External Boundary Research Articles

Kinetic model describing self-limiting CO2 diffusion in supported amine adsorbents

A reaction–diffusion shrinking core model describing the decay in diffusivity of supported amine sorbents upon CO2 sorption under both simulated direct air capture and point source capture conditions is described. The decay in CO2 diffusivity is associated with crosslinking in the aminopolymer samples and general pore blockage in the amino-silane derived samples, which occurs as CO2 is adsorbed. The model is used to extract four kinetic parameters that govern the CO2 uptake kinetics and working capacity: an apparent reaction rate constant, an initial effective diffusivity, and two dimensionless decay parameters. Ideally, an initially reaction limited system would allow for direct determination of the intrinsic reaction rate constant; however, sorption experiments suggest mass transfer resistances related to gas mixing, external boundary layers and intraparticle diffusion are present. Reaction rate constants are determined and agree well with theoretical values predicted with the Eyring equation parameterized using density functional theory energies from literature sources. The kinetic performance is expressed as the average effective diffusivity as a function of average conversion, which can be correlated to the dispersion of sorption sites on the support and the morphology of the active sorbent phase. Four supports are impregnated or grafted with amines, SBA-15, single-walled zeolite nanotubes (ZNT), Syloid SiO2, and γ-Al2O3. Due to its pore structure, γ-Al2O3 supported amines can be modeled at the μm scale or at the nm scale, where the shell balance is on the μm-sized macroporous particle aggregate or on the nm-sized amine film on the surface of the Al2O3 nanoparticles, which comprise the spherical particle aggregates. Faster diffusion rates are maintained under 400 ppm rather than 10% CO2 due to a slower reaction rate giving a slower decay in diffusivity. This work provides a first principles kinetic analysis of CO2 sorption where previous models are semi-empirical and use arbitrary kinetic parameters.

On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity

In this paper, the linear mathematical model of thermoelastic nanomaterials with triple porosity is proposed in which the coupled phenomenon of Darcy’s law and the concept of the volume fractions of three levels of pores (macro-, meso- and micropores) is considered. Then, the 3D internal and external basic boundary value problems (BVPs) of steady vibrations of this model are formulated. The radiation conditions are established and Green’s identities are obtained in the considered theory. Finally, the uniqueness theorems for classical solutions of the above mentioned BVPs are proved.

SPATIAL STRUCTURE OF SMALL CITIES: THE APPROACHES TO TYPOLOGY (BASED ON THE MATERIALS FROM CENTRAL RUSSIA)

The article examines the spatial structure of small towns in Central Russia. The information base of the study covers satellite images of 190 small towns. The paper proposes a concept of morphological structure of the city, which is determined by the nature (shape) of external boundaries, the presence of significant internal barriers leading to the fragmentation of space, and isolated urban areas. A methodology for assessing the complexity of urban space is suggested. It is based on the scoring of the impact of various geographical barriers on the urban environment. The most significant barriers include rivers and railways; the relief features, the location of industrial enterprises and the presence of protected areas were also considered. Special emphasis was given to urban areas isolated from the main built-up territories, i. e. exclaves. Five classes of urban space complexity have been identified, from very simple to very complex. The most complex space is typical of five small towns, which were initially clusters of workers’ settlements. The combination of data on the morpho-logical structure and complexity of space made it possible to identify six final forms of the spatial structure of the city. More often than others, there are cities with a dissected morphological structure in combination with a medium-complex space. One third of the cities under consideration have such parameters. The smallest number of cities has a dissected complex space. The cities tend to increase the complexity of their space in the process of development. The study showed that despite small population, the towns under consideration have very complex spatial structure

Phase field model for brittle fracture in multiferroic materials

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.

A Minkowski difference‐based advancing front packing technique for generating convex noncircular particles in complex domains

AbstractIn this work, a Minkowski difference‐based advancing front approach is proposed to generate convex and non‐circular particles in a predefined computational domain. Two specific algorithms are developed to handle the contact conformity of generated particles with the boundaries of the computational domain. The first, called the open form, is used to handle the smooth contact of generated particles with (external) boundaries, while the other, called the closed form, is proposed to handle the internal boundaries of a computational domain with a complex cavity. The Gilbert‐Johnson‐Keerthi (GJK) method is used to efficiently solve the contact detection between the newly generated particle at the front and existing particles. Furthermore, the problem of one‐sided particle lifting, which can cause some defects in the packing structure in existing advancing front methods during packing generation, is highlighted and an effective solution is developed. Several examples of increasing complexity are used to demonstrate the efficiency and applicability of the proposed packing generation approach. The numerical results show that the generated packing is not only more uniform, but also achieves a higher packing density than existing advancing front methods.

Modeling the Effects of Thermal Pad Voiding on Quad Flatpack No-lead (QFN) Components

Finite element modeling was used to evaluate the effects of thermal pad solder voiding on the thermal resistance of Quad Flatpack No Lead components. This included two different approaches for modeling solder voids: many small, distributed voids, the effects of which were averaged across the entire solder contact area or a single discrete void. Two approaches were used for defining the thermal path established in the solder. The effects of other design parameters - thermal boundary conditions, the presence of thermal vias under the package, and the size of the die power dissipation area – were also addressed. Modeling showed that thermal vias and external boundary conditions had the most significant impact on the package thermal resistance. Solder pad voids and concentrated die-level heat dissipation, for the range used in this study, had noticeable but less significant impacts on thermal resistance. The study also compared different approaches for simulating solder voiding and identified ranges in which modeling simulations are most appropriate.

NEW WATERFLOODING EFFICIENCY EVALUATION METHOD (ON THE EXAMPLE OF 9th HORIZON OF THE GUNESHLI FIELD)

The purpose of the research in the article is to develop a method for evaluating the efficiency of the water injection process. For this purpose, a number of computer studies are carried out. In view of this, a computer simulation of water injection process is applied. Using oil parameters from IX horizon of Guneshli field as PVT-properties of oil in reservoir conditions, the process of oil displacement by water injection in various technological modes is studied, the correlation between the injection rate and the amount of incremental oil production is determined. For this purpose the process of oil displacement in a hypothetical field is modeled on the basis of the idea of «enlarged well» at different injection rates, such as 10, 20, 30, 40, 50, 60, 70. and 75 m3/day. Water injection is carried out in the area of external reservoir boundary. In addition, the reservoir development process in the depletion regime is predicted for comparison. In both cases, the formation radius is considered as a circular layer equivalent to the real layer. Analysis of the obtained results determines the criteria for minimizing economic risks during water injection process. It is shown that at low rates of water injection, the numerical value of this parameter decreases with an increase of water volume injected per day. However, after a certain value of the injection rate, the efficiency factor increases with an increase of the water injected volume per day. Keywords: Displacement; Waterflooding; Waterflooding efficiency; Enlarged well.

Unstable Convection in a Vertical Double–Layer Porous Slab

A convective stability analysis of the flow in a vertical fluid-saturated porous slab made of two layers with different thermophysical properties is presented. The external boundaries are isothermal with one of them impermeable while the other is open to an external fluid reservoir. This study is a development of previous investigations on the onset of thermal instability in a vertical heterogeneous porous slab where the heterogeneity may be either continuous or piecewise as determined by a multilayer structure. The aim of this paper is investigating whether a two-layer structure of the porous slab may lead to the onset of cellular convection patterns. The linear stability analysis is carried out under the assumption that one porous layer has a thermal conductivity much higher than the other layer. This assumption may be justified for the model of a heat transfer enhancement system involving a saturated metal foam. A flow model for the natural convection based on Darcy’s momentum transfer in a porous medium is adopted. The buoyancy-induced basic flow state is evaluated analytically. Small-amplitude two-dimensional perturbations of the basic state are introduced, thus leading to a linear set of governing equations for the disturbances. A normal mode analysis allows one to formulate the stability eigenvalue problem. The numerical solution of the stability eigenvalue problem provides the onset conditions for the thermal instability. Moreover, the results evidence that the permeability ratio of the two layers is a key parameter for the critical conditions of the instability.

Modeling microvoiding kinetics of rare‐earth disilicates in flowing atmospheres containing water vapor

AbstractRare‐earth disilicate (REDS, RE2Si2O7) layers that may be used as environmental barrier coatings (EBCs) on ceramic matrix composite (CMC) components in high‐temperature stages of turbine engines are subject to microvoiding to form porous rare‐earth monosilicate (REMS, RE2SiO5) layers in flowing atmospheres containing water vapor. A simple microvoiding kinetic model that incorporates both mass transfer of the reaction product Si(OH)4(g) through the external gas phase boundary layer and pore diffusion of Si(OH)4(g) through the microvoided layer has been developed. Model predictions are in good agreement with measured growth rates of microvoided layers under low‐flowrate steam furnace test and high‐flowrate burner rig conditions. Since pore diffusion is generally the rate‐limiting step for EBC microvoiding in turbine engines, furnace testing under conditions of kinetic control by gas phase mass transfer is not generally capable of predicting REDS microvoiding rates under engine conditions. The kinetic model can be extended to incorporate changes in pore size and distribution, cracking of the microvoided layer, and introduction and cracking of an additional REMS topcoat to the system. The model can be used to generate a reasonable prediction of the time required to fully microvoid a REDS EBC layer on a CMC component in the hot gas path of an aircraft engine or stationary gas turbine.

Luenberger compensator theory for heat-Kelvin-Voigt-damped-structure interaction models with interface/boundary feedback controls

Abstract An optimal, complete, continuous theory of the Luenberger dynamic compensator (or state estimator or state observer) is obtained for the recently studied class of heat-structure interaction partial differential equation (PDE) models, with structure subject to high Kelvin-Voigt damping, and feedback control exercised either at the interface between the two media or else at the external boundary of the physical domain in three different settings. It is a first, full investigation that opens the door to numerous and far reaching subsequent work. They will include physically relevant fluid-structure models, with wave- or plate-structures, possibly without Kelvin-Voigt damping, as explicitly noted in the text, all the way to achieving the ultimate discrete numerical theory, so critical in applications. While the general setting is functional analytic, delicate PDE-energy estimates dictate how to define the interface/boundary feedback control in each of the three cases.

Navigation-Oriented Topological Model Construction Algorithm for Complex Indoor Space

Indoor space information is the basis of indoor location services such as indoor navigation, path planning, emergency evacuation, etc. Focusing on indoor navigation needs, this paper proposes a fast construction algorithm for a complex indoor space topology model based on disjoint set for the problem of lacking polygon description and topological relationship expression of indoor space entity objects in building plan drawings. Firstly, the Tarjan algorithm is used for identifying the hanging edges existing in the indoor space. Secondly, each edge is stored as two different edges belonging to two adjacent polygons that share the edge. A ring structure is introduced to judge the geometric position of walls, and then an efficient disjoint set algorithm is used to perform set merging. After that, disjoint set is queried to obtain all indoor space contours and external boundary contours, thereby the complete indoor space topological relationship at multiple levels is established. Finally, the connectivity theory of graph is used for solving the problem of a complex isolated polygon in topology information generation. The experimental results show that the proposed algorithm has generality to efficiently complete the automatic construction of a topological model for complex scenarios, and effectively acquire and organize indoor space information, thus providing a good spatial cognition mode for indoor navigation.

Similarity of length scales in high-Reynolds-number wall-bounded flows

The wall dependence of length scales used to describe large- and small-scale structures of turbulence is examined using highly resolved experiments in zero-pressure-gradient turbulent boundary layers and pipe flows spanning the range $2000< Re_\tau <37\ 700$ . Of particular interest is the influence of external intermittency on the scaling of these length scales. It is found that when suitable scaling parameters are selected and external intermittency is accounted for, the dissipative motions follow inner scaling even into the outer-scaled regions of the flow, and that certain large-scale descriptions follow outer scaling even in the inner-scaled regions of the flow. The wall dependence is the same for both internal pipe and external boundary layer flows, and the different length scales can be related to recognizable features in the longitudinal wavenumber spectrum.

Phase-field modeling of thermal cracking in hardening mass concrete

The manuscript is concerned with the phase-field modeling of thermal cracking in massive hardening concrete structures. Owing to the exothermic reactions, known as hydration, a considerable amount of heat is generated during the setting and hardening of concrete. Since concrete has relatively low thermal conductivity and fairly high heat capacity, sharp temperature gradients may occur between the interior and exterior parts of massive concrete structures. This uneven temperature distribution results in a non-uniform thermal expansion that, in turn, may lead to thermal cracking in conjunction with restraining external boundary conditions. Hence, it is of key importance to conduct the crack risk assessment of massive concrete structures at various stages of their construction and thereafter where real-size experiments are often unrealizable. To this end, we develop a multi-field computational approach to simulate thermal cracking in hardening concrete. In particular, we propose a novel chemo-thermo-mechanical model developed within the framework of the theory of reactive porous media coupled with a quasi-brittle phase-field regularized cohesive zone model to explicitly account for the initiation and propagation of thermal cracks. In the model, chemical, thermal, mechanical, and phase-field fracture problems are coupled through the constitutive equations. To our best knowledge, this is the first study where a quasi-brittle phase-field fracture model is used to model thermal cracking in hardening massive concrete through a novel incremental formulation. The potential of the proposed approach is demonstrated through the benchmark thermomechanical problems of a normal concrete member and a roller-compacted concrete dam. In the latter, original multi-field interface elements are devised between the lifts.

Study on the inter-porosity transfer rate and producing degree of matrix in fractured-porous gas reservoirs

Abstract The inter-porosity transfer is one of the decisive factors for gas development in fractured-porous gas reservoirs. In this article, we establish an analytical solution for the inter-porosity transfer rate and producing degree of matrix. Then, we study the law of inter-porosity transfer based on the solution. Through the Stehfest inversion transform, the typical curves of inter-porosity transfer rate and producing degree of matrix are plotted. It is found that the producing degree of matrix is close to zero in the initial period. Then, the inter-porosity transfer rate begins to increase, and the producing degree of matrix becomes larger. In the late period, the producing degree of matrix remains constant. In addition, the differences between the quasi-steady state model and the three kinds of unsteady state models are compared. It is found that the inter-porosity transfer occurs earlier in unsteady models. However, when pressure propagates to the external boundary, the transfer rate is equal between quasi-steady and unsteady models. It is also found that the inter-porosity transfer rate is slightly different in the three unsteady models, whereas in the spherical model it is largest at the intermediate period. Next, we discuss the influence of key parameters. The results reveal that gas reservoir radius, storage ratio, and inter-porosity flow factor can play an essential role in inter-porosity transfer. The findings of this study can improve our understanding of gas flow between fractures and matrix. Besides, it helps field engineers better understand the variation law of gas productivity in fractured-porous gas reservoirs, which can provide the scientific basis for making a development scheme.

Modelling of fire-suppressant injection into engine nacelle for various flight regimes

In this study, the injection of Halon 1301, an effective fire-suppressing agent, into a helicopter engine nacelle is modelled to provide insights into dispersion behaviour alongside complex flow physics. The injection velocity as well as the mass flow rate were retrieved via a 1-D pipe model to simulate nitrogen-pressurized flow of Halon 1301 in a four-branch pipe system. The Discrete Phase Model in ANSYS Fluent was then used to model the injection of Halon 1301 into an engine nacelle. To simulate engine operation conditions in forward flight and hover regime, external boundary conditions were prescribed to the pressure inlets in the nacelle. When Halon 1301 is injected into the engine bay via the first pair of injection points, the droplets immediately reach their boiling point of 215 K. This resulted in an explosive-dispersion behaviour with a cone angle in the range of 80°–90°. As the agent evaporates, the engine cools and another pair of injection points located at the rear of the engine is subsequently activated, helping to cool the engine further. The two flight regimes considered, namely, hover and forward flight, showed contrast in flow dynamics which affected the cooling of the engine as well as the spray dynamics. In particular, the forward flight case showed more recirculation zones compared to the hover case. The volume concentrations of Halon 1301 were plotted for 11 probe points within the nacelle, and it was observed that two locations showed traces of low concentration levels.

Static behavior of elastically supported transversely inhomogeneous porous functionally graded plate with different thickness variations under a variety of external loadings

The static behavior of a porous functionally graded material plate (FGMP) with variable thickness placed on two parametric elastic foundations exposed to various boundary conditions is investigated in this study. Thickness variation in the plate is assumed to vary in uni-direction/bi-direction with linear and parabolic variations. The properties of the constituent of FGMs are expected to change in the direction of thickness following the power law. The plate is subjected to three types of external loadings: uniformly distributed load (UDL), linearly increasing load (LIL), and linearly increasing decreasing load (LIDL). To explore the static behavior, numerical parameters (NP) linked with the bending and normal stresses of the plate have been determined. Classical plate theory is used to derive the governing equation using the energy principle. The transverse displacement functions are indigenously developed in the form of simple algebraic polynomials (using Pascal’s triangle) to handle any set of mixed- boundary conditions. The Rayleigh–Ritz method along with the algebraic polynomial is employed in the numerical simulation for getting NP. This method is straightforward, precise, and computationally efficient as it can handle any set of boundary conditions and the solution converges with very few iterations. Following the convergence and validation analyses, new findings are presented. The influence of aspect ratios, power-law exponents, porosity volume fraction, taper ratios, and the Winkler and Pasternak modulus on the NP of the plate has been thoroughly examined. The effect of various types of external loading and boundary conditions on deformed shapes and co-ordinate of maximum deflection of elastically supported porous FGMP with different thickness variations have also been reported. One of the important findings is that the effect of homogeneous porosity distribution on NP is more pronounced than in situations with non-homogeneous distributions. Also, the change in thickness of the plate and the distribution of various types of porosity has a substantial effect on the deformed shape of the plate. One of the interesting observations of this study is that the deformation in the plate is more significant in the case of bi-linear thickness variation compared to the uni-linear case. The results reported in this article are accurate enough to consider for further research and experimentation.

Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy Approach.

By taking enthalpy-an internal energy of a diffusion-type system-as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.

Experimental Research of the Heat Transfer into the Ground at Relatively High and Low Water Table Levels

During the cold period, the heat transferred through the building’s external boundaries to the environment changes the naturally established heat balance between atmospheric air and soil layers. The process of the heat transfer into the ground was investigated experimentally in the cases of the relatively high and low levels of the water table. The first part of each experiment was the research of the heat transfer into the soil from the heating surface. The second part was monitoring the heat dissipation in the ground until the return to the initial natural thermodynamic equilibrium after the heating is intercepted. The heating device was installed into the clay at a one-meter depth, and its surface temperature was kept constant at 20 degrees Celsius. The ground was warmed up in contact with the heating surface. The heat spread to other soil layers and transformed the temperature distribution. A new thermodynamic equilibrium was reached six days after the heating started at an initial temperature of 4.4 degrees Celsius. The intensity of the heat flux density approached a stable value equal to 117.4 W/m2, which is required to maintain this thermodynamic equilibrium, as the heat was dissipating in the large volume of the surrounding soil. The heating was turned off, and the natural initial heat balance was reached after two weeks.

Temperature behavior of cable-stayed bridges. Part I — Global 3D temperature distribution by integrating heat-transfer analysis and field monitoring data

Varying temperatures significantly affect long-span cable-stayed bridges. However, quantitative studies on their temperature behaviors are limited. Existing studies focus on 2D or 3D models of bridge segments only, exclude cables from heat-transfer analysis, and utilize inaccurate environmental conditions. For the first time, this study comprehensively and accurately investigates the global 3D temperature distribution of long-span cable-stayed bridges by integrating the heat-transfer analysis and field monitoring data. A navigation channel bridge of the Hong Kong‒Zhuhai‒Macao Bridge is used as the testbed. A global 3D refined finite element model of the entire bridge is established. The external thermal boundary conditions of the outer surfaces of the structure are carefully determined based on the real-time ambient temperature, wind, and solar radiation, which are tailored for each surface to reflect the influence of the geometric configuration. The internal thermal boundary conditions of the inner surfaces of the box girder and tower are dependent on the measured ambient temperature, considering the vertical temperature difference of the girder and the uniform temperature inside the tower. Then, the numerical heat-transfer analysis and field monitoring data are integrated to calculate the detailed temperature distribution of the entire bridge in different seasons. Results show that ambient temperature, wind, and solar radiation significantly affect the temperature distribution. For the girder, the vertical temperature difference is significant throughout the year, and the transverse temperature difference is nonnegligible in winter and summer, while the longitudinal temperature difference is trivial. The internal temperature of the tower remains stable owing to the insulation of the concrete. The temperatures of the cables vary from each other, which may cause stress redistribution within the structure. The calculated temperatures are in good agreement with their measured counterparts. The temperature results will be used to calculate the thermal-induced responses in the companion paper in a unified manner.

HERMES CubeSat Payload Thermal Balance Test and Comparison with Finite Volume Thermal Model

Scientific payloads onboard CubeSats usually have complex geometries and occasionally narrower allowed temperature ranges with respect to the rest of the spacecraft. In these cases, the capability to correctly predict the thermal behaviour of the payload once in orbit is mandatory. To achieve this ability, a thermal balance test is required to correctly identify the thermal model of the payload. The test consists in the application of different external thermal boundary conditions together with the addition of heat dissipation to simulate the thermal load produced by active electronics during operation. Those experimental data are fundamental to validate the numerical thermal model and make its predictions reliable. This paper presents the configuration and procedures of the thermal balance test performed on the Demonstration Model of the payload to be embarked on each satellite of the HERMES constellation. The test data is compared with the results of a finite volume thermal model of the payload, proving the application of this method to be reliable for space thermal analyses. The obtained test results show the temperature jumps caused by the heat dissipation applied to active components. A weak correlation between the payload interface and internal equipment has been observed, thus proving that the payload is almost decoupled from the Service Module temperature variations. Based on test outcomes, some modifications in the payload design have been implemented, with the aim to lower the operative temperature on critical, temperature-sensitive equipment.