Hydrodynamic loads acting on an oscillating cylinder submerged in a stratified fluid with ice cover

The two-dimensional problem of steady oscillations of a horizontal cylinder submerged in a linearly stratified fluid layer whose upper boundary is ice cover is considered in a linear treatment using the Boussinesq approximation. The method of mass sources distributed along the body contour is used for the internal wave generation regime, and the integral equation for the disturbed pressure in the fluid is used for the regime of no internal waves. The hydrodynamic load acting on the body was calculated as a function of the oscillation frequency for the case of a continuous ice cover and for special cases (broken ice, free surface, and rigid lid).     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

Modeling of transverse self-oscillations of a circular cylinder in an incompressible fluid flow in a plane channel with circulation

Experimentally observed self-oscillations of a cylinder in a plane channel whose width is slightly greater than the cylinder diameter under the impact of the incoming fluid flow are modeled. Within the model of a nonseparated potential flow around the cylinder, the coefficients of added mass of the cylinder are calculated with the help of the generalized method of images. When the cylinder touches the channel wall, the circulation sign changes, and its value is determined by the boundary element method and the no-slip condition for the fluid at the contact point. The Joukowski force and the drag force proportional to the square of velocity are taken into account in the equations of motion of cylinder.     

Small oscillations of a liquid in a partitioned cylindrical vessel

The equations of motion of a rigid body whose cavity is partially filled with an ideal fluid have been obtained in works of Moiseev [1, 2, 3], Okhotsimskii [4], Narimanov [5], and Rabinovich [6]. All the equation coefficients have been calculated for a cavity in the form of a circular cylinder or two concentric cylinders.The problem of fluid motion in a partitioned cylindrical cavity was considered by Rabinovich [7]. It was also considered by Bauer [8], who analyzed the particular case of vessel motion in the plane of one of the partitions.In the following we consider the two-dimensional motion of a cylinder with radial and annular baffles, and a definition is given of the velocity potential in the case of arbitrary positioning of the radial baffles with respect to the motion plane. Formulas are obtained for determining the parameters of a mechanical analog of the wave oscillations, which consists of two mathematical pendulum subsystems.     

Secondary flow in the neighborhood of a cylinder oscillating in a viscoelastic fluid

Measurements were made of the steady secondary flow which is caused by a cylinder executing small-amplitude oscillations perpendicular to the cylinder generators. Test fluids were a water-glycerine mixture and two non-Newtonian fluids: aqueous solutions of Separan AP-30 and PolyHall 295 polyacrylamide polymers. The fluids were contained in a cylinder whose center coincides with the rest position of the oscillating cylinder. Experimental results are consistent with a theoretical analysis for a three-constant Oldroyd fluid model in its simplified convected-Maxwell form. Both experiment and theory show that at an oscillation frequency of 40 Hz the secondary flow of the dilute polymer solutions is, essentially, in a sense opposite from that of a Newtonian fluid.     

Free circular viscoplastic fluid flow with a hydrolubricant layer in the gap between coaxial cylinders

Free circular viscoplastic fluid flow in the gap between coaxial cylinders with a hydrolubricant layer on the inner cylinder is investigated theoretically. Mathematical models of the velocities and shear stresses for the transported and lubricating fluids in the laminar flow regime are proposed.     

Immersion of a Cylinder in a Fluid Through a Cylindrical Free Surface

The plane problem of the immersion of a cylinder in a fluid in a cylindrical cavity whose radius varies with time is considered. The dependence of the wetted width of the circle submerged on the submergence for various gaps is determined. The results obtained are compared with asymptotic dependencies.     

Vibrations of a circular cylinder submerged in a fluid with a non-homogeneous upper boundary

Results of solving a linear problem on steady vibrations of a horizontal cylinder submerged in a fluid, whose upper boundary is partially closed by a solid lid, whereas the rest of the surface is free, are presented. Multipole and eigenfunction expansion methods are used. Reciprocity relations are derived. Added-mass and damping coefficients and the wave amplitudes on the free surface of the fluid are calculated.     

Instability of an Oscillating Cylinder in a Circulation Flow of Ideal Fluid

The problem of the stability of a circular cylinder in a circulation flow is considered under the condition that the cylinder can perform both free (free cylinder) and forced oscillations (cylinder on a spring). It is shown that this simple system can be unstable in the presence of flow vorticity. Particular cases of vorticity distributions which make it possible to obtain an analytic solution are considered. The case of weak monotonically decreasing vorticity of an arbitrary form is analyzed for an arbitrary relation between the densities of the cylinder and the fluid. It turns out that the instability can develop only for a cylinder whose density is greater than that of the fluid. An approximate method of solving this problem based on consideration of the energy balance in the system is constructed. This makes it possible to obtain an expression for the growth rates and explain the physical mechanism realizing the instability, which is associated with the possibility of energy transfer from perturbations in the critical layer to the cylinder oscillations.     

Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall

A circular cylinder placed in a uniform flow, and that spans the entire length between two side walls, may experience either parallel or oblique vortex shedding depending on the end conditions. It was shown by Mittal and Sidharth (2014) that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by the cylinder. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. The free vibrations of a circular cylinder, in the presence of a wall, are investigated. For comparison, computations with end walls, where a slip condition on velocity is specified, are also carried out. The Reynolds number, based on the diameter of the cylinder and free-stream speed of the flow, is Re=100. The initial condition for the free vibrations is the fully developed unsteady flow past a stationary cylinder with oblique shedding. It is found that as the amplitude of vibration of the cylinder builds up, the vortices shed from the cylinder align with its axis leading to parallel shedding. The response of the cylinder is associated with two branches: initial and lower. On the lower branch, the response of the cylinder is virtually identical from two- and three-dimensional computations. The flow as well as the response is different on the initial branch and outside the synchronization regime. Forced vibrations confirm the phenomena.     

On the Arnold Stability of a Solid in a Plane Steady Flow of an Ideal Incompressible Fluid

We study the stability of a rigid body in a steady rotational flow of an inviscid incompressible fluid. We consider the two-dimensional problem: a body is an infinite cylinder with arbitrary cross section moving perpendicularly to its axis, a flow is two-dimensional, i.e., it does not depend on the coordinate along the axis of a cylinder; both body and fluid are in a two-dimensional bounded domain with an arbitrary smooth boundary. Arnold's method is exploited to obtain sufficient conditions for linear stability of an equilibrium of a body in a steady rotational flow. We first establish a new energy-type variational principle which is a natural generalization of the well-known Arnold's result (1965a, 1966) to the system “body + fluid.” Then, by Arnold's technique, a general sufficient condition for linear stability is obtained. Received 21 February 1997 and accepted 23 June 1997     

The slow rotation of an axisymmetric solid submerged in a fluid with a surfactant surface layer—II. The rotating solid in a bounded fluid

This paper extends the work in Shail (1979) on the problem of an axisymmetric submerged solid rotating slowly and steadily in a fluid whose surface is covered with a surfactant film. The bulk fluid is of finite extent, and both asymptotic and numerical results (the latter in the case of a thin circular disk) are given for boundary effects on the resistive torque and surface velocity profile when the container is a right circular cylinder and the fluid is of finite depth.     

Finite Oscillations of a Cylinder in a Coaxial Duct Subjected to Annular Compressible Flow

As a generalization considering small fluid-structural vibrations, the present paper examines the finite magnitude oscillatory motion of an elastically supported rigid cylinder in a cylindrical rigid duct conveying a compressible flow. The fluid is assumed to be inviscid and irrotational and free purely transverse vibrations of the body are dealt with. The governing equations of motion are the fully nonlinear Euler equations together with the continuity equation and a state equation (here for an ideal gas), the ordinary differential equation for the vibrating cylinder, and the kinematical transition and boundary conditions at the moving contact interface between fluid and body and the outside fluid border, respectively. A pertubation analysis is performed to calculate not only the dynamic characteristics for small coupled oscillations but also the corrections due to the inherent nonlinearities of the vibroacoustic problem. To make the calculation steps more transparent, the simpler problem of a two-dimensional channel flow between a rigid wall and an elastically supported rigid plate is also included in the present study. As an outlook, the influence of flexibility of the cylinder (or the plate) is addressed and the problem of forced vibrations is touched. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermodynamic analysis of a thermal storage unit under the influence of nano-particles added to the phase change material and/or the working fluid

The thermal storage unit consists of two concentric cylinders where the working fluid flows through the internal cylinder and the annulus is filled with a phase change material. The system carries out a cyclic operation; each cycle consists of two processes. In the charging process the hot working fluid enters the internal cylinder and transfers heat to the phase change material. In the discharging process the cold working fluid enters the internal cylinder and absorbs heat from the phase change material. The differential equations governing the heat transfer between the two media are solved numerically. The numerical results are compared with the experimental results available in the literature. The performance of an energy storage unit is directly related to the thermal conductivity of nano-particles. The energy consumption of a residential unit whose energy is supplied by a thermal storage system can be reduced by 43?% when using nano-particles.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

Oscillations of a cylindrical body submerged in a fluid with ice cover

The linear plane problem of oscillations of an elliptic cylinder in an ideal incompressible fluid of finite depth in the presence of an ice cover of finite length is solved. The ice cover is modeled by an elastic plate of constant thickness. The hydrodynamic loads acting on the body are determined as functions of the oscillation frequency and the positions of the cylinder and plate.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

On the validity of the independence principle applied to the vortex-induced vibrations of a flexible cylinder inclined at 60°

The vortex-induced vibrations (VIV) of a flexible cylinder inclined at 60° are investigated by means of direct numerical simulation, at a Reynolds number equal to 500, based on the cylinder diameter and inflow velocity. The cylinder has a circular cross-section and a length to diameter aspect ratio equal to 50; it is modeled as a tension-dominated structure which is free to oscillate in the in-line and cross-flow directions. The behavior of the coupled fluid–structure system is examined for two values of the tension. Particular attention is paid to the validity of the independence principle (IP) which states that the inclined and normal-incidence body cases are comparable if the inflow velocity normal component is used to scale the physical quantities.The flexible cylinder exhibits regular VIV for both values of the tension. In the high-tension configuration, where the in-line bending of the structure remains small, the IP is shown to be valid for the prediction of the cylinder responses and the fluid forces. In contrast, in the lower-tension configuration, the behavior of the fluid–structure system deviates from the IP. It is shown that this deviation is connected to the larger in-line bending of the structure which leads to considerably different profiles of the flow velocity locally perpendicular to the body in the inclined and normal cylinder cases. Since the system behavior appears to be mainly driven by this component of the flow, the profile modification induced by the larger in-line bending results in distinct responses: multi-frequency vibrations are observed in the inclined cylinder case whereas mono-frequency oscillations of larger amplitudes develop at normal incidence.     

Further contributions on the flow past a stationary and confined cylinder: Creeping and slowly moving flow of Power law fluids

The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values. The values of the Reynolds number, based on physical and rheological properties, cylinder radius and bulk velocity, were varied between 0.0001≤Re≤10, while the Power law index values mapped the 0.50≤n≤1.50 range, allowing for the investigation of both shear-thinning and shear-thickening effects at the creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on the most important characteristics of fluid flow past circular cylinder. It is shown that for the creeping flow regime there exist finite sized redevelopment length, drag and loss coefficient. Last but not least, the present numerical results indicate that the shear-thinning viscous behaviour decreases the onset of flow separation.     

A light cylinder under horizontal vibration in a cavity filled with a fluid

The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency.