The article deals with the flow over a roughwalled
circular cylinder in the critical area at high Re
numbers. The subject of the paper is a comparison of
the standard calculation of the aerodynamic drag coefficient
with numerical modeling. Numerical tasks are
solved by the simplified geometry of the smooth cylinder,
where the influence of the rough surface is given
by the equivalent aerodynamic roughness, and also by
the model with the real geometry of the rough casing of
the cylinder

Kolos, Ivan

Lausová, Lenka

Michalcová, Vladimíra

Transactions of the VŠB - Technical University of Ostrava Civil Engineering Series

English

DSpace at VSB Technical University of Ostrava

SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 1 | 2018 | JUNEFlow over Rough–Walled Circular Cylinderin the Critical AreaLenka LAUSOVA 1, Ivan KOLOS 2, Vladimira MICHALCOVA 31Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of OstravaLudvika Podeste 1875/17, 708 33 Ostrava - Poruba, Czech Republic2Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of OstravaLudvika Podeste 1875/17, 708 33 Ostrava - Poruba, Czech Republic3Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of OstravaLudvika Podeste 1875/17, 708 33 Ostrava - Poruba, Czech Republiclenka.lausova@vsb.cz, ivan.kolos@vsb.cz, vladimira.michalcova@vsb.czDOI: 10.31490/tces-2018-0001Abstract. The article deals with the flow over a rough-walled circular cylinder in the critical area at high Renumbers. The subject of the paper is a comparison ofthe standard calculation of the aerodynamic drag coef-ficient with numerical modeling. Numerical tasks aresolved by the simplified geometry of the smooth cylin-der, where the influence of the rough surface is givenby the equivalent aerodynamic roughness, and also bythe model with the real geometry of the rough casing ofthe cylinder.KeywordsCFD, SST k-omega, circular cylinder, highReynolds number, boundary layer, wall func-tion, aerodynamic roughness, near-wall model-ing, aerodynamic drag coefficient.1. IntroductionThe purpose of this study is to show the approachto determining sheathing roughness of flow over acircular cylinder at high Re numbers by numericalmodeling using the finite volume method in AN-SYS Fluent software. This is a complex problemof flow in the critical area, the solution of whichis dealt with by many international departments,whether in experimental [1], [2], [3], [4] or numerical[5], [6], [7], [8], [9], [10], [11], [12], [13] research.The article is based on a practical task to determinethe effect of the load (aerodynamic drag coefficient cd)of the flow over a smokestack, the casing of which isformed by a shaped sheet. Calculation of the dragcoefficient cd according to the currently valid standarddepends on the value of the Reynolds number (Re)and takes into account the roughness of the flow overbody. This study follows the previous papers [14], [15].Drag coefficient cd is in standards referred to as thecoefficient forces cf,0 [16]. It takes into account theshape and quality of the body surface and thus affectsthe size of the resistance force on object.In the case of a solved smokestack, the unevennessof the surface (roughness) is given by the height of thesheet metal. However, according to the standard, thespecific shape of the surface of the flow over a cylin-der cannot be distinguished. Due to the ratio of thesmokestack diameter and a wave height of the shapedmetal sheet, it can be assumed that the shape of thewave can affect the resulting drag coefficient.The aim of the article is to compare the standardcalculation of the drag coefficient cd with numericalmodeling with a real geometry, where the grid is de-signed to respect the shape of the waves, and also withthe simplified geometry of the smooth cylinder, wherethe influence of the rough surface is expressed by theequivalent aerodynamic roughness with using the mod-ified wall function in ANSYS Fluent [14], [15].2. Near–Wall Modeling in theCritical AreaThe study deals with the task of the flow over a circularsmokestack, when the air flow rate is defined with theReynolds number Re = 2.4 ·106 which means, that thec© 2018 TRANSACTIONS OF THE VSB-TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 1SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 1 | 2018 | JUNEFig. 1: a) cd coefficient - Re number diagram [14],b) eddy structures behind the cylinder [14]fluid flow problem belongs to the critical area and fullyadvanced turbulence can be assumed in the boundarylayer around the cylinder wall [9]. The effect of theload on the cylinder is expressed by the drag coeffi-cient cd. This coefficient changes with the Reynoldsnumber and it is also influenced by the roughness ofthe surface. This dependency is schematically shownin Fig. 1a). It is clear from the figure how the positionof the minimum of a drag coefficient is moved withrespect to the surface roughness.In general, turbulent flows are significantly affectedby the presence of wall. The near–wall region can besubdivided into three layers. The innermost layer iscalled the viscous sublayer, buffer layer follows, theouter layer is called the fully–turbulent layer and tur-bulence plays there a major role. Toward the outerpart of the near–wall region the turbulence is rapidlyenlarged by the production of turbulence kinetic energydue to the large gradients in mean velocity. Therefore,accurate representation of the flow in the near–wall re-gion determines successful predictions of wall–boundedturbulent flows [17]. Fig. 1b) is for illustrative purposesonly and it shows the formation of eddies behind theflow around a cylinder at high Re numbers [14].Two basic approaches can be used in modeling thenear–wall region: using wall functions and near–wallmodeling approach [17], see the following paragraphs.2.1. Wall FunctionsIn the approach of using wall functions for modelingthe near–wall region model, the viscosity - affected in-ner region (viscous sublayer and buffer layer) is notresolved. With these laws it is possible to expressthe mean velocity parallel to the wall and turbulencequantities outside the viscous sublayer in terms of thedistance to the wall. The wall functions are semi -empirical formulas and they are used to bridge theviscosity - affected region between the wall and thefully–turbulent region. The use of wall functions ob-viates the need to modify the turbulence models toaccount for the presence of the wall [17]. The func-tions are applied in the first cell at the wall, whichbridge the distance between the wall and the cell nearthe wall. Bridging of inner layers reduces the meshsize requirements of the near–wall region and it givesa sufficiently precise solution when dealing with tur-bulence at the fully–turbulent layer. The use of wallfunction is therefore suitable for calculations where weare more interested in the center of the system thanat the wall. These functions express the dependenceof velocity on the distance from the wall, most oftenin the form dimensionless velocity to the dimensionlessdistance.Fluid flows in atmospheric boundary layers over arough terrain affects the drag coefficient (resistance).It can be possible to include the wall roughness ef-fects through the law–of–the–wall modified for rough-ness [14]. There can be used the simplified geometryand the effect of the shaped casing can be expressed bythe so-called equivalent aerodynamic roughness.2.2. Near–Wall Modeling ApproachIn another approach, the turbulence models are mod-ified to enable the viscosity–affected region to be re-solved with a mesh all the way to the wall, includ-ing the viscous sublayer. This approach is particularlyuseful where wall flow is the most important or rec-ommended for turbulent models for a lower Reynoldsnumber [17]. In this task the influence of the roughcasing (the shaped sheathing of the smokestack) can af-fect the resulting drag coefficient, so a model includingnear–wall modeling has also been chosen for compari-son with the wall functions approach. Detailed mod-eling of ineer layers means that the radial height ofthe mesh cells at the wall is sufficiently reduced duringcrosslinking. With the fineness of the mesh, a detaileddescription of the flow over the wall including the vis-cous sublayer is obtained. Since the fluid behavior ofthe wall is often predictive, it is usually the more ef-fective using the wall functions instead of fine mesh inthe case of near–wall modeling.3. Task DescriptionThe study presents the possibility to solve the ef-fects of loads on corrugated sheet metal casing of thesmokestack with a numerical solution in ANSYS Fluentsoftware. A numerical SST k-omega model was chosenfor the solution, because it is suitable for modeling offlow in near–wall region. Length of computational areaL = 140 m, diameter of the smokestack D = 3.6 m.The height of the wave of the shaped sheet is 18 mm.Fig. 2 shows the dimensions of the model and the loca-tion of the flow over the cylinder in the computationalarea. Other parameters of the solved task are: veloc-ity v = 10 m/s, turbulence intensity i = 10 % andkinematic viscosity = 1.5 · 10−5 m2/s.c© 2018 TRANSACTIONS OF THE VSB-TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 2SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 1 | 2018 | JUNEFig. 2: Computational area of the solved taskNumerical tasks are solved by two approaches. Onetask solves the effects of load on the simplified model,when the geometry of the chimney is formed by asmooth sheet and the influence of the rough casing isexpressed in the calculation by the so-called equivalentaerodynamic roughness. In the second task, the ge-ometry of the model is made up of the real shape ofthe casing by two different grids, a tetrahedral and ahexahedral grid. All models are in 2D. Figure 3 showsdetails of the meshes of all the models being solved andthey are described in the following paragraphs.3.1. Simplified Geometry with theUse of Equivalent AerodynamicRoughnessIn this option of the calculations, the real shape ofthe sheathing (corrugated sheet) was replaced with asmooth cross–section of the circular cylinder. The ef-fect of the shaped casing is given by the physical rough-ness height KS and the roughness constant CS , whichare used in the calculation for the boundary conditionsand which define the aerodynamic roughness equiv-alent to the actual roughness of the flow around abody [14], [15]. Physical roughness heightKS = 18mm(height of a wave of the sheet metal) and roughnessconstant CS = 0.5. Roughness constant CS dependson the type of the roughness, in the Fluent Manual [17]it is recommended value of 0.5 with a range of 0.5 - 1.1.The mesh is formed by a mix of the hexahedral grid andtetrahedral, see Fig. 3a). When creating the mesh, thesize of the first cell on the wall must be at least twiceas large as the roughness of the sheathing (here theheight of the sheet metal) [17]. The hexahedral gridforms the inner layers of the boundary layer to ensurethat the wall function works properly. The tetrahedralgrid continues further in the computational area.Fig. 3: Meshing of solved models:a) simplified geometry - hexa/tetra mesh,b) real geometry - tetrahedral mesh,c) real geometry - hexahedral mesh3.2. Real Geometry of the CylinderCasing–Tetrahedral MeshingIn the other two variants, the calculation of the flowover the cylinder with the real sheet metal casing isperformed.The first model has a tetrahedral grid and it is alsosolved using the wall function in ANSYS Fluent soft-ware, see figure Fig. 3b). Unlike the previous option(simplified geometry and aerodynamic roughness), theroughness of the sheathing is given by the real geom-etry of the casing. Fig. 2 shows a computational areacreated by a tetrahedral meshing and it is possible tonotice the fine mesh around the wall and the enlargingcells in the computational area, which is easily realizedin 2D using a tetrahedral grid.3.3. Real Geometry of the CylinderCasing–Hexahedral MeshingIn this variant, the calculation is also performed onthe real geometry of the smokestack casing modeledby the hexahedral grid, see Fig. 3c) and the task issolved in ANSYS Fluent software as a task of near–wall modeling approach. The created grid respects theshape of the casing and thus the real geometry andit was created to prepare calculations in 3D in futureresearch.4. Results of the SolutionThe results of drag coefficients obtained from all vari-ants of the numerical models are compared to the stan-dard calculation and described in the following para-graphs.4.1. Drag Coefficient fromNumerical ModelingThe time record of the solved drag coefficient ob-tained from all three variants of numerical simulationsis shown in the graphs in Fig. 4. The average value ofc© 2018 TRANSACTIONS OF THE VSB-TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 3SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 18 | NUMBER: 1 | 2018 | JUNEFig. 4: Drag coefficient obtained from numerical simulations:a) simplified geometry,b) real geometry–tetrahedral mesh,c) real geometry– hexahedral meshFig. 5: The value of the aerodynamic drag coefficient–schemefrom EN 1991-1-4 [17]drag coefficient cd in the task with simplified geometrycd = 0.72, in the variant based on a real geometry withthe tetrahedral mesh cd = 0.96 and in a real geometrytask with hexahedral mesh cd = 1.31.4.2. Drag Coefficient According tothe StandardDetermining of the drag coefficient according to thestandard depends on the size of the Reynolds number(Re = 2.4·106) and on the ratio of the roughnessK andthe diameter D of the cylinder (K/D = 0.018/3.6 = 5 ·10−3). Drag coefficient is determined according to thestandard graph from EN 1991-1-4. Scheme of the graphcan be seen on Fig. 5 and drag coefficient according tostandard is cd = 0.95.The graph on Fig. 5 also shows the average resul-tant of the drag coefficients obtained by the numeri-cal solutions of all three mentioned variants both onthe simplified and the real geometry of the jacketedsmokestack.5. ConclusionThe study presented the possibility to solve the effectsof load on smokestack with the rough casing by numer-ical solution in 2D in ANSYS Fluent software, whichwas compared with the standard calculation. Numer-ical tasks were solved by two approaches. The firstsolution of the task was achieved on a simplified ge-ometry, when the casing was made of a smooth sheetand the influence of the rough casing was expressedin the calculation by the so-called equivalent aerody-namic roughness. In the second task, the geometry ofthe smokestack was made up of a real shape of cas-ing using two models, one of which was created by atetrahedral grid, and the second one by a hexahedralgrid. As it has been assumed, numerical solutions haveachieved different drag coefficient values.The result obtained by calculating with the realgeometry modeled by the tetrahedral mesh almostmatches with the standard results and it can be evalu-ated as the best one. However, the results obtained inthe two other variants differ from the standard calcu-lation. In the case of the real hexa–shaped geometrytask, it is problematic to create a grid just close to thewall (the shaped metal sheet), by adjusting the ratioof sides in the grid may be achieved a more relevantresult.In the case of simplified smooth geometry using theaerodynamic roughness it is a relatively complex prob-lem of correct setting of the physical roughness heightKS, because in the numerical solution the coefficientKS was given only by the height of the wave and theshape of the chimney casing could not be taken intoaccount. This issue will be the subject of further re-search.AcknowledgmentThe paper has been supported by the project of"Conceptual development of science and research ac-tivities 2018" on the Faculty of Civil Engineering,VSB–TU Ostrava and by the Ministry of Educa-tion, Youth and Sports from the Large Infrastructuresfor Research, Experimental Development and Innova-tions project "IT4Innovations National Supercomput-ing Center–LM2015070".References[1] MERRICK, R. and G. BITSUAMLAK. Controlof flow around a circular cylinder by the use ofsurface roughness: A computational and experi-mental approach. In: Proceeding of the 4th Inter-national Conference Advances on Wind and Struc-tures (AWAS08). Jeju, Korea, 2008.[2] DOBES, J. and M. KOZUBKOVA. The influenceof numerical models on determining the drag co-efficient. In: Proceeding of the International Con-ference on Experimental Fluid Mechanics. 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Flow over rough-walled circular cylinder in the critical area

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Flow over rough-walled circular cylinder in the critical area

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