2D Circular Cylinder Research Articles

Lifting Stokes' paradox by accelerating flow past a circular cylinder and extension of the analysis to the sphere

It is known that Stokes' paradox exhibits in various flow conditions, most notably, in flow past a two-dimensional (2D) circular cylinder. In this study, we provide an example through detailed analytical solution that Stokes' paradox can be lifted by accelerating flow past a stationary cylinder. The analysis is also extended to the case of the accelerating flow past a stationary sphere although in this case, there is no Stokes' paradox. The effects of the acceleration parameter on the flow streamlines, the pressure, and the vorticity distributions, as well as on the drag coefficient, are investigated. The drag comprises the potential component and vorticity component, which are further due to form drag and frictional drag receiving a separate investigation. However, the drag decomposition is also examined the viewpoint of the force decomposition: the total drag = the potential component + surface vorticity component + volume vorticity component.

Numerical Investigation of Vortex-Induced Vibration of a Circular Cylinder with Control Rods and Its Multi-Objective Optimization

The flow past a 2D circular cylinder with control rods is numerically simulated in the present paper. The suppression effects of the control rods on the vortex-induced vibration (VIV) characteristics of the cylinder are investigated using the overlapping grid method and user defined function. By setting the cylinder’s vibration amplitude and drag force coefficient as the expected objective function, a multi-objective optimization is carried out to enhance the suppression performance at different reduced velocities, for which the rod-to-cylinder diameter ratio, gap ratio, incidence angle and reduced velocity are used as design variables. The regression expressions, which are obtained by Box–Behnken design (BBD), are employed in nondominated sorting genetic algorithm II (NSGA-II) to minimize the objectives. It is found that both the optimized vibration amplitude and drag force coefficient exhibit a monotonically decreasing linear trend with the reduced velocity, and as the reduced velocity decreases, the range of the optimized points gradually decreases. Subsequently, the optimized cases are verified by CFD simulations and compared with the original cases. For the samples at the reduced velocity of 4, 5, and 6, the vibration amplitude after optimization decreases by 15.1%, 24.8%, and 21.6%, respectively.

Improved dynamical modelling of freely falling underwater cylinder based on CFD

An improved dynamic modelling approach using CFD is proposed to study the underwater motion of a dropped cylinder. Firstly, validation studies on RANS simulated flow past two dimensional (2D) and three dimensional (3D) cylinders (circular and square sectioned) are carried out. The predicted drag coefficients and pressure distribution for 2D and 3D cylinders are both in good agreement with corresponding experiments. URANS simulated results including quantification of mean surface pressure coefficient, fluid velocity and instantaneous drag coefficient and streamlines are compared between 2D circular cylinder, 3D circular cylinder and 3D square prism. Finally, the CFD predicted drag coefficients are applied to study the free falling of a horizontal cylinder under calm water and current respectively. Both 3D effects and cylinder shape effects are studied and found to greatly affect the motion of the cylinder by changing the drag coefficient.

Numerical Analysis of Drag Force Acting on 2D Cylinder Immersed in Accelerated Flow

In this study, the drag exerted by an accelerating fluid on a stationary 2D circular cylinder is numerically investigated using Fluent 19.2 based on the finite-volume method. The SST k–ω model is chosen as the turbulence model because of its superiority in treating the viscous near-wall region. The results are compared to literature, and the numerical methods are validated. The acceleration of the inflow is analyzed for the range of 0.0981–9.81 m/s2, and the drag for each acceleration is compared. Additionally, the effect of the initial velocity on the drag acting on the circular cylinder is investigated at two initial velocities. As a result, a supercritical region, typically found under steady state conditions, is observed. Furthermore, vortex shedding is observed at a high initial velocity. This flow characteristic is explained via comparison with respect to the recirculation length and separation angle.

유입 유동의 가속도가 2D 원형실린더의 항력 및 후류에 미치는 영향

Computational studies of accelerating flow around 2D Circular Cylinder was performed to investigate characteristics of wake field and drag forces. Previous studies had revealed that drag on the cylindrical body in accelerating flow is much greater than that in the flow with constant velocity; however, the underlying physics on the drag increase has not been clearly investigated. In order to investigate the drag increase and its relationship with wake development, this study employed a finite-volume based CFD code, Fluent 13.0 with k-ω SST model for turbulence effects. Inflows are modeled with varied accelerations from 0.4905 to 9.81m/s². The drag computed in the present study is in good agreement with previous studies, and clearly shows the increase compared to the drag on the body in the flow with constant velocity. The results also show that drag crisis observed at high Reynolds number in the case of the flow with constant velocity is also found in the case of accelerating flow. The analysis for wake and recirculation length shows that conventional vortex shedding does not occur even at high Reynolds number and the drag increase is larger at higher acceleration.

Flow control around a circular cylinder with swinging thin plates

Flow around a 2D circular cylinder with attached swinging thin splitter plates is numerically investigated. The ratio of the plates’ length to the cylinder diameter is 1 (LD=1) where L is the Plates’ length and D is the cylinder diameter. The plates are attached at ±55 degrees (trigonometric angle) downstream and are forced to oscillate at different ratios of the natural vortex shedding frequencies with magnitudes of FR=0.75,1,1.25,1.5 and 2. The oscillation amplitude “α” as the other main variable ranges from 10 to 18 degrees. Two-dimensional simulations are carried out at the Reynolds number 100, and then extended to higher Reynolds number of 200. The results show that in certain configurations, an in-phase vortex-shedding pattern is dominant and the oscillatory nature of the lift force completely vanishes. Different flow patterns are observed and classified as well. The effects of the splitter plates’ oscillation on the lift and drag forces, flow patterns and vortex shedding frequencies are also discussed to develop a link between different flow patterns and the acting lift force on the cylinder.

Model Predictive Control of a Separated Flow around a Circular Cylinder at a Low Reynolds Number

This paper deals with model predictive control (MPC) of a separated flow around a 2D circular cylinder at a low Reynolds number. The magnitude of the radial velocity on a small region of the cylind...

A novel stencil selection method for the gradient reconstruction on unstructured grid based on OpenFOAM

For the unstructured finite volume algorithms, the stencil utilized for gradient reconstruction is important for the accuracy, efficiency and robustness. In this paper, we present a novel stencil selection method for the gradient reconstruction of the cell-centered finite volume methodology. In the novel stencil selection method, two local directions are generated for each control volume, and the stencil is generated based on the local directions. In this way, the characteristics of the structured grid are able to be reflected on the unstructured grid. To obtain the suitable local directions, an advancing front technique (AFT) is utilized to guide their generation. Through AFT, the direction of the boundary normal vector, along which the flow fields change dramatically, is obtained and propagated from the boundaries to the internal regions. Finally, the novel stencil extends in two directions, one of which is approximately aligned with the direction of the boundary normal vector. Hence, the gradient reconstruction methods with the new stencil are able to use the information along the boundary normal. In order to verify the validity of the new stencil, we present a new gradient reconstruction method, the structured least squares (struLSQR) method, by applying the new stencil to the least squares (LSQR) method. The performance of struLSQR, and two existing gradient reconstruction methods in OpenFOAM is tested by adopting the 2D channel flow and the 2D circular cylinder flow on both the quadrilateral and the triangular grids. A laminar flow past a flat plate is also adopted to verify the applicability of struLSQR to the viscous flow. The numerical results illustrate that the new stencil is able to solve the blow-up problem of LSQR. It can also obtain a higher order of accuracy compared to extLSQR. Moreover, the convergence speed of struLSQR can be up to 1.64 ∼ 2.60x of that of extLSQR.

High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates.

In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

Comparison of Handling Pressure in Poisson Solver for Immersed Boundary Method Considering Pressure Condition

In the Cartesian grid approach, the immersed boundary method (IBM) is well used to handle the boundary of an object with complicated shape on the Cartesian grid. However, the conventional IBM generates the unphysical pressure oscillations near the boundary because of the pressure jump between inside and outside of the boundary. The IBM considering pressure condition was proposed in order to remove the pressure oscillations by solving the governing equations considering the pressure condition on the boundary. In this method, there are two ways of the handling the pressure on the boundary in the Poisson solver. In this paper, the effect of removing the pressure oscillations by the IBM considering the pressure condition is investigated. And, the influence by the difference in the handling of the pressure on the boundary in the Poisson solver is investigated. In the numerical simulations of incompressible flow around a 2D circular cylinder, the present IBM indicates a greate effect of removing the pressure oscillations. And, it does not occur difference of the result by the difference of the handling the pressure on the boundary in the Poisson solver. Therefore, it is possible to select a method with less computational amount in the Poisson solver without degrading the quality of the result. It is concluded that the present IBM is very promising as improved method in order to remove the pressure oscillations in the conventional IBM.

Adding ecology to particle capture models: numerical simulations of capture on a moving cylinder in crossflow.

The particle capture efficiency, η, of systems that remove suspended particles from ambient flow (e.g. suspension feeding, abiotic pollination) has been studied using static collectors in steady flows. Particle deposition on collectors moving due to fluid flow remains largely unknown, despite its ecological relevance. We used numerical modeling to simulate particle deposition on a 2D circular cylinder subject to flow-induced oscillation in a cross flow. Using parameter values relevant to wind pollination and other natural biological systems, we examined the influence of the direction, amplitude and frequency of the oscillation, the Stokes number (Stk=0.01-5, characterizing particle behavior), as well as the Reynolds number (Re=662 and 3309, characterizing flow regime) in steady and unsteady flow, on η. The numerical model was validated with empirical results for parts of the parameter space. Particle capture occurred via "inertial impaction", "direct interception" and "leeward deposition", as well as via a new mechanism, "collector chasing" for moving collectors. The η of an oscillating cylinder varied significantly relative to a static cylinder, depending on the parameters used, and on the magnitude of a numerical error that caused loss of particles. This variance of η was due to a change in relative momentum between the particle and the moving collector, which depends on Re, Stk and the oscillation parameters. Collector oscillation transverse to oncoming flow direction strongly increased η, whereas collector motion parallel to flow had little effect on capture efficiency. The oscillation also changed leeward capture significantly in some cases. For most conditions, however, leeward deposition was small. Results suggest that collector motion could have significant influence on the particle capture efficiency of natural systems, which indicates the need to incorporate these ecologically more relevant findings into current models. Empirical studies, however, are still necessary to validate these results and provide reliable data.

Heat Transfer Suppression in Flow Around a Rotating Circular Cylinder at High Prandtl Number

Forced convection heat transfer across a 2D circular cylinder rotating at constant speed is investigated. Numerical simulations are carried out at constant values of Reynolds number in the range of 80–160. The non-dimensional rotation rate, α, is examined up to a maximum value of 5.3 for Prandtl number (Pr) 7. At constant Reynolds number, heat transfer suppression kicks off even at lower rotation rates contrary to the systems with lower values of Pr. Moreover, the heat transfer suppression parameter in such cases saturates at almost the double value at intermediate rotation rates as compared to the systems with low Pr.

Three-dimensional aspects of cylinder drag reduction by suction and oscillatory blowing

An efficient and robust active flow control (AFC) system was applied to a nominally 2D circular cylinder, an archetype bluff-body configurations, with the purpose of drag reduction and wake stabilization. This is a fundamental cornerstone of a larger research program aimed at similar objectives but focusing on more realistic engineering applications such as heavy vehicles, rotorcraft fuselage and buildings subjected to cross-winds.The current study is focused on drag reduction by separation delay and manipulation of the natural vortex shedding regime, affected by the Suction and Oscillatory Blowing (SaOB) actuator, as part of the development of a new active flow control device for heavy vehicles aerodynamic drag reduction and fuel savings.The experiments were carried out in a low-speed, low-turbulence wind tunnel at cylinder diameter Reynolds numbers between 50,000 and 250,000, with smooth and rough surface conditions. With the rough surface, the Reynolds number became a weak parameter, between Re=100,000 and 200,000. Several key aspects of the AFC system operation and its interaction with the external-flow were tested: the number of actuators placed along the span of the model, which directly affect the energetic efficiency of the system and the influence of different actuation parameters such as the excitation magnitude, its frequency, suction distribution and phase relations between adjacent actuators. The measurements included steady and unsteady pressures on the model and in its wake. Optimal operational conditions were identified, leading to significant drag reduction (up to 60%), complete suppression of vortex shedding and increased overall system efficiency, by about 15%. The three-dimensional span-wise structure of the flow was examined and successfully utilized for enhanced energetic efficiency and significant drag reduction. The preferred wave-length was one to two cylinder diameters, in agreement with known low Reynolds number instabilities.

Large Eddy Simulation of Flow Past Circular Cylinder Based on the Least Square Meshless Method

Large Eddy Simulation (LES) based on the least square meshless method was proposed in the present paper to simulate the classical turbulent flow around a stationary 2D circular cylinder. The subgrid scale model of Smagorinsky-Lily was employed to close the Navier-Stokes equations filtered by Favre filter. The Reynolds number is 3900 which means that the flow is subcritical and the wake is fully turbulent but the cylinder boundary is still laminar. Results obtained in this paper were evaluated by comparison with published experimental results and other numerical results. The results obtained in the present work show better agreement with the experimental values than other two-dimensional LES results .

Vortex shedding from a two-dimensional cylinder beneath a rigid wall and a free surface according to the discrete vortex method

We investigated the hydrodynamic characteristics and vorticity fields for flow past a 2D circular cylinder beneath a rigid wall and an air–water free surface. It is of practical importance to generalize the viscous mesh-free DVM to cases of flow past a 2D circular cylinder beneath a rigid wall and a free surface. We adopted the image method, which replaces the rigid wall with image singularities, to study the vortex shedding from a circular cylinder in proximity to a rigid wall. Using the Green function for the unsteady motion of a point vortex under a deformable free surface, we applied a linear free surface effect to investigate the hydrodynamic parameters and vortex shedding generated by a 2D stationary circular cylinder under a free surface.

Experimental Investigation of Wake-Induced Bypass Transition Control by Surface Roughness

Surface roughness is experimentally used to control the flat-plate boundary layer bypass transition induced by an upstream convected two-dimensional (2D) circular cylinder wake. It is shown that the later stage of this bypass transition is successfully postponed, at the price of accelerating the earlier transition stage. A regularisation process of the hairpin vortices, which are the dominant coherent structures to promote the transition process, are observed under the influence of roughness elements. Significant scale reduction and localisation of these hairpins are achieved, which enhances the possibility of a hairpin self-annihilation process. Therefore, the cascade to large-scale structures in the later transition stage might be impeded/weakened.

Advances in multi-domain lattice Boltzmann grid refinement

Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed to pass form the coarse to the fine grid. In this context, we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation. We show this operation to be extremely important, because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high Reynolds numbers. Then we demonstrate that to reconstruct the information, a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice Boltzmann method.These two fundamental extra-steps are validated on two classical 2D benchmarks, the 2D circular cylinder and the 2D dipole–wall collision. The latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high Reynolds number of 5000. A very good agreement is found between the single grid and the refined grid cases.The proposed grid refinement strategy has been implemented in the parallel open-source library Palabos.

SIMPLE Algorithm기반의 비압축성 Navier-Stokes Solver를 이용한 Immersed Boundary Method의 적용

Immersed boundary method(IBM) is a numerical scheme proposed to simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies, the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. The weight coefficients of the bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies. For an analysis of moving boundary, we smulated an oscillating circular cylinder with Re=100 and KC(Keulegan-Carpenter) number of 5. The predicted flow fields were compared with experimental data and they also showed good agreements.

Rising of 3D catalyst particles in a natural convection dominated flow by a parallel DNS method

Abstract We investigate the problem of particulate flows with heat transfer by parallel direct numerical simulation (DNS). Among other heat transfer problems, we examine in detail the case of a 3D spherical catalyst rising in an enclosure due to natural convection though it is heavier than the suspending fluid. Natural convection is created by heat transferred from the warmer particle to the fluid. Heat is assumed to be produced at a constant rate in the particle bulk. As expected, there exists a critical production rate that leads to the rising of the catalyst. Compared to the 2D circular cylinder counterpart, momentum and heat transfers are slower in 3D and the spherical catalyst rises for a lower production rate. At the numerical level, we employ a Distributed Lagrange Multiplier/Fictitious Domain formulation together with an operator-splitting algorithm to solve the coupled problem. Two families of Lagrange multiplier are introduced to relax the velocity and temperature constraints respectively. As suggested in Wachs (2009), particle collisions are handled by an efficient Discrete Element Method granular solver. As it is, the model is restricted to the case of homogeneous temperature over the particles. From a computational viewpoint, this work might be regarded as an extension of the method proposed in our previous contributions (Dan & Wachs, 2010; Yu, Shao, et al., 2006) to distributed computing with our new parallel code PeliGRIFF. 1 1 ▪ Parallel Efficient LIbrary for GRains In Fluid Flow, see Wachs (2011) for details. This opens up new possibilities to study a broad range of applications in 3D and to get more insight in the comprehension of particulate flows with heat transfer. In particular, we examine how a bed of spherical catalysts can be self-fluidized as a result of the heat produced in the particles bulk, mimicking an exothermic catalyst reaction in a chemical engineering reactor.

CFD Analysis and Reduced Order Modeling of Uncontrolled and Controlled Laminar Flow Over a Circular Cylinder

:The main idea of flow control is the improvement of aerodynamic characteristics of flow. This study analyzes the laminar flow over a two-dimensional (2D) circular cylinder and its control by air blowing from several slots located on the cylinder surface, computationally. The Computational Fluid Dynamics (CFD) results are validated using the experimental results available in the literature for Strouhal number, time-averaged drag coefficient and pressure coefficient distribution around the cylinder. Air blowing from four slots on the cylinder with a velocity of 50% of the free-stream velocity yields a reduction of the drag coefficient by 9%. Flow structures are separated according to their frequency content by Proper Orthogonal Decomposition (POD) method. It is seen from POD results that 99% of the total energy content can be modeled by considering only four most energetic POD modes of the flow. POD analysis of the controlled cases also show that the flow structure around the cylinder changes with the help of air blowing. For real-time flow control applications, it is important to predict the flow based on surface sensors, placed at a few discrete points. In this study, optimum sensor locations on the cylinder surface are also obtained by utilization of a one-dimensional POD analysis based on surface pressure data obtained from CFD results.