral sphere chain, the chiral cube array, and the complex models composed of aggregated chiral spheres. This study may provide critical support to analytically understand the optical scattering characteristics with aggregated chiral particles of complex shapes, and may find important applications in manipulating collective chiral particles.

Effects of continuous and discrete boundary conditions on the movement of upper-convected maxwell and Newtonian mucus layers in coughing and sneezing.

Mucociliary clearance is an important phenomenon inside the respiratory system as a first defensive mechanism against pathogens. Therefore, any assumption considered for the mucociliary clearance and affects its functionality must be validated. The present research deals with the effects of boundary conditions on the movement of upper-convected Maxwell and high viscosity Newtonian mucus layers, numerically. Furthermore, the validity of replacing the viscoelastic mucus layer with a high viscosity Newtonian layer is evaluated. The airway surface liquid layer is considered a two-layer model including non-Newtonian mucus and Newtonian periciliary layers. Four cyclic boundary conditions are imposed at the mucus-periciliary interface as the cilia movement to obtain variations of mucociliary clearance. The upper boundary of the mucus layer is also exposed to different shear stress levels including free slip, cough, and sneeze conditions. By investigation of velocity variations inside mucus and periciliary layers, it is concluded the differences between viscoelastic and Newtonian mucus are not negligible. The maximum velocity differences between the two fluids are more than 52% and 215% during cough and sneeze, respectively. The results show there is a high order of dependency between the relaxation time and the imposed boundary conditions at the mucus-periciliary interface that leads to the invalidation of replacing two fluids with each other. Moreover, the results show substituting the viscoelastic mucus with a high viscosity Newtonian one depends on the mucus-periciliary interface boundary condition. If an independent time-varying boundary condition is used, the substitution leads to an error less than 7% under different shear stress levels. However, time-varying boundary condition shows 38% and 88% differences between high viscosity Newtonian and viscoelastic mucus layers. Furthermore, neglecting the recovery stroke leads to a velocity underestimation up to 50% by substituting viscoelastic mucus with a high viscosity Newtonian one. Therefore, replacing the viscoelastic mucus with a high viscosity Newtonian one is not acceptable for numerical simulations.

PERFORMANCE ANALYSIS AND OPTIMIZATION OF A HELICAL CROSS-FLOW WATER TURBINE

In this study, a Computational Fluid Dynamics model is designed to investigate the performance analysis of a helical cross-flow water turbine by using Comsol Multiphysics. In order to predict the main performance characteristics of turbine such as power output and torque, a numerical model is developed which is accurate, fast and quite simple to be used for a simulation. The flow field around turbine is solved with the Rotating Machinery feature in the Comsol CFD Module using a k-ω turbulence model and a steady state formulation. The Navier-Stokes equations are used in the model which are arranged in a rotating frame in the inner domain and in fixed coordinates in the outer domain. The boundary between the inner and the outer domain is a continuity boundary condition that transfers momentum to the fluid in the inner domain. This model also uses the Frozen Rotor study type which speeds up the computation time. Then, to increase the performance of the cross-flow water turbine, a new angular velocity profile is explored with Comsol Optimization Module. Thus, a variable speed turbine control method is developed. Compared to the constant velocity control method, new angular velocity control method yielded a 3% increase in the efficiency of turbine.

Physics-informed neural networks for consolidation of soils

PurposePrediction of excess pore water pressure and estimation of soil parameters are the two key interests for consolidation problems, which can be mathematically quantified by a set of partial differential equations (PDEs). Generally, there are challenges in solving these two issues using traditional numerical algorithms, while the conventional data-driven methods require massive data sets for training and exhibit negative generalization potential. This paper aims to employ the physics-informed neural networks (PINNs) for solving both the forward and inverse problems.Design/methodology/approachA typical consolidation problem with continuous drainage boundary conditions is firstly considered. The PINNs, analytical, and finite difference method (FDM) solutions are compared for the forward problem, and the estimation of the interface parameters involved in the problem is discussed for the inverse problem. Furthermore, the authors also explore the effects of hyperparameters and noisy data on the performance of forward and inverse problems, respectively. Finally, the PINNs method is applied to the more complex consolidation problems.FindingsThe overall results indicate the excellent performance of the PINNs method in solving consolidation problems with various drainage conditions. The PINNs can provide new ideas with a broad application prospect to solve PDEs in the field of geotechnical engineering, and also exhibit a certain degree of noise resistance for estimating the soil parameters.Originality/valueThis study presents the potential application of PINNs for the consolidation of soils. Such a machine learning algorithm helps to obtain remarkably accurate solutions and reliable parameter estimations with fewer and average-quality data, which is beneficial in engineering practice.

Analytical study on the upheaval thermal buckling of sandwich pipes

Sandwich pipe is one of the most promising subsea pipelines for oil and gas transportation in deep waters due to its high-strength performance and thermal insulation. The gradient of the temperature distribution through the cross-section of sandwich pipes may be significant due to good thermal insulation of the core layer, so it is necessary to consider the temperature distribution in the upheaval thermal buckling analysis. In this study, analytical solutions are derived for the temperature distribution through the cross-section of a sandwich pipe by using the heat conduction equation, and they agree well with the results in the literature. Taking the temperature distribution into account, a mathematical model is proposed to simulate the upheaval buckling of sandwich pipes based on the von-Kármán type of geometrical nonlinearity and the Euler-Bernoulli beam theory. The coupled transverse and axial deflections of sandwich pipes are considered. The buckled section and the slip section are connected by the continuous boundary conditions. The force and moment resultants in the inner pipe, the core layer and the outer pipe are solved separately. Different material properties of different layers can be considered in this mathematical model. Semi-analytical solutions are derived and verified. The typical buckling process is analysed, and the forces, moments and stresses in different layers of sandwich pipes are discussed. Finally, several simplified models for the temperature distributions are proposed. The results show that the temperature distributions in the inner and outer pipes can be assumed to be constant and equal to the temperatures of the internal and external fluids, respectively.

An Analytical Solution of the Multiple Scattering from a Buried Medium Coated Conducting Sphere

Based on the image method and addition theorem of spherical vector wave functions, an analytical solution of the multiple scattering by a buried medium-coated conducting sphere is proposed in this paper. An iterative process to obtain the scattered electromagnetic field is discussed on the basis of the continuous boundary condition in the plane boundary, the medium inner and the outer surface of a coated conducting sphere, respectively. Applying an image method and the addition theorem of spherical vector wave functions, the scattering electromagnetic fields by the plane in a local coordinate system can be transformed into the globe coordinate, and they can be regarded as the next incident electromagnetic fields to the buried medium-coated conducting sphere. This process does not end until the scattering electrical field on the plane boundary is accurate enough. Numerical results are given and compared with commercial software FEKO, they coincide enough; the calculation times of the present method are very short compared to those of the software FEKO, and some discussion is given at the end of this paper.

Vibration of variable stiffness composite laminate and hybrid composite laminate plates coupled to sloshing fluid

In the present article, Reddy shear deformation plate theory is employed to investigate the free vibration of vertical laminated composite plates coupled to sloshing liquid. Two different types of composite plate are considered; hybrid composite laminate (HCL) plate, which consists of two types of fiber, and variable stiffness composite laminate (VSCL) plate, which is made of curvilinear fibers. The applied Reddy shear deformation theory introduces a nonlinear through-thickness distribution for the transverse shear stress, and it satisfies the zero stress conditions at the bottom and top surfaces of the plate. The sloshing fluid, which is partly in contact with the plate, is modeled as ideal, and the bulging and sloshing modes related to that are calculated using the fluid velocity potential. The interaction between fluid and solid is modeled through the continuity equation and boundary conditions at the fluid–solid interface. To extract the vibrational characteristics of the structure coupled to fluid, a polynomial approximation based on the Rayleigh-Ritz method is employed. After validating the proposed methodology, a parametric study is conducted to show the effects of various parameters associated with the fluid and structure on the natural frequencies of the system.

Correction to: Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions

Correction to: Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions

Efficacy of applying discontinuous boundary condition on the heat transfer and entropy generation through a slip microchannel equipped with nanofluid

In this study, the laminar nanofluid flow in the microchannel with a discontinuous-boundary condition was investigated. Considering the slip condition, heat transfer and entropy generation were studied. Different layouts with the discontinuous-boundary condition (i.e. layouts A, B and C) were introduced and compared with the basic microchannel (microchannel with the continuous-boundary condition). Reynolds number and non-slip coefficient parameters on the effect of using discontinuous-boundary condition were discussed. The results revealed that the application of discontinuous-boundary condition affects the heat transfer as well as entropy generation so that the effects are more pronounced at higher Reynold number. By applying discontinuous-boundary condition, the heat transfer through the layouts of A, B and C was 34, 45 and 53% higher than the base microchannel. Simultaneously, the entropy generation through the layouts of A, B and C intensified by 31, 39 and 46%, respectively. The results proved that the applying slip condition has two positive effects as well as a negative effect. It enhanced the heat transfer and diminished the viscose entropy generation, but on the other hand, it intensified the thermal entropy generation.

Estimation of Interface Parameter for One-Dimensional Consolidation with Continuous Drainage Boundary Conditions

Estimation of Interface Parameter for One-Dimensional Consolidation with Continuous Drainage Boundary Conditions

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.

Free vibration analysis of perforated composite cylindrical shell and panel using multi-domain generalized differential quadrature (GDQ) method

Free vibration behavior of a composite shell/panel with and without a central square cutout has been studied using Multi-domain Generalized Differential Quadrature (GDQ) method. A physical domain is decomposed into several elements in such a way that all the elements have uniform thickness and material properties, as well as continuous loading and boundary conditions at their edges. The governing equations are derived based on the first-order shear deformation theory. They are formulated in a general form and can be converted to Donnell’s, Love’s, and Sanders’ theories. In addition, compatibility conditions are considered at the interface boundaries of adjacent elements as well as proper boundary conditions on other elements edges. The GDQ method is employed to discretize these equations in both longitudinal and circumferential directions. By assembling these discretized relations, a system of algebraic equations will be generated. These equations can be solved throughan eigenvalue solution to compute the natural frequencies of the whole shell/panel. Numerical results obtained by the presented method are compared with ABAQUS results and those available in the literature. After verifying the accuracy and precision of the proposed method, it is employed to study the effect of an opening on the vibrational behavior of composite shells and panels through a parametric study. The influence of the presence of a cutout and its size is investigated on shells/panels with various material properties, layup orientations, thicknesses, dimensions, and boundary conditions. The obtained results can be used as a benchmark for further researches.

Effects of adjacent paleochannel sedimentary on the seismic response of structure with incident SH-wave

This paper combines the indirect boundary element method and the idea of “region-matching technique” to study the impact of adjacent paleochannel on structures in a layered half-space with incident SH-wave. It decomposes the model into paleochannel closed region, layered half-space open region, and rigid foundation-elastic structure. Wave field in the closed region only have scattered wave, and wave field in the open region includes scattered and free field. The scattered and free field are simulated by the dynamic Green's function and the direct stiffness method, respectively. Then, response of soil-structure system is solved by employing the boundary continuity conditions and dynamic equilibrium of structure. After verification of the method, seismic response of structure under the influence of adjacent paleochannel shape, distance between the paleochannel and structure, and shear wave velocity ratio of the paleochannel were analyzed. Results show: All three paleochannel shapes (ellipse, trapezoid, triangle) are adverse to the structure compared to the case of no paleochannel, and ellipse is the most unfavorable shape; Effect of paleochannel should be taken into account when paleochannel distance L/a<100; Higher shear wave velocity ratios result in larger peak of structural displacement; Structural response is more amplified in oblique incidence than vertical incidence.

Propagation of double zero-order Bessel beam and its scattering properties to uniaxial anisotropic spheres

Based on the generalized Lorenz Mie theory, the propagation and scattering properties of a uniaxial anisotropic spherical particle illuminated separately by double zero-order Bessel beam with arbitrary propagation direction and polarization direction are studied. The propagation and scattering characteristics are compared with those of a uniaxial anisotropic spherical particle illuminated by a single zero-order Bessel beam. Using the orthogonal relation of the spherical vector wave function and coordinate rotation theorem, the expanded forms of double zero-order Bessel beams with arbitrary propagation direction and polarization direction are derived. The analytical expressions of the expansion coefficients are derived by the integral method. The expansion coefficients of total incident field are obtained through the vector superposition principle. Based on the Fourier transform and tangentially continuous boundary conditions, the internal electromagnetic field of the uniaxial anisotropic sphere is expanded in terms of the spherical vector wave function and the scattering coefficients are derived. By comparing the angular distribution of the radar cross section of the particle illuminated by single and double zero-order Bessel beam when degenerating into plane waves with those results given by the literature, the correctness of the theory and the program in this paper are both verified. The effects of the incidence angle, conic angle and polarization angle on angle distribution of the radar cross section are numerically analyzed. The theoretical and numerical results in this paper are expected to be used to study the scattering properties, particle size analysis and optical trapping for anisotropic particles, biological cells and other particles illuminated by multi-beams.

Continuous boundary condition propagation model for topology optimization

Continuous boundary condition propagation model for topology optimization

Absorption performance of nonplanar periodic structures solved by layered rigorous coupled-wave analysis

Porous materials with corrugated surfaces are widely used in the field of noise control, as they can effectively convert sound energy into heat resulting in sound absorption. It is important to predict the absorption coefficients of sound-absorbing devices for the design of appropriate shape and size. In this study, a semi-analytic method of layered rigorous coupled-wave analysis (LRCWA) is proposed to predict the absorption of nonplanar periodic materials. Starting from the division of corrugated surfaces into multiple layers, we process the sound behavior in each layer as in a rectangular periodic modulation structure. By connecting the interlayer boundary continuity conditions, the acoustic coupling equation of the whole structure can be established. The effectiveness and practicability of the LRCWA method is validated based on the comparisons with the experimental data and the simulation of finite element method. Besides the absorption coefficient that is mainly discussed in this work, the proposed method is universal in analyzing the physical properties of nonplanar periodic structures, which can greatly accelerate the delicate design and optimization of such structures.

Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions

Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions

Subdivision based isogeometric analysis for geometric flows

AbstractWe present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second‐order, fourth‐order, and sixth‐order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean‐curvature‐variation flow, which are generally derived by minimizing the associate energy functionals with ‐gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box‐splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high‐order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi‐implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high‐order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.

Optimization and analysis of the acoustic and resistance performance of the plenum chamber via sample entropy and large eddy simulation

The noise of the plenum chamber plays an important role in the acoustic performance evaluation of ventilation and air condition (VAC) systems. The large eddy simulation (LES) model and Ffowcs Williams & Hawkings (FW–H) equation were used to obtain the transient flow and aerodynamic noise, respectively, and a continuous and uniform impedance boundary condition was introduced to calculate the transmission loss (TL) of the perforated board plenum chamber. The aerodynamic noise, TL, resistance and velocity uniformity distribution characteristics of the plenum chamber were predicted by numerical simulation. A full-scale test bed was built to verify the flow field prediction results, and the acoustic prediction results were verified by analog experiments. In addition, based on the sample entropy theory, the pressure fluctuation on the inner surface of the plenum chamber was evaluated. The results show that the perforated board changes the vortex structure in the plenum chamber and reduces the local resistance and the pressure fluctuation on the inner surface wall, and the local resistance coefficient can be reduced by up to 34%. However, the coefficient of velocity uniformity in the plenum chamber decreases by 4%. Furthermore, the perforated board can significantly reduce the TL and peak sound pressure level (SPL) of the plenum chamber. At the receiving point, the overall SPL can be reduced by up to 2.5 dB.

An equivalent pipe network model for free surface flow in porous media and its comparison with the continuum model

A simple and efficient equivalent pipe network method is developed for unconfined seepage problems in porous media. Instead of the continuum-based method, the porous media is represented by an orthogonal of pipe elements rather than triangular and quadrilateral elements in which water flow occurs. The equivalent expressions of the hydraulic conductivity parameters, the continuity equation, boundary conditions and finite element analysis are reduced to a one-dimensional problem of line elements. Two typical examples are applied to investigate the validity and advantages of the proposed equivalent pipe element method in comparison with the continuum-based method. From the steady-state free surface flow in the homogeneous, the equivalent pipe network method can well reproduce the free surface locations with the numerical solutions. However, the calculated results from the fractured porous media illustrate that the performance of the proposed method is better than the continuum-based method when considering a high- hydraulic conductivity horizontal fracture in the porous media.