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The main obstacle of the PCMs which restricts their usage for thermal energy storage (TES) applications is their poor thermal conductivity. Utilizing metal fins is the most popular solution to enhance the performance of PCM-TES. In this work, PCM thermal performance enhancement in a shell and tube heat exchanger (STHX) was numerically investigated. Tee shaped fins is suggested as an innovative fin shape to accelerate the PCM melting process in the STHX. The tee fin was compared with the traditional longitudinal fin shape to evaluate its thermal performance. In this test, many heat exchangers with various fin shapes were tested and compared. These heat exchangers were: heat exchanger without fins, heat exchanger with six tee fins, heat exchanger with six longitudinal fins and heat exchanger with six tree fins. 2D numerical models were developed. The melting process was considered during the simulation. The results showed that the case without fins had about 15% of the PCM melted after 6 h, while, with the tee fins the PCM totally melted after 3.5 h. The total PCM melting time reduced by 33% when the tee fins were used, as compared to utilizing the longitudinal fins. It is observed that the geometry of the fins has an important influence on the PCM melting.

The well-known Shear Stress Transport (SST k–ω) turbulence model was modified and examined. Two industrially relevant problems with curved and rotating channels have been selected to assess the modification potential: a rotating lid in a confined cylinder and swirling flow through a three-dimensional abrupt expansion pipe. The postulated amendment simplified the rotation and curvature correction term that was suggested earlier by Smirnov and Menter [J. Turbomach. 2009, 131 (4) 041010]. The new formulation avoids the calculation of the complex Lagrangian derivatives by implementing the Richardson number (Ri) in the applied rotation function. The numerical computations were performed using OpenFOAM-2.4.x. The results show the expected capability of the Shear Stress Transport model with Curvature Correction Modification (SSTCCM) to handle the curvature effects and system rotation. The paper compares the SSTCCM model with the conventional eddy viscosity models (EVMs): standard k–ϵ; Re-Normalization Group (RNG) k–ϵ, and the original SST k–ω.

We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In the state ${\bf R}$ an individual is assumed to stay immune within a finite time interval. In the first part, we introduce a random life time or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and cannot be captured by standard SIR models., Comment: 10 pages, 13 Figures

International audience; We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the time-fractional Poisson renewal process. This process introduces a non-Markovian walk with long-time memory effects and fat-tailed characteristics in the waiting time density. We analyze `generalized space-time fractional diffusion' in the infinite $\it d$-dimensional integer lattice $\it \mathbb{Z}^d$. We obtain in the diffusion limit a `macroscopic' space-time fractional diffusion equation. Classical CTRW models such as with Laskin's fractional Poisson process and standard Poisson process which occur as special cases are also analyzed. The developed generalized space-time fractional CTRW model contains a four-dimensional parameter space and offers therefore a great flexibility to describe real-world situations in complex systems.

In this study, the phase change materials (PCM) thermal energy storage system utilizing a novel webbed tube heat exchanger was designed and numerically investigated. The obtained simulation results were then compared with three types of conventional heat exchangers. These included: shell and tube heat exchanger, triplex tube heat exchanger and multi-tube heat exchanger. The proposed innovative webbed tube heat exchanger consisted of four horizontal inner heat transfer fluid tubes contained in a shell. The inner heat transfer fluid tubes were connected together by using metal plates welded to these tubes. The additional plates were designed to increase heat transfer surface area. Two-dimensional numerical models were developed. The process of melting (charging) was monitored during the simulation. The acceleration in melting process in the new design was observed owing to improved thermal conductivness.

The paper investigates the confined swirling flow in a cyclone. The numerical simulations are performed using a proposed eddy viscosity turbulence model, which accounts for the effects of the streamline curvature and rotation. This distinguishes the current model from the conventional Eddy Viscosity Models (EVMs) that are known to fail to predict the Rankine vortex in swirling flows. Although computationally more expensive approaches, the Reynolds Stress Model (RSM) and Large Eddy Simulation (LES), have demonstrated a high capability of dealing with such flows, these techniques are often unsuited for use in complex design studies where computational speed and robustness are key factors. In the present approach, the Shear Stress Transport with Curvature Correction (SSTCC) turbulence model is modified by the introduction of the Richardson number to account for the rotation and curvature effects. The numerical predictions were validated using experimental results and also compared to the data obtained using the RSM model and various EVMs without the proposed modifications. The investigations started with a benchmark case of a flow through a channel duct with a U-turn, after which more challenging simulations of a high swirling flow within a cyclone separator device were performed. The results show that the proposed model is competitive in terms of accuracy when compared to RSM and proves to be superior to the RSM model in terms of computational cost. Furthermore, it is found that the proposed model preserves the ability to represent the Rankine vortex profile at different longitudinal levels of the cyclone. It is also more efficient in terms of the computational cost than the SSTCC model without the introduced modifications.

Summary The distribution of atherosclerotic plaque burden in the human coronary arteries is not uniform. Plaques are located mostly in the left anterior descending artery (LAD), then in the right coronary artery (RCA), circumflex branch (LCx) and the left main coronary artery (LM) in a decreasing order of frequency. In the LAD and LCx, plaques tend to cluster within the proximal segment, while in the RCA their distribution is more uniform. Several factors have been involved in this phenomenon, particularly flow patterns in the left and right coronary artery. Nevertheless, it does not explain the difference in lesion frequency between the LAD and the LCx as these are both parts of the left coronary artery. Branching points are considered to be the risk points of atherosclerosis. In the LCx, the number of side branches is lower than in the LAD or RCA and there are no septal perforators with intramuscular courses like in the proximal third of the LAD and the posterior descending artery (PDA). We hypothesized that septal branches generate disturbed flow in the LAD and PDA in a similar fashion to the myocardial bridge (myocardial bridging effect). This coronary architecture determines the non-uniform plaque distribution in coronary arteries and LAD predisposition to plaque formation.

We analyze a random walk strategy on undirected regular networks involving power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a `simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks' with admissible interval $0 \alpha$ (recurrent for $d\leq\alpha$) of the lattice. As a consequence for $0, Comment: 28 pages, 5 figures. HAL Id : hal-01543330, version 1

A new mathematical model for non-equilibrium evaporation/condensation including boiling effect is proposed. A simplified differential-algebraic system of equations is obtained. A code to solve numerically this differential-algebraic system has been developed. It is designed to solve both systems of equations with and without the boiling effect. Numerical calculations of ammonia-water systems with various initial conditions, which correspond to evaporation and/or condensation of both components, have been performed. It is shown that, although the system evolves quickly towards a quasi equilibrium state, it is necessary to use a non-equilibrium evaporation model to calculate accurately the evaporation/condensation rates, and consequently all the other dependent variables., 20 pages, 6 figures

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow problems. The model, which accounts for pressure non-equilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include: weak to high planar shock waves with a Mach number ranging from $1.2$ to $3$ and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation., 41 pages, 21 figures

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamics determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions L\'evy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions. In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like L\'evy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks., Comment: 33 pages, 5 figures

In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of particle inertia and drift velocity. The different cases are characterised by different pairs of Stokes number $St$ and Froude number $Fr$. For the present study $0\leq St \leq 1$ and {$0.4 \leq Fr \leq 1.4$}. The main focus is to identify and then quantify the clustering attractor - when it exists - that is the set of points in the physical space where the particles settle when time goes to infinity. Depending on gravity effect and inertia values, the Lagrangian attractor can have different dimensions varying from the initial three-dimensional space to two-dimensional layers and one-dimensional attractors that can be shifted from a horizontal to a vertical position., Comment: 12 pages, 11 figures. arXiv admin note: text overlap with arXiv:1706.07284

We analyze the “fractional continuum limit” and its generalization to n dimensions of a self-similar discrete spring model which we introduced recently [21]. Application of Hamilton’s (variational) principle determines in rigorous manner a self-similar and as consequence non-local Laplacian operator. In the fractional continuum limit the discrete self-similar Laplacian takes the form of the fractional Laplacian\( - ( - \Delta )^{\tfrac{\alpha } {2}} \) with 0 n - 1 \) being always greater than n−1 characterizing a regular lattice with local interparticle interactions. Furthermore, we study in this setting anomalous diffusion generated by this Laplacian which is the source of Levi flights in n-dimensions. In the limit of “large scaled times” ∼ t/rα >> 1 we show that all distributions exhibit the same asymptotically algebraic decay ∼ t-n/α → 0 independent from the initial distribution and spatial position. This universal scaling depends only on the ratio n/α of the dimension n of the physical space and the Levi parameter α.

In this manuscript we present a multidisciplinary approach to prevention of cervical cancer (CC) in Poland. We summarized epidemiology of CC and precancerous lesions in the country. We present the current situation in secondary prevention (screening) of CC and propose changes to increase its effectiveness. Primary prevention of CC – the vaccines against human papillomavirus (HPV) – are currently one of the most effective ways of CC prevention. Solutions aimed at increasing access to primary prevention of CC are presented in this article. Reimbursement act provides an opportunity to partially reimburse HPV vaccines from public resources with patients’ co-payment which should increase access to primary prevention of CC. We emphasize the role of education and increasing the awareness of the problem, as a key element in realization of both primary and secondary prevention.

Three-dimensional laminar-separation bubbles on a cambered thin wing with an aspect ratio of 6 at a Reynolds number of 60,000 have been investigated by solving the Reynolds-averaged Navier–Stokes equations. The k-ω shear-stress transport γ-Reθ turbulence-transition model is used to account for the effect of transition on the laminar separation-bubble development. The aerodynamic forces are compared with the experimental data available for validation. The laminar-separation bubble is shown to evolve in its shape and dimension in both chord and span directions with increasing incidence due to its interaction with the wing-tip flow and the trailing-edge separation. The strongest three-dimensional effects are found at a moderate incidence of 6 deg and at higher incidences beyond 10 deg. Within the incidence range, the two-dimensional airfoil results are not reproduced at any of the span locations, including the symmetry plane, in the three-dimensional wing case. Generally, the chordwise development of the thr...

We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and infinite lattice in n=1,2,3,..n=1,2,3,.. dimensions. The present model which is based on Hamilton's variational principle is confined to conservative non-dissipative isolated systems. The present approach yields the discrete analogue of the continuous space fractional Laplacian kernel. As continuous fractional calculus generalizes differential operators such as the Laplacian to non-integer powers of Laplacian operators, the fractional lattice approach developed in this paper generalized difference operators such as second difference operators to their fractional (non-integer) powers. Whereas differential operators and difference operators constitute local operations, their fractional generalizations introduce nonlocal long-range features. This is true for discrete and continuous fractional operators. The nonlocality property of the lattice fractional Laplacian matrix allows to describe numerous anomalous transport phenomena such as anomalous fractional diffusion and random walks on lattices. We deduce explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractional derivative continuum limit kernels., arXiv admin note: text overlap with arXiv:1604.01725

International audience; We study the clustering of inertial particles using a periodic kinematic simulation. Particle clustering is observed for different pairs of Stokes number and Froude number and different spectral power laws (1.4≤p≤2.1). The main focus is to identify and then quantify the effect of p on the clustering attractor—by attractor we mean the set of points in the physical space where the particles settle when time tends to infinity. It is observed that spectral power laws can have a dramatic effect on the attractor shape. In particular, we observed an attractor type which was not present in previous studies for Kolmogorov spectra (p=5/3).

Hemodynamic forces play an important role in vascular pathology, particularly in relation to the localization of atherosclerotic lesions and plaque structure. Rapid advances in clinical imaging modalities and more sophisticated methods for assessment of blood flow in conjunction with the development of computational fluid dynamics (CFD) offers the possibility to predict and study flow in the vascular system. It is expected that image-based simulation of flow dynamics and progress in CFD technology may be an important and effective tool for biomechanical research on a new research field of atherosclerosis pathophysiology, risk stratification of plaque progression, prediction of in-stent neointimal hyperplasia and degeneration of bypasses. The paper presents basic data describing components of CFD processing and the emerging applications of CFD in cardiology in the example of pulsatile blood flow simulation in the left coronary artery. The plaque distribution and stability are discussed in relation to local wall shear stress.

The air core is an interesting and not well understood phenomenon that occurs in hydrocyclones and drastically affects the efficiency of separation. This study uses numerical code based on a three dimensional finite element solver which was designed specifically for hydrocyclones. A numerical examination of different flows at varying viscosities shows interesting results, which provides qualitative proof that the numerical code is predicting the general fluid flow in the hydrocyclone. The numerical results reveal that low viscosity feeds tend to develop a larger low pressure area in the center region of the cyclone than feeds at high viscosity. The comparison at different cross-section across the hydrocyclone at different viscosities act accordingly. The simulation results demonstrate pressure contours and are used to explain the initial stages of air core formation.

An investigation of decomposition of Trigonox 21S in Shellsol T has been carried out using the proposed algorithm. A series of calorimetry experiments were performed, where temperature and pressure of the system were monitored. The numerical code has been developed using an annealing optimisation algorithm to find chemical kinetics and the solubility of carbon dioxide in the reacting solutions. The overall decomposition reaction can be represented by a first-order reaction mechanism with a chemical reaction rate approximated by an Arrhenius type expression with a pre-exponential factor of 4.300 × 10 13 s −1 and an activation energy 1.227 × 10 5 J/mol with heat of reaction 1.904 × 10 5 J/mol. Sensitivity analysis has been performed as well. It has been shown that the system is the most sensitive to the value of activation energy and logarithm of the pre-exponential factor.

Swirl flow is the primary mechanism for separation of particles in a hydrocyclone and hence influences the performance. The study of examining the basic swirl flow mechanism is accomplished by using a cylindrical apparatus with rotating lids. The upper and lower lids of the cylinder are able to rotate in the counter and clockwise direction at different angular velocities. In this study, the basic mechanisms of swirling in the laminar regime are investigated using an optically clear cylinder with rotating lids. The cylinder is filled with a liquid and the upper and lower lids of the cylinder are allowed to rotate in the clockwise and counter-clockwise directions. The induced flow is measured with a laser doppler anemometer and is compared to the velocity predictions from an in house developed software which solves the equations of motion. The results presented here constitute the first step in a series of experiments with the ultimate goal to improve the separation mechanism of hydrocyclones by means of controlling swirling flow characteristics.

Coronary artery atherosclerosis presents characteristic patterns of plaque distribution despite systemic exposure to risk factors. We hypothesized that local hemodynamic forces induced by the systolic compression of intramuscular septal perforators could be involved in atherosclerotic processes in the left anterior descending artery (LAD) adjacent to the septal perforators' origin. Therefore we studied the spatial distribution of atherosclerosis in coronary arteries, especially in relation to the septal perforators' origin.64-slice computed tomography angiography was performed in 309 consecutive patients (92 male and 217 female) with a mean age of 59.9 years. Spatial plaque distribution in the LAD was analyzed in relation to the septal perforators' origin. Additionally, plaque distribution throughout the coronary artery tree is discussed.The coronary calcium score (CCS) was positive in 164 patients (53.1%). In subjects with a CCS0, calcifications were more frequent in the LAD (n = 150, 91.5%) compared with the right coronary artery (RCA) (n = 94, 57.3%), circumflex branch (CX) (n = 76, 46.3%) or the left main stem (n = 42, 25.6%) (p0.001). Total CCS was higher in the LAD at 46.1 (IQR: 104.2) and RCA at 34.1 (IQR: 90.7) than in the CX at 16.8 (IQR: 61.3) (p = 0.007). In patients with calcifications restricted to a single vessel (n = 54), the most frequently affected artery was the LAD (n = 42, 77.8%). In patients with lesions limited to the LAD, the plaque was located mostly (n = 37, 88.1%) adjacent to the septal perforators' origin.We demonstrated that coronary calcifications are most frequently located in the LAD in proximity to the septal branch origin. A possible explanation for this phenomenon could be the dynamic compression of the tunneled septal branches, which may result in disturbed blood flow in the adjacent LAD segment (milking effect).Miażdżyca tętnic wieńcowych objawia się charakterystycznym wzorem dystrybucji blaszki miażdżycowej pomimo ogólnoustrojowego narażenia na czynniki ryzyka. Autorzy przedstawiają hipotezę, że miejscowe siły hemodynamiczne wywołane przez skurczowy ucisk wewnątrzmięśniowych perforatorów przegrody mogą mieć udział w procesach miażdżycowych w gałęzi międzykomorowej przedniej lewej tętnicy wieńcowej (Badanie angiograficzne za pomocą 64-rzędowej tomografii komputerowej przeprowadzono u 309 kolejnych pacjentów (92 mężczyzn i 217 kobiet), średnia wieku 59,9 roku. Przestrzenną dystrybucję blaszki w gałęzi LAD przeanalizowano w odniesieniu do miejsca odejścia gałęzi przegrodowych. Omówiono dystrybucję blaszki w całym układzie tętnic wieńcowych.Dodatni wynik wskaźnika uwapnienia tętnic wieńcowych (Zwapnienia wieńcowe występują najczęściej w gałęzi międzykomorowej przedniej LAD w pobliżu odejścia gałęzi przegrodowej. Wyjaśnieniem tego zjawiska może być dynamiczny ucisk wewnątrzmięśniowych tętnic przegrodowych, który może powodować zaburzenia przepływu w sąsiadującym segmencie gałęzi LAD.

The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length.We obtain explicit expressions for this fractional Laplacianmatrix and deduce also its periodic continuum limit kernel. The continuum limit kernel gives an exact expression for the fractional Laplacian (Riesz fractional derivative) on the finite periodic string.In this approach we introduce two material parameters, the particle mass $\mu$ anda frequency $\Omega\_{\alpha}$. The requirement of finiteness of the the total mass and total elastic energy in the continuum limit (lattice constant $h\rightarrow 0$) leads to scaling relations for the two parameters, namely$\mu \sim h$ and $\Omega\_{\alpha}^2\sim h^{-\alpha}$.The present approach can be generalized to define lattice fractional calculus on periodic lattices in full analogy to the usual `continuous' fractional calculus., Comment: arXiv admin note: text overlap with arXiv:1412.5904

Many empirical models have been used widely for designing hydrocyclones in industry. These empirical models consist of a set of design equations. Most of the design equations are based on the correlations obtained experimentally, using dimensionless similarity numbers. These equations have their limitations due to the specific systems used for model development. Therefore, in many cases, they cannot be used with confidence to predict the design of an individual separator, or the overall plant configuration that is required to meet different user requirements. A modified version of the existing design equations presented by previous researchers was developed. The design equations, describing four fundamental parameters: pressure drop, flow recovery to underflow, corrected cut size and classification function, were modified by fitting with set of experimental data to obtain the system-specific constant parameters. These modified design equations were then called, the fine-tuned design equations. Four sets of fine-tuned design equations describing all the fundamental parameters were constructed and used to predict the separation performance of many hydrocyclone operational systems at the Dow Chemical Company, Texas, USA. The performance of these equations is evaluated, and the limitations of their use are discussed, thus providing useful insights into hydrocyclone design.

Three-dimensional simulations of incompressible fluid flow within hydrocyclone have been performed using the developed numerical technique. A discretization of the physical problem has been done by using a finite element method based on mixed approximation of the velocity and pressure space. The approach offers significant advantages in the solution process of convection dominated internal flows having one inlet and more than one outlet. It deals with the complex geometry of the head entry part of hydrocyclone. The boundary conditions represent forces and are efficiently incorporated into the numerical formulation. Such formulation is very useful since it allows modeling the characteristic velocity profile in the outlet. We investigate the interaction between the swirling flow and velocity profile at the outlet. The studies are carried out for fluids with different properties and can be extended to hydrocyclones with different geometrical configurations.

The effect of the particle–fluid and particle–particle interactions of the flow within a hydrocyclone is investigated. These were studied by applying the time scale analysis. It is shown that the particle–particle interactions, due to the lubrication and collision mechanisms, only play an important role in the vicinity of a hydrocyclone wall, and near the air core. In the remaining region, particle–fluid interactions are dominating. These play a vital role on the separation efficiency as illustrated by the significance of the wakes generated behind larger particles on dragging finer particles.

This paper presents a laboratory feasibility study aiming at the development of a dual modality sensor for development within an oil and gas extraction plant to measure the composition of heterogeneous mixtures. The technology of manufacturing the sensor is briefly described and the preliminary measurements, conducted for mixtures of vegetable oil and saline water, using two modalities: ultrasound and electrical, are presented. The experimental results obtained from ultrasonic measurements are compared with theoretical predictions. Finally, conclusions and recommendations for future work are presented.

This paper introduces a mathematical model to analyze the dynamic behavior of a novel rotary vane engine (RVE). The RVE can be considered to have a number of advantages when compared to a majority of other reciprocating engine types. The advantages are found in the simple structure and the small number of moving parts. In this paper the geometrical structure and dynamical behavior of engines with a different number of work units is considered in detail. This has been examined through a study of torque transmission with a particular reference to how this is affected by the noncircular geometry of gear pitch curves. Using the Coulomb friction model, consideration has been given to the mechanical power loss due to friction in different parts of the engine, which must be taken into account. The study also proposes a possible method for balancing of asymmetric cogwheels. The analysis concludes that by using an appropriate design and arrangement of cogwheels and all moving parts, vibration can be attenuated due to impulsive gas torque.

The search continues for accurate and efficient 3D computational fluid dynamics algorithms for hydrocyclone flows. A review of recent work and new developments are presented. This contribution is based on the authors' past experience both in creating their own specialized numerical approaches and using commercial packages for simulating swirling flow. In particular, the paper presents the application of the developed 3D finite element code to hydrocyclone modelling. Some important factors in the numerical solution of the model equations, namely proper representation of geometry, imposition of boundary conditions and the choice of turbulence model, are discussed. Numerical results indicate the versatility and the effectiveness of the new approaches. A scheme that utilizes numerical results in the multi-objective design is also suggested. Remaining technical difficulties are highlighted in order to suggest key directions for future work.

Three-dimensional simulations of incompressible fluid flow within hydrocyclones have been performed using the developed numerical technique. The computational approach, based on the finite element method, has the capability to deal with the complex geometry of the head entry part of the hydrocyclone. The boundary conditions represent forces and are efficiently incorporated into the numerical formulation. Such formulation has not been used before for hydrocyclone simulation. Three different swirling angles were investigated and the simulations were carried out for fluids with different properties. The numerical results clearly indicate the presence of an asymmetrical flow not only close to the entrance region, but also in the conical part of hydrocyclone. The different methods for modelling the particle distribution are also discussed.

International audience; The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finite number $N$ of identical particles is introduced. We suggest a ''fractional elastic harmonic potential", and obtain the $N$-periodic fractional Laplacian operator in the form of a power law matrix function for the finite chain ($N$ arbitrary not necessarily large) in explicit form. In the limiting case $N\rightarrow \infty$ this fractional Laplacian matrix recovers the fractional Laplacian matrix of the infinite chain.The lattice model contains two free material constants, the particle mass $\mu$ and a frequency $\Omega_{\alpha}$.The ''periodic string continuum limit" of the fractional lattice model is analyzed where lattice constant $h\rightarrow 0$ and length $L=Nh$ of the chain (''string") is kept finite: Assuming finiteness of the total mass and total elastic energy of the chain in the continuum limit leads to asymptotic scaling behavior for $h\rightarrow 0$ of the two material constants, namely $\mu \sim h$ and $\Omega_{\alpha}^2 \sim h^{-\alpha}$. In this way we obtain the $L$-periodic fractional Laplacian (Riesz fractional derivative) kernel in explicit form. This $L$-periodic fractional Laplacian kernel recovers for $L\rightarrow\infty$ the well known 1D infinite space fractional Laplacian (Riesz fractional derivative) kernel. When the scaling exponent of the Laplacian takes integers, the fractional Laplacian kernel recovers, respectively, $L$-periodic and infinite space (localized) distributional representations of integer-order Laplacians.The results of this paper appear to be useful for the analysis of fractional finite domain problems for instance in anomalous diffusion (Levy flights), fractional Quantum Mechanics, and the development of fractional discrete calculus on finite lattices.

The concept and principles of applying a multi-continuum model for calculating a hydrocyclone performance is presented. In this model the carrying liquid is described as one continuum, and each particle fraction, with its characteristic size is described as a separate continuum. Particle–particle and particle–fluid interactions derived from a lubrication theory and a collision theory are discussed. A set of governing partial differential equations consisting of mass and momentum conservation equations together with constitutive expressions is discussed. These equations were discretized by applying an unstructured grid consisting of tetrahedral elements. A numerical solver based on a finite element method combined with a segregated approach is described. The numerical approach is subject to ongoing research.

In the paper we present an effective method to compute forces in external flows of viscous incompressible fluids. It is an extension of the variational approach proposed initially by Quartapelle and Napolitano (1983, AIAA J. 21, 911) and is particularly well adapted to the case where a vortex method is used to solve the hydrodynamic problem. The derived formula involves a harmonic function ? and a convenient method for its determination is also shown. The effectiveness of the presented approach is confirmed by computational examples.

Numerical simulation of compressible two-component flows that consider different materials and physical properties is conducted. An explicit finite volume numerical framework based on an extended second order Godunov approach is developed and implemented to solve an Eulerian type mathematical model. This model consists of five partial differential equations in one space dimension and it is known as the transport reduced model. A fixed Eulerian mesh is considered and the hyperbolic problem is tackled using a robust and efficient HLL Riemann solver. The performance of the numerical solver is verified against a comprehensive suite of numerical and experimental case studies in multi-dimensional space. Computing the evolution of interfaces between two immiscible fluids is considered as a major challenge for the present model and the numerical technique. The achieved numerical results demonstrate a very good agreement with all reference data.

The paper deals with the problem of recovering pressure from the given vorticity and velocity fields. Both fields result from the stochastic vortex-blob simulation of the viscous incompressible flow. The vorticity field is a discontinuous function. The method is presented here to find pressure as a solution to the variational problem which forms the weak version of the momentum equation. No explicit boundary condition for pressure are required and no derivatives of vorticity have to be calculated in this approach.

The simulation of multiphase compressible flows through high pressure nozzles is presented. The study uses the developed numerical approach. There are many important engineering applications which are concerned with multiphase flows and convergent-divergent nozzles. This work presents the developed extension of the model and numerical algorithm based on the so called parent model earlier introduced by Saurel and Abgrall [Saurel, R. and Abgrall, R., A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys. 150 (1999), 425–467]. This model which consists of conservation laws for each phase complemented with the volume fraction evolution equation is modified by adding a source term to simulate area variation. The model is strictly hyperbolic and non-conservative due to the existence of non-conservative terms. The model is able to deal with compressible and incompressible flows. Moreover, it can deal with mixtures and pure fluids, where each fluid has its own pressure and velocity. The presence of velocity and pressure relaxation terms in the governing equations has made the velocity and pressure relaxation processes essential to tackle the boundary conditions at the interface. The interface separating phases is considered as a numerical diffusion zone in this method. The model is solved using an efficient Eulerian numerical method. A second order Godunov-type scheme with approximate Riemann solver is used to enable capturing of a physical interface by the resolution of the Riemann problem. The solution is obtained by splitting the hyperbolic part and source terms parts in the numerical algorithm. The source terms, including relaxation parts of the model, are tackled in succession using Strang splitting technique. The governing equations are solved at each computational cell using the same numerical algorithm for the whole domain including the interface. The main aim of this work has been to study different flow regimes with respect to pressure boundary conditions through the numerical solutions of single and multiphase flows. The performance of the programme has been verified via well established benchmark test problems for multiphase flows.Copyright © 2012 by ASME

In this article we study the return to axi-symmetry for a flow generated after fractal plates in a circular wind tunnel. We consider two sets of plates: one orifice-like and one perforated-like. The mean velocity profiles are presented at different distances from the plate and we study the convergence of a flow rate based on these profiles. The return to axi-symmetry depends on how far was the original plate from an axi-symmetric design. It also depends on the level of iteration of the fractal pattern. In line with results for other flow properties [1, 2] It seems that there is not much to be gained by manufacturing fractal plates with more than three iteration levels.

A numerical scheme for computing compressible multi-component flows is examined. The numerical approach is based on a mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high-resolution HLLC scheme on a fixed Eulerian mesh. The scheme for the non-conservative terms is derived to fulfill the interface condition. The results are demonstrated for several one and two-dimensional test cases.

We analyse some fundamental problems of linear elasticity in one-dimensional (1D) continua where the material points of the medium interact in a self-similar manner. This continuum with ‘self-similar’ elastic properties is obtained as the continuum limit of a linear chain with self-similar harmonic interactions (harmonic springs) which was introduced in [19] and (Michelitsch T.M. (2011) The self-similar field and its application to a diffusion problem. J. Phys. A Math. Theor.44, 465206). We deduce a continuous field approach where the self-similar elasticity is reflected by self-similar Laplacian-generating equations of motion which are spatially non-local convolutions with power-function kernels (fractional integrals). We obtain closed-form expressions for the static displacement Green's function due to a unit δ-force. In the dynamic framework we derive the solution of the Cauchy problem and the retarded Green's function. We deduce the distributions of a self-similar variant of diffusion problem with Lévi-stable distributions as solutions with infinite mean fluctuations. In both dynamic cases we obtain a hierarchy of solutions for the self-similar Poisson's equation, which we call ‘self-similar potentials’. These non-local singular potentials are in a sense self-similar analogues to Newtonian potentials and to the 1D Dirac's δ-function. The approach can be a point of departure for a theory of self-similar elasticity in 2D and 3D and for other field theories (e.g. in electrodynamics) of systems with scale invariant interactions.

The turbulence energy spectrum is a significant input parameter of KS modeling. In parallel to KS, fractal approaches have been developed in fluid mechanics (often by the same team of researchers doing KS) either experimentally or numerically to interfere with spectral law. We add another direction of research to this interesting problem by looking at what analytical mechanics can teach us about the vibration spectrum of a self similar chain hoping that one day that knowledge will help our understanding of spectral laws and fractal forcing in fluid mechanics. We consider some general aspects of the construction of self-similar functions and linear operators and deduce a self-similar variant of the Laplacian operator and of the d’Alembertian wave operator. The derived self-similar wave operator describes the dynamics of a quasi-continuous linear chain of infinite length with a spatially self-similar distribution of nonlocal inter-particle springs. The self-similarity of the nonlocal harmonic particle-particle interactions results in a dispersion relation of the form of a Weierstrass-Mandelbrot function which exhibits self-similar and fractal features. We also show that the self-similar wave equation in a certain approximation corresponds to (nonlocal) fractional derivatives.

The impact of Kinematic Simulations on quantum turbulence theory, by Demosthenes Kivotides.- 1 Introduction.- 2 Mathematical model 3 Results.- 4 Conclusion.- References.- Detached Eddy Simulation for turbulent flows in a pipe with a snowflake fractal orifice, by H. W. Zheng, F. C. G. A. Nicolleau and N. Qin.- 1 Introduction - motivation.- 2 Governing equations 3 Numerical discretization.- 4 Results.- 5 Conclusions.- References.- KS input spectrum, some fundamental works on the vibration spectrum of a self-similar linear chain, by T. M. Michelitsch, F. C. G. A. Nicolleau, A. F. Nowakowski and S. Derogar.- 1 Introduction 1.1 Input spectrum in the Kinematic simulation technique.- 1.2 Richardson's locality-in-scale hypothesis.- 2 Experimental studies of fractal generated turbulence.- 3 Fundamental modelling 4 Spectral Graphs for self-similar linear chains.- 5 Construction of self-similar functions and linear operators.- 5.1 Construction of self-similar functions.- 5.2 A self-similar analogue to the Laplace operator.- 5.3 Continuum approximation - link to fractional integrals.- 6 The physical chain model.- 7 Conclusions.- References.- Can Kinematic Simulation predict Richardson's regime? , by F. C. G. A. Nicolleau and A. Abou El-Azm Aly.- 1 Introduction.- 1.1 The two-particle dispersion problem.- 1.2 Observation of the Richardson law.- 2 Kinematic simulation.- 2.1 Kinematic simulation technique.- 2.2 Kinematic Simulation's predictions of Richardson's law.- 2.3 The KS method for isotropic turbulence.- 2.4 The Eulerian field time dependence.- 3 KS and Richardson Regime Validation.- 3.1 Particle pair diffusivity.- 3.2 Sensitivity to the energy spectrum power law.- 3.3 Effect of varying the unsteadiness parameter on the Validity of Richardson Regime.- 4 Conclusion.- References.- Incorporating linear dynamics and strong anisotropy in KS. Application to diffusion in rotating, stratified, MHD turbulence, and to aeroacoustics, by C. Cambon, F. S. Godeferd and B. Favier.- 1 KS for homogeneous isotropic turbulence. What remains to be done ?.- 1.1 Is the randomization process optimal?.- 1.2 Are the temporal random frequencies really random variables ?.- 2 Incorporating linear dynamics in KS. Application to rotatin and/or stratified flows.- 2.1 Analogy with the Rapid Distortion Theory.- 2.2 The role of inertial waves.- 2.3 Stable stratification with or without rotation.- 3 The linear dynamics of MHD turbulence.- 3.1 Basic equations.- coexistence of waves with anisotropic ohmic dissipation.- 3.2 Preliminary MHD results with and without rotation.- 4 Accounting for strong anisotropy.- 4.1 Anisotropy created by linear mechanisms from isotropic initial data.- 4.2 Anisotropic initialization, link to 'structures'.- 4.3 Some applications.- 5 Application to aeroacoustics in turbulence with and without rotation.- 5.1 Isotropic turbulence.- 5.2 Rotating turbulence.- 6 Conclusions and perspectives.- Appendices.- References.- Advances in Particle Representation Modeling of homogeneous turbulence. From the linear PRM version to the interacting viscoelastic IPRM , by S.C. Kassinos and E. Akylas.- 1 Introduction.- 2 The RDT formulation.- 3 The Structure Tensors.- 4 Particle Representation of the RDT of Homogeneous Turbulence.- 4.1 Particle Properties.- 4.2 Vector Identities of the Particle Properties.- 4.3 Evolution Equations of the Particle Properties.- 4.4 Representation of the One Point Statistics.- 5 The Interacting Particle Representation Model.- 5.1 Formulation of the IPRM.- 5.2 Evaluation of the IPRM.- 6 Summary and Conclusions.- References.- Oscillation-free Adaptive Simulation of Compressible Two-fluid Flows with Different Types of Equation of State, by H. W. Zheng, C. Shu, Y. T. Chew, and N. Qin.- 1 Introduction.- 2 Compressible Two-fluid Flows.- 2.1 Modelling with general form of equation of state.- 2.2 Oscillation-free analysis.- 3 Discretization on quadrilateral-cell based adaptive mesh.- 4 Results.- 4.1 Interface translation problem.- 4.2 Bubble-shock interaction.- 5 Conclusions.- References.- Computing the evolution of interfaces using multi-component flow equations, by Fatma Ghangir and Andrzej F. Nowakowski.- 1 Introduction.- 2 The parent flow model.- 3 The hyperbolic 2D model and its primitive variable form.- 4 Numerical Solution.- 4.1 The discretization of hyperbolic system with non-conservative terms.- 4.2 Velocity and pressure relaxation.- 5 The numerical results.- 5.1 Test problems for one-dimensional compressible multiphase flows.- 5.2 Test Problems For 2D Compressible Multiphase Flows.- 5.3 Interface test.- 5.4 Bubble explosion under water test.- 6 Conclusion.- References.- The effect of turbulence on the spreading of infectious airborne droplets in hospitals , by C.A. Klettner, I. Eames and J.W. Tang.- 1 Introduction.- 2 Mathematical model.- 2.1 Synthetic model of turbulence.- 2.2 Equation of motion of an evaporating droplet.- 2.3 Diagnostics.- 3 Numerical results.- 4 Conclusion.- 5 Acknowledgments.- References.

The laminar and turbulent flow in an enclosed chamber with a centrally placed obstacle was studied numerically using unsteady solution of Navier–Stokes equations. The flow behaviour was investigated over a wide range of geometrical parameters and Reynolds numbers up to 4000. The study included various geometrical shapes of the obstacle and the effects of nozzle aspect ratio. The computations were performed using the Detached Eddy Simulation (DES) approach for unsteady flows. The numerical technique allowed predicting three dimensional flow structures, which were validated using experimental studies conducted earlier. The regular features of the observed flows enabled signal analysis of the obtained numerical results. The considered geometric configurations could be used for flow metering purposes with a number of factors such as a chamber geometry and obstacle aspect ratio influencing the range of applications and performance of such a flowmeter. A minimum Reynolds number constraint for the measurements to be accurate was evaluated for the selections of design parameters. The significance of using design modifications such as additional knife edges in the chamber design can be demonstrated when observing their influence on boundary layer separation.

In this paper we investigate kinematic simulation (KS) consistency with the theory of Richardson [Proc. Roy. Soc. A 110, 24 (1926)] for two-particle diffusivity. In particular we revisit the sweeping problem. It has been argued by Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).] that due to the lack of sweeping of small scales by large scales in kinematic simulation, the validity of Richardson's power law might be affected. Here, we argue that the discrepancies between authors on the ability of kinematic simulation to predict Richardson power law may be linked to the inertial subrange they have used. For small inertial subranges, KS is efficient and the significance of the sweeping can be ignored, as a result we limit the KS agreement with the Richardson scaling law t(3) for inertial subranges k(N0/k(1)≤10000. For larger inertial range KS does not fully follow the t(3) law. Unfortunately, there is no experimental data to compare KS with and draw conclusions for such large inertial subranges. It cannot be concluded either that the discrepancy between KS and Richardson's theory for larger inertial subranges is exactly taken into account by the theory developed in Thomson and Devenish [J. Fluid Mech. 526, 277 (2005).].

Many systems in nature have arborescent and bifurcated structures such as trees, fern, snails, lungs, the blood vessel system, but also porous materials etc. look self-similar over a wide range of scales. Which are the mechanical and dynamic properties that evolution has optimized by choosing self-similarity so often as an inherent material symmetry? How can we describe the mechanics of self-similar structures in the static and dynamic framework? In order to analyze such material systems we construct self-similar functions and linear operators such as a self-similar variant of the Laplacian and of the D’Alembertian wave operator. The obtained self-similar linear wave equation describes the dynamics of a quasi-continuous linear chain of infinite length with a spatially self-similar distribution of nonlocal inter-particle springs. The dispersion relation of this system is obtained by the negative eigenvalues of the self-similar Laplacian and has the form of a Weierstrass-Mandelbrot function which exhibits self-similar and fractal features. We deduce a continuum approximation that links the self-similar Laplacian to fractional integrals which also yields in the low-frequency regime a power law scaling for the oscillator density with strictly positive exponent leading to a vanishing oscillator density at frequency zero. We suggest that this power law scaling is a characteristic and universal feature of self-similar systems with complexity well beyond of our present model. For more details we refer to our recent paper [7].

The hyperbolic Eularian model is used as a mathematical framework for compressible multiphase flows. The formulation was obtained after an averaging process of the single phase Navier-Stokes equations. The closure of multi-component system leads to the volume fraction equation containing a non-conservative term and a pressure equilibrium condition. As a result the model equations cannot be written in a conservative form. To solve the equations a finite volume Godunov type computational approach is developed which uses an approximate Riemann solver combined with a numerical scheme to tackle the non-conservative terms. The approach accounts for pressure non-equilibrium. It enables resolving interfaces separating compressible fluids and captures the baroclinic source of vorticity generation. The computations are performed for various initial conditions and compared with theoretical and experimental data for a shock-bubble interaction problem. The investigated cases include acoustic wave transmission through isolated bubbles of helium and krypton. The numerical results illustrate the characteristic features of the evolving interfaces. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock and by the vorticity generation within the media. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)