Bleeding flow characteristics downstream of isotropic porous square cylinders

Flow around porous square cylinders with a periodic and scalable structure

Effects of Prandtl number on the forced convection heat transfer from a porous square cylinder

Unsteady convection heat transfer for a porous square cylinder varying cylinder-to-channel height ratio

Various engineering applications commonly involve the flow of nanofluids over a porous 45° inclined square cylinder. Therefore, the current study is to assess the impact of the Darcy parameter (Da), nanoparticle volume fraction (ϕ), and Reynolds number (Re) on the momentum transport characteristics over the 45° inclined porous square cylinder. The governing equations were solved numerically using the Darcy–Brinkman–Forchheimer model for different values of Da ( ), nanoparticle volume fraction ϕ ( ), and Reynolds number Re ( ). The results for each parameter were visualized using streamline plots, velocity profiles within the porous cylinder, and vorticity contours. Complex flow behaviors were observed between Da = 10−3–10−2, flow separation detached and disappeared at the cylinder's downstream side at critical Darcy number. Drag and pressure coefficents are used to represent the global and local parameter of the flow fields. The pressure coefficient on the surface of the cylinder showed an inverse relationship with the nanoparticles volume fraction and Darcy number. The strength of the drag coefficient decreased with the addition of nanoparticles to the base fluid, with a decreasing trend observed for Da = 10−4–10−2 and no change observed for Da = 10−6–10−4. At last, the comparative analysis has been conducted between a porous square cylinder at 0° inclined and another 45° inclined.

Application of flow past bluff bodies like (cylinders, spheres etc) has been spread to other engineering fields (e.g., ship hydrodynamics, pipelines, heat exchangers in nuclear reactors, cooling systems, skyscrapers etc.) and no more a topic of interest only to aerodynamicists. Porous cylinders with sufficient mechanical properties and strength as of solid cylinders will be preferred due to their better fluid flow and heat transfer properties. In this work, an attempt using computational fluid dynamics (CFD) approach was made to compare the fluid flow and heat transfer properties of the porous square cylinder and square solid cylinder for different low Reynolds numbers. An Unsteady Reynolds Averaged Navier-Stokes (URANS) Equations were solved for the two chosen cylinders where turbulence is introduced into the equations through Shear Stress Transport (SST) k-w model. Heat transfer to the flowing fluid from the cylinders is estimated using the Nusselt number. Brinkman model in conjunction with Forchheimer term has been used to develop the flow through the porous media. The study carried out on 3-Dimensional space using commercial software Ansys. Dependence on grid and mesh has been studied by increasing the number of elements by √2 to verify and validate the methodology followed. The study has been done for different low Reynolds numbers, namely, Re = 170, 185, 200 and 250. The results are encouraging the preference of porous square cylinder than solid square cylinder for few applications.

This study experimentally investigates the wake structure of a porous square cylinder in terms of permeability over two decades of $Da$ (i.e. $2.4 \times 10^{-5} < Da < 2.9 \times 10^{-3}$ ). The porous cylinder, featuring a simple cubic lattice structure, was fabricated using an additive manufacturing technique. This unique method, combined with a periodic and scalable lattice structure, effectively isolates permeability from porosity, making it suitable for an in-depth parametric study. The key parameter, permeability, was directly estimated by measuring the pressure drop and superficial velocity for each porous case in an open-loop pipe flow system. The downstream flow fields were obtained using standard planar particle image velocimetry measurements in an open-loop wind tunnel. Based on the experimental data, structural modifications in the near wake were examined in relation to permeability, leading to the identification of four distinct flow regimes depending on $Da$ . Additionally, the downstream flow adjustment length ( $L_i$ ) was assessed by introducing a permeability-based source term into the momentum equation, facilitating the development of an analytical model for $L_i$ . The present experimental data support this analytical model, and our results further confirmed that $L_i$ plays a crucial role as a characteristic length scale in the near wake.

Incompressible, two-dimensional flow around a porous square cylinder placed in an infinite stream is simulated using the d2q9i model of the lattice Boltzmann method. The Reynolds number (based on the height of the cylinder) is kept at 100. The porosity ϕ of the cylinder is varied from 0.25 to 0.9 and permeability through the Darcy number Da from 0.0001 to 0.1. The velocity data at a point downstream of the cylinder are collected at each time step. Discrete Fourier transform analysis of this data is carried out to extract the dominant frequencies of the unsteady flow field behind the cylinder. Strouhal numbers (St) calculated using these dominant frequencies are compared with those of corresponding solid cylinder to bring out the effect of the porous medium on the wake structure and the vortex shedding. At Re=100, as the nondimensional permeability Da is increased from the solid cylinder limit, more flow results through the porous cylinder. The reduction in the value of the dominant frequency with increasing porous medium permeability Da and porosity ϕ indicates a substantial reduction in the vortex shedding. Corresponding static pressure plots and St values corroborate this observation at Re=100 and 200.

This article investigates the laminar flow of power-law fluids through two porous square cylinders in a side-by-side configuration. The effects of power-law index (n), Darcy number (Da), and gap ratio (g/W) are examined within ranges of g/W = 0.5–5, n = 0.4–0.8, and Da = 10−6–10−2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re = 1 where Darcy's law is applicable; second, for a viscous dominant flow at Re = 100, where Darcy–Forchheimer-extended model is exercised. Flow patterns behind the porous cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular nonperiodic vortex shedding characterized by a single large vortex street far off the downstream for g/W = 0.5. However, synchronized wake patterns were observed in either antiphase or in-phase modes for higher gap ratios. Leading-edge separation with two-side recirculation induces quasi-periodicity in the flow for all g/W. It was found that increasing the permeability can prevent the leading edge separation. Additionally, a transition from antiphase to in-phase mode occurs when the permeability is altered while maintaining constant flow-time. The presence of a jet-like flow between cylinders significantly impacts unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. A jump in some flow parameters was observed at higher Re for the midrange Darcy number, but no such increase was noted for the high shear-thinning behavior. These findings provide a potential approach for improving the design of fluidic systems involving porous cylinders.

This numerical study investigates flow and turbulence structure through and around a circular array of solid circular cylinders of diameter$d$. The region containing the array of rigid cylinders resembles a porous circular cylinder of diameter$D$. The porous cylinder Reynolds number defined with the steady incoming flow velocity is$\mathit{Re}_{D}=10\,000$. Fully three-dimensional (3D) large eddy simulations (LES) are conducted to study the effects of the volume fraction of solids of the porous cylinder ($0.023<\text{SVF}<0.2$) and$d/D$on the temporal variation and mean values of the drag/lift forces acting on the solid cylinders and on the porous cylinder. The effects of the bleeding flow through the circular porous cylinder on the wake structure and the influence of the SVF and$d/D$on the onset of flow three-dimensionality within or downstream of the porous cylinder and transition to turbulence are discussed. Results are compared with experimental data, predictions of theoretical models available in the literature and also with the canonical case of a solid cylinder ($\text{SVF}=1,d/D=1$). Three-dimensional LES predict that large-scale wake billows are shed in the wake of the porous cylinder for$\text{SVF}>0.05$, similar to the von Karman vortex street observed for solid cylinders. As the SVF decreases, the length of the separated shear layers (SSLs) of the porous cylinder and the distance from the back of the porous cylinder at which wake billows form increase. For sufficiently low volume fractions of solids (e.g. $\text{SVF}=0.05$, 0.023), no wake billows are shed and the interactions among the wakes of the solid cylinders are weak. Even for$\text{SVF}=0.023$, SSLs containing large-scale turbulent eddies form on the two sides of the porous cylinder, but their ends cannot interact to generate wake billows. In both regimes, the force acting on some of the solid cylinders within the array is highly unsteady. As opposed to results obtained based on 2D simulations, no intermediate regime in which the force acting on the solid cylinders is close to steady is present. Interestingly, an energetic low frequency corresponding to a Strouhal number defined with the diameter of the porous cylinder of approximately 0.2 is present within the porous cylinder and near-wake regions not only for cases where wake billows are generated but also for cases where no wake billows form. In the latter cases, this frequency is due to an instability acting on the SSLs which induces in-phase large-scale undulatory deformations of the two SSLs. A combined drag parameter for the porous cylinder${\it\Gamma}_{D}=\overline{C}_{d}\,aD/(1-\text{SVF})$is introduced, where$aD$is the non-dimensional frontal area per unit volume of the porous cylinder. This parameter characterizes by how much the velocity of the bleeding flow at the back of the porous cylinder is reduced compared with the incoming flow velocity for a given total drag force acting on the porous cylinder. Results from simulations conducted with different values of the SVF,$d/D$and mean time-averaged solid cylinder streamwise drag parameter,$\overline{C}_{d}$, show that${\it\Gamma}_{D}$increases monotonically with increasing$aD$. Several ways of defining the spatial extent of the wake region in a less ambiguous way are proposed.

The laminar mixed convection flow across the porous square cylinder with the heated cylinder bottom at the axis in the channel has been carried out numerically in this paper using a semi-implicit projection finite element method. The governing equations with the Brinkman–Forcheimer-extended Darcy model for the region of square porous cylinder were solved. The parameter studies including Grashof number, Darcy number, and channel-to-cylinder height ratio on heat transfer performance have been explored in detail. The results indicate that the heat transfer is augmented as the Darcy number and channel-to-cylinder height ratio increase. The buoyancy effect on the local Nusselt number is clearer for B/H=0.1 than for B/H=0.3 and B/H=0.5.

The study of flow around bluff bodies like cylinders, spheres, etc. is very popular as it finds applications not only in aerodynamics but also in many other engineering fields (e.g., heat exchangers in nuclear reactors, ship hydrodynamics, skyscrapers, cooling systems, pipelines, etc.). Porous cylinders with equivalent strength and other mechanical properties will be preferred over solid cylinders due to their better fluid flow and heat transfer performance. This work deals with the comparison of fluid flow properties of the square solid cylinder to the square porous cylinder at low Reynolds number using computational fluid dynamics (CFD). The cylinder with square as cross section and D as length is placed symmetrically in a three-dimensional computational domain with upstream and downstream distances of 7.5D and 20D, respectively. The height and span-wise distance of the domain are considered as 15D and 6D, respectively. Velocity inlet with a velocity of 1 m/s and 0 Pa pressure is considered as the boundary condition at the inlet. The boundary condition at the outlet is considered as a pressure outlet with 0 Pa pressure. A no-slip boundary condition with stationary wall condition is considered for the walls of the domain along with the cylinder surface. A circular cylinder cross section and a diameter D from the literature have been considered for validation of the computations. The analysis is carried out at low Reynolds numbers, namely Re = 170, 185, 200 and 250. The results obtained proved that square porous cylinder outperforms solid square cylinder in all aspects.KeywordsPorous square cylinderCFDReynolds number

The wake structure behind a porous square cylinder is numerically investigated by using both pore-scale and macroscopic approaches. The pore-scale simulations (PSSs) concern about the steady flow through and around square arrays of multiple circular cylinders with a wide range of solid fraction. The macroscopic porous media model (PMM) employed is the generalized equation, where the dimensionless permeability Dam is assigned based on the macroscopic permeability Das estimated from PSS via Darcy’s law. The connection between pore-scale and macroscopic flow properties is studied in terms of the flow pattern, the geometric parameters, and the occurrence of the recirculating wake behind the array. It is found that the consistency between PSS and PMM is highly dependent on the ratio of Das and Dam. Discussions in terms of the scale analysis of PMM, the discrepancy between Dam and Das, and the effects of stress-jump parameters are also provided.

PurposeThis paper aims to predict the effects of uniform injection or suction through a porous square cylinder on the flow field and on some aerodynamic parameters.Design/methodology/approachThe finite volume method has been used for solving the ensemble averaged Navier–Stokes equations for incompressible flow in conjunction with the k‐ ε turbulence model equations including the Kato and Launder modification.FindingsThe parameters taken into account are injection or suction velocity, position of injection and suction surface, drag and lift coefficients and Strouhal number. The numerical results show that increasing suction velocity decreases the drag coefficient for all the suction configurations considered in the present study, except that of suction through rear surface. The vortex‐shedding motion gets weak by the suction application through top and bottom surfaces.Research limitations/implicationsThe problem is restricted with a 2‐D simple geometry such as square cylinder due to the limited computer capability. Further extensions of the present study could include the more complex configurations and some other aspects such as heat transfer between porous cylinder and main flow.Practical implicationsThe injection or suction application through a porous bluff body can be used as an efficient drag and vortex control method in aerodynamics.Originality/valueThis paper describes an attempt to simulate numerically the flow around square cylinder with uniform injection and suction in a manner different from what is given in the literature.

This study numerically evaluates fluid flow and natural convection heat transfer of a porous square cylinder in an L-shaped enclosure using the Lattice Boltzmann method. Three layouts along vertical and horizontal centrelines are explored, investigating the effects of Rayleigh number (Ra) (103 ≤ Ra ≤ 106), Darcy number (Da) (10−6 ≤ Da ≤ 10−2), and cylinder size. Results show that increasing Rayleigh numbers enhances heat transfer, with higher Mean Nusselt number (NuMean) values observed. Doubling the cylinder’s width at Da = 10−6 increases NuMean by 46.5%, and tripling the width results in a 118% enhancement. Higher Rayleigh values enhance buoyant forces’ intensity, improving heat transfer; for example, at Ra = 105 and Da = 10–2, there is a 42% increase in Nu mean for a cylinder with a 0.6 L side length compared to Ra = 103. Optimal cylinder orientation significantly maximizes convective heat transfer, especially at high Rayleigh and Darcy numbers. This study provides valuable insight for optimizing the orientation of electronic blocks in compact L-shaped enclosures for better thermal management.

The aim of this numerical work is to study the improvement of the heat and mass transfers during the evaporation of a liquid film with neglected thickness in a heated channel with a built-in porous square cylinder. The cylinder has a constant porosity and permeability. The calculations have been completed for a Reynolds number ranging from 20 to 100, Darcy number Da ≤ 10-6, and a blockage ration of H/h = 1/4. To achieve this, we solved the classic equation of forced convection and the Darcy-Brinkman-Forchheimer model. Results are presented to show the influence of the porous cylinder on the mass transfer. There is an improvement in the mass transfer with the presence of the porous cylinder. This improvement is greater with an increase in air inlet velocity and heat flux density. It is also greater with a decrease in temperature and relative humidity of the air at the inlet. At Da = 10-6, the flow does not penetrate through the porous cylinder; the flow pattern is similar to that of a solid square cylinder.With an increase of the Darcy number, the flow starts to pass through and around the cylinder. Finally, a correlation has been proposed for the Sherwood number as a function of the Reynolds and Biot numbers.