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Momentum Balance (momentum + balance)
Selected AbstractsMomentum Balance for Two-Phase Horizontal Pipe Flow Part 1: Friction FactorsASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 1-2 2004P. L. Spedding Estimations of gas wall, liquid wall and interfacial friction factors for two-phase horizontal co-current pipe flow are discussed critically after being checked against reliable data obtained under a wide range of conditions. The use of equivalent diameters and the Blasius relation were shown to be valid for estimation of the gas wall friction. Prediction of liquid wall and interfacial friction factors proved to be more difficult but estimation improved if consideration was given to the effects of liquid holdup and interfacial liquid shape. [source] Momentum Balance for Two-Phase Horizontal Pipe Flow Part 2: Testing of ModelsASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 1-2 2004P. L. Spedding Momentum balance models were tested against reliable data for both holdup and pressure drop. The best prediction performance was achieved using a model that considered the actual shape of the liquid phase in the pipe. In such circumstances the momentum balance calculation tended to under predict both the holdup and pressure drop for some of the annular and stratified regimes. Suggestions are made for improvements in the momentum balance approach. [source] An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fractureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Reza Abedi Abstract This paper describes an adaptive numerical framework for cohesive fracture models based on a spacetime discontinuous Galerkin (SDG) method for elastodynamics with elementwise momentum balance. Discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction,separation laws in the SDG framework; no special cohesive elements or other algorithmic devices are required. We use unstructured spacetime grids in a h -adaptive implementation to adjust simultaneously the spatial and temporal resolutions. Two independent error indicators drive the adaptive refinement. One is a dissipation-based indicator that controls the accuracy of the solution in the bulk material; the second ensures the accuracy of the discrete rendering of the cohesive law. Applications of the SDG cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature: an unexpected quasi-singular structure in the velocity response. Numerical examples demonstrate the use of adaptive analysis methods in resolving this structure, as well as its importance in reliable predictions of fracture kinetics. Copyright © 2009 John Wiley & Sons, Ltd. [source] A finite volume method for large strain analysis of incompressible hyperelastic materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005I. Bijelonja Abstract This paper describes development of a displacement,pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney,Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement,pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free. Copyright © 2005 John Wiley & Sons, Ltd. [source] Design of mixed conducting ceramic membranes/reactors for the partial oxidation of methane to syngasAICHE JOURNAL, Issue 10 2009Xiaoyao Tan Abstract The performance of mixed conducting ceramic membrane reactors for the partial oxidation of methane (POM) to syngas has been analyzed through a two-dimensional mathematical model, in which the material balance, the heat balance and the momentum balance for both the shell and the tube phase are taken into account. The modeling results indicate that the membrane reactors have many advantages over the conventional fixed bed reactors such as the higher CO selectivity and yield, the lower heating point and the lower pressure drop as well. When the methane feed is converted completely into product in the membrane reactors, temperature flying can take place, which may be restrained by increasing the feed flow rate or by lowering the operation temperature. The reaction capacity of the membrane reactor is mainly determined by the oxygen permeation rate rather than by the POM reaction rate on the catalyst. In order to improve the membrane reactor performance, reduction of mass transfer resistance in the catalyst bed is necessary. Using the smaller membrane tubes is an effective way to achieve a higher reaction capacity, but the pressure drop is a severe problem to be faced. The methane feed velocity for the operation of mixed conducting membrane reactors should be carefully regulated so as to obtain the maximum syngas yield, which can be estimated from their oxygen permeability. The mathematical model and the kinetic parameters have been validated by comparing modeling results with the experimental data for the La0.6Sr0.4Co0.2Fe0.8O3-, (LSCF) membrane reactor. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Equilibrium problem for thermoelectroconductive body with the Signorini condition on the boundaryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001D. Hömberg Abstract We investigate a boundary value problem for a thermoelectroconductive body with the Signorini condition on the boundary, related to resistance welding. The mathematical model consists of an energy-balance equation coupled with an elliptic equation for the electric potential and a quasistatic momentum balance with a viscoelastic material law. We prove the existence of a weak solution to the model by using the Schauder fixed point theorem and classical results on pseudomonotone operators. Copyright © 2001 John Wiley & Sons, Ltd. [source] A multiphase finite element simulation of biological conversion processes in landfillsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Tim Ricken Worldwide, landfills are the most common way to dispose of waste, but have an impact on the environment as a result of harmful gas and leachate production. Estimating the long-term behaviour of a landfill in regard to this gas production and organic degrading, as well as to settlement and waste water production, is of high importance. Therefore, a model has been developed to simulate these processes. This constitutive model is based on the multiphase Theory of Porous Media. The body under investigation consists of an organic and an inorganic phase as well as a liquid and a gas phase. The equations of the model are developed on the basis of a consistent thermo-mechanical approach including the momentum balance for the solid phase and the mixture, the energy balance for the mixture and the mass balance for the gas phase. All interactions between the constituents such as mass transfers, interaction forces and energy fluxes are taken into consideration. The strongly coupled set of partial differential equations is implemented in the finite element code FEAP. The theoretical framework and the results of meantime successfully performed simulation of a real landfill body will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Design Considerations for Plate and Frame Ultrafiltration Modules by Computational Fluid Dynamics Analysis,THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2006Mauro M. Dal-Cin Abstract Pressure and flow maldistributions were studied in a full-scale industrial plate and frame ultrafiltration module, operating in a Z flow pattern, for the recovery of used motor oils. Solutions were obtained using (1) a three-dimensional solution of the Navier-Stokes equation using computational fluid dynamics and (2) Bernoulli's equation and a momentum balance in one dimension. Fluid decelerations and accelerations generated pressure increases and decreases in the distributor and collector, respectively, biasing the flow distribution to the last channel. Several modifications to the original design were evaluated; the most effective was larger distributor and collector diameters, which greatly improved the uniformity of the flow distribution and transmembrane pressure, and reduced the overall pressure drop in a bank. A variable diameter distributor and collector module was designed using the 1-D model. Flow distribution was significantly improved but also yielded an undesirable overall higher pressure drop and a pressure maldistribution in the bank. The maldistribution of the main inlet manifold to the distributors in the first bank was strongly dependent on the module design. The flow distribution across the width of a channel became uniform within a short distance, essentially eliminating the need to consider this design aspect any further. Flows at the bank outlets, and hence inlets of the following bank, showed uniform lateral distribution in all cases, suggesting that future modelling work can be limited to a fraction of the module width, based on symmetry, in order to gain computational efficiency. On a étudié les mauvaises distributions de pression et d'écoulement dans un module d'ultrafiltration à plateaux et à cadres à l'échelle industrielle, fonctionnant dans un schéma d'écoulement en Z, pour la récupération des huiles de moteurs usées. Des solutions ont été obtenues avec (1) une solution tridimensionnelle de l'équation de Navier-Stokes utilisant la mécanique des fluides par ordinateur, et (2) l'équation de Bernoulli et un bilan de quantité de mouvement unidimensionnel. Les décélérations et accélérations de fluide entraînent des augmentations et diminutions de pression dans le distributeur et le collecteur, respectivement, ce qui fausse la distribution d'écoulement dans le dernier canal. On a évalué plusieurs modifications du concept original; la plus efficace sont des diamètres de distributeur et de collecteur plus larges, qui permettent d'améliorer grandement l'uniformité de la distribution d'écoulement et la pression transmembranaire, et qui réduisent la perte de charge globale dans une batterie. Un module de distributeur et de collecteur de diamètres variables a été conçu au moyen du modèle 1D. La distribution d'écoulement est significativement améliorée mais cause une perte de charge globale plus grande indésirable et une mauvaise distribution de pression dans la batterie. La mauvaise distribution du manifold d'entrée principal vers les distributeurs dans la première batterie est fortement dépendante de la conception du module. La distribution d'écoulement dans toute la largeur d'un canal devient uniforme sur une courte distance, éliminant essentiellement le besoin d'approfondir cet aspect de la conception. L'écoulement en sortie de batteries et donc à l'entrée des batteries suivantes montre une distribution latérale uniforme dans tous les cas, ce qui suggère que le travail de modélisation futur peut se limiter à une fraction de la largeur du module, pour des raisons de symétrie, pour gagner de l'efficacité numérique. [source] Three-bed PVSA process for high-purity O2 generation from ambient airAICHE JOURNAL, Issue 11 2005Jeong-Geun Jee Abstract A three-bed PVSA (pressure vacuum swing adsorption) process, combining equilibrium separation with kinetic separation, was developed to overcome the 94% O2 purity restriction inherent to air separation in the adsorption process. To produce 97+% and/or 99+% purity O2 directly from air, the PVSA process with two zeolite 10X beds and one CMS bed was executed at 33.44,45.60 to 253.31 kPa. In addition, the effluent gas from the CMS bed to be used for O2 purification was backfilled to the zeolite 10X bed to improve its purity, recovery, and productivity in bulk separation of the air. PVSA I, which made use of a single blowdown/backfill step, produced an O2 product with a purity of 95.4,97.4% and a recovery of 43.4,84.8%, whereas PVSA II, which used two consecutive blowdown/backfill steps, produced O2 with a purity of 98.2,99.2% and a recovery of 47.2,63.6%. Because the primary impurity in the O2 product was Ar, the amounts of N2 contained in the product were in the range of 4000,5000 ppm at PVSA I and several tens of ppm at PVSA II. A nonisothermal dynamic model incorporating mass, energy, and momentum balances was applied to predict the process dynamics. Using the linear driving force (LDF) model with constant diffusivity for the equilibrium separation bed and a modified LDF model with concentration dependency of the diffusion rate for the kinetic separation bed, the dynamic model was able to accurately predict the results of the experiment. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source] | |||||||||||||