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Basic Equations (basic + equation)
Selected AbstractsBasic equations of mass transfer through biocatalytic membrane layerASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2009Endre Nagy Abstract The diffusive and convective mass transport through biocatalytic membrane layer (membrane bioreactor), without and with biochemical reactions, have been investigated. Similarly to the two-film theory for gas-liquid system with diffusive mass transport, only, mass transfer rates have been developed for the biocatalytic membrane layer and for the concentration boundary layer on the feed side of the membrane. Overall mass transfer coefficient has also been defined involving the two-layer, simultaneous mass transfer, namely the mass transfer through the concentration boundary layer and biocatalytic membrane layer. The effect of the convective velocity (Pe number) and the biochemical reaction rate, namely first-order and zero-order reactions as limiting cases of the Monod kinetics, are demonstrated on the mass transfer coefficients accompanied by chemical reaction and on the concentration profiles. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Plasma Edge Physics with B2-EireneCONTRIBUTIONS TO PLASMA PHYSICS, Issue 1-2 2006R. Schneider Abstract The B2-Eirene code package was developed to give better insight into the physics in the scrape-off layer (SOL), which is defined as the region of open field-lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma-wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape-off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices. The paper presents the basic equations for the plasma transport and the basic models for the neutral transport. This defines the basic ingredients for the SOLPS (Scrape-Off Layer Plasma Simulator) code package. A first level of understanding is approached for pure hydrogenic plasmas based both on simple models and simulations with B2-Eirene neglecting drifts and currents. The influence of neutral transport on the different operation regimes is here the main topic. This will finish with time-dependent phenomena for the pure plasma, so-called Edge Localised Modes (ELMs). Then, the influence of impurities on the SOL plasma is discussed. For the understanding of impurity physics in the SOL one needs a rather complex combination of different aspects. The impurity production process has to be understood, then the effects of impurities in terms of radiation losses have to be included and finally impurity transport is necessary. This will be introduced with rising complexity starting with simple estimates, analysing then the detailed parallel force balance and the flow pattern of impurities. Using this, impurity compression and radiation instabilities will be studied. This part ends, combining all the elements introduced before, with specific, detailed results from different machines. Then, the effect of drifts and currents is introduced and their consequences presented. Finally, some work on deriving scaling laws for the anomalous turbulent transport based on automatic edge transport code fitting procedures will be described. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009A. Zolochevsky Abstract A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under plane stress conditions. The variational approach of establishing the basic equations of the plane stress problem under consideration has been introduced. For the solution of two-dimensional creep problems, the fourth-order Runge,Kutta,Merson's method of time integration, combined with the Ritz method and R-functions theory, has been used. Numerical solutions to various problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension,compression asymmetry on the stress,strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd. [source] A CBS-type stabilizing algorithm for the consolidation of saturated porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005V. A. Salomoni Abstract The presented method stems from the works by Zienkiewicz and co-workers for coupled fluid/thermal problems starting from the early 1990s. They propose algorithms to overcome the difficulties connected to the application of the FEM to the area of fluid mechanics, which include the problems of singular behaviour in incompressibility and the problems connected to convective terms. The major step forward was to introduce the concept of characteristic lines (the particle paths in a simple convection situation): for a class of problems with a single scalar variable, the equations in the characteristic co-ordinates regain self-adjointness. The procedure is called characteristic based split algorithm (CBS). We use here a CBS-type procedure for a saturated deformable elastic porous medium, in which the fluid velocity is governed by Darcy's equation (which comes directly from Navier,Stokes ones). The physical,mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains. The power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual ,u,p' problem into a ,u,v,p' one, where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid, respectively. Attention is focused on the expression of Darcy's velocity which is considered as the starting point of the algorithm. The accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u,p solutions. A good fitting among different results has been obtained. It is further shown that the procedure eliminates the oscillations at the onset of consolidation, typical for many schemes. The FEM code Ed-Multifield has been used for implementing and testing the procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical and analytical calculations of the temperature and flow field in the upwind power plantINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 6 2004Henry Pastohr Abstract The upwind power plant is an interesting system to generate electrical power from free solar energy. The authors have carried out an analysis to improve the description of the operation mode and efficiency. The pressure drop at the turbine and the mass flow rate have a decisive influence on the efficiency. This can be determined only by coupling of all parts of an upwind power plant. In this study the parts ground, collector, chimney and turbine are modelled together numerically. The basis for all sections is the numerical CFD programme FLUENT. This programme solves the basic equations of the thermal fluid dynamics. Model development and parameter studies particularly arise with this tool. Additional to the calculations using FLUENT a simple model is developed for comparison purposes and parameter studies. The numerical results with FLUENT compare well with the results given by the simple model, therefore, we can use the simple model for parameter studies. The basis for the geometry is the prototype Manzanares. Copyright © 2004 John Wiley & Sons, Ltd. [source] On linear electromagnetic constitutive laws that define almost-complex structuresANNALEN DER PHYSIK, Issue 3 2007D.H. Delphenich Abstract It is shown that not all linear electromagnetic constitutive laws will define almost-complex structures on the bundle of 2-forms on the spacetime manifold when composed with the Poincaré duality isomorphism, but only a restricted class of them that includes linear spatially isotropic and some bi-isotropic constitutive laws. Although this result does not trivialize the formulation of the basic equations of pre-metric electromagnetism, it does affect their reduction to metric electromagnetism by its effect on the types of media that are reducible, and possibly its effect on the way that such media support the propagation of electromagnetic waves. [source] Empirical Challenges and Concept Formation in the History of HydrodynamicsCENTAURUS, Issue 3 2008Olivier Darrigol Abstract Although the fundamental equations of hydrodynamics were known at an early stage of its history, this theory long remained irrelevant to most of the practical problems of flow. The advent of a more efficient fluid mechanics in the early twentieth century depended on conceptual schemes that could not be read directly from the basic equations. Attention to concrete problems of flow, rather than purely mathematical deduction or purely intuitive guessing, permitted the gradual introduction of relevant substructures and their ultimate combination in powerful approximation schemes. This history is in part singular, owing to the extreme difficulty of dealing with non-linear systems with infinitely many degrees of freedom. But it is also typical as an illustration of the futility of reducing a physico-mathematical theory to its fundamental equations. Any advanced theory of physics must include an evolving modular structure that plays an essential role in melding the formal with the empirical. [source] | |||||||||||||