# Numerical studies of flow over a circular cylinder at ReD=3900

TL;DR: In this paper, a high-order accurate numerical method based on B-splines and compared with previous upwindbiased and central finite-difference simulations and with the existing experimental data is presented.

Abstract: Flow over a circular cylinder at Reynolds number 3900 is studied numerically using the technique of large eddy simulation. The computations are carried out with a high-order accurate numerical method based on B-splines and compared with previous upwind-biased and central finite-difference simulations and with the existing experimental data. In the very near wake, all three simulations are in agreement with each other. Farther downstream, the results of the B-spline computations are in better agreement with the hot-wire experiment of Ong and Wallace [Exp. Fluids 20, 441–453 (1996)] than those obtained in the finite-difference simulations. In particular, the power spectra of velocity fluctuations are in excellent agreement with the experimental data. The impact of numerical resolution on the shear layer transition is investigated.

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TL;DR: In this paper, the authors used the Detached-Eddy Simulation (DES) technique for smooth surface separation with laminar separation (LS) and turbulent separation (TS) at Reynolds numbers 50,000 and 140,000.

Abstract: The flow is calculated with laminar separation (LS) at Reynolds numbers 50,000 and 140,000, and with turbulent separation (TS) at140,000 and 3 × 106. The TS cases are effectively tripped, but compared with untripped experiments at very high Reynolds numbers. The finest grid has about 18,000 points in each of 56 grid planes spanwise; the resolution is far removed from Direct Numerical Simulations, and the turbulence model controls the separation if turbulent. The agreement is quite good for drag, shedding frequency, pressure, and skin friction. However the comparison is obscured by large modulations of the vortex shedding and drag which are very similar to those seen in experiments but also, curiously, durably different between cases especially of the LS type. The longest simulations reach only about 50 shedding cycles. Disagreement with experimental Reynolds stresses reaches about 30%, and the length of the recirculation bubble is about double that measured. The discrepancies are discussed, as are the effects of grid refinement, Reynolds number, and a turbulence-model curvature correction. The finest grid does not give the very best agreement with experiment. The results add to the validation base of the Detached-Eddy Simulation (DES) technique for smooth-surface separation. Unsteady Reynolds-averaged simulations are much less accurate than DES for LS cases, but very close for TS cases. Cases with a more intricate relationship between transition and separation are left for future study.

625 citations

### Cites background from "Numerical studies of flow over a ci..."

...The upper limit for complete success today appears to be a Reynolds number of a few thousand [11, 18], and these simulations are essentially direct simulations....

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...Two-dimensional simulations give too much drag [11, 14, 22, 23]....

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TL;DR: In this article, the authors discuss the development of a numerical algorithm and solver capable of performing large-eddy simulation in very complex geometries often encountered in industrial applications, such as unstructured hybrid grids.

Abstract: We discuss the development of a numerical algorithm, and solver capable of performing large-eddy simulation in the very complex geometries often encountered in industrial applications. The algorithm is developed for unstructured hybrid grids, is non-dissipative, yet robust at high Reynolds numbers on highly skewed grids. Simulation results for a variety of flows are presented.

502 citations

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TL;DR: In this paper, the authors investigated the flow over a circular cylinder at Reynolds number Re=3900 with a large eddy simulation and experimentally with hot-wire anemometry and particle image velocimetry.

Abstract: This work contributes to the study of flow over a circular cylinder at Reynolds number Re=3900. Although this classical flow is widely documented in the literature, especially for this precise Reynolds number that leads to a subcritical flow regime, there is no consensus about the turbulence statistics immediately just behind the obstacle. Here, the flow is investigated both numerically with large eddy simulation and experimentally with hot-wire anemometry and particle image velocimetry. The numerical simulation is performed using high-order schemes and a specific immersed boundary method. The present study focuses on turbulence statistics and power spectra in the near wake up to ten diameters. Statistical estimation is shown to need large integration times increasing the computational cost and leading to an uncertainty of about 10% for most flow characteristics considered in this study. The present numerical and experimental results are found to be in good agreement with previous large eddy simulation da...

441 citations

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TL;DR: The application of the Immersed Boundary ~IB! method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations.

Abstract: The application of the Immersed Boundary ~IB! method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references. @DOI: 10.1115/1.1563627# 1 CONTEXT The continuous growth of computer power strongly encourages engineers to rely on computational fluid dynamics ~CFD! for the design and testing of new technological solutions. Numerical simulations allow the analysis of complex phenomena without resorting to expensive prototypes and difficult experimental measurements. The basic procedure to perform numerical simulation of fluid flows requires a discretization step in which the continuous governing equations and the domain of interest are transformed into a discrete set of algebraic relations valid in a finite number of locations ~computational grid nodes! inside the domain. Afterwards, a numerical procedure is invoked to solve the obtained linear or nonlinear system to produce the local solution to the original equations. This process is simple and very accurate when the grid nodes are distributed uniformly ~Cartesian mesh! in the domain, but becomes computationally intensive for disordered ~unstructured! point distributions. For simple computational domains ~a box, for example! the generation of the computational grid is trivial; the simulation of a flow around a realistic configuration ~a road vehicle in a wind tunnel, for example!, on the other hand, is extremely complicated and time consuming since the shape of the domain must include the wetted surface of the geometry of interest. The first difficulty arises from the necessity to build a smooth surface mesh on the boundaries of the domain ~body conforming grid!. Usually industrially relevant geometries are defined in a CAD environment and must be translated and cleaned ~small details are usually eliminated, overlapping surface patches are trimmed, etc! before a surface grid can be generated. This mesh serves as a starting point to generate the volume grid in the computational domain. In addition, in many industrial applications, geometrical complexity is combined with moving boundaries and high Reynolds numbers. This requires regeneration or deformation of the grid during the simulation and turbulence modeling, leading to a considerable increase of the computational difficulties. As a result, engineering flow simulations have large computational overhead and low accuracy owing to a large number of operations per node and high storage requirements in combination with low order dissipative spatial discretization. Given the finite memory and speed of computers, these simulations are very expensive and time consuming with computational meshes that are generally limited to around one million nodes. In view of these difficulties, it is clear that an alternative numerical procedure that can handle the geometric complexity, but at the same time retains the accuracy and high efficiency of the simulations performed on regular grids, would represent a significant advance in the application of CFD to industrial flows.

396 citations

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TL;DR: In this article, the viability and accuracy of large-eddy simulation with wall modeling for high Reynolds number complex turbulent flows is investigated by considering the flow around a circular cylinder in the supercritical regime.

Abstract: The viability and accuracy of large-eddy simulation (LES) with wall modeling for high Reynolds number complex turbulent flows is investigated by considering the flow around a circular cylinder in the supercritical regime. A simple wall stress model is employed to provide approximate boundary conditions to the LES. The results are compared with those obtained from steady and unsteady Reynolds-averaged Navier–Stokes (RANS) solutions and the available experimental data. The LES solutions are shown to be considerably more accurate than the RANS results. They capture correctly the delayed boundary layer separation and reduced drag coefficients consistent with experimental measurements after the drag crisis. The mean pressure distribution is predicted reasonably well at ReD=5×105 and 106. However, the Reynolds number dependence is not captured, and the solution becomes less accurate at increased Reynolds numbers.

315 citations

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TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.

Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

6,747 citations

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TL;DR: In this article, a direct numerical simulation of a turbulent channel flow is performed, where the unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points.

Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

4,788 citations

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TL;DR: A review of wake vortex dynamics can be found in this article, with a focus on the three-dimensional aspects of nominally two-dimensional wake flows, as well as the discovery of several new phenomena in wakes.

Abstract: Since the review of periodic flow phenomena by Berger & Wille (1972) in this journal, over twenty years ago, there has been a surge of activity regarding bluff body wakes. Many of the questions regarding wake vortex dynamics from the earlier review have now been answered in the literature, and perhaps an essential key to our new understandings (and indeed to new questions) has been the recent focus, over the past eight years, on the three-dimensional aspects of nominally two-dimensional wake flows. New techniques in experiment, using laser-induced fluorescence and PIV (Particle-Image-Velocimetry), are vigorously being applied to wakes, but interestingly, several of the new discoveries have come from careful use of classical methods. There is no question that strides forward in understanding of the wake problem are being made possible by ongoing three- dimensional direct numerical simulations, as well as by the surprisingly successful use of analytical modeling in these flows, and by secondary stability analyses. These new developments, and the discoveries of several new phenomena in wakes, are presented in this review.

3,206 citations