Incompressible Flow 1 - Fundamental Equations of Fluid Flows Flashcards
Examples of fluid flows
Liquid flow
Gas flow
Reacting flow
Pollutant transport
Two fundamental principles of incompressible fluid flow
Mass is conserved (continuity equation)
Newton’s 2nd Law (Navier-Stokes equation)
Defining quality of incompressible flow
Density is constant
Parts making up pollutant transport in fluid flow
Convection
Diffusion
Define convection
Mass/energy transfer process due to the bulk motion of a fluid
Define diffusion
Will proceed until the concentration gradient diminishes, when there will be no more net diffusion
What is Fick’s Law of Dissuasion?
The mass flux of a fluid across a unit area by diffusion is proportional to the concentration gradient and its diffusivity
Why is there a minus sign in Fick’s Law of Dissuasion?
Indicates that mass always diffuses to the opposite direction of the concentration gradient (i.e. to the low concentration region)
Why are boundary conditions for dependent variables in convection-diffusion equations required at all boundaries enclosing the flow?
A disturbance to the flow at any point of the boundary is able to travel across the entire flow field and be felt everywhere else (due to the presence of the diffusion term)
Two ways to specify a boundary condition for a PDE
Fixed value (Dirichlet)
Normal gradient (Neumann)
Points about fixed value/Dirichlet BC
Specifies a specific value of a quantity to be solved for
e.g. for 2D flow between two plates, can specify values for u1 and u2 on inlet and top and bottom walls
Points about normal gradient/Neumann BC
Specifies normal gradient of quantity to be solved for
For 2D flow between two plates, this can be used if plates are long and flow is fully developed at outlet
e.g. for 2D flow between two plates, can specify values of velocity gradient for u1 and u2 at the outlet (can also set p=0)
