B Mutlu Sumer is Professor at the Technical University of Denmark, MEK, Coastal, Maritime and Structural Engineering Section (formerly ISVA, Institute of Hydrodynamics and Water Resources). He graduated with MSc and PhD at the Istanbul Technical University (ITU). He was a postdoctoral research fellow at the University of Cambridge, UK. He was professor of Hydraulics at ITU before he moved to Denmark in 1984. His main fields of research are flow around marine structures, scour, sediment transport and liquefaction of marine soils. He has done consultancy work for consulting companies in Denmark and abroad.
Flow around circular cylinder has been extensively studied by researchers for several decades due to its wide range of engineering applications such as in heat exchangers, marine cables, high rise building, chimneys, and offshore structures. The lack of clear understanding of the unsteady flow dynamics in the wake of circular cylinder and high computational cost are still an area of high interest amongst the researchers. The aim of the current study is to investigate the effect of variation in spanwise length and grid resolution in the spanwise direction on the recirculation length, separation angle of wake flow by performing large eddy simulations (LES). This study is an extension to previous work by Khan, NB et al, 2019 in which the spanwise length is restricted to 4D only. In current study, the spanwise length is changed from 0.5D to 8D where D is diameter of cylinder and mesh resolution in the spanwise direction is changed from 1 to 80 elements in the present study. The recirculation length, separation angle and wake characteristics are analyzed in detail. It is concluded that after getting optimize spanwise length, mesh resolution in the spanwise direction is the only parameter contributing toward better result.
Citation: Ali H, Khan NB, Jameel M, Khan A, Sajid M, Munir A, et al. (2022) Numerical investigation of the effect of spanwise length and mesh density on flow around cylinder at Re = 3900 using LES model. PLoS ONE 17(4): e0266065.
Breuer  performed large eddy simulations at Re = 3900 and investigated the effect of near-wall modeling, sub-grid scale modeling and spanwise resolution on the accuracy of numerical model. In another study Breuer  computed the low recirculation length (of less than 1.1) with a Smagorinsky model and comparatively high value of recirculation length when using the dynamic model. Unlike dynamic Smagorinsky model, the traditional Smagorinsky model over-predicted the importance of drag coefficient and separation angle. While systematically investigating the accuracy of LES model on flow past a cylinder at Re = 3900,  found that the resolution in spanwise direction effects the three-dimensionality of flow and hence, accuracy of results significantly. Tremblay et al.  studied the effects of the SGS model and grid resolution on large eddy simulations using technique known as cartesian grid. The length of recirculation and profiles of mean velocity could not be reliably predicted in this analysis. Lysenko et al.  used OpenFOAM tool to investigate the flow aroud a cylinder using a dynamic k-equation SGS model and the large eddy simulations model. Parnaudeau et al.  used LES with a high order scheme to simulate a flow around cylinder. The numerical analysis resulted in power spectra and turbulence statistics up to 10 D. Moreover, Wissink and Rodi, Dong et al. [15, 16] used direct numerical simulations (DNS) to investigate flow around cylinder.
Dong et al.  and MA, Karamanos, and Karniadakis  studied flow around cylinder with spanwise length of 10D using Direct Numerical simulations. At a moderate to high values of Reynolds number, Rajani et al.  investigated the limitation of URANS in measuring drag forces, skin friction coefficients and mean pressure coefficients. Zhang et al.  investigated the both the effects of infinite and finite cylinders on flow characteristics and observed that free end of cylinder has significant impact on wake characteristics. Wissink et al. [15, 19] used direct numerical simulations in order to run a series of simulations at Reynolds number = 3300 and compared the findings to experimental studies at Reynolds number = 3900. The roll-up of the splitting shear layer, which transformed to turbulence, was observed. Even at low Reynolds numbers, direct numerical simulations are costly and provides accurate and reliable performance. Due to the deficiencies in the URANS method and the high computational cost of direct numerical simulations, large eddy simulations (smagorinsky model) with fixed coefficient but without model, and with a dynamic model is most attractive choice to analyze the unsteady nature of flow around cylinder.
Fluid flow around cylinder is highly dependent on the flow domain size. In the past studies, as referred earlier, size of the domain varies from 15D to 70D in crossflow (Y) and streamflow (X) directions. To resolve the wake region and boundary layers, grid points are being clustered in wake region and over the cylinder. In past studies, range of crossflow (Ly) domain is kept between 80D to 20D, while range of streamflow (Lx) domain is usually kept from 40D to 20D. In several cases, mesh is designed in such a way that it is divided into several regions i.e., O-Grid meshing is surrounded over cylinder and remaining region will then meshed using structured method. In the current study, domain size of 40D×20D (inflow x cross flow) is used, whereas the spanwise length is varied from 8D to 0.5D.
Velocity at inlet is 0.6 m/s, which is on right side of domain, maintaining Reynolds number Re = 3900 by keeping diameter of cylinder D = 0.1m, viscosity = 0.000016 kg/ms, density = 1.04 kg/m3. At the outflow border, a static reference pressure of 0 Pa is applied on average. A symmetric wall condition is applied to both upper and lower walls of flow domain. To investigate the boundary layer separation and vortex generation phenomenon, a no-slip condition is given to cylinder wall. The modeling and analysis are performed using ANSYS tool (design modeler and ICEM CFD respectively). All the meshes are designed using structured method of meshing and the computational domain is then divided into number of regions in a manner that O-Grid near the boundary wall of cylinder and then structured meshed away from the cylinder, as shown in Fig 2. Rectangular domain is used in all numerical studies. Greifzu  concluded that, value of y+ must be smaller or equal to unity in order to ensure the proper resolutions of grids near the wall of cylinder. In all case studies, y+ value equal or less than 1 is maintained near the cylinder wall. First node is placed at 0.002D in all numerical studies, in order to completely ensure y+ less than unity. Fig 2 gives details of overall mesh design and view near the wall of cylinder respectively. Multiple meshes are designed with different spanwise lengths and in some cases, study with different mesh resolution is performed in order to validate previous study. Table 1 review the mesh type used in literature to perform flow around cylinder study.
In this study, flow around cylinder at Re = 3900 has been investigated using LES model, with main focus on optimization of spanwise length and mesh distribution. This study mainly extended the previous studies by analyzing the case studies from (8D to 0.5D) with mesh density in the range of (2 to 0.0125). The study concluded that irrespective of the spanwise length, mesh density should not be kept greater than 0.1. Mesh density greater than 0.1 result in delay in separation angle, shorter recirculation length and over-predicted value of hydrodynamic coefficients. It is also observed that coarse mesh in spanwise direction result in V-shape profile of mean streamwise velocity which is improved to U-shaped with improvement in mesh density. With mesh density equal to 0.1, it has been concluded that optimum spanwise length of 2D is able to extract the reliable results of hydrodynamic coefficients, Strouhal number, separation angle and recirculation length. It is also observed that further reducing the spanwise length results in shorter recirculation length, even with high mesh density in spanwise length. It is also concluded that drag coefficient and Strouhal number are comparatively less sensitive parameters as the change is spanwise length and mesh resolution have minor impact on the result.
In this article is given the new insight about the affection of stress on the increase of level of low density lipoproteins (LDL) in the blood, which is connected with the disturbance of hydrodynamics in the bloodstream, the attention was paid to the cylindrical cholesterol plaque, and it's classification. The disturbance of hydrodynamics of blood under the stress leads to the formation of a cylindrical cholesterol plaque, which repeats the contour of the vessel, and leads to the ischemic disorders of the heart and brain. The cylindrical cholesterol plaque goes through several stages of development: friable, yielding, dense, old. In the case of destruction of friable, fresh cholesterol plaque, releases a big quantity of low-density lipoproteins. This leads to the pathological increase of level of LDL in the blood. In the case of long disturbance of hydrodynamics, occurs the formation of strong links between low-density lipoproteins. Yielding cholesterol plaque is formed. Further maturation of cylindrical cholesterol plaque, leads to it's densifying and damage. We may emphasize, that short periods of strong contraction and expansion of vessels lead to the increase of level of LDL in the blood. Self-dependent restoration of normal level of LDL in blood occurs in the case of restoration of pressure in the limits of numbers, which are specific for particular person, and which don't exceed the physiological standard. Among patients with long duration of stress, the duration of vasospasm increases. LDL, without having a possibility to crumble, begin to stick together and form the yielding cylindrical plaque. It is characterized by having of not so strong connection with the vascular wall, and maintains only at the expanse of iteration of the vascular wall, it has cylindrical shape, is elastic and yellow. The thickness and length of walls depends on the degree of cross-clamping during the time of formation of yielding cylindrical plaque. In the case of stopping of spasm, yielding cylindrical plaque can resolve slowly. Among hypotensive and individuals, which have normal pressure, the increase of level of LDL isn't noted. There aren't such investigations, where such link was noted. The increasing of level of LDL among these people (especially under the stress) can say about cases of short-term increase of pressure, which could be unnoticed. These patients require pressure monitoring and, accordingly, the adjustment of the state of stress and anger. 2b1af7f3a8