A passive control method is a numerical technique adopted to control flow and thus save energy by modifying the shape and size of an object or by attaching/detaching some additional tools such as control rods or cylinders with the main object [
1,
2,
3]. This method is simple and cheap compared to an active control method, in which energy is externally supplied to control the flow. When flow interacts with an object, a damaging of the structure occurs with a loss of energy. Therefore, it is essential to control flow and save energy. A limited number of stationary object studies have been conducted with the passive control method in order to reduce the fluid forces and to suppress vortex shedding (see [
4,
5,
6,
7,
8] and so on). In the passive control method, the control rods/cylinders can be placed horizontally or vertically either upstream or downstream of the main rod. Many experimental and numerical studies based on these types of arrangements are available in the literature. A numerical study of fluid past a square rod detached from a thin rod placed downstream was conducted by Alam et al. [
9] at
. Tsutsui and Igrashi [
10] used the passive control method using a control rod placed upstream of the main rod by considering
They observed a 63% drag reduction along with two different types of flow modes. Turki [
11] numerically simulated the flow structure mechanism past a square rod attached with a controlling rod by taking
using a control volume finite element method. The author noted two different phenomena for Strouhal number (St) values: firstly, for
, the value of St reduces and approaches a local minima at control rod length
and then increases afterward; for
, the values of
St increase by increasing the length of the rod. A numerical investigation of drag and lift coefficients on a square rod detached from a control rod through a finite volume code was performed by Malikzadeh and Sohankar [
12] with a Reynolds number ranging from 50 to 200. The highest reduction in fluid forces was found at
and
Furthermore, they obtained three types of flow modes. In the first two modes, the vortex shedding was suppressed completely. Islam et al. [
13] numerically studied the influence of gap spacing for flow past a main rod detached from a horizontal control rod. They obtained optimum spacing values at
A study of fluid force reduction using two controlling rods was conducted by Vamsee et al. [
14]. One rod was placed upstream and the second one was placed downstream of the main rod. They found a 27% reduction in drag force using the upstream controlling rod and a 35% drag reduction by fixing the upstream controlling rod and varying the gap between the main rod and the downstream controlling rod. A numerical examination of flow past a square rod detached from an upstream controlling rod at the low value of
was performed by Islam et al. [
15]. They focused on the effect of gap spacing with a
and an
Re = 80–200, and the size of the controlling rod (
h) ranged from 0.1
d to 1
d. They obtained a maximum reduction in
of 142 at
for
De Araujo et al. [
16] numerically investigated the flow behavior over a square rod detached from a controlling rod considering
, and the length of the controlling rod varied up to twice the size of the square rod. The flow simulation over a single circular rod in the presence of a controlling rod was performed by Vu et al. [
17] to study the effect of the length of the controlling rod and the
on the flow structure mechanism. It was reported that flow was suppressed completely when the length of the controlling rod was greater than its critical value, which is proportional to
Furthermore, they observed two different types of flow mode. Another numerical study based on flow past a square rod with an upstream detached circular bar and a downstream horizontal splitter rod was carried out by Yuan et al. [
18]. They considered an
where the diameter (
d) of the circular bar was in the range
, gap spacing
g = 0–7, and the splitter rod length
The maximum reduction found in
was 68.7% at
Gupta [
19] also numerically studied vortex shedding suppression around a square rod at
Re = 100 and observed a 10–15% drag reduction using a small control rod downstream of the main rod. A comparative study for weakly compressible (WCSPH) and incompressible smoothed particle hydro dynamics (ISPH) method was conducted by Shadloo et al. [
20] for a numerical solution of fluid flows over an airfoil and a square obstacle. They used improved WCSPH and ISPH techniques to solve flow problems generated by the flow past these two bluff bodies. The comparison of WCSPH and ISPH methods indicated that a weakly compressible method produces numerical results as accurate and reliable as those of the incompressible smoothed particle method. Numerical simulations for flow over an airfoil and a square obstacle using the ISPH method with an improved solid boundary treatment approach such as the multiple boundary tangents (MBT) method were performed by Shadloo et al. [
21], and they found that the MBT boundary treatment technique is very effective for tackling the boundaries of complex shapes. Furthermore, the usage of the repulsive component of the Lennard-Jones potential (LJP) in the advection equation for repairing particle fractures occurring in the SPH method has also been proposed and examined, and the ISPH method was found to be is effective at naturally capturing the complex physics of bluff-body flows. The numerical Lattice Boltzmann method was used to solve the complex fluid flow problems. Such flows are single-phase or multi-phase. This method is effective and can easily handle the problem. Many studies are available in literature that are based on complex flow problems and have been solved by the lattice Boltzmann method. The laminar-forced convection heat transfer of water–Cu nano-fluids in a micro channel was studied by D’Orazio et al. [
22] using the double population thermal lattice Boltzmann method (TLBM). Simulations were performed for nanoparticle volume fractions equal to 0.00, 0.02, and 0.04% and slip coefficients equal to 0.001, 0.01, and 0.1. The selected values of the Reynolds number were 1, 10, and 50. It was found that a micro channel performs better heat transfers at higher Reynolds number values. Meanwhile, for all selected values of Re, the average Nusselt number increases slightly as the solid volume fraction increases and the slip coefficient increases. The nano-scale lattice Boltzmann method was developed to predict the fluid flow and heat transfer of air through the inclined lid-driven 2-D cavity, considering a large heat source by Goodarzi et al. [
23]. Pure natural convection at Grashof numbers from 400 to 4,000,000 and mixed convection at Richardson numbers from 0.1 to 10 at various cavity inclination angles were considered, and it was observed that the present LBM model is appropriately able to simulate the supposed domain. Moreover, the effects of inclination angle are more important at higher Richardson number values.
The above-mentioned literature shows limited knowledge about vortex shedding suppression and force reduction through the passive control method using controlling rods at different positions. Therefore, the present study sought to determine the influence of dual detached controlling rods with different gap spacing at a fixed Reynolds number value, i.e., .