Convection in porous media

Abstract

Porous media are used for a wide variation of applications in energy production and storage. One of those applications is the storage of heat which are of great importance in the renewable energy transition. Most literature reported limit itself only to one single thermal conductivity for the porous media. In reality however, the porous media often consist of multiple materials with different conductivities. This thesis researches numerically natural convective heat transfer in a porous media with both conductive and insulating objects.
The porous medium is simplified to a side heated cavity filled with water as fluid (Pr = 7), 32 aluminum objects with a thermal conductivity ratio of λ* = λal/λf = 337.33 and 32 wooden objects at thermal conductivity ratio λ* = λw/λf = 0.29. 4 cases, each with the aluminum and wooden cubes differently configured are simulated at a Rayleigh number(Ra) of 105, 106 and 107. Conjugate heat transfer (the fluid fase and solid fase are modelled as separate regions) simulations are done with direct Navier-Stokes where Ra = 105 and 106 are run steady and Ra = 107 is run transient. There are two different geometries simulated. One when the objects are unattached (heat cannot directly conduct into the objects from the walls) to the wall and when they are attached (heat can directly conduct into the objects) to the wall. From these simulations the temperature profile, the velocity field and the Nu profile is obtained. Also the average Nu at the hot wall and the Urms are calculated and compared between the different cases. Lastly the thermal disequilibrium %|DT| between the solid temperature and fluid temperature is calculated and compared between place of the object in the cavity and between the cases. The simulations show that conductive objects increased heat transfer at Ra = 105 when they are close to the wall. This is because they decrease the thermal resistance heat travels in the thermal boundary layer. Insulating objects on the other hand show decreased heat transfer as they increase the thermal resistance in the thermal boundary layer. At Ra = 106 and at Ra = 107 the circulation is to strong and the thermal boundary layer is mostly in between the wall and the objects so there is little difference seen in the flow and heat transfer. When the objects are attached to the wall the simulations show very different results for the flow and heat transfer and is very dependent on the conductivity and position of the object. Conductive objects attached at the wall, especially at the bottom of the wall where the temperature-gradient is the biggest, greatly improve the flow and heat transfer. They improve the area heat is transported from the wall to the fluid and thus increase the buoyancy force significantly. Insulting objects attached to the wall on the other hand prevent heat from flowing through the object and also prevents flow from reaching the wall. A big decrease in velocity and heat transfer is seen for all Ra values. For a case where conductive objects are placed against the wall and there are insulating objects in the middle, heat transfer can be improved compared to a fluid-only cavity for Ra ≥106.