A porous medium is a body that contains pores or cavities and is permeable to fluids. A porous medium is a kind of object that can be used in many industries, such as oil and gas, water treatment, and agriculture. The porous medium has unique properties that can be used in special applications such as energy storage, absorption of sound waves, particle filter, and fluid purification.
Porosity is the presence of space and holes in the structure of solid objects, and objects or areas with space in their design are called porous media. Examples of porous mediums include sponges, filters, soil, sand, wood, etc. It should be noted that porous mediums can be malleable and compressible, like sponges, which increase in length and decrease cross-sectional area as they are stretched.
Porosity in all porous media is calculated using a simple relationship. This relationship is the ratio of empty space volume to the environment’s total volume. An answer is always a number between zero and one; of course, it is expressed as a percentage. Depending on whether the porous areas under the effect of external forces can pass the currents or not, those environments are called permeable or impermeable.
Simulation of porous mediums using CFD
As mentioned, porous media are porous bodies with small and large holes. Therefore, CFD simulation of these environments is complicated and even impossible. Because generally, the holes in porous media do not have the same shape and are randomly repeated with small and large dimensions, it is impossible to produce the geometry of these objects. On the other hand, if we manage to design the geometry of these objects, networking these objects is a challenging task. Due to the difficulty of creating and meshing porous media, models have been developed to simulate these bodies.
If we think a little, we will realize that the effect of the porous media in the fluid flow can be seen in the pressure drop of that fluid when it passes through the porous area. For this purpose, two relations are used to calculate inertial and viscous pressure drops in the model used to simulate these objects. An inertial pressure drop is caused by the impact of a mass of fluid on a porous medium, such as when we put a perforated plate in front of the water flow, and the flow collides with that plate; due to this impact, a pressure drop occurs in the flow.
Another pressure drop that can be seen in porous media is the viscous pressure drop, which is caused by the fluid’s viscosity. When the fluid moves in a pipe (or the holes in the porous medium) due to the no-slip condition on the walls, a velocity gradient is created near the wall (called the boundary layer). Due to the viscous nature of the flow, this velocity gradient creates shear stress in the walls, which causes a pressure drop in the flow.
To simulate porous media, we need to calculate inertial and viscous pressure drop coefficients to calculate the pressure drop in the porous medium and input them into Fluent software. To calculate these coefficients, we need laboratory work and a small sample to Test the porous media underflow at different speeds and calculate the coefficients of viscous resistance and inertial resistance (in another section, we will discuss how to calculate these coefficients in detail).
Application of using porous mediums in CFD simulation
So far, we have introduced porous media and how to simulate them. In this section, we want to point out some examples that may not be porous media; still, to simplify the simulation and consume less time and cost, we simulate them using the CFD software definition of porous media.
If we want to simulate the flow passing through the leaves of a tree and calculate the pressure drop caused by the flow passing through it, we have the difficult task of designing the area through which the flow passes. We cannot design all the tree leaves and get the airflow area. Therefore, we consider the area of tree foliage as a porous environment. And by defining the coefficients of viscous resistance and inertial resistance for it, we can perform the simulation and calculate the pressure drop caused by the flow passing through one or more trees using CFD.
Of course, because the viscous pressure drop is not very important in this problem, and most of the pressure drop is due to inertial resistance, we can enter only inertial resistance coefficients and zero viscous resistance coefficients and ignore it.
Reverse osmosis is a physical process in which an almost pure solvent can be prepared from a solution with the help of a semi-permeable membrane. For example, with the help of this method, it is possible to prepare desirable drinking water from salty water. Reverse osmosis is one of the best methods for removing water-soluble ions. Since only water molecules can pass through the semi-permeable membrane’s pores, almost all dissolved ions and molecules (including salt, sugar, and solutes in water) remain behind the membrane and are removed from the water. Reverse osmosis can remove up to 98% of dissolved minerals and organic and colloidal substances from water.
A “semi-permeable membrane” is a membrane that allows only some atoms or molecules to pass through. A simple example of a semi-permeable membrane is a mesh door. These doors only allow air molecules to pass through and not pests or anything more extensive than the openings in the door. Another example is Gore-Tex fabric, a thin plastic film with billions of tiny holes. The pores are large enough for water vapor to pass through. On the other hand, the diameter of the pores is small enough to prevent the passage of liquid water.
If we want to simulate this process using CFD, we will face how to define a semi-permeable membrane. We know that this membrane allows the passage of water and prevents the passage of solutes. We can clarify multiphase models and explain the membrane region as a porous medium to determine this problem. In this porous medium, we enter zero coefficients of viscous resistance and inertial resistance for water, and we enter a large number for the other phase (i.e., the solutes in water). With this, we can simulate reverse osmosis.