Multidimensional Numerical Models Research Articles

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution

Aims. The initial stages of planet formation may start concurrently with the formation of a gas-dust protoplanetary disk. This makes the study of the earliest stages of protoplanetary disk formation crucially important. Here we focus on dust growth and pebble formation in a protoplanetary disk that is still accreting from a parental cloud core. Methods. We have developed an original three-dimensional numerical hydrodynamics code, which computes the collapse of rotating clouds and disk formation on nested meshes using a novel hybrid Coarray Fortran-OpenMP approach for distributed and shared memory parallelization. Dust dynamics and growth are also included in the simulations. Results. We found that the dust growth from ~1 µm to 1–10 mm already occurs in the initial few thousand years of disk evolution but the Stokes number hardly exceeds 0.1 because of higher disk densities and temperatures compared to the minimum mass Solar nebular. The ratio of the dust-to-gas vertical scale heights remains rather modest, 0.2–0.5, which may be explained by the perturbing action of spiral arms that develop in the disk soon after its formation. The dust-to-gas mass ratio in the disk midplane is highly nonhomogeneous throughout the disk extent and is in general enhanced by a factor of several compared to the fiducial 1:100 value. Low St hinders strong dust accumulation in the spiral arms compared to the rest of the disk and the nonsteady nature of the spirals is also an obstacle. The spatial distribution of pebbles in the disk midplane exhibits a highly nonhomogeneous and patchy character. The total mass of pebbles in the disk increases with time and reaches a few tens of Earth masses after a few tens of thousand years of disk evolution. Conclusions. We found that protoplanetary disks with an age ≤20 kyr can possess notable amounts of pebbles and feature dust-togas density enhancements in the disk midplane. Hence, these young disks can already be ripe for the planet formation process to start. Multidimensional numerical models of disk formation that consider the coevolution of gas and dust including dust growth are important to improve our understanding of planet formation.

Multidimensional nonlinear numerical simulation of post‐tensioned concrete girders with different prestressing levels

AbstractMost of the Italian infrastructures have been built since the mid‐twentieth century. Prestressed concrete (PC) has been widely used, especially for bridges and viaducts. These structures have proved effective over time, but their performance could be affected by degradation phenomena (i.e., corrosion of the tendons and residual prestressing) or construction defects (i.e., grouting of the ducts), which need to be accurately modeled. This paper focuses on the flexural response of two reduced‐scale, posttensioned, PC bridge girders, prestressed with two different jacking forces and tested under four‐point bending configuration. Four multidimensional numerical models were developed to simulate the experimental behaviors of the selected specimens, using two alternative computational strategies, namely, the finite element method (FEM) and applied element method (AEM). Three FEM modeling were considered, ranging from one‐dimensional lumped‐plasticity models to two‐dimensional and three‐dimensional (3D) spread‐plasticity models. Besides, 3D AEM models were developed into another software package. The accuracy and the computational costs of the two numerical strategies are discussed in this paper. Also, the main features of each numerical modeling technique are addressed, including comparisons between numerical and experimental global response data as well as the statistical characterization of the model error. Based on these different features, the authors also suggest the most suitable numerical strategy for future studies on PC girders.

On the estimation of the radiant heating surface temperature and the heat transfer rate calculation: New transient simplified analytical model

In this paper, a new semi-analytical model based on a hybrid approach that combines a numerical approach and a sensitivity analysis is developed to evaluate the surface temperature of the underfloor heating system and analyse its thermal behaviour under transient conditions. The model is validated by measurements which are performed in a full-scale test cell. Furthermore, a good agreement is obtained by comparing the developed semi-analytical model with two multidimensional numerical models based on the finite difference method and the finite volume method that are previously developed. The sensitivity analysis, based on the Design of experiments method, indicated that the most influencing parameters on the thermal response of the heating slab, are respectively the specific heat capacity and the heating water flowrate.

Experimental and multidimensional numerical analysis of the thermal behavior of an anhydrite radiant slab floor heating system: A multi-objective sensitivity study

In this study, experimental and comprehensive multidimensional numerical models are developed for the analysis of the thermal behavior of an anhydrite slab floor heating system (FHS). Three different modeling approaches are employed, including a one dimension (1D) Modelica® method based on an object-oriented approach, a two dimension (2D) finite difference method (FDM), and a three dimension (3D) finite volume method (FVM), using the ANSYS/Fluent® software. The comparison between the numerical results and the measured data is performed for the inlet and outlet water temperatures, the average slab surface temperature, the depth local temperatures, and the average total heat flux. Experiments and simulations were in agreement regarding the thermal response of the FHS in accordance to the well-known 2D FDM. A multi-objective sensitivity study is then performed, based on a design of experiments method (DoE) in order to analyze the effects of the design and physical control factors and their interactions on the average surface temperature and the thermal time constant. A full factorial design, generating 128 simulations based on our validated 2D FDM model is used to construct polynomial meta-models using the aforementioned thermal parameters. As a result, the water volume flow rate and the inner diameter are the most influential factors on the surface temperature, whilst the thermal time constant is shown to be considerably influenced by the slab thickness, density, and specific heat, as well as their interactions. The elicited results may be exploited in order to help practicing building engineers to optimize the FHS, and to enhance its energy performance.

Radiative magnetohydrodynamics simulations on solar corona

The outmost layer of solar atmosphere, corona, has many activities, such as flares, coronal mass ejections, solar prominences, and coronal rains. In order to fully understand the nonlinear physical process of these activities, one of the most popular approaches is to construct multidimensional numerical models via radiative magnetohydrodynamic numerical simulations. To simulate macroscopic coronal physics, we need to numerically solve magnetohydrodynamic equations coupled with radiative cooling, thermal conduction, and heating. The mainstream numerical methods to numerically solve these problems are introduced. The numerical scheme to solve the magnetohydrodynamic equations is composed of reconstruction to cell-interface values, approximate Riemann solver, methods to control divergence of magnetic field, and time integrator. We then review on the state of art in numerical studies on solar active region, flares, prominences, and coronal rains.

Multi-dimensional Analysis, Information Mining and Numerical Modeling for Small Samples of Biomedical Microfluidic Droplets

Information mining has turned to be increasingly important in the modern digital world. The mining results lead to the essential advances in not only information technology, but general natural science, such as life science, mechanics, numerical analysis, calculation technology, <i>etc</i>. These innovations permitted for the manipulation of biomicrofluidic droplets at micrometer-scale. Through the acquisition of raw data and the multidimensional analysis, numerical modeling can possibly be established and the further optimization can be processed. This work was focused on the multi-dimensional analysis based on small samples of the biomicrofludic droplet generation. Then numerical modeling was used to describe the fabrication of microdroplets in complex circumstances. Both linear modeling and nonlinear optimization were performed while the artificial intelligence technology was applied. Although the linear model presented the rough descriptive capacities of microdroplets variation, non-linear optimization improved its descriptive properties. Artificial neural network was established to depict the microfluidic droplets and its accuracy was validated satisfactorily.

Elucidating modeling aspects of thermoelectric generator

Multidimensional numerical models are useful tools for understanding the heat transfer mechanisms and performance optimization of thermoelectric generators (TEGs). In this study, two three-dimensional numerical models are developed for TEGs based on different formulations, but with similar abilities for heat and electricity transfer analysis and performance prediction. Model 1 solves the conservation equations of the Seebeck potential and the Ohmic potential separately, and the total built-in potential can be obtained based on the solved Seebeck and Ohmic potentials. Model 2 solves the conservation equation of the total built-in potential directly, and the conservation equation for the Ohmic potential is also solved. The comparison between Model 1 and Model 2 shows that Model 2 is slightly more precise for power output prediction. The detailed formulations of these two models are described, and the difference among the present and previous models is also discussed. Some important modeling aspects are elucidated for the TEG models, such as the conservation equations and boundary conditions. Parametric studies are carried out based on various thermal boundary conditions. The influence of the TEG semiconductor shape on performance is investigated in details. It is found that for the nearly same volume of semiconductor materials, changing the shape from normal cuboid (constant cross-sectional area) to hexahedrons (variable cross-sectional area) could increase the power output significantly. The reason is that the temperature gradient could be enhanced when proper variable cross-sectional areas are used.

Multi-timescale and correlated dynamic adaptive chemistry modeling of ignition and flame propagation using a real jet fuel surrogate model

A new correlated dynamic adaptive chemistry (CO-DAC) method is developed and integrated with the hybrid multi-timescale (HMTS) method for computationally efficient modeling of ignition and unsteady flame propagation of real jet fuel surrogate mixtures with a detailed and comprehensively reduced kinetic mechanism. A concept of correlated dynamic adaptive chemistry (CO-DAC) method in both time and space coordinates is proposed by using a few key phase parameters which govern the low, intermediate, and high temperature chemistry, respectively. Correlated reduced mechanisms in time and space are generated dynamically on the fly from the detailed kinetic mechanism by specifying thresholds of phase parameters of correlation and using the multi-generation path flux analysis (PFA) method. The advantages of the CO-DAC methods are that it not only provides the flexibility and accuracy of kinetic model and chemistry integration but also avoids redundant model reduction in time and space when the chemistry is frequently correlated in phase space. To further increase the computational efficiency in chemistry integration, the hybrid multi-timescale (HMTS) method is integrated with the CO-DAC method to solve the stiff ordinary differential equations (ODEs) of the reduced chemistry generated on the fly by CO-DAC. The present algorithm is compared and validated against the conventional VODE solver, DAC and HMTS/DAC methods for simulating ignition and unsteady flame propagation of real jet fuel surrogate mixtures consisting of four component fuels, n-dodecane, iso-octane, n-propyl benzene, and 1,3,5-trimethyl benzene. The results show the present HMTS/CO-DAC algorithm is not only computationally efficient but also robust and accurate. Moreover, it is shown that compared to the DAC and HMTS/DAC methods, the computation time of model reduction in CO-DAC is almost negligible even for a large kinetic mechanism involving hundreds of species. In addition, the results show that computation efficiency of CO-DAC increases from homogeneous ignition to one-dimensional flame propagation for both the first and second generation PFA reduction. Therefore, the present HMTS/CO-DAC method can enable high-order model reduction and achieve higher computation efficiency for multi-dimensional numerical modeling.

Near-Cathode Plasma Layer on CuCr Contacts of Vacuum Arcs

A model of near-cathode layers in vacuum arcs is developed. The model relies on a numerical solution of the problem of near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface, and allows the self-consistent determination of all parameters of the near-cathode layer, including the ion backflow coefficient. The dependence of the density of energy flux from the plasma to the cathode surface on the local surface temperature is nonmonotonic with a maximum, a feature that plays an important role in the physics of plasma–cathode interaction. The developed model may be used for a variety of purposes, including as a module of complex nonstationary multidimensional numerical models of plasma–cathode interaction in vacuum arcs. As a simple example, an analytical evaluation of parameters of stationary spots on copper and chromium is given. In the case of composite CuCr contacts with large grains, spots with current of several tens of amperes burning on the copper matrix coexist with spots with currents of the order of 1 A burning on the chromium grains.

New Directions in Advanced Modeling and in Situ Measurements Near Reacting Surfaces

Multidimensional numerical modeling and in situ spatially-resolved measurements of gas-phase thermoscalars over the catalyst boundary layer have fostered fundamental investigation of the heterogeneous and homogeneous chemical reaction pathways and their coupling at realistic operating conditions. The methodology for validating catalytic and gas-phase reaction mechanisms is firstly outlined for industrially-relevant fuels. Combination of advanced modeling and in situ near-wall species and velocity measurements is then used to address the intricate interplay between interphase fluid transport (laminar or turbulent) and hetero-/homogeneous kinetics. Controlling parameters of this interplay are the homogeneous ignition chemistry, flame propagation characteristics, competition between the catalytic and gaseous pathways for fuel consumption, diffusional imbalance of the limiting reactant, flow laminarization due to heat transfer from the hot catalytic walls, and fuel leakage through the gaseous reaction zone. Dynamic reactor operation and intrinsic flame dynamics driven by interactions between homogeneous kinetics and catalytic walls are outlined using detailed transient simulation. It is shown that the presence of catalytic reactions moderates flame instabilities. Future directions for transient modeling and for temporally-resolved in situ near-wall measurements are finally summarized.

The effect of combustion chamber geometry on injection and mixture preparation in a CNG direct injection SI engine

In pursuing a project to convert a four cylinder gasoline multi-point port fuel injection engine to a CNG direct injection engine, a numerical model has been developed in AVL FIRE software to undertake a detailed numerical investigation on the effects of combustion chamber geometry in such engines. Two main phases have been considered in the present study. In the first phase, aiming to fully investigate flow field and mixing process, multi-dimensional numerical modeling of transient gas injection has been performed. In order to verify the accuracy of the model, two different validation cases have been employed. The results showed that the models are quite capable of grasping all the significant physical phenomena in the process. Adoption of such a modeling was found to be a challenging task because of required computational effort and numerical instabilities. In all validation cases, experimental and numerical results were observed to have excellent agreement with each other.In the second phase, using the moving mesh capability the validated model has been developed to include methane direct injection into the cylinder of a direct injection engine for various combustion chamber geometries. Five different piston head shapes along with two injector types of single hole and multi hole have been taken into consideration. A centrally mounted injector location has been adapted to all cases. The effects of combustion chamber geometry, injection parameters, injector type and cylinder head shape have been studied on mixing of air–fuel inside cylinder. Based on the results, suitable geometrical configuration for the new NG DI engine has been discussed.

Comparing biofilm models for a single species biofilm system

A benchmark problem was defined to evaluate the performance of different mathematical biofilm models. The biofilm consisted of heterotrophic bacteria degrading organic substrate and oxygen. Mathematical models tested ranged from simple analytical to multidimensional numerical models. For simple and more or less flat biofilms it was shown that analytical biofilm models provide very similar results compared to more complex numerical solutions. When considering a heterogeneous biofilm morphology it was shown that the effect of an increased external mass transfer resistance was much more significant compared to the effect of an increased surface area inside the biofilm.

Thermal and Hydraulic Effects of Dimples on Performance of Clamshell Heat Exchangers in Residential Gas Furnaces

This paper investigates the thermal and hydraulic effects of dimples on clamshell heat exchangers in residential gas furnaces through experimental studies and by using one-dimensional and multidimensional numerical models. Calculated results from the one-dimensional thermal model show that six dimples in a clamshell heat exchanger improve the heat transfer of the clamshell heat exchanger by only 1.5%. In contrast, experimental results and one-dimensional calculations show that the dimples cause a 360% increase in the pressure drop. Multidimensional numerical calculations of flow and heat transfer in the channels show that a single dimple significantly increases total pressure drop (60 to 125%) but only minimally increases heat transfer (3 to 9%) for the Reynolds number range of 6 × 102 to 1.5 × 104. A new clamshell heat exchanger design without dimples is proposed. This new design has a reduced cross-sectional area but the same perimeter as the original dimpled clamshell heat exchanger. The new furnace design has better or equal heat transfer and less pressure drop than the original dimpled heat exchanger. Based on the results, it is concluded that dimples are not an efficient means to increase heat transfer in clamshell heat exchangers because the pressure drop penalty is high and heat transfer enhancement is minimal.

An improved method for roughening floodplains on physical river models

physical (hydraulic) modelling of river systems subject to overbank flow require the simulation of floodplain roughness. significant full and reduced scale experiments have now been carried out to establish the flow resistance of a range of real and simulated floodplain vegetation. one use for this improved knowledge of hoodplain hydraulics is to provide a basis for an improved method for overbank roughening in hydraulic models. it can also be of value in multi-dimensional numerical models the first part of this paper reviews briefly this work on floodplain vegetation resistance, leading to both empirical and theoretical relationships to describe floodplain roughness, and assesses the appropriate use of these methods. the second and greater part of the paper examines in more detail two methods used recently to roughen floodplains in large scale hydraulic models: non-submerging vertical rods, and a method based on expanded aluminium mesh units. a comparison is made between these two methods by reference to recent tests in the uk flood channel facility at hr wallingford. practical recommendations are made for designing a roughness system appropriate for use in future river model tests.

Solar energy deposition rates in the mesosphere derived from airglow measurements: Implications for the ozone model deficit problem

We derive rates of energy deposition in the mesosphere due to the absorption of solar ultraviolet radiation by ozone. The rates are derived directly from measurements of the 1.27‐μm oxygen dayglow emission, independent of knowledge of the ozone abundance, the ozone absorption cross sections, and the ultraviolet solar irradiance in the ozone Hartley band. Fifty‐six months of airglow data taken between 1982 and 1986 by the near‐infrared spectrometer on the Solar‐Mesosphere Explorer satellite are analyzed. The energy deposition rates exhibit altitude‐dependent annual and semi‐annual variations. We also find a positive correlation between temperatures and energy deposition rates near 90 km at low latitudes. This correlation is largely due to the semiannual oscillation in temperature and ozone and is consistent with model calculations. There is also a suggestion of possible tidal enhancement of this correlation based on recent theoretical and observational analyses. The airglow‐derived rates of energy deposition are then compared with those computed by multidimensional numerical models. The observed and modeled deposition rates typically agree to within 20%. This agreement in energy deposition rates implies the same agreement exists between measured and modeled ozone volume mixing ratios in the mesosphere. Only in the upper mesosphere at midlatitudes during winter do we derive energy deposition rates (and hence ozone mixing ratios) consistently and significantly larger than the model calculations. This result is contrary to previous studies that have shown a large model deficit in the ozone abundance throughout the mesosphere. The climatology of solar energy deposition and heating presented in this paper is available to the community at the Middle Atmosphere Energy Budget Project web site at http://heat.budget.gats.inc.com.

Multi-channel laser doppler velocimetry (LDV) and digital image processing (DIP) in fluvial hydromechanics

Recent efforts in fluvial hydromechanics aim at the capability of reliably predicting fluvial flow, turbulence and mass transport by means of multi-dimensional hydrodynamic numerical models. For this purpose, most detailed and highly accurate experimental data are needed in order to calibrate and verify the simulation tools. An optimum, but so far non-existing measurement technique would provide the complete state-space representation of the investigated water body at a high spatial and temporal resolution. While this is far from being available, already well established optical methods, such as Laser Doppler Velocimetry (LDV) and Digital Image Processing (DIP), seem to bear the potential for coming close to the optimum if applied in effective combination. Within this paper, several corresponding applications of LDV and DIP to the investigation of compound open-channel flow are described and discussed regarding their characteristic results, advantages and disadvantages as well as possible future improvements.

Accurate Resolution of Physical Dispersion in the Multidimensional Numerical Modeling of Miscible and Chemical Displacement

Summary This paper presents a finite-difference scheme for numerical modeling of the convection-dominated flows common in miscible or chemical flooding in porous media. The proposed difference operator possesses desirable phase and amplitude properties capable of resolving sharp fronts with negligible over- and undershoot. The scheme is generalized to multidimensions. Difference analogs have been derived for variable grid sizes for large-scale compositional simulations. Application to 3D miscible displacement problems and comparison with other standard industry methods have demonstrated the scheme's effectiveness in controlling numerical diffusion and grid-orientation sensitivity without any significant additional computational effort.

Modern and ancient geotherms beneath southern Africa

Estimates of subsurface temperatures in the Archean craton of southern Africa during the Archean derived from diamond thermobarometry studies are remarkably similar to temperatures estimated for the same depths today, even though heat production in the earth and the mean global heat flow were probably substantially higher in the Archean. We present multi-dimensional numerical models for the thermal environment of the Archean craton in southern Africa during the Archean in which deep mantle heat is diverted away from the craton toward the surrounding oceanic lithosphere by a lithospheric root beneath the craton. Extrapolation of present-day models to thermal conditions appropriate for the Archean is inadequate to explain the similarity of present-day and Archean temperatures in the cratonic root. Reconciliation of the modern and ancient temperature estimates requires either relaxation of the constraints that the cratonic crustal heat production and/or the earth's mean mantle temperature were higher in the Archean than they are today, or that substantial “erosion” of the lithosphere comprising the cratonic root has occurred since the Archean. The latter possibility could perhaps result from revolatilization of the cratonic root in association with thermal perturbations in the mantle, for which there is evidence in southern Africa in the form of post-Archean tectonic and igneous activity.

Mathematical modelling of radionuclide migration in groundwater

Summary This paper reviews recent work on the development of mathematical models for the transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. Firstly, general multi-dimensional numerical models for the flow of water and the transport of dissolved radionuclides through permeable media are described. Their use in assessing the importance of possible transport pathways is illustrated by examples of flow in rocks with high permeability fracture zones. Secondly, recent advances in the description of flow and transport through fractured rock masses are considered. The results of field experiments are used to examine the characteristics of single fractures such as transmissivity, the proportion taking flow and the diffusion of ions into the surrounding rock. In addition, network models are used to examine the connectivity, flow and hydrodynamic dispersion through fracture systems and to assess how well transport can be modelled by an equivalent permeable medium model. The fracture systems are defined by probability distributions for the orientations, lengths and hydraulic apertures of fractures together with information about the number of fractures per unit volume. It is found that, providing the region size is much bigger than the mean fracture length, the permeability is constant, but that hydrodynamic dispersion is not adequately modelled by a diffusion-like term.

A time-dependent and two-dimensional numerical model for MOSFET device operation

A time-dependent and multi-dimensional numerical modeling for semiconductor device operation is proposed, in which the quasi-Fermi potentials for electrons and holes rather than the carrier densities are directly analyzed. Fundamental equations for the quasi-Fermi potential are reduced to a diffusion equation that includes a drift term. Boundary conditions are straightforwardly derived from the device physics and are shown in a mathematically simple manner, independent of device structure complexities. From the viewpoint of numerical procedure, a combination of an implicit time integral and upwind difference scheme is adopted. The quasi-Fermi potential is a gradually changing value between the maximum and minimum external applied voltages, and the present method is suitable for numerical modeling. A time dependent and two dimensional analysis program has been developed. The advantages of the present modeling are demonstrated through the carrying out of sample calculations of, for example, MOSFET switching characteristics. Quick and stable convergence in the numerical scheme has been obtained over the range of practically used operation voltages.