Numerical simulation of flow of a micropolar fluid between a porous disk and a non-porous disk

Two dimensional steady, laminar and incompressible motion of a micropolar fluid between an impermeable disk and a permeable disk is considered to investigate the influence of the Reynolds number and the micropolar structure on the flow characteristics. The main flow stream is superimposed by constant injection velocity at the porous disk. An extension of Von Karman’s similarity transformations is applied to reduce governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. An algorithm based on finite difference method is employed to solve these ODEs and Richardson’s extrapolation is used to obtain higher order accuracy. The numerical results reflect the expected physical behavior of the flow phenomenon under consideration. The study indicates that the magnitude of shear stress increases strictly and indefinitely at the impermeable disk while it decreases steadily at the permeable disk, by increasing the injection velocity. Moreover, the micropolar fluids reduce the skin friction as compared to the Newtonian fluids. The magnitude of microrotation increases with increasing the magnitude of R and the micropolar parameters. The present results are in excellent comparison with the available literature results.     

Direct Numerical Simulation of turbulent heat transfer behind a backward-facing step at low Prandtl number

The paper presents Direct Numerical Simulations of the turbulent flow of a low Prandtl number fluid over a backward-facing step with heat transfer. The backward-facing step flow is investigated as a generic configuration for sudden changes in cross section. Several simulations are reported: for isothermal conditions, for heat transfer with the Prandtl number of air, and for heat transfer with the Prandtl number of liquid sodium. The simulation for air is compared to results from literature. The differences induced by reduction of the Prandtl number are then assessed by comparison of the two cases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of the basic stationary spherical couette flows at low Reynolds numbers

Previously developed iterative numerical methods with splitting of boundary conditions intended for solving an axisymmetric Dirichlet boundary value problem for the stationary Navier-Stokes system in spherical layers are used to study the basic spherical Couette flows (SCFs) of a viscous incompressible fluid in a wide range of outer-to-inner radius ratios R/r (1.1 ≤ R/r ≤ 100) and to classify such SCFs. An important balance regime is found in the case of counter-rotating boundary spheres. The methods converge at low Reynolds numbers (Re), but a comparison with experimental data for SCFs in thin spherical layers show that they converge for Re sufficiently close to Re_cr. The methods are second-order accurate in the max norm for both velocity and pressure and exhibit high convergence rates when applied to boundary value problems for Stokes systems arising at simple iterations with respect to nonlinearity. Numerical experiments show that the Richardson extrapolation procedure, combined with the methods as applied to solve the nonlinear problem, improves the accuracy up to the fourth and third orders for the stream function and velocity, respectively, while, for the pressure, the accuracy remains of the second order but the error is nevertheless noticeably reduced. This property is used to construct reliable patterns of stream-function level curves for large values of R/r. The possible configurations of fluid-particle trajectories are also discussed.     

Operator splitting for the numerical solution of free surface flow at low capillary numbers

Free surface flows are pervasive in engineering and biomedical applications. In many interesting cases—particularly when small length scales are involved—surface forces (capillarity) dominate the flow dynamics. In these cases, computing the flow together with the shape of the surfaces, requires specialized solution techniques. This article investigates the capabilities of an operator splitting/finite elements method at handling accurately incompressible viscous flow with free surfaces at low capillary numbers. The test case of flow in the downstream section of a slot coater is used for three reasons: (1) it is an established benchmark; (2) it represents an idealized, yet industrially relevant flow; (3) high-fidelity results obtained with monolithic algorithms are available in literature. The flow and free surface shape attained with the new operator splitting scheme agree very satisfactorily with the results obtained with monolithic solvers. Because of its inherent computational simplicity, the new operator splitting scheme is attractive for large-scale simulations, three-dimensional flows, and flows of complex fluids.     

On the steady flow between a rotating and a stationary disk with a uniform suction at the stationary disk

Summary The steady axisymmetric flow of a viscous incompressible fluid between two coaxial disks, one rotating and the other stationary, with uniform suction at the stationary disk is discussed. Similarity solutions of Navier-Stokes equations are obtained by the method of regular perturbation for small suction Reynolds number and numerically for an arbitrary suction Reynolds number by a series expansion method and also by integrating directly by a Newton-Raphson technique. It is found that for a fixed rotational Reynolds number and varying suction Reynolds number there is an overall increase in the velocity components as the suction increases.

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Zusammenfassung Es wird die stationäre axisymmetrische Strömung zwischen zwei koaxialen Platten untersucht, von denen die eine rotiert und die andere stationär ist, wobei an der stationären Platte eine gleichförmige Absaugung stattfindet. Ähnlichkeitslösungen der Navier-Stokesschen Gleichungen werden erhalten, durch eine reguläre Störungsrechnung bei kleinen Absaug-Reynoldszahlen, während bei beliebigen Werten dieses Parameters numerische Resultate sowohl durch eine Reihenentwicklung wie auch durch direkte Integration mit Hilfe der Newton-Raphson-Technik gefunden werden. Bei fester Rotations-Reynoldszahl und variabler Absaugung findet man eine allgemeine Erhöhung der Geschwindigkeits-komponenten mit der Absaugung.

     

Kinetic model of the Boltzmann equation with limiting gas flow regimes at low Knudsen numbers

A new model of the Boltzmann kinetic equation is constructed that describes both slow nonisothermal and Navier-Stokes continuum gas flows. The model is used to compute the slow nonisothermal flow past a circular cylinder. It is shown that the force exerted by the gas on the cylinder is affected by thermal stresses.     

The asymptotic form of the stationary separated circumfluence of a body at high reynolds numbers

An asymptotic theory of the stationary separated circumfluence of bodies at high Reynolds numbers, Re, is constructed. It is shown that the length and width of the separated zone (SZ) is proportional to Re and that the drag cofficient is proportional to Re⁻¹. A cyclic boundary layer is located around the separated zone with a constant vorticity. In the scale of the body, the flow tends towards a Kirchhoff flow with a velocity on a free line of flow of the order of Re^−1/2 which satisfies the Brillouin-Villat condition.

A review of the attempts which have been made to describe the two-dimensional separated circumfluence of a body at high Reynolds numbers is given in /1, 2/. Certain features of the asmyptotic structure of the solution based on qualitative arguments were pointed out in /3, 4/. The corresponding shape of the separated zone was calculated in /5/. However, no complete theory was constructed in these papers. The appearance of the numerical calculations in /6, 7/ stimulated further investigations and a model with a non-zero jump in the Bernoulli constant on the boundary of the separated zone was proposed in /8/. A number of hypotheses concerning the limiting structure of the flow were put forward in /9/.

In the solution obtained below the flow in the scale of the body is described as in /1, 2/ but the velocity is of the order of Re^−1/2. The flow characteristics in this zone are correspondingly renormalized. The flow in the scale of the separated zone corresponds to the assumptions made in /3, 4/. Unlike in /1–4/, the flow in the scale of the body is not directly combined with the flow in the scale of the separated zone. There are several embedded zones and the possibility of uniting these ensures the selfconsistency of the expansion. Moreover, the cyclic boundary layer on the boundary of the separated zone plays an important role.     

Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk

In this investigation, thermal radiation effect over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour diffusion effects is investigated. The partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically using fourth order Runge–Kutta based shooting method. The effects of the magnetic interaction parameter, slip flow parameter, Soret number, Dufour number, Schmidt number, radiation parameter, Prandtl number and suction parameter on the fluid velocity, temperature and concentration distributions in the regime are depicted graphically and are analyzed in detail. The corresponding skin-friction coefficients, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on them.     

Numerical and experimental investigation of the turbulent flow through a low-pressure turbine cascade in the endwall region

In the present work, direct numerical simulations (DNS) of the flow through a low-pressure linear turbine cascade T106 with parallel endwalls were conducted to investigate the effects of unsteady passing wakes of the upstream blade row on the secondary flow in the endwall region of the passage. The impact of the wakes on the secondary flow is discussed by means of the time-averaged values. Furthermore, the results of DNS are compared with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk

The purpose of present research is to derive analytical expressions for the solution of steady MHD convective and slip flow due to a rotating disk. Viscous dissipation and Ohmic heating are taken into account. The nonlinear partial differential equations for MHD laminar flow of the homogeneous fluid are reduced to a system of five coupled ordinary differential equations by using similarity transformation. The derived solution is expressed in series of exponentially-decaying functions using homotopy analysis method (HAM). The convergence of the obtained series solutions is examined. Finally some figures are sketched to show the accuracy of the applied method and assessment of various slip parameter γ, magnetic field parameter M, Eckert Ec, Schmidt Sc and Soret Sr numbers on the profiles of the dimensionless velocity, temperature and concentration distributions. Validity of the obtained results are verified by the numerical results.     

MHD non-Newtonian flow due to non-coaxial rotations of an accelerated disk and a fluid at infinity

The magnetohydrodynamic (MHD) flow due to non-coaxial rotations of a porous disk, moving with uniform acceleration in its own plane and a second grade fluid at infinity is examined. The fluid is electrically conducting in the presence of a uniform magnetic field. The effects of non-Newtonian fluid characteristics and uniform acceleration of the disk on the velocity field are presented both analytically and numerically. A very good accuracy has been seen.     

On the numerical solution of the flow between a rotating and a stationary disk

The flow between two co-axial, infinite disks, one rotating with constant angular velocity and one stationary is treated in this paper. The problem is reduced to that of finding the solution of a two-point boundary value for a sixth order nonlinear ordinary differential equation and three boundary conditions at each of a finite interval. The numerical solutions are obtained by using a fourth order Runge-Kutta integration scheme in modification due to Gill and in conjunction with a modified shooting method to correct the initial guesses at one boundary. The numerical calculations for different Reynolds numbers are carried out. The results obtained by this method are compared with available results. The comparison shows excellent agreement.     

Numerical investigation of the effect of helix angle and leaf margin on the flow pattern and the performance of the axial flow cyclone separator

A two-stage turbulence model based on the RNG κ–ε model combined with the Reynolds stress model is developed in this paper to analyze the gas flow in an axial flow cyclone separator. Five representative simulation cases are obtained by changing the helix angle and leaf margins of the cyclone. The pressure field and velocity field of the five cases are simulated, and then the effects of helix angle and leaf margins on the internal flow field of the cyclone are analyzed. When the continuum fluid (air) flow is relatively convergent, the discrete particle phase is added into the continuous phase and the gas-solid two-phase flow is simulated. One-way coupling method is used to solve the two-phase flow and a stochastic trajectory model is implemented for simulation of the particle phase. Finally, the pressure drop and separation efficiency of one case are measured and compare quantitatively well with the numerical results, which validates the reliability and accuracy of the simulation method based on the two-stage turbulence model.     

On the steady flow of a viscous fluid past a sphere at small reynolds numbers using Oseen's approximation

Sommaire On a obtenu une expression générale pour la fonction de courant deStokes pour l'écoulement d'un liquide visqueux autour d'une sphère. Les lignes de courant ont été tracés pour les nombres deReynolds=1, 4 et 10. Le décollement du courant fluide n'a pas lieu pour les N. R.=1 et 4, tandis que pour le N. R.=10 les tourbillons attachés se forment dans le sillage.     

Large eddy simulations of the turbulent flow between a rotating and a stationary disk

Large eddy simulations of the flow between a rotating and a stationary disk have been performed using a dynamic and a mixed dynamic subgrid-scale model. The simulations were compared to direct numerical simulation results. The mixed dynamic model gave better overall predictions than the dynamic model. Modifications of the near-wall structures caused by the mean flow three-dimensionality were also investigated. Conditional averages near strong stress-producing events led to the same conclusions regarding these modifications as studies of the flow generated by direct numerical simulation, namely a distinct asymmetry of the vortices producing sweeps and ejections.     

Large eddy simulations of the turbulent flow between a rotating and a stationary disk

Large eddy simulations of the flow between a rotating and a stationary disk have been performed using a dynamic and a mixed dynamic subgrid-scale model. The simulations were compared to direct numerical simulation results. The mixed dynamic model gave better overall predictions than the dynamic model. Modifications of the near-wall structures caused by the mean flow three-dimensionality were also investigated. Conditional averages near strong stress-producing events led to the same conclusions regarding these modifications as studies of the flow generated by direct numerical simulation, namely a distinct asymmetry of the vortices producing sweeps and ejections.     

Analytical and numerical simulation investigation in effects of radiation and porosity on a non-orthogonal stagnation-point flow towards a stretching sheet

The steady two-dimensional non-orthogonal flow near the stagnation point on a stretching sheet embedded in a porous medium in the presence of radiation effects is studied. Using similarity variables, the nonlinear boundary-layer equations are solved analytically by homotopy perturbation method (HPM) employing Padé technique. Comparison between the results of HPM-Padé solution and numerical simulation as well as some other results which are available in the literature, demonstrates a very good agreement between them and the HPM-Padé solution provides a convenient way to control and adjust the convergence region of a system of nonlinear boundary-layer problems with high accurate. The effect of involved parameters such as striking angle, radiation parameter, porosity parameter and the Prandtl number on flow and heat transfer characteristics have been discussed with more details.     

Numerical modeling of baffle location effects on the flow pattern of primary sedimentation tanks

Computational fluid dynamics (CFD) is used extensively by engineers to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance and supply efficiency. In order to find the optimal position of a baffle in a rectangular primary sedimentation tank, computational investigations are performed. Also laboratory experiments are conducted to verify the numerical results and the measured velocity fields which were by Acoustic Doppler Velocimeter (ADV) are used. The GMRES algorithm as a pressure solver was used in the computational modeling. The results of computational investigations performed in the present study indicate that the favorable flow field (uniform in the settling zone) would be enhanced for the case that the baffle position provide small circulation regions volume and dissipate the kinetic energy in the tank. Also results show that the GMRES algorithm can obtain the good agreement between the results of numerical models and experimental tests.     

Integral analysis of the flow dynamics and mass transfer in a wavy liquid film on a spinning disk

In the present work the complex process of diffusion-controlled wet chemical etching of a rotating silicon wafer is analyzed in the framework of an unsteady integral boundary layer approximation. The obtained results reproduce the waviness and the associated enhancement of the mass transfer in the wavy region, and are in good agreement with experimental findings. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intercellular edema as a result of the reduced efficiency of the cellular membranes at low body temperatures

The desirability of pre-operative preparation of the patient with preparations rich in highly unsaturated fatty acids is demonstrated with reference to the results of a biochemical investigation of the blood serum and a morphological investigation of myocardial biopsy material obtained in experments on 60 nonpedigreed dogs and in the course of 80 clinical operations.