Peristaltic flow of a Williamson fluid in an asymmetric channel

In this work, we have presented a peristaltic flow of a Williamson model in an asymmetric channel. The governing equations of Williamson model in two dimensional peristaltic flow phenomena are constructed under long wave length and low Reynolds number approximations. A regular perturbation expansion method is used to obtain the analytical solution of the non-linear problem. The expressions for stream function, pressure gradient and pressure rise have been computed. The pertinent features of various physical parameters have been discussed graphically. It is observed that, (the non-dimensional Williamson parameter) for large We , the curves of the pressure rise are not linear but for very small We it behave like a Newtonian fluid.     

Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no-slip condition, continuity of velocity and stresses at interfaces along with Happle's no-couple stress condition as the boundary conditions. The expressions for the linear velocity, micro-rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro-rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work.     

Some Remarks on Modelling and Simulation of Thin Film Flow

Recenty, convergent and nonnegativity preserving numerical schemes for the thin film equation have been developed and applied successfully to model the flow of thin films of Newtonian liquids on homogeneous surfaces. It is the aim of this paper to discuss two related, but more involved physical settings. The first topic is flow on chemically structured surfaces which is of great interest in a number of microfluidic applications. We will formulate a convergent, nonnegativity preserving scheme and compare the simulations with recent physical experiments. The second part deals with power‐law‐fluids. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient C_d and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.     

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach.     

The FENE viscoelastic model and thin film flows

This Note has as objective to determine, in a rigorous way, a simplified expression of the constitutive law for a visco-elastic fluid of FENE type in thin domains. The proof uses the FENE model behavior for long times and the existence of a stationary solution for this behavioral law. Some possible applications of this study are then briefly described in the domains of lubrication, blood flow, microfluidic, boundary layers, …. To cite this article: L. Chupin, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Development of POD reduced-order model and its closure scheme for 2D Rayleigh–Bénard convection

Reduced-order model (ROM) based on proper orthogonal decomposition (POD) is a fast computational fluid dynamics (CFD) method and has been widely applied to pure flow or heat conduction problems in the past. In this paper, the typical 2D Rayleigh–Bénard convection (RBC) in a square cavity was set as a research target. Firstly, the POD-ROM of 2D RBC problem was constructed at Ra = 10⁷, Pr = 0.71. Combining with direct numerical simulation (DNS) databases, a closure model (CM) was then proposed to correct the evolution process of POD-ROM. Based on the proposed CM, we realized the prediction of flow evolution for a new flow case under the parameters different from that used to get its POD eigenmodes. It showed that the proposed POD-ROM with CM could be able to predict the dynamics of new flow cases. Moreover, the corresponding method proposed in the present study can be also easily extended to other types of flow-heat coupling problems, such as natural heat convection, etc.     

Existence of solutions for a finite nonlinearly hyperelastic rod

A theoretical investigation of a mathematical model for the capillary-tissue fluid exchange, including the characteristics and influence of the boundaries and media through which the fluid flows, has been studied. Filtration from the cylindrical capillary into the concentrically surrounding tissue-space and flow from a capillary into the tissue across the thin membrane are analyzed in detail. It has been observed that the filtration efficiency of the functional unit decreases as the peripherallayer viscosity increases, and that contrary to the results of Apelblat, Katziv-Kutchalsky and Silborberg (Biorheology2 (1974), 1–49), the slip velocity plays dominant role on filtration efficiency. It is also noted that he filtration efficiency decreases as the slip velocity at the porous boundary increases.     

Computational fluid dynamics modelling of an entrained flow biomass gasifier

A mathematical model, based on the Computational Fluid Dynamics package CFX4, has been developed to study the flow within an entrained flow biomass gasifier. The gasifier is designed to convert sawdust and chopped cotton gin trash into a low calorific value gas which can be burned in a modified engine to run a generator. Calculations of the flowfield are performed using the standard k–ϵ model and a Differential Reynolds Stress Model (DSM). In line with current thinking, it is shown that the k–ϵ model gives unphysical results for complex swirling flows, whereas the DSM model performs well. Particle tracking was performed to determine typical trajectories for the biomass and char and the results used to determine means of avoiding slagging in the gasifier base. The simulations have proved to be very useful to the designers who are now using the model to optimise the design.     

Capturing coalescence and break-up processes in vertical gas–liquid flows: Assessment of population balance methods

Gas–liquid flows are commonly encountered in industrial flow systems. Numerical studies have been performed to assess the performances of different population balance approaches – direct quadrature method of moments (DQMOMs), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) model – in tracking the changes of gas void fraction and bubble size distribution under complex flow conditions and to validate the model predictions against experimental measurements from medium- and large-sized vertical pipes. Subject to different gas injection method and flow conditions, bubble size evolution exhibited a coalescence dominant trend in the medium-sized pipe; while bubble break-up was found to be dominant in large-sized pipe. The two experiments were therefore strategically selected for carrying out a thorough examination of existing population balance models in capturing the complicated behaviour of bubble coalescence and break-up. In general, predictions of all the different population balance approaches were in reasonable agreement with experimental data. More importantly, encouraging results have been obtained in adequately capturing the dynamical changes of bubbles size due to bubble interactions and transition from wall peak to core peak gas void fraction profiles. As a compromise between numerical accuracy and computational time, DQMOM has performed rather well in capturing the essential two-phase flow structures within the medium- and large-sized vertical pipes when compared to those of ABND and homogeneous MUSIG models. From a practical perspective, the ABND model may still be considered as a more viable approach for industrial applications of gas–liquid flow systems.     

Turbulent diffusion of mass in circular pipe flow

An implicit finite difference scheme was used to solve the convective-diffusion equation to predict the steady-state transport of a conservative, neutrally bouyant tracer injected along the centreline into a fully developed turbulent pipe flow. Three different distributions for the radial mass diffusivity have been compared with two independent sets of experimental data. The results indicate that the distribution based on the turbulent kinematic eddy viscosity predicted by a k?l model produces the closest agreement between the numerical model predictions and the experimentally observed tracer distribution.     

Determination of vorticity,gradients of flow parameters and curvature of stream-lines behind unsteady curved shock waves

In this paper the gradients of flow parameters and the expression for vorticity vector behind three-dimensional unsteady curved shock waves in fluids obeying anarbitrary equation of state have been explicitly determined. A transformation of coordinates defined by Taub [1](¹), has been used and various conservation equations have been obtained in the new coordinate system, assuming the dissipative mechanisms such as viscosity and heat-conduction as absent. The flow quantities on the upstream side of the shock are assumed to be uniform and known and those on its downstream side have been determinedin principle in terms of known quantities for the flow obeying anarbitrary equation of state. For the flow of a perfect gas all the unknown quantities have been explicitly calculated in terms of known quantities. The derivatives of entropy and curvature of stream-lines behind the unsteady shock wave have also been explicitly determined.     

Parameter identification and optimization algorithm in microbial continuous culture

In this study, a novelty mathematical model is established to formulate the continuous culture of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae, in which the inhibition of 3-hydroxypropionaldehyde (3-HPA) to cells growth and activity of some enzymes (such as glycerol dehydratase (GDHt) and 1,3-PD oxidoreductase (PDOR)), and the passive diffusion and active transport of glycerol and 1,3-PD across cell membrane are all taken into consideration. Taking the mean relative error between the experimental data and calculated values as the performance index, a parameter identification model involving multiple nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results not only show that the established model can be used to describe the continuous fermentation reasonably, but also the improved PSO algorithm is valid.     

Mathematical modeling of catalytic wet oxidation in trickle-bed reactors by a diffusion–convection–reaction approach embedded with an interstitial CFD framework

In this work, we propose a diffusion–convection–reaction methodology to gain further insights into the heterogeneous multiphase flow of trickle beds. Our case-study encompasses a multi-fluid model embedded within an interstitial framework on the numerical simulation of continuous catalytic wet oxidation of hazardous compounds. First, with the proviso that phase holdup, pressure drop, and liquid distribution are fundamental criteria for the efficient design of trickle beds, the multiphase flow constitutive equations have been developed and solved by the conservative unstructured finite volume method. Second, several numerical variables were parametrically optimized based on the application of different under-relaxation parameters, mesh densities, and time stepping strategies. The segregated solver has been found to reveal good properties in terms of convergence and stability criteria, which endorsed the further corroboration. Finally, this theoretical probing-sensing scheme enabled the characterization of liquid flow texture accomplished by three-dimensional flow patterns exposing their deviation from ideal plug flow. The diffusion–convection–reaction framework coupled within a CFD model can then be further exploited on the simulation of complex multiphase reactive flows with adjustable parameters.     

Modeling and simulation of phenol removal from wastewater using a membrane contactor as a bioreactor

Diverse methods have been introduced for phenol removal from wastewater. Among them, membrane bioreactors have attracted considerable attention in the last decade. In this study, modeling and simulation of a hollow fiber membrane contactor as a bioreactor was carried out. The effects of the various parameters such as flow rate, ratio of membrane porosity to tortuosity, membrane length, initial phenol concentration, number of fibers, and inner and outer radius of the membrane on phenol removal efficiency were studied. A proposed set of partial differential equations and related boundary conditions in the model were solved by the finite element method via simulation with computational fluid dynamics techniques. The simulation results were compared with existing empirical data from literature and acceptable agreement was observed. Based on the obtained results, increasing the initial concentration had a reverse impact on the phenol removal efficiency. However, increasing the cell phase flow rate slightly enhanced the removal efficiency. Moreover, extending the membrane length had a desirable effect. Also, augmentation of the number of fibers within the contactor initially increased and then decreased the efficiency.     

Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries – A mathematical model

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n. Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ, amplitude A, and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.     

Design optimization and forming methods for toroidal composite shells

Based on the example of a toroidal membrane, a model for calculating the winding trajectory and the shape of a shell billet and its transformation into given surface elements, as well as for calculating the shape of the membrane under an internal pressure loading, is developed. The problem of choosing optimum design variables and manufacturing parameters of the membrane is also investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 147–164, March–April, 2006.     

The effect of actuator parameters on the critical flow velocity of a fluidic amplifier

The effect of actuator parameters on the critical flow velocity of the fluidic amplifier in liquid-jet hammers has been investigated numerically and experimentally. The flow in the fluidic amplifier and actuators coupled with the rigid body movement of the impacting body has been simulated using a commercial CFD software package, Fluent. The flow is modeled by the RNG-based κ–ε turbulence model and the incompressible Navier–Stokes equations. Dynamic layering method and a user-defined function written in C programming language are used to update the mesh in the simulations. The results show that, increasing the piston diameter decreases rapidly the critical flow velocity as the piston diameter is less than a certain value. The critical flow velocity increases sharply as the piston rod diameter is greater than a certain value, and increases nearly linearly with mass of the impacting body, and is independent on stroke length of the impacting body. The findings of the numerical investigations agree well with corresponding experimental results.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of substances across cell membrane, the metabolic network contains multiple possible metabolic systems. In this paper, we establish a complex metabolic network and the corresponding nonlinear hybrid dynamical system aiming to determine the most possible metabolic system. The existence, uniqueness and continuity of solutions are discussed. We quantitatively describe biological robustness and present a system identification model on the basis of robustness performance. The identification problem is decomposed into two subproblems and a procedure is constructed to solve them. Numerical results show that it is most possible that both glycerol and 1,3-PD pass the cell membrane by active transport coupling with passive diffusion under substrate-sufficient conditions, whereas, under substrate-limited conditions, glycerol passes cell membrane by active transport coupling with passive diffusion and 1,3-PD by active transport.