M. Breuer

Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume

The confined flow around a cylinder with square cross-section mounted inside a plane channel (blockage ratio B=1/8) was investigated in detail by two entirely different numerical techniques, namely a lattice-Boltzmann automata (LBA) and a finite-volume method (FVM). In order to restrict the approach to 2D computations, the largest Reynolds number chosen was Re=300 based on the maximum inflow velocity and the chord length of the square cylinder. The LBA was built up on the D2Q9 model and the single relaxation time method called the lattice-BGK method. The finite-volume code was based on an incompressible Navier–Stokes solver for arbitrary non-orthogonal, body-fitted grids. Both numerical methods are of second-order accuracy in space and time. Accurate computations were carried out on grids with different resolutions. The results of both methods were evaluated and compared in detail. Both velocity profiles and integral parameters such as drag coefficient, recirculation length and Strouhal number were investigated. Excellent agreement between the LBA and FVM computations was found.

A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow

Abstract A thorough numerical investigation of high Reynolds number ( Re =140,000) circular cylinder flow was performed based on large eddy simulation (LES). The objective was to evaluate the applicability of LES for practically relevant high- Re flows and to investigate the influence of subgrid scale modeling and grid resolution on the quality of the predicted results. Because the turbulent von Karman vortex street past circular cylinders involves most of the characteristic features of technical applications, it is an ideal test case for this purpose. Based on a parallelized finite-volume Navier–Stokes solver, computations were carried out on a series of grids applying both the Smagorinsky and the dynamic subgrid scale model. The simulations yielded information on the time-averaged flow field, the resolved Reynolds stresses and integral parameters such as drag coefficient, recirculation length and Strouhal number. The results were analyzed in detail and compared with experimental data. In general, the LES results agreed fairly well with the experimental data, especially in the near wake. Owing to the coarse resolution in the far wake, larger deviations were observed here. As expected, the importance of the subgrid scale model significantly increased for the high- Re case in comparison with a low- Re case predicted earlier. A critical issue for LES is grid refinement which did not automatically lead to an improved agreement between the predicted results and the experimental measurements. Possible explanations are offered in the paper.

Momentum and heat transfer from cylinders in laminar crossflow at 10-4 ≤ Re ≤ 200

Abstract A summary of results of numerical investigations of the two-dimensional flow around a heated circular cylinder located in a laminar crossflow is presented. Numerical investigations were carried out for the Reynolds number range 10 −4 ⩽ Re ⩽ 200 and for temperature loadings of 1.003–1.5. The computations yield information on Nu and C D variation with Reynolds number. The temperature dependence of the fluid properties (air) was taken into account and this resulted in a temperature dependence of the Nu – Re and C D – Re results. Information is also provided on the Strouhal number dependence on the Re number and on the critical Re number where vortex shedding starts.

Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers

This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers ReD=ρUbD/μ below approximately 400 (Ub= bulk velocity and D= hydraulic diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, 10−4≤ReD≤800. In the limiting case of ReD→0, a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at ReD=1. The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number ReD=648. This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

Effect of high rotation rates on the laminar flow around a circular cylinder

A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01⩽Re⩽45) and rotation rates (0⩽α⩽6) were considered for the steady flow regime, where α is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with α varying in the range 0⩽α⩽2. Additionally, the investigations were extended to very high rotation rates (α⩽12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi...

Numerical and modeling influences on large eddy simulations for the flow past a circular cylinder

Abstract In the present work the turbulent flow past a circular cylinder (Re=3900) was computed by large eddy simulation (LES). The objective was not to investigate the physical phenomena of this flow in detail but to study numerical as well as modeling aspects which influence the quality of LES solutions. Concerning the numerical method the most important component is the discretization of the non-linear convective fluxes. Five different schemes were investigated. Moreover, the influence of different grid resolutions was examined. On the modeling side two aspects play an important role, namely the near-wall model and the subgrid scale (SGS) model. Owing to the restriction to a low Reynolds number in this study, no-slip boundary conditions were used at solid walls. Hence only the second aspect was taken into account. Two different subgrid scale models (Smagorinsky and dynamic model) were applied. Additionally, LES computations without any subgrid scale modeling were carried out in order to prove the performance of the above mentioned SGS models.

Flow structure around trains under side wind conditions: a numerical study

Results of numerical investigations of high Reynolds number flows past a simplified train geometry under different yawing conditions are summarised. Variations of the incidence flow angle from parallel to normal with respect to the direction of the forward train motion resulted in the development of distinctively different flow patterns. To compute numerically the different flow structures, the three-dimensional Reynolds-averaged Navier–Stokes equations, combined with the k–ϵ turbulence model, were solved on a multi-block structured grid using a finite volume technique. The pressure–velocity fields were coupled using the SIMPLE algorithm. Despite the geometrical simplifications of the computed train configuration, the resulting flow fields show significant complexities.

Computation of fluid-structure interaction on lightweight structures

Abstract In this paper a numerical approach of a time-dependent fluid-structure coupling for membrane and thin shell structures with large displacements is presented. The frame algorithm is partitioned, yet fully implicit because of a predictor-corrector scheme being applied to the structural displacements within each time step. In order to reach a high modularity, two powerful codes—one of them highly adapted to flow simulation and the other one to structural dynamics—run simultaneously and exchange fluid loads and displacements within each fluid-structure iteration. The finite volume based CFD code is able to compute three-dimensional, incompressible, turbulent flows. The structural simulations are performed using a finite element program including algorithms for geometrically and physically non-linear problems. In this paper the coupled algorithm will first be applied to some geometrically simple test cases to validate the interaction scheme. Then a real-life textile tent structure of glass-fibre synthetics with a complex shape is taken into account. This example was investigated under turbulent flow conditions at a high wind speed leading to a steady deformation state.

On the new vortex shedding mode past a rotating circular cylinder

To examine in detail the behavior of a new vortex shedding mode found in a previous investigation [Phys. Fluids 14, 3160 (2002)], a two-dimensional numerical study on the laminar incompressible flow past a rotating circular cylinder in the Reynolds number range 60⩽Re⩽200 and at rotational rates 0⩽α⩽6 was carried out. The results obtained clearly confirm the existence of the second shedding mode for the entire Reynolds number range investigated. A complete bifurcation diagram α(Re) was compiled defining both kind of shedding modes. The unsteady periodic flow in the second mode is characterized by a frequency much lower than that known for classical von Karman vortex shedding of the first mode. The corresponding Strouhal number shows a strong dependence on the rotational velocity of the cylinder, while only a weak dependence is observed for the Reynolds number. Furthermore, the amplitudes of the fluctuating lift and drag coefficients are much larger than those characterizing classical vortex shedding behind...

Steady and Unsteady Computations of Turbulent Flows Induced by a 4/45° Pitched-Blade Impeller

The present paper summarizes steady and unsteady computations of turbulent flow induced by a pitched-blade turbine (four blades, 45° inclined) in a baffled stirred tank. Mean flow and turbulence characteristics were determined by solving the Reynolds averaged Navier-Stokes equations together with a standard k-e turbulence model. The round vessel had a diameter of T = 152 mm. The turbine of diameter T/3 was located at a clearance of T/3. The Reynolds number (Re) of the experimental investigation was 7280, and computations were performed at Re = 7280 and Re = 29,000. Techniques of high-performance computing were applied to permit grid sensitivity studies in order to isolate errors resulting from deficiencies of the turbulence model and those resulting from insufficient grid resolution. Both steady and unsteady computations were performed and compared with respect to quality and computational effort. Unsteady computations considered the time-dependent geometry which is caused by the rotation of the impeller within the baffled stirred tank reactor. Steady-state computations also considered neglect the relative motion of impeller and baffles. By solving the governing equations of motion in a rotating frame of reference for the region attached to the impeller, the steady-state approach is able to capture trailing vortices. It is shown that this steady-state computational approach yields numerical results which are in excellent agreement with fully unsteady computations at a fraction of the time and expense for the stirred vessel configuration under consideration.