Mecanica de los Fluidos Research Papers (original) (raw)

The so-called moist-convective shallow-water model, which incorporates moist convection in a simple albeit self-consistent way is used to analyse how intense localized vortices, with distributions of horizontal velocity and relative vorticity close to those observed in tropical cyclones (TC), evolve and interact with topography on the β -plane at low latitudes. Instabilities of such TC-like vortices are studied first in the f -plane approximation, and their development, interplay with beta-gyres and the role they play in vorticity redistribution and intensification are then analysed along the vortex trajectories on the β -plane, both in dry and moist-convective environments. Interactions of the vortices with an idealized topography in the form of zonal and meridional ridges and islands of elliptic form and the role of moist convection in these processes are then investigated, revealing rich vortex-dynamics patterns. The results can be helpful in crude analyses and predictions of the evolution of the barotropic component of TC, of their trajectories over the ocean and during landfall and of related condensation/precipitation patterns.

In this work a review about the most relevant methods found in the literature to model the multiphase flow in pipelines is presented. It includes the traditional simplified and mechanistic models, moreover, principles of the drift flux model and the two fluid model are explained. Even though, it is possible to find several models in the literature, no one is able to reproduce all flow conditions presented in the oil industry. Therefore, some issues reported by different authors related to model validation are here also discussed.
MSC:76T10 | PACS:47.55.Ca

- by D. Fuentes and +3
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- Kinetics And Mechanistic Studies, Fluid Dynamics, Stratified Flows, Mecanica de los Fluidos

Three-dimensional instabilities for two circular lid-driven cavities are investigated by linear stability analysis and Direct Numerical Simulations using high order spectral techniques. Two circular geometries have been analysed and compared: a circular cavity with an horizontal top boundary and a circular cavity with circular lid. Compared to more classic results for squared and rectangular lid driven cavities, the corners of these rounded geometries have been partially or totally removed. Critical Reynolds numbers, neutral curves and three dimensional structures associated to the least stable modes have been identified by linear stability analysis and then confirmed by spectral Direct Numerical Simulations. We show that the geometries that present fewer sharp corners have enhanced stability: the circular cavity with a flat lid presents the first bifurcation at (Rec, kc) ≈ (1362, 25) whilst the circular lid bifurcates at (Rec, kc) ≈ (1438, 18), where Rec is the critical Reynolds number based on the cavity diameter and lid tangential velocity, and kc is the spanwise wavenumber. Neutral curves and properties of the leading three dimensional flow structures are documented and analogies to instabilities in other lid-driven cavities discussed. Additionally, we include results for the adjoint problem and structural sensitivity 3D iso-maps (i.e. wavemaker regions), to show that the cavity corners play a relevant role in the generation of 3D instabilities.

- by Esteban Ferrer and +1
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- Hydrodynamics (Physics), Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics

Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli-trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging microchannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0 o to 17 o are described at different pressure ratios (1.5≤Π≤2.5) and Knudsen numbers (0.03≤Kn≤12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent microchannels and are compared with those of a microchannel with a uniform cross-section. The variations of the flow field properties in divergent microchannels, which are influenced by the area change, the channel pressure ratio and the rarefication are discussed. The results show no flow separation in divergent microchannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through microchannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro-and Nano-channels with non-uniform cross-sections.

- by Amin Ebrahimi
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- Engineering, Mechanical Engineering, Physics, Thermodynamics

It is shown that steady large-scale slowly eastward-moving twin-cyclone coherent structures, the equatorial modons, exist in both one-and two layer versions of the rotating shallow water model on the equatorial beta plane. They arise via the process of "ageostrophic adjustment" from the analytic asymptotic modon solutions of the vorticity equation obtained in the limit of small pressure perturbations. Evolution of these structures in adiabatic and moist-convective environments, and also in the presence of topography is analyzed, showing their robustness in the one-layer model. It is demonstrated that moist convection enhances and helps maintain the modons. In the two-layer model the barotropic and quasi-barotropic modons display similar to one-layer modon features, while increasing baroclinicity leads to eventual loss of coherence and arrest of the eastward propagation. Some features of equatorial modons resemble those observed in the Madden-Julian Oscillation events in tropical atmosphere, which hints at their possible relevance to the dynamics of this phenomenon.

- by Masoud Rostami
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- Physics, Climate Change, Computational Fluid Dynamics, Fluid Mechanics

We prove the existence of a strong–weak solution (u, p, T) (= velocity, pressure, temperature) of the steady Bénard problem in a 2D quadrangular cavity, heated/cooled on two opposite sides and thermally insulated on the other sides. Applying the tools of non-linear analysis, we study the structure of the set of solutions in dependence on the acting volume force and on the given temperature profiles on the heated/cooled sides. Particularly, in the case when the cavity has the form of a
trapezoid, we also study the structure of the solution set in dependence on the angle of inclination from the horizontal–vertical position.

- by Dennis A . Siginer
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- Engineering Physics, Mathematics, Applied Mathematics, Fluid Mechanics

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

- by Taha Sochi
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- Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics, Rheology

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

- by Masoud Rostami
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- Physics, Computational Fluid Dynamics, Fluid Mechanics, Atmospheric Science

ABSTRACT: A predetermined flow pattern in a magnetorheological damper providing continuously variable resistance to flow is required for efficient damping of a given load. The required predetermined flow pattern rests on the a priori determination of the constitutive properties of the magnetorheological (MR) fluid determined to generate variable resistance to flow. The inverse problem of constructing the predetermined response of the damper with a specific displacement pattern of the piston in the damper for efficient damping of a given load is solved. The magnetorheological (MR) fluid in the damper is modeled as a Bingham phase change material with time dependent yield stress offering continuously variable resistance to the flow in the piston to achieve the required specific displacement pattern. The governing equations are solved for any time history of the dimensionless yield stress of the fluid which in turn is determined from the imposed response of the damper. Analytical tools developed can be used in optimizing damper performance. The application of the method to resonance mitigation is illustrated.

ABSTRACT: The unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo-Fabrizio time fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson-Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique used is new, leads to exact solutions, is completely different from those available in the literature, and applies to other similar problems. The new expression for the velocity field displays experimentally observed 'velocity overshoot' as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo-Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

An analytical study of the forced convection of nonlinear elastoviscoplastic fluids in tubes of arbitrary cross section is presented. The constitutive structure of the fluid is described by a frame indifferent linear combination of the Modified Phan-Thien-Tanner model of non-linear viscoelastic fluids and the Bingham model of non-linear viscoplastic fluids. Arbitrary tube cross sections are modeled by a continuous one-to-one mapping of the circular base contour into a wide spectrum family of non-circular tube contours. Field variables are expanded into double asymptotic series in terms of the elasticity measure Weissenberg number Wi, and a mapping parameter leading to a set of linearized hierarchical momentum balance, constitutive structure and thermal field equations which are solved successively up to and including the third order in Wi for the velocity and temperature fields. The general algorithm developed is applied to the study of forced convection in tubes with exact equilateral triangular and approximately square cross sections. The analysis also yields the solution of the forced convection of linear (Newtonian) fluids in non-circular tubes and the forced convection in circular tubes of the family of non-linear fluids (viscoplastic, viscoelastic, elastoviscoplastic) described by the constitutive structure under consideration thereby providing as well validation for the computations carried out for non-linear fluids in non-circular cross-sections. A thorough comparison of the velocity and thermal fields of the Newtonian, vis-coplastic, viscoelastic and elastoviscoplastic fluids in tubes of equilateral triangular and pseudo square cross-sectional tubes is presented as specific cases.

Resonance phenomenon is investigated in pulsating flows in straight circular tubes for the class of constitutively non-linear affine viscoelastic fluids represented by the Johnson-Segalman constitutive model. The relaxation response of non-linear viscoelastic fluids associated with the natural frequencies of oscillation that arise as a consequence of the structure of the constitutive equation is explored. An analytical solution, which circumvents the high-Weissenberg number problem, which plagues numerical solutions of highly viscoelastic fluids, based on an asymptotic expansion in terms of a small material parameter is developed. At the lowest order of the asymptotic expansion the velocity field of the Maxwell fluid in round tubes is recovered, therefore providing validation of the computations. The analytical solution allows insights into the high Weissenberg number behavior of highly elastic fluids and thus avoids the difficulties the numerical solutions of high Weissenberg number problems are fraught with such as instability and lack of convergence. The analysis reveals that the forcing frequency associated with the pressure gradient generates a sequence of resonances of rapidly decaying intensity with increasing forcing frequency for a fixed value of the Weissenberg number. The intensity of the resonance is a rapidly increasing function of the increasing Weissenberg numbers, in particular at the first natural frequency. The latter is a decreasing function of the increasing elasticity of the fluid that is of the increasing Weissenberg numbers. The intensity of the resonance at the first natural frequency is a rapidly increasing function of the increasing elasticity. We show the existence of a limit point for the enhancement in energy savings with increasing elasticity. The effect of resonance on the flow rate, maximum amplitude of the average velocity, the mean flow rate and the oscillating velocity field is explored.

- by Dennis A . Siginer and +1
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- Engineering, Engineering Physics, Polymer Engineering, Mechanical Engineering

ABSTRACT: Steady two-dimensional natural convection in fluid filled cavities is numerically investigated for the case of non- Newtonian shear thickening power law liquids. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume method for Newtonian and non-Newtonian fluids. The computations were performed for a Rayleigh number, based on cavity height, of 10(exponent 5) and a Prandtl number of 100. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for aspect ratios of 1 and 4. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the dependence of the average Nusselt number on angle of inclination. It is shown that despite significant variation in heat transfer rate both Newtonian and non-Newtonian fluids exhibit similar behavior with the transition from multi-cell flow structure to a single-cell regime.

- by Dennis A . Siginer
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- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

- by Dennis A . Siginer
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- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

The flow of Ree-Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally-obtained solutions are compared to the analytical solutions derived from the Weissenberg-Rabinowitsch-Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.

The process of geostrophic adjustment of localized large-scale pressure anomalies in the standard adiabatic shallow-water model on the equatorial beta-plane is revisited, and it is shown that the standard scenario of generation of westward-moving Rossby and eastward-moving Kelvin waves, which underlies the classical Gill theory of tropical circulation due to a localized heating, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response to the initial perturbation in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can be totally different and produces, depending on parameters, either Gill-like response or eastward-moving coherent dipolar structures of the type of equatorial modons, which do not appear in the “dry” adjustment, or vortices traveling, respectively, northwest in the Northern and southwest in the Southern hemispheres. (Physics of Fluids 31, 081702 (2019); https://doi.org/10.1063/1.5110441)

- by Masoud Rostami
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- Physics, Computational Fluid Dynamics, Fluid Mechanics, Atmospheric Science

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of Computational Fluid Dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

ABSTRACT: A Fourier-Galerkin spectral method is proposed and used to analyze a system of quasilinear partial differential equations governing the drainage of liquids of the Oldroyd four-constant type. It is shown that, Fourier-Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier-Galerkin approximations to the system of quasilinear partial differential equations are developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.

The present work is a numerical simulation of a turbulent free jet issuing from an axisymmetric orifice into quiescent air environment. The numerical simulation was carried out by solving the Reynolds Averaged Navier-Stokes equations using OpenFOAM. The standard two-equation k-ɛ eddy viscosity turbulence model was used to simulate the turbulent flow field in a three dimensional cylindrical domain. The numerical predictions are compared with experimental data in order to assess the capability/limitations of the turbulence model to reproduce the physics involved and the code using jet case examined in this work. The standard k-ɛ model predictions in terms of centre line mean velocity decay, spread rate, entrainment, self-similarity, turbulence intensities and Reynolds stress, are found to reproduce the physics of the jet flow and agree approximately with experimental data. New information such as evolution of turbulent kinetic energy budget, length scales and time scales is provided.

- by KANNAN B T
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- Computational Fluid Dynamics, Computational Mechanics, Fluid Mechanics, Turbulence

Conventional method of defining half velocity widths is applicable only for axisymmetric jets. Hence, geometry based definition of half velocity width is used for non-circular jets. Usefulness of this method becomes less when there is no symmetry based on geometry. Hence, a new half velocity width is proposed based on equivalent area method. Newly proposed half velocity width is computed for a conventional circular jet and a non-circular jet. The comparison of half velocity widths obtained using conventional method and newly proposed method shows good agreement with each other for circular jet. Geometry based half width and equivalent area based half velocity width agree in the near field for the non-circular jet. Equivalent area based method is found as better representation of half velocity width for non-circular turbulent jets.

- by KANNAN B T
- •
- Engineering, Mechanical Engineering, Civil Engineering, Aerospace Engineering

The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this issue using a numerical stochastic method, specifically simulated annealing, where we demonstrated the problem by some illuminating examples and concluded that energy minimization principle can be a valid hypothesis. The investigation in this paper is more general as it is based to a certain extent on an analytical approach.

- by Taha Sochi
- •
- Fluid Mechanics, Energy, Fluid structure interaction, Fluid flow in porous media

ABSTRACT: Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.

ABSTRACT: Flow of Giesekus fluids in straight, arbitrary but axially-symmetric non-circular tubes is investigated. The cross-sectional shapes are obtained through a one-to-one continuous mapping of the circular base contour. The primary longitudinal and the secondary fields are elucidated up to and including the third order in the Weissenberg number Wi.

ABSTRACT: The fluid dynamics of dampers is investigated for the case where the damping fluid flows through passages in which a magnetic field is applied. This is a specific case of a new and promising field of applications that has emerged through the design of devices that take advantage of some properties of the so-called electrorheological fluids and magnetorheological fluids (ERF and MRF). These fluids are created when a base fluid is seeded with very small dielectric or iron particles, so that it reacts to electric or magnetic fields by developing some non-Newtonian characteristics, most prominently a yield stress, viscosity change, and also viscoelasticity. These fluid properties can be controlled through controlling the strength of the electric or magnetic fields. In this paper, a typical damping load is modeled and related to the required flow of a MRF inside the damper. To this end the fluid is modeled as a Bingham fluid with time-varying yield-stress. The analysis here developed makes it possible to determine the magnetic field variation necessary in order to achieve a specific displacement of the damper’s piston. The flow equations are analytically solved for any time-history of the dimensionless fluid’s yield-stress. Main results are some simplified relationships that correlate damping load and magnetic field time-variations. These results aim at providing analytical tools that may facilitate the design of dampers.

ABSTRACT: Quality of laminates produced by Seeman Composite Resin Infusion Molding Process (SCRIMP) is studied by comparing their Fiber Volume fraction and void content. SCRIMP is a variant of Vacuum Assisted Resin Transfer Molding (VARTM). Manufacturing process parameters are then identified and varied to study the impact on mechanical properties of laminated composites. Modification to SCRIMP is carried out by infusing the resin under additional pressure. Optimal process parameters for this modified SCRIMP process are suggested to yield laminates that are repeatable and consistent in quality. Void content is reduced in the composite laminates by altering the vacuum pressure level. Thickness gradient commonly found in SCRIMP processed laminates is eliminated by allowing longer de-bulking time. Final laminate quality is measured using ASTM standardized mechanical testing.

In this paper, transversal flow field of nonlinear viscoelastic fluids abiding by the modified-Phan-Thien-Tanner (MPTT) constitutive model in straight tubes of eccentric-annular cross-section is investigated. An analytical solution is developed based on an asymptotic expansion in terms of the Weissenberg number coupled with the shape factor method a one-to-one mapping taking the circular cross-section into the eccentric annular cross section. The analysis reveals the formation of transversal flows due to elasticity and to the eccentricity parameter. The number of vortices in the cross-section depends on the ratio of the diameters in addition to the eccentricity parameter. The effect of these parameters on the vortical structure is explored for different values of the material parameters.

- by Dennis A . Siginer
- •
- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

A new approach to the numerical simulation of incompressible viscoelastic Rayleigh-Bénard convection in a cavity is presented. Due to the fact that the governing equations are of elliptic-hyperbolic type, a quasi-linear treatment of the hyperbolic part of the equations is proposed to overcome the strong instabilities that can be induced and is handled explicitly in time. The elliptic part related to the mass conservation and the diffusion is treated implicitly in time. The time scheme used is semi-implicit and of second order. Second-order central differencing is used throughout except for the quasi-linear part treated by third order space scheme HOUC. Incompressibility is handled by a projection method. The numerical approach is validated first through comparison with a Newtonian benchmark of Rayleigh-Bénard convection and then by comparing the results related to the convection setup in a 2 : 1 cavity filled with an Oldroyd-B fluid. A preliminary study is also conducted for a PTT fluid and shows that PTT fluid is slightly more unstable than Oldroyd-B fluid in the configuration of Rayleigh-Bénard convection.

- by Dennis A . Siginer
- •
- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

ABSTRACT: The unsteady transversal flow field in the tube flow of a memory integral fluid of order type driven by rotational boundary waves is investigated. A perturbation in terms of the amplitude of the sinusoidal boundary waves is used. Qualitative conclusions are independent of the explicit forms of the constitutive functions. Quantitative results are obtained by assuming Maxwell type of behavior for the latter. It is shown that transversal steady flows is a possibility if several rotational waves with frequencies in a certain ratio are imposed on the boundary. As a result helical steady flows may be possible in the longitudinal direction in a round tube. A parametrical study of the oscillating transversal field is presented for highly elastic and shear thinning liquids.

- by Dennis A . Siginer
- •
- Engineering, Mechanical Engineering, Chemical Engineering, Viscoelasticity

ABSTRACT: The flow dynamics of a finite two layered fluid system driven by thermocapillary effects when heated from the side is studied in the absence of gravity. The configuration is of low aspect ratio with a third dimension several orders of magnitude larger. The case of a low Prandtl number Newtonian fluid in the bottom layer encapsulated by a high Prandtl number viscoinelastic fluid with a shear rate and temperature dependent viscosity in the top layer is investigated numerically using the method of finite volumes together with the case of a high Prandtl number viscoinelastic fluid encapsulating another high Prandtl number viscoinelastic fluid in the lower layer both when the top surface is free and a no-slip solid cover. In either case, the top surface is considered to be insulated together with the bottom and viscous dissipation is taken into account. Free surface and interface deformations are neglected. The results are reported for both high and low Marangoni numbers. Appropriate values of the ratio of the interfacial Marangoni number to the free surface Marangoni number are determined to bring the convective motion in the lower layer to a virtual halt.

ABSTRACT: The dynamics of the flow in two layered systems heated from the side is investigated both when the fluids are viscoinelastic and viscoelastic. The system is two dimensional and confined to a box of low aspect ratio in reduced gravity. Interfaces are assumed to be flat. The free top surface is taken to be insulated together with the bottom wall. Results are reported for both high and low values of the interfacial Marangoni number when a low Prandtl number Newtonian fluid in the lower layer is encapsulated by a high Prandtl number viscoinelastic or viscoelastic fluid in the top layer.

ABSTRACT: A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively non-linear simple fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is summarized. The transversal field arises at the second order of the perturbation of the nonlinear constitutive structure, and is driven by first order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

ABSTRACT: Heat transfer enhancement in steady pressure gradient driven laminar flow of a class of non-linear viscoelastic fluids in straight tubes of non-circular cross-section at constant temperature is discussed together with the flow structure, and the physics is clarified. The variation of the average Nusselt number Nu with the Weissenberg Wi and Reynolds Re numbers in cross-sections with n axes of symmetry is analysed. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D0. The analytical method presented is capable of predicting the velocity and temperature fields in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at the lowest order. Heat transfer enhancements represented by average Nusselt numbers of an order of magnitude larger as compared to their Newtonian counterparts are predicted as a function of the Reynolds and Weissenberg numbers even for slightly non-Newtonian dilute fluids. The asymptotic independence of Nu = f(Pe,Wi) → Nu= f(Pe) with increasing Wi is shown analytically for the first time. The implications on the heat transfer enhancement of the change of type of the vorticity equation is discussed in particular for slight deviations from Newtonian behaviour where a rapid rise in enhancement seems to occur as opposed to the behaviour for larger values of the Weissenberg number where the rate of increase is much slower. The coupling between viscoelastic and inertial nonlinearities is crucial to enhancement. Fluid vorticity will change type when the velocity in the centre of the tube is larger than a critical value defined by the propagation of the shear waves. The asymptotic independence of Nu from elasticity with increasing Wi is related to the thickness of the supercritical region around the tube axis controlled by the interaction of the viscoelastic Mach number M and the Elasticity number E. The physics of the interaction of the effects of the Elasticity E, Viscoelastic Mach M, Reynolds Re and Weissenberg Wi numbers on generating the heat transfer enhancement is discussed.

ABSTRACT: This edition of the Journal of Non-Newtonian Fluid Mechanics contains several papers which were presented at the conference on Mechanics of Non-linear Materials, held in Banff, 13-16 May 1998. The attendees agreed that such a meeting was both desirable and timely. The papers contained in this edition illustrate recent advances in such areas as those dealing with liquid crystalline polymers, polymer blends, electro-rheological fluids, extensional flows, suspension rheology, flows in porous media, diffusion, bubble dynamics and splashing. All contributions were reviewed according to the Journal's policy.

- by Dennis A . Siginer
- •
- Engineering, Mechanical Engineering, Chemical Engineering, Applied Mathematics

ABSTRACT:A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid in straight tubes of arbitrary cross-sections is summarized. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

- by Dennis A . Siginer
- •
- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

ABSTRACT: The fully developed thermal field in constant pressure gradient driven laminar flow of viscoelastic fluids in straight pipes of arbitrary contour ∂D is investigated. The nonlinear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large and inertial effects are accounted for. Asymptotic series in terms of the Weissenberg number Wi are employed to represent the field variables. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is the result of secondary flows in the cross-section. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Large enhancements are possible even with dilute fluids. Isotherms for the temperature field are presented and discussed for several non-circular contours such as the ellipse and the equilateral triangle together with heat transfer behavior in terms of the Nusselt number Nu.

ABSTRACT: Steady two-dimensional natural convection in rectangular two dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0° and 90° and two cavity height based Rayleigh numbers, Ra = 104 and 105 , a Prandtl number of Pr = 102 and two cavity aspect ratios of 1, 4. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra = 104 and 105 and three Prandtl numbers of Pr = 102 , 103 and 104 . In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number Nu on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination O̸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. Despite significant differences in the heat transfer rate and flow configurations both Newtonian and non-Newtonian fluids of the power law type exhibit qualitatively similar behavior.

ABSTRACT: Steady two-dimensional natural convection in rectangular cavities has been investigated numerically. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume technique embedded in the Fluent code for a Newtonian (water) and three non Newtonian carbopol fluids. The highly accurate Quick differential scheme was used for discretization. The computations were performed for one Rayleigh number, based on cavity height, of 105 and a Prandtl number of 10 and 700, 6,000 and 1.2×104 for the Newtonian and the three non-Newtonian fluids respectively. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for one aspect ratio of 6. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the behaviour of the average Nusselt number with angle of inclination. Both Newtonian and non-Newtonian fluids exhibit similar behavior with a sudden drop around an angle of 50° associated with flow mode transition from multi-cell to single-cell mode.

ABSTRACT: An investigation of heat transfer with viscoelastic fluids in straight pipes of circular and some non-circular cross-sections is carried out. The influence of the rheological parameters on heat transfer enhancement with viscoelastic fluids in the entrance region of tube flow is investigated with negligible axial heat conduction and viscous dissipation. Numerical simulations are conducted with constant wall heat flux for the Graetz problem using the finite element based software Polyflow for viscoelastic fluids of the simplified Phan-Thien Tanner (SPPT) type. It is found that increasing the fluid elasticity, for all cross-sections, raises the normalized heat transfer coefficient for relatively low elasticity values but for high level of fluid elasticity the normalized heat transfer coefficient decreases.

- by Dennis A . Siginer
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- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

Fluid Kinematics: Streamline, path line, streak line, stream surface, stream tube, classification of flows: steady, unsteady, uniform, non-uniform, laminar, turbulent flows. One dimensional approximation, examples of real 1-D flows, two dimensional approximations, 2-D flow in wind tunnel, continuity equations for 1-D and 2-D flows both compressible and incompressible, stream function for two dimensional incompressible flows. Vorticity, rotational flow, Velocity potential function.

Unsteady laminar nonlinear slip flow of power law fluids in a microchannel is investigated. The nonlinear partial differential equation resulting from the momentum balance is solved with linear as well as nonlinear boundary conditions at the channel wall. We prove the existence of the weak solution, develop a semi-analytical solution based on the pseudo-spectral-Galerkin and Tau methods, and discuss the influence and effect of the slip coefficient and power law index on the time-dependent velocity profiles. Larger slip at the wall generates increased velocity profiles, and this effect is further enhanced by increasing the power law index. Comparatively, the velocity of the Newtonian fluid is larger and smaller than that of the power law fluid for the same value of the slippage coefficient if the power index is smaller and larger, respectively, than one.

- by Dennis A . Siginer
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- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

En nuestro diario vivir, inconscientemente nos encontramos interactuando con un fluido, por ejemplo, cuando respiramos estamos inhalando y exhalando el aire de la atmósfera, que es un fluido en estado gaseoso, o cuando bebemos agua, estamos interactuando con un fluido en estado líquido, pero también lo hacemos cuando caminamos, corremos, nadamos, saltamos, sudamos, y un sin número más de actividades que podamos realizar, por tanto, sin importar donde vayamos en el planeta, y la actividad o el trabajo que realicemos, siempre estaremos interactuando con un fluido.

- by Kevin Toala Vite
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- Fluid Mechanics, Applied Mechanics, Mecanica de los Fluidos
- by Diego Peralta Guevara
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- Chemical Engineering, Civil Engineering, Biochemistry, Chemistry

En el presente trabajo, se realiza un análisis teórico de los cálculos para determinar la velocidad de salida de un flujo permanente incompresible (agua), en una tobera cónica, usada como elemento de un sistema hidráulico de riego de un invernadero. Para determinar la velocidad de salida se emplea el método analítico de la ecuación de continuidad y un análisis por elemento finito (FEA), utilizando el software SOLIDWORKS y su complemento Flow Simulation versión 2016.

ABSTRACT: The interplay of yield stress and elasticity on the temperature field and heat transfer rates in tube flow of elastoviscoplastic (EVP) fluids is investigated in this paper. The constitutive structure of the EVP fluid obeys a linear combination of the Phan-Thien-Tanner model for viscoelastic fluids and the Bingham model for viscoplastic fluids. The momentum and energy equations are solved asymptotically under constant wall heat flux. The fluid behavior is governed by the Weissenberg Wi and the Bingham N numbers.

- by Dennis A . Siginer and +1
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- Engineering, Engineering Physics, Mechanical Engineering, Chemical Engineering

ABSTRACT: This paper presents the preliminary findings of an optimization study of transversal flow strength in tube cross-sections with arbitrary external contours and an internal inclusion. The eccentric tube contours are generated through a one-to-one mapping of a base circular cross-section. The working fluid obeys the non-linear modified Phan-Thien-Tanner (MPTT) constitutive model. The computation of the total transversal flow rate leads to the determination of effective cross-sections for heat transfer enhancement.

- by Dennis A . Siginer and +1
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- Engineering Physics, Mechanical Engineering, Chemical Engineering, Applied Mathematics

ABSTRACT: The temperature distribution and heat transfer coefficient are investigated in forced convection with Newtonian fluids in pressure gradient driven hydrodynamically and thermally fully developed steady laminar flow in transversally corrugated pipes. The governing equations are solved by means of the epitrochoid conformal mapping and exact analytical solutions are derived for the velocity and temperature fields without viscous dissipation. The effect of the corrugations and the number of waves on the friction factor, the temperature distribution and the heat transfer enhancement is discussed.

This paper examines the fundamental characteristics of an inverse liquid - solid inverse fluidized bed reactor. In this reactor , many experiments were performed using three sizes of polypropylene spherical solid, lighter than water with... more

This paper examines the fundamental characteristics of an inverse liquid -
solid inverse fluidized bed reactor. In this reactor , many experiments were performed using three sizes of polypropylene spherical solid, lighter than water with different diameters ..................

- by Inge Hinterwaldner
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- Scientific Visualization, Visual Studies, Visualization, Photography