Cylindrical Research Articles

CFD Study for Wave Run-up Characteristics Around a Truncated Cylinder with Damper

In this study, numerical simulations for a single fixed truncated circular cylinder in regular waves were conducted to investigate the nonlinear wave run-up under various dampers and wave period conditions. The present study used the volume of fluid (VOF) technique to capture the air-water interface. The unsteady Reynolds-averaged Navier–Stokes (URANS) equation with the k– ϵ turbulence model was solved using the commercial computational fluid dynamics (CFD) software STAR-CCM+. First, a systematic spatial convergence study was conducted to assess the performance and precision of the present numerical wave tank. The numerical scheme was validated by comparing the numerical results of wave run-up on a bare truncated cylinder with the experimental results, and a good agreement was achieved. Then, a series of parametric studies were carried out to examine the wave run-up time series around the truncated cylinder with single and dual dampers in terms of the first- and second-order harmonic and mean set-up components. Additionally, the local wave field and the flow velocity vectors adjacent to the cylinder were evaluated. It was confirmed that under short wave conditions, the high position of the damper led to a noticeable increase in the wave run-ups with significant changes in the first- and second-order harmonic components.

Theoretical and Experimental Investigation of Material Removal Rate in Magnetorheological Shear Thickening Polishing of Ti–6Al–4V Alloy

Abstract Magnetorheological shear thickening polishing (MRSTP) is a novel hybrid polishing method that combines the magnetorheological effect and the shear thickening effect. It has great potential for ultra-precision machining of complex surfaces. However, the absence of a correlation between material removal and the rheological properties of the polishing media has posed difficulties for further improvements in polishing efficiency and quality in MRSTP. In this work, a material removal model for MRSTP was established based on the principles of magneto-hydrodynamics, non-Newtonian fluid kinematics, and microscopic contact mechanics. This model combines the material removal model for a single abrasive particle with a statistical model of active grits. When comparing the experimental and theoretical results, it became evident that the developed material removal model can accurately predict the material removal depth of the workpiece under different processing parameters such as rotational speed of the rotary table and magnetic field strength. The average prediction error was found to be less than 5.0%. Furthermore, the analysis of the rheological behavior and fluid dynamic pressure of the polishing media reveals the coupling effects between the magnetic, stress, and flow fields. This provides theoretical guidance for the actual processing of MRSTP. Finally, the maximum material removal rate of 3.3 μm/h was achieved on the cylindrical surface of the Ti–6Al–4V workpiece using the MRSTP method. These results demonstrate that the MRSTP method holds great potential in the field of ultra-precision machining of difficult-to-machine materials.

Quantifying instantaneous flow reversal of tracer particles in subsonic, transonic and supersonic flows past a circular cylinder

Tracer pathline statistics have rarely, if at all, been used in the investigation of compressible subsonic, transonic and supersonic flows past a circular cylinder. Here, we report pathline histogram, conditional histogram and zonal histogram data, focusing on the characteristics of particle instantaneous flow reversal and their dependencies on Mach number and tracer release position. The far-upstream Mach number and the diameter-based Reynolds number used for these three flow regimes are ( 0.2 , 10000 ) , ( 0.9 , 3900 ) and ( 1.2 , 10000 ) , respectively. The subsonic surface-release histogram profiles display unexpected persistent oscillations at a frequency 50 times of the periodic vortex shedding frequency, reflecting the effect of a very small magnitude zig-zagging type of particle motion in a region very close to the wall and slightly behind the mean flow separation location. No similar high-frequency oscillation is observed in the corresponding transonic and supersonic histograms likely because, at Ma ≥ 0.9 , periodic vortex shedding ceases to exist and the near-wake becomes a quasi-laminar recirculation zone bounded by a pair of converging slip-layers with a neck opening to the far-wake. At the instant of 5 subsonic vortex-shedding periods after being released from the cylinder surface, there are 1.67 % , 35.2 % and 39.7 % particles that experience flow reversal in the subsonic, transonic and supersonic flows, respectively. Surprisingly, in the present transonic flow, growth of the turbulent far-wake behind the pair of lambda-shocks is constrained over a considerable streamwise distance.

Axial shift mapping: a self-referencing test for measuring the axial figure of near-cylindrical surfaces

Lateral shearing self-referencing interferometry methods shift the surface under test between measurements to separate its topography from that of the reference surface. However, rigid body errors occur during shifting, creating an ambiguity in the quadratic term of the extracted surfaces. We present axial shift mapping, a lateral shearing self-referencing interferometry method for cylinders, in which the quadratic ambiguity is resolved by measuring the rigid body errors using known artifact mirrors residing in the interferometer’s field of view. First, one-dimensional lines of a flat mirror are measured with 2.8 nm RMS difference compared to a three flat test. Then, axial shift mapping is extended to cylindrical surfaces using a computer generated hologram. We find that axial shift mapping results in full surface extraction of cylindrical optics, along the axial direction, with a repeatability of 4.4 nm RMS. We also find that the reference surface extracted through axial shift mapping is within 4.5 nm RMS of the transmitted wavefront error of the computer generated hologram substrate, which was expected to be the largest contribution of reference wavefront error.

Supersonic dusty gas flow past a cylinder in Eulerian–Lagrangian framework

The present study utilizes computational methods to analyze two-dimensional particle-laden flow over a circular cylinder. The effect of seeding of dust particles in the viscous flow of a compressible gas is analyzed. A new solver has been developed for the purpose of studying multi-phase flows in the supersonic regime. Most of the prior research has primarily focused on flows characterized by low Mach numbers and the absence of shock waves, and there have been very few studies dealing with supersonic dusty gas flows. This study considers a supersonic Mach number and investigates the effect of particle size and particle volume fraction on dusty-gas flow over a circular cylinder. The simulation results reveal that the seeding of particles in the flow creates perturbations. The present work also highlights the influence of particles on flow separation and the subsequent increase in the skin friction coefficient and coefficient of drag. The study shows that for supersonic flows, at the same volume fraction, larger particle size creates more instabilities in the flow, while smaller particles are responsible for increased drag on the cylinder, owing to a greater frequency of collisions.

Influence of the slip boundary on square cylinders with lattice Boltzmann method

In this investigation, two-dimensional flow past square cylinders with slip boundary have been studied with the lattice Boltzmann method. Three modes, which are a single cylinder, an oblique cylinder, and side-by-side cylinders, are investigated with Reynolds numbers from 25 to 200 while relative slip length ranges from 0 to 0.1. It can be concluded that both the flow state and the slip boundary have a great effect on the drag reduction rate. For a single square cylinder, drag forces decrease with larger slip length while the Strouhal number is almost constant. For an oblique cylinder, the slip length also has effects on the stability of the flow except the drag and lift forces. Vortex separation delays with a slip wall of oblique cylinder. For side-by-side cylinders, the jet between two cylinders is not conducive to the drag reduction rate of the slip boundary. Moreover, the application of slip boundary may also lead to additional drag force as vortex separation intensifies, which is extremely different from simple channel flows. Studies have shown that the slip boundary does not always reduce the drag in some complex flow fields. It can be concluded that the drag reduction effect of slip boundaries is more effective in uniform flow.

Flow-induced response and wake characteristics of a flexible splitter plate attached to a circular cylinder in laminar flow

This paper reported the numerical results of the flow past a flexible splitter plate attached to the rear of a rigid circular cylinder at a low Reynolds number of 160. The finite-volume method (FVM) in OpenFOAM-9 and the finite-element method (FEM) in deal.ii are utilized to solve the fluid and solid domains of the fluid–structure interaction (FSI) issue, respectively. The effects of the plate length L/D and normalized Young's modulus E* are examined. According to the equilibrium position and bending deformation order, five response modes are identified, including the symmetry-I, symmetry-II, symmetry-III, bifurcation-I, and bifurcation-II. The amplitude of the plate-tip is enhanced as the vortex shedding frequency approaches the natural frequency. Nevertheless, the bifurcation is observed between the symmetry-I and symmetry-II modes, where the vibration amplitude sharply drops. The number of local vortices occurring along the surface of flexible plate increases with the plate length, leading to more local negative pressure regions. Consequently, the higher mode response is excited. The greater shear stress occurs at the position of small curvature radius during the plate deformation. The 2S (a pair of vortices is alternately shed per cycle) vortex shedding mode is recognized in most cases. In contrast, the P + S (a pair of vortices shedding from one side and a single vortex shedding from the other side) mode is observed in the bifurcation-II mode with a relatively large amplitude. Due to the deflection, the wake flow becomes asymmetrical with a significant elongation of the recirculation region. Four interaction behaviors between the boundary layers and the plate are identified. The significant reduction of hydrodynamic forces is achieved when the flexible plate experiences the bifurcation.

Smoothed particle hydrodynamics simulations of microstructure induced stress overshoot in structured fluids

Stress overshoot/undershoot is an important phenomenon in structured fluids undergoing dynamic and transient flow. To accurately capture the flow process, it is important to have a better understanding of and include in the numerical modeling the microstructure evolution that leads to the stress overshoot/undershoot phenomenon. We present a procedure for incorporating a microstructure model into a Lagrangian framework based on the smoothed particle hydrodynamics fluid solver. The numerical simulation is performed for a typical structured fluid under an applied strain rate history flow. Good agreement between the numerical results and the experimental data lends credence to and validates the proposed procedure for simulations of complex mixture flows. Additionally, the interaction between a flow of structured fluid and a circular cylinder placed in a channel is investigated. The viscous force is found to overshoot together with the applied gradient pressure and decrease over time as the fluid approaches the equilibrium state.

Relationship between wake and cylinder dynamics for a cylinder undergoing modulated vortex-induced vibrations

Vortex-induced vibrations (VIV) in the initial branch are investigated for a 2-degree-of-freedom circular cylinder placed near a plane boundary (Re=UDν=200, where U is the inflow average streamwise velocity, D is the cylinder diameter, and ν is the kinematic viscosity) with imposed sinusoidal perturbations of the free stream at resonant, 2fo, and near-resonant conditions, 2.2fo (fo is the natural shedding frequency). The cylinder exhibits a quasi-periodic response, which challenges the comprehension of its relationship with the wake dynamics obtained through conventional VIV models. The total force acting on the cylinder is decomposed into a vortex-induced force, FV, linearly coupled to VIV, and a force induced by the effective mass of the cylinder, FS, which is non-linearly coupled to VIV. The proposed semi-empirical model reveals that the time-varying nature of the effective mass in FS drives the non-linear response. The model's physical consistency is verified against simulation results. While focusing on VIV in the initial branch, the validity of the proposed model is expected to extend to other branches of response, offering a promising avenue for developing a robust predictive model for VIV under various flow conditions.

A note on the topographic bias of a right circular cylinder and a cone

A note on the topographic bias of a right circular cylinder and a cone

Modified stable methods and effect of artificial diffusion in the numerical study of viscoelastic fluid flow

The trace of the polymer conformation tensor in numerical simulations is bounded by applying a logarithmic transformation to the elastic force in the finitely extensible nonlinear elastic-Peterlin model. This method, called elastic stress logarithmic transformation (EL), is combined with the artificial diffusion (AD) and square-root conformation reformulation (SRCR) methods to establish EL-AD and EL-SRCR methods, respectively. The accuracy and stability of these methods have been investigated by conducting direct numerical simulations of viscoelastic laminar flows around a circular cylinder at a Reynolds number Re = 100, considering a wide range of rheological parameters: the maximum polymer extensibility L = 10 and 100, and the Weissenberg number Wi=1−80. Specifically, effects of artificial diffusion coefficients measured by dimensionless Schmidt number Scc=10−106 on the flow are studied. The results indicate that the EL method can effectively ensure the boundedness and accuracy of the conformation tensor trace, making the EL-AD method a valuable modification of the AD method for simulations with larger L and Wi. The impact of the polymer stress diffusion on the simulation is complex. It can stabilize the simulation by reducing sharp gradients and peak positions of elastic stress. However, inappropriate artificial diffusion coefficients lead to flow artifacts when L is large (L = 100). One consequence is an amplification of the solid-like phenomenon caused by polymer near the upstream stagnation point of the cylinder. Another consequence is an enhanced suppression of vortices by polymer downstream of the cylinder. The challenge in determining a suitable AD coefficient emphasizes the superiority of the EL-SRCR method in terms of stability and accuracy.

The Consequence of Velocity Ratio and Curvature of the Surface on MHD Forced Convection Boundary Layer Nanofluid Flow Over an Axisymmetric Cylindrical Surface

The present study has considered the steady laminar incompressible non-Newtonian fluid over an axisymmetric stretching cylindrical surface under the effect of the curvature parameter, Brownian motion parameter, and thermophoresis parameter within the boundary layer region. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the curvature parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving thirdorder ordinary differential equations that include both linear and nonlinear terms. The governing equations have been converted into ordinary differential equations (ODEs) by using appropriate transformations. Runge–Kutta’s fourth-order method is used to find the numerical solutions by exploiting symbolic software MATLAB via the shooting method. It is found that the temperature profile increases for the effect of the thermophoresis parameter and heat generation parameter while decreasing for the effect of the curvature parameter. This study makes an essential contribution to the nanofluids field to solve numerically nonlinear differential equations (DEs). Brownian motion and thermophoresis parameters are considered for the nanofluid effect which plays an important role in the variation of temperature and concentration.

Extension of Pick’s Theorem to Spherical Geometry using Girard’s Theorem

In this article, Pick’s theorem is extended to three-dimensional bodies with two-dimensional surfaces, namely spherical geometry. The equation for the area of a polygon consisting of equilateral spherical triangles is obtained by combining Girard’s theorem used to find area of any spherical triangle and Pick’s theorem used to find area of a simple polygon with lattice point vertices in Euclidian geometry. Vertices of the polygon are represented by integer points. In this way, an equation to find area of a spherical polygon is presented. This equation could give an idea to be applied on cylindrical surfaces, hyperbolic geometry and more general surfaces. The theorem proposed in this article which is the extension of Pick’s theorem using Girard’s theorem seems to be a special case of a more general theorem.

Non‐invasive experiments on the fluid film behavior in a horizontal rotating cylinder

AbstractSubject of our investigations is the spatial distribution of a Newtonian liquid within a partially filled horizontal rotating hollow cylinder in dependence of the variables angular velocity and angular acceleration, cylinder filling and cylinder geometry as well as viscosity of the liquid. We focus on the development of a thin liquid film at the inner cylinder wall. The layer thickness was measured using a non‐invasive laser‐induced fluorescence measurement technique. In addition, the liquid distribution and flow topologies were observed and described using optical measurements.The occurring liquid distributions can be distinguished in three different states. At low angular velocities most of the liquid is located at the bottom area of the cylinder. However, a thin liquid film is always pulled out of the reservoir from the rotating cylinder wall. With increasing angular velocity more and more liquid is deflected and the locally measured film thickness increases. Exceeding a critical angular velocity, a centrifuged distribution of the whole liquid establishes. In this state the measured film thickness fits the theoretical calculated value quite well. Very complex liquid distributions and flow patterns develop in particular at critical angular velocities. In detail, at all investigated cylinder systems two critical angular velocities were verifiable, the so‐called transition points of liquid distribution. At the first critical velocity, the centrifuged state develops. With deceleration of the system a second critical angular velocity exists. Below this value the centrifuged distribution of the liquid collapses and moves back again to the bottom of the cylinder. A thin film is still pulled out of this reservoir. The second critical angular velocity of the break down is always smaller compared to the first one at which the centrifuged state develops. Both of them can be influenced using the investigated parameters. Eventually, we show that the locally measured film thickness also depends on these parameters.

The Spectral Integral Method (SIM) for the Scattering from an Arbitrary Number of Circular PEC Cylinders

The Spectral Integral Method (SIM) for the Scattering from an Arbitrary Number of Circular PEC Cylinders

Antiresonance quadrupole system based on a circular conductive cylinder

Antiresonance quadrupole system based on a circular conductive cylinder

A combined volume penalization/selective frequency damping approach for immersed boundary methods: Application to moving geometries

High-order numerical techniques and immersed boundary methods (IBMs) are gaining popularity to avoid constructing body-fitted meshes while accurately resolving complex flows on Cartesian grids. Recently, we have presented a new treatment for the immersed boundary method based on the combination of volume penalization and selective frequency damping (SFD) [J. Kou and E. Ferrer, “A combined volume penalization/selective frequency damping approach for immersed boundary methods applied to high-order schemes,” J. Comput. Phys. 472, 111678 (2023).], that offers improved accuracy for nonmoving geometries. The objective of SFD is to remove nonphysical, high-frequency oscillations inside the solid body and by doing so enhance the accuracy in the fluid region. The present paper extends the new immersed boundary treatment to moving geometries. The convergence of this approach is first validated by the method of manufactured solutions, where we design a one-dimensional advection–diffusion case, with a moving interface, to validate the numerical accuracy. Second, we simulate an unsteady flow past a plunging circular cylinder (Navier–Stokes solver). In this case, we show that the combination of volume penalization and SFD provides improved accuracy for moving geometries.

Application of singular spectrum analysis to nonstationary time series in flow-induced vibrations of a circular cylinder

In numerical simulations of flow-induced vibrations (FIV) of a circular cylinder, abundant time series data are available, including cylinder displacement and acting forces. Singular spectrum analysis (SSA) is employed to deal with nonstationary multi-component time series produced in two FIV cases with proper interpretation in physics. In the first case, the cylinder displacement time series is decomposed into two oscillatory components using SSA. The instantaneous frequencies of these two components are obtained by Hilbert transform (HT) and found to be in agreement with the wavelet transform of the cylinder displacement. In the second case, three oscillatory components are extracted from the cylinder displacement time series by SSA. The dominant component is characterized by steady oscillations at the vortex shedding frequency, which suggests a relatively steady vortex shedding process behind the rear cylinder. In contrast, the second component, which is closely associated with the alternate boundary layer separations from the front cylinder, features in the increasing amplitude with time. This implies that the unsteady flow field in the gap might be attributed to the nonstationary cylinder oscillations. This work demonstrates that SSA, in conjunction with HT, enables a comprehensive time-frequency analysis of nonstationary time series obtained in FIV.

Symmetry-breaking response of a flexible splitter plate attached to a circular cylinder in uniform flow

Static and dynamic fluid–structure interaction of a flexible plate behind a stationary cylinder in uniform flow is explored for a body-to-fluid mass ratio of 10. Steady flow-structure computations for Re = 150, based on the diameter of cylinder and free-stream speed, reveal four regimes with respect to increasing flexibility of the plate. The plate does not undergo any lateral deflection in regime 1 beyond which it undergoes a symmetry-breaking bifurcation causing it to spontaneously deflect laterally. The curvature is of the same sign along the entire length of plate in regime 2 while it changes sign along the plate in regime 3. The lateral deflection, however, is still maximum at the plate tip. The location of maximum deflection moves away from the plate tip in regime 4. The evolution of flow structures including the strength of various standing vortices, with flexibility, is studied. The role of reattachment of flow on the surface of the plate and the modification of the pressure distribution is explored. The critical Re, beyond which the splitter plate spontaneously achieves a deflected shape, decreases with increase in flexibility. It is estimated to be Re = 122.33 for the limiting case of an infinitely flexible plate. Computations for dynamic fluid–structure interaction reveal several regimes of lock-in with different natural vibration modes of the plate and related hysteresis. No lateral bias in the time-averaged deflection is found during lock-in; it occurs in the desynchronization regime that precedes the lock-in regime with second mode. For the mass ratio considered, the bias in the static and dynamic simulations start at the same flexibility.

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder: Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder: Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution