*In this article, I will describe a fairly common procedure to model porous media accurately and address frequently-asked questions.*

Tesla Model 3 was recently launched amid much media reporting. In fact, Elon Musk tweeted to his followers about filtration. There was an article which said that Tesla’s Model X purifies air in less than 2 minutes!

So, how does Tesla make it possible? Porous media cane help them achieve this. By *p**orous, *we can infer a substance to have minute interstices through which fluid may pass through it. Porous material is permeable if the interstices are interconnected or continuous thereby making a fluid to flow through them. Massive amount of consolidated energy wastage (due to improper combustion and left of un-burnt particles) happens due to this impure air. For efficient fuel burning, there is the pressing need to filter air before passing it through any combustion device. Another application that is quite relevant to this topic is of air conditioners – all pervasive at homes and our workplaces. In all these applications, impure air passes through a series of filters. The interstices present in these porous zone filter holds off solid dust particles and parses clean air.

These concepts are ubiquitous in nano- and micro-scale applications, oil reservoirs and geophysics applications, electronics cooling, thermal insulation engineering, nuclear waste repository, biomedical, biological and environmental applications, grain storage and enhanced recovery of petroleum reservoirs among many others. Today we need to explore innovative approaches to effectively apply existing porous media technologies to these applications. These porous media play a vital role in gas turbine inlet filtration systems. A typical pollution eliminator contains different type of filters such as bag filters, cartridge filters, EPA (Efficient Particulate Air), HEPA (high efficiency particulate air) and ULPA (Ultra Low Particulate Air) filters etc.: each filter has a specific purpose and level of efficiency.

###### Fluid Flow Effects in Porous Media

Design and shape of the filter plays a crucial role in evading compressor surge and improving the performance of a system as a whole. It is very crucial to keep the flow conditions at a minimum total pressure drop by adopting a filtration system that suits the operational environment.

During filtration, fluid experiences certain changes such as:

- static pressure rise due to diffusion,
- reduction in the flow energy, thereby making it more laminar based on the porous medium’s permeability,
- heat transfer effects through the porous zone, etc.

Today simulation plays a significant role in understanding filter performance and filter housing design to deliver adequate air flow distribution by translating a physical scenario into a math-based numerical model. As simulation engineers, we will need to model porous media to recreate these effects.

Using ANSYS FLUENT interface, I will explain the process here onward. In ANSYS FLUENT, porous media model adds a momentum sink in the governing momentum equations. You can model this in two ways:

- Using cell zone conditions
- Porous jump boundary conditions, especially if our only concern is about the pressure drop.

The approach to model porous media using porous jump boundary conditions is useful when we don’t have all the necessary flow transport properties. With this approach, however, you can expect a decline in accuracy because you need to assign the boundary conditions only on the surfaces. This makes it critical for the solver to understand a sudden rise in the pressure value at the imposed location.

###### Modeling Porous Media using Cell Zone Conditions

Once you import your meshed model into ANSYS FLUENT, you can edit the fluid cell zone condition. Here you will find options like Frame Motion, 3D Fan Zone, Source Terms, Laminar Zone, Fixed Values and Porous Zone. By selecting the Porous Zone feature, you will find input options mainly related to Inertial and Viscous resistances and direction vectors.

Inertial and Viscous resistances are the coefficients combined with other parameters of the Hagen-Darcy’s equation. This equation calculates pressure drop across the porous zone. This zone provides the capability to model pressure drop inside the fluid volume in the axial direction. The pressure drop in this medium is contributed due to viscous and inertial resistances; we can define it as:

∆p = ∆p_{Viscous} + ∆p_{Inertial}

where the pressure drop due to viscous resistance is given as the product of viscous resistance coefficient, thickness of the porous zone, viscosity of the fluid and the velocity of the flow. Since we provide viscosity, thickness (from the geometric model), velocity of the fluid (as calculated by the solver at the corresponding place in the domain through iterations) and the coefficient (user input values), solver calculates the pressure drop attributed due to this viscous effect loss.

Similarly, the pressure drop due to inertial losses is given as the half product of inertial resistance coefficient, square of the velocity of the fluid, thickness of the porous zone and density of the fluid. Take sufficient care while entering coefficient values into the software; sometimes the values may be given of the negative exponential order. Confusion arises because coefficient is represented as C¹= 1/K. In the software, you need to enter the value of K to accurately account for the right coefficient value.

###### Achieve Faster Convergence

Occasionally, the convergence rate slows down when the pressure drop is relatively large in the flow direction. For example, when the coefficient value of C² is large or permeability (alpha) is low, convergence rate is slower. You can resolve this by providing a good initial guess for the pressure drop across the medium. You can obtain the initial guess from two ways:

- by performing standard initialization, or
- by supplying an initial flow field without the effect of the porous region by temporarily disabling the porous media model.

###### Frequently-Asked Questions: The Top Three

*Direction vectors*, especially for conical or cylindrical faces, are automatically calculated by ANSYS FLUENT. Engineers fail to check if the direction vectors are normal to the surface. If the direction vectors are not normal to the surface, then results will be incorrect. Be careful, there!*Does every porous flow application have pressure losses due to the combination of both the viscous and inertial effects?*The CADFEM’s Support Hotline gets this question quite often. The answer is no. For laminar flows, you’ll not find any inertial effects. Whereas for flows through a planar porous media (not a standard industrial use case though), you’ll not find viscous effects as well.*I don’t have the either of the viscous or inertial coefficient values. With information about pressure drop across the porous zone, can I simulate the fluid flow?*This one is tricky because the pressure drop is due to the combined effect of both the inertial and viscous effects. Without knowledge about the significant contribution to the pressure loss due to either effect, it’s impossible to accurately model the flow. However if you are willing to ignore one of the two effects, then you can utilize the information about pressure drop to model the flow.

It’s not difficult to model porous flow problems, however you need to right software and the right partner to guide you through the solution. Talk to us, and we’ll glad to help you!