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Advanced cooling techniques involving internal enhanced heat transfer and external film cooling and thermal barrier coatings (TBCs) are employed for gas turbine hot components to reduce metal temperatures and to extend their lifetime. A deeper understanding of the interaction mechanism of these thermal protection methods and the conjugate thermal behaviours of the turbine parts provides valuable guideline for the design stage. In this study, a conjugate heat transfer model of a turbine vane endwall with internal impingement and external film cooling is constructed to document the effects of TBCs on the overall cooling effectiveness using numerical simulations. Experiments on the same model with no TBCs are performed to validate the computational methods. Round and crater holes due to the inclusion of TBCs are investigated as well to address how film-cooling configurations affect the aero-thermal performance of the endwall. Results show that the TBCs have a profound effect in reducing the endwall metal temperatures for both cases. The TBC thermal protection for the endwall is shown to be more significant than the effect of increasing coolant mass flow rate. Although the crater holes have better film cooling performance than the traditional round holes, a slight decrement of overall cooling effectiveness is found for the crater configuration due to more endwall metal surfaces directly exposed to external mainstream flows. Energy loss coefficients at the vane passage exit show a relevant negative impact of adding TBCs on the cascade aerodynamic performance, particularly for the round hole case.
The work presents the analysis of the free boundary value problem related to the one-dimensional invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of a system of non-linear hyperbolic partial differential equations governing the microbial species growth and a system of semi-linear elliptic partial differential equations describing the substrate trends. The model is completed with a system of elliptic partial differential equations governing the diffusion and reaction of planktonic cells, which are able to switch their mode of growth from planktonic to sessile when specific environmental conditions are found. Two systems of non-linear differential equations for the substrate and planktonic cells mass balance within the bulk liquid are also considered. The free boundary evolution is governed by a differential equation that accounts for detachment. The qualitative analysis is performed and a uniqueness and existence result is presented. Furthermore, two special models of biological and engineering interest are discussed numerically. The invasion of Anammox bacteria in a constituted biofilm inhabiting the deammonification units of the wastewater treatment plants is simulated. Numerical simulations are run to evaluate the influence of the colonization process on biofilm structure and activity.
The generalized theory of terawatt laser pulse interaction with a low-dense porous substance of light chemical elements including laser light absorption and energy transfer in a wide region of parameter variation is developed on the base of the model of laser-supported hydrothermal wave in a partially homogenized plasma. Laser light absorption, hydrodynamic motion, and electron thermal conductivity are implemented in the hydrodynamic code, according to the degree of laser-driven homogenization of the laser-produced plasma. The results of numerical simulations obtained by using the hydrodynamic code are presented. The features of laser-supported hydrothermal wave in both possible cases of a porous substance with a density smaller and larger than critical plasma density are discussed along with the comparison with the experiments. The results are addressed to the development of design of laser thermonuclear target as well as and powerful neutron and X-ray sources.
In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reaction-diffusion system that models the spatial interrelationship between two preys and predator species. The major result is centered on the analysis of the system for linear stability. Analysis of the main model reflects that the dynamical system is locally and globally asymptotically stable. We propose some useful theorems based on the existence and permanence of the species to validate our theoretical findings. Reliable and efficient methods in space and time are formulated to handle any space fractional reaction-diffusion system. We numerically present the complexity of the dynamics that are theoretically discussed. The simulation results in one, two and three dimensions show some amazing scenarios.
Louvered cavities are extensively employed in engineering applications. In the configurations of flow past these cavities, self-sustained oscillations will be excited. This can give rise to structure vibrations or noise. Numerical models are established to analyze excitation condition for of these oscillations. Computational results reveal that the excitation condition can be quantitatively described by the ratio of gap width G to the boundary layer thickness δ at the separation edge. When G/δ exceeds a certain critical value G/δc, self-sustained oscillations are excited. Otherwise, disturbances will dissipate and the flow configuration along the louver will be like a parallel plate flow. The critical value G/δc decreases with the ratio of G to the thickness of the louver plate H. This suggests that the excitation condition is more easily satisfied for a louver with sparse fins. The bottom boundary of the cavity restricts the feedback flow and then suppresses the excitation of self-sustained oscillations. With an increasing cavity height Hc, which reflects the distance between the louver and the bottom boundary, the critical value G/δc decreases and the decreasing rate reduces gradually. In contrast, because G/δc is relatively insensitive to the cavity length Lc, the side boundaries have no obvious influence on the excitation condition.
We here discuss the various dynamo models which have been designed to explain the generation and evolution of large-scale magnetic fields in stars. We focus on the models that have been applied to the Sun and can be tested for other solar-type stars now that modern observational techniques provide us with detailed stellar magnetic field observations. Mean-field flux-transport dynamo models have been developed for decades to explain the solar cycle and applications to more rapidly-rotating stars are discussed. Tremendous recent progress has been made on 3D global convective dynamo models. They do not however for now produce regular flux emergence that could be responsible for surface active regions and questions about the role of these active regions in the dynamo mechanism are still difficult to address with such models. We finally discuss 3D kinematic dynamo models which could constitute a promising combined approach, in which data assimilation could be applied.
An optimal control problem is considered to find a stable surface traction, which minimizes the discrepancy between a given displacement field and its estimation. Firstly, the inverse elastic problem is constructed by variational inequalities, and a stable approximation of surface traction is obtained with Tikhonov regularization. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. Finally, a numerical algorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.
A fully three-dimensional kinematic model is applied to simulate the evolution of the magnetic field in a small (120 pc in size) volume of the turbulent interstellar medium (ISM) in the presence of the field diffusion. The turbulent motions arc approximated by a sequence of non-overlapping in time vortices, which have the form of the rotating (with a non-zero hclicity) columns much longer than the parcel size. They moved vertically and at the inclination of ±30° to the galactic plane. The resulting magnetic field structure closely resembles a fragment of a classical twisted flux tube, well-ordered over the whole parcel of the ISM.
We present the first model that couples high-resolution simulations of the formation of local group galaxies with calculations of the galactic habitable zone (GHZ), a region of space which has sufficient metallicity to form terrestrial planets without being subject to hazardous radiation. These simulations allow us to make substantial progress in mapping out the asymmetric three-dimensional GHZ and its time evolution for the Milky Way (MW) and Triangulum (M33) galaxies, as opposed to works that generally assume an azimuthally symmetric GHZ. Applying typical habitability metrics to MW and M33, we find that while a large number of habitable planets exist as close as a few kiloparsecs from the galactic centre, the probability of individual planetary systems being habitable rises as one approaches the edge of the stellar disc. Tidal streams and satellite galaxies also appear to be fertile grounds for habitable planet formation. In short, we find that both galaxies arrive at similar GHZs by different evolutionary paths, as measured by the first and third quartiles of surviving biospheres. For the MW, this interquartile range begins as a narrow band at large radii, expanding to encompass much of the Galaxy at intermediate times before settling at a range of 2–13 kpc. In the case of M33, the opposite behaviour occurs – the initial and final interquartile ranges are quite similar, showing gradual evolution. This suggests that Galaxy assembly history strongly influences the time evolution of the GHZ, which will affect the relative time lag between biospheres in different galactic locations. We end by noting the caveats involved in such studies and demonstrate that high-resolution cosmological simulations will play a vital role in understanding habitability on galactic scales, provided that these simulations accurately resolve chemical evolution.
In high-power laser systems (HPLSs), understanding debris-removal trajectories is important in eliminating debris from the surfaces of transport mirrors online and keeping other optical components free from contamination. NS equations, the RNG
model and the discrete phase model of the Euler–Lagrange method are used to conduct numerical simulations on the trajectories of contaminant particles of different sizes and types on the mirror surface using Fluent commercial software. A useful device is fabricated based on the simulation results. This device can capture and collect debris from the mirror surface online. Consequently, the effect of debris contamination on other optical components is avoided, cleaning time is shortened, and ultimately, the cleanliness of the mirrors in HPLSs is ensured.
A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.
A phase field approach for structural topology optimization which allows for topology
changes and multiple materials is analyzed. First order optimality conditions are
rigorously derived and it is shown via formally matched asymptotic
expansions that these conditions converge to classical first order conditions obtained in
the context of shape calculus. We also discuss how to deal with triple junctions where
e.g. two materials and the void meet. Finally, we present several
numerical results for mean compliance problems and a cost involving the least square error
to a target displacement.
This paper presents numerical results based on a macroscopic blood coagulation model
coupled with a non-linear viscoelastic model for blood flow. The system of governing
equations is solved using a central finite-volume scheme for space discretization and an
explicit Runge-Kutta time-integration. An artificial compressibility method is used to
resolve pressure and a non-linear TVD filter is applied for stabilization. A simple test
case of flowing blood over a clotting surface in a straight 3D vessel is solved. This work
presents a significant extension of the previous studies  and .
A new class of history-dependent quasivariational inequalities was recently studied in
[M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in
contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491].
Existence, uniqueness and regularity results were proved and used in the study of several
mathematical models which describe the contact between a deformable body and an obstacle.
The aim of this paper is to provide numerical analysis of the quasivariational
inequalities introduced in the aforementioned paper. To this end we introduce temporally
semi-discrete and fully discrete schemes for the numerical approximation of the
inequalities, show their unique solvability, and derive error estimates. We then apply
these results to a quasistatic frictional contact problem in which the material’s behavior
is modeled with a viscoelastic constitutive law, the contact is bilateral, and friction is
described with a slip-rate version of Coulomb’s law. We discuss implementation of the
corresponding fully-discrete scheme and present numerical simulation results on a
In this paper we present a fluid-structure interaction model of neuron’s membrane
deformation. The membrane-actin is considered as an elastic solid layer, while the
cytoplasm is considered as a viscous fluid one. The membrane-actin layer is governed by
elasticity equations while the cytoplasm is described by the Navier-Stokes equations. At
the interface between the cytoplasm and the membrane we consider a match between the solid
velocity displacement and the fluid velocity as well as the mechanical equilibrium. The
membrane, which faces the extracellular medium, is free to move. This will change the
geometry in time. To take into account the deformation of the initial configuration, we
use the Arbitrary Lagrangian Eulerian method in order to take into account the mesh
displacement. The numerical simulations, show the emergence of a filopodium, a typical
structure in cells undergoing deformation.
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.
In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau–Lifshitz–Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic.
In this paper, we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method, which incorporates the convection effects and the action of magnetic field. The model consists of flow, concentration, phase field and energy systems which are nonlinear evolutive and coupled systems. It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field. To illustrate our model, numerical simulations of the influence of magnetic-field on the evolution of dendrites during the solidification of the binary mixture of Nickel-Copper (Ni-Cu) are developed. The results demonstrate that the dendritic growth under the action of magnetic-field can be simulated by using our model.
Discs are a key element in star and planet formation; however, magnetic fields can efficiently transport angular momentum away from the central region of the collapsing core during the dense core collapse, preventing disc formation. We perform numerical simulations of magnetically supercritical collapsing cores with a misalignment between the rotation axis and the magnetic field (Joos et al. 2012) and in a turbulent environment (Joos et al. 2013). The early formation of massive discs can take place at moderate magnetic intensities if the rotation axis is tilted or in a turbulent environment, because of misalignment and turbulent diffusion.
We study Rayleigh–Taylor instability (RTI) at the coronal–prominence boundary by means of 2.5D numerical simulations in a single-fluid MHD approach including a generalized Ohm's law. The initial configuration includes a homogeneous magnetic field forming an angle with the direction in which the plasma is perturbed. For each field inclination we compare two simulations, one for the pure MHD case, and one including the ambipolar diffusion in the Ohm's law, otherwise identical. We find that the configuration containing neutral atoms is always unstable. The growth rate of the small-scale modes in the non-linear regime is larger than in the purely MHD case.