Controlling the hydrodynamic forces on a square cylinder in a channel via an upstream porous plate

Abstract

Drag and lift forces are very important in engineering applications and, therefore, many research projects have been conducted to control these forces. In this paper, the effects of an upstream porous plate on the hydrodynamic forces over a square cylinder are investigated using lattice Boltzmann method. The main idea is to separate the obstacle from the upstream flow by adding such a porous plate, since the magnitudes of the drag and lift forces have a direct relationship with the phenomena of vortices shedding from the obstacle. In order to have a better insight into the problem, streamlines, vorticity contours and lift and drag coefficients are presented for different case studies. Results proved that the porous plate can reduce the drag and lift coefficients. Furthermore, increasing the height and the gap spacing (i.e., the surface-to-surface distance between the porous plate and the obstacle) could significantly affect the flow field characteristics and the forces acting on the obstacle.

Introduction

It is an undeniable fact that boundary layer separation happens during the passage of viscous flow over an obstacle due to the pressure gradient. This separation induces forces on the obstacle and leads to energy loss. Controlling these forces is an important topic in different industrial applications since they can cause many damages to the structure of the obstacles, e.g., in bridges and buildings. These forces are generated by the wakes regions and can be controlled by the wake vortex dynamics [1]. One of the important approaches to control such forces is to use the active methods, which affect the flow field by implementing an extra force or momentum, e.g., fluid injection strategies [2]. The other promising solution, which has also been considered in the present work, is to use the passive control techniques, where the flow field is manipulated by making special changes in the geometry of the problem, e.g., by adding splitter plates, wavy surfaces and porous layer strategies that can reduce the drag forces [1], [3].

Some of the researches conducted on the passive control techniques are as follows. Bruneau et al. [1] studied the effects of adding a porous layer between the solid obstacle and the main flow field. They found that the permeability coefficient and the thickness of the porous layer have strong effects on the boundary layer characteristics and hence on the flow field. The effects of adding a porous slice to some parts of an obstacle were considered by Bruneau et al. [4] in order to find the optimum location of the porous layer to decrease the drag coefficient, which has a direct relationship with the size of wake transverse. They found that the maximum reduction in the drag coefficient was achieved by putting the porous slices on the upper front corner and roof. Yucel et al. [5] investigated the hydrodynamic and heat transfer effects of adding a porous layer to the discrete heat sources, which were located on the bottom of the channel wall. Their results showed that, in optimum cases, heat transfer was enhanced by adding a porous layer with high thermal conductivity but the pressure drop was negligible due to the thin thickness of the porous layer. Chatterjee et al. [6] conducted a numerical simulation of flow passing over a column of square cylinders. Their results showed that the jets and the shed vortices can interact with each other so that at small vertical gaps, clusters could be formed by wake merging and jets deviations. These effects, however, could be controlled by the vertical distance between obstacles. Bao et al. [7] conducted research about the flow field around six inline square cylinders. They reported that the distances between the obstacles had significant effects on the wake patterns and, hence, on the flow characteristics. They also found that the spacing between the obstacles is the key factor for the transition from symmetrical flow to asymmetric vortex shedding pattern affecting the forces on the obstacles. Rashidi et al. [8] simulated the flow around a cylinder covered with a porous media. They reported that the wake length was increased by the porous layer and the adverse pressure gradient was reduced by increasing the Darcy number. The flow over a porous circular cylinder was studied by Zhu et al. [9]. Their results confirmed that the porous cylinder had a lower critical Reynolds (Re) number of the recirculating wake than a solid cylinder since the recirculating wake could be suppressed by the flow through the porous layer. Laminar flow around a heated cylinder covered by a porous layer was investigated by Salimi et al. [10]. They demonstrated that the porous layer caused an increment in the pressure drop but its trend was not changed with the Re number. They also found that the blockage ratio had stronger effects than the porous layer. Vijaybabu et al. [11] studied the flow over a permeable obstacle and reported that the vortex shedding strength was decreased by converting the solid obstacle to a permeable one as flow could pass through the permeable obstacle. This reduction in the vortex shedding strength led to a decrease in the drag coefficient. In order to control the vortex shedding, Xu et al. [2] investigated the off-body passive method, in which, porous materials were added at the downstream of the obstacle. They found that this approach could convert the turbulent flow pattern around the obstacle to the laminar pattern and, hence, had a direct effect on the lift fluctuations and aerodynamic noise reduction. This method did not have a positive effect on the drag coefficient. Sooraj et al. [12] carried out an experimental study on the fluid flow around three obstacles placed side-by-side. Their results illustrated that the flow pattern was significantly affected by the Re number and the gap spacing between the obstacles so that increments in the Re number and the gap ratio led to a reduction in the drag coefficient. Ma et al. [13] studied the effects of a circular bar placed upstream and downstream of a square cylinder on the aerodynamic forces using a lattice Boltzmann method (LBM). They found that the bar affects mainly the drag force if placed upstream of the cylinder while it suppresses the lift fluctuations if placed downstream. The other important parameter is the distance between the obstacle and the bar, which could significantly affect the flow patterns. Ma et al. [14] performed LBM simulations to consider the effects of a circular bar and a splitter plate placed respectively upstream and downstream of a square cylinder. The results showed that vortex shedding can be suppressed by the splitter plate and that the amount of suppression is very sensitive to the distance between the splitter plate and the cylinder. Besides, they found that the drag force is very sensitive to the distance between the cylinder and the splitter plate because the bar could not act as a shelter for the square cylinder from the direct interaction with approaching flow.

In the available literature there is a real scarcity for the drag reduction for the flow past a square cylinder using an upstream porous plate and to the best of the authors’ knowledge, there is no reported work on this subject. In the present paper, this new passive strategy and the associated parameters shall be presented. First, the flow over a square cylinder with and without an attached porous layer in a channel is considered and validated against available numerical results. Then, the effects of an upstream porous layer with different heights, locations, gap distances, porosity values, as well as the effect of Re number on the drag and lift coefficient are investigated.