A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Phase relaxation model for 2-phase flows

A phase relaxation model (PRM) for 2-phase flows is presented in this paper on the basis of three principal assumptions. The basic equations for PRM arc derived from the Boltzmann equations for gas-partlcle mixture, The general characteristics and solving process of the PRM's basic equations are also presented and discussed. Many terms in the PRM's basic equations contain a factor ε= ρgρp/ρg+ρp2 which is an intrinsic small parameter for 2-phase mixture, with ρg and ρp being respectively the densities of gas and particle phases.This makes it possible to simplify the computation of the PRM's basic equations. The model is applied to for example, studying file steady propagation of shock waves in gas-particle mixture. The analysis shows that with an increase of shock wave strength the relaxation process behind a gasdynamics shock front becomes a kind of dynamics relaxation instead of the standard exponential relaxation process. A method of determining experimentally the velocity and tem...更多perature relaxation rates (or times) of gas-particle flows is suggested and analyzed.

Characterising noise signals in 2-phase solid gas flows

Pneumatic conveying of powder and granular material involve the mixed flow of solid particles in air. Characterisation of solid/gas flow regimes is important for the design, operation and control of plants involving such two-phase processes. This paper describes preliminary studies directed at identifying flow regimes in solid/gas flows by analysis of the process `noise' signals from a flow transmitter which has a relatively wide frequency response.

The kinetic-theory for dilute solid liquid 2-phase flow

On the basis of a brief review of the continuum theory for macroscopic descriptions and the kinetic theory for microscopic descriptions in solid/liquid two-phase flows, some suggestions are presented, i.e. the solid phase may be described by the Boltzmann equation and the liquid phase still be described by conservation laws in the continuum theory. Among them the action force on the particles by the liquid fluid is a coupling factor which connects the phases. For dilute steady solid/liquid two-phase flows, the particle velocity distribution function can be derived by analogy with the procedures in the kinetic theory of gas molecules for the equilibrium state instead of being assumed, as previous investigators did. This done, more detailed information, such as the velocity probability density distribution, mean velocity distribution and fluctuating intensity etc. can be obtained directly from the particle velocity distribution function or from its integration. Experiments have been performed for dilute solid/liquid two-phase flow in a 4 x 6 cm2 sized circulating square pipe system by means of laser Doppler anemometry so that the theories can be examined. The comparisons show that the theories agree very well with all the measured data.

A marker-and-cell approach to free surface 2-D multiphase flows

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

CFD modeling of two-phase boiling flows in the slug flow regime with an interface capturing technique

The objective of this thesis was to improve the commercial CFD software Ansys Fluent to obtain a tool able to perform accurate simulations of flow boiling in the slug flow regime. The achievement of a reliable numerical framework allows a better understanding of the bubble and flow dynamics induced by the evaporation and makes possible the prediction of the wall heat transfer trends. In order to save computational time, the flow is modeled with an axisymmetrical formulation. Vapor and liquid phases are treated as incompressible and in laminar flow. By means of a single fluid approach, the flow equations are written as for a single phase flow, but discontinuities at the interface and interfacial effects need to be accounted for and discretized properly. Ansys Fluent provides a Volume Of Fluid technique to advect the interface and to map the discontinuous fluid properties throughout the flow domain. The interfacial effects are dominant in the boiling slug flow and the accuracy of their estimation is fundamental for the reliability of the solver. Self-implemented functions, developed ad-hoc, are introduced within the numerical code to compute the surface tension force and the rates of mass and energy exchange at the interface related to the evaporation. Several validation benchmarks assess the better performances of the improved software. Various adiabatic configurations are simulated in order to test the capability of the numerical framework in modeling actual flows and the comparison with experimental results is very positive. The simulation of a single evaporating bubble underlines the dominant effect on the global heat transfer rate of the local transient heat convection in the liquid after the bubble transit. The simulation of multiple evaporating bubbles flowing in sequence shows that their mutual influence can strongly enhance the heat transfer coefficient, up to twice the single phase flow value.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.

Integrated analysis of CANVAS 1 and 2: phase 3, multicenter, randomized, double-blind studies to evaluate the safety and efficacy of ceftaroline versus vancomycin plus aztreonam in complicated skin and skin-structure infection.

BACKGROUND: Methicillin-resistant Staphylococcus aureus (MRSA) is a common cause of complicated skin and skin-structure infection (cSSSI). Increasing antimicrobial resistance in cSSSI has led to a need for new safe and effective therapies. Ceftaroline was evaluated as treatment for cSSSI in 2 identical phase 3 clinical trials, the pooled analysis of which is presented here. The primary objective of each trial was to determine the noninferiority of the clinical cure rate achieved with ceftaroline monotherapy, compared with that achieved with vancomycin plus aztreonam combination therapy, in the clinically evaluable (CE) and modified intent-to-treat (MITT) patient populations. METHODS: Adult patients with cSSSI requiring intravenous therapy received ceftaroline (600 mg every 12 h) or vancomycin plus aztreonam (1 g each every 12 h) for 5-14 days. RESULTS: Of 1378 patients enrolled in both trials, 693 received ceftaroline and 685 received vancomycin plus aztreonam. Baseline characteristics of the treatment groups were comparable. Clinical cure rates were similar for ceftaroline and vancomycin plus aztreonam in the CE (91.6% vs 92.7%) and MITT (85.9% vs 85.5%) populations, respectively, as well as in patients infected with MRSA (93.4% vs 94.3%). The rates of adverse events, discontinuations because of an adverse event, serious adverse events, and death also were similar between treatment groups. CONCLUSIONS: Ceftaroline achieved high clinical cure rates, was efficacious against cSSSI caused by MRSA and other common cSSSI pathogens, and was well tolerated, with a safety profile consistent with the cephalosporin class. Ceftaroline has the potential to provide a monotherapy alternative for the treatment of cSSSI. TRIAL REGISTRATION: ClinicalTrials.gov identifiers: NCT00424190 for CANVAS 1 and NCT00423657 for CANVAS 2.

Ab initio calculation of the BCC Fe-Al-Mo (Iron-Aluminum-Molybdenum) phase diagram: Implications for the nature of the tau(2) phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe-Al-Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order-disorder equilibrium between Fe(3)Al-D0(3) and FeAl-B2 is increased by Mo additions, while the critical temperature for the FeAl-B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2-(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the tau(2) phase, stable at high temperatures in overstoichiometric B2-FeAl. (C) 2009 Elsevier Ltd. All rights reserved.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).