HYDRODYNAMIC DAMPING OF A CYLINDER AT β≈10

This paper describes delicate, but large-scale, experiments aimed at measuring the hydrodynamic damping of a circular cylinder oscillating in still water and transversely in a current. Attention is concentrated on the regime of very small Keulegan–Carpenter numbers, in which the drag coefficient is inversely proportional to the Keulegan–Carpenter number. Measurements in still water at β=650 000 and 1250 000 point to drag coefficients about twice those appropriate to two-dimensional laminar flow, in common with earlier measurements at β≈10⁵. In the presence of a slowly varying transverse current (generated by placing the cylinder at the node of standing waves of long period), the damping increased with the reduced velocity of the ambient flow at a rate that increased with the Reynolds number.     

Spacing effects on hydrodynamics of heave plates on offshore structures

The nonlinear viscous flow problem associated with a heaving vertical cylinder with two heave plates in the form of two circular disks attached is solved using a finite difference method. Numerical experiments are carried out to investigate the spanwise length effects on the hydrodynamic properties, such as added mass and damping coefficients. Over a Keulegan–Carpenter (KC) number range from 0.1 to 0.6 at frequency parameter (β=7.869×10⁷), calculations indicate that a KC-dependent critical value of spanwise length L/D_d (L—the distance between the disks, and D_d—the diameter of the disks) exists. A significant influence of L/D_d on the vortex shedding patterns around the disks and the hydrodynamic coefficients is revealed when L/D_d is smaller than the critical value due to strong interaction between vortices of different disks. Beyond that limit, however, both added mass and damping coefficients are shown to be rather stable, indicating the independence of the vortex shedding processes of different disks.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

Interaction between an incompressible flow and elastic cantilevers of circular cross-section

The purpose of this work is to study the deformation of elastic cantilevers due to hydrodynamic forces by coupled fluid–structure interaction simulations. The cantilever is placed in a rectangular duct and the Reynolds number based on bulk velocity and cantilever diameter is 400. Reduced velocities in the range π/4 to 2π are studied, which covers both un-synchronised motion and the initial branch of synchronisation. The cantilever surface is represented by a virtual boundary method which replaces a solid object in flow by additional force distribution to satisfy local boundary condition. The flow field is solved using a Cartesian finite difference code and the deformation of the cylinder a finite element approach using one-dimensional beam elements is used.     

Aerodynamic loading on a cylinder behind an airfoil

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re_d=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Re_c=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Re_c<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re_c>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding.     

Effects of an asymmetrical confined flow on a rectangular cylinder

The effects of an asymmetric confined flow on a cylinder of rectangular cross-section are investigated and discussed. Experiments are performed in a wind tunnel by placing cylinders of different cross-sections at various elevations from the floor of the test-section. The Reynolds number is varied within the range 6×10³–4×10⁴. Forces exciting the cylinder are measured by built-in dynamometers placed inside the cylinder structure. The flow is characterized by mean and fluctuating local velocity components to define the inflow distribution and the ensuing wake region. The mean dimensionless force coefficients are then calculated and analyzed. The frequency analysis of the force components acting on the cylinder provides the dynamic characterization of the loading and of the wake shedding. The experimental results highlight that the presence of the wall strongly influences the system dynamics also when the cylinder is placed at a relatively large elevation from the wall itself. The cylinder aspect ratio governs effects of the wall condition on the force coefficients and the Strouhal number.     

Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory ambient flows

Steady incident flow past a circular cylinder for sub- to supercritical Reynolds number has been simulated as an unsteady Reynolds-averaged Navier–Stokes (RANS) equation problem using nonlinear eddy-viscosity modelling assuming two-dimensional flow. The model of Craft et al. (Int. J. Heat Fluid Flow 17 (1996) 108), with adjustment of the coefficients of the ‘cubic’ terms, predicts the drag crisis at a Reynolds number of about 2×10⁵ due to the onset of turbulence upstream of separation and associated changes in Strouhal number and separation positions. Slightly above this value, at critical Reynolds numbers, drag is overestimated because attached separation bubbles are not simulated. These do not occur at supercritical Reynolds numbers and drag coefficient, Strouhal number and separation positions are in approximate agreement with experimental measurements (which show considerable scatter). Fluctuating lift predictions are similar to sectional values measured experimentally for subcritical Reynolds numbers but corresponding measurements have not been made at supercritical Reynolds numbers. For oscillatory ambient flow, in-line forces, as defined by drag and inertia coefficients, have been compared with the experimental values of Sarpkaya (J. Fluid Mech. 165 (1986) 61) for values of the frequency parameter, β=D²/νT, equal to 1035 and 11240 and Keulegan–Carpenter numbers, KC=U₀T/D, between 0.2 and 15 (D is cylinder diameter, ν is kinematic viscosity, T is oscillation period, and U₀ is the amplitude of oscillating velocity). Variations with KC are qualitatively reproduced and magnitudes show best agreement when there is separation with a large-scale wake, for which the turbulence model is intended. Lift coefficients, frequency and transverse vortex shedding patterns for β=1035 are consistent with available experimental information for β≈250−500. For β=11240, it is predicted that separation is delayed due to more prominent turbulence effects, reducing drag and lift coefficients and causing the wake to be more in line with the flow direction than transverse to it. While these oscillatory flows are highly complex, attached separation bubbles are unlikely and the flows probably two dimensional.     

Investigation of the flow around a circular cylinder under the influence of an electromagnetic force

An investigation of the effect of the local electromagnetic body force on the flow behavior around a circular cylinder is conducted. The electromagnetic force is applied locally on the cylinder surface in the range of 70–130° from the stagnation point along the cylinder circumference in both clockwise and counterclockwise directions. The numerical results predict that the Lorentz force applied in the circumferential direction on the cylinder moves the separation point rearward, and reduces the drag. To validate the numerical results, an experiment is conducted with a circular cylinder of 5 cm diameter. The electrodes and permanent magnets are flush mounted on the cylinder in such a way that the Lorentz force is generated in the circumferential direction. Flow visualization with polystyrene particles and direct drag measurement using strain gages are made. The fluid used is natural sea water of electric conductivity of about 4 (Ω m)^-1. Induction effect can be neglected in the present investigation due to the low flow speed and the Lorentz force is proportional to E×B where E is an applied electric field and B is a magnetic field. Received: 7 June 1998/Accepted: 28 April 1999     

Spectral and correlation characteristics of the turbulent boundary layer on an extended flexible cylinder

In marine geophysical seismological prospecting extensive use is made of towed receiving systems consisting of extended flexible cylinders containing acoustic sensors over which the water flows in the longitudinal direction. The boundary layer pressure fluctuations on the cylinder surface are picked up by the sensors as hydrodynamic noise. This paper is concerned with the study of the energy and spacetime characteristics of the pressure fluctuations in the turbulent boundary layer on an extended flexible cylinder in a longitudinal flow. The pressure fluctuations on the cylinder surface have been investigated experimentally for Re_X=(2–4)·10⁷, a dimensionless diameter of the pressure fluctuation sensors d _p ⁺ =d_pu^*/=500, where d_p is the sensor diameter, u^* the dynamic viscosity, and the viscosity coefficient, and frequencies 0.02311.259 (=^*/U). The spectral and correlation characteristics of the pressure fluctuations on the surface of the flexible cylinder are found to differ from the corresponding characteristics for a rigid cylinder [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i aza, No, 5, pp. 49–54, September–October, 1989.     

Simulation of cross-flow-induced vibration of cylinder arrays by surface vorticity method

The surface vorticity method (SVM), which is a fast and practical grid-free two-dimensional (2-D) method, and a fluid–structure interaction model incorporating the effects of cylinder motions and displacements is used to simulate the vortex-induced vibration of cylinder arrays at sub-critical Reynolds number Re=2.67×10⁴. The SVM is found to be most suitable for simulating a 2-D cylinder row with large-amplitude vibrations where the vorticity field and the fluid forces of the cylinder row change drastically, and the effect of the stream on the transverse direction vibration is very significant. The fluidelastic instability of a flexible cylinder row at small pitch ratio is also investigated, and the critical reduced velocity of the cylinder row at a reduced damping parameter S_G=1.29 is calculated, which is in good agreement with experimental and analytical results of the unsteady model. Vortex-induced vibration of a staggered cylinder array is simulated using different structural parameters. When the cylinders are relatively more flexible, the flow pattern changes dramatically and the fluid–structure interaction has a dominant impact on the flow field. Compared with grid-based methods, the grid-free SVM is a fast and practical method for the simulation of the FIV of cylinder arrays due to vortex shedding at sub-critical Reynolds numbers.     

Self-oscillational motion of a cylinder towed in weak aqueous polymer solution

A study is made of the effect of polymer additions on the nonstationary vibrational motion of a cylinder towed in a weak aqueous solution of the polymer and capable of making transverse displacements under the action of the force arising from asymmetry of the periodic detachment of the boundary layer. The Reynolds number was 3·10³–10⁴.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 162–164, 1973.The authors wish to thank V. P. Borovikov for his assistance in organizing the experiments.     

HYDRODYNAMIC DAMPING OF A CYLINDER AT β≈106

This paper describes delicate, but large-scale, experiments aimed at measuring the hydrodynamic damping of a circular cylinder oscillating in still water and transversely in a current. Attention is concentrated on the regime of very small Keulegan–Carpenter numbers, in which the drag coefficient is inversely proportional to the Keulegan–Carpenter number. Measurements in still water at β=650 000 and 1250 000 point to drag coefficients about twice those appropriate to two-dimensional laminar flow, in common with earlier measurements at β≈10⁵. In the presence of a slowly varying transverse current (generated by placing the cylinder at the node of standing waves of long period), the damping increased with the reduced velocity of the ambient flow at a rate that increased with the Reynolds number.     

Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Drag Reduction of a Circular Cylinder Using an Upstream Rod

Experimental studies on the drag reduction of the circular cylinder were conducted by pressure measurement at a Reynolds number of 82 000 (based on the cylinder diameter). A rod was placed upstream of and parallel to the cylinder to control the flow around the cylinder. The upstream rod can reduce the resultant force of the cylinder at various spacing between the rod and the cylinder for α < 5^∘(α defined as the staggered angle of the rod and the cylinder). For α > 10^∘, the resultant force coefficient has a large value, so the upstream rod cannot reduce the force on the cylinder any more. For α = 0^∘ and d/D = 0.5 (where d and D are the diameter of the rod and the cylinder, respectively), the maximum drag of the cylinder reduces to 2.34% that of the single cylinder. The mechanism of the drag reduction of the cylinder with an upstream rod in tandem was presented by estimating the local contributions to the drag reduction of the pressure variation. In the staggered arrangement, the flow structures have five flow patterns (they are the cavity mode, the wake splitting mode, the wake merge mode, the weak boundary layer interaction mode and the negligible interaction mode) according to the pressure distribution and the hydrogen bubble flow visualization. The half plane upwind of the cylinder can be divided to four regions, from which one can easily estimates the force acting on the circular cylinder with an upstream rod in staggered arrangement.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Experimental investigation of the heat exchange in separation zones ahead of cylindrical obstacles

Results of an experimental investigation of the heat exchange in turbulent boundary layer separation zones ahead of cylindrical obstacles at a subsonic air stream velocity are elucidated. The investigation was conducted for changes in the ratio between the obstacle diameter and altitude between 0.25 and 4, between the boundary layer thickness at the separation point and the obstacle altitude between 0.09 and 0.7, between the Reynolds number computed by means of the free stream parameters and the obstacle height between 10⁴ and 4·10⁵. The Mach number reached 0.85. The temperature factor was 0.7. It is shown that the distribution of the heat transfer coefficients in the separation zone depends on the Reynolds and Euler numbers, the ratio between the boundary layer displacement thickness and the diameter (or altitude) of the obstacle, and the ratio between the diameter and the altitude. Criterial dependences are obtained which extend the heat-exchange results at characteristic points of the separation zones, as are also dimensionless distributions of the heat transfer coefficients to determine the heat fluxes on a plate in the plane of symmetry of the separation zone ahead of obstacles.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 6, pp. 83–89, November–December, 1972.The authors are grateful to V. S. Avduevskii for discussing the research results.     

UNSTEADY LIFT FORCE ON A TOWED SPHERE

An experimental effort to characterize the broadband flow-induced lift forces on a spherical body that is towed underwater is described. The body itself is the transducer which is comprised of a small geophone encased in a near-neutrally-buoyant sphere, 7·62 cm in diameter. The research described in this paper quantifies the flow-induced unsteady lift force signal as a function of the sphere diameter Reynolds number (7620<Re<34 290) and the Strouhal number (1·5<St<30). It is found that the broadband flow-induced unsteady lift forces are proportional to the product of an area and the dynamic pressure of the flow, as expected. These data are compared to similar data measured previously on a finite-length, right-circular cylinder in cross flow. This comparison indicates that the cylindrical body creates more unsteady side force than does the spherical one, particularly at the lower end of the Strouhal number range.     

Excitation,inertia, and drag forces on a cylinder vibrating transversely to a steady flow

We present a computational study of the forces on a cylinder oscillating harmonically in the direction perpendicular to a uniform flow. The two-dimensional Navier–Stokes equations are solved on a coordinate system fixed on the cylinder. The Reynolds number is equal to 400. Several oscillation frequencies are considered: (a) resonant forcing, (b) forcing at frequency below the natural frequency of the wake, and (c) forcing at frequency above the natural frequency of the wake. Once the flow has reached a statistical steady state, the lift and drag forces on the cylinder are computed. The lift force in particular is decomposed into one component that is in phase with the velocity (excitation force), and one component that is ${180}^{\circ }$ out of phase with the acceleration (inertia or added mass force). The variation of the forces as a function of the amplitude-over-diameter-ratio is studied in detail. It is found that the scaling of the so-called inertia component of the force with the acceleration of the cylinder can lead to serious problems at small amplitudes of oscillation, and that it is overall preferable to scale both components of the force with the dynamic pressure of the fluid. Through extensive flow visualization, it is shown that changes in the state of the flow are related to the abrupt changes of the forces with the amplitude-over-diameter-ratio. Moreover, qualitative differences are found between the results for the below resonance and the resonant or above resonance forcing. The former are characterized by smooth variation of the hydrodynamic force coefficients and spatially ordered vortex streets. The latter are characterized by continuous and sharp, even jump-like, changes of the forces, and a variety of vortex patterns in the wake, resulting for some combinations of frequency and amplitude of oscillation to spatially disordered vortex streets.