An h4 accurate vorticity-velocity formulation for calculating flow past a cylinder

A method of solution for the two-dimensional Navier-Stokes equations for incompressible flow past a cylinder is given in which the euquation of continuity is solved by a step-by-step integration procedure at each stage of an interative process. Thus the formulation involves the solution of one first-order and one second-order equation for the velocity components, together with the vorticity transport equation. the equations are solved numerically by h⁴-accurate methods in the case of steady flow past a circular cylinder in the Reynolds number range 10–100. Results are in satisfactory agreement with recent h⁴-accurate calculations. An improved approximation to the boundary conditions at large distance is also considered.     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

Experimental Investigation of the Transverse Self-Oscillations of Circular Cylinders Mounted with a Narrow Clearance in a Plane Channel

The results of an investigation of the flow past and the behavior of free bluff bodies mounted in pipes and channels with a narrow clearance, conducted in the Institute of Mechanics of Moscow State University, are presented. The drag of circular cylinders of different size and mass in a circulation-free water flow in a plane channel of rectangular cross-section was studied in the transverse self-oscillation regime. The experiments were conducted for Reynolds numbers based on the cylinder diameter 1.7 ? 10⁴ ≤ Re ≤ 7.2 ? 10⁴, relative clearances \(\bar S\) based on a cross-sectional area ranging from 0.76 to 0.9, and cylinder-to-water density ratios ρ _c /ρ ranging from 1.29 to 8.2. Only the case of intense transverse self-oscillations accompanied by impact interaction with the channel wall was considered. The dependence of the period-average cylinder drag coefficient C _x on the basic dimensionless relevant parameters is obtained. The dependence of the dimensionless self-oscillation frequency determined in [1] is refined. The kinematic and dynamic features of the flows past spheres in cylindrical pipes and cylinders in plane channels are compared in the transverse self-oscillation regime.     

A volume-agglomeration multirate time advancing for high Reynolds number flow simulation

A frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Two examples of such situations are the travel of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, multistage explicit time advancing schemes with global time stepping are very accurate but very CPU consuming. In order to reduce this problem, the multirate (MR) time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions that would become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new MR scheme based on control volume agglomeration is proposed for the solution of the compressible Navier-Stokes equations equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macrocells for the smaller elements for stability purpose and a correction step in which small time steps are employed. The accuracy and efficiency of the proposed method are evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with a hybrid turbulence model of flows around bluff bodies like a flow around a space probe model at Reynolds number 10⁶, a circular cylinder at Reynolds number 8.4 × 10⁶, and two tandem cylinders at Reynolds number 1.66 × 10⁵ and 1.4 × 10⁵.     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

CONTROL OF FLOW PAST BLUFF BODIES USING ROTATING CONTROL CYLINDERS

Computational results for control of flow past a circular cylinder using small rotating cylinders are presented. A well-proven stabilized finite-element method, that has been applied to various flow problems earlier, is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The formulation is first applied to study flow past an isolated rotating cylinder. Excellent match with experimental results, reported earlier, is observed. It is found that in purely two-dimensional flows, very high lift coefficients can be realized. However, it is observed, via three-dimensional Navier–Stokes simulations, that the end-effects and centrifugal instabilities along the cylinder span lead to a loss of lift and increase in drag. The aspect ratio of the cylinder plays an important role. The flow past a bluff body with two rotating control cylinders is studied using 2-D numerical simulations. The effect of the Reynolds number is studied by carrying out simulations for Re=10²and 10⁴. Finite element meshes with an adequate number of grid points are employed to resolve the flow in the gap between the main and control cylinders. Two values of the gap are considered: 0·01D and 0·075 D, where D is the diameter of the main cylinder. It is observed that when the control cylinders rotate at high speed, such that the tip speed is 5 times the free-stream speed, the flow at Re=100 achieves a steady state. For Re=10⁴, even though the flow remains unsteady, the wake is highly organized and narrower compared to the one without control. The results are in good agreement with the flow-visualization studies conducted by other researchers for bluff bodies using similar control concepts. In all the cases, a significant reduction in the overall drag coefficient and the unsteady aerodynamic forces acting on the main cylinder is observed. Results are also presented for the power requirements of the system for translation and rotation. It is found that the coefficient of power required for the rotation of control cylinders is significant for Re=100 but negligible for Re=10⁴flow. The size of the gap is found to be more critical for the Re=10⁴flows. This study brings out the relevance of the gap as a design parameter for such flow control devices.     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

Oblique shock/bow shock interference in rarefied flow past a cylinder

Direct statistical simulation is employed to study the flow of a rarefied diatomic gas past a cylinder in the presence of an incident oblique shock. The distinctive features of the formation of a high-pressure compressed-gas jet in the case of interference between the oblique shock and the bow shock are studied for different Reynolds numbers. The variation of the pressure and the heat transfer to the surface with the shock position relative to the center of the cylinder, the Reynolds number, and the surface temperature is analyzed. The results obtained are compared with the experimental data and the results of the numerical solutions of the Euler and boundary layer equations. Free-molecular-to-continuum flow transition is demonstrated with reference to the example of interference-free flow past a cylinder.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 171–180. Original Russian Text Copyright © 2004 by Gusev and Erofeev.     

Numerical simulation of high‐Reynolds number flow around circular cylinders by a three‐step FEM–BEM model

An innovative computational model, developed to simulate high‐Reynolds number flow past circular cylinders in two‐dimensional incompressible viscous flows in external flow fields is described in this paper. The model, based on transient Navier–Stokes equations, can solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the projection method. The pressure is assumed to be zero at infinite boundary and the external flow field is simulated using a direct boundary element method (BEM) by solving a pressure Poisson equation. A three‐step finite element method (FEM) is used to solve the momentum equations of the flow. The present model is applied to simulate high‐Reynolds number flow past a single circular cylinder and flow past two cylinders in which one acts as a control cylinder. The simulation results are compared with experimental data and other numerical models and are found to be feasible and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

Influence of viscosity on the flow over the sharp edge of bodies consisting of a spherical segment joined to an inverted cone

The results are given of an experimental investigation of the supersonic axisymmetric flow over a body consisting of a spherical segment joined to an inverted cone in the neighborhood of the point of inflection of the profile (Fig. 1a). For the limiting case of a cylinder with a flat end and M = 3, a study was made of the influence of the Reynolds number and the state of the boundary layer on the parameters of the local separation region formed near the inflection (Fig. 1b). It was found that there is an appreciable decrease in the length of the separation region and the pressure in it when the Reynolds number increases in the range Re = 10⁵– 10⁷ in the case of a laminar boundary layer on the flat end near the inflection point. A low level of the pressure on the surface of the body was achieved — of the order of thousandths of the pressure behind a normal shock. There was found to be a sharp increase in the pressure in the separation region when the boundary layer on the end becomes turbulent with transition to a flow regime that is self-similar with respect to the Reynolds number. Under conditions of a turbulent boundary layer, systematic experimental data on the pressure on the inverted cone near the point of inflection of such bodies were obtained and generalized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–157, January–February, 1981.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

The Unsteady Wake of a Circular Cylinder near a Free Surface

The behaviour of the wake Strouhal number for flow past a cylinder close to a free surface at both low and moderate Froude numbers is investigated numerically. For the low Froude number case (i.e., gravity-dominated), the results obtained are similar to those for flow past a cylinder close to an adjacent no-slip boundary. As the distance between the wall and the cylinder is reduced, the Strouhal number, as measured from the time varying lift, increases to a maximum at a gap ratio of 0.70. Further gap reduction leads to a rapid decrease in the Strouhal number, with shedding finally ceasing altogether at gap ratios below 0.16. The agreement between the results for a free surface and a no-slip boundary suggests that the mechanism behind the suppression of vortex shedding is common. For flow at a fixed gap ratio and a moderate Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo-periodic fashion. Even though there is a significant difference in Reynolds number, the predicted numerical two-dimensional behaviour is found to compare favourably with the experimental observations at higher Reynolds number.     

Prediction of unsteady,separated boundary layer over a blunt body for laminar,turbulent, and transitional flow

The focus of this paper is to study the ability of unsteady RANS‐based CFD to predict separation over a blunt body for a wide range of Reynolds numbers particularly the ability to capture laminar‐to‐turbulent transition. A perfect test case to demonstrate this point is the cylinder‐in‐crossflow for which a comparison between experimental results from the open literature and a series of unsteady simulations is made. Reynolds number based on cylinder diameter is varied from 10⁴ to 10⁷ (subcritical through supercritical flow). Two methods are used to account for the turbulence in the simulations: currently available eddy–viscosity models, including standard and realizable forms of the k–ε model; and a newly developed eddy–viscosity model capable of resolving boundary layer transition, which is absolutely necessary for the type and range of flow under consideration. The new model does not require user input or ‘empirical’ fixes to force transition. For the first time in the open literature, three distinct flow regimes and the drag crisis due to the downstream shift of the separation point are predicted using an eddy–viscosity based model with transition effects. Discrepancies between experimental and computational results are discussed, and difficulties for CFD prediction are highlighted. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of oseen flows past a circular cylinder at low reynolds numbers

The velocity, pressure, vorticity and streamfunction are computed in the Oseen hydrodynamic field of an unbounded fluid past a circular cylinder in the Reynolds Number range going from 0.4 to 12. The boundary condition is satisfied by means of the method of least squares that determines suitable coefficients for Faxén series. Particular investigation is made of the wake region in which calculations are made of flow patterns, velocity and vorticity distributions. It is shown that, attached vortices arise at the rear of the cylinder at Reynolds Number Re=3.025. Calculated drag coefficients are in good agreement with known results of the works of several authors up to a Reynolds Number of 20.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

High-order ghost-point immersed boundary method for viscous compressible flows based on summation-by-parts operators

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.     

Numerical Simulation of the Negative Magnus Effect of a Two-Dimensional Spinning Circular Cylinder

Based on the finite volume method, the flow past a spinning circular cylinder at a low subcritical Reynolds number (Re =1 × 10 ⁵), high subcritical Reynolds number (Re =1.3 ×10 ⁵), and critical Reynolds number (Re =1.4 ×10 ⁵) were each simulated using the Navier-Stokes equations and the γ-Re _?? transition model coupled with the SST k?ω turbulence model. The system was solved using an implicit algorithm. The freestream turbulence intensity decay was effectively controlled by the source term method proposed by Spalart and Rumsey. The variations in the Magnus force as a function of the spin ratio, α were obtained for the three Reynolds numbers, and the flow mechanism was analyzed. The results indicate that the asymmetric transitions induced by spin affect the asymmetric separations at the top and bottom surfaces of the circular cylinder, which further affects the pressure distributions at the top and bottom surfaces of the circular cylinder and ultimately result in a negative Magnus force, whose direction is opposite to that of the classical Magnus force. This study is the first to use a numerical simulation method to predict a negative Magnus force acting on a spinning circular cylinder. At the low subcritical Reynolds number, the Magnus force remained positive for all spin ratios. At the high subcritical Reynolds number, the sign of the Magnus force changed twice over the range of the spin ratio. At the critical Reynolds number, the sign of the Magnus force changed only once over the range of the spin ratio. For relatively low spin ratios, the Magnus force significantly differed by Reynolds number; however, this variation diminished as the spin ratio increased.     

Fluctuating lift on a circular cylinder: review and new measurements

Apart from providing some new experimental data the paper reviews previous investigations concerning fluctuating lift acting on a stationary circular cylinder in cross-flow. In particular, effects of Reynolds number in the nominal case of an infinitely long and nonconfined cylinder in a smooth oncoming flow are discussed. The Reynolds number range covered is from about Re=47 to 2×10⁵, i.e., from the onset of vortex shedding up to the end of the subcritical regime. At the beginning of the subcritical regime (Re≃0.3×10³) a spanwise correlation length of about 30 cylinder diameters is indicated, the correlation function being based on near-cylinder velocity fluctuations in outer parts of the separated shear layer. In between Reynolds numbers 1.6×10³ and 20×10³, an approximate 10-fold increase in the sectional r.m.s. lift coefficient is indicated. This range contains a fundamental change-over from one flow state to another, starting off at Re≃5×10³ and seemingly fully developed at Re≃8×10³.