Irrotational and Porous-Media Flows

A conservative vector field is a gradient of a function, known as scalar potential in vector calculus. The main property of conservative vectors that the line integral from one point to another is independent of the choice of path connecting the two points. External flows around bodies are mostly frictional and irrational. The vortices of an irrotational flow are zero.

Determining irrotational flow

Rotational motions cannot satisfy the boundary conditions. This problem is associated with difficulties in forming boundary conditions for vorticity. The potential is a harmonic function. It can be selected so that the values of the sum of rotational and irrotational fields can be chosen to balance prescribed conditions at the boundary. The irrotational fields that are allowed can be selected from harmonic functions that enter into the purely irrotational solution of the same problem on the same domain. An important property of potential flow arises from the fact that the irrotational viscous stresses do not give rise to irrotational viscous forces in the equations of motions. The dependence of irrotational field on viscosity can be generated by the boundary conditions

Porous Media

Materials like soil, sand and packed catalyst beds consist of a large number of fibers packed together closely. There will be open space in between solid particles or fibers that are closely packed thus giving rise to pores through which fluids can flow easily. For an object to be porous it is not necessary that it should contain many particles. For example it could simply contain single continuous solid body that has many pores or holes in it. It is the same with several rocks and filters. It is not important how the porous medium is constructed. Some simple models are introduced and when combined with experimental data, it can be used to calculate quantities of interest such as dissipation or head loss or pressure drop across porous media during fluid flow. The information is vital in several chemical engineering operations like filtration units, packed beds and certain types of chemical reactors.

Porous media flows

Porous media is used for a wide variety of engineering applications like flow through packed beds, filters, perforated plates, flow distributors and tube banks. It is better to determine the pressure drop across the porous medium to predict the flow in order to optimize a given design. Two dimensions are used to represent the fluid region. The skeletal portion or matrix may be solids or foam.

Questions:

• Define irrotational flow?
• What is porous media flows?