Moving Boundary Conditions Research Articles

Mechanistic interpretation of vitamin B6 transport from swelling matrices of genipin-crosslinked gelatin, BSA and WPI

Vitamin entrapment in matrices made of natural polymers and its controlled release has application to a variety of added value foods and nutraceuticals. This communication utilises data from published literature on the molecular transport of vitamin B6 from condensed matrices of genipin-crosslinked gelatin, bovine serum albumin and whey protein isolate to develop a mechanistic model that accounts for moving boundary conditions. In doing so, it utilises the apparent diffusion coefficient of the micronutrient, the molecular weight of the uncrosslinked polymer chain and the average molecular weight between neighbouring crosslinks. The derived mathematical expression for swellable matrices in an aqueous environment can follow the progression of diffusivity with degree of crosslinking in the polymeric excipients. Model fitting provides a minimisation parameter, which is interpreted in terms of the extent of coupling between solute diffusion and matrix structural relaxation. Parallel predictions of polymer network mesh and critical molecular weight between crosslinks indicate that values of normalised size well above one are required for anomalous (non-Fickian) release due to obstructed diffusion.

Modeling the laser-polymer interaction of laser propulsion systems considering progressive surface removal, thermal decomposition and non-Fourier effect

During the laser-polymer interactions of laser propulsion systems, the surface of the target progressively recedes, which in turn necessitates accounting for the moving front boundary, and the decomposition rate varies with the temperature resolution, which accordingly updates the internal heat flux. The non-Fourier effect existing in ultra-short pulse laser heating also needs to account for the finite propagation speed of the thermal wave. Therefore, developing an accurate predictive simulation model that captures materials moving front, simultaneously updates the internal heat source, and characterizes the non-Fourier effect is an important and challenging task. In this study, a mathematical model of the laser-polymer interaction was numerically implemented using a two-dimensional finite volume method considering progressive surface removal, thermal decomposition, and non-Fourier effect. The proposed model utilizes a robust coupling scheme that enables us to track the moving boundary condition owing to the progressive surface material removal, simultaneously updates the internal heat source by varying the pyrolysis rate, and re-meshes the computational domain after the material surface is progressively removed. Moreover, the thermal relaxation time is introduced into the heat conduction equation to characterize the non-Fourier effect. In addition, the temperature-dependent material and optical properties of the target material were considered in the proposed model. Simulations were performed for the laser ablation of polyoxymethylene with a carbon dioxide laser under different parameters. The theoretical estimations of the ablation depths and area mass densities agree well with the experimental results.

Drag and heat transfer coefficients for axisymmetric nonspherical particles: A LBM study

In this work, the thermal lattice Boltzmann method with immersed moving boundary conditions has been employed to calculate the drag coefficients and Nusselt numbers for isolated axisymmetric nonspherical particles in uniform flow for a wide range of Reynolds numbers (Re) and aspect ratios (Ar). The simulation results demonstrate that the drag coefficient for ellipsoids and a spherocylinder evolves as sin2θ, viz. θ being the incident angle of the particle. However, the Nusselt number for prolate ellipsoids evolves as sinmθ, viz. m being a function of particle aspect ratio. A correlation for m has been developed for 1<Ar≤4 based on the simulation data. The Nusselt number for a spherocylinder of aspect ratio 4 evolves as sin1.278θ. Moreover, we observe that the drag coefficients and Nusselt numbers for a prolate ellipsoid of aspect ratio 4 and a spherocylinder of aspect ratio 4 are comparable with a maximal relative deviation 5%. Based on the simulation data and the data from literature, a drag correlation for oblate (0.2≤Ar<1 and 1≤Re≤100) and prolate (1≤Ar≤5 and 1≤Re≤2000) ellipsoids has been developed to broaden the range of applicability of existing drag correlations. The average relative deviation between the drag correlation and the fitting data is 9.4%. The Nusselt number correlation for prolate ellipsoids is valid for 1≤Ar≤4 and Re≤500. On the other hand, the Nusselt number correlation proposed for a spherocylinder is valid for Ar=4 and Re≤500. The new drag and Nusselt number correlations are expected to improve the accuracy of Euler-Lagrangian simulations of non-isothermal particulate flows comprising ellipsoids or spherocylinders.

Lattice Boltzmann Simulation of Industrial Axial Fan Noise

Noise simulation of an industrial axial fan has been conducted by implicit large-eddy simulation with Lattice Boltzmann simulation which is based on Cumulant Lattice Boltzmann method with wall model and diffuse-interface method for a moving boundary condition. Simulation results are compared with experimental results of a factory test of an industrial fan for a thermal power generation. The result shows a good agreement and overall value is within 3dB error.

Modeling the high temperature behavior of all-composite, corrugated-core sandwich panels undergoing ablation

Owing to their structural efficiency, the development of structurally integrated thermal protection systems (SITPS) for the next generation aerospace vehicles is currently of interest. Herein, an all-composite sandwich structure with corrugated core is devised and fabricated. After homogenization of the corrugated core, a one-dimensional (1-D) analytical model is developed. The surface ablation is described by considering thermal decomposition, phase transition and thermochemical ablation. With the thermal loading and moving boundary conditions determined by the surface ablation calculation, a heat transfer analysis is performed. To provide insight into the effect of lateral heat transfer and thermal short through the sandwich structures, a two-dimensional (2-D) finite element model is also presented. In addition, a thermal exposure experimental test with oxyacetylene flame is carried out to validate the proposed models. The 1-D analytical model is found to be of satisfactory accuracy, which is useful for rapid preliminary SITPS design.

Development of a computational approach for a space–time fractional moving boundary problem arising from drug release systems

This paper presents an iterative procedure based on an implicit finite difference method to solve a mathematical model of drug delivery from a planar matrix with a moving boundary condition. This model includes the diffusion equation with space–time fractional-order derivatives. We establish the stability and convergence analysis of the method. We compare the numerical results with the scale-invariant and the homotopy perturbation solutions for different space–time-fractional orders and the problem parameters.

Numerical simulation of pile installations in a hypoplastic framework using an SPH based method

This paper presents a tool to estimate the stresses, and thus the expected forces, at a retaining wall by the installation of piles. The solution method is based on Smoothed Particle Hydrodynamics (SPH) and the soil is modeled using a simplified hypoplastic material law. In order to correctly compute the forces on the soil due to the contact between the pile and the soil, a formulation for imposing frictional boundary conditions using SPH is developed. Modeling the soil with the chosen hypoplastic approach also allows for tensile forces in the soil. However, these are not physical. Therefore, an alternative formulation is presented which directly eliminates unphysical tensile stresses in the cohesionless soil without any additional numerical parameters. The numerical code is firstly validated against benchmark problems. Then several test cases are simulated including monotonic and cyclic penetration of piles into the soil. A good agreement with the experimental observation is found. Additionally, the impact of pile driving in the presence of sheetpiles (retainers) is investigated to see how the pile driving can alter the applied forces on the sheet piles. The simulation of such complex geotechnical problems that involve large deformation, material nonlinearity, and moving boundary conditions demonstrates the applicability and versatility of the proposed numerical tool in this field.

Thermal Model for Timber Fire Exposure with Moving Boundary

Fire exposure of timber leads to charring, surface cracking and timber burnout, shifting the external thermal load deeper into the timber domain. This phenomenon plays its role mainly in situations of longer fire exposure. The majority of current approaches and models assume initial geometry during the whole analysis, leading generally to the overestimation of the insulation effect of the charred layer and to a limited burnout. This paper presents a heat transport model which is supplemented with a moving boundary condition, a criterion for the finite element deactivation and the internal heat source. Comparison with experiments using a constant radiative load testifies that the moving boundary condition becomes important after approximately 10 min of fire exposure and rather leads to a constant charring rate observed in several experiments.

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.Graphic abstract

Unsteady free convection flow of water-based carbon nanotubes due to non-coaxial rotations of moving disk

ABSTRACT Nanofluid is one of the significant developments for having an efficient heat transport process. Its implementation in a non-coaxial rotating system has benefited from designing a mixer machine with two stirrer blades, cooling fan, and jet engines. This study analytically investigates the free convection of unsteady non-coaxial rotating nanofluid flow through a moving disk. The suspension of single-wall or multi-wall carbon nanotubes in water is known as the nanofluid in this study. The fluid motion is affected by the effects of rotation and buoyancy forces. Using suitable dimensionless variables, the dimensional coupled partial differential of momentum and energy equations along with their initial and moving boundary conditions are converted into the dimensionless form. The expressions for temperature and velocity profiles are obtained by solving governing equations using Laplace transform method. The validity of obtained solution is confirmed by having a good agreement when comparing present results with the published result. The results show that the insertion of CNTs particles into the rotating water causes the temperature and velocity profiles to increase. The amount of heat transferred by SWCNTs is greater than MWCNTs. Increasing CNTs particles has descended both primary and secondary skin friction but increase Nusselt number. Further analysis with the help of pictorial discussion for the fluid flows and heat transfer under the influences of nanoparticle volume fraction, Grashof number, the amplitude of disk, and time is carried out.

A variable time‐step method for a space fractional diffusion moving boundary problem: An application to planar drug release devices

AbstractIn this article, we consider an anomalous diffusion model in a planar polymeric matrix as a space fractional diffusion problem with moving boundary conditions. An iterative implicit finite difference method with variable time‐steps is established to solve the proposed problem. The stability and consistency of the numerical method are proved and the estimation of the numerical error is conducted. The numerical results are compared with the scale‐invariant and homotopy perturbation solutions when the diffusion coefficient is a constant. Furthermore, the numerical results for a test case with time‐dependent diffusion coefficient are reported.

Physical Observation of a Robust Acoustic Pumping in Waveguides with Dynamic Boundary

Research on breaking time-reversal symmetry to realize one-way wave propagation is a growing area in photonic and phononic crystals and metamaterials. In this Letter, we present physical realization of an acoustic waveguide with spatiotemporally modulated boundary conditions to realize nonreciprocal transport and acoustic topological pumping. The modulated waveguide inspired by a water wheel consists of a helical tube rotating around a slotted tube at a controllable speed. The rotation of the helical tube creates moving boundary conditions for the exposed waveguide sections at a constant speed. We experimentally demonstrate acoustic nonreciprocity and topologically robust bulk-edge correspondences for this system, which is in good agreement with analytical and numerical predictions. The nonreciprocal waveguide is a one-dimensional analog to the two-dimensional quantum Hall effect for acoustic circulators and is characterized by a robust integer-valued Chern number. These findings provide insight into practical implications of topological modes in acoustics and the implementation of higher-dimensional topological acoustics where time serves as a synthetic dimension.

A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions

The objective of this novel research is assessment of dynamic stability of a viscoelastic defective single layered graphene sheet (SLGS). Further, various kinds of defects including single vacancy (SV), double vacancy (DV) and Stone-Wales (SW) are regarded and the effects of vacancy defect reconstruction is studied as well. So as to assume this nanostructure much more realistic, Kelvin model is utilized and it is rested upon elastic foundation. This SLGS is under hygrothermal loads and in-plane magnetic forces. In addition to sinusoidal higher order shear deformation theory for modeling this nanostructure mathematically, Hamilton's principle is utilized to obtain the motion equations and furthermore nonlocal strain gradient theory (SGT) is used which considers size effects accurately. Differential quadrature method (DQM) as well as transformed weighing (TW) will be handled to solve the governing equations and determine the dynamic stability region for this nanostructure. Moreover, various moving boundary edges are studied because of hygrothermal loads. Various parameters focusing on hygrothermal loads, magnetic forces, defect kinds, defect degree, various SLGS, boundary edges and coefficients of elastic foundation and their effects upon the dynamic stability behavior of nanostructure will be investigated. In order to assess the validity, the results are compared with other papers. Based on the results, rise of defect degree causes shift of stability region to the less excitation frequencies.

Flatness based trajectory planning and open-loop control of shallow-water waves in a tube

Open-loop control design for a fluid in a pipe is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations with a moving boundary condition. Rest-to-rest transitions are parameterized by means of the so called flatness-based approach to the control of dynamical systems the flat output being the water level at the uncontrolled boundary. The control algorithms are implemented on a test bench and verified in numerical and experimental studies.

A Comparison of Time-Frequency Methods for Real-Time Application to High-Rate Dynamic Systems

High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 gn for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and even be critical to their deployment. However, these systems are characterized by large uncertainties, high non-stationarities, and unmodeled dynamics, and it follows that the design of real-time state-estimators for such purpose is difficult. In this paper, we compare the promise of five time-frequency representation (TFR) methods at conducting real-time state estimation for high-rate systems, with the objective of providing a path to designing implementable algorithms. In particular, we examine the performance of the short-time Fourier transform (STFT), wavelet transformation (WT), Wigner–Ville distribution (WVD), synchrosqueezed transform (SST), and multi-synchrosqueezed transform (MSST) methods. This study is conducted using experimental data from the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research) testbed, consisting of a rapidly moving cart on a cantilever beam that acts as a moving boundary condition. The capability of each method at extracting the beam’s fundamental frequency is evaluated in terms of precision, spectral energy concentration, computation speed, and convergence speed. It is found that both the STFT and WT methods are promising methods due to their fast computation speed, with the WT showing particular promise due to its faster convergence, but at the cost of lower precision on the estimation depending on circumstances.

Billion degree of freedom granular dynamics simulation on commodity hardware via heterogeneous data-type representation

We discuss modeling, algorithmic, and software aspects that allow a simulation tool called Chrono::Granular to run billion-degree-of-freedom dynamics problems on commodity hardware, i.e., a workstation with one GPU. The ability to scale the solution to large problem sizes is traced back to an adimensionalization process combined with the use of mixed-precision data types that reduce memory pressure and improve arithmetic intensity, judicious use of the memory ecosystem on GPU cards as exposed by CUDA on Nvidia architectures, and a software implementation that prioritizes execution speed over modeling generality. The simulation approach is demonstrated for 3D scenarios with up to 710 million bodies for the frictionless case (of relevance in emulsions), and up to 210 million bodies for scenarios with friction (of relevance in terradynamics, additive manufacturing, soft-matter physics). The frictional contact model used draws on the Discrete Element Method (DEM). A performance benchmark shows linear scaling with problem size up to GPU memory capacity. The implementation has an application programming interface that enables it to interact in a cosimulation framework with third-party dynamics engines. This interaction is anchored by a force–displacement data exchange protocol that brings in external bodies as geometries defined by triangle meshes. We demonstrate the cosimulation mechanism by interfacing to an open source, multiphysics simulation engine called Chrono. Therein, triangular meshes define moving boundary conditions for Chrono::Granular, which in turn provides forces and torques acting on the triangular meshes. Several tests are considered for validation and scaling analysis purposes. The limiting aspects of the current implementation are its exclusive support of monodisperse granular systems, and its lack of handling geometries beyond spheres. These limitations are addressed by ongoing work.

Moving and reactive boundary conditions in moving-mesh hydrodynamics

ABSTRACT We outline the methodology of implementing moving boundary conditions into the moving-mesh code manga. The motion of our boundaries is reactive to hydrodynamic and gravitational forces. We discuss the hydrodynamics of a moving boundary as well as the modifications to our hydrodynamic and gravity solvers. Appropriate initial conditions to accurately produce a boundary of arbitrary shape are also discussed. Our code is applied to several test cases, including a Sod shock tube, a Sedov–Taylor blast wave, and a supersonic wind on a sphere. We show the convergence of conserved quantities in our simulations. We demonstrate the use of moving boundaries in astrophysical settings by simulating a common envelope phase in a binary system, in which the companion object is modelled by a spherical boundary. We conclude that our methodology is suitable to simulate astrophysical systems using moving and reactive boundary conditions.

A practical proposal to obtain solutions of certain variational problems avoiding Euler formalism

The aim of this article is to show the way to get both, exact and analytical approximate solutions for certain variational problems with moving boundaries but without resorting to Euler formalism at all, for which we propose two methods: the Moving Boundary Conditions Without Employing Transversality Conditions (MWTC) and the Moving Boundary Condition Employing Transversality Conditions (METC). It is worthwhile to mention that the first of them avoids the concept of transversality condition, which is basic for this kind of problems, from the point of view of the known Euler formalism. While it is true that the second method will utilize the above mentioned conditions, it will do through a systematic elementary procedure, easy to apply and recall; in addition, it will be seen that the Generalized Bernoulli Method (GBM) will turn out to be a fundamental tool in order to achieve these objectives.

Fuel Tank Vertical Sloshing during Aircraft Landing

In this article, the influence of the fuel sloshing on the tank under the landing condition is investigated to explain the skin deformation of wing tank. Based on the SPH method, a simplified fuel tank model of gas-liquid-solid three-phase is established. NanoFluidX, a fluid dynamics simulation tool, is used to calculate fuel sloshing through a given load and the pressure on the tank. The pressure on the lower wall of tank is then imported into the ABAQUS to calculate the stress distribution on the skin. A measured acceleration curve within 0.56s is used as the moving boundary condition of the fuel tank. It is found through simulation that the air has less influence on the pressure on the lower wall during the aircraft landing. By changing the liquid filling rate, the differences of the pressure on the lower wall are compared. Based on the above research, an empirical relationship among the wall pressure, the external load and the liquid filling rate is obtained.

Exact analytical solution of a generalized multiple moving boundary model of one-dimensional non-Darcy flow in heterogeneous multilayered low-permeability porous media with a threshold pressure gradient

A nonlinear generalized multiple moving boundary model of one-dimensional non-Darcy flow in heterogeneous multilayered low-permeability porous media with a threshold pressure gradient is constructed, in which the total rate of fluid injection into the porous media remains constant. The number of layers in the model can be arbitrary, and thus the generalized model will be very suitable for describing the one-dimensional non-Darcy flow characteristics in low-permeability reservoirs with strong heterogeneity. Through the similarity transformation method, the exact analytical solution of the multiple moving boundary model is obtained, and the formula for the subrate of fluid injection into every layer is provided. Moreover, it is strictly proved that the exact analytical solution can reduce to the solution of Darcy flow as the threshold pressure gradient in different layers simultaneously tends to zero. Through the exact analytical solution, the effects of the layer threshold pressure gradient, the layer permeability ratio, and the layer elastic storage ratio on the moving boundaries, the spatial pressure distributions, the transient pressure, and the layer subrate in low-permeability porous media are discussed. Through comparison of the exact analytical solutions, it is also demonstrated that incorporation of the multiple moving boundary conditions is very necessary in the modeling of non-Darcy flow in heterogeneous multilayered porous media with a threshold pressure gradient, especially when the threshold pressure gradient is large. In particular, an explicit formula is presented for estimating the relative error of the transient pressure introduced by ignoring the moving boundaries in the modeling. All in all, solid theoretical foundations are provided for non-Darcy flow problems in stratified reservoirs with a threshold pressure gradient. They can be very useful for strictly verifying numerical simulation results, and for giving some guidance for project design and optimization of layer production or injection during the development of heterogeneous low-permeability reservoirs and heavy oil reservoirs so as to enhance oil recovery.