- Email: [email protected]
Double wavy geometric disturbance to the bluff body flow at a subcritical Reynolds number
Ocean Engineering 195 (2020) 106713
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Double wavy geometric disturbance to the bluff body flow at a subcritical Reynolds number Hyun Sik Yoon *, Kyung Jin Oh, Hyo Ju Kim, Min Il Kim, Jahoon Moon Department of Naval Architecture and Ocean Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Gumjeong-Gu, Busan, 46241, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Keywords: Double wavy cylinder Flow control Geometric disturbance Large eddy simulation
A double wavy (DW) disturbance is newly proposed to obtain the reduction of drag and the fluctuating lift as the passive control for the bluff body flow. The present study expanded the asymmetry of Yoon et al. (2017) and combined two optimum wavelengths in the short and long wavelength ranges of Lam and Lin (2008) and Lin et al. (2016) to realize the DW geometric disturbance. Eventually, the flow past the DW cylinder was computed at the subcritical Reynolds number of 3000 using a large eddy simulation. The DW cylinder achieved the significant reduction of drag and fluctuating lift, compared to those of the smooth cylinder. It is noted that the DW cylinder achieved more reduction of drag and lift fluctuation than the wavy cylinder with the optimum wavelength. The DW cylinder formed the common characteristics of flow which associates with the reduction of drag and the fluctuating lift. The DW cylinder showed the double wavy profile of vortex formation length, which is due to the double wavy distribution of flow. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, the saddle plane forms a longer formation length than the nodal plane.
1. Introduction The bluff body is one of the most commonly encountered structures in the real life, industries and academics. In the fluid mechanics, the bluff body is characterized by vortex shedding beyond the critical Reynolds number. The various methods to control vortex shedding, which derives a large portion of the drag, noise, vibration to bodies, have been suggested. Among the flow control methods, the shape modification is adopted as geometric disturbances. (Zdravkovich, 1981; Naudascher and Rockwell, 2005; Ekmekci and Rockwell, 2010). In nature, the unique geometries have been found to be applied as the bluff body flow control, classified as the biomimetics. The daffodil stem contributes to design the helically twisted elliptic (HTE) cylinder. Eventually, the HTE geometry is confirmed by the effective passive control method (Kim et al., 2012, 2016; Wei et al., 2016; Jung and Yoon, 2014). Recently, the unique shape of a harbor seal vibrissa was intro duced as a tool for VIV (vortex-induced vibration) (Hanke et al., 2010) and hydrodynamic forces (Hans et al., 2013). But, the detail researches in the view of fluid dynamics are very seldom (Wang and Liu, 2016; Kim and Yoon, 2017, 2018). In this regard, Yoon et al. (2017) considered the asymmetry to find the effect of the asymmetry on the fluid flow. The harbor seal vibrissa come up this asymmetry. They considered the
symmetric wavy cylinder to apply the asymmetry. The symmetric wavy cylinder is confirmed as a good passive control by many researches (Jung and Yoon, 2014; Ahmed et al., 1993; Lam and Lin, 2009; Lin et al., 2016; Ahmed and Bays-Muchmore, 1992; Lam et al., 2004a, 2004b; Lee and Nguyen, 2007; Zhang and Lee, 2005; Xu et al., 2010). For the first time, Yoon et al. (2017) considered an asymmetric wavy disturbance as the passive control. They considered that the optimum wavelength of λ=Dm ¼ 6:06 for the wavy cylinder gives a decrease in fluid forces (Lin et al., 2016), where Dm is the mean value of the maximum and minimum diameters. Lam and Lin, 2007, 2008, 2009 reported the optimal wavelengths for the maximum reduction of forces in the laminar and subcritical regimes. The present study intends to expand the asymmetry of Yoon et al. (2017) and combine two optimum wavelengths of λ=Dm � 2:0 and λ= Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance. We simply call this modified geometric disturbance as a double wavy (DW) disturbance which will be precisely described in a chapter of the identification of geometries. To our knowledge, the present study is an original research which applies the double wavy geometry as the passive control to the bluff body flow. The main purpose of the present study is to evaluate the feasibility of the double wavy geometry as the passive control by the geometric disturbance to the circular cylinder. Therefore, we estimate
* Corresponding author. E-mail address: [email protected] (H.S. Yoon). https://doi.org/10.1016/j.oceaneng.2019.106713 Received 4 March 2019; Received in revised form 1 October 2019; Accepted 10 November 2019 Available online 17 November 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Nomenclature Symbols a CD CL Dm Dmax Dmin fs Lfc p St t Re ui xi
Amplitude of waviness Drag coefficient Lift coefficient Mean diameter of cylinder Maximum local diameter of cylinder Minimum local diameter of cylinder Vortex shedding frequency Vortex formation length Pressure Strouhal number Time Reynolds number Velocity Cartesian coordinates
Greek symbols λ wavelength of waviness ν Kinematic viscosity ρ Density Sub/superscripts rms Root mean square ∞ Free-stream Time-averaged quantity
the time variation of the drag and lift due to vortex shedding and their mean values. Additionally, in order to estimate the efficiency of the double wavy geometry, force coefficient of the double wavy (DW) ge ometry are compared with those of the smooth and symmetric wavy (CY and WC) geometries. Therefore, flows around three different geometries (CY, WC, and DW) are computationally simulated. The present study considers the subcritical Reynolds number of 3000 where wake flow is fully turbulent, resulting in using the large eddy simulation (LES). The present wavelength and amplitude of WC are the same as Lin et al. (2016) where identified the long optimal wavelength as λ=Dm ¼ 6:06 which minimizes the force coefficients. As mentioned above, in order to test the feasibility of DW geometry as the passive control, we consider the optimal wavelength of WC. In future, the wavelength, amplitude, and Reynolds number should be considered to generalize the performance of DW as the passive control.
Fig. 1. The geometries of the cylinders: (a) CY, (b) WC, and (c) DW cylinders.
∂ui ∂ui uj ¼ þ ∂t ∂xj
2. Numerical details
∂τij ∂xj
(2)
where the overbar denotes the resolved scale. In equations, t, xi , ui and p are the time, Cartesian coordinates, the corresponding velocity compo nents, and the pressure, respectively. The τij is the subgrid scale stress tensor. The details of the present LES model can be referred in authors’ previous works (Jung and Yoon, 2014; Germano et al., 1991; Lilly, 1992). The spatial discretization is done by a second-order central differ ence scheme based on finite volume method. The Crank-Nicolson scheme and a second-order Adams-Bashforth scheme are adopted for the diffusion and convection terms, respectively, for the temporal
2.1. Governing equations and numerical methods For the large eddy simulation, the grid filters are used for NavierStokes and continuity equations under the assumptions of the un steady three-dimensional incompressible flow. The governing equations are as follows:
∂ui ¼0 ∂xi
∂p 1 ∂2 ui þ ∂xi Re ∂xj ∂xj
(1)
2
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 2. Definition of the geometries for (a) the WC (b) the DW cylinders.
Table 1 Grid dependence test for a CY and WC cylinders at Re ¼ 3000 compared with experimental and LES results. Case CY
WC
Fig. 3. Schematic of the computational domain and boundary conditions.
discretization. These numerical methods have been successfully used in Yoon et al. (2009) and Yoon et al. (2017).
Coarse Medium Fine Norberg ( Norberg, 1987) Norberg ( Norberg, 2003) Lam and Lin ( Lam and Lin, 2009) Jung and Yoon ( Jung and Yoon, 2014) Yoon et al. (Yoon et al., 2017) Coarse Medium Fine Lin et al. (Lin et al., 2016) Yoon et al. (Yoon et al., 2017)
Nr � Nθ � Nz
CD
CL;rms
St
25000 � 100 29640 � 120 32142 � 140 Experimental
1.0288 1.0287 1.0286 0.98–1.03
0.1295 0.1296 0.1298 N/A
0.210 0.210 0.210 0.210–0.213
Summarized
N/A
0.210
16000 � 80
1.0800
0.05, 0.07 0.1770
39240 � 90
0.9934
0.1150
0.211
23664 � 148
1.0229
0.1648
0.210
25000 � 100 29640 � 120 32142 � 140 16000 � 100
0.8753 0.8748 0.8749 0.9040
0.0099 0.0101 0.0101 0.0130
0.180 0.180 0.180 0.187
23664 � 148
0.8926
0.0148
0.180
0.210
The abbreviations N(Node), M(Middle) and S(Saddle), marked in Fig. 2 (a), correspond to the positions at these local diameters Dmax , Dm , and Dmin , respectively. The λ1 is an optimum wavelength of λ=Dm ¼ 6:06 for the WC cylinder (Lin et al., 2016). Thus, the present study choose the optimum wavelength of λ=Dm ¼ 6:06 and wave amplitude of a=Dm ¼ 0:152. These the optimum condi tions provided the maximum reduction of force coefficients for the WC cylinder (Lin et al., 2016). Eventually, using these optimum conditions, we can evaluate whether the DW geometry can provide the additional reduction. Recently, Yoon et al. (2017) considered the asymmetric wavy
2.2. Definition of the geometries Fig. 1 shows three different shapes of the CY, WC and DW cylinders. The local diameter (Dz ) of the WC cylinder is defined as follows; � � 2π z Dz ¼ Dm þ 2a cos (3) λ1 where λ1 and a are the wavelength and amplitude, respectively. The Dm is the mean diameter of the maximum and minimum local diameters (Dmax and Dmin ), which is the same as the diameter of the CY cylinder. 3
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 4. Mean streamwise velocity U=U∞ (a) and r.m.s. streamwise velocity u’=U (b) distributions of a smooth cylinder at different positions in the wake centerline compared with experimental and LES results at Re ¼ 3000. Table 2 Grid dependence test for a DW cylinder at Re ¼ 3000.
2.3. Boundary conditions, grid, and validation
Case
N r � N θ � Nz
CD
CL;rms
Coarse Medium Fine
25000 � 100 29640 � 120 32142 � 140
0.8616 0.8615 0.8614
0.0039 0.0040 0.0042
The computational domain and boundary conditions adopted in the present study is presented in Fig. 3. The size of domain is 24Dm , 16Dm and 6:06Dm ( ¼ λ) along the streamwise, transverse and spanwise di rection, respectively. The cylinder is set to the location with a distance of 8Dm and 16Dm from the inflow and outflow boundaries, respectively. The fluid flow uniformly in the inflow boundary, and the symmetry and periodic boundary conditions were imposed in the transverse and spanwise directions. A convective boundary condition, ð∂ui =∂tÞ þ ðc∂ui =∂xÞ ¼ 0(where c is the space-averaged streamwise outlet veloc ity), was imposed for velocity and Neumann condition was used for pressure on the outflow region,. No-slip and no-penetration conditions were applied at the cylinder surface. In this present study, the typical grid distribution of the OH-type is considered, including an O-type grid distribution around the cylinder for the purpose of refining the mesh in normal and circumferential di rections. In the spanwise direction, the grid distributed uniformly. In order to verify the present numerical method and grid system, the comparisons with the previous researches for the time-averaged drag coefficient (CD ), root-mean-square (rms) of lift fluctuation (CL;rms ) and Strouhal number (St) and also grid dependency test have been carried out. The definitions of CD , CL;rms and St can be found in (Jung and Yoon, 2014; Yoon et al., 2009, 2017). First, the present results of three different grid systems (coarse, medium and fine) are compared with those of experiments (Norberg, 1987, 2003) and computation (Lam and Lin, 2008) for the CY cylinder, and LES results (Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016) for the WC cylinder, as arranged in Table 1. These grid systems consist of
geometric disturbance for flow control. They also used this optimum wavelength of λ1 . The double wavy geometry in Fig. 2(b) is formed by two different wavelengths as follows; � �� � � � 2π z 2πz þ cos (4) Dz ¼ Dm þ a cos λ1 λ2 where, λ2 is λ1 =3 of the wavelength of the WC cylinder. Thus, λ2 is λ= Dm ¼ 2:02 which is about the optimum wavelength in the small wave length region (Lam and Lin (2008)). The double wavy geometry is shown in Fig. 2(b). For the DW cylinder, there are two node and saddle positions in the half wavelengths. Thus, the positions at the maximum and minimum local diameters of the DW cylinder are named N1(Node1) and S2(Saddle2), respectively, another node and saddle positions of the middle part of the half cylinder are named N2(Node2) and S1(Saddle1), respectively, as shown in Fig. 2(b). Each node and saddle has double wavy formation. Therefore, the double wavy geometry reflects the asymmetry of Yoon et al. (2017) and the combination of two optimum wavelengths of λ=Dm ¼ 2:02 and λ=Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance.
4
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 6. Power spectral densities of the time-dependent lift coefficients for three different cylinders. DW ¼ 0.175.
2.5, 3.5, and 4.5 million grids, respectively. The results of the present computations agree well with those of the previous experimental and numerical researches. Also, the results for three different grid systems have the nearly same values. In addition, by using the medium grid system, the comparison of the present profiles of mean (U=U∞ ) and the r. m.s (u’=U∞ ) of the streamwise velocity along the crosswise direction at different downstream locations with the results of experiments (Lam et al., 2004b; Norberg, 1987) and computation (Yoon et al., 2017) is shown in Fig. 4. Regardless of the streamwise location, both of (U=U∞ ) and the r.m.s (u’=U∞ ) give a good agreement with those of the previous studies, as shown in Fig. 4. Additionally, for the DW cylinder which has no previous data, the computations of three grid systems have been carried out to evaluate the dependence of the solutions on the grid, as listed in Table 2. Similarly, the discrepancies of the results among those grid systems are negligible. Therefore, the medium grid system was employed to discuss the following results dealt with in next chapter. 3. Results and discussion 3.1. Force coefficients and Strouhal number The drag and lift coefficients (CD and CL ) are usually considered as the objectives of the flow control to mainly reduce these force co efficients. Therefore, first time histories of CD and CL for the CY, WC, and DW cylinders are illustrated in Fig. 5. The WC cylinder gives smaller CD and CL compared to the CY cyl inder, which well regenerates the results of Lin et al. (2016). The opti mum wavelength of λ=Dm ¼ 6:06 (Lin et al., 2016) is consistent with Darekar and Sherwin (2000) who achieved a large reduction in CD for a front-and-rear-face-wavy square cylinder. The DW cylinder provides a significant reduction of CD and CL in comparison with the smooth cylinder in Fig. 5(a–b). Especially, the DW cylinder gives more reduction of CD and CL than the optimal WC cylinder (Lin et al., 2016).
Fig. 5. The time-history of (a) the drag and (b) the fluctuation lift coefficients for the CY, WC, and DW cylinder at Re ¼ 3000.
Table 3 Comparisons of the force coefficients for the CY, WC, and DW cylinders. Cylinder type
CD
Diff. (%)
CL;rms
Diff. (%)
CY WC DW
1.0318 0.8972 0.8592
-
0.1293 0.0152 0.0035
-
13.05 16.74
88.26 97.27
5
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 7. Top view (left column) and Perspective view (right column) of the iso-surface of swirl strength for the (a) CY, (b) WC, and (c) DW cylinders at Re ¼ 3000.
elongation, the spanwise wavy fashion of the flow, the regimes of the zero, the new transverse and streamwise vorticities.
Table 3 shows mean force coefficients of CD and CL;rms . The WC cylinder provides about 13.05% and 88.26% reduction of CD and CL;rms , respectively, in comparison with the CY cylinder. The DW cylinder gives approximately 16.74% and 97.27%, respectively, in comparison with the CY cylinder. Therefore, the DW cylinder provides more reduction than the optimal WC cylinder. The Strouhal numbers (St) for different cylinders are achieved by performing the Fourier transform of the time history of the lift coeffi cient to evaluate the effect of the DW shape on the vortex-shedding frequency. Fig. 6 presents the power spectral densities of the time his tories of the lift coefficients for different cylinders. The values of the smooth cylinder and the symmetric wavy cylinder are 0.21 and 0.18, as early in Table 1. The DW cylinder provides almost the same as the WC cylinder, as shown in Fig. 6. As a result, the of the WC and DW cylinders is smaller than that of a smooth cylinder at this Re. For the WC cylinder, Lin et al. (Ahmed and Bays-Muchmore, 1992) reported that the greatest deviation of between the WC and CY cylinder takes place at the optimum values of wavelength (2.0 and 6.0). Thus the present result is consistent with the finding of Lin et al. (Ahmed and Bays-Muchmore, 1992). The geometric disturbances of helically twisted elliptic shape, the symmetric waviness and the asymmetric waviness ((Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016)) provide smaller than the smooth cylinder, which is associated with the suppression of vortex shedding in the near wake. The DW shape is also related to the lower frequency by the suppressed vortex-shedding in the near wake, which will be identified by the instantaneous flow structures later.
3.2.1. Delay of the vortex roll-up The retard of the vortex roll-up and almost the disappearance of the vortex shedding in near-wake are derived by the passive flow control using the surface modifications of the WC cylinder (Jung and Yoon, 2014; Lin et al., 2016; Lam et al., 2004b; Zhang and Lee, 2005; Xu et al., 2010; Lam and Lin, 2008), the helically twisted elliptic (HTE) cylinder (Kim et al., 2016; Wei et al., 2016; Jung and Yoon, 2014), stranded cable models (Nebres et al., 1993) and asymmetric wavy (ASW) cylinder (Yoon et al., 2017). This delay of the vortex roll-up contributes to the drag reduction and the suppression of the lift fluctuation. Because the DW cylinder as a passive control based on the surface modification gives rise to the reduction of the force coefficients as shown in Fig. 5 and Table 3, we observe the instantaneous 3D vortical struc tures and the 2D vorticity distribution to identify the feature of the vortex roll-up and vortex shedding. In order to define these 3-D vortical structures, we adopted the swirl strength given by Zhou et al. (1999). They defined a vortical region as a region with negative λ2 , the second largest eigenvalue of S2ij þ Ω2ij , where S2ij and Ω2ij are the strain rate tensor
and rotation rate tensor, respectively. �rma �n vortices The smooth cylinder clearly forms that large-scale Ka in the near-wake region, as shown in Fig. 7(a). However, the separated shear layer from the WC and DW cylinders are considerably elongated to the downstream, as shown in Fig. 7(b) and (c), respectively. Thus, the vortex roll-up of the separated shear layer from the WC and DW cylin ders is delayed to a downstream position, which is well identified by the distribution of the spanwise vorticity in x-y plane in Fig. 8. Therefore, the vortex shedding nearly disappears in the near-wake of the WC and DW cylinders and reappears weakly in the far wake, compared to the smooth cylinder. This modification of the vortical structures due to waviness is consistent with the findings from previous studies (Wei
3.2. Common characteristics of flow structures for force reduction The drag reduction and the suppression of the lift fluctuation by the wavy, helical and spiral type of the geometric disturbance for the bluff body are associated with generally the common flow characteristics such as the shear layer elongation, a longer vortex formation length 6
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 8. Contours of instaneous spanwise vorticity in the x-y plane: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z=Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z= Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
7
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 9. Top views of the iso-surface of transverse (left column) and streamwise (right column) vorticities. (a & d) for the CY cylinder; (b & e) for the WC cylinder; and (c & f) for the DW cylinder at Re ¼ 3000.
8
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 10. Instantaneous velocity vector (left column) and transvers vorticity contours (right column), in the horizontal (x WC and (c) the DW at Re ¼ 3000.
9
z) plane at y=Dm ¼
0:6 for (a) the CY, (b)
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 11. Mean velocity vector (a & d), streamwise vorticity contours (b & e), and transverse vorticity contours (c & f) in the horizontal (x column) and DW (right column) at y=Dm ¼ 0:6 at Re ¼ 3000.
10
z) plane for the WC (left
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 12. Mean streamwise velocity (U=U∞ ) along the wake centerline (y= Dm ¼ 0) of the smooth (CY), wavy (WC) and double wavy (DW) cylinders at Re ¼ 3000. (N: Node, M: Middle, S: Saddle, N1: Node1, N2: Node2, S1: Saddle1 and S2: Saddle2).
Fig. 13. Vortex formation length (Lfc =Dm ) of the smooth (CY), wavy (WC) and double wavy (DW) cylinders at Re ¼ 3000.
et al., 2016; Jung and Yoon, 2014; Yoon et al., 2017; Lam et al., 2004b; Zhang and Lee, 2005; Xu et al., 2010; Lam and Lin, 2008). In addition, the transverse and streamwise vorticities additionally appear over the surface of the WC and DW cylinders, as shown in Fig. 9b, c, e and f, respectively. These long additional vortices over the surface of the WC and DW cylinders attenuate the spanwise vortices, which con tributes to the delay of the vortex roll-up.
The regions of zero vorticity were also formed by the WC (Fig. 9(b) and (e)) and ASW cylinders (Jung and Yoon, 2014; Yoon et al., 2017; Lam and Lin, 2008), and HTE cylinder (Wei et al., 2016; Jung and Yoon, 2014). The present DW geometry forms the regions of the zero vorticities which are associated by the elongated shear layer and the delay of vortex shedding in Fig. 9(c) and (f). 3.2.3. Formation of jet-like flow The smooth cylinder forms the positive and negative vorticities in the instantaneous velocity field of the smooth cylinder, they are distributed in a seemingly random manner, especially near the rear stagnation point (Zhang and Lee, 2005; Lin et al., 1995), as shown in Fig. 10(a and d). The WC, ASW and HTE cylinders form the local acceleration and decelera tion flow owing to the spanwise dependent diameter which roles to block and suck the flow along the span (Jung and Yoon, 2014). Thus, in contrast to the smooth cylinder in Fig. 10(a), the WC forms the jet-like flow in Fig. 10(b) showing the instantaneous velocity vectors in the horizontal (x z) plane at y=Dm ¼ 0:6. The magnitude of the velocity vectors near-wake for WC is smaller than that of the smooth cylinder. Also, the elongated shear layer is dominant to the near-wake. Therefore, the near-wake of the WC is more stable than that of the smooth cylinder. Especially, the DW cylinder shows that jet-like flow covers wider wake region and sustains downstream, as shown in Fig. 10(c and f). Additionally, the jet-like flow of the DW cylinder creates the spatially locked vorticities to farther downstream, as shown in Fig. 10(f). Behind the rear surface of the DW, the vorticities are much sparser than the smooth cylinder and also the WC cylinder, which associates to wider zero vorticity region for the DW cylinder. From the patterns behind the DW cylinder, the separated free shear layers are relatively more stable, and then roll up into vortices farther downstream, leading to a reduction of the suction near the base region of the twisted cylinder. This stabilized wake also associates to the large reduction of the turbulent kinetic en ergy behind the DW cylinder, which will be discussed in later. Fig. 10 shows the mean velocity vectors and vorticity contours in the
3.2.2. Additional vorticities and regimes of the zero vorticity The streamwise and transverse vorticities additionally appear over the surface of the WC, ASW and HTE cylinders. These additional vortices are formed by three dimensional geometric effect on the flow separation (Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016). Generally, the additional vorticities on WC surface in Fig. 9(b) and (e) elongate to downstream, and then they are split in several branches. The additional appearance of the streamwise and transverse vorticities over the modi fied surfaces show the very weak dependence on the time and space. Particularly, these additional streamwise and transverse vorticities are formed periodically in the spanwise direction over the time, as shown in Fig. 9(b and c) and 9(e, f) for the WC and DW cylinders, respectively. Eventually, these additional vorticities are spatially and temporally locked and stabilize the shear layers to farther downstream and retard vortices roll-up (Lin et al., 2016). These distributions of additional vorticities can also be observed in Fig. 10(e) and (f) for the contours of the transverse vorticity. These spatially and temporally locked vortices are clearly confirmed in the time-averaged flow filed in Fig. 11. The double wavy configuration of the DW cylinder forms alterna tively the vorticities with the positive and negative sign along the span, as shown in Fig. 9(c) and (f). These vorticities are much closer to each other than the WC cylinder. Thus, the wider spanwise regions of the wake are covered by these vorticities originated from the surface. As a result, these stabilized additional vorticities delay vortices roll-up, associating to more drag reduction and the suppression of the lift fluctuation.
11
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 14. Contours of the time averaged spanwise vorticity at various spanwise positions for different cylinder: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z= Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z=Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
12
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
horizontal (x z) plane at y=Dm ¼ 0:6 for the WC and DW cylinders. These mean velocity vectors and contours of vorticities clarify the temporal and spatially lock. Especially, the DW cylinder shows the extension of the streamwise spatial lock, compared to the WC, which clarified by the contours of vorticities in Fig. 10(b and c) and 8(e & f) for the WC and the DW cylinders, respectively. The DW cylinder forms the double wavy formation of vorticities like the ASW cylinder (Yoon et al., 2017) due to the relatively high and low speed flows by different spanwise geometric gradients. 3.2.4. A longer vortex formation length elongation A longer vortex formation length associating with the drag reduction and the suppression of the lift fluctuation has been found by the WC cylinder (Lam and Lin, 2008), the ASW cylinder (Yoon et al., 2017), and HTE cylinder (Wei et al., 2016; Jung and Yoon, 2014). The vortex formation length can be evaluated along its centerline. The wake closure length (Lfc ) corresponds to the location of the timeaveraged closure point where the mean streamwise velocity on the wake centerline is zero, is considered in this study to quantitatively identify and compare the spanwise vortex formation lengths for 3-D geometric disturbances. Recently, many researches have used the wake closure length (Lfc ) to measure the formation length (Jung and Yoon, 2014; Yoon et al., 2017; Lam et al., 2004b; Lam and Lin, 2008; Norberg, 1998), even the definition of the vortex formation length is not universal. The dependence of the recovery location of U=U∞ on the spanwise geometric disturbances is assured in Fig. 12 where the previous results for the CY and WC cylinders are included for the purpose of the com parison. Additionally, the vortex formation length (Lfc ) as s function of the spanwise direction is presented in Fig. 12. For the WC with long wavy length, the zero position moves down stream with moving from the saddle to the node, which is consistent with that of Lin et al. (2016), as shown in Figs. 12 and 13. Thus, the nodal plane forms a larger reversal flow region than the saddle plane. For the ASW cylinder, the Lfc has an asymmetric profile along the spanwise direction (Yoon et al., 2017). The DW cylinder shows the double wavy profile of Lfc in each half wavelength, which is due to the double wavy distribution of flow, as indicated in the velocity vectors and the transverse vorticity contours in the horizontal (x z) plane. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, in contrast to a longer wavelength, the saddle plane forms a longer formation length than the nodal plane (Lin et al., 2016), as shown in Figs. 12 and 13. The DW cylinder also identified by the mean spanwise vorticity in Fig. 14. The DW shape generates longer vorticity than the WC geometry over the span. The vortex formation length is strongly related to the force coefficients and pressure. Therefore, the DW cylinder gain more force reduction than the WC cylinder. The largest mean base pressure of the DW cylinder confirm the association of the vortex formation length, as shown in Fig. 15. 3.2.5. Turbulence suppression Figs. 16 and 17 show the contours of the turbulent kinetic energy (TKE) for three cylinders in the x-y plane and x-z plane, respectively. In cases of WC and DW cylinders, different spanwise planes are considered due to three dimensional geometries. In addition, the profiles of TKE along the spanwise direction at different streamwise directions are plotted in Fig. 18. Turbulent fluctuations are also associated with the variation of the fluctuating forces exerted on a body (Wu et al., 2007). The WC cylinder in Fig. 16(b–d) exhibits negligibly small TKE in the near-wake in comparison with the CY cylinder in Fig. 16(a), regardless of the spanwise direction. For the WC cylinder, this wide region covered by minor TKE is clearly identified in Fig. 17(b) in comparison with the CY cylinder in Fig. 17(a). In the near-wake, the appearance of the minor TKE along the span at x= ¼ 1 for the WC is identified in Fig. 18(a). Dm
Fig. 15. Variation of (a) the mean circumferential pressure distributions, (b) the coefficient of mean base pressure along the span for the CY, WC, and DW cylinders at Re ¼ 3000.
13
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 16. Contours of the turbulent kinetic energy (TKE) in the x-y plane: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z=Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z= Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
14
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
The maximum TKE of the CY cylinder appears at about x=D � 2:0 in m Fig. 18(b). Otherwise, the TKE of the WC cylinder at x=D � 2:0 is much m
smaller than that of the CY cylinder. The positions of the maximum TKE are farther from the back of the WC cylinder than from that of the CY cylinder. The maximum TKE of the WC cylinder appears at about x=D � m
3:5 in Fig. 18(d). Generally, the WC cylinder forms the periodic varia tions of TKE distribution along the spanwise direction and resembles the geometric shape of the cylinder. Thus, the positon of the maximum TKE for the WC cylinder is dependent on the spanwise direction, as shown in Figs. 17(b) and 18(d). This spanwise dependence of the maximum TKE position is associated with the vortex formation length and the shear layer elongation due to the 3D geometric disturbance. The longer vortex formation length and the elongated shear layer contribute to the delay of the vortex roll-up and the late vortex shedding, which weaken the TKE and leads to the relatively stable flow. These characteristics of the TKE distribution of the WC cylinder are consistent with the findings of Zhang et al. (Zhang and Lee, 2005) and Lam and Lin (2008). The TKE behind the DW cylinder exhibits the similar distribution with the WC cylinder. Therefore, the positions of the maximum TKE values are farther from the back of the DW cylinder than from those of the CY, as shown in Fig. 16(e–h). The DW cylinder forms wider region with very small TKE than the WC cylinder, as shown in Fig. 17(b) and (c). This weak TKE is clearly identify by the spanwise profiles of TKE at different streamwise positions in Fig. 18. The overall values of TKE for the DW cylinder near the wake region are smaller than those of the CY and WC cylinders. Consequently, the significant reduction in TKE in the near-wake of the DW cylinder contributes to a reduction in the drag and fluctuating lift. 4. Conclusions For the first time, a double wavy (DW) disturbance is introduced to achieve the drag reduction and the suppression of fluctuating lift as the passive control for the bluff body flow. The present study expanded the asymmetry of Yoon et al. (2017) and combined two optimum wave lengths of λ=Dm ¼ 2:0 and λ=Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance. We simply call this modified geometric disturbance as a double wavy disturbance. Eventually, we numerically investigated flow past as a double wavy cylinder at Re ¼ 3000 using LES. The DW geometric disturbance achieved the significant reduction of drag and the suppression of fluctuating lift, compared to those of the CY cylinder. The DW cylinder gave a reduction of 16.74% of CD and 97.27% of CL;rms in comparison with the CY cylinder. It is noted that the DW cylinder achieved more reduction of CD and CL;rms than the WC cylinder with long optimum wavy length where the maximum reduction of CD and CL;rms is achieved (Lin et al., 2016). The DW geometric disturbance formed the common characteristics of flow structures which associates with the drag reduction and the suppression of the lift fluctuation for the bluff body. Also, the DW disturbance forms the additional streamwise and transverse vorticities by the 3D effect of the geometric disturbance on the flow separation. These additional vorticities locked temporally and spatially and stabilize the shear layers to farther downstream and delay vortices roll-up, associating to more drag reduction and the suppression of the lift fluctuation. The jet-like flow of the DW cylinder creates the spatially locked vorticities to farther downstream, which more stabilize the wake and achieves more reduction of the drag and lift fluctuation. The DW cyl inder forms the double wavy formation of vorticities due to the rela tively high and low speed flows by different spanwise geometric gradients. The DW cylinder shows also the double wavy profile of vortex for mation length in each half wavelength, which is due to the double wavy
Fig. 17. Contours of the turbulent kinetic energy (TKE) in the x-z plane for (a) the CY, (b) the WC and (c) the DW at y=Dm ¼ 0.
15
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 18. Profiles of the turbulent kinetic energy (TKE) in y=Dm ¼ 0 for the CY, the WC and the DW at different x-positions.
distribution of flow. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, in contrast to a longer wavelength, the saddle plane forms a longer formation length than the nodal plane (Lin et al., 2016).
Jung, J., Yoon, H., 2014. Large eddy simulation of flow over a twisted cylinder at a subcritical Reynolds number. J. Fluid Mech. 759, 579–611. Kim, H., Yoon, H., 2017. Effect of the orientation of the harbor seal vibrissa based biomimetic cylinder on hydrodynamic forces and vortex induced frequency. AIP Adv. 7, 105015. Kim, H., Yoon, H., 2018. Forced convection heat transfer from the biomimetic cylinder inspired by a harbor seal vibrissa. Int. J. Heat Mass Transf. 117, 548–558. Kim, W., Lee, J., Choi, H., 2012. Flow past a helically twisted elliptic cylinder. In: Proceedings of the 8th KSME-JSME Thermal and Fluids Engineering Conference, Songdo, Incheon, Korea, pp. 18–21. Kim, W., Lee, J., Choi, H., 2016. Flow around a helically twisted elliptic cylinder. Phys. Fluids 28 (5), 053602. Lam, K., Lin, Y.F., 2007. Drag force control of flow over wavy cylinders at low Reynolds number. J. Mech. Sci. Technol. 21, 1331–1337. Lam, K., Lin, Y.F., 2008. Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number. Int. J. Heat Fluid Flow 29, 1071–1088. Lam, K., Lin, Y.F., 2009. Effects of wavelength and amplitude of a wavy cylinder in crossflow at low Reynolds numbers. J. Fluid Mech. 620, 195–220. Lam, K., Wang, F.H., Li, J.Y., So, R.M.C., 2004. Experimental investigation of the mean and fluctuating forces of wavy (varicose) cylinders in a cross-flow. J. Fluids Struct. 19, 321–334. Lam, K., Wang, F.H., So, R.M.C., 2004. Three-dimensional nature of vortices in the near wake of a wavy cylinder. J. Fluids Struct. 19, 815–833. Lee, S.J., Nguyen, A.T., 2007. Experimental investigation on wake behind a wavy cylinder having sinusoidal cross-sectional area variation. Fluid Dyn. 39, 292–304. Lilly, D.K., 1992. A proposed modification of the Germano subgrid-scale closure method,. Phys. Fluids 4, 633–635. Lin, J.C., Towfighi, J., Rockwell, D., 1995. Instantaneous structure of the near-wake of a circular cylinder: on the effect of Reynolds number. J. Fluids Struct. 9, 409–418. Lin, Y.F., Bai, H.L., Alam, M.M., Zhang, W.G., Lam, K., 2016. Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder. J. Fluids Struct. 61, 392–409. Naudascher, E., Rockwell, D., 2005. Flow-Induced Vibrations: An Engineering Guide. Dover Publications. Nebres, J., Barill, S., Nelson, R., 1993. Flow about yawed, stranded cables. Exp. Fluid 14, 49–58. Norberg, C., 1987. Effects of Reynolds Number and a Low-Intensity Freestream Turbulence on the Flow Around a Circular Cylinder. Department of Applied Thermodynamics and Fluid Mechanics, Chalmers University of Technology. Norberg, C., 1998. LDV-measurements in the Near Wake of a Cir-Cular Cylinder, ASME Paper No. FEDSM98–521.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) through GCRC-SOP (No. 2011-0030013) and (NRF-2019R1A2C1009081). References Ahmed, A., Bays-Muchmore, B., 1992. Transverse flow over a wavy cylinder. Phys. Fluids 4, 1959–1967. Ahmed, A., Khan, M.J., Bays-Muchmore, B., 1993. Experimental investigation of a threedimensional bluff-body wake. AIAA J. 31, 559–563. Darekar, R.M., Sherwin, S.J., 2000. Flow past a square-section cylinder with a wavy stagnation face. J. Fluid Mech. 426, 263–295. Ekmekci, A., Rockwell, D., 2010. Effect of a geometrical surface disturbance on flow past a circular cylinder: a large-scale spanwise wire. J. Fluid Mech. 665, 120–157. Germano, M., Piomelli, U., Moin, P., Cabot, W.H., 1991. A dynamic subgrid-scale eddy viscosity model,. Phys. Fluids 3, 1760–1765. Hanke, W., Witte, M., Miersch, L., Brede, M., Oeffner, J., Michael, M., Hanke, F., Leder, A., Dehnhardt, G., 2010. Harbor seal vibrissa morphology suppresses vortexinduced vibrations. J. Exp. Biol. 213, 2665–2672. Hans, H.H., Miao, J., Weymouth, G., Triantafyllou, M., 2013. Whisker-like geometries and their force reduction properties. In: OCEANS-Bergen MTS/IEEE.
16
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Norberg, C., 2003. Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 57–96. Wang, S., Liu, Y., 2016. Wake dynamics behind a seal-vibrissa-shaped cylinder: a comparative study by time-resolved particle velocimetry measurements. Exp. Fluid 57, 1–20. Wei, D., Yoon, H., Jung, J., 2016. Characteristics of aerodynamic forces exerted on a twisted cylinder at a low Reynolds number of 100. Comput. Fluids 136, 456–466. Wu, J.Z., Lu, X.Y., Zhuang, L.X., 2007. Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286. Xu, C.Y., Chen, L., Lu, X., 2010. Large-eddy simulation of the compressible flow past a wavy cylinder. J. Fluid Mech. 665, 238–273.
Yoon, H., Balachandar, S., Ha, M., 2009. Large eddy simulation of flow in an unbaffled stirred tank for different Reynolds numbers. Phys. Fluids 21, 1–16. Yoon, H., Shin, H., Kim, H., 2017. Asymmetric disturbance effect on the flow over a wavy cylinder at a subcritical Reynolds number. Phys. Fluids 29, 095102. Zdravkovich, M.M., 1981. Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. J. Wind Eng. Ind. Aerodyn. 7, 145–189. Zhang, W., Lee, S.J., 2005. PIV measurements of the near-wake behind a sinusoidal cylinder. Exp. Fluid 38, 824–832. Zhou, J., Adrian, R.J., Balachadar, S., Kendall, T.M., 1999. Mechanisms for generating coherent packets of hairpin vorticies in channel flow. J. Fluid Mech. 387, 353–396.
17
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Double wavy geometric disturbance to the bluff body flow at a subcritical Reynolds number Hyun Sik Yoon *, Kyung Jin Oh, Hyo Ju Kim, Min Il Kim, Jahoon Moon Department of Naval Architecture and Ocean Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Gumjeong-Gu, Busan, 46241, Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Keywords: Double wavy cylinder Flow control Geometric disturbance Large eddy simulation
A double wavy (DW) disturbance is newly proposed to obtain the reduction of drag and the fluctuating lift as the passive control for the bluff body flow. The present study expanded the asymmetry of Yoon et al. (2017) and combined two optimum wavelengths in the short and long wavelength ranges of Lam and Lin (2008) and Lin et al. (2016) to realize the DW geometric disturbance. Eventually, the flow past the DW cylinder was computed at the subcritical Reynolds number of 3000 using a large eddy simulation. The DW cylinder achieved the significant reduction of drag and fluctuating lift, compared to those of the smooth cylinder. It is noted that the DW cylinder achieved more reduction of drag and lift fluctuation than the wavy cylinder with the optimum wavelength. The DW cylinder formed the common characteristics of flow which associates with the reduction of drag and the fluctuating lift. The DW cylinder showed the double wavy profile of vortex formation length, which is due to the double wavy distribution of flow. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, the saddle plane forms a longer formation length than the nodal plane.
1. Introduction The bluff body is one of the most commonly encountered structures in the real life, industries and academics. In the fluid mechanics, the bluff body is characterized by vortex shedding beyond the critical Reynolds number. The various methods to control vortex shedding, which derives a large portion of the drag, noise, vibration to bodies, have been suggested. Among the flow control methods, the shape modification is adopted as geometric disturbances. (Zdravkovich, 1981; Naudascher and Rockwell, 2005; Ekmekci and Rockwell, 2010). In nature, the unique geometries have been found to be applied as the bluff body flow control, classified as the biomimetics. The daffodil stem contributes to design the helically twisted elliptic (HTE) cylinder. Eventually, the HTE geometry is confirmed by the effective passive control method (Kim et al., 2012, 2016; Wei et al., 2016; Jung and Yoon, 2014). Recently, the unique shape of a harbor seal vibrissa was intro duced as a tool for VIV (vortex-induced vibration) (Hanke et al., 2010) and hydrodynamic forces (Hans et al., 2013). But, the detail researches in the view of fluid dynamics are very seldom (Wang and Liu, 2016; Kim and Yoon, 2017, 2018). In this regard, Yoon et al. (2017) considered the asymmetry to find the effect of the asymmetry on the fluid flow. The harbor seal vibrissa come up this asymmetry. They considered the
symmetric wavy cylinder to apply the asymmetry. The symmetric wavy cylinder is confirmed as a good passive control by many researches (Jung and Yoon, 2014; Ahmed et al., 1993; Lam and Lin, 2009; Lin et al., 2016; Ahmed and Bays-Muchmore, 1992; Lam et al., 2004a, 2004b; Lee and Nguyen, 2007; Zhang and Lee, 2005; Xu et al., 2010). For the first time, Yoon et al. (2017) considered an asymmetric wavy disturbance as the passive control. They considered that the optimum wavelength of λ=Dm ¼ 6:06 for the wavy cylinder gives a decrease in fluid forces (Lin et al., 2016), where Dm is the mean value of the maximum and minimum diameters. Lam and Lin, 2007, 2008, 2009 reported the optimal wavelengths for the maximum reduction of forces in the laminar and subcritical regimes. The present study intends to expand the asymmetry of Yoon et al. (2017) and combine two optimum wavelengths of λ=Dm � 2:0 and λ= Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance. We simply call this modified geometric disturbance as a double wavy (DW) disturbance which will be precisely described in a chapter of the identification of geometries. To our knowledge, the present study is an original research which applies the double wavy geometry as the passive control to the bluff body flow. The main purpose of the present study is to evaluate the feasibility of the double wavy geometry as the passive control by the geometric disturbance to the circular cylinder. Therefore, we estimate
* Corresponding author. E-mail address: [email protected] (H.S. Yoon). https://doi.org/10.1016/j.oceaneng.2019.106713 Received 4 March 2019; Received in revised form 1 October 2019; Accepted 10 November 2019 Available online 17 November 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Nomenclature Symbols a CD CL Dm Dmax Dmin fs Lfc p St t Re ui xi
Amplitude of waviness Drag coefficient Lift coefficient Mean diameter of cylinder Maximum local diameter of cylinder Minimum local diameter of cylinder Vortex shedding frequency Vortex formation length Pressure Strouhal number Time Reynolds number Velocity Cartesian coordinates
Greek symbols λ wavelength of waviness ν Kinematic viscosity ρ Density Sub/superscripts rms Root mean square ∞ Free-stream Time-averaged quantity
the time variation of the drag and lift due to vortex shedding and their mean values. Additionally, in order to estimate the efficiency of the double wavy geometry, force coefficient of the double wavy (DW) ge ometry are compared with those of the smooth and symmetric wavy (CY and WC) geometries. Therefore, flows around three different geometries (CY, WC, and DW) are computationally simulated. The present study considers the subcritical Reynolds number of 3000 where wake flow is fully turbulent, resulting in using the large eddy simulation (LES). The present wavelength and amplitude of WC are the same as Lin et al. (2016) where identified the long optimal wavelength as λ=Dm ¼ 6:06 which minimizes the force coefficients. As mentioned above, in order to test the feasibility of DW geometry as the passive control, we consider the optimal wavelength of WC. In future, the wavelength, amplitude, and Reynolds number should be considered to generalize the performance of DW as the passive control.
Fig. 1. The geometries of the cylinders: (a) CY, (b) WC, and (c) DW cylinders.
∂ui ∂ui uj ¼ þ ∂t ∂xj
2. Numerical details
∂τij ∂xj
(2)
where the overbar denotes the resolved scale. In equations, t, xi , ui and p are the time, Cartesian coordinates, the corresponding velocity compo nents, and the pressure, respectively. The τij is the subgrid scale stress tensor. The details of the present LES model can be referred in authors’ previous works (Jung and Yoon, 2014; Germano et al., 1991; Lilly, 1992). The spatial discretization is done by a second-order central differ ence scheme based on finite volume method. The Crank-Nicolson scheme and a second-order Adams-Bashforth scheme are adopted for the diffusion and convection terms, respectively, for the temporal
2.1. Governing equations and numerical methods For the large eddy simulation, the grid filters are used for NavierStokes and continuity equations under the assumptions of the un steady three-dimensional incompressible flow. The governing equations are as follows:
∂ui ¼0 ∂xi
∂p 1 ∂2 ui þ ∂xi Re ∂xj ∂xj
(1)
2
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 2. Definition of the geometries for (a) the WC (b) the DW cylinders.
Table 1 Grid dependence test for a CY and WC cylinders at Re ¼ 3000 compared with experimental and LES results. Case CY
WC
Fig. 3. Schematic of the computational domain and boundary conditions.
discretization. These numerical methods have been successfully used in Yoon et al. (2009) and Yoon et al. (2017).
Coarse Medium Fine Norberg ( Norberg, 1987) Norberg ( Norberg, 2003) Lam and Lin ( Lam and Lin, 2009) Jung and Yoon ( Jung and Yoon, 2014) Yoon et al. (Yoon et al., 2017) Coarse Medium Fine Lin et al. (Lin et al., 2016) Yoon et al. (Yoon et al., 2017)
Nr � Nθ � Nz
CD
CL;rms
St
25000 � 100 29640 � 120 32142 � 140 Experimental
1.0288 1.0287 1.0286 0.98–1.03
0.1295 0.1296 0.1298 N/A
0.210 0.210 0.210 0.210–0.213
Summarized
N/A
0.210
16000 � 80
1.0800
0.05, 0.07 0.1770
39240 � 90
0.9934
0.1150
0.211
23664 � 148
1.0229
0.1648
0.210
25000 � 100 29640 � 120 32142 � 140 16000 � 100
0.8753 0.8748 0.8749 0.9040
0.0099 0.0101 0.0101 0.0130
0.180 0.180 0.180 0.187
23664 � 148
0.8926
0.0148
0.180
0.210
The abbreviations N(Node), M(Middle) and S(Saddle), marked in Fig. 2 (a), correspond to the positions at these local diameters Dmax , Dm , and Dmin , respectively. The λ1 is an optimum wavelength of λ=Dm ¼ 6:06 for the WC cylinder (Lin et al., 2016). Thus, the present study choose the optimum wavelength of λ=Dm ¼ 6:06 and wave amplitude of a=Dm ¼ 0:152. These the optimum condi tions provided the maximum reduction of force coefficients for the WC cylinder (Lin et al., 2016). Eventually, using these optimum conditions, we can evaluate whether the DW geometry can provide the additional reduction. Recently, Yoon et al. (2017) considered the asymmetric wavy
2.2. Definition of the geometries Fig. 1 shows three different shapes of the CY, WC and DW cylinders. The local diameter (Dz ) of the WC cylinder is defined as follows; � � 2π z Dz ¼ Dm þ 2a cos (3) λ1 where λ1 and a are the wavelength and amplitude, respectively. The Dm is the mean diameter of the maximum and minimum local diameters (Dmax and Dmin ), which is the same as the diameter of the CY cylinder. 3
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 4. Mean streamwise velocity U=U∞ (a) and r.m.s. streamwise velocity u’=U (b) distributions of a smooth cylinder at different positions in the wake centerline compared with experimental and LES results at Re ¼ 3000. Table 2 Grid dependence test for a DW cylinder at Re ¼ 3000.
2.3. Boundary conditions, grid, and validation
Case
N r � N θ � Nz
CD
CL;rms
Coarse Medium Fine
25000 � 100 29640 � 120 32142 � 140
0.8616 0.8615 0.8614
0.0039 0.0040 0.0042
The computational domain and boundary conditions adopted in the present study is presented in Fig. 3. The size of domain is 24Dm , 16Dm and 6:06Dm ( ¼ λ) along the streamwise, transverse and spanwise di rection, respectively. The cylinder is set to the location with a distance of 8Dm and 16Dm from the inflow and outflow boundaries, respectively. The fluid flow uniformly in the inflow boundary, and the symmetry and periodic boundary conditions were imposed in the transverse and spanwise directions. A convective boundary condition, ð∂ui =∂tÞ þ ðc∂ui =∂xÞ ¼ 0(where c is the space-averaged streamwise outlet veloc ity), was imposed for velocity and Neumann condition was used for pressure on the outflow region,. No-slip and no-penetration conditions were applied at the cylinder surface. In this present study, the typical grid distribution of the OH-type is considered, including an O-type grid distribution around the cylinder for the purpose of refining the mesh in normal and circumferential di rections. In the spanwise direction, the grid distributed uniformly. In order to verify the present numerical method and grid system, the comparisons with the previous researches for the time-averaged drag coefficient (CD ), root-mean-square (rms) of lift fluctuation (CL;rms ) and Strouhal number (St) and also grid dependency test have been carried out. The definitions of CD , CL;rms and St can be found in (Jung and Yoon, 2014; Yoon et al., 2009, 2017). First, the present results of three different grid systems (coarse, medium and fine) are compared with those of experiments (Norberg, 1987, 2003) and computation (Lam and Lin, 2008) for the CY cylinder, and LES results (Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016) for the WC cylinder, as arranged in Table 1. These grid systems consist of
geometric disturbance for flow control. They also used this optimum wavelength of λ1 . The double wavy geometry in Fig. 2(b) is formed by two different wavelengths as follows; � �� � � � 2π z 2πz þ cos (4) Dz ¼ Dm þ a cos λ1 λ2 where, λ2 is λ1 =3 of the wavelength of the WC cylinder. Thus, λ2 is λ= Dm ¼ 2:02 which is about the optimum wavelength in the small wave length region (Lam and Lin (2008)). The double wavy geometry is shown in Fig. 2(b). For the DW cylinder, there are two node and saddle positions in the half wavelengths. Thus, the positions at the maximum and minimum local diameters of the DW cylinder are named N1(Node1) and S2(Saddle2), respectively, another node and saddle positions of the middle part of the half cylinder are named N2(Node2) and S1(Saddle1), respectively, as shown in Fig. 2(b). Each node and saddle has double wavy formation. Therefore, the double wavy geometry reflects the asymmetry of Yoon et al. (2017) and the combination of two optimum wavelengths of λ=Dm ¼ 2:02 and λ=Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance.
4
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 6. Power spectral densities of the time-dependent lift coefficients for three different cylinders. DW ¼ 0.175.
2.5, 3.5, and 4.5 million grids, respectively. The results of the present computations agree well with those of the previous experimental and numerical researches. Also, the results for three different grid systems have the nearly same values. In addition, by using the medium grid system, the comparison of the present profiles of mean (U=U∞ ) and the r. m.s (u’=U∞ ) of the streamwise velocity along the crosswise direction at different downstream locations with the results of experiments (Lam et al., 2004b; Norberg, 1987) and computation (Yoon et al., 2017) is shown in Fig. 4. Regardless of the streamwise location, both of (U=U∞ ) and the r.m.s (u’=U∞ ) give a good agreement with those of the previous studies, as shown in Fig. 4. Additionally, for the DW cylinder which has no previous data, the computations of three grid systems have been carried out to evaluate the dependence of the solutions on the grid, as listed in Table 2. Similarly, the discrepancies of the results among those grid systems are negligible. Therefore, the medium grid system was employed to discuss the following results dealt with in next chapter. 3. Results and discussion 3.1. Force coefficients and Strouhal number The drag and lift coefficients (CD and CL ) are usually considered as the objectives of the flow control to mainly reduce these force co efficients. Therefore, first time histories of CD and CL for the CY, WC, and DW cylinders are illustrated in Fig. 5. The WC cylinder gives smaller CD and CL compared to the CY cyl inder, which well regenerates the results of Lin et al. (2016). The opti mum wavelength of λ=Dm ¼ 6:06 (Lin et al., 2016) is consistent with Darekar and Sherwin (2000) who achieved a large reduction in CD for a front-and-rear-face-wavy square cylinder. The DW cylinder provides a significant reduction of CD and CL in comparison with the smooth cylinder in Fig. 5(a–b). Especially, the DW cylinder gives more reduction of CD and CL than the optimal WC cylinder (Lin et al., 2016).
Fig. 5. The time-history of (a) the drag and (b) the fluctuation lift coefficients for the CY, WC, and DW cylinder at Re ¼ 3000.
Table 3 Comparisons of the force coefficients for the CY, WC, and DW cylinders. Cylinder type
CD
Diff. (%)
CL;rms
Diff. (%)
CY WC DW
1.0318 0.8972 0.8592
-
0.1293 0.0152 0.0035
-
13.05 16.74
88.26 97.27
5
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 7. Top view (left column) and Perspective view (right column) of the iso-surface of swirl strength for the (a) CY, (b) WC, and (c) DW cylinders at Re ¼ 3000.
elongation, the spanwise wavy fashion of the flow, the regimes of the zero, the new transverse and streamwise vorticities.
Table 3 shows mean force coefficients of CD and CL;rms . The WC cylinder provides about 13.05% and 88.26% reduction of CD and CL;rms , respectively, in comparison with the CY cylinder. The DW cylinder gives approximately 16.74% and 97.27%, respectively, in comparison with the CY cylinder. Therefore, the DW cylinder provides more reduction than the optimal WC cylinder. The Strouhal numbers (St) for different cylinders are achieved by performing the Fourier transform of the time history of the lift coeffi cient to evaluate the effect of the DW shape on the vortex-shedding frequency. Fig. 6 presents the power spectral densities of the time his tories of the lift coefficients for different cylinders. The values of the smooth cylinder and the symmetric wavy cylinder are 0.21 and 0.18, as early in Table 1. The DW cylinder provides almost the same as the WC cylinder, as shown in Fig. 6. As a result, the of the WC and DW cylinders is smaller than that of a smooth cylinder at this Re. For the WC cylinder, Lin et al. (Ahmed and Bays-Muchmore, 1992) reported that the greatest deviation of between the WC and CY cylinder takes place at the optimum values of wavelength (2.0 and 6.0). Thus the present result is consistent with the finding of Lin et al. (Ahmed and Bays-Muchmore, 1992). The geometric disturbances of helically twisted elliptic shape, the symmetric waviness and the asymmetric waviness ((Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016)) provide smaller than the smooth cylinder, which is associated with the suppression of vortex shedding in the near wake. The DW shape is also related to the lower frequency by the suppressed vortex-shedding in the near wake, which will be identified by the instantaneous flow structures later.
3.2.1. Delay of the vortex roll-up The retard of the vortex roll-up and almost the disappearance of the vortex shedding in near-wake are derived by the passive flow control using the surface modifications of the WC cylinder (Jung and Yoon, 2014; Lin et al., 2016; Lam et al., 2004b; Zhang and Lee, 2005; Xu et al., 2010; Lam and Lin, 2008), the helically twisted elliptic (HTE) cylinder (Kim et al., 2016; Wei et al., 2016; Jung and Yoon, 2014), stranded cable models (Nebres et al., 1993) and asymmetric wavy (ASW) cylinder (Yoon et al., 2017). This delay of the vortex roll-up contributes to the drag reduction and the suppression of the lift fluctuation. Because the DW cylinder as a passive control based on the surface modification gives rise to the reduction of the force coefficients as shown in Fig. 5 and Table 3, we observe the instantaneous 3D vortical struc tures and the 2D vorticity distribution to identify the feature of the vortex roll-up and vortex shedding. In order to define these 3-D vortical structures, we adopted the swirl strength given by Zhou et al. (1999). They defined a vortical region as a region with negative λ2 , the second largest eigenvalue of S2ij þ Ω2ij , where S2ij and Ω2ij are the strain rate tensor
and rotation rate tensor, respectively. �rma �n vortices The smooth cylinder clearly forms that large-scale Ka in the near-wake region, as shown in Fig. 7(a). However, the separated shear layer from the WC and DW cylinders are considerably elongated to the downstream, as shown in Fig. 7(b) and (c), respectively. Thus, the vortex roll-up of the separated shear layer from the WC and DW cylin ders is delayed to a downstream position, which is well identified by the distribution of the spanwise vorticity in x-y plane in Fig. 8. Therefore, the vortex shedding nearly disappears in the near-wake of the WC and DW cylinders and reappears weakly in the far wake, compared to the smooth cylinder. This modification of the vortical structures due to waviness is consistent with the findings from previous studies (Wei
3.2. Common characteristics of flow structures for force reduction The drag reduction and the suppression of the lift fluctuation by the wavy, helical and spiral type of the geometric disturbance for the bluff body are associated with generally the common flow characteristics such as the shear layer elongation, a longer vortex formation length 6
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 8. Contours of instaneous spanwise vorticity in the x-y plane: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z=Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z= Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
7
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 9. Top views of the iso-surface of transverse (left column) and streamwise (right column) vorticities. (a & d) for the CY cylinder; (b & e) for the WC cylinder; and (c & f) for the DW cylinder at Re ¼ 3000.
8
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 10. Instantaneous velocity vector (left column) and transvers vorticity contours (right column), in the horizontal (x WC and (c) the DW at Re ¼ 3000.
9
z) plane at y=Dm ¼
0:6 for (a) the CY, (b)
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 11. Mean velocity vector (a & d), streamwise vorticity contours (b & e), and transverse vorticity contours (c & f) in the horizontal (x column) and DW (right column) at y=Dm ¼ 0:6 at Re ¼ 3000.
10
z) plane for the WC (left
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 12. Mean streamwise velocity (U=U∞ ) along the wake centerline (y= Dm ¼ 0) of the smooth (CY), wavy (WC) and double wavy (DW) cylinders at Re ¼ 3000. (N: Node, M: Middle, S: Saddle, N1: Node1, N2: Node2, S1: Saddle1 and S2: Saddle2).
Fig. 13. Vortex formation length (Lfc =Dm ) of the smooth (CY), wavy (WC) and double wavy (DW) cylinders at Re ¼ 3000.
et al., 2016; Jung and Yoon, 2014; Yoon et al., 2017; Lam et al., 2004b; Zhang and Lee, 2005; Xu et al., 2010; Lam and Lin, 2008). In addition, the transverse and streamwise vorticities additionally appear over the surface of the WC and DW cylinders, as shown in Fig. 9b, c, e and f, respectively. These long additional vortices over the surface of the WC and DW cylinders attenuate the spanwise vortices, which con tributes to the delay of the vortex roll-up.
The regions of zero vorticity were also formed by the WC (Fig. 9(b) and (e)) and ASW cylinders (Jung and Yoon, 2014; Yoon et al., 2017; Lam and Lin, 2008), and HTE cylinder (Wei et al., 2016; Jung and Yoon, 2014). The present DW geometry forms the regions of the zero vorticities which are associated by the elongated shear layer and the delay of vortex shedding in Fig. 9(c) and (f). 3.2.3. Formation of jet-like flow The smooth cylinder forms the positive and negative vorticities in the instantaneous velocity field of the smooth cylinder, they are distributed in a seemingly random manner, especially near the rear stagnation point (Zhang and Lee, 2005; Lin et al., 1995), as shown in Fig. 10(a and d). The WC, ASW and HTE cylinders form the local acceleration and decelera tion flow owing to the spanwise dependent diameter which roles to block and suck the flow along the span (Jung and Yoon, 2014). Thus, in contrast to the smooth cylinder in Fig. 10(a), the WC forms the jet-like flow in Fig. 10(b) showing the instantaneous velocity vectors in the horizontal (x z) plane at y=Dm ¼ 0:6. The magnitude of the velocity vectors near-wake for WC is smaller than that of the smooth cylinder. Also, the elongated shear layer is dominant to the near-wake. Therefore, the near-wake of the WC is more stable than that of the smooth cylinder. Especially, the DW cylinder shows that jet-like flow covers wider wake region and sustains downstream, as shown in Fig. 10(c and f). Additionally, the jet-like flow of the DW cylinder creates the spatially locked vorticities to farther downstream, as shown in Fig. 10(f). Behind the rear surface of the DW, the vorticities are much sparser than the smooth cylinder and also the WC cylinder, which associates to wider zero vorticity region for the DW cylinder. From the patterns behind the DW cylinder, the separated free shear layers are relatively more stable, and then roll up into vortices farther downstream, leading to a reduction of the suction near the base region of the twisted cylinder. This stabilized wake also associates to the large reduction of the turbulent kinetic en ergy behind the DW cylinder, which will be discussed in later. Fig. 10 shows the mean velocity vectors and vorticity contours in the
3.2.2. Additional vorticities and regimes of the zero vorticity The streamwise and transverse vorticities additionally appear over the surface of the WC, ASW and HTE cylinders. These additional vortices are formed by three dimensional geometric effect on the flow separation (Jung and Yoon, 2014; Yoon et al., 2017; Lin et al., 2016). Generally, the additional vorticities on WC surface in Fig. 9(b) and (e) elongate to downstream, and then they are split in several branches. The additional appearance of the streamwise and transverse vorticities over the modi fied surfaces show the very weak dependence on the time and space. Particularly, these additional streamwise and transverse vorticities are formed periodically in the spanwise direction over the time, as shown in Fig. 9(b and c) and 9(e, f) for the WC and DW cylinders, respectively. Eventually, these additional vorticities are spatially and temporally locked and stabilize the shear layers to farther downstream and retard vortices roll-up (Lin et al., 2016). These distributions of additional vorticities can also be observed in Fig. 10(e) and (f) for the contours of the transverse vorticity. These spatially and temporally locked vortices are clearly confirmed in the time-averaged flow filed in Fig. 11. The double wavy configuration of the DW cylinder forms alterna tively the vorticities with the positive and negative sign along the span, as shown in Fig. 9(c) and (f). These vorticities are much closer to each other than the WC cylinder. Thus, the wider spanwise regions of the wake are covered by these vorticities originated from the surface. As a result, these stabilized additional vorticities delay vortices roll-up, associating to more drag reduction and the suppression of the lift fluctuation.
11
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 14. Contours of the time averaged spanwise vorticity at various spanwise positions for different cylinder: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z= Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z=Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
12
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
horizontal (x z) plane at y=Dm ¼ 0:6 for the WC and DW cylinders. These mean velocity vectors and contours of vorticities clarify the temporal and spatially lock. Especially, the DW cylinder shows the extension of the streamwise spatial lock, compared to the WC, which clarified by the contours of vorticities in Fig. 10(b and c) and 8(e & f) for the WC and the DW cylinders, respectively. The DW cylinder forms the double wavy formation of vorticities like the ASW cylinder (Yoon et al., 2017) due to the relatively high and low speed flows by different spanwise geometric gradients. 3.2.4. A longer vortex formation length elongation A longer vortex formation length associating with the drag reduction and the suppression of the lift fluctuation has been found by the WC cylinder (Lam and Lin, 2008), the ASW cylinder (Yoon et al., 2017), and HTE cylinder (Wei et al., 2016; Jung and Yoon, 2014). The vortex formation length can be evaluated along its centerline. The wake closure length (Lfc ) corresponds to the location of the timeaveraged closure point where the mean streamwise velocity on the wake centerline is zero, is considered in this study to quantitatively identify and compare the spanwise vortex formation lengths for 3-D geometric disturbances. Recently, many researches have used the wake closure length (Lfc ) to measure the formation length (Jung and Yoon, 2014; Yoon et al., 2017; Lam et al., 2004b; Lam and Lin, 2008; Norberg, 1998), even the definition of the vortex formation length is not universal. The dependence of the recovery location of U=U∞ on the spanwise geometric disturbances is assured in Fig. 12 where the previous results for the CY and WC cylinders are included for the purpose of the com parison. Additionally, the vortex formation length (Lfc ) as s function of the spanwise direction is presented in Fig. 12. For the WC with long wavy length, the zero position moves down stream with moving from the saddle to the node, which is consistent with that of Lin et al. (2016), as shown in Figs. 12 and 13. Thus, the nodal plane forms a larger reversal flow region than the saddle plane. For the ASW cylinder, the Lfc has an asymmetric profile along the spanwise direction (Yoon et al., 2017). The DW cylinder shows the double wavy profile of Lfc in each half wavelength, which is due to the double wavy distribution of flow, as indicated in the velocity vectors and the transverse vorticity contours in the horizontal (x z) plane. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, in contrast to a longer wavelength, the saddle plane forms a longer formation length than the nodal plane (Lin et al., 2016), as shown in Figs. 12 and 13. The DW cylinder also identified by the mean spanwise vorticity in Fig. 14. The DW shape generates longer vorticity than the WC geometry over the span. The vortex formation length is strongly related to the force coefficients and pressure. Therefore, the DW cylinder gain more force reduction than the WC cylinder. The largest mean base pressure of the DW cylinder confirm the association of the vortex formation length, as shown in Fig. 15. 3.2.5. Turbulence suppression Figs. 16 and 17 show the contours of the turbulent kinetic energy (TKE) for three cylinders in the x-y plane and x-z plane, respectively. In cases of WC and DW cylinders, different spanwise planes are considered due to three dimensional geometries. In addition, the profiles of TKE along the spanwise direction at different streamwise directions are plotted in Fig. 18. Turbulent fluctuations are also associated with the variation of the fluctuating forces exerted on a body (Wu et al., 2007). The WC cylinder in Fig. 16(b–d) exhibits negligibly small TKE in the near-wake in comparison with the CY cylinder in Fig. 16(a), regardless of the spanwise direction. For the WC cylinder, this wide region covered by minor TKE is clearly identified in Fig. 17(b) in comparison with the CY cylinder in Fig. 17(a). In the near-wake, the appearance of the minor TKE along the span at x= ¼ 1 for the WC is identified in Fig. 18(a). Dm
Fig. 15. Variation of (a) the mean circumferential pressure distributions, (b) the coefficient of mean base pressure along the span for the CY, WC, and DW cylinders at Re ¼ 3000.
13
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 16. Contours of the turbulent kinetic energy (TKE) in the x-y plane: (a) z=Dm ¼ 3.03 for the CY cylinder; (b) z=Dm ¼ 0 (N), (c) z=Dm ¼ 1.515 (M), (d) z= Dm ¼ 3.03 (S) for the WC cylinder, (e) z=Dm ¼ 0 (N1), (f) z=Dm ¼ 1.109 (S1), (g) z=Dm ¼ 1.921 (N2) and (h) z=Dm ¼ 3.03 (S2) for the DW cylinder.
14
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
The maximum TKE of the CY cylinder appears at about x=D � 2:0 in m Fig. 18(b). Otherwise, the TKE of the WC cylinder at x=D � 2:0 is much m
smaller than that of the CY cylinder. The positions of the maximum TKE are farther from the back of the WC cylinder than from that of the CY cylinder. The maximum TKE of the WC cylinder appears at about x=D � m
3:5 in Fig. 18(d). Generally, the WC cylinder forms the periodic varia tions of TKE distribution along the spanwise direction and resembles the geometric shape of the cylinder. Thus, the positon of the maximum TKE for the WC cylinder is dependent on the spanwise direction, as shown in Figs. 17(b) and 18(d). This spanwise dependence of the maximum TKE position is associated with the vortex formation length and the shear layer elongation due to the 3D geometric disturbance. The longer vortex formation length and the elongated shear layer contribute to the delay of the vortex roll-up and the late vortex shedding, which weaken the TKE and leads to the relatively stable flow. These characteristics of the TKE distribution of the WC cylinder are consistent with the findings of Zhang et al. (Zhang and Lee, 2005) and Lam and Lin (2008). The TKE behind the DW cylinder exhibits the similar distribution with the WC cylinder. Therefore, the positions of the maximum TKE values are farther from the back of the DW cylinder than from those of the CY, as shown in Fig. 16(e–h). The DW cylinder forms wider region with very small TKE than the WC cylinder, as shown in Fig. 17(b) and (c). This weak TKE is clearly identify by the spanwise profiles of TKE at different streamwise positions in Fig. 18. The overall values of TKE for the DW cylinder near the wake region are smaller than those of the CY and WC cylinders. Consequently, the significant reduction in TKE in the near-wake of the DW cylinder contributes to a reduction in the drag and fluctuating lift. 4. Conclusions For the first time, a double wavy (DW) disturbance is introduced to achieve the drag reduction and the suppression of fluctuating lift as the passive control for the bluff body flow. The present study expanded the asymmetry of Yoon et al. (2017) and combined two optimum wave lengths of λ=Dm ¼ 2:0 and λ=Dm ¼ 6:06 of Lam and Lin (2009) and Lin et al. (2016) for the geometric disturbance. We simply call this modified geometric disturbance as a double wavy disturbance. Eventually, we numerically investigated flow past as a double wavy cylinder at Re ¼ 3000 using LES. The DW geometric disturbance achieved the significant reduction of drag and the suppression of fluctuating lift, compared to those of the CY cylinder. The DW cylinder gave a reduction of 16.74% of CD and 97.27% of CL;rms in comparison with the CY cylinder. It is noted that the DW cylinder achieved more reduction of CD and CL;rms than the WC cylinder with long optimum wavy length where the maximum reduction of CD and CL;rms is achieved (Lin et al., 2016). The DW geometric disturbance formed the common characteristics of flow structures which associates with the drag reduction and the suppression of the lift fluctuation for the bluff body. Also, the DW disturbance forms the additional streamwise and transverse vorticities by the 3D effect of the geometric disturbance on the flow separation. These additional vorticities locked temporally and spatially and stabilize the shear layers to farther downstream and delay vortices roll-up, associating to more drag reduction and the suppression of the lift fluctuation. The jet-like flow of the DW cylinder creates the spatially locked vorticities to farther downstream, which more stabilize the wake and achieves more reduction of the drag and lift fluctuation. The DW cyl inder forms the double wavy formation of vorticities due to the rela tively high and low speed flows by different spanwise geometric gradients. The DW cylinder shows also the double wavy profile of vortex for mation length in each half wavelength, which is due to the double wavy
Fig. 17. Contours of the turbulent kinetic energy (TKE) in the x-z plane for (a) the CY, (b) the WC and (c) the DW at y=Dm ¼ 0.
15
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Fig. 18. Profiles of the turbulent kinetic energy (TKE) in y=Dm ¼ 0 for the CY, the WC and the DW at different x-positions.
distribution of flow. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, in contrast to a longer wavelength, the saddle plane forms a longer formation length than the nodal plane (Lin et al., 2016).
Jung, J., Yoon, H., 2014. Large eddy simulation of flow over a twisted cylinder at a subcritical Reynolds number. J. Fluid Mech. 759, 579–611. Kim, H., Yoon, H., 2017. Effect of the orientation of the harbor seal vibrissa based biomimetic cylinder on hydrodynamic forces and vortex induced frequency. AIP Adv. 7, 105015. Kim, H., Yoon, H., 2018. Forced convection heat transfer from the biomimetic cylinder inspired by a harbor seal vibrissa. Int. J. Heat Mass Transf. 117, 548–558. Kim, W., Lee, J., Choi, H., 2012. Flow past a helically twisted elliptic cylinder. In: Proceedings of the 8th KSME-JSME Thermal and Fluids Engineering Conference, Songdo, Incheon, Korea, pp. 18–21. Kim, W., Lee, J., Choi, H., 2016. Flow around a helically twisted elliptic cylinder. Phys. Fluids 28 (5), 053602. Lam, K., Lin, Y.F., 2007. Drag force control of flow over wavy cylinders at low Reynolds number. J. Mech. Sci. Technol. 21, 1331–1337. Lam, K., Lin, Y.F., 2008. Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number. Int. J. Heat Fluid Flow 29, 1071–1088. Lam, K., Lin, Y.F., 2009. Effects of wavelength and amplitude of a wavy cylinder in crossflow at low Reynolds numbers. J. Fluid Mech. 620, 195–220. Lam, K., Wang, F.H., Li, J.Y., So, R.M.C., 2004. Experimental investigation of the mean and fluctuating forces of wavy (varicose) cylinders in a cross-flow. J. Fluids Struct. 19, 321–334. Lam, K., Wang, F.H., So, R.M.C., 2004. Three-dimensional nature of vortices in the near wake of a wavy cylinder. J. Fluids Struct. 19, 815–833. Lee, S.J., Nguyen, A.T., 2007. Experimental investigation on wake behind a wavy cylinder having sinusoidal cross-sectional area variation. Fluid Dyn. 39, 292–304. Lilly, D.K., 1992. A proposed modification of the Germano subgrid-scale closure method,. Phys. Fluids 4, 633–635. Lin, J.C., Towfighi, J., Rockwell, D., 1995. Instantaneous structure of the near-wake of a circular cylinder: on the effect of Reynolds number. J. Fluids Struct. 9, 409–418. Lin, Y.F., Bai, H.L., Alam, M.M., Zhang, W.G., Lam, K., 2016. Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder. J. Fluids Struct. 61, 392–409. Naudascher, E., Rockwell, D., 2005. Flow-Induced Vibrations: An Engineering Guide. Dover Publications. Nebres, J., Barill, S., Nelson, R., 1993. Flow about yawed, stranded cables. Exp. Fluid 14, 49–58. Norberg, C., 1987. Effects of Reynolds Number and a Low-Intensity Freestream Turbulence on the Flow Around a Circular Cylinder. Department of Applied Thermodynamics and Fluid Mechanics, Chalmers University of Technology. Norberg, C., 1998. LDV-measurements in the Near Wake of a Cir-Cular Cylinder, ASME Paper No. FEDSM98–521.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) through GCRC-SOP (No. 2011-0030013) and (NRF-2019R1A2C1009081). References Ahmed, A., Bays-Muchmore, B., 1992. Transverse flow over a wavy cylinder. Phys. Fluids 4, 1959–1967. Ahmed, A., Khan, M.J., Bays-Muchmore, B., 1993. Experimental investigation of a threedimensional bluff-body wake. AIAA J. 31, 559–563. Darekar, R.M., Sherwin, S.J., 2000. Flow past a square-section cylinder with a wavy stagnation face. J. Fluid Mech. 426, 263–295. Ekmekci, A., Rockwell, D., 2010. Effect of a geometrical surface disturbance on flow past a circular cylinder: a large-scale spanwise wire. J. Fluid Mech. 665, 120–157. Germano, M., Piomelli, U., Moin, P., Cabot, W.H., 1991. A dynamic subgrid-scale eddy viscosity model,. Phys. Fluids 3, 1760–1765. Hanke, W., Witte, M., Miersch, L., Brede, M., Oeffner, J., Michael, M., Hanke, F., Leder, A., Dehnhardt, G., 2010. Harbor seal vibrissa morphology suppresses vortexinduced vibrations. J. Exp. Biol. 213, 2665–2672. Hans, H.H., Miao, J., Weymouth, G., Triantafyllou, M., 2013. Whisker-like geometries and their force reduction properties. In: OCEANS-Bergen MTS/IEEE.
16
H.S. Yoon et al.
Ocean Engineering 195 (2020) 106713
Norberg, C., 2003. Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 57–96. Wang, S., Liu, Y., 2016. Wake dynamics behind a seal-vibrissa-shaped cylinder: a comparative study by time-resolved particle velocimetry measurements. Exp. Fluid 57, 1–20. Wei, D., Yoon, H., Jung, J., 2016. Characteristics of aerodynamic forces exerted on a twisted cylinder at a low Reynolds number of 100. Comput. Fluids 136, 456–466. Wu, J.Z., Lu, X.Y., Zhuang, L.X., 2007. Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286. Xu, C.Y., Chen, L., Lu, X., 2010. Large-eddy simulation of the compressible flow past a wavy cylinder. J. Fluid Mech. 665, 238–273.
Yoon, H., Balachandar, S., Ha, M., 2009. Large eddy simulation of flow in an unbaffled stirred tank for different Reynolds numbers. Phys. Fluids 21, 1–16. Yoon, H., Shin, H., Kim, H., 2017. Asymmetric disturbance effect on the flow over a wavy cylinder at a subcritical Reynolds number. Phys. Fluids 29, 095102. Zdravkovich, M.M., 1981. Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. J. Wind Eng. Ind. Aerodyn. 7, 145–189. Zhang, W., Lee, S.J., 2005. PIV measurements of the near-wake behind a sinusoidal cylinder. Exp. Fluid 38, 824–832. Zhou, J., Adrian, R.J., Balachadar, S., Kendall, T.M., 1999. Mechanisms for generating coherent packets of hairpin vorticies in channel flow. J. Fluid Mech. 387, 353–396.
17