Double-diffusive convection in a circular cylinder

Summary A theoretical study is made of the onset of steady double-diffusive convection in a circular cylinder of small to moderate aspect ratio. An eigenfunction expansion method is used to derive systems of amplitude equations for weakly nonlinear evolution of critical disturbances. It is shown that the nature of the convective solution near criticality depends strongly on the cylinder's aspect ratio; this is particularly the case at or near aspect ratios where two modes become unstable at the same Rayleigh number. There is also a strong dependence on Prandtl number, which is discussed.With 7 Figure     

Study on postbuckling of axial compressed elastoplastic functionally graded cylindrical shells

Postbuckling of plates and shells is an important and cumbersome problem in the structural stability field. Presently, postbuckling behaviors of elastoplastic functionally graded cylindrical shells are investigated by a numerical simulation. The elastoplastic material properties are assumed to be of a multilinear hardening type, according to the constituent distributions, and are modeled using the laminate method. The Riks algorithm is used to obtain the equilibrium path. The postbuckling deformation and stain history of elastoplastic functionally graded cylindrical shells are investigated and various effects of the shell thickness and the constituent distributions are discussed. The results show material unloading effects in the postbuckling state.     

Uniform shear flow past a circular cylinder

Summary This paper solves the two-dimensional problem of the unsteady shear flow of a viscous incompressible fluid past a circular cylinder. The flow is calculated using two methods. The first takes the form of a double series solution where an expansion is carried out in powers of the time, t, and in powers of the parameter where R is the Reynolds number. This approximate analytical solution is valid for small times following the start of the motion and for large Reynolds numbers. The second method involves a spectral-finite difference procedure for numerically integrating the full Navier-Stokes equations expressed in terms of a stream function and vorticity. Our results demonstrate that for small times and moderately large R the two methods of solution are in good agreement. Results are presented for a wide range of Reynolds numbers. Comparisons with previous studies are also carried out and discussed.     

Magnetothermoelastic stress waves in a circular cylinder

The problem of axisymmetric axial stress wave generation is considered in a thermoelastic circular cylindrical bar in the presence of an applied magnetic field. It is assumed that the surface of the cylinder is free from mechanical loadings and thermal radiation. A general solution is obtained by perturbation technique and is annihilated to a particular case wherein the applied magnetic field is constant in space and time. The problem is analysed numerically for carbon steel material.     

Steady magnetohydrodynamic flow past a circular cylinder

The steady two-dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values of R, R_mand β, where R is the Reynolds number, R_m the magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted to R = 40, R_m = 1 and infinity and 0 ? β ? 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder. The numerical computations for the non-magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances are examined.     

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. We show that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.     

The micropolar elastic vibrations of a circular cylinder

The fundamental vibrations of a long circular cylinder of a micropolar elastic solid are analysed and their dispersion equations are discussed. Solutions of these equations, valid in the cases of small cylinder radius or of weak coupling, are obtained explicitly.     

Radiation from a dislocation oscillating in a circular cylinder

The exact closed-form solution is derived for standing waves due to an oscillating screw dislocation which is located in a circular infinite cylinder. The resonance behavior of the emitted waves and the effect of energy losses are explicitly shown.     

The initial oscillatory flow past a circular cylinder

This paper presents results obtained from an initial approximation for the flow around a circular cylinder in two-dimensional oscillating flow. The analysis is developed in terms of the scalar vorticity and stream function. An expansion in powers of time from the start of the motion is obtained using an exact analysis which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds number. The time development of the physical properties of the flow are determined both by means of analytical expressions and by an accurate numerical procedure. The surface pressure, drag and surface vorticity are calculated and various estimates of the time of separation and the distance moved in this time are obtained. The phenomenon of steady streaming is not considered in this paper since the time of validity of the expansions is small. The agreement between the analytical and numerical results at small times is excellent.     

Longitudinal shear of a crack in a multi-material circular cylinder

This is an article dealing with the longitudinal shear of a crack contained in a circular cylinder, which is embedded in and fixed by perfect bonding to a composed hollow circular cylinder, consisting of a number of hollow sub-cylinders of different materials. A rigorous solution to the problem is developed. With the material and geometric constants of the composed hollow circular cylinder as parameters, numerical values of stress intensity factors for the crack are worked out. The delicate behavior in the variation of the stress intensity factors, when the number of the hollow sub-cylinders becomes large, is analyzed and discussed. The solution is developed by utilizing a simplified and improved technique using complex variables.     

A proportional-integral-differential control of flow over a circular cylinder

In the present study, we apply proportional (P), proportional-integral (PI) and proportional-differential (PD) feedback controls to flow over a circular cylinder at Re=60 and 100 for suppression of vortex shedding in the wake. The transverse velocity at a centreline location in the wake is measured and used for the feedback control. The actuation (blowing/suction) is provided to the flow at the upper and lower slots on the cylinder surface near the separation point based on the P, PI or PD control. The sensing location is varied from 1d to 4d from the centre of the cylinder. Given each sensing location, the optimal proportional gain in the sense of minimizing the sensing velocity fluctuations is obtained for the P control. The addition of I and D controls to the P control certainly increases the control performance and broadens the effective sensing location. The P, PI and PD controls successfully reduce the velocity fluctuations at sensing locations and attenuate vortex shedding in the wake, resulting in reductions in the mean drag and lift fluctuations. Finally, P controls with phase shift are constructed from successful PI controls. These phase-shifted P controls also reduce the strength of vortex shedding, but their results are not as good as those from the corresponding PI controls.     

Penetration of circular vortices into a superconducting hollow cylinder

The Gibbs free energy circular vortices for an ideal type II superconducting hollow cylinder with a cylindrically symmetric applied field is calculated in the London approximation. The physical analysis of the results indicates the presence of a special kind of Bean-Livingstone barriers, as well as other features related to the symmetry of the system.     

MHD Flow past a circular cylinder – a numerical study

 The steady, two-dimensional, incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow is studied using the finite difference method. The magnetic Reynolds number is assumed to be small. Results are presented up to the Reynolds number R=500 and interaction parameter N=1.3. As N increases suppression of the separation is observed. Drag coefficient is decreasing for the small values of N and then increasing as N increases. It is found that a smaller value of far field distance is required as N increases. Received 6 March 2000     

On the thermal stresses in a finite circular cylinder

Summary A solution is presented for the determination of thermal stresses in a finite cylinder heated axisymmetrically over the curved surface. The solution is obtained by constructing the thermoelastic displacement potential and the biharmonic Love function to satisfy all the boundary conditions. It considers the steady state stresses as well as the transient stresses.Based on a doctoral thesis in applied mechanics submitted by the first author to Kansas State University, Manhattan, Kansas.     

Numerical simulation of unsteady viscous flow around a circular cylinder

A finite difference solution is obtained for the time-dependent viscous incompressible 2-dimensional flow past a circular cylinder by direct integration of the Navier-Stokes equations expressed in a general curvilinear coordinate system. The solution describes the development of the vortex street developed behind the cylinder. Evolution of flow configuration is studied by means of streamlines, pressure contours, and vorticity contours for different Reynolds numbers. The time-dependent lift and drag coefficients are also obtained.     

Theoretical modeling of a thickness-shear mode circular cylinder piezoelectric transformer

We propose a piezoelectric transformer operating with thickness-shear modes of a circular cylinder and perform a theoretical analysis on the transformer. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The output voltage, input admittance, and efficiency of the transformer are determined. The basic behaviors of the transformer are shown by numerical results.     

No-slip images of certain line singularities in a circular cylinder

The no-slip images of a line rotlet, a Stokeslet, a potential source and a potential doublet in a circular cylinder are obtained. It is shown that the far field is either a uniform flow or an eccentric rotational flow. Consequently, the uniform flow past a cylinder or an eccentric rotational flow around a cylinder becomes a well-posed problem if a singularity of a suitably chosen strength is present in the flow field.