Introduction:
Porous media, as systems with special properties, consist of porous structures that play an important role in many industrial and natural processes such as filtration, material separation, and fluid transport. Due to their specific physical properties, such as porosity and permeability, these media can exhibit interesting and unpredictable behaviors. Therefore, a detailed understanding of the fluid flow behavior in these media not only helps to improve existing processes, but can also lead to the optimal design of new and more efficient systems. For this reason, accurate simulation and analysis of the flow behavior in porous-walled tubes is of great importance. The main objective of this research was to investigate the effect of various factors on the flow of fluid through a porous-walled tube. This study sought to clarify the flow-related processes in these systems by analyzing the data and results obtained from numerical simulations and to reach reliable results regarding the optimization of tube design and its applications. Also, this research attempts to provide solutions to optimize the performance of filtration and fluid transfer systems.
Methods:
In this study, the governing equations for flow in porous media, including the continuity equations, Navier-Stokes, and Darcy's law, were introduced. The continuity and momentum equations were thoroughly defined mathematically, along with a detailed examination of boundary conditions and the properties of the fluid and porous media, such as geometry and technical parameters. Fluid flow in a tube with a porous wall was simulated numerically using ANSYS Fluent 2021 software. A tube with a diameter of 2.4 cm and a length of 120 cm was selected, with boundary conditions set for an axial Reynolds number of 500, indicating a transitional flow regime. Air was modeled as the fluid, characterized by a density of 1.29 kg/m³ and a dynamic viscosity of 1.87 × 10⁻⁵ Pascal seconds. The porous medium in the tube wall was designed to be 2 mm thick, with a permeability of 1.85 × 10^⁻17 m², based on findings from previous research. A comprehensive mesh convergence analysis was conducted to ensure the accuracy of the simulation results, leading to a selection of 203150 elements that provided an optimal balance between the results accuracy and the computational time required. The study compared flow velocity parameters at two different Reynolds numbers, investigating the effect of wall seepage on flow by varying the porous medium Reynolds number (R_ew) from0 to 0.1. The axial Reynolds number (R_e) was also used as a key criterion to describe flow behavior within the tube. The results were analyzed to understand the influence of porosity, thickness, and tube length on flow velocity. Furthermore, the simulation outcomes were compared with data from previous studies to validate the findings and enhance understanding of flow behavior in porous media.

Results:
The results obtained revealed that the Reynolds number had a significant effect on the flow performance in the porous tube. For example, when the Reynolds number associated with fluid seepage through the porous wall was equal to zero, the velocity profile of the flow through the tube showed good agreement with the data in the study of Belhouideg (2017). Also, at a Reynolds number of 0.1, the difference between the simulation results and the reference data was only 0.03%, which indicated the high accuracy of the simulation and proper validation of the results. The study of the effects of different tube wall thicknesses, porosity, and tube length on the velocity profile showed that the wall thickness and the application of different porosities from 0.2 to 0.8 had no significant effect on the fluid flow behavior. In contrast, with the lengthening in tube from 0.6 to 2.4 m, the difference in flow velocity between the regions close to the wall and the tube axis decreased as well as the overall flow velocity. The changes in the axial velocity of the flow were analyses for different Reynolds numbers in the radial direction. In the impermeable state, the velocity at the center of the tube was equal to the initial velocity, whereas in the presence of a porous medium, the flow penetration led to the creation of a compensatory force that prevented a sharp drop in velocity. This research also showed that in tu especially its length bes with porous walls, the flow seepage from the wall reduced in the velocity drop, which is clearly evident in comparison with impermeable tubes. The obtained results also emphasized the effect of wall thickness and porosity on the velocity profile and showed that these parameters did not have a significant effect under certain conditions. In addition, the results of the research indicated that the effect of the Reynolds number and the physical characteristics of the tube, especially its length, were factors affecting the behavior of the fluid flow in tubes with porous walls. So that an increase in the tube length leads to a decrease in the flow penetration velocity in the porous wall.
This research clearly shows that the Reynolds number and the physical properties of the tube, especially its length, are factors affecting the fluid flow behavior in porous-walled tubes. The results of this research can help optimize filtration systems and design optimal tubes in industrial and engineering applications. These results can be used as a basis for future studies in the field of design and optimization of fluid transport and filtration systems in porous media. Finally, the importance of this research in improving processes related to material separation and designing more efficient systems is demonstrated. Also, it can be concluded that improving simulation methods and further investigating flow behavior under different conditions can lead to a deeper understanding of flow processes in porous-walled tubes and ultimately help to promote science and technology in this field.