Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infi- nite circular cylinder subjected to certain boundary conditions. An analytical procedure for evaluation of thermal stresses, displacements, and temperature in rotating cylinder subjected to thermal load along the radius is presented. The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed. Such situation can arise due to melting of insulating material deposited on the surface cylinder. A solution and numerical results are obtained for the stress components, displacement components, and temperature. The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.

Rotational Flow in a Narrow Annular Gap Based on Lattice Boltzmann Method

For comprehensive characteristics of flow in a gas bearing,lattice Boltzmann method(LBM)is applied for study of the two-dimensional flow between two eccentric cylinders with the inner one rotating at a high speed.The flow pattern and circumferential pressure distribution are discussed based on critical issues such as eccentricity ranging from 0.2 to 0.9,clearance ratio varying from 0.005 to 0.01 and rotating speed in the range of 3×104—1.8×105 r/min.The analysis and discussion on the circumferential pressure distribution affirmed the quasilinear relation between the extremum pressure and rotating speed.Furthermore,a high eccentricity and small clearance ratio contributes most to the fluctuation of the circumferential pressure distribution.The flow pattern inside the channel exhibits separation vortex under a large eccentricity.The conclusions drawn in this work give rise to prediction of the flow pattern in the gas bearing which is beneficial for evaluating the performance of as well as instructing the design and development.

Stresses in rotating heterogeneous viscoelastic composite cylinders with variable thickness

An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material. It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions, the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin＇s approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness variation, constitutive, time parameters on the radial displacement, and stresses are investigated.

Geometric shapes of the interface surface of bicomponent flows between two concentric rotating cylinders

In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.

Experimental Study on Flow past A Rotationally Oscillating Cylinder

A series of experiments was carried out to study the flow behaviour behind a rotationally oscillating cylinder at a low Reynolds number （Re=300） placed in a recirculation water channel. A stepper motor was used to rotate the cylinder clockwise- and- counterclockwise about its longitudinal axis at selected frequencies. The particle image velocimetry （PIV） technique was used to capture the flow field behind a rotationally oscillating cylinder. Instantaneous and time-averaged flow fields such as the vorticity contours, streamline topologies and velocity distributions were analyzed. The effects of four rotation angle and frequency ratios Fr （Fr=fn/fv, the ratio of the forcing frequency fn to the natural vortex shedding frequency fv） on the wake in the lee of a rotationally oscillating cylinder were also examined. The significant wake modification was observed when the cylinder undergoes clockwise-and-counterclockwise motion with amplitude of π, especially in the range of 0.6≤Fr≤1.0.

Rotational Oscillation Effect on Flow Characteristics of a Circular Cylinder at Low Reynolds Number

Two dimensional numerical simulations of flow around a rotationally oscillating circular cylinder were performed at Re = 1000. A wide range of forcing frequencies, fr, and three values of oscillation amplitudes, A, are considered. Different vortex shedding modes are observed for a fixed A at several values of fr, as well as for a fixed fr at different values of A. The 2C mode of vortex shedding was obtained in the present study. It is important to point out that this mode has not been observed by other investigators for rotationally oscillating case. Also, it is verified that this mechanism has great influence on the drag coefficient for high frequency values. Furthermore, the lift and pressure coefficients and the power spectra density are also analyzed.

Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads

The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Rey- nolds number 40〈 Re 〈200 and various rotation rate 8i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method （FVM）. The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re in- creases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θi〈θcrit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder

In this paper,the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied.The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow.Further,the novel features of heat generation/absorption,thermal radiation,and Joule heating are studied to control the rate of heat transfer.The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno.The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations(PDEs)and transformed into nonlinear ordinary differential equations(ODEs)with the help of the suitable flow ansatz.Numerically acquired results through the technique bvp4c are reported graphically with physical explanation.Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature(CWT)as compared with the prescribed surface temperature(PST).Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid.Moreover,the temperature distribution increases with increasing values of the radiation parameter and the Eckert number.It is also noted that an increase in Reynolds number reduces the penetration depth,and as a result the flow and transport of energy occur only near the surface of the cylinder.

WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors（SIF） of internally pressurized thick-walled cylinder was used as the reference case. SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method. The weight function formulas were worked out and can be used for all kinds of depth of cracks, rotating speed, material, size of thick-walled cylinder to calculate the stress intensity factors. The results indicated the validity and effectiveness of these formulas. Meanwhile, the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.

Coriolis effect on responses of rotating thin piezoelectric hollow cylinder

Coriolis effect is considered in the analysis of a rotating piezoelectric hollow cylinder. An inhomogeneous Bessel equation governing the radial mechanical displacement is derived, which can be approximated as an Euler type differential equation when the cylinder is very thin. Numerical examples show that the Coriolis effect can he significant under certain conditions.

Numerical and Experimental Analysis of the Hydrodynamic Performance of a Three-Dimensional Finite-Length Rotating Cylinder

The hydrodynamic performance of a three-dimensional finite-length rotating cylinder is studied by means of a physical tank and numerical simulation.First,according to the identified influencing factors,a hydrodynamic performance test of the rotating cylinder was carried out in a circulating water tank.In order to explore the changing law of hydrodynamic performance with these factors,a particle image velocimetry device was used to monitor the flow field.Subsequently,a computational field dynamics numerical simulation method was used to simulate the flow field,followed by an analysis of the effects of speed ratio,Reynolds number,and aspect ratio on the flow field.The results show that the lift coefficient and drag coefficient of the cylinder increase first and then decrease with the increase of the rotational speed ratio.The trend of numerical simulation and experimental results is similar.

Comparison and Analysis of Erosion-Corrosion Test Apparatus IJR and RCE

The test apparatus used for investigating erosion-corrosion in aqueous media, including the pipe flow loop, impinging jet, rotating disk and rotating cylinder rigs is reviewed. With combining the impinging jet rig and rotating cylinder electrode rig, the hydrodynamic characteristics of both rigs are analysed.

MILU-CG METHOD AND THE NUMERICAL STUDY ON THE FLOW AROUND A ROTATINGCIRCULAR CYLINDER

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Leaching Phenomena of Antifouling Agents from Ships＇ Hull Paints

The effects ofpH, dissolved ion content and relative water velocity on the release rate of an antifouling agent, cuprous oxide, from ships＇ hull paint have been investigated by rotating cylinder tests. Additionally, test paint panels were attached to a vessel and recovered after a certain period of voyage for the validation of the laboratory tests. In the initial period, the release rates are influenced by pH, dissolved ion content and water velocity, but once after a certain period of test, those effects become less significant. These phenomena can be explained when the paint film is fresh, the rate is controlled by chemical reaction, the surface and/or diffusion layer in the water phase governs the rate. After the antifouling substance in the paint film leached out from the near-surface region, a diffused layer （leached layer）, that has little antifouling agent remained, is formed at the surface of the coating, and the diffusion in that layer can be a rate-determining process. The development of the leached layer is affected by a balance between the leaching rate of the antifouling ingredient and paint resin determined by the chemical properties and speed of the water. Thus, the leaching rates of antifouling agents are affected by the history of the paint in the water.

FLOW PAST TWO ROTATING CIRCULAR CYLINDERS IN A SIDE-BY-SIDE ARRANGEMENT

Measurements were performed using Particle Image Velocimetry （PIV） to analyze the modification of flow by the combined effects of the rotation and the Reynolds number on the flow past two rotating circular cylinders in a side-by-side-arrangement at a range of 425 〈 Re ≤ 1130,0 ≤α ≤4 （ α is the rotational speed） at one gap spacing of T / d = 1.11 （T and d are the distance between the centers of two cylinders and the cylinder diameter, respectively）. A new Immersed-Lattice Boltzmann Method （ILBM） scheme was used to study the effect of the gap spacing on the flow. The results show that the vortex shedding is suppressed as rotational speed increases. The flow reaches a steady state when the vortex shedding for both cylinders is completely suppressed at critical rotational speed. As the rotational speed further increases, the separation phenomenon in the boundary layers disappears at the attachment rotational speed. The critical rotational speed and attachment rotational speed become small as Reynolds number increases. The absolute rotational speed of cylinders should be large at same critical rotational speed and attachment rotational speed in the case of large Reynolds number. The gap spacing has an important role in changing the pattern of vortex shedding. It is very different in the mechanism of vortex shedding suppression for the flows around two rotating cylinders and single rotating cylinder.

Active flow control with rotating cylinders by an artificial neural network trained by deep reinforcement learning

In this paper,an artificial neural network(ANN)trained through a deep reinforcement learning(DRL)agent is used to perform flow control.The target is to look for the wake stabilization mechanism in an active way.The flow past a 2-D cylinder with a Reynolds number 240 is addressed with and without a control strategy.The control strategy is based on using two small rotating cylinders which are located at two symmetrical positions back of the main cylinder.The rotating speed of the counter-rotating small cylinder pair is determined by the ANN and DRL approach.By performing the final test,the interaction of the counter-rotating small cylinder pair with the wake of the main cylinder is able to stabilize the periodic shedding of the main cylinder wake.This demonstrates that the way of establishing this control strategy is reliable and viable.In another way,the internal interaction mechanism in this control method can be explored by the ANN and DRL approach.

A numerical investigation of the flow between rotating conical cylinders of two different configurations

The flow between two coaxial conical cylinders is numerically studied for two different configurations, with the inner cone rotating and the outer one at rest. It is found that, in one configuration,at least at a small Reynolds number（Re）, the pressure is a decreasing function of z while in the other configuration, it is an increasing function of z. In the first configuration, the pressure curves for different Re have intersections, while in the second configuration they do not. The gap between two conical cylinders is filled with six pairs of Taylor vortices at about the same Reynolds number and in each pair of vortices in the first configuration, the upper vortex is larger than the bottom one while in the second configuration, the bottom vortex is larger than the upper one.

VANISHING OF THREE-DIMENSIONALITY IN THE WAKE BEHIND A ROTATIONALLY OSCILLATING CIRCULAR CYLINDER

The flow behind a three-dimensional rotationally oscillating circular cylinder was studied by a numerical method. The computations were performed at a Reynolds number of 260, which is at a level that the flow wake has developed into a three-dimensional state called Mode-B. The purpose of this paper is to examine the influence of various rotational amplitudes （0.1-0.7） on the wake instability of the flow, while the oscillation frequency is fixed to the value of that measured in the wake of a stationary cylinder. The results show that the rotation with sufficiently high amplitude brings the flow back to its nominal two-dimensional state. Moreover, it is found that the value of the time-averaged drag and the RMS value of the lift are larger than those of a stationary circular cylinder.