Radius Of Inner Cylinder Research Articles

Effects of the parameters of inner air cylinder on evolution of annular SF6 cylinder accelerated by a planar shock wave

Based on the compressible Navier–Stokes equations combined with the fifth-order weighted essentially non-oscillatory scheme, this paper discusses the interaction of a planar shock wave with an annular SF6 cylinder. The influence of the position and radius of inner cylinder on the evolution of the annular cylinder is examined in detail. Numerical schlieren results clearly show the evolution of the inner and outer interfaces induced by the Richtmyer–Meshkov instability and reveal the evolution of complex shock wave structures as the incident planar shock interacts with the annular cylinder. Shock transformation from the free precursor refraction pattern to the free precursor von Neumann refraction pattern occurs when the inner cylinder position shifts forward, while the shock transformation from the twin von Neumann refraction pattern to the free precursor refraction pattern and the shock transformation from free precursor refraction pattern to the free precursor von Neumann refraction pattern occur when the radius of the inner cylinder gradually becomes larger. The generation and transportation of vorticity on the interfaces are also analyzed, revealing that changes to the inner cylinder play a significant role. The distribution and evolution of vorticity on the interfaces influence the formation of the primary vortex structure at later stages. Quantitative analysis of the circulation and enstrophy indicates that the smaller the inner radius, the larger the value of circulation and enstrophy at the later stage.

A numerical study on the three-dimensional natural convection with a cylinder in a long rectangular enclosure. Part I: Size effect of a circular cylinder or an elliptical cylinder

This study conducted three-dimensional numerical simulations of the natural convection in a long, cold, rectangular enclosure containing a hot, circular cylinder or an elliptical cylinder. The immersed boundary method (IBM) was used to capture the virtual wall boundary of the cylinder based on the finite volume method (FVM). Four radii of inner cylinders were considered in the Rayleigh number range of 104 ≤ Ra ≤ 106 as key simulation parameters to investigate the size effect of the circular and elliptical cylinders. The detailed effects were analyzed by visualization of the three-dimensional iso-surfaces of the temperature and vortical structures, as well as the three-dimensionality in the system. The heat transfer characteristics from the surfaces of a circular cylinder or elliptical cylinder and the walls of enclosure were addressed. The heat transfer characteristics were affected by the radius of the circular and elliptical cylinders.

Magnetohydrodynamic nanofluid convection in a porous enclosure considering heat flux boundary condition

Magnetohydrodynamic CuO-water nanofluid flow in a porous semi annulus with constant heat flux is studied by means of Control Volume based Finite Element Method. Koo-Kleinstreuer-Li correlation and Darcy model are applied for nanofluid and porous media, respectively. Effective parameters are radius of inner cylinder, CuO-water volume fraction, Hartmann and Rayleigh numbers for porous medium. A formula for Nuave is presented. Results revealed that heat transfer augmentation decreases with rise of buoyancy forces. Influence of adding nanoparticle augments with increase of Lorentz forces. Increasing Hartmann number leads to a reduction in temperature gradient.

Transient free convective flow in an annular porous medium: A semi-analytical approach

The transient fully developed free-convective flow of viscous incompressible fluid between two concentric vertical cylinders filled with porous material and saturated with the same fluid have been analysed due to isothermal or isoflux heating of the outer surface of inner cylinder. The governing partial differential equations of motion and energy are transformed into ordinary differential equations using Laplace transform technique. The ordinary differential equations are then solved analytically in Laplace domain. The Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparison with closed form solution obtained for steady states which has been obtained separately. An excellent agreement was found for transient and steady state solution at large value of time. The governing partial differential equations are also solved by implicit finite difference method to verify the present proposed method. The variation of temperature, velocity, skin-frictions and mass flow rate with dimensionless parameter controlling the present physical situation are illustrated graphically and discussed. It is observed that velocity and temperature increases with time and finally attains its steady state status. Furthermore, both velocity as well as temperature of the fluid is higher in case of isothermal heating of the outer surface of the inner cylinder compared with the isoflux heating case when the gap between the cylinder is less or equal to the radius of inner cylinder while reversed trend is observed when the gap between the cylinders is greater than the radius of inner cylinder for all considered values of time.

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli. The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening tendency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.

Pengurangan Hambatan Aliran pada Celah Silinder Koaksial Akibat Slip

Slip effect which occurs at the wall due to the layer of water repellent wall can reduce the pressure drop. The highly water repellent wall coating on the inside coaxial viscometer slip will be occur. The aim of experiment is proving drag reducing of the torque on the cylinder and the coefficient of velocity slip due to the water repellent coating on the wall. Teflon and wax materials are used to coat the surface of the wall. Contact angle of water droplets with a Teflon-coated walls and waxed each of about 110o and 130o into flat surface. The ratio of the radius of inner cylinder and outer cylinder are 0.932 and 0.676. Glycerin solution with concentration 60%, 70% and 80% wt used the test fluid. The maximum drag reduction occurred is 12% for 80% wt glycerin solution at the 0.932 ratio of the radius. The calculation analysis of the moment coefficient fit with experimental data.

Stress Concentrations of a Hollow Circular Cylinder with a Semicircular Notch under Internal Pressure.

This paper deals with the stress concentration problem of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressure. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick plate. The Green's functions are defined as solutions for a thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. A principle of the method of solution is to imagine a hollow cylinder with a notch and to distribute axisymmetric body forces in the thick plate so as to satisfy the boundary conditions of the hollow cylinder. The problem is formulated by an intergral equation with unknown functions of body forces. Stress concentrations at the notch are investigated by numerical calculations and stress distributions near the notch and form factors are shown. The maximum stress appears at the bottom of notch or the inner boundary of smallest cross section depending on the inner radius of cylinder and the notch radius.

123 半円切欠きみぞをもつ厚肉円筒の内圧による応力集中(GS-1 構造解析・応力解析(1))

This paper deals with the stress concentration problem of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressure. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick plate. The Green's functions are defined as solutions for a thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. A principle of the method of solution is to imagine a hollow cylinder with a notch and to distribute axisymmetric body forces in the thick plate so as to satisfy the boundary conditions of the hollow cylinder. The problem is formulated by an intergral equation with unknown functions of body forces. Stress concentrations at the notch are investigated by numerical calculations and stress distributions near the notch and form factors are shown. The maximum stress appears at the bottom of notch or the inner boundary of smallest cross section depending on the inner radius of cylinder and the notch radius.

Natural convection in vertical concentric annuli under a radial magnetic field

Exact solutions for fully developed natural convection in open-ended vertical concentric annuli under a radial magnetic field are presented. Expressions for velocity field, temperature field, mass flow rate and skin-friction are given, under more general thermal boundary conditions. It is observed that both velocity as well as temperature of the fluid is more in case of isothermal condition compared with constant heat flux case when gap between cylinders is less or equal to radius of inner cylinder while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.

Swirling flows between coaxial cylinders with injection by radial jets

An experimental program has been carried out to investigate a class of flows which is of interest with regard to the aeroelastic flutter of flexible cylinders. The flowfield of interest is the swirling flow between two concentric cylinders, of which the inner one is stationary and the outer one rotates. Air is admitted into the annulus between the cylinders through inlets in the wall of the rotating outer cylinder near one end of the apparatus and is exhausted through an annular outlet surrounding the inner cylinder near the other end. Measurements of the resulting flowfield have been made for a wide range of flow rates, outer cylinder rotational speeds, and inlet geometries. Approximate scaling laws for the velocity field have been developed, and dimensionless parameters have been defined which correlate the effects of the various inlet conditions which were tested. Nomenclature Aan = cross-sectional area of annulus A„ = total cross-sectional area of inlets d = internal diameter of inlet tubes / = inner cylinder structural frequency I = length of inlet tubes m =mass flow, Ibm/sec M = dimensionless momentum flux quantity, Eq. (4) N = number of inlets p,pt = static pressure, pitot pressure r = radius from cylinder axis Rj = radius of inner cylinder (outside) R0 = radius of outer cylinder (inside) R = dimensionless radius = (r-Rt)/(R0 —/?/) t = dimensionless residence time quantity, Eq. (5) Um = average axial velocity in the annulus =m/pAan V = magnitude of fluid velocity Vn = average radial velocity in inlets =m/pAn Vt = tangential component of fluid velocity Vz = axial component of fluid velocity z = axial coordinate 0 = yaw angle A = pitot pressure referenced to the static pressure at the inner cylinder =prp(Ri) T =Vtr, circulation T0 =uR20, (ideal) circulation at outer cylinder oj = angular velocity of outer cylinder

Potential distribution in a cylindrical condenser terminated by Matsuda plates

The ion optical nature of an electric field is investigated by means of computer simulation. The electric field is produced by a cylindrical condenser terminated by Matsuda plates and is similar to a toroidal one. The characteristic constants c, c′ and c″ are derived from the potential distribution calculated by solving Laplace's equation under very many boundary conditions. The variable parameters are the potential on the Matsuda plate, φ m, the inner radius of cylinder, r a, the gap distance, 2 k, the length of cylinder, 2 l, and the distance, h, between the cylinder and the Matsuda plate. The results are given as many chart diagrams which are useful for the design of electrode structures. Any kind of c value can be obtained by adjusting φ m, and a desirable c′ value would be obtained by choosing a suitable value of h/k. A large k/r o would be better to reduce the third order aberration.

定常流停止後の弾性反動測定装置の試作とNa-PAA溶液の流動弾性

An apparatus for measuring the elastic recovery, exhibited by viscoelastic fluids after the cessation of steady flow, is designed. This is a coaxial double cylinder type viscometer, in which the shaft of the inner cylinder is set free to rotate by an elastic force of the sample immediately after the revolution of the outer cylinder is stopped. By using the concept of internal strain, the following equation can be derived._??_(1)θe: angular displacement of inner cylinder caused by the elastic recovery of sample after the cessation of flow, σi: shearing stress at the inner cylinder surface, Ri: radius of inner cylinder, R0: radius of outer cylinder, n, k: constants for the sample.For Na-PAA solutions eq.(1) agrees with experimental results.Concentration and temperature dependence of θe at various σi for Na-PAA was measured.For the range of 1-2%, n=1/2 and for the region smaller than 1%, n approached to zero.n=0 means that the strain obeys the Hooke's law in shear.It is considered that the contribution of orientation entropy to the fluid elasticity of Na-PAA solutions is remarkable, because θe is depressed with increasing temperature.Elastic recovery after the cessation of steady flow, which was a kind of non-linear creep recovery, was observed as a function of time.

Resistance of a Flow through an Annulus with an Inner Rotating Cylinder

In this paper, the resistance of a water flow through co-axial cylinders when the inner cylinder rotates, is studied experimentally. The resistances are measured for six gap sizes (s/r1=0.0136∼0.115, s : gap, r1 : radius of inner cylinder) and for various combinations of axial and rotational flows. Results obtained are as follows : 1. When the axial flow is laminar, the resistance of a flow is unaffected up to a certain rotating speed (Rωc : critical rotating Reynolds number), but beyond this speed the flow resistance increases as the Rω increases. 2. The value of critical Taylor number Rωc(s/r1)1/2 increases as the axial Reynolds number (Re=vms/ν) increases up to a certain value (Re=600), beyond this value Rωc(s/r1)1/2 decreases to zero with the increase of Re. When the axial flow is turbulent, such a critical rotating Reynolds number cannot be recognized. 3. When Rω>10 000, the resistance coefficient of a flow λ can be expressed by λ= 0.26 Re-0.24 ×{1+(7/8)2(Rω/2Re)2}0.38 even for small Re.

Resistance of Flow through an Annulus with an Inner Rotating Cylinder

In this paper, the resistance of water flow throush co-axial cylinders is studied experimentally, when the inner cylinder rotates. The resistances are measured for six gap sizes (s/r1=0.0136∼0.115, s : gap, r1 : radius of inner cylinder) and for various combination of axial and rotational flows. Results obtained are as follows : 1. When the axial flow is laminar, the resistance of flow is unaffected up to a cartain rotating speed (Rωe : critical rotatins Reynolds number), but beyond this speed the flow resistance increases as the Rω increases. 2. The value of critical Taylor number Rωe(s/r1)1/2 increases as the axial Reynolds number(Re=vm s/ν) increases up to a certain value (Re=600), beyond this value Rωe (s/r1)1/2 decreasee to zero with the increase of Re. When the axial flow is turbulent, such a critical rotating Reynolds number Rωe cannot be recognized. 3. When Rω>10 000, resistance coefficient of flow λ can be expressed by [numerical formula]even for small Re.

Investigation of the Cavitation Caused by Vibrative Two Concentric or Eccentric Circular Cylinders

When two concentric or eccentric circular cylinders vibrate relatively, the phenomenon of cavitation may be caused by a vibratory hydrodynamic pressure set up in a water bounded by two cylinders. The author confirmed this phenomenon using a model with full scale tail shaft diameter and reported in the previous paper.In the present paper, the author shows some results found by the experimental resarch using 3 sets of newly built testing machines. The principal contents of these results are as follows : 1) The approximate empirical formula was derived from the experimental reserch to estimate the critical cavitation frequency. The negative amplitude of vibratory hydrodynamic pressure set up in a water is shown as|hm|= [0.9+1.6 (α/δ] [1+1.9 (e/δ-α) 2] (103·a2/δ) (αω2/g) Where “ω” is the angular frequency of vibration in rad/s, “α” the amplitude of vibration in mm, “a” the radius of inner cylinder in m, “δ” the mean clearance in mm and “g” the accelerlaion of gravity in mm/s2.Using this formula, it is possible to estimate, whether or not cavitation is liable to occur.2) Relations between a vibratory hydrodynamic pressure set up in a water and the cavitation phenomenon were explained using oscillograms showing the vibratory pressure and results of stroboscopic observation with external synchronizer.3) The peculiarites of the cavitation and the erosion damage caused dy such cavitation were explained.4) Using the model test result, one method to avoid cavitation on actual ships was suggested.