Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Hydrodynamics and oxygen transfer in a novel extra-loop fluidized bed bioreactor

In this paper, the characteristics of fluid mixing time in a novel extra-loop fluidized bed were studied. The results showed that the mixing time was shortened with the increase of fluid velocity. All the discrete numbers of the reactor were above 0.2. The serial number n was 2.5 -3.0. It was judged accordingly that the reactor fluid state was continous stirred tank reactor （CSTR） mainly. When the inspiratory capacity increased the mixing time of the reactor was shortened. Thus the air input was beneficial for the fluid mixing. During the three phases mixing process, the mixing time of the reactor could be decreased by the n increase of carrier and air loading together, but the change was not significant. The parameters affecting the reactor fluid state were fluid velocity, inspiratory capacity and carrier. KLa could be increased with the air loading increase, and at the same gas/liquid ratio when the pressure drop was high, KL~ value was increased. The amount of carrier complex influence on KLa. As the carrier loading continued to increase, its value had been dropped but the changes was not significant, and optimization condition was found at above 800 1 000 g carrier loading （pouzzolane） or 600 g PVC. Under gas/liquid ratio of 0.8% -5.2%, KLa was （0.62-1.37）×10^-2· s^-1.

Fluid flow characteristics of single inclined circular jet impingement for ultra-fast cooling

The fluid flow characteristics of the single bunch inclined jet impingement were investigated with different jet flow velocities,nozzle diameters,jet angles and jet-to-target distances for ultra-fast cooling technology.The results show that the peak pressure varying significantly from nearly 0.5 to above 13.4 kPa locates at the stagnation point with different jet diameters,and the radius of impact pressure affected zone is small promoted from 46 to 81 mm in transverse direction,and 50 to 91 mm in longitude direction when the jet flow velocity changes from 5 to 20 m/s.However,the fluid flow velocity is relatively smaller near the stagnation point,and increases gradually along the radius outwards,then declines.There is an obvious anisotropic characteristic that the flow velocity component along the jet direction is about twice of the contrary one where the jet anlge is 60°,jet diameter is 5 mm,jet length is 8 mm and jet height is 50 mm.

COMPUTATIONAL FLUID DYNAMICS RESEARCH ON PRESSURE LOSS OF CROSS-FLOW PERFORATED MUFFLER

The pressure loss of cross-flow perforated of physical modeling, simulation and data processing. muffler has been computed with the procedure Three-dimensional computational fluid dynamics （CFD） has been used to investigate the relations of porosities, flow velocity and diameter of the holes with the pressure loss. Accordingly, some preliminary results have been obtained that pressure loss increases with porosity descent as nearly a hyperbolic trend, rising flow velocity of the input makes the pressure loss increasing with parabola trend, diameter of holes affects little about pressure loss of the muffler. Otherwise, the holes on the perforated pipes make the air flow gently and meanly, which decreases the air impact to the wall and pipes in the muffler. A practical perforated muffler is used to illustrate the available of this method for pressure loss computation, and the comparison shows that the computation results with the method of CFD has reference value for muffler design.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

COMPUTER SIMULATION OF CONTINUOUS ELECTROMAGNETIC STIRRING FOR MAKING RHEOLOGIC SEMI-SOLID SLURRY OF ZL112Y ALUMINUM ALLOY

To realize the technology of fabricating the rheologic semi-solid slurry of ZL112Y aluminum alloy via continues electromagnetic stirring process, ANSYS software was used to simulate electromagnetic force field and fluid velocity field in the alloy melt in a crucible tube in three coils. In the first section of the paper, eletromagnetic force field and fluid velocity field caused by single coil were simulated. The result of this simulation gives an average velocity of 3.2 cm/s and it is called critical velocity because a fluid velocity over it will cause a fine and spherical structure of solid primary a in a semi-solid melt. And, from this result, a reasonable temperature of semi-solid of the alloy and an electrical current intensity were established. The electrical current intensity of the result of this simulation corresponded to the current intensity used in a practice experiment, in which the primary α was obviously refined and sphericized. Based on this simulation of single coil electromagnetic stirring, in the second section of the paper, eletromagnetic force field and fluid velocity field caused by three coils were simulated. The result of the simulation shows that, 1） there is a semi-solid zone of 32 mm from bottom of the crucible tube to the upper; 2） the electrical current intensities of three coils of 400 A, 600 A, and 400 A, which were set to top range, middle range and bottom range of the tube, respectively, were the optimum parameters of electromagnetic current intensity under the condition of this investigation; and 3） under effect of these electromagnetic current intensity, the fluid velocities of the melt in the tube were 6.3 cm/s in top range, 3.75 cm/s in middle range, and 3.9 cm/s in bottom range of it, respectively.

Breaking of Solitary Waves on Uniform Slopes

The propagation, shoaling and breaking of solitary waves on mild slopes are simulated by boundary element method. In this paper, the criterion of breaking solitary waves on mild slopes is discussed. The criterion is that the ratio of horizontal velocity of water particles on the wave crest to wave celerity equals one. However, the case that the ratio of horizontal velocity of water particles on the wave crest to wave celerity is below one but the front face of wave profile becomes vertical is also considered as a breaking criterion. According to the above criteria, the breaking index for slopes 1:10 to 1:25 is studied. The result is compared to other researchers'. The deformation of solitary waves on slopes is discussed and the distribution of fluid velocities at breaking is shown.

A High-Mathematical Model Optimizing Cuttings Transport in Oil Drilling Engineering

With special drilling operation equipment and specific conditions of geology, how does drilling fluid carry cuttings effectively? So far, it is still an urgent problem for drilling researchers to study. This work just aims at the actual engineering background to develop studying model. In this paper, according to non Newtonian fluid mechanics, the law of the solid liquid, two phase fluid flow and actual drilling engineering, the major factors affecting cuttings transport are drilling fluid velocity, hole inclination and fluid rheological properties. Getting a clear understanding of the law of drilling fluid and its cutting taking mechanism, this paper puts forward a model for analysis of field data and quantitative forecast of cutting taking capability of drilling fluid. The full scale annular test section was 6.1 m with 76 and 114 mm drillpipe in a 203 mm ID (wellbore diameter). Hole angle varied from 0° to 90°.

Experimental Investigation of Instantaneous Properties of Wave Slamming on the Plate

The purpose of this paper is to investigate the instantaneous properties of wave slanuning on the plate structure of an open structure. The advanced instantaneous measuring technique-Particle Image Velocimetry （PIV） is applied to acquire the instantaneous velocity field of wave slamming. From the cross-correlation analysis results of the images captured by the CCD camera, the flow fields of wave impacting on the structure are displayed visually, and the instantaneous whole- field fluid velocity vectors are obtained. The relation between the instantaneous peak impacting pressures and the instantaneous velocities of water particles is studied by probability analysis.

AN IMPROVEMENT FOR LOWER－ORDER PANEL METHOD BASED ON THE DIRICHLET BOUNDARY CONDITION

An improved algorithm for velocity field of general configurations ispresentd for low-order panel method based on the internal Dirichlet boundary condi-tion. A direct calculating method for the velocity distribution by means of a limit pro-cess combining with analytic evaluation of higher-order singular integrals instead of theconventional method of doublet strength gradient is devised in order to avoid the diffi-culty of edge extrapolation of doublet strength. The problem of substantialunderpredictions of the induced drag coefficient obtained from the VSAERO analysisdisappears for the present improved algorithm. Illustrative calculations for several testcases such as swept back wing, swept forward wing and wing-body combination showthat the accuracy of results may be improved and is competitive with high-order panelmethod. In addition, the present direct integral method can be used to evaluate the ve-locity distribution for external flow field correctly, where the method of gradient cannot be used at all.

Theoretical investigation on the cavitation bubble dynamics near three spherical particles based on Weiss theorem

To research the dynamics of the cavitation bubble under the interaction of particle clusters,the bubble morphological evolutionary characteristics near three equal-sized spherical particles are theoretically explored in the present study based on the Weiss theorem and the velocity potential superposition theory.The three particles are arranged symmetrically,and the fluid velocity field near the three particles and the cavitation bubble is obtained.Moreover,the effects of the bubble-particle distance and the maximum radius of the cavitation bubble on the fluid velocity are investigated,and the contribution mechanisms of the fluid velocity field constituents are compared.The analysis has found that:(1)The fluid velocity between the bubble and the particle is lower than that at the other locations in both the growth and collapse phases,thus the bubble cannot always maintain a standard spherical shape.(2)The bubble-particle distance and the maximum radius of the cavitation bubble are the key parameters affecting the circumferential inhomogeneity of the radial velocity of the fluid around the bubble.The larger the maximum radius or the smaller the bubble-particle distance is,the more visible the non-circularity of the bubble morphology.(3)The image bubbles and the linear sinks contribute oppositely to the fluid velocity field,and the presence of the image bubble reduces the fluid velocity.In the low velocity region,the image bubble is the main mechanism contributing to the effect of the particle on the fluid velocity.

Flow field and pressure loss analysis of junction and its structure optimization of aircraft hydraulic pipe system

The flow field in junction is complicated due to the ripple property of oil flow velocity and different frequencies of two pumps in aircraft. In this study, the flow fields of T-junction and Y-junction were analyzed using shear stress transport （SST） model in ANSYS/CFX software. The simulation results identified the variation rule of velocity peak in T-junction with different frequencies and phase-differences, meanwhile, the eddy and velocity shock existed in the corner of the T-junction, and the limit working state was obtained. Although the eddy disappeared in Y-junction, the velocity shock and pressure loss were still too big. To address these faults, an arc-junction was designed. Based on the flow fields of arc-junction, the eddy in the junction corner disappeared and the maximum of velocity peak declined compared to T-and Y-junction. Additionally, 8 series of arc-junction with different radiuses were tested to get the variation rule of velocity peak. Through the computation of the pressure loss of three junctions, the arc-junction had a lowest loss value, and its pressure loss reached the minimum value when the curvature radius is 35.42 mm, meanwhile, the velocity shock has decreased in a low phase.

Measurements of Water-Air Flow Phenomena in a Chamber with a Rotating Shaft

The paper concerns the phenomena of the fluid film that occurs in the bearing chamber of an aircraft engine.The geometry of the system includes two concentric cylinders,between which there is a mixture of oil and air.The fluid circulates in a closed circuit.The rotary movement of the inner cylinder causes creation of the fluid film on the walls of the chamber.The article proposes a measurement method that is allowing observation of this fluid film and,in particular,analysis of the movement of the air bubbles occurring in the film.An own model of the bearing chamber with transparent walls was constructed for the research.For the investigation,water was used instead of oil.Observation of the behaviour of the flow was possible thanks to video recordings made with the use of a fast-capture camera.The results presented in the paper include velocity magnitudes of the air bubbles in the fluid film in dependence on the rotational speed of the shaft and water volume fraction and with a range from 0.37 to 0.91 m/s.The results presented in this article can be used for the bearing chamber numerical models validation.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.