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The internal flow over a backward-facing step in the transitional regime ( Re - D = 6000) was studied based on direct numerical simulations. The predictions were carried out with the help of a finite-volume Navier-Stokes solver equipped with a co-visualization facility which allows one to investigate the flow dynamics at high temporal resolution. First, grid-induced oscillations were precluded by a careful grid design. Second, the strong influence of the velocity profile approaching the step was studied and outlined. The main objective, however, was to provide a comprehensive insight into the dynamic flow behaviour, especially oscillations of the reattachment length of the primary recirculation region. The origin of this well-known flapping behaviour of the reattachment line is not yet completely understood. In the present work, the mechanisms leading to the oscillations of the reattachment length were extensively investigated by analysing the time-dependent flow. Besides the oscillations of the primary recirculation region, oscillations of the separation and the reattachment line of the secondary recirculation bubble at the upper channel wall were also observed. The results clearly show that in the present flow case the flapping of the primary reattachment and the secondary separation line is due to vortical structures in the unstable shear layers between the main flow and the recirculation bubbles. Vortices emerging in the shear layers and sweeping downstream convectively induce small zones of backward-flowing fluid at the channel walls while passing the recirculation regions. In the case of the primary recirculation region, the rotational movement of the shear-layer vortices impinging on the lower channel wall was found to cause zones of negative fluid velocity at the end of the recirculation bubble and thus flapping of the reattachment line. In contrast, in the case of the secondary recirculation region, the shear-layer vortices moved away from the upper channel wall so that their rotational movement did not reach the boundary. In this case, the pressure gradients originating from local pressure minima located in the shear-layer vortices were identified as being responsible for the oscillations of the separation line at the upper channel wall. While moving downstream with the shear-layer vortices, the pressure gradients were found to influence the top boundary of the channel and create alternating zones of forward- and backward-flowing fluid along the wall. All of these unsteady processes can best be seen from animations which are provided on the Journal of Fluid Mechanics website. [ABSTRACT FROM AUTHOR]

Abstract: The combination of turbulent buoyant flow with a free surface (Rayleigh–Bénard–Marangoni convection) and rotation is hardly investigated in detail, especially for low Prandtl number fluids, although it can be found in several applications such as Czochralski (Cz) crystal growth. Therefore, a Direct Numerical Simulation (DNS) of such a Cz case with an idealized cylindrical crucible geometry of 170mm radius and a rotating crystal of 50mm radius was conducted applying realistic boundary conditions, which lead to the dimensionless numbers of , and . The computational grid contained ca. 8.4 million control volumes to resolve all turbulent scales based on a finite-volume scheme for curvilinear block-structured grids and an explicit time discretization. The resulting velocity and temperature fields show fully developed three-dimensional turbulence and are characterized by thermal buoyant plumes rising from the bottom of the crucible to the free surface, surface tension effects, and the strong impact of the counterrotating crystal. The analysis of the instantaneous flow revealed that in the rotating melt a large, slowly moving spiral vortex evolves. The averaged data show the formation of Bénard cell-like structures. Below the crystal, along the free surface, and especially at the corner of the crystal, the turbulence intensity is strongest. The DNS results were generated and analyzed in detail in order to serve as a reference and will also be made available to the public for further investigations. Within an ongoing study these data will be used to validate computations for practical applications employing the Large-Eddy Simulation (LES) technique, which is used to model the turbulent flow and temperature field in order to save computational time compared to DNS. [Copyright &y& Elsevier]

In order to reduce the high computational effort of wall-resolved large-eddy simulations (LES), the present paper suggests a hybrid LES–RANS approach which splits up the simulation into a near-wall RANS part and an outer LES part. Generally, RANS is adequate for attached boundary layers requiring reasonable CPU-time and memory, where LES can also be applied but demands extremely large resources. Contrarily, RANS often fails in flows with massive separation or large-scale vortical structures. Here, LES is without a doubt the best choice. The basic concept of hybrid methods is to combine the advantages of both approaches yielding a prediction method, which, on the one hand, assures reliable results for complex turbulent flows, including large-scale flow phenomena and massive separation, but, on the other hand, consumes much fewer resources than LES, especially for high Reynolds number flows encountered in technical applications. In the present study, a non-zonal hybrid technique is considered (according to the signification retained by the authors concerning the terms zonal and non-zonal), which leads to an approach where the suitable simulation technique is chosen more or less automatically. For this purpose the hybrid approach proposed relies on a unique modeling concept. In the LES mode a subgrid-scale model based on a one-equation model for the subgrid-scale turbulent kinetic energy is applied, where the length scale is defined by the filter width. For the viscosity-affected near-wall RANS mode the one-equation model proposed by Rodi et al. (J Fluids Eng 115:196–205, 1993) is used, which is based on the wall-normal velocity fluctuations as the velocity scale and algebraic relations for the length scales. Although the idea of combined LES–RANS methods is not new, a variety of open questions still has to be answered. This includes, in particular, the demand for appropriate coupling techniques between LES and RANS, adaptive control mechanisms, and proper subgrid-scale and RANS models. Here, in addition to the study on the behavior of the suggested hybrid LES–RANS approach, special emphasis is put on the investigation of suitable interface criteria and the adjustment of the RANS model. To investigate these issues, two different test cases are considered. Besides the standard plane channel flow test case, the flow over a periodic arrangement of hills is studied in detail. This test case includes a pressure-induced flow separation and subsequent reattachment. In comparison with a wall-resolved LES prediction encouraging results are achieved. [ABSTRACT FROM AUTHOR]

This paper describes the authors' utilization of both post- and co-visualization techniques to indicate details of the fluid motion in a Czochralski crucible. Different visualization methods (particle tracing, isosurface extraction and line integral convolution) are discussed and applied to time-dependent flow in the crucible. Co-visualization is used to investigate the dynamic evolution of the flow structures at high temporal resolution. Moreover, the co-visualization approach also allows for interactive online visualization and computational steering, which strongly increases the user's ability to visualize the results and to supervise and dynamically control the entire computational process. By means of the resulting pictures and animations, the interaction of the different forces, which are responsible for the complex flow in the crucible is illuminated. In this way, the transport processes in the melt flow are characterized. Special attention is paid to the Marangoni-driven convection close to the interface between the melt and the crystal. The methodology for visualization and computational steering described in the paper can be applied to all kinds of complex three-dimensional and unsteady flow simulations. Its application is essential for handling the overwhelming amount of data produced by modern flow predictions. Consequently, it will play a decisive role in the next generation of CFD codes. [ABSTRACT FROM AUTHOR]

Extensive numerical experiments were carried out to study the effect of cylinder heating on the characteristics of the flow and heat transfer in a two-dimensional horizontal laminar flow of air past a heated circular cylinder for the range of Reynolds numbers 0.001≼Re≼170. The fluid was treated as incompressible (density is independent of the pressure) while the variation of the fluid properties with temperature was taken into account. By including the transient density term of the continuity equation, which was neglected in a previous study by Lange, Durst, and Breuer [Int. J. Heat Mass Transfer 41, 3409 (1998)], we were able to predict correctly the vortex shedding frequency at various overheat ratios using an incompressible flow solver. The effect of dynamic viscosity and density variations on the flow dynamics occurring with the cylinder heating was analyzed separately. Another emphasis of the work was to investigate the physical mechanism behind the “effective Reynolds number” concept widely applied in engineering correlations. Similarity was discovered for the distribution of the local dimensionless viscous force, the vorticity and the Nusselt number at the cylinder surface and the pressure force in the rear part of the cylinder. Two characteristic temperatures, Teff=T∞+0.28(TW-T∞) for the flow dynamics and Tf=T∞+0.5(TW-T∞) for the heat transfer, were identified. [ABSTRACT FROM AUTHOR]

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 a(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 Kármán 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 nonrotating or slowly rotating cylinders. Additionally, negative values for the mean drag denoting thrust are found within the second shedding mode. [ABSTRACT FROM AUTHOR]

A partitioned coupling approach for time-dependent fluid–structure interactions is applied to thin shells and membranous structures with large displacements. The frame algorithm connects a three-dimensional, finite volume-based multi-block flow solver for incompressible fluids with a finite element code for geometrically nonlinear structural problems using a commercial coupling interface. Thus a high modularity is achieved and the whole range of opportunities with these two powerful codes — each of them highly adapted to its specific field of application — can be used also for coupled simulations.Two completely different configurations were investigated. First, the coupling algorithm was applied to an academic test configuration consisting of one, two, and three flexible L-shaped plates being loaded by a steady far-field flow. Various investigations were carried out at different Reynolds numbers (Re=50,200, and 500) in order to study phenomena such as vortex shedding, resonance, influence of the interaction between several flexible plates, whereas the second and third plates were placed in the wake of the first.The second part of the paper shows that in principle the coupling procedure can also deal with real-life structures as they occur in civil engineering. A membranous roof of glass-fiber synthetics with a complex shape was exposed to a time-dependent wind gust from diagonally above which was superimposed on a constant basic wind flow parallel to the ground. The structural model contains the pre-stressed textile roof including the taut cables at its circumference which are fastened at the pylons. As a structural response, the wind gust led to a displacement of the textile roof which disappeared again when the gust subsided. With the coupled algorithm proposed in the paper it is possible to study dynamic interactions for engineering applications. [Copyright &y& Elsevier]

Two-dimensional numerical investigations of the forced heat convection from a microcylinder in laminar cross-flow, both in free stream and in near-wall flow, were carried out aiming at a better understanding of the physics behind the wall effects on hot-wire near-wall measurements. In the physical model, an infinitely thin plate with the same properties as the fluid (air) was used as an artificial wall. The conjugate heat transfer between the flow regions on both sides of the plate was taken into account. The effect of the conjugate thermal conditions (temperature distribution and diffusive heat flux) at the interface of the two flow regions on the heat transfer from the wire was investigated by varying the flow conditions on the side opposite to the wire location. Careful energy balance analysis was performed for both the free-stream case and the near-wall case. This enabled the authors to verify their own understanding of the physical mechanism responsible for the wall effect on hot-wire measurements and to examine other mechanisms proposed in the literature. The numerical results showed that the heat diffusion from the wire is significantly enhanced in the case of small wire-to-wall distances (Y[sup +] <3). This is mainly caused by modifications of the thermal boundary condition (diffusive effect) at the fluid-wall interface. In contrast, the flow distortion (enhanced convection) was shown not to be the most important influencing factor for the heat transfer of a hot wire. Although the present model study was performed for a laminar flow, the results obtained are applicable to hot-wire measurements in turbulent flows, as stated in the literature. [ABSTRACT FROM AUTHOR]

Abstract: A key technology for large eddy simulation (LES) of complex flows is an appropriate wall modeling strategy. In this paper we apply for the first time a fully nonparametric procedure for the estimation of generalized additive models (GAM) by conditional statistics. As a database, we use DNS and wall-resolved LES data of plane channel flow for Reynolds numbers, Re =2800, 4000 (DNS) and 10,935, 22,776 (LES). The statistical method applied is a quantitative tool for the identification of important model terms, allowing for an identification of some of the near-wall physics. The results are given as nonparametric functions which cannot be attained by other methods. We investigated a generalized model which includes Schumann’s and Piomelli et al.’s model. A strong influence of the pressure gradient in the viscous sublayer is found; for larger wall distances the spanwise pressure gradient even dominates the τ w,zy component. The first a posteriori LES results are given. [Copyright &y& Elsevier]

Abstract The present paper is the numerical counterpart of a recently published experimental investigation by Wood et al. (2018). Both studies aim at the investigation of instantaneous fluid–structure interaction (FSI) phenomena observed for an air-inflated flexible membrane exposed to a turbulent boundary layer, but looking at the coupled system based on different methodologies. The objective of the numerical studies is to supplement the experimental investigations by additional insights, which were impossible to achieve in the experiments. Relying on the large-eddy simulation technique for the predictions of the turbulent flow, non-linear membrane elements for the structure and a partitioned algorithm for the FSI coupling, three cases with different Reynolds numbers (Re = 50,000 , 75,000 and 100,000) are simulated. The time-averaged first and second-order moments of the flow are presented as well as the time-averaged deformations and standard deviations. The predictions are compared with the experimental references data solely available for 2D planes. In order to better comprehend the three-dimensionality of the problem, the data analysis of the predictions is extended to 3D time-averaged flow and structure data. Despite minor discrepancies an overall satisfying agreement concerning the time-averaged data is reached between experimental data in the symmetry plane and the simulations. Thus for an in-depth analysis, the numerical results are used to characterize the transient FSI phenomena of the present cases either related to the flow or to the structure. Particular attention is paid to depict the different vortex shedding types occurring at the top, on the side and in the wake of the flexible hemispherical membrane. Since the fluid flow plays a significant role in the FSI phenomena, but at the same the flexible membrane with its eigenmodes also impacts the deformations, the analysis is based on the frequencies and Strouhal numbers found allowing to categorize the different observations accordingly. [ABSTRACT FROM AUTHOR]

The quality of eddy-resolving turbulence simulations strongly depends on appropriate inflow conditions. In most cases they have to be time-dependent and satisfy certain conditions for the first (mean velocities) and second-order moments (Reynolds stresses) as well as concerning suitable length scales. To mimic a physically realistic incoming flow, synthetically generated turbulent velocity fluctuations superimposed on the mean velocity field are a valuable solution. However, the resolution of the grid near the inlet has to be sufficiently fine to avoid excessive damping of the turbulence intensity. In order to circumvent this problem, the injection of synthetically generated inflow data not at the inlet itself but inside the flow domain near the area of interest, where the grid is typically much finer, is an elegant loophole. In the present study two different injection techniques based on a source-term formulation are analyzed and evaluated. In addition to these techniques the injected data are weighted by a Gaussian distribution defining the influence area. In the recent work the definition of the influence area is enhanced compared to the initial version of Schmidt and Breuer (2017) extending the application range. The case of a rather small influence area in comparison with the grid cell size is now tackled which is often relevant for industrial applications. The flow past a wall-mounted hemisphere is chosen as test case. The bluff body is exposed to a thick turbulent boundary layer at Re = 50,000. The generation of the turbulent velocity fluctuations in the present investigation relies on the digital filter concept, but the injection techniques evaluated are not restricted to this inflow generator. The synthetic turbulent velocity fluctuations are injected about one diameter upstream of the hemisphere. Wall-resolved large-eddy simulations are carried out for two grid resolutions and the corresponding results are analyzed and compared with the reference measurements by Wood et al. (2016). Finally, one injection technique is found to be clearly superior to the other, since it guarantees the correct level of the velocity fluctuations and the reproduction of the autocorrelations. [ABSTRACT FROM AUTHOR]