Semi-infinite Circular Cylinder Research Articles

Hygrothermal analysis of a semi-infinite cylinder: an integral transform approach

PurposeThe purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered.Design/methodology/approachThis study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture.FindingsThe paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings.Research limitations/implicationsThe research presented in this article is primarily hypothetical and focused on the analysis of mathematical models.Originality/valueTo the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field.

THERMAL STRESSES IN A SEMI-INFINITE SOLID CYLINDER SUBJECTED TO INTERNAL HEAT GENERATION

The present paper deals with the determination of displacement and thermal stresses in a semi-infinite circular cylinder defined as <TEX>$0{\leq}r{\leq}b$</TEX>, <TEX>$0{\leq}z</TEX><TEX><</TEX><TEX>{\infty}$</TEX>, due to internal heat generation within it. A circular cylinder is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary (r = b) whereas the zero temperature at the lower surface (z = 0) of the semi-infinite circular cylinder. The governing heat conduction equation has been solved by using integral transform method. The results are obtained in series form in terms of Bessel functions. The results for displacement and stresses have been computed numerically and illustrated graphically.

Inverse Heat Conduction Problem in a Semi-infinite Hollow Cylinder and its Thermal Deflection by Quasi-static Approach

In this study inverse heat conduction problem is to simultaneously determine unknown temperature and thermal deflection on the outer curved surface of a semi-infinite hollow circular cylinder from the knowledge of temperature distribution within the cylinder. The hollow circular cylinder is subjected to an arbitrary known temperature under unsteady state condition. Initially the cylinder is at zero temperature and temperature at the lower surface is at zero heat flux. Also the inner boundary surface of the cylinder is at zero temperature. The governing heat conduction equation has been solved by using integral transform method. The results are obtained in series form in terms of Bessel’s functions. Mathematical model has also been constructed with the help of numerical illustration.

The normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi-infinite circular cylinder

The Neumann boundary value problem is presented for the time harmonic excited steady-state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi-infinite baffle. The system of two coupled differential equations is solved for this purpose, one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations. First, the acoustic pressure is presented in its spectral form using the Weber inverse transform. Then, the time-averaged acoustic power is presented using the plate׳s modal impedance coefficients and the coupling factors. The modal coefficients are presented as the integrals together with the corresponding asymptotic formulations. The influence of the cylindrical baffle on the acoustic power is analyzed numerically. The fluid loading and the internal attenuation of the plate׳s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected.

Mechanics of spheroidal fullerenes and carbon nanotubes for drug and gene delivery

There is considerable interest in the mechanics of carbon nanostructures, such as carbon nanotubes and fullerenes, and the manner of their interactions at the intermolecular level. Medical applications include the use of carbon nanotubes for targeted drug and gene delivery, for which issues relating to the acceptance and containment of drugs or genes are not properly understood. A spheroid is an ellipsoid with two equal axes and the general spheroidal shape includes a wide variety of possible molecular configurations such as spheres, capped cylindrical tubes and ellipsoids of revolution, and therefore the determination of the interaction forces for this general shape may have many applications. Phenomena such as the suction of fullerenes into carbon nanotubes due to the van der Waals interatomic interactions and ultra-low friction of a molecule moving inside a carbon nanotube give rise to the possibility of constructing nanoscaled oscillators with frequencies in the gigahertz range. This paper models the mechanics of such a system by employing a six-twelve Lennard-Jones potential taken over two surfaces assumed to be composed of mean distributions of atoms over the two idealized surfaces of an open-ended semi-infinite circular cylinder and a spheroid. Following the methodology of previous work with spherical surfaces, the acceptance energy and suction energy for spheroidal molecules are given and the special case of spherical molecules is also reproduced to validate the method. The results for elliptical molecules are novel and cannot be validated experimentally at this stage, but the results for the special case of spherical molecules are given and shown to be in good agreement with published molecular dynamical simulations. Finally, a general numerical-analytical procedure is proposed to calculate the Lennard-Jones potential for any axially symmetric surface, and the prior results obtained for the spheroid are used to validate the procedure.

Acoustic scattering in a duct with mean swirling flow

In this paper we consider the diffraction of waves by a sharp edge in three-dimensional flow with non-zero mean vorticity. This is an extension of the famous Sommerfeld problem of the diffraction of waves by a sharp edge in quiescent conditions. The precise problem concerns an infinitely long annular circular cylinder, which contains a concentric semi-infinite circular cylinder which acts as a splitter. The mean flow has both axial and swirl components, and cases in which the splitter is arranged with either a leading edge or a trailing edge relative to the axial flow are considered. This is a model of a number of practical situations in the aeroengine context. We treat both sonic and nearly-convected incident disturbances, and two regimes are considered; one in which the azimuthal order, $m$ , of the incident waves is $O(1)$ , and a second in which $m\,{\gg}\,1$ . A solution for $m\,{=}\,O(1)$ in the case of rigid-body swirl is found using the Wiener–Hopf technique, and special care is needed to handle the infinite accumulation of scattered nearly-convected modes which results from the presence of the mean vorticity. Simplification in the limit $m\,{\gg}\,1$ then allows us to consider more general swirl distributions. A number of effects arise due to the presence of mean vorticity. This includes the generation of sound at a trailing edge due to the scattering of a nearly-convected disturbance, which is to be contrasted with the way in which a convected gust passes a trailing edge silently in uniform mean flow.

A hybrid GMT–PO method for calculating the NDC of the irregular edge of a semi‐infinite circular cylinder

AbstractIn this paper, the GMT–PO hybrid method accompanied by the iterative technique is applied successfully to calculate 3‐D numerical diffraction coefficients (3‐D NDC) of the irregular circular‐cylinder edge. The computed RCS of the circular cylinder with 3‐D NDC of the irregular edge is in good agreement with the measured data from the reference. © 2001 John Wiley &amp; Sons, Inc. Microwave Opt Technol Lett 31: 108–110, 2001.

Edge resonance in an elastic semi-infinite cylinder

We study the three-dimensional elasticity operator in a semi-infinite circular cylinder subject to free boundary conditions, in the case of zero Poisson ratio. We prove, adapting the method from [15], i.e., by first finding an invariant subspace for the elasticity operator such that the essential spectrum has a strictly positive lower bound and then finding a test function in this space for which the variational quotient takes a value below the bottom of the essential spectrum, that there is an eigenvalue embedded in the continuous spectrum. Physically, an eigenvalue corresponds to a "trapped mode", that is, a harmonic oscillation localized near the edge. This effect, known in mechanics as the "edge resonance" has been extensively studied numerically and experimentally. Our paper extends the mathematical justification of such phenomena provided by [15] to a three-dimensional setting

The three-dimensional boundary layer on a yawed body of revolution

A three-dimensional boundary layer calculation is carried out for the flow over a semi-infinite circular cylinder which is placed at a small angle of incidence to an oncoming uniform stream. To elucidate the details of the flow both a spectral and a finite difference method of solution has been employed. The results show that separation of ‘open’ type on a body of revolution is characterized by a line of Goldstein singularities that originates, spontaneously, at a finite distance from the nose of the body.

Acoustic radiation from two opposed semi-infinite coaxial cylindrical waveguides. I: overlapping edges

This paper is the first part of an investigation into the axisymmetric radiation of sound waves from two semi-infinite circular cylinders. Both pipes have a common axis, measured by the Cartesian variable z, but the smaller cylinder extends to infinity in the direction z → -∞ whilst the larger extends in the direction z → ∞. The boundary value problem is formulated as a matrix Wiener-Hopf equation and a solution is obtained here for the case when the ducts overlap. The reflected, transmitted, and radiated far-field waves are determined for a range of values of the inner and outer pipe diameters, and the overlap spacing. A full discussion is made of the relevance of this model to physical problems in electromagnetic and acoustic wave propagation, and this is backed-up by conclusions drawn from the presented data.

Wake structure and dispersion

Wake structure and dispersion were investigated in the lee of two bluff bodies in an atmospheric boundary layer wind tunnel. The two bodies are a semi-infinite circular cylinder, and a rectangular body (power plant model). A so-called time-based wake model provides excellent estimates of the lateral wake structure at different downwind distances in the lee of the cylinder, but does not perform nearly as well in the lee of the rectangular body. However, the wind speed dependence of the time-based model was not tested. The frontal area wake model is independent of wind speed. Recent evaluations [1] have shown that the time-based model yields significantly better concentration estimates than the frontal area wake model under ambient conditions with varying wind speeds. When the frontal area wake model was evaluated with the dispersion measurements in the lee of the rectangular body, the results were very good. Lastly, the wake structure was virtually insensitive to source height for the two locations tested (ground surface and mid-level roof). It appears that the frontal area wake model accurately describes the spatial variation of wake dispersion, while the time-based model may more properly describe wake variations with wind speed.

Effect of moving wall on the three-dimensional separation of an incompressible fluid in front of an obstacle

The problem of the laminar boundary layer formed on the surface of a semiinfinite plate with a perpendicular semi-infinite circular cylinder in a uniform steady incompressible flow normal to the leading edge is considered. Near its sharp edge the plate has a stationary part and, located at a finite distance further downstream, a part of the surface moving downstream at a constant velocity. The first-order boundary layer equations are solved numerically by an implicit finite-difference method. The effect of the moving wall on the variation of the dimensions of the separation zone ahead of the obstacle over a broad range of the governing parameters and flow characteristics is investigated. The flow in the laminar boundary layer on the surface of a plate ahead of such an obstacle was calculated in [1, 2] without motion of the wall. Data on the structure of the separated flow are given in [3].

Flow around Two Circular Cylinders in Tandem Arrangement at Various Spacings on a Flat Plate.

The flow around two semi-infinite circular cylinders of the same diameter in the tandem arrangement at various spacings on a flat plate has been investigated experimentally. The cylinders were aligned with the axis normal to both the flat plate and the free stream. The time-mean surface pressures on the cylinders and the frequency of the vortex shedding in the direction of the cylinder axis were measured. The flow patterns on the cylinder were visualized using an oil-film technique and the flow visualization around the cylinders was performed by the liquid-parafine-mist technique. The flow patterns near the end of the cylinder were essentially different from two-dimensional flow. The flow passing along the end surface of the upstream cylinder became oscillating flow at the frequency lower than that of Karman vortex.

Flow around a pair of circular cylinders arranged side-by-side at various spacings on flat plate.

The flow around a pair of semi-infinite circular cylinders arranged side-by-side at various spacings on a flat plate has been investigated experimentally. The two cylinders were aligned with the axis normal to both the flat plate and the free stream. Pressure distributions on the cylinders and velocity distributions in the wake were measured. The flow patterns on the cylinders and on the plate were visualized using an oil-film-technique, and the flow visualization around the cylinders was done by the smoke-wire method. As the distance between the two cylinders increased in order, the flow changed from the biased flow pattern deviated from one cylinder to the straight advancing flow pattern, showing a violent variation at the boundary region between two patterns. For large spacing of cylinders on the flat plate, the change of the flow pattern occurred more quickly, resulting in the reduction of the distance between the two cylinders.

Interpretation of separation lines from surface tracers in a shock-induced turbulent flow

IN experimental studies of shock wave turbulent boundarylayer interactions, surface-tracer methods, which have essentially zero frequency response, are widely used to determine the locations of separation lines. However, recent research has shown that in many cases the separation shockwave structure undergoes large-scale motion, raising questions about the physical meaning of separation lines deduced from such techniques. In the present study at Mach 5, the separation induced by an uriswept semi-infinite circular cylinder has been studied using platinum thin films. Conditional sampling analysis of the signals suggests that this line is the downstream boundary of a region of intermittent separation. Contents In experimental studies of shock wave turbulent boundarylayer interactions, surface tracer techniques are widely used to locate separation lines.1 Such methods are easy to use and generate sharply defined, repeatable separation lines (S). Quantitative measurements of flow length scales and angles are made using these methods and are used for evaluating the predictive capabilities of numerical methods and turbulence models. It is, therefore, important to understand what these lines physically represent. In many of these flows, dynamic wall-pressure measurements show that the separation shock is unsteady and moves from the upstream boundary of the flowfield, where the wall

The static electric field distribution between two semi-infinite circular cylinders: A model for the feed gap field of a dipole antenna

The static electric field distribution in the gap between two solid perfectly conducting semi-infinite cylinders is obtained in terms of a Fourier-Bessel eigenfunction series. For dipole antennas whose cylinder diameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2a</tex> and gap length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2d</tex> are both much less than the operating wavelength <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> , this field can serve as the quasistatic excitation field in the gap of the dipole. However, the Fourier-Bessel series is slowly convergent. It is transformed into a rapidly convergent series of ultrasphetical polynomials whose weighting function explicitly satisfies the Meixner edge condition. Numerical results are presented graphically for both the axial electric field on the gap surface and the associated potential distribution. Gap ratios of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d/a</tex> from 0.01 to 10.0 are considered and it is shown that as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d/a \rightarrow 0</tex> the solution approaches the two-dimensional solution obtainable by conformal mapping.

A three-dimensional treatment of transient thermal stresses in a transversely isotropic semi-infinite circular cylinder subjected to an asymmetric temperature on the cylindrical surface

This paper deals with a three-dimensional transient thermal stress problem in a transversely isotropic semi-infinite circular cylinder subjected to an asymmetrical temperature on the cylindrical surface and a convective heat loss on the surfaces. In analyzing the problem, the generalized Fourier transform to a temperature and the modified transversely isotropic potential functions method to stresses are used. For the numerical example, the temperature and the thermal stresses are calculated for a grafite which belongs under a transverse isotropy, and compared with the values under isotropic conditions. The effects of the various anisotropies of the material properties on the temperature and the thermal stresses are studied.

Flow around a vertical cylinder at various spacings to a horizontal flat plate.

The flow around a semi-infinite circular cylinder placed at various spacings to a flat plate has been investigated experimentally. The cylinder was aligned with its axis normal both to the flat plate and to the free stream. Then, the pressure distributions along the plate and on the cylinder surface were measured and the velocity distributions were measured in the field of the flow behind the cylinder. The flow patterns on the plate and on the end face of the cylinder were visualized using the oil-film-technique, and the flow visualization around the cylinder was done by using the liquid-parafine-mist-technique. When the spacing was small, three flow patterns were observed around the cylinder : a horseshoe-like vortex, a symmetrical vortex and a Kaman vortex ; and one or two separation points along the plate were observed, too.

Transient thermal stresses in a transversely isotropic semi infinite circular cylinder with an asymmetric temperature distribution on the end surface and a convective heat loss

In this paper, the three-dimensional transient thermal stress problem in a transversely isotropic semi-infinite circular cylinder subjected to an asymmetric temperature distribution on the end surface and convective heat losses into the surrounding medium from the surfaces is analyzed by means of the modified transversely isotropic potential function method.

The stokes flow from half-space into semi-infinite circular cylinder

The infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The inlet length in this case is comparable to that computed for a finite circular cylinder pore by Dagan et al.[1]. In the half-space outside the cylinder pore region, the flow is strongly affected by the wall. Beyond one radius of the tube from the orifice, the solutions match almost exactly the flow through an orifice of zero thickness given by Sampson[2]. The relationship between the pressure drop and the volumetric flow rate is also computed in the present paper for the semi-infinite tube.