Journal Of Applied Fluid Mechanics
Volume:7 Issue: 4, Sep-Oct 2014

This paper reports a high accurate solution of the Blasius function f (h) in the form of a converging Taylor’s series for a higher range of h 2 [0;9]. The method used consists of conversion of the boundary value problem into an initial value problem and solution by differential transform method. The initial value of the second derivative of the Blasius function is determined from the final value of first derivative of another function. The final value of first derivative of the latter function is determined by the Taylor’s series expansions with center at h = 15. The series expansion for the Blasius function is obtained with center of expansion at h = 4, is alternating and is accurately converging for higher values of h, with the number of used for summation equal to 2000. The present expansion is obtained without resorting to approximations and has a higher radius of convergence. The first 200 coefficients of the series, the second derivative of the function at h = 0, the parameters of the asymptotic solution are reported with 21 decimal places accuracy. The level of accuracy of the results presented is higher than any other results reported so far. This note also reports the mathematical steps involved in the derivation of the similarity variable of Blasius problem.

Numerous aerodynamic designs of automotive vehicle have been made to reduce aerodynamic drag for lower fuel consumption. Indeed, automotive industry was primarily interested in the passive control based on the shape changes. But, as shape modifications are limited by several factors, this industry is recently more focused on active flow control. In this experimental investigation, the influence of continuous blowing along the sharp edge between the roof and the rear window is addressed. This actuation represents a new configuration based on a steady blowing tangentially to the surface of the rear window of the 25 slanted Ahmed body model. The study was carried out in a wind tunnel at Reynolds numbers based on the model length up to 2:78106. The actuation leads to a maximum drag reduction slightly upper than 10% obtained with a Reynolds number of 1:74106 and a blowing velocity of 0:65V0, where V0 is the freestream velocity. Reductions between 6% and 7% were obtained for the other studied cases. These aerodynamic drag measurements were used to evaluate the actuator efficiency which reveals a maximum efficiency of 9. Visualizations show that tangential steady blowing increase the separated region on the rear window and consequently disrupt the development of the counter-rotating longitudinal vortices appearing on the lateral edges of the rear window. It is also noted that the flow is reattached to the upper half of the rear window. As the actuation occurred directly on the recirculation region at the top of the rear window wall, the flow control was seen very effective.

The Rayleigh-Taylor instability (RIT) at the interface of two superposed Couple-stress Casson fluids flowing in porous medium and in the presence of a uniform normal magnetic field is studied. The fluids have different densities. For mathematical simplicity, the stability analysis based on fully developed approximations is used. The maximum wave numbers and the corresponding maximum frequency are obtained. The Growth rate of Rayleigh-Taylor instability in the case of non-Newtonian Casson fluid with couple-stress through porous medium is discussed. The effects of physical parameters of the problem such as the permeability parameter, magnetic parameter, non-Newtonian Parameter and couple-stress parameter on the regions of stability are discussed numerically and illustrated graphically through a set of figures.

A linear stability analysis is performed to study the effects of through-flow and internal heat generation on the preferred mode of stationary thermal convection in a variable viscosity liquid saturating an anisotropic porous medium. The Rayleigh-Ritz technique is used to obtain the eigenvalue of the problem. The influence of porous parameter, mechanical anisotropy parameter, Peclet number, thermal anisotropy parameter, Brinkman number and variable viscosity parameter on the stability of the system is analyzed. The problem suggests another method of controlling convection by externally controlling porous media damping and shear. This is in addition to the through-flow mechanism of regulating convection.

In the present paper the problem of natural convection of Al2O3-water nanofluid with consideration of variable properties inside a square cavity with different linear temperature distribution on the left wall is investigated numerically. Effects of variations of Rayleigh number, temperature distributions, and volume fraction of nanoparticles on flow and temperature field and rate of heat transfer are studied. The obtained results show that as the temperature distribution on the left wall varies, the flow and temperature patterns inside the cavity vary too. Moreover the existence of the nanoparticles in the base fluid enhances or reduces the average Nusselt number depending on the Rayleigh number and value of the nanoparticles concentration. It is found that at convection dominated regime (Ra=105 and 106), high values of nanoparticles volume fraction motivated the rate of heat transfer to decreases. When the lower end of left wall is cooled and its temperature increases by moving toward the top, a higher Nusselt number is obtained.

An analysis of visco-elastic free convective transient MHD flow over a vertical porous plate through porous media in presence of radiation and chemical reaction with heat and mass transfer is presented. A transverse variable suction velocity is applied on the porous plate. The equations governing the fluid flow, heat and mass transfer are solved by applying multiple perturbation technique. The expressions for transient velocity, temperature, species concentration and non-dimensional skin friction at the plate are obtained and the expressions for transient velocity and non-dimensional skin friction at the plate are illustrated graphically to observe the visco-elastic effect in combination of other flow parameters involved in the solution.

The local scour of a non-cohesive bed due to a 2-D submerged horizontal jet is investigated experimentally in presence of a protection apron. Previous researches conducted without protection apron demonstrate that, when the tailwater depth is either deep or shallow, the equilibrium state characteristics of the scoured bed profile are mainly a function of the densimetric Froude number. However, when the submergence is between these two extremes, at fixed Froude number, three different scour regimes are possible. For relatively shallow tailwater depths, the jet mainstream directs towards the free surface (surface jet scouring regime), determining shallow and elongated scour profiles. For relatively large tailwater depths, the jet remains attached to the channel bottom (bed jet scouring regime), leading to deeper and shorter scour profiles. For intermediate conditions, the flicking of the jet between the erodible bed and the water free-surface is possible. When this instability occurs, the shape of the scour hole rapidly changes as a response of the jet mainstream position (bed-surface jet scouring regime). This paper aims to give an experimental description of the three mentioned regimes when a protection apron partly reduces the action of the flow on the loose bed. Scour hole profile evolution and velocity profile measurements obtained by LDA and ADV velocimetry are discussed.

In this study, we aimed to determine the relationship between thrust generation and fish fin shape. To compare the effect fin shape had on thrust generation, we categorized the morphological shapes of fish fins into equilateral polygonal shapes. Polygonal fins were used to generate thrust that depended only on shape. These fins were constructed of a hard elastic material to eliminate any influence of shape deformation. A servomotor with a reciprocal rotation moved a fin cyclically, and thrust was experimentally measured using a strain gage system. Thrust tended to be proportional to the inertia moment of a fin, which indicated difficulty with rotation. Moreover, this trend for thrust generation was directly related to the number of apexes of a polygonal fin. The force translated ratio, which was thrust divided by the force required for fin rotation, was evaluated to determine the hydrodynamic characteristics of fins. This finding showed that the force translated ratio of a fin increased with increased movable perimeter length. The greatest thrust was generated by a triangular fin rotated at its apex, which is often seen in general fish tail fins, whereas the hydrodynamic characteristics were the worst in polygonal fins.

Flow of a viscoelastic fluid through a channel with stretching walls in the presence of a magnetic field has been investigated. The viscosity of the fluid is assumed to vary with temperature. Convective heat transfer is considered along with viscous dissipation and Ohmic dissipation. The equations that govern the motion of the fluid and heat transfer are coupled and non-linear. The governing partial differential equations are reduced to a set of ordinary differential equations by using similarity transformation. The transformed equations subject to the boundary conditions are solved by developing a suitable finite difference scheme. Numerical estimates of the flow and heat transfer variables are obtained by considering blood as the working fluid. The computational values are found to be in good agreement with those of previous studies.

A numerical analysis has been carried out to study the effects radiation and heat source/sink on the steady two dimensional magnetohydrodynamic (MHD) boundary layer flow of heat and mass transfer past a shrinking sheet with wall mass suction. In the dynamic system, a uniform magnetic field acts normal to the plane of flow. The governing partial differential equations are transformed into self-similar equations are solved by employing finite difference using the quasilinearization technique. From the analysis it is found that the velocity inside the boundary layer increases with increase of wall mass suction and magnetic field and accordingly the thickness of the momentum boundary layer decreases. The temperature decreases with Hartmann number, Prandtl number, and heat sink parameter and the temperature increases with heat source parameter, radiation parameter. The concentration decreases with an increase of Hartmann number, mass suction parameter, Schmidt number, chemical reaction parameter.

We report on applications of a moiré deflectometry to observations of anisotropy in the statistical properties of atmospheric turbulence. Specifically, combining the use of a telescope with moiré deflectometry allows enhanced sensitivity to fluctuations in the wave-front phase, which reflect fluctuations in the fluid density. Such phase fluctuations in the aperture of the telescope are imaged on the first grating of the moiré deflectometer, giving high spatial resolution. In particular, we have measured the covariance of the angle of arrival (AA) between pairs of points displaced spatially on the telescope aperture which allows a quantitative measure of anisotropy in the atmospheric surface layer. Importantly, the telescope-based moiré deflectometry measures directly in the spatial domain and, besides being a non-intrusive method for studying turbulent flows, has the advantage of being relatively simple and inexpensive.

The numerical simulation and wind tunnel experiment were employed to investigate the aerodynamic characteristics of three typical rear shapes: fastback, notchback and squareback. The object was to investigate the sensibility of aerodynamic characteristic to the rear shape, and provide more comprehensive experimental data as a reference to validate the numerical simulation. In the wind tunnel experiments, the aerodynamic six components of the three models with the yaw angles range from -15 and 15 were measured. The realizable k-ε model was employed to compute the aerodynamic drag, lift and surface pressure distribution at a zero yaw angle. In order to improve the calculation efficiency and accuracy, a hybrid Tetrahedron-Hexahedron-Pentahedral-Prism mesh strategy was used to discretize the computational domain. The computational results showed a good agreement with the experimental data and the results revealed that different rear shapes would induce very different aerodynamic characteristic, and it was difficult to determine the best shape. For example, the fastback would obtain very low aerodynamic drag, but it would induce positive lift which was not conducive to stability at high speed, and it also would induce bad crosswind stability. In order to reveal the internal connection between the aerodynamic drag and wake vortices, the turbulent kinetic, recirculation length, position of vortex core and velocity profile in the wake were investigated by numerical simulation and PIV experiment.

A steady multiple reference frame segregated compressible solver and an unsteady sliding mesh one are developed using OpenFOAM® to simulate turbomachinery. For each of the two solvers, governing equations, numerical approach and solver structure are explained. Pressure and energy equation are implemented so as to obtain the best numerical properties, such as the ability to use large time-steps. Sod shock tube test case is used to assess the prediction of compressible phenomena by the transient scheme, which shows proper resolution of compressible waves. Both solvers are used to simulate a turbocharger turbine, comparing their solutions to corresponding ones using ANSYS® Fluent® as a means of validation. The multiple reference frame solver global results quantitatively differ from those computed using ANSYS Fluent, although predicted flow features match. The solution obtained by the sliding mesh solver presents better agreement compared to ANSYS Fluent one.

The effects of Hall currents and radiation on MHD flow of a viscous incompressible electrically conducting fluid past a moving vertical plate with variable temperature in the presence of a uniform transverse magnetic field have been studied. The governing equations are solved analytically using the Laplace transform technique. Effects of the physical parameters on the velocity (both primary and secondary) profiles and temperature distribution are shown graphically and the results are discussed.

Finite-element based CFD solvers like the family of Discontinuous Galerkin (DG) solvers suffer severely from inaccurate boundary reconstruction. In this matter, developing an accurate and flexible strategy is highly demanded to provide high-order curved boundary representation in DG simulations. In this paper, a general framework is introduced to design the curved elements in discontinuous Galerkin finite-element (DGFEM) simulations. The aim is to connect the boundary to the surrounding mesh by defining an appropriate set of basis functions which deliver the curvature information inside the mesh region adjacent to the boundary. This information is then used in flux integral calculations. The proposed framework is applied in Lagragian and Hermitian boundary representations. The efficiency of the method is analyzed for compressible inviscid flow test cases using the discontinuous Galerkin scheme. It is illustrated that using the curved-side elements in the present approach, is adequate to reduce the artificial entropy generation near the boundaries. This leads to the simulations with the desired order of accuracy. The results show a well consistency in h/p-refinement which advocates the use of the proposed approach in high-order CFD simulations.

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a shrinking sheet is studied. The effects of an induced magnetic field and thermal radiation are taken into account. Velocity and thermal slip conditions have also been incorporated in the study. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using Newton’s linearization method. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented graphically and in tabular form. Study reveals that the surface velocity gradient and heat transfer are enhanced by decreasing magnetic parameter.

A spectral homotopy analysis method (SHAM) is used to find numerical solutions for the unsteady viscous flow problem due to an infinite rotating disk. The problem is governed by a set of two fully coupled nonlinear partial differential equations. The method was originally introduced for solutions of nonlinear ordinary differential equations. In this study, its application is extended to a system of nonlinear partial differential equations (PDEs) that model the unsteady von Kàrmàn swirling flow. Numerical values of the pertinent flow properties were generated and validated against results obtained using the Keller-box numerical scheme. The results indicate that the present method is very accurate and can be used as an efficient tool for solving nonlinear PDEs of the type discussed in this paper.