Control over Vortex Shedding and Drag Force on a Circular Obstacle Using a Pair of Downstream Splitter Plates in a Transient Flow

Ain, Qurrat Ul; Mahmood, Rashid; Abbasi, Waqas Sarwar

doi:https://doi.org/10.1155/2023/6142773

Mathematical Problems in Engineering

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 6142773 | https://doi.org/10.1155/2023/6142773

Control over Vortex Shedding and Drag Force on a Circular Obstacle Using a Pair of Downstream Splitter Plates in a Transient Flow

Qurrat Ul Ain,¹Rashid Mahmood,¹and Waqas Sarwar Abbasi¹

Academic Editor: Hamid Rahman

Received18 Nov 2022

Revised24 Jan 2023

Accepted02 Feb 2023

Published21 Feb 2023

Abstract

The current work is an analysis of the laminar, two-dimensional, and transient flow over a circular cylinder with a two-branched splitter plate. For complex nonlinear governing equations, the finite element method is used as a computational approach. The objective of the current study is to determine the best conditions using geometrical characteristics along with the impact of Reynolds number .The geometric parameters, which is the angle of separation between the pair of splitter plates of length and which is the gap from diameter ratio of the splitter plate to cylinder diameter, are the controlling tools for the present study. Due to its little impact on flow characteristics, it was discovered that using a two-branched splitter plate in Reynolds numbers under 100 is not desirable. A complete vortex shedding has been achieved with and at and also the periodic behavior of velocity has been controlled. The least drag force is observed at an angle of between the two plates compared to another angle of . It is not advised to use two splitter plates at angles more than because this will not further contribute in the drag reduction. Since the gap to diameter ratio between the splitter plates and the cylinder increased up to a significant value, the overall control on hydrodynamic effects is achieved. It is concluded that the maximum drag reduction of 48% over the cylinder has taken place when the .

1. Introduction

The flow past circular obstacles have been an issue of many studies so far due to the fact that many industrial applications such as heat exchangers, bridges, risers, and chimneys have such obsatcles as their componenets. The undesirable phenomena of vortex shedding and broad wake region downstream cause significant drag force. Various attempts that have been made include both passive and active control systems [1–3]. One of the simple passive ways to accomplish such enhancements will be to use the so-called splitter plates. A thin, rigid, 2D plate on the wake centerline is positioned parallel to the flow. The device works as a “near-wake stabilizer” [1] and alters the location where near-wake vortex development occurs. When a circular cylinder is two-dimensional or infinite, the splitter plate is crucial because it lowers drag and prevents vortex shedding [4–7].

Apelt and West [4] studied the effectiveness of the splitter plate in controlling the vortex shedding of the circular-shaped cylinder and wake oscillation’s reduction. They detected that at a greater value of Reynolds number , the existence of a control device in the cylinder’s wake has enough propensity to reduce the aerodynamic forces and vortex shedding. The studies are done by taking various values of gap spacing and plate’s length. In [5], an experimental study is done by Apelt and West. They have fixed a plate with the cylinder’s base at and plate’s length . It is found that the plates of short length lessen the wake’s width and the separation points of the boundary layers stabilized, thus creating the vortices near the plate’s rear edge. The impact of the control plate’s length was numerically examined by Kwon and Choi [6] at lower Reynolds numbers (between 80 and 160) for the fluid flow over a round-shaped obstacle. They reported that the rate of vortices formed near the round cylinder diminished with increasing the control plate’s length. A complete vortex shedding suppression was attained by exceeding the size of the control plate about the required length. Anderson and Szewczyk [7] investigated the impact of a control plate on the wake region of a round cylinder in configurations representing 2D and 3D flow and inferred the superposition principle. They discussed that specific 3D geometry and configuration of the flow could be shared to develop a minimal 2D wake. In majority of the work done by the researchers, they utilized the inflexible plate, although the effects of hinged, undulatory, and elastic control plates have also been studied [8, 9]. In [8], Wu and Shu investigated control over flow at adopting the boundary-lattice Boltzmann technique. They attained classic patterns of fluid flow and reduction of drag due to the flicking motion of the plate. Wu et al. [9] did a numerical investigation of flow features around a fixed circular-shaped cylinder with a nonstationary plate. They extensively observed the effectiveness of flexibility of splitter on the flow features by changing the amplitude and frequency of motion, the plate’s length, and attained drag reduction with some exciting flow patterns.

For square and rectangle cylinders, splitter plates are also employed [10, 11]. Experimental research on the impact of plates on the distribution of base pressure was done by Mansingh and Oosthuizen [10]. A 15% addition was observed in the linearly average mean pressure as soon as the control plate is mounted in the flow region. In a numerical study [11] done by Park and Higuchi, it is reported that employing the vortex tracing method, the flow over a square shaped cylinder with a splitter plate reduces drag force and suppresses vortex shedding. Rathakrishnan [12] conducted an experimental study on the impact of a splitter plate on the flow through a bluff object. On the basis of pressure measurements and force, he recognized the pressure hill as the leading reason of the bluff object’s high drag force. By changing the control plate’s length from 0.5 to 6, Mat Ali et al. [13]numerically discovered three distinct patterns for the flow over a cylinder of square shape at a less value of Reynolds number. Considering a fixed value of Reynolds number Re = 150, Islam et al. [14] presented a numerical analysis of a wake fluctuation including a detachable plate located downstream of the solid body. In the gap between the splitter plate and the core cylinder as well as behind the splitter plate’s downstream location, two separate flow patterns are reported. Sukri Mat Ali et al. [15]havedone a numerical study of acoustic emission by flow across a square-shaped cylinder either in the presence or absence of the adjacent plate. They reported G = 2.3 as a critical gap separation. The effects of a solo control plate installed in the upstream position and twin plates for a low Reynolds number are numerically evaluated by Vamsee et al. [16]. They discovered that the upstream plate is important for reducing drag.

With the assumption that , Barman and Bhattacharya [17] concentrated solely on the size of flat plates and Reynolds number in their numerical experiments to lower fluid forces employing twin splitter plates. Turki [18] used the control volume finite element approach to examine numerically the impact of control plates in both connected and disconnected arrangements for the flow past a square body. Doolan [19] investigated how the control plate affected the flow past the obstacle by altering the size of the control plate from L = 0.5 to 6. He discovered great effects of the control plate on the flow pattern and generates a powerful hydrodynamic contact to the cylinder’s wake region. The influence of a control plate connected to a round cylinder on the suppression of vortices and the decrease of wake oscillation were also experimentally investigated by Roshko [20]. The frequency of vorticity is decreased and the drag force is reduced as a result of the splitter plates.

In addition to the connected control plates, the detachable rear plates were also investigated. The computational outcomes presented by Hwang et al. [21] showed that at , where is the separation between the obstacle and the plates, a separated plate having a size of can greatly minimize the drag force as well as lift instability. On the other hand, once the plate was positioned further downstream, the hydrodynamic forces rose quickly. The innovative findings of a spherical cylinder with a detachable splitter of equal length by Akilli et al. [22] highlighted that when the separation was larger than , the rear plate lacked its influence on suppression. According to Wang et al. [23], the forceful reaction was caused by vortices forming in the space and successively impinging on the detachable splitter plate once the space was wide enough. Similar results on the instability of a circular cylinder with a separated splitter plate were obtained from numerical simulations by Liang et al. [24] and Serson et al. [25]. As a result, the near-wake detachable splitter plate s performance is highly correlated with the distance between the plate and the cylinder, the plate’s size, and the velocity of the incoming flow. We still do not fully understand the mechanisms governing wake adjustment, related changes in fluid flow, and the beginning of galloping for such separated control plates.

The analysis of passive control using a control plate employed in the upstream flow or a couple of plates individually positioned on the front and back sides of the obstacle received substantially less attention in the literature than the extensive studies on wake-mounted splitter plates. According to experimental findings by Chutkey et al. [26], an upstream positioned plate with a size of 1D can postpone the boundary layer disconnection point from 82° to 122° when compared to a plain cylinder. The impact of the gap separation on an obstacle with a pair of unattached control plates was numerically studied by Hwang and Yang [27]. According to their findings, the downstream-mounted plate raised the pressure in the back of the cylinder and the latency of vorticity, while the upstream plate decreased the pressure along the front stagnation point. These changes together significantly reduced drag. Similar outcomes were seen for the wind tunnel tests by Qiu et al. [28].

The flow pattern over three obstacles that were put side by side was the subject of an experimental research by Sooraj et al. [29]. Their findings showed that changes in the and the separation ratio resulted in a drop of the drag coefficient value because these variables greatly altered the flow pattern. Ain et al. [30, 31] studied the influence of the downstream plate to control hydrodynamic forces over round-shaped cylinder using the finite element method (FEM). They found that for slighter gap separation, a larger drag coefficient reduction is achieved. However, for a small plate, the lift is irregular; moreover, with a growth of the plate’s length, it is convergent to a static value and dropped its irregular behavior. Using the lattice Boltzmann approach, Ma et al. [32]investigated how the aerodynamic forces were affected by a circular rod positioned upstream as well as downstream of a cylinder (LBM). They discovered that if the bar is positioned in the upstream region of the cylinder, it mostly influences the drag force, whereas if it is put downstream, it reduces the lift variations. The gap between the obstruction and the bar is another crucial factor that could have a big impact on the fluid flow. The impacts of a circular bar and a controlling plate positioned upstream and downstream of a square shaped cylinder, respectively, were examined by Ma et al. [33] using the LBM. The outcomes showed that the splitter plate can control vortex shedding although the degree of suppression is highly dependent on the separation among the splitter plates as well as the obstacle. Additionally, they discovered that the drag force is highly dependent on the separation between both the obstacle and the splitter plate since the bar was unable to shield the square cylinder from interacting directly with the incoming flow.

Although a variety of studies found horizontal splitter plates of various lengths as a passive control device in different configurations, a few works have been done using nonhorizontal splitter plates. Indeed, the bifurcated splitter plates can be used in several practical problems, such as behind heat exchanger tubes to enhance the heat transfer while keeping the drag to a minimum. Recently, the flow through a round cylinder with a pair of crossed-splitters is analyzed by Razavi et al. [34]. Because a two-branched splitter plate has a negligible impact on flow characteristics, it was discovered that using one in Reynolds numbers under 100 is not advisable. To the utmost knowledge of the author, the published literature does not contain any comprehensive or in-depth analyses of the laminar flow patterns for passive control using a two-branched splitter with different gap separations from the obstacle at downstream locations. For the present study, by choosing the angle between two plates and varying the ratio of the gap between the two crossed splitter plates and the cylinder to the diameter of the cylinder , different flow patterns are obtained. Therefore, numerical analysis is performed to find out the influence of several parameters on the control of fluid force factors. Finally, the effect of the presence of a splitter plate on the reduction of the drag coefficient and vorticity suppression is discussed at various values of

The current article is structured as follows: After introduction and literature review in the first section, the second section describes briefly the description of the present problem. The third section is devoted to share the mathematical method adopted. The validation of the results for bare cylinder against the results present in the literature is provided in section four. The grid independence test results are also provided for the computational domain considered for the present study. The effect of vertical splitter plates of two different heights, for various gap separation ratios at upstream, downstream, and bilateral positions, is presented and discussed thoroughly in section five. In the final section, conclusions are made.

2. Problem Description

The key goal of the current work includes simulating laminar flow around a circular body and the examination of the effect of cross splitter plates with angle between them. Figure 1 illustrates the problem’s schematic diagram and the related terminology. The effectiveness of the gap between the position of the two-branched splitter plate and the round cylinder (diameter ) on suppression of vortex shedding and the minimization of drag force is analyzed by introducing the branch of two plates (length ). The gap-to-diameter ratio of the controlling plates placed at downstream location of a channel (height ) is introduced. The implementation of the attached plate to the obstacle and the plate located at various gap separations are studied at in the present work. Moreover, the simulations are carried out using the finite element method.

3. Mathematical Formulation and Methodology

In this work, the effectiveness of a controlling plate on the laminar flow past a circular body located near the centerline of the domain is examined. The continuity and momentum equations governing the flow field of the present study are as follows [35]:

The nondimensional equations (1)–(3) have been formed by choosing the dimensionless variables time, velocity, and pressure, respectively. The nondimensional parameter Reynolds number where reference velocity , reference length and is the kinematic viscosity [35].

FEM simulations have been carried out to solve governing equations (1)–(3) using stable finite element pair satisfying the inf-sup condition. The discrete nonlinear systems are linearized and solved using the Newton’s iterative technique with a stopping criterion . The PARDISO solver, which operates for the generic system depending on with a particular rearrangement of unknown variables and minimizes the number of iterations necessary to attain the appropriate convergence level, is used to solve linearized systems. A cross-wind stabilisation approach is also used to stabilise the flow at larger levels of . The quantity of interest determined at the postprocessing stage is the drag coefficient given mathematically as

The nondimensional drag force acts on the circular obstacle.

4. Code Validation and Grid Independence

The situation being addressed in this section is the laminar flow around a circular cylinder in a 2D channel (Figure 2), and the results are shown in Table 1 with the comparable numerical findings presented by Schafer et al. [35]and Ain et al. [31], Table 2 shows the variation for the values of with respect to the corresponding values used in reference work. The width of the channel is same for the present work as taken in the reference work, and also the diameter of the obstacle is identical. Moreover, for all simulations, is considered. The boundary conditions are also provided in Table 3. On the upper and lower walls of the channel, the boundary conditions are taken as no-slip conditions, and the inlet velocity is assumed to be parabolic at the entrance.

The main objective of this work is to control vortex shedding and to minimize the drag produced in the presence of the obstacle. It is obvious from the results obtained for the present work (Table 4) that the variation in reference configuration is valid. A visible control over hydrodynamic forces is achieved by introducing the new configuration for the present study. Tables 1 and 4 provide the results, which show that the present computer algorithm could reasonably forecast the flow over a circular cylinder in a channel (Figures 2 and 3) either with or without cross splitter plates.

To determine the ideal number of grid sizes, we also conduct grid independence testing in this case. Three possible grid sizes are taken into consideration for this purpose and are listed in Table 5. The simulation time considered here is 4 seconds to compare the values of the drag coefficient . The values of are presented for each time refinement level against the corresponding number of elements and degrees of freedom. The variation in the refinement level from a lower to higher level shows an increment in the number of elements and degrees of freedom which give rise to more accuracy of the results. The value of the drag coefficient obtained at the mesh size at the extra fine refinement level is in good agreement with the last refinement level. Therefore, we select the grid size of (elements) as the optimum grid size.

Figures 3(a) and 3(b) show the variation of drag coefficient and lift coefficient for three different time step sizes It can be seen that does not have too much impact on the amplitude of drag and lift values. For the present study, has been chosen for all simulations.

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(b)

5. Results and Discussion

In the present section, the findings relevant to the situation discussed in Section 2 (Figure 1) are provided in relationships of the drag coefficient , as well as the contours of the vorticity. The investigation is done into how the downstream pair of branched/cross splitter plates with angle between them affect the suppression of vorticity and drag minimization along with two more effective parameters and . The velocity profiles for each gap separation ratio at are provided graphically. The results are obtained for the plates attached to the circular bluff body, i.e., , as well as at gap separations from the bluff body. For all the cases, the Reynolds number is chosen as and ; for further values of , the results are found insignificant for the present study.

Figures 4–9 are velocity profiles for the implementation of a two-branched splitter plate with angle and the gap-to-diameter ratio . Figures 4(a), 5(a), 6(a), 7(a), 8(a), and 9(a) represent the velocity profile at whereas Figures 4(b), 5(b), 6(b), 7(b), 8(b), and 9(b) are velocity profile snap shots at The fluid enters with a velocity as an inlet velocity and is parabolic, creating a stagnation point region at a right angle to the flow direction and bifurcating around the obstacle of the circular shape with more velocity. In contrast, the fluid within the side walls admits zero velocity because there is no-slip condition. A bifurcation in the velocity is visible when the fluid passes the obstacle, and an increase in the velocity is seen as compared with the inflow parabolic profile.

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(b)

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Figure 4(a) is the visualization of the velocity profile at , when a pair of plates with angle and are present in the downstream region of the circular cylinder. The periodicity shown in Figure 4(b) is less than the periodic behavior of velocity at seen in Figure 4(b). The same behavior is evident in Figures 5(a) and 5(b), although for the two-branched splitter plate with the separation angle between plates and .

The effectiveness of variation in the value of the gap to diameter ratio on the velocity profile at two different values of could be seen in Figures 6(a), 6(b), 8(a), and 8(b) by implementing splitter plates with among them. Figures 7(a), 7(b), 9(a), and 9(b) are representing that the impact of the two-branched splitter plate on the periodicity of velocity is much more improved for both values of However, with the pair of plates made the velocity more stable at location (see Figure 6(a)) and at the two-branched splitter plate with (see Figure 9(a)) are more effective to overcome velocity periodicity at low Reynolds number

The energy cascade, vortex shedding occurring near the obstacle in the flow path needs to be controlled to avoid any destruction. In this section, the passive control technique is used to suppress the vortex shedding by means of the two-branched splitter plate of length , with effective parameters and . The control plates with the angle of separation between them being added downstream of the circular body at various gap-to-diameter ratio causes vortices to form after the cylinder and shed from the top and the bottom of the plate, as can be seen in Figures 10–15. The results for each implementation of splitter plates with respect to various and are different for two different values of at

Figure 10 gives two different representations of vortex shedding using splitter plates with , and the energy carried by vortices shown in Figure 10(a) at Re = 100 is low in strength as compared to vortices visible in Figure 9(b) at Re = 200. Figure 11 shows that when the two-branched splitter plate () is located close to the circular cylinder (), the separated shear layers are responsible for generating vortices, the energy carriers. Figure 11(a) shows that the number of vortices appeared for are less as compared to the vortices generated for the same case for Figure 11(b) shows that the vorticity layers in this flow pattern are extended in the direction of the stream, and the vortex shedding site is relatively distant from the splitter plate.

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The effect of the parameter is visible in Figure 12, and the splitter plates located in downstream region with controlled vortex shedding at (see Figures 12(a) and 12(b)). Figure 13 provides the visualization of the implementation of the two-branched splitter plate with . The number of vortices formed for the simulation at are eight (see Figure 13(a)), whereas at , eleven vortices (see Figure 13(b)) can be seen in the downstream flow. The strength of vortices increases with an increase in Reynolds number .

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The control plates used for the suppression of vorticity become more active with the gap to diameter ratio . The instantaneous vorticity contour visualization plots in Figures 14 and 15 serve as illustrative example of the vorticity control by introducing the downstream splitter plate s for The splitter plates with showed their significance to control vortex shedding at in Figures 14(a) and 15(b), respectively. Regarding the strength of vortices, number of vortices downstream of the obstacle can be seen in Figure 15(b) by introducing control plates , at . At low Reynolds number , the strength of the vorticity is weakened, and a stability is seen in Figure 15(a).

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A significant comparison between the values for the bare cylinder and the cylinder with two-branched splitter plate is presented to analyze the maximum effectiveness of controlling plates. A graphical representation of drag coefficient reduction w.r.t at is shown in Figure 16.

Table 6 is a detailed illustration of the effectiveness of the two-branched splitter plate of length along with active parameters introduced in the present study to control drag force over the circular cylinder immersed in a transient fluid flow. All the values presented in this table of the drag coefficient are attained at dimensionless time .

At for the bare cylinder (taken as the reference value for this particular ), this value is reduced by introducing a pair of splitter plates with between them along with implementation at various downstream locations with respect to When the values of are 2.3915, 2.2816, and 2.2379 with , respectively. For the maximum gap to diameter ratio , the splitter plates reduced 22% of the reference value that is, a significant reduction. Further reduction is attained by taking between the plates, such that with , at , and that is, 28% reduction in the reference value at .

The reference value of observed for the bare cylinder to investigate the reduction of drag force at is 3.1881. Indeed, by using a two-branched splitter plate as a passive control device with , reduced values of are 2.2003, 2.0379, and 1.9327 with respect to respectively. The last value attained for shows the maximum reduction of reference , i.e., 39%. The usage of the two-branched splitter plate improved this reduction more with the variation in The reduced values in comparison to the reference value are 2.0143, 1.9010, and 1.8281 with respect to respectively. The implementation of the two-branched splitter plate in the downstream region at provided the most interesting results for the current study to control drag force experienced by the circular cylinder. However, the value of with achieved at is 43% reduction of and is evidence of maximum reduction by means of passive control plates with maximum values of the parameters

6. Conclusion

In this work, the two-branched splitter plate has been introduced, and the effect of angle among the plates of dimensionless length along with the effect of Reynolds number and the gap to diameter ratio were investigated. The variation of these parameters has played an important role to enhance the usefulness of the passive control device splitter plate to control the periodic behavior of velocity, vortex shedding, and drag force. The results have been compared to overcome the periodicity of velocity and demonstrated that when Reynolds number is low , the use of a pair of splitter plates with is very effective. The variation in parameters as has not been found as much effective as the lower values of these parameters. A complete suppression of vortex shedding has been observed by implementing the downstream branch of plates with at However, the minimization of energy carried by vortices in the downstream region has also been observed by introducing between the plates with , at The most interesting outcomes have been achieved for the reduction of drag coefficients and experienced by the bare cylinder at , respectively. At the maximum reductions 22% and 28% have been achieved with respect to the reference value of by introducing a two-branched splitter plate with and with , respectively. The reference value at has been taken as and the most exciting reductions have been achieved as 39% and 48% by using splitter plates with between them and with a maximum gap to diameter ratio , respectively.

Nomenclature

:	Angle of separation
:	Length of splitter plates
:	Gap separation between cylinder and plates
:	Cylinder’s diameter
:	Gap to diameter ratio
:	Height of the channel
:	Width of the channel
:	Upstream location
:	Downstream location
:	Kinematic viscosity
:	Maximum velocity
:	Reference velocity
:	Reference length
:	Reynold’s number
:	Time step size
:	Drag coefficient
:	Lift coefficient
:	Maximum drag coefficient
:	Maximum lift coefficient.

Data Availability

Data used in this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2023 Qurrat Ul Ain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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