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Numerical investigations of pipe flow downstream a flow conditioner with bundle of tubes

Numerical investigations of pipe flow downstream a flow conditioner with bundle of tubes ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 2023, VOL. 17, NO. 1, 2154850 https://doi.org/10.1080/19942060.2022.2154850 Numerical investigations of pipe flow downstream a flow conditioner with bundle of tubes a a b Guang Yin , Muk Chen Ong and Puyang Zhang a b Department of Mechanical and Structural Engineering and Materials Science, University of Stavanger, Stavanger, Norway; State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, People’s Republic of China ABSTRACT ARTICLE HISTORY Received 1 August 2022 Flow conditioners are widely utilized in pipeline systems to improve the precision of flow rate mea- Accepted 29 November 2022 surement in the pipeline systems of the offshore and subsea oil and gas industry. There is a lack of knowledge about the influences of the conditioners on the flow inside a bend pipe due to the KEYWORDS measurement inaccuracy caused by geometries complexity. In this study, numerical simulations Flow conditioners; 3D RANS; are carried out solving the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations pipe flow; the k-ω SST with the κ–ω SST model to investigate the large-scale flow characteristics inside a double bend turbulence model pipe and the performance of a conditioner with a bundle of 19 tubes. The obtained axial velocity inside a double bend pipe flow with no flow conditioner are compared with those of the previously published numerical simulations results and experimental data as the validation study. Helical flow structures are found behind the double bend and effectively removed by the flow conditioner. The performance of the flow conditioner is evaluated based on the axial flow velocity profiles, the swirl intensities and the deviation from the flow inside a straight pipe. The effects of Reynolds numbers and the lengths of the tube bundle on the flow downstream the flow conditioner are discussed. Nomenclature 1. Introduction D Pipe diameter In the pipeline systems for oil and gas in subsea and r Radial position offshore technology, due to the space limitations, the R Pipe radius pipelines are not always straight. The transport of u fl - Rc radius of the bend ids through bend sections, which are used as tfi tings in Re Reynolds number pipeline systems, is commonly observed. The redirection ν Turbulent eddy viscosity of the flow after a bend section will generate a centrifugal ν Kinematic viscosity force along the cross section acting on the u fl id particles. u Reynolds-averaged velocities The centrifugal force is proportional to U /R (the value I Turbulence intensity U represents the characteristic axial velocity inside the l Turbulent length scale pipe flow and R represents the curvature radius of the U Bulk velocity bend section). Therefore, the centrifugal force is larger x Pipe axis location around the centerline of the pipe than that near the pipe Ld Pipe length downstream the tube bundle walls due to the higher flow velocity along the pipe center- Lu Pipe length before the bend line than that near the pipe walls, where the flow velocity Lt Length of the tube bundle is almost zero because of the nonslip condition at the wall. k Turbulent kinetic energy As a result, the force sweeps the flow near the pipe axis ω Specific turbulence dissipation rate towardstheouterwallofthebend.Whentheflowreaches ε Turbulent dissipation the outer wall of the bend, it will move back along the wall in the azimuthal direction towards the inner side of the bend. Then, a secondary flow in a pair of counter- Abbreviations rotating motions within the cross section will be induced, which is called Dean vortices (Dean, 1927). The Dean SST shear stress transport CONTACT Puyang Zhang zpy@tju.edu.cn © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 G. YIN ET AL. vortices continue to existalong thepipeflow afterthe rate measurement of the pipe systems. A precise measure- bend. The properties of this secondary flow created by ment of the flow rate using flow meters is important in a single bend have been extensively studied using experi- industrial applications. For example, in subsea pipeline ments. For example, Sudo et al. (1998) obtained the mean systems, the flow rate monitoring is crucial for the trans- velocities and also the Reynolds stress inside a 90° bend port safety andecffi iencyofoil andgas.Inpetrochemical by the means of laser doppler velocimetry. Kalpakli and industries,the flowrateisanimportant quantity to con- Örlü (2013) used particle image velocimetry (PIV) to trol the chemical reactions. Flow meters such as oricfi e study the swirling flow behind a 90 bend. The temporal plate (Sahin & Ceyhan, 1996;Tunay et al., 2004;Yin et al., and spatial evolution of the vortices were also investi- 2021) usually have the best performance when subjected gated by Hellström et al. (2013) using PIV. To gain bet- to an axisymmetric pipe flow velocity profile with no terknowledge of theflow structuredownstreamabend swirling flow. Therefore, to achieve an accurate measure- and the spatial variation of the secondary flow, three- ment of the flow rate in a pipe system, a flow conditioner dimensional numerical simulations should be employed. is usually installed behind any installation which creates However, alongpipelengthisusuallyrequiredfor the disturbances to the pipe flow and before a flow meter. The fully developed pipe flow. In addition, the high Reynolds objective of installing the flow conditioner is to remove numbers of the pipe flow in industries also lead to a high theswirlingflow,strengthenthe skewed pipe flowand computational cost. Therefore, scale-resolving numer- accelerate the recovery of a fully developed pipe flow. ical simulationssuchasTanakaand Ohshima(2012) There are different types of flow conditioners. The most using Large Eddy Simulations (LES) and Wang et al. commonly used types are the perforated plate type intro- (2018) using Direct Numerical Simulations (DNS) are duced by Akashi et al. (1978)and Laws (1990)and the rare. Other relevant studies employing scale-resolving tube bundle type as used in Xiong et al. (2003). The per- simulations are performed for low Re flow. The vor- forated plate type conditioner is a plate of n fi ite thickness tex breakdown process behind a bend pipe was studied with an arrangement of the circular holes. The tube bun- by Ault et al. (2015)at Re ∼ O(10 ) using DNS. The dle type conditioner usually consists of 19 small tubes of vortex dynamic and characteristic flow structures past finite length arranged in three concentric circles accord- a T-junction was studied by Chen et al. (2015)using ing to the ISO 5167 standard. The performance of the the linear stability analysis at Re ∼ O(10 ).The global flow conditioners in reducing the swirling flow after bend stability analysis was adopted by Lupi et al. (2020)to sections highly depends on the bends geometries, the explore the flow transition and coherent flow structure flowpropertiesandalsothegeometriesofflowcondition- caused by the pipe bend at Re = 2000 ∼ 3000. Han et al. ers. Therefore, it is important to investigate the influences (2022a) performed DNS for the flow mixing process due of these parameters to achieve optimal design of the flow to ablind-tee inside asubseapipeline. Theeeff ctsof conditioners. Due to the geometrical complexity of the the blind-tee lengths, shapes and Re with the range of flow conditioners, early studies on their performances 500 ∼ 1500 were discussed. For high Re at Reynolds- mainly relies on experiments. The eeff cts of different Averaged Navier-Stokes (RANS) simulations using tur- positions of the tube bundle with respect to an orifice flow bulencemodelswerecommonlyusedbyPatankaretal. meter were studied by Karnik (1995) to prove the feasi- (1975), Sugiyama and Hitomi (2005), Dutta and Nandi bility of decreasing the deviations of the mean pipe flow (2015)and Duttaetal. (2016, 2022). It was shown by caused by a single bend. The flow behavior downstream Hilgenstock and Ernst (1996)and Kimetal. (2014)that thesetwotypesofflowconditionershasbeeninvestigated a satisfactory agreement with the experimental measure- using experiments by Xiong et al. (2003). It was found ments can be achieved by employing RANS models. Han that the disturbances created by the flow conditioners et al. (2022b)usedReynoldsstressmodel to studythe decay rapidly downstream. The pressure drops due to secondary flow characteristics through a double-curved the perforated plate inside a pipe flow was investigated pipe in different configurations. The pipe bend induced by Tanner et al. (2019) using CFD simulations. Swirling corrosioninatwo-phasepipeflow wasquantiefi d by flows through a Zanker plate, one of the perforated plate Liu et al. (2022) using the renormalization group (RNG) type flow conditioners, were studied using CFD simu- k − ε model combined with the volume of u fl id (VOF) lations with different turbulence models by El Drainy method. et al. (2009). The performance of the swirl reduction was It was found that due to the bend sections or other proved to be correlated with the thickness of the plate. An installations such as valves and contraction sections, increasing plate thickness leads to a decreasing tangen- swirling flows will be generated along the pipe and creates tial velocity and decreasing swirl angle downstream the distorted pipe flow velocity profiles and pressure losses. plate. Most of the previous investigations focused on the These disturbances will influence the accuracy of the flow perforated plate type conditioners while the performance ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 3 of thetubebundletypehas notbeencompletelystudied equations (RANS) for the conservations of mass and due to the uncertainties and the measurement inaccuracy momentum of incompressible flow, which are given as by carrying out experiments introduced by the complex ∂u geometries. However, there is a lack of knowledge on the =0(1) ∂x flow detail inside the flow conditioner and the mecha- i nism of the swirl removal by using the flow conditioner. ∂u ∂u 1 ∂p ∂ ∂u i i j u =− + (ν + ν ) + (2) j T Furthermore, the perforated properties of the flow condi- ∂x ρ ∂x ∂x ∂x ∂x j i j j i tioner, the nonuniformity and distortion of the pipe flow caused by theflow conditionerresults in thedicffi ulty where u and u are the Reynolds-averaged flow velocities. i j for the scale-resolving numerical simulations especially The subscripts i, j = 1, 2, 3 refer to the three spatial direc- at high Re. The size difference between the small tubes tions (the corresponding velocity components are also and the pipes bring challenge to the meshing for the denoted as u, v, w). p is the Reynolds-averaged pressure simulations. and ρ is the density of the uid fl . The parameter ν is the The purpose of the present study is to conduct a com- kinematic viscosity of the uid fl . The variable ν is the tur- prehensive investigation using CFD simulations to evalu- bulent eddy viscosity under the Boussinesq assumption. ate the performance of a 19-tube bundle flow conditioner The two-equation k − ω SST turbulence model devel- behind an out-of-plane double 90 bend. The inu fl ences oped by Menter (1994) is adopted to obtain the values of Re (defined as Re = U D/ν. U is the bulk mean of ν .The k − ω SST turbulence model combines the m m T velocity of the inlet flow and D is the pipe diameter) standard k − ω model developed by Wilcox (1998)used 4 5 ranging from 10 ∼ 10 and the length of the small tube within the boundary layer in the vicinity of the pipe on the flow efi lds downstream the flow conditioner are wall and the standard k − ε model introduced by Jones discussed. To save the computational cost at these high and Launder (1973)inthe free-streampipeflow around Re, Reynolds-averaged equations are solved and the main thepipeaxis. Theturbulent eddy viscosityiscalculated focus is on the large-scale flow characteristics inside the as ν = a k/max(a ω, SF ).Inthisequation, S repre- T 1 1 2 bend pipe and downstream the flow conditioner in the sent the strain rate, a = 0.31 and F is calculated as 1 2 2 2 present study. A hybrid mesh is used within the cross F = tanh(arg ) (arg = max(2 k/0.09ωy, 500ν/y ω, y 2 2 section of the conditioner and a refined mesh is used is the distance to the wall). Detailed description of the within the small tube. A unified cross-sectional mesh turbulence model can be found in Menter et al. (2003). congfi uration is used along the whole pipe. It should be The open-source CFD toolbox OpenFOAM is used to notedthatdieff rentfromthe single bend section, thepipe solve Eqs. (1) and (2). The toolbox uses a ni fi te volume flow through the out-of-plane double 90 bend section method. The steady-state solver simpleFoam, which is has not been thoroughly studied using CFD simulations. based on a semi-implicit method for pressure coupling In addition, compared with the previous experimental equations (also known as the SIMPLE algorithm), is used studies, detailed three-dimensional information of the to solve the steady governing equations using iterations. flowstructuresand theirspatial variations alongthe pipe The spatial discretization schemes for the gradient terms behind the double bend can be obtained. The inu fl ence of in the governing equations are Gauss linear. For the diver- the flow conditioner on the pipe flow can be better quan- genceterms,the Gausslinearcorrected scheme is used. tified, which can provide further guidance and references Allthese spatialdiscretizationschemes areinthe sec- for the design of the flow conditioner. ond order. The residuals of all solved quantities after In this paper, the numerical model used to carry out the iterations at each step of the SIMPLE algorithm are −6 the CFD simulations will be introduced in Section 2, kept below 10 for all simulation cases. It is also worth including a detailed grid resolution convergence study mentioning that the large-scale secondary flow structures and a validation study. Section 3 gives the results and induced by the pipe bend are caused by the centrifugal relevant discussions. The main conclusions of the inves- forces acting on the flow and they can still exist after tigation are n fi ally provided in Section 4. time-averaging of the flow data according to Kalpakli Vester et al. (2016). Therefore, the spatial distribution and evolution of the steady secondary flow inside the bend 2. Numerical setup pipe can be obtained by solving steady governing equa- tions and the steady simulations were also carried out in 2.1. Governing equations and computational many previously published studies such as Thakre and overview Joshi (2000), Arvanitis et al. (2018), Ayala and Cimbala The governing equations solved in the present study are (2021), Ault et al. (2015), Jurga et al. (2022)and Hanetal. the three-dimensional (3D) steady Reynolds-averaged (2022b). 4 G. YIN ET AL. Flows inside a bend pipe with and without the 19-tube bundle flow conditioner are simulated to gain an intu- itiveknowledge on theswirlingflow removal. Forthe one without the flow conditioner, the computational domain as shown in Figure 1(a) consists of a pipe with an axial length of Lu = 30D installed upstream the bend section and another pipe with an axial length of Ld = 64D (D = 0.1m) installed downstream the bend section. The axial length of the pipe installed upstream the bend section is set the same as that used in Reghunathan Valsala et al. (2019) and the axial length of the pipe installed down- stream the bend section is even larger than that used in Dutta et al. (2016). A 2 × 90 out-of-plane double bend is used to connect the upstream and downstream pipes. Thevalue of thecurvature ratio(denfi ed as Rc/D where Rc is the radius of the center pipe axis in the bend section) is 2. For the one with the flow conditioner as shown in Figure 1(b), the distance between the tube bundle inlet and the outlet of the bend section is Lb = 2D,which is thesameasthatusedinthe experimentsinXiong et al. (2003). The origin of the global coordinate system is set at the inlet of the conditioner as shown in Figure 1(a). Dif- ferent lengths of the tube bundle Lt are considered. The wall thickness of the small tubes is set to be 0.02D and the outer diameter of the small tubes is set to be 0.18D.The selection of these parameters of the small tubes is based on the ISO 5167 standard and the sizes of engineering Figure 1. Computational domain (a) the two-90-degree out-of- products. plane double bend; (b) the tube-bundle flow conditioner. Theboundaryconditionsofthe flowquantitiesfor solving the governing equations are prescribed as fol- to resolve the near-wall boundary layer in the present lows: at the inlet, a fully developed turbulent pipe flow study. It worth mentioning that although it is difficult for is assumed and the radial profile for the axial velocity is the two-equation turbulence models based on the eddy approximated by the 1/7th power law of U(r)/U = max 1/7 viscosity hypothesis such as the present adopted k − ω (1 − r/R) ,where r is the radius of the pipe and U max SST model to predict the curvature eeff cts at the bend is chosen to achieve a bulk velocity of U = 1m/s. section. However, the Reynolds stress transport models, The value of k and ω at theinlet aregiven as k = whichcan capturethe curvatureeeff cts, mayleadtoa 1.5(U I) accordingtoDutta et al.and ω = k/l where high computational cost and numerical instability issues I represents the turbulence intensity calculated as I = −1/8 due to the geometrical complexity of the flow conditioner. 0.16(Re) and l = 0.038D is the length scale of the In addition, it was shown by Kim et al. (2014)aswell turbulent pipe flow. The normal gradient of the pres- sure at the inlet of the pipe is prescribed as zero. At the as Reghunathan Valsala et al. (2019) that a satisfactory pipe outlet, the normal gradients of the three velocity agreement of the resulting velocity profile with the exper- components and k, ω are set as zero. A reference value imentaldatainthe bend canbeobtainedbyusing the of zero is used for the pressure at the pipe outlet. On k − ω SST model. the wall surfaces of the pipe and the tubes of the con- ditioner, a nonslip condition is prescribed for the three 2.2. Mesh convergence study and validation study velocity components. The standard near-wall conditions areapplied forthe valueof k and ω,which is thesame The grid resolution studies are conducted for the bend + 5 as used in Yin et al. (2021). An averaged value of y = pipe with a flow conditioner at Re = 1 × 10 to deter- yu /ν (y is the distance between the center of the mine the optimal grid resolutions. The curvature ratio rfi st grid and the pipe wall and u is the friction at the is Rc/D = 1 and length of the conditioner is Lt = wall) in the range of 30 ∼40 at thepipewall is maintained 2.5D.These values areset similartothose used in the for all the simulations since the wall function is used experiment setups as reported by Xiong et al. (2003). ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 5 Figure 2. An example of the meshes (a) the cross section of the flow conditioner; (b) the cross section of the pipe; (c) the XY view of the flow conditioner. To discretize the complex tube bundle region, a hybrid out of the small tubes. However, at further downstream mesh is used within the cross section of the conditioner locations, the velocity profiles obtained using different as shown in Figure 2(a), where a structured mesh is meshes display no significant difference. Therefore, it can used within the small tube and an unstructured mesh be concluded that that the grid resolution of M2 can be is used between the small tubes. This cross-sectional regarded as sufficient to balance the mesh convergence mesh congfi uration is also used along the pipe section and computational cost. with an additional ren fi ement close to the pipe wall Forthe validation study, thesimulationfor theflow as shown in Figure 2(b). The cross-sectional grids are inside thedoublebendpipewithout theflow conditioner extruded along the pipe axis direction to form the three- using the same grid resolutions of M2 is carried out. The dimensional grids as shown in Figure 2(c). Using this obtained radial profiles of the axial velocity at several meshing method, there is no need to set additional tran- axiallocations alongthe pipe areselectedand compared sition meshing regions between the main pipe flow part with the experimentally measured profiles and the CFD and the flow conditioner part, where the tube diam- simulations results using the k − ε turbulence model eter is much smaller than that of the pipe. The total reported by Hilgenstock and Ernst (1996)at Re = 2.25 × grids numbers for each case are M1: 3898746 cells; M2: 10 in Figure 4. The axis velocity profiles at a distance of 5453937 cells; M3: 11419618 cells; M4: 15616958 cells. x/D = 5tothe outlet of thebendfor four dieff rent tra- o o o o The axis velocity profiles u(r)/U for different meshes verse angles (ϕ = 0 ,45 ,90 , 135 as shown in Figure 1) max at different distances to the conditioner outlet are shown are compared in Figure 4. An overall good agreement in Figure 3. It can be observed that there is an overall canbeobserved. It canbeseenthatat ϕ = 0 as shown agreement of the velocity profiles between the different in Figure 4(a), the high-speed region close to z = R is meshes. At the distance of x/D = 0.5 close to the out- pushed towards the wall compared with the experimental let of the flow conditioner, there are small differences measurement. Around this region, this difference is also betweeneachmesh. This maybedue to thesensitivity observed for the numerical simulation using the k − ε caused by the interaction between the strong jet flows turbulence model. There is also an overprediction of the 6 G. YIN ET AL. Figure 3. The axis velocity profiles behind the flow conditioner for different meshes. near-wall velocity around the low-speed region close to to the experimental measurements. Especially, the two z =−R and the wall-normal gradient of the near-wall peaks of the axis velocity close to z =±R and the concave velocity is larger compared with the experimental data. region close to the center axis at ϕ = 90 are well pre- At ϕ = 45 in Figure 4(b), there is an underestimation of dicted by the present numerical simulations. The average the velocity in the low-speed region close to z = R.These relative deviations of the predicted velocity profiles from o o dieff rences near thepipewall maybedue to thesensitiv- the experimental data at ϕ = 90 and 135 are 4.6% and itycausedbythe flowseparations in thepresenceofthe 2.2% bend section. The average relative deviations of the veloc- o o ity profiles at the two angles of ϕ = 0 and 45 between 3. Results and discussions the experimental data and the present numerical simula- 3.1. Flow fields without the flow conditioner tions are 4.87% and 4.4%, respectively. At ϕ = 90 shown in Figure 4(c) and 135 shown in Figure 4(d), the velocity Firstly, the flows downstream the double bend with- profiles obtain by the present numerical model are close out the flow conditioner are presented to display the ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 7 Figure 4. The present predicted axis velocity profiles at a distance of x/D = 5 to the outlet of the bend for four different traverse angles (denoted by the arrow) compared with the experimental data and numerical results reported in Hilgenstock and Ernst (1996). influence of the double bend on the pipe flow. The vorti- shows the 3D iso-surfaces of λ for the perturbation cal structures inside the pipe are identified using λ crite- velocity defined as u = u − U n,where n is the unit 2 sm rion, which is calculated as the second largest eigenvalue vector normal to the cross section and U (r) is fully sm of the symmetric tensor S S + .Inthisequation, developed turbulent pipe flow approximated by the 1/7th ij ij ij ij S and represent the symmetric and anti-symmetric power. There are strong vortical structures filling the pipe ij ij parts of the gradient tensor of the flow velocity. Figure 5 bend part. In the further downstream region, dieff rent 8 G. YIN ET AL. Figure 5. The iso-surfaces of λ =−8 coloured by the velocity amplitude for the perturbation velocity. from the two straight tube-like structures indicating the distributed on the cross section compared with that of the counter rotation vortices observed downstream a single low Re. pipe bend or a T-junction (Ault et al., 2015), a long heli- cal structure is presented and can exist up to x/D ∼ 40. 3.2. Influences of the flow conditioner on the flow In addition, with the increasing Re, the decay length of fields the vortices becomes longer. The streamlines for differ- ent Re at dieff rent streamwise locations of x/D =−2, 1 and 10 after the double bend are shown in Figure 6. The influences of the flow conditioner on the flow eld fi downstream are then examined in the comparison of axis Thestreamlines arecolouredbythe in-plane tangen- velocity profiles at ϕ = 90 . Several streamwise locations tial velocity given as ||u − u · n||/U (U is the bulk m m of x/D = 3, 5, 10, 15, 20 and 30 between the bend pipe velocity). It can be seen that close to the bend pipe at with and without the flow conditioner at Re = 1.0 × 10 x/D =−2, there are multiple recirculation motions and as shown in Figure 7.At x/D = 3 close to the flow con- strong tangential motions between these motions. Two ditioner, there are strong jet flows indicated by three small secondary motions (denoted as ‘S’) are shown in sharp peaks. Compared with that without the conditioner Figure 6(a,b) close to the corner of the cross section. With which are skewed and asymmetric, the small tubes tend the increasing Re, the secondary motions become weaker to recoverthe symmetry of theradialprofiles of theflow while in the downstream regions, the tangential motions velocity. From x/D = 5 ∼ 20, there is a changing asym- become stronger, which can be observed at x/D = 1. metry in the velocity profiles for the case without the At Re = 2.0 × 10 ,the secondarymotions almost disap- conditioner which is indicated by the changing location pear and the tangential motions energy seem to be more ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 9 Figure 6. Streamlines for different Re at three selected streamwise locations. 10 G. YIN ET AL. Figure 7. The comparison of axis velocity profiles between the case with and without flow conditioner at the same streamwise locations. of the high-speed region. This is due to the helical flow flow rate can be obtained after this location. The com- behind thedoublebendaswillbeshown later. Forthe parison of the tangential velocity profile for the two case with the flow conditioner, the strong jet flows quickly cases at x/D = 3, 20 and 30 is shown in Figure 8.It decay at x/D = 5shown in Figure 7(b). Figure 7(c,d) can be seen that there remains a strong cross-sectional show that the velocity profile becomes bulged around the motion at x/D = 20 while the conditioner can effectively center pipe axis. The slight asymmetry of velocity pro- remove this motion and the tangential velocity almost file becomes weaken in the further downstream region. disappear. It becomesclose to thevelocityprofileofthe straight For the two cases, Figuer 9. shows the comparison of pipe flow after x/D = 20 as shown in Figure 7(e,f), theaxisvelocitycontoursatthe locationsof x/D =−2 which indicates that an accurate measurement of the before the flow conditioner; x/D = 1withinthe flow ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 11 Figure 8. The comparison of the tangential velocity profiles between the case with and without flow conditioner at the same streamwise locations. conditioner; x/D = 4 close to the outlet of the flow con- Figure 10(e). There are still randomly distributed vortex ditioner and three locations of x/D = 20, 30 and 40 in cores after the conditioner. Due to their smaller size com- the downstream region. It can be seen that after the dou- paredwiththe cross-sectionalsecondary motions, they blebend, thetwo casesare similarand theflow is highly are quickly dissipated downstream. In the far eld fi down- deformed with two peaks located close to the pipe wall. stream, although there is still cross-sectional rotation, its A weak separation indicated by a negative axis velocity strength is much weaker than that without conditioner as happens close to the upper wall due to the second bend. indicated by the tangential velocity in Figure 10(d). For the case with no conditioner, there is only one peak The comparison of the three-dimensional streamlines region of the axis velocity further downstream. However, colored by the velocity magnitudes for the two cases dieff rent from that observed after a single bend where is shown in Figure 11. For the case with no condi- thelocationofthe peak valueregionremains unchanged tioner, the distorted flow velocity profiles are due to the along the pipe axis as widely reported in Patankar et al. skewed streamlines after the bend. Within the second (1975), Sugiyama and Hitomi (2005)and Duttaetal. bend section, the flow in the outer side is skewed towards (2016, 2016), the second bend breaks the symmetry of theinner side.There seemstobemultiplesmall vor- the contours and the peak value region rotates in the tex tubes close to the bend outlet. In the downstream cross section. For the case with the flow conditioner, the region, the overall pipe flow is highly swirled and helical. flowishighlyacceleratedwithinthe tubesand between However, for the case with the conditioner, the swirled the tubes. Finally, in the further downstream region, the flow after the bend is confined within the small tubes peak value region becomes almost a circle around the and forced to accelerate and becomes streamlined after center line of the pipe. The cross-sectional streamlines thetubebundle. Theaxisvorticity ω contours on the for the two cases at three streamwise locations are shown cross section at some streamwise locations are also shown in Figure 10. There are two vortex cores with counter in Figure 12.The ω contours obtained in the down- rotating secondary motions close to the double bend stream region behind a single bend pipe flow are shown while in the further downstream region, only one vortex in Figure 12 (b) for comparison. Behind a single bend, core remains, which is different from the flow behind a the positive and negative ω are almost symmetry with single bend. For the case with the conditioner, the break- almost the same strength due to the counter rotating ing of the large counter rotating secondary motions into motions. However, the negative ω behind the double some small pieces by using the small tubes as shown in bend is largely dominant and because of the helical flow, 12 G. YIN ET AL. Figure 9. The contours of the axis velocity at different axial locations. ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 13 Figure 10. The cross-sectional streamlines at three different axial locations. the high ω region also rotates within the cross-sectional Re inside a straight pipe) are measured. Figure 14 shows planes along the axis direction. The sign of ω is deter- D at dieff rent transverse angles along the pipe axis for x v mined by the relative position between the upstream and the two cases with and without the flow conditioner. It downstream pipes. With the conditioner, there remains canbeseenthatwithout theconditioner,there areperi- small-scale ω with high intensities at x/D = 1and after odical increase of D due to the helical flow caused by x v x/D = 3, ω almost disappears. Figure 13 shows the com- the double bend, which are also alternate for the four θs. parison of the 3D iso-surfaces of λ at the same level for The spatial periodicity between two peaks may be due the perturbation velocity u with and without the con- to the radius of the bend section. As indicated by Han ditioner. Although there remain some small-scale struc- et al. (2022b), a decreasing bend radius may decrease the tures right after the conditioner, a significant removal spatial periodicity between the two peaks in D and as of the vortical structures in the downstream region is a result, a faster decay of the deviation from the straight achieved by the conditioner. pipe flow may be expected due to the energy dissipation To quantitatively evaluate the performance of the flow of the helical motions. With the conditioner, the values conditioner on the removal of the swirling flow, the devi- of D are signicfi antly reduced. However, since the helical ation of the axis velocity from that inside a straight pipe flowstructuresare nothomogenousalong theazimuthal as calculated by D = ∫ |U − U |dr/ ∫ |U |dr (where directioninthe crosssection,the reductionofD are v sm sm v U (r) is thefully developedvelocityprofileatthe same different for the four transverse directions. The velocity sm 14 G. YIN ET AL. The values of I for the case without and with the con- ditioner (Lt = 2.5D) at different Re of Re = 1 × 10 ,2 × 4 4 5 5 10 ,4 × 10 ,1 × 10 and 2 × 10 along the axis direc- tion are shown in Figure 15. It can be seen that there is an exponentialdecay in thevaluesof I behind the double bend. In addition, with the increasing Re, the val- ues of I are almost the same close to the bend section whileincreases furtherdownstream. Theincreasing I may be due to the increasing inertial eeff cts with the increasing Re. With the conditioner, there is an abrupt increase in the values of I which may be due to the block- ageeeff ctscreated by theflow conditioner. Inside the small tubes, they are significantly reduced compared with those with no conditioner. This is because of the break- ing of the large-scale cross-sectional secondary motions into smaller vortices inside the tube and their energy can be more quickly dissipated. In the further down- stream region, the values of I also undergo an exponen- tial decay and there is also a Re effect on the swirl intensity reduction. The contours of the turbulent kinetic energy k/u (u is the friction velocity near the pipe wall) for Lt/D = 4 5 2at Re = 1 × 10 and 1 × 10 close to the outlet of the flow conditioner on the slice at z = 0are shownin Figure 16. It can be seen that due to the shear layer out of the conditioner, a high turbulent kinetic energy is produced. According to Xiong et al. (2003), the gen- eration of turbulence by the conditioner also promote therecoveryofthe turbulentpipeflow afterthe bend. Figure 11. The three-dimensional streamlines coloured by the 2 The high k/u region around thecenterlinequickly velocity magnitudes: (a) without the flow conditioner; (b) with the decays compared with that near the pipe wall. With the flow conditioner. increasing Re, there is an overall increasing intensity of k/u behind the conditioner and especially near the profile in the vertical direction is closest to that in a pipe wall. straight pipe while in the horizontal direction there is still There is another aspect which should be considered deviation from the straight pipe. Therefore, special con- for the design and installation of the flow conditioner. sideration should be given to the nonuniform reduction Different lengths of Lt/D = 2, 3, 4, 5 of the small tubes of D in different radial direction for the double bend in at Re = 1 × 10 is considered in the present study. The the conditioner design. Due to the removal of the heli- values of I for different Lt are shown in Figure 17.It cal flow, the deviation monotonically decays along the shows a similar exponential decay trend for these cases. axis direction. The values of D with the two cases at With the increasing Lt, there is a constant decrease of 4 5 two different Re of Re = 1 × 10 and 1 × 10 are further the I value, which is due to the enhanced acceleration compared in Figure 14(b). It seems that the reduction effects and turbulent productions by the longer small of thedeviation from thestraightpipeachievedbythe tubes. conditioner is independent on Re. Furthermore, the profiles of the Reynolds shear stress u u at the transverse angle of ϕ = 0 for Lt/D = 2 x r and 5 at Re = 1 × 10 at the streamwise locations of 3.3. Swirl intensity and the turbulent fluctuation x/D = 6, 8, 16 and 20 are shown in Figure 18.Itcan The swirl intensity is calculated by I = ∫ [u − (u · n)n] be seen that close to the outlet of the conditioner, due dA/ (U ∫ dA) (where u is the velocity vector and n is the to the flow development of the pipe flow through the unit vector normal to the cross section and the surface small tubes, astrongerinteractionofthe jetflow with the integration is conducted within the cross section as dA) pipe flow and a higher turbulence production is gener- as also used in Kim et al. (2014). ated,which leadstoahigher Reynolds shearstressfor ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 15 Figure 12. The cross-sectional axis vorticity ω contours: (a) with the flow conditioner; (b) behind a single bend section; (c) without the flow conditioner. Lt/D = 5. However, at the same streamwise location of indicate that increasing the tube length has little eect ff x/D = 16 and 20, a similar Reynolds shear stress profile on enhancing the recovery to the fully developed turbu- for the two small tube length indicate that the recovery lent pipe flow. For economic consideration, a long flow of the turbulent flow eld fi is independent on the length conditioner may not be a good choice. of the conditioner. At x/D = 16, the peak values near thepipewall arealready closetothose forthe straight 4. Conclusion pipe while there is deformation around the pipe center- line. At x/D = 20, although there is a slight deviation, the CFD simulations are conducted to investigate the turbu- straight-line behavior in the Reynolds shear stress pro- lent flow characteristics through a two-90-degree out-of- fileisachievedfor theflow conditionercase. This may plane bend. The performance of a 19-tube-bundle flow 16 G. YIN ET AL. Figure 13. The iso-surfaces of λ =−8 coloured by the velocity amplitude for the perturbation velocity (a) without the flow conditioner; (b) with the flow conditioner (the green lines indicate the inlet and outlet of the flow conditioner). Figure 15. The streamwise variation of the values of I with and without the conditioner. conditioner of reducing the flow swirl and straighten- ing the pipe flow behind the double bend is evaluated. The numerical simulations are performed based on 3D steady RANS equations. The turbulent eddy viscosity is obtained to model the Reynolds stress employing the two-equation k − ω SST turbulence model. The resulting axis velocity profiles at four transverse directions inside a double bend pipe flow with no conditioner are in a satisfactory agreement with the previously published data by experiments and other numerical simulations, which validates the present numerical model. A detail description of the helical flow structures behind a dou- ble pipe bend and their dependence on Re are shown. Systematical analysis is conducted based on the over- Figure 14. The streamwise variations of the D values at different all three-dimensional flow fields, the velocity profiles, transverse angles (shown in (a)) along the pipe axis with (dashed theswirlingintensity to assess theinufl enceofthe flow lines) and without (solid lines) the flow conditioner. conditioner. The qualitive and quantitative eeff cts of dif- 4 5 ferent Re within O(10 ) ∼ O(10 ) and the length of ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 17 2 4 5 Figure 16. The contours of the turbulent kinetic energy k/u at (a) Re = 1 × 10 and (b) 1 × 10 close to the outlet of the flow conditioner on the slice at z = 0. the conditioner on the performances are discussed. The main conclusions drawn from this study are outlined as follows: • The flow behind the double bend is highly dis- torted and swirled and become helical along the axis direction, which causes different locations of high- speed flow regions and rotating high axis vorticity regions. By using the tube-bundle flow conditioner, the helical flow is removed and straightened to become afully developedpipeflow.Althoughthere are strong jet flows right after the conditioner due to the flow acceleration of the small tubes, the flow becomes close to the straight pipe flow at around 20 D behind the conditioner. The tangential velocity is also removed. Figure 17. The streamwise variation of the values of I for differ- ent Lt/D at Re = 1 × 10 . • The swirl intensity behind the double bend exponen- tially decreases along the axis direction and increases with the increasing Re.The swirlintensity canbefur- • The performance of the conditioner to reduce the ther significantly decreased by the flow conditioner swirl intensity slightly increases with the length of and there is still Re eect ff on the swirl reduction. the small tubes. Similar Reynolds shear stress profiles 18 G. YIN ET AL. o 5 Figure 18. The profile of the Reynolds shear stress u u at ϕ = 0 for Lt/D = 2and5at Re = 1 × 10 at different streamwise locations. x r are obtained downstream the conditioner for different performing scale-resolving simulations such as Large small tube lengths. Eddy Simulations. The ndin fi gs through CFD simulations can provide Acknowledgement guidance for quantifying and evaluating the performance of the flow conditioners, which is useful for their design This studywas supportedbyState KeyLaboratoryof and optimization. The present study only considers the Hydraulic Engineering Simulation and Safety (Tianjing Uni- 19-tube bundle flow conditioner and the influence of versity) (Project No: HESS-2126) and also with compu- tational resources provided by the Norwegian Metacen- its length on the flow elds fi in the bend pipe. The ter for Computational Science (NOTUR), under Project performance of other types of flow conditioner for the No: NN9372 K. internal flow inside different pipe configuration such as T-junction, blind-tee or other bending shapes can also be evaluated using the present numerical tool, which can be Disclosure statement carried out in the future study. In addition, the unsteadi- No potential conflict of interest was reported by the author(s). ness of the turbulence properties will be obtained by ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 19 Han, F.,Liu,Y., Ong, M. C.,Yin,G., Li,W., &Wang, Z. Funding (2022a). CFD investigation of blind-tee eeff cts on flow mix- This work was supported by State Key Laboratory of Hydraulic ing mechanism in subsea pipelines. Engineering Applica- Engineering Simulation and Safety (Tianjing University): tions of Computational Fluid Mechanics, 16(1), 1395–1419. [Grant Number HESS-2126]; UNINETT Sigma2—the National https://doi.org/10.1080/19942060.2022.2093275 Infrastructure for High Performance Computing and Data Hellström, L. H., Zlatinov, M. B., Cao, G., & Smits, A. J. (2013). Storage in Norway [Grant Number NN9372K]. Turbulent pipe flow downstream of a bend. Journal of Fluid Mechanics, 735. https://doi.org/10.1017/jfm.2013.534 Hilgenstock, A., & Ernst, R. (1996). 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Numerical sim- 6.210 ulations of turbulent flow through an orifice plate in a Tanner, P., Gorman, J., & Sparrow, E. (2019). Flow–pressure pipe. Journal of Offshore Mechanics and Arctic Engineering , drop characteristics of perforated plates. International 143(4). https://doi.org/10.1115/1.4049250 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Applications of Computational Fluid Mechanics Taylor & Francis

Numerical investigations of pipe flow downstream a flow conditioner with bundle of tubes

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ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 2023, VOL. 17, NO. 1, 2154850 https://doi.org/10.1080/19942060.2022.2154850 Numerical investigations of pipe flow downstream a flow conditioner with bundle of tubes a a b Guang Yin , Muk Chen Ong and Puyang Zhang a b Department of Mechanical and Structural Engineering and Materials Science, University of Stavanger, Stavanger, Norway; State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, People’s Republic of China ABSTRACT ARTICLE HISTORY Received 1 August 2022 Flow conditioners are widely utilized in pipeline systems to improve the precision of flow rate mea- Accepted 29 November 2022 surement in the pipeline systems of the offshore and subsea oil and gas industry. There is a lack of knowledge about the influences of the conditioners on the flow inside a bend pipe due to the KEYWORDS measurement inaccuracy caused by geometries complexity. In this study, numerical simulations Flow conditioners; 3D RANS; are carried out solving the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations pipe flow; the k-ω SST with the κ–ω SST model to investigate the large-scale flow characteristics inside a double bend turbulence model pipe and the performance of a conditioner with a bundle of 19 tubes. The obtained axial velocity inside a double bend pipe flow with no flow conditioner are compared with those of the previously published numerical simulations results and experimental data as the validation study. Helical flow structures are found behind the double bend and effectively removed by the flow conditioner. The performance of the flow conditioner is evaluated based on the axial flow velocity profiles, the swirl intensities and the deviation from the flow inside a straight pipe. The effects of Reynolds numbers and the lengths of the tube bundle on the flow downstream the flow conditioner are discussed. Nomenclature 1. Introduction D Pipe diameter In the pipeline systems for oil and gas in subsea and r Radial position offshore technology, due to the space limitations, the R Pipe radius pipelines are not always straight. The transport of u fl - Rc radius of the bend ids through bend sections, which are used as tfi tings in Re Reynolds number pipeline systems, is commonly observed. The redirection ν Turbulent eddy viscosity of the flow after a bend section will generate a centrifugal ν Kinematic viscosity force along the cross section acting on the u fl id particles. u Reynolds-averaged velocities The centrifugal force is proportional to U /R (the value I Turbulence intensity U represents the characteristic axial velocity inside the l Turbulent length scale pipe flow and R represents the curvature radius of the U Bulk velocity bend section). Therefore, the centrifugal force is larger x Pipe axis location around the centerline of the pipe than that near the pipe Ld Pipe length downstream the tube bundle walls due to the higher flow velocity along the pipe center- Lu Pipe length before the bend line than that near the pipe walls, where the flow velocity Lt Length of the tube bundle is almost zero because of the nonslip condition at the wall. k Turbulent kinetic energy As a result, the force sweeps the flow near the pipe axis ω Specific turbulence dissipation rate towardstheouterwallofthebend.Whentheflowreaches ε Turbulent dissipation the outer wall of the bend, it will move back along the wall in the azimuthal direction towards the inner side of the bend. Then, a secondary flow in a pair of counter- Abbreviations rotating motions within the cross section will be induced, which is called Dean vortices (Dean, 1927). The Dean SST shear stress transport CONTACT Puyang Zhang zpy@tju.edu.cn © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 G. YIN ET AL. vortices continue to existalong thepipeflow afterthe rate measurement of the pipe systems. A precise measure- bend. The properties of this secondary flow created by ment of the flow rate using flow meters is important in a single bend have been extensively studied using experi- industrial applications. For example, in subsea pipeline ments. For example, Sudo et al. (1998) obtained the mean systems, the flow rate monitoring is crucial for the trans- velocities and also the Reynolds stress inside a 90° bend port safety andecffi iencyofoil andgas.Inpetrochemical by the means of laser doppler velocimetry. Kalpakli and industries,the flowrateisanimportant quantity to con- Örlü (2013) used particle image velocimetry (PIV) to trol the chemical reactions. Flow meters such as oricfi e study the swirling flow behind a 90 bend. The temporal plate (Sahin & Ceyhan, 1996;Tunay et al., 2004;Yin et al., and spatial evolution of the vortices were also investi- 2021) usually have the best performance when subjected gated by Hellström et al. (2013) using PIV. To gain bet- to an axisymmetric pipe flow velocity profile with no terknowledge of theflow structuredownstreamabend swirling flow. Therefore, to achieve an accurate measure- and the spatial variation of the secondary flow, three- ment of the flow rate in a pipe system, a flow conditioner dimensional numerical simulations should be employed. is usually installed behind any installation which creates However, alongpipelengthisusuallyrequiredfor the disturbances to the pipe flow and before a flow meter. The fully developed pipe flow. In addition, the high Reynolds objective of installing the flow conditioner is to remove numbers of the pipe flow in industries also lead to a high theswirlingflow,strengthenthe skewed pipe flowand computational cost. Therefore, scale-resolving numer- accelerate the recovery of a fully developed pipe flow. ical simulationssuchasTanakaand Ohshima(2012) There are different types of flow conditioners. The most using Large Eddy Simulations (LES) and Wang et al. commonly used types are the perforated plate type intro- (2018) using Direct Numerical Simulations (DNS) are duced by Akashi et al. (1978)and Laws (1990)and the rare. Other relevant studies employing scale-resolving tube bundle type as used in Xiong et al. (2003). The per- simulations are performed for low Re flow. The vor- forated plate type conditioner is a plate of n fi ite thickness tex breakdown process behind a bend pipe was studied with an arrangement of the circular holes. The tube bun- by Ault et al. (2015)at Re ∼ O(10 ) using DNS. The dle type conditioner usually consists of 19 small tubes of vortex dynamic and characteristic flow structures past finite length arranged in three concentric circles accord- a T-junction was studied by Chen et al. (2015)using ing to the ISO 5167 standard. The performance of the the linear stability analysis at Re ∼ O(10 ).The global flow conditioners in reducing the swirling flow after bend stability analysis was adopted by Lupi et al. (2020)to sections highly depends on the bends geometries, the explore the flow transition and coherent flow structure flowpropertiesandalsothegeometriesofflowcondition- caused by the pipe bend at Re = 2000 ∼ 3000. Han et al. ers. Therefore, it is important to investigate the influences (2022a) performed DNS for the flow mixing process due of these parameters to achieve optimal design of the flow to ablind-tee inside asubseapipeline. Theeeff ctsof conditioners. Due to the geometrical complexity of the the blind-tee lengths, shapes and Re with the range of flow conditioners, early studies on their performances 500 ∼ 1500 were discussed. For high Re at Reynolds- mainly relies on experiments. The eeff cts of different Averaged Navier-Stokes (RANS) simulations using tur- positions of the tube bundle with respect to an orifice flow bulencemodelswerecommonlyusedbyPatankaretal. meter were studied by Karnik (1995) to prove the feasi- (1975), Sugiyama and Hitomi (2005), Dutta and Nandi bility of decreasing the deviations of the mean pipe flow (2015)and Duttaetal. (2016, 2022). It was shown by caused by a single bend. The flow behavior downstream Hilgenstock and Ernst (1996)and Kimetal. (2014)that thesetwotypesofflowconditionershasbeeninvestigated a satisfactory agreement with the experimental measure- using experiments by Xiong et al. (2003). It was found ments can be achieved by employing RANS models. Han that the disturbances created by the flow conditioners et al. (2022b)usedReynoldsstressmodel to studythe decay rapidly downstream. The pressure drops due to secondary flow characteristics through a double-curved the perforated plate inside a pipe flow was investigated pipe in different configurations. The pipe bend induced by Tanner et al. (2019) using CFD simulations. Swirling corrosioninatwo-phasepipeflow wasquantiefi d by flows through a Zanker plate, one of the perforated plate Liu et al. (2022) using the renormalization group (RNG) type flow conditioners, were studied using CFD simu- k − ε model combined with the volume of u fl id (VOF) lations with different turbulence models by El Drainy method. et al. (2009). The performance of the swirl reduction was It was found that due to the bend sections or other proved to be correlated with the thickness of the plate. An installations such as valves and contraction sections, increasing plate thickness leads to a decreasing tangen- swirling flows will be generated along the pipe and creates tial velocity and decreasing swirl angle downstream the distorted pipe flow velocity profiles and pressure losses. plate. Most of the previous investigations focused on the These disturbances will influence the accuracy of the flow perforated plate type conditioners while the performance ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 3 of thetubebundletypehas notbeencompletelystudied equations (RANS) for the conservations of mass and due to the uncertainties and the measurement inaccuracy momentum of incompressible flow, which are given as by carrying out experiments introduced by the complex ∂u geometries. However, there is a lack of knowledge on the =0(1) ∂x flow detail inside the flow conditioner and the mecha- i nism of the swirl removal by using the flow conditioner. ∂u ∂u 1 ∂p ∂ ∂u i i j u =− + (ν + ν ) + (2) j T Furthermore, the perforated properties of the flow condi- ∂x ρ ∂x ∂x ∂x ∂x j i j j i tioner, the nonuniformity and distortion of the pipe flow caused by theflow conditionerresults in thedicffi ulty where u and u are the Reynolds-averaged flow velocities. i j for the scale-resolving numerical simulations especially The subscripts i, j = 1, 2, 3 refer to the three spatial direc- at high Re. The size difference between the small tubes tions (the corresponding velocity components are also and the pipes bring challenge to the meshing for the denoted as u, v, w). p is the Reynolds-averaged pressure simulations. and ρ is the density of the uid fl . The parameter ν is the The purpose of the present study is to conduct a com- kinematic viscosity of the uid fl . The variable ν is the tur- prehensive investigation using CFD simulations to evalu- bulent eddy viscosity under the Boussinesq assumption. ate the performance of a 19-tube bundle flow conditioner The two-equation k − ω SST turbulence model devel- behind an out-of-plane double 90 bend. The inu fl ences oped by Menter (1994) is adopted to obtain the values of Re (defined as Re = U D/ν. U is the bulk mean of ν .The k − ω SST turbulence model combines the m m T velocity of the inlet flow and D is the pipe diameter) standard k − ω model developed by Wilcox (1998)used 4 5 ranging from 10 ∼ 10 and the length of the small tube within the boundary layer in the vicinity of the pipe on the flow efi lds downstream the flow conditioner are wall and the standard k − ε model introduced by Jones discussed. To save the computational cost at these high and Launder (1973)inthe free-streampipeflow around Re, Reynolds-averaged equations are solved and the main thepipeaxis. Theturbulent eddy viscosityiscalculated focus is on the large-scale flow characteristics inside the as ν = a k/max(a ω, SF ).Inthisequation, S repre- T 1 1 2 bend pipe and downstream the flow conditioner in the sent the strain rate, a = 0.31 and F is calculated as 1 2 2 2 present study. A hybrid mesh is used within the cross F = tanh(arg ) (arg = max(2 k/0.09ωy, 500ν/y ω, y 2 2 section of the conditioner and a refined mesh is used is the distance to the wall). Detailed description of the within the small tube. A unified cross-sectional mesh turbulence model can be found in Menter et al. (2003). congfi uration is used along the whole pipe. It should be The open-source CFD toolbox OpenFOAM is used to notedthatdieff rentfromthe single bend section, thepipe solve Eqs. (1) and (2). The toolbox uses a ni fi te volume flow through the out-of-plane double 90 bend section method. The steady-state solver simpleFoam, which is has not been thoroughly studied using CFD simulations. based on a semi-implicit method for pressure coupling In addition, compared with the previous experimental equations (also known as the SIMPLE algorithm), is used studies, detailed three-dimensional information of the to solve the steady governing equations using iterations. flowstructuresand theirspatial variations alongthe pipe The spatial discretization schemes for the gradient terms behind the double bend can be obtained. The inu fl ence of in the governing equations are Gauss linear. For the diver- the flow conditioner on the pipe flow can be better quan- genceterms,the Gausslinearcorrected scheme is used. tified, which can provide further guidance and references Allthese spatialdiscretizationschemes areinthe sec- for the design of the flow conditioner. ond order. The residuals of all solved quantities after In this paper, the numerical model used to carry out the iterations at each step of the SIMPLE algorithm are −6 the CFD simulations will be introduced in Section 2, kept below 10 for all simulation cases. It is also worth including a detailed grid resolution convergence study mentioning that the large-scale secondary flow structures and a validation study. Section 3 gives the results and induced by the pipe bend are caused by the centrifugal relevant discussions. The main conclusions of the inves- forces acting on the flow and they can still exist after tigation are n fi ally provided in Section 4. time-averaging of the flow data according to Kalpakli Vester et al. (2016). Therefore, the spatial distribution and evolution of the steady secondary flow inside the bend 2. Numerical setup pipe can be obtained by solving steady governing equa- tions and the steady simulations were also carried out in 2.1. Governing equations and computational many previously published studies such as Thakre and overview Joshi (2000), Arvanitis et al. (2018), Ayala and Cimbala The governing equations solved in the present study are (2021), Ault et al. (2015), Jurga et al. (2022)and Hanetal. the three-dimensional (3D) steady Reynolds-averaged (2022b). 4 G. YIN ET AL. Flows inside a bend pipe with and without the 19-tube bundle flow conditioner are simulated to gain an intu- itiveknowledge on theswirlingflow removal. Forthe one without the flow conditioner, the computational domain as shown in Figure 1(a) consists of a pipe with an axial length of Lu = 30D installed upstream the bend section and another pipe with an axial length of Ld = 64D (D = 0.1m) installed downstream the bend section. The axial length of the pipe installed upstream the bend section is set the same as that used in Reghunathan Valsala et al. (2019) and the axial length of the pipe installed down- stream the bend section is even larger than that used in Dutta et al. (2016). A 2 × 90 out-of-plane double bend is used to connect the upstream and downstream pipes. Thevalue of thecurvature ratio(denfi ed as Rc/D where Rc is the radius of the center pipe axis in the bend section) is 2. For the one with the flow conditioner as shown in Figure 1(b), the distance between the tube bundle inlet and the outlet of the bend section is Lb = 2D,which is thesameasthatusedinthe experimentsinXiong et al. (2003). The origin of the global coordinate system is set at the inlet of the conditioner as shown in Figure 1(a). Dif- ferent lengths of the tube bundle Lt are considered. The wall thickness of the small tubes is set to be 0.02D and the outer diameter of the small tubes is set to be 0.18D.The selection of these parameters of the small tubes is based on the ISO 5167 standard and the sizes of engineering Figure 1. Computational domain (a) the two-90-degree out-of- products. plane double bend; (b) the tube-bundle flow conditioner. Theboundaryconditionsofthe flowquantitiesfor solving the governing equations are prescribed as fol- to resolve the near-wall boundary layer in the present lows: at the inlet, a fully developed turbulent pipe flow study. It worth mentioning that although it is difficult for is assumed and the radial profile for the axial velocity is the two-equation turbulence models based on the eddy approximated by the 1/7th power law of U(r)/U = max 1/7 viscosity hypothesis such as the present adopted k − ω (1 − r/R) ,where r is the radius of the pipe and U max SST model to predict the curvature eeff cts at the bend is chosen to achieve a bulk velocity of U = 1m/s. section. However, the Reynolds stress transport models, The value of k and ω at theinlet aregiven as k = whichcan capturethe curvatureeeff cts, mayleadtoa 1.5(U I) accordingtoDutta et al.and ω = k/l where high computational cost and numerical instability issues I represents the turbulence intensity calculated as I = −1/8 due to the geometrical complexity of the flow conditioner. 0.16(Re) and l = 0.038D is the length scale of the In addition, it was shown by Kim et al. (2014)aswell turbulent pipe flow. The normal gradient of the pres- sure at the inlet of the pipe is prescribed as zero. At the as Reghunathan Valsala et al. (2019) that a satisfactory pipe outlet, the normal gradients of the three velocity agreement of the resulting velocity profile with the exper- components and k, ω are set as zero. A reference value imentaldatainthe bend canbeobtainedbyusing the of zero is used for the pressure at the pipe outlet. On k − ω SST model. the wall surfaces of the pipe and the tubes of the con- ditioner, a nonslip condition is prescribed for the three 2.2. Mesh convergence study and validation study velocity components. The standard near-wall conditions areapplied forthe valueof k and ω,which is thesame The grid resolution studies are conducted for the bend + 5 as used in Yin et al. (2021). An averaged value of y = pipe with a flow conditioner at Re = 1 × 10 to deter- yu /ν (y is the distance between the center of the mine the optimal grid resolutions. The curvature ratio rfi st grid and the pipe wall and u is the friction at the is Rc/D = 1 and length of the conditioner is Lt = wall) in the range of 30 ∼40 at thepipewall is maintained 2.5D.These values areset similartothose used in the for all the simulations since the wall function is used experiment setups as reported by Xiong et al. (2003). ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 5 Figure 2. An example of the meshes (a) the cross section of the flow conditioner; (b) the cross section of the pipe; (c) the XY view of the flow conditioner. To discretize the complex tube bundle region, a hybrid out of the small tubes. However, at further downstream mesh is used within the cross section of the conditioner locations, the velocity profiles obtained using different as shown in Figure 2(a), where a structured mesh is meshes display no significant difference. Therefore, it can used within the small tube and an unstructured mesh be concluded that that the grid resolution of M2 can be is used between the small tubes. This cross-sectional regarded as sufficient to balance the mesh convergence mesh congfi uration is also used along the pipe section and computational cost. with an additional ren fi ement close to the pipe wall Forthe validation study, thesimulationfor theflow as shown in Figure 2(b). The cross-sectional grids are inside thedoublebendpipewithout theflow conditioner extruded along the pipe axis direction to form the three- using the same grid resolutions of M2 is carried out. The dimensional grids as shown in Figure 2(c). Using this obtained radial profiles of the axial velocity at several meshing method, there is no need to set additional tran- axiallocations alongthe pipe areselectedand compared sition meshing regions between the main pipe flow part with the experimentally measured profiles and the CFD and the flow conditioner part, where the tube diam- simulations results using the k − ε turbulence model eter is much smaller than that of the pipe. The total reported by Hilgenstock and Ernst (1996)at Re = 2.25 × grids numbers for each case are M1: 3898746 cells; M2: 10 in Figure 4. The axis velocity profiles at a distance of 5453937 cells; M3: 11419618 cells; M4: 15616958 cells. x/D = 5tothe outlet of thebendfor four dieff rent tra- o o o o The axis velocity profiles u(r)/U for different meshes verse angles (ϕ = 0 ,45 ,90 , 135 as shown in Figure 1) max at different distances to the conditioner outlet are shown are compared in Figure 4. An overall good agreement in Figure 3. It can be observed that there is an overall canbeobserved. It canbeseenthatat ϕ = 0 as shown agreement of the velocity profiles between the different in Figure 4(a), the high-speed region close to z = R is meshes. At the distance of x/D = 0.5 close to the out- pushed towards the wall compared with the experimental let of the flow conditioner, there are small differences measurement. Around this region, this difference is also betweeneachmesh. This maybedue to thesensitivity observed for the numerical simulation using the k − ε caused by the interaction between the strong jet flows turbulence model. There is also an overprediction of the 6 G. YIN ET AL. Figure 3. The axis velocity profiles behind the flow conditioner for different meshes. near-wall velocity around the low-speed region close to to the experimental measurements. Especially, the two z =−R and the wall-normal gradient of the near-wall peaks of the axis velocity close to z =±R and the concave velocity is larger compared with the experimental data. region close to the center axis at ϕ = 90 are well pre- At ϕ = 45 in Figure 4(b), there is an underestimation of dicted by the present numerical simulations. The average the velocity in the low-speed region close to z = R.These relative deviations of the predicted velocity profiles from o o dieff rences near thepipewall maybedue to thesensitiv- the experimental data at ϕ = 90 and 135 are 4.6% and itycausedbythe flowseparations in thepresenceofthe 2.2% bend section. The average relative deviations of the veloc- o o ity profiles at the two angles of ϕ = 0 and 45 between 3. Results and discussions the experimental data and the present numerical simula- 3.1. Flow fields without the flow conditioner tions are 4.87% and 4.4%, respectively. At ϕ = 90 shown in Figure 4(c) and 135 shown in Figure 4(d), the velocity Firstly, the flows downstream the double bend with- profiles obtain by the present numerical model are close out the flow conditioner are presented to display the ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 7 Figure 4. The present predicted axis velocity profiles at a distance of x/D = 5 to the outlet of the bend for four different traverse angles (denoted by the arrow) compared with the experimental data and numerical results reported in Hilgenstock and Ernst (1996). influence of the double bend on the pipe flow. The vorti- shows the 3D iso-surfaces of λ for the perturbation cal structures inside the pipe are identified using λ crite- velocity defined as u = u − U n,where n is the unit 2 sm rion, which is calculated as the second largest eigenvalue vector normal to the cross section and U (r) is fully sm of the symmetric tensor S S + .Inthisequation, developed turbulent pipe flow approximated by the 1/7th ij ij ij ij S and represent the symmetric and anti-symmetric power. There are strong vortical structures filling the pipe ij ij parts of the gradient tensor of the flow velocity. Figure 5 bend part. In the further downstream region, dieff rent 8 G. YIN ET AL. Figure 5. The iso-surfaces of λ =−8 coloured by the velocity amplitude for the perturbation velocity. from the two straight tube-like structures indicating the distributed on the cross section compared with that of the counter rotation vortices observed downstream a single low Re. pipe bend or a T-junction (Ault et al., 2015), a long heli- cal structure is presented and can exist up to x/D ∼ 40. 3.2. Influences of the flow conditioner on the flow In addition, with the increasing Re, the decay length of fields the vortices becomes longer. The streamlines for differ- ent Re at dieff rent streamwise locations of x/D =−2, 1 and 10 after the double bend are shown in Figure 6. The influences of the flow conditioner on the flow eld fi downstream are then examined in the comparison of axis Thestreamlines arecolouredbythe in-plane tangen- velocity profiles at ϕ = 90 . Several streamwise locations tial velocity given as ||u − u · n||/U (U is the bulk m m of x/D = 3, 5, 10, 15, 20 and 30 between the bend pipe velocity). It can be seen that close to the bend pipe at with and without the flow conditioner at Re = 1.0 × 10 x/D =−2, there are multiple recirculation motions and as shown in Figure 7.At x/D = 3 close to the flow con- strong tangential motions between these motions. Two ditioner, there are strong jet flows indicated by three small secondary motions (denoted as ‘S’) are shown in sharp peaks. Compared with that without the conditioner Figure 6(a,b) close to the corner of the cross section. With which are skewed and asymmetric, the small tubes tend the increasing Re, the secondary motions become weaker to recoverthe symmetry of theradialprofiles of theflow while in the downstream regions, the tangential motions velocity. From x/D = 5 ∼ 20, there is a changing asym- become stronger, which can be observed at x/D = 1. metry in the velocity profiles for the case without the At Re = 2.0 × 10 ,the secondarymotions almost disap- conditioner which is indicated by the changing location pear and the tangential motions energy seem to be more ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 9 Figure 6. Streamlines for different Re at three selected streamwise locations. 10 G. YIN ET AL. Figure 7. The comparison of axis velocity profiles between the case with and without flow conditioner at the same streamwise locations. of the high-speed region. This is due to the helical flow flow rate can be obtained after this location. The com- behind thedoublebendaswillbeshown later. Forthe parison of the tangential velocity profile for the two case with the flow conditioner, the strong jet flows quickly cases at x/D = 3, 20 and 30 is shown in Figure 8.It decay at x/D = 5shown in Figure 7(b). Figure 7(c,d) can be seen that there remains a strong cross-sectional show that the velocity profile becomes bulged around the motion at x/D = 20 while the conditioner can effectively center pipe axis. The slight asymmetry of velocity pro- remove this motion and the tangential velocity almost file becomes weaken in the further downstream region. disappear. It becomesclose to thevelocityprofileofthe straight For the two cases, Figuer 9. shows the comparison of pipe flow after x/D = 20 as shown in Figure 7(e,f), theaxisvelocitycontoursatthe locationsof x/D =−2 which indicates that an accurate measurement of the before the flow conditioner; x/D = 1withinthe flow ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 11 Figure 8. The comparison of the tangential velocity profiles between the case with and without flow conditioner at the same streamwise locations. conditioner; x/D = 4 close to the outlet of the flow con- Figure 10(e). There are still randomly distributed vortex ditioner and three locations of x/D = 20, 30 and 40 in cores after the conditioner. Due to their smaller size com- the downstream region. It can be seen that after the dou- paredwiththe cross-sectionalsecondary motions, they blebend, thetwo casesare similarand theflow is highly are quickly dissipated downstream. In the far eld fi down- deformed with two peaks located close to the pipe wall. stream, although there is still cross-sectional rotation, its A weak separation indicated by a negative axis velocity strength is much weaker than that without conditioner as happens close to the upper wall due to the second bend. indicated by the tangential velocity in Figure 10(d). For the case with no conditioner, there is only one peak The comparison of the three-dimensional streamlines region of the axis velocity further downstream. However, colored by the velocity magnitudes for the two cases dieff rent from that observed after a single bend where is shown in Figure 11. For the case with no condi- thelocationofthe peak valueregionremains unchanged tioner, the distorted flow velocity profiles are due to the along the pipe axis as widely reported in Patankar et al. skewed streamlines after the bend. Within the second (1975), Sugiyama and Hitomi (2005)and Duttaetal. bend section, the flow in the outer side is skewed towards (2016, 2016), the second bend breaks the symmetry of theinner side.There seemstobemultiplesmall vor- the contours and the peak value region rotates in the tex tubes close to the bend outlet. In the downstream cross section. For the case with the flow conditioner, the region, the overall pipe flow is highly swirled and helical. flowishighlyacceleratedwithinthe tubesand between However, for the case with the conditioner, the swirled the tubes. Finally, in the further downstream region, the flow after the bend is confined within the small tubes peak value region becomes almost a circle around the and forced to accelerate and becomes streamlined after center line of the pipe. The cross-sectional streamlines thetubebundle. Theaxisvorticity ω contours on the for the two cases at three streamwise locations are shown cross section at some streamwise locations are also shown in Figure 10. There are two vortex cores with counter in Figure 12.The ω contours obtained in the down- rotating secondary motions close to the double bend stream region behind a single bend pipe flow are shown while in the further downstream region, only one vortex in Figure 12 (b) for comparison. Behind a single bend, core remains, which is different from the flow behind a the positive and negative ω are almost symmetry with single bend. For the case with the conditioner, the break- almost the same strength due to the counter rotating ing of the large counter rotating secondary motions into motions. However, the negative ω behind the double some small pieces by using the small tubes as shown in bend is largely dominant and because of the helical flow, 12 G. YIN ET AL. Figure 9. The contours of the axis velocity at different axial locations. ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 13 Figure 10. The cross-sectional streamlines at three different axial locations. the high ω region also rotates within the cross-sectional Re inside a straight pipe) are measured. Figure 14 shows planes along the axis direction. The sign of ω is deter- D at dieff rent transverse angles along the pipe axis for x v mined by the relative position between the upstream and the two cases with and without the flow conditioner. It downstream pipes. With the conditioner, there remains canbeseenthatwithout theconditioner,there areperi- small-scale ω with high intensities at x/D = 1and after odical increase of D due to the helical flow caused by x v x/D = 3, ω almost disappears. Figure 13 shows the com- the double bend, which are also alternate for the four θs. parison of the 3D iso-surfaces of λ at the same level for The spatial periodicity between two peaks may be due the perturbation velocity u with and without the con- to the radius of the bend section. As indicated by Han ditioner. Although there remain some small-scale struc- et al. (2022b), a decreasing bend radius may decrease the tures right after the conditioner, a significant removal spatial periodicity between the two peaks in D and as of the vortical structures in the downstream region is a result, a faster decay of the deviation from the straight achieved by the conditioner. pipe flow may be expected due to the energy dissipation To quantitatively evaluate the performance of the flow of the helical motions. With the conditioner, the values conditioner on the removal of the swirling flow, the devi- of D are signicfi antly reduced. However, since the helical ation of the axis velocity from that inside a straight pipe flowstructuresare nothomogenousalong theazimuthal as calculated by D = ∫ |U − U |dr/ ∫ |U |dr (where directioninthe crosssection,the reductionofD are v sm sm v U (r) is thefully developedvelocityprofileatthe same different for the four transverse directions. The velocity sm 14 G. YIN ET AL. The values of I for the case without and with the con- ditioner (Lt = 2.5D) at different Re of Re = 1 × 10 ,2 × 4 4 5 5 10 ,4 × 10 ,1 × 10 and 2 × 10 along the axis direc- tion are shown in Figure 15. It can be seen that there is an exponentialdecay in thevaluesof I behind the double bend. In addition, with the increasing Re, the val- ues of I are almost the same close to the bend section whileincreases furtherdownstream. Theincreasing I may be due to the increasing inertial eeff cts with the increasing Re. With the conditioner, there is an abrupt increase in the values of I which may be due to the block- ageeeff ctscreated by theflow conditioner. Inside the small tubes, they are significantly reduced compared with those with no conditioner. This is because of the break- ing of the large-scale cross-sectional secondary motions into smaller vortices inside the tube and their energy can be more quickly dissipated. In the further down- stream region, the values of I also undergo an exponen- tial decay and there is also a Re effect on the swirl intensity reduction. The contours of the turbulent kinetic energy k/u (u is the friction velocity near the pipe wall) for Lt/D = 4 5 2at Re = 1 × 10 and 1 × 10 close to the outlet of the flow conditioner on the slice at z = 0are shownin Figure 16. It can be seen that due to the shear layer out of the conditioner, a high turbulent kinetic energy is produced. According to Xiong et al. (2003), the gen- eration of turbulence by the conditioner also promote therecoveryofthe turbulentpipeflow afterthe bend. Figure 11. The three-dimensional streamlines coloured by the 2 The high k/u region around thecenterlinequickly velocity magnitudes: (a) without the flow conditioner; (b) with the decays compared with that near the pipe wall. With the flow conditioner. increasing Re, there is an overall increasing intensity of k/u behind the conditioner and especially near the profile in the vertical direction is closest to that in a pipe wall. straight pipe while in the horizontal direction there is still There is another aspect which should be considered deviation from the straight pipe. Therefore, special con- for the design and installation of the flow conditioner. sideration should be given to the nonuniform reduction Different lengths of Lt/D = 2, 3, 4, 5 of the small tubes of D in different radial direction for the double bend in at Re = 1 × 10 is considered in the present study. The the conditioner design. Due to the removal of the heli- values of I for different Lt are shown in Figure 17.It cal flow, the deviation monotonically decays along the shows a similar exponential decay trend for these cases. axis direction. The values of D with the two cases at With the increasing Lt, there is a constant decrease of 4 5 two different Re of Re = 1 × 10 and 1 × 10 are further the I value, which is due to the enhanced acceleration compared in Figure 14(b). It seems that the reduction effects and turbulent productions by the longer small of thedeviation from thestraightpipeachievedbythe tubes. conditioner is independent on Re. Furthermore, the profiles of the Reynolds shear stress u u at the transverse angle of ϕ = 0 for Lt/D = 2 x r and 5 at Re = 1 × 10 at the streamwise locations of 3.3. Swirl intensity and the turbulent fluctuation x/D = 6, 8, 16 and 20 are shown in Figure 18.Itcan The swirl intensity is calculated by I = ∫ [u − (u · n)n] be seen that close to the outlet of the conditioner, due dA/ (U ∫ dA) (where u is the velocity vector and n is the to the flow development of the pipe flow through the unit vector normal to the cross section and the surface small tubes, astrongerinteractionofthe jetflow with the integration is conducted within the cross section as dA) pipe flow and a higher turbulence production is gener- as also used in Kim et al. (2014). ated,which leadstoahigher Reynolds shearstressfor ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 15 Figure 12. The cross-sectional axis vorticity ω contours: (a) with the flow conditioner; (b) behind a single bend section; (c) without the flow conditioner. Lt/D = 5. However, at the same streamwise location of indicate that increasing the tube length has little eect ff x/D = 16 and 20, a similar Reynolds shear stress profile on enhancing the recovery to the fully developed turbu- for the two small tube length indicate that the recovery lent pipe flow. For economic consideration, a long flow of the turbulent flow eld fi is independent on the length conditioner may not be a good choice. of the conditioner. At x/D = 16, the peak values near thepipewall arealready closetothose forthe straight 4. Conclusion pipe while there is deformation around the pipe center- line. At x/D = 20, although there is a slight deviation, the CFD simulations are conducted to investigate the turbu- straight-line behavior in the Reynolds shear stress pro- lent flow characteristics through a two-90-degree out-of- fileisachievedfor theflow conditionercase. This may plane bend. The performance of a 19-tube-bundle flow 16 G. YIN ET AL. Figure 13. The iso-surfaces of λ =−8 coloured by the velocity amplitude for the perturbation velocity (a) without the flow conditioner; (b) with the flow conditioner (the green lines indicate the inlet and outlet of the flow conditioner). Figure 15. The streamwise variation of the values of I with and without the conditioner. conditioner of reducing the flow swirl and straighten- ing the pipe flow behind the double bend is evaluated. The numerical simulations are performed based on 3D steady RANS equations. The turbulent eddy viscosity is obtained to model the Reynolds stress employing the two-equation k − ω SST turbulence model. The resulting axis velocity profiles at four transverse directions inside a double bend pipe flow with no conditioner are in a satisfactory agreement with the previously published data by experiments and other numerical simulations, which validates the present numerical model. A detail description of the helical flow structures behind a dou- ble pipe bend and their dependence on Re are shown. Systematical analysis is conducted based on the over- Figure 14. The streamwise variations of the D values at different all three-dimensional flow fields, the velocity profiles, transverse angles (shown in (a)) along the pipe axis with (dashed theswirlingintensity to assess theinufl enceofthe flow lines) and without (solid lines) the flow conditioner. conditioner. The qualitive and quantitative eeff cts of dif- 4 5 ferent Re within O(10 ) ∼ O(10 ) and the length of ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 17 2 4 5 Figure 16. The contours of the turbulent kinetic energy k/u at (a) Re = 1 × 10 and (b) 1 × 10 close to the outlet of the flow conditioner on the slice at z = 0. the conditioner on the performances are discussed. The main conclusions drawn from this study are outlined as follows: • The flow behind the double bend is highly dis- torted and swirled and become helical along the axis direction, which causes different locations of high- speed flow regions and rotating high axis vorticity regions. By using the tube-bundle flow conditioner, the helical flow is removed and straightened to become afully developedpipeflow.Althoughthere are strong jet flows right after the conditioner due to the flow acceleration of the small tubes, the flow becomes close to the straight pipe flow at around 20 D behind the conditioner. The tangential velocity is also removed. Figure 17. The streamwise variation of the values of I for differ- ent Lt/D at Re = 1 × 10 . • The swirl intensity behind the double bend exponen- tially decreases along the axis direction and increases with the increasing Re.The swirlintensity canbefur- • The performance of the conditioner to reduce the ther significantly decreased by the flow conditioner swirl intensity slightly increases with the length of and there is still Re eect ff on the swirl reduction. the small tubes. Similar Reynolds shear stress profiles 18 G. YIN ET AL. o 5 Figure 18. The profile of the Reynolds shear stress u u at ϕ = 0 for Lt/D = 2and5at Re = 1 × 10 at different streamwise locations. x r are obtained downstream the conditioner for different performing scale-resolving simulations such as Large small tube lengths. Eddy Simulations. The ndin fi gs through CFD simulations can provide Acknowledgement guidance for quantifying and evaluating the performance of the flow conditioners, which is useful for their design This studywas supportedbyState KeyLaboratoryof and optimization. The present study only considers the Hydraulic Engineering Simulation and Safety (Tianjing Uni- 19-tube bundle flow conditioner and the influence of versity) (Project No: HESS-2126) and also with compu- tational resources provided by the Norwegian Metacen- its length on the flow elds fi in the bend pipe. The ter for Computational Science (NOTUR), under Project performance of other types of flow conditioner for the No: NN9372 K. internal flow inside different pipe configuration such as T-junction, blind-tee or other bending shapes can also be evaluated using the present numerical tool, which can be Disclosure statement carried out in the future study. In addition, the unsteadi- No potential conflict of interest was reported by the author(s). ness of the turbulence properties will be obtained by ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 19 Han, F.,Liu,Y., Ong, M. C.,Yin,G., Li,W., &Wang, Z. Funding (2022a). CFD investigation of blind-tee eeff cts on flow mix- This work was supported by State Key Laboratory of Hydraulic ing mechanism in subsea pipelines. Engineering Applica- Engineering Simulation and Safety (Tianjing University): tions of Computational Fluid Mechanics, 16(1), 1395–1419. [Grant Number HESS-2126]; UNINETT Sigma2—the National https://doi.org/10.1080/19942060.2022.2093275 Infrastructure for High Performance Computing and Data Hellström, L. H., Zlatinov, M. B., Cao, G., & Smits, A. J. (2013). Storage in Norway [Grant Number NN9372K]. Turbulent pipe flow downstream of a bend. Journal of Fluid Mechanics, 735. https://doi.org/10.1017/jfm.2013.534 Hilgenstock, A., & Ernst, R. (1996). 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Journal

Engineering Applications of Computational Fluid Mechanics – Taylor & Francis

Published: Jan 1, 2

Keywords: Flow conditioners; 3D RANS; pipe flow; the k-ω SST turbulence model

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