Steady-state Axisymmetric Flow Research Articles

Axisymmetric forced flow of nonhomogeneous nanofluid over heated permeable cylinders

Investigation of nanofluid properties around a cylinder is carried out for laminar steady-state axisymmetric flow. This study focuses on the porous medium with the existence of laminar and incompressible Newtonian nanofluid in two dimensions and develops an alternative model to avoid the single-phase model limitations considering the influence of Brownian motion and thermophoresis parameter for the nonhomogeneous nanofluid on permeable cylinders. Employing group method and similarity transformation, the governing mathematical model was transformed into a simpler system of ordinary differential equations. The system of equations is numerically computed. The numerical investigation included different governing parameters namely: Prandtl number , thermophoresis parameter , Brownian motion parameter , Reynolds number , and Schmidt number, Sc. Studying these parameters helps to obtain the characteristic of the flow and heat transfer. The numerical examination is illustrated in graphs to examine their effect on different fluid characteristics. Increasing Pr hurdles the nanofluid velocity, temperature, and nanoparticles concentration, while it increases the pressure due to the viscosity increment. Moreover, increasing Nt activates the thermal energy of the nanofluid which in turn increases velocity, temperature distribution, and nanoparticles concentration. A comparison between the obtained results and the previously published results indicated an excellent agreement.

Steady-state axisymmetric flows of an incompressible fluid through rotating porous media with regard to the Coriolis force

Exact solutions to the problem of steady-state axisymmetric flow of an incompressible fluid through rotating rigid body with regard to the centrifugal and Coriolis forces are constructed. The case of the locally transversally isotropic porous skeleton and the quadratic resistance force in the law of flow is considered. Estimates of the practical applicability of the solutions obtained are given. An analysis of increase in the length of the trajectory of a liquid particle due to its deviation from the radial direction in the frame of reference connected with the skeleton is carried out. This is of interest for applications related to deep-bed filtration of suspensions.

Interaction of two spherical particles rotating in a micropolar fluid

The steady-state axisymmetric flow of an incompressible micropolar fluid past two spherical particles is considered. The spherical particles are in general of different sizes and are rotating with different angular velocities about the line connecting their centers. Under the Stokes flow approximation, a general solution is constructed using superposition of the basic solutions in two moving spherical coordinate systems based on the centers of the particles. A collocation technique is used to satisfy the boundary conditions on the surfaces of the particles. Numerical results for the normalized couples acting on each particle are obtained with rapid convergence for various values of the employed parameters.

Sufficient conditions for linear long-wave instability of steady-state axisymmetric flows of an ideal liquid with a free boundary in an azimuthal magnetic field

The problem of linear stability of steady-state axisymmetric shear jet flows of an inviscid ideally conducting incompressible liquid with a free surface and “frozen-in” azimuthal magnetic field is analyzed. The sufficient conditions for theoretical (on semi-infinite time intervals) and practical (on finite time intervals) instability of these flows relative to small axisymmetric long-wave perturbations are obtained by the direct Lyapunov method. An a priori lower estimate indicating (at least) an exponential increase with time of small perturbations under investigation is constructed in the case when these conditions are valid for theoretical as well as practical instability. In addition, an illustrative analytic example of steady-state flows under investigation and small axisymmetric long-wave perturbations superimposed on them is constructed (according to our estimate, these perturbations increase with time).

Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

The results of a numerical study of the laminar-turbulent transition in unsteady isothermal three-dimensional flows of viscous incompressible fluid in a thick spherical layer between counter-rotating spherical boundaries are presented. The calculations are performed for the governing parameters corresponding to the experimental data [1, 2]. The numerical investigations include both solving the complete system of Navier-Stokes equations and analyzing the linear stability of steady-state axisymmetric flows with respect to three-dimensional disturbances. A stochastic flow regime is calculated for the first time. The limits of existence of different flow regimes and the hysteresis regions are found. The spatial flow patterns and frequency characteristics are obtained, which makes it possible to extend and refine the existing experimental data.

Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems

The application of pneumatic metrology to control dimensional accuracy on machined parts is based on the measurement of gas flow resistance through a restricted section formed by a jet orifice placed at a small distance away from a machined surface. The backpressure, which is sensed and indicated by a pressure gauge, is calibrated to measure dimensional variations. It has been found that in some typical industrial applications, the nozzles are subject to fouling, e.g., dirt and oil deposits accumulate on their frontal areas, thus requiring more frequent calibration of the apparatus for reliable service. In this paper, a numerical and experimental analysis of the flow behavior in the region between an injection nozzle and a flat surface is presented. The analysis is based on the steady-state axisymmetric flow of an incompressible fluid. The governing equations, coupled with the appropriate boundary conditions, are solved using the SIMPLER algorithm. Results have shown that for the standard nozzle geometry used in industrial applications, an annular low-pressure separated flow area was found to exist near the frontal surface of the nozzle. The existence of this area is believed to be the cause of the nozzle fouling problem. A study of various alternate nozzle geometries has shown that this low-pressure recirculation area can be eliminated quite readily. Well-designed chamfered, rounded, and reduced frontal area nozzles have all reduced or eliminated the separated recirculation flow area. It has been noted, however, that rounded nozzles may adversely cause a reduction in apparatus sensitivity.

Numerical Analysis on a Flow Field of Liquid Metals Under a Magnetic Field, Using a Spectral Finite Difference Scheme

A steady-state axisymmetric flow field of a liquid metal in a coreless induction furnace under an axisymmetric magnetic field is analyzed numerically, using a spectral finite difference method. Vorticity-stream function formulation is used in conjunction with Maxwell's equations, in a boundary-fitted coordinate system. For boundary conditions, both no-slip on the wall and no shear stress tensor on the free surface are used as dynamic conditions, and a field equivalent to the magnetic field induced by external coils is adopted as an electromagnetic field condition. Presented are streamlines, magnetic streamlines, and radial profiles of the axial velocity component at two Reynolds numbers for various parameters. It is found that the flow field varies remarkably according to the Reynolds number, the dimensionless height of the liquid metal, and the dimensionless height of external coils.

Numerical Simulation of the Fluid Flow and Heat Transfer Processes During Scavenging in a Two-Stroke Engine Under Steady-State Conditions

A numerical simulation of the scavenging process in a two-stroke flat-piston model engine has been developed. Air enters the cylinder circumferentially, inducing a three-dimensional turbulent swirling flow. The problem was modeled as a steady-state axisymmetric flow through a cylinder with uniform wall temperature. The steady-state regime was simulated by assuming the piston head fixed at the bottom dead center. The calculation was performed employing the k–ε model of turbulence. A comparison of the results obtained for the flow field with available experimental data showed very good agreement, and a comparison with an available numerical solution revealed superior results. The effects of the Reynolds number, inlet port angles, and engine geometry on the flow and in-cylinder heat transfer characteristics were investigated. The Nusselt number substantially increases with larger Reynolds numbers and a smaller bore-to-stroke ratio. It is shown that the positioning of the exhaust valve(s) is the main parameter to control the scavenging process.

Helical waves in a liquid film on a rotating disk

The stability of steady-state axisymmetric flow against non-axisymmetric perturbations is considered.

Flow of a viscous liquid film on the surface of a rotating disk

Results are presented from numerical calculations of steady-state axisymmetric flow of a film of viscous incompressible liquid over the surface of a plane rotating disk.

Group properties of the equations of a single jet stream of an ideal fluid

As is well known, considerable mathematical difficulties are encountered in study of the three-dimensional motions of an ideal fluid with free surfaces, since for this case we do not have a powerful mathematical tool at our disposal such as the theory of complex variables, used in the case of two-dimensinnal jet streams [1]. Thus. it is of interest to study a particular form of three-dimensional jet streams of an ideal fluid propagating in a thin layer over an arbitrary hard surface [2-4]. Fluid motions of this type are observed when a hydromonitor jet flows over rock, in the operation of Pelton hydroturbines [2], in equipment for determination of dynamic surface tension [5,6], in the theory of the jet flap and gashydrodynamic vane [7-9], in the atomization of fuel by injectors [:tO], and in various kinds of equipment encountered in chemical engineering [11,12]. In this paper the author investigated the group properties of equations for the axisymmetric jet flow of a thin layer of weightless fluid propagating over an arbitrary surface of rotation, and he constructed some,invariant solutions for these equations. 1. Consider a thin-layer jet stream of an ideal incompressible fluid flowing over an impenetrable smooth surface of rotation S. This motion is referred to a curvilinear orthogonaI coordinate system connected directly to the surface over which the flow passes. An orthogonal family of curvature lines [2] (parallels and meridians) is chosen for the coordinate lines q~ = const and qz = eonst on the surface S. The third coordinate qa is taken in the direction of the external normal of the surface S. In this system of coordinates the Euler equations and the equation of continuity for steady-state axisymmetric flow have the form

Viscous Flow in a Pipe With Absorbing Walls

A study is made of the steady-state axisymmetric flow of a homogeneous viscous liquid in a straight circular pipe with absorbing walls. The complete equations are solved numerically and the streamlines and other features of the flow are computed. Comparison is made with earlier results obtained by various approximate methods.