 # CFD 9 : Boundary Conditions – Wall and Inlet/exit

In principle, one can say that all parts of the universe are connected to each other by fluxes of heat and mass and, thus, must be included into a good CFD solution.

Since such an enterprise is hardly feasible, we have to compromise and formulate CFD problems for finite domains limited by boundaries.

Such boundaries often appear naturally. For example, they can follow rigid walls. Sometimes, however, the choice is, by necessity, artificial. In any case, a correctly formulated CFD problem should include a set of proper boundary conditions for velocity, temperature, and other variables.

No correct CFD solution can be obtained without them.

Rigid Wall Boundary Condition

At the rigid walls, the velocity boundary conditions are different for viscous (μ !=(not equal) 0) and inviscid (μ = 0) flows.

For viscous flows, the no-slip conditions are applied:

In our example, if we use a reference frame moving with the car, the conditions are

For inviscid flows, the impermeable wall conditions are applied, only the velocity component normal to the wall is required to match the corresponding component of the wall velocity. The tangential component can slip:

We will assume that the normal n faces outward with respect to a fluid element and into the wall.

For temperature, two asymptotic limits can be used. One is the condition of known wall temperature T(wall) (imagine a wall in the form of a large copper slab kept at this temperature):

Another is the condition of known normal heat flux into the wall q(wall):

The special case of the latter is a perfectly insulating wall:

The Newton’s cooling law can be used as a more realistic boundary condition when neither of the two asymptotic limits is acceptable. The heat flux is taken to be proportional to the difference between the temperatures on two sides of the boundary:

where h is an empirical cooling constant (also know as convective constant).Final equation becomes

Inlet and Exit Boundary Conditions

If the computational domain has open boundaries, such as the inlet and exit in our example(ahmed body CFD), special boundary condition must be set at them. The common choice for the inlet is to prescribe velocity and temperature:

Parameters of turbulent fluctuations should also be prescribed if the flow is turbulent.

At the exit, any boundary condition would be artificial since we artificially cut off a part of the flow generated in the car-tunnel system and
have no possibility to predict what happens there and how this can affect the flow inside the computational domain. One commonly used approximation is that of zero stream wise gradient

In many situations, we can make more or less plausible assumptions about the nature of the solution before it is actually computed. This can help to reduce the size of the computational domain, computational grid, and, thus, the amount of computations. . A flow in a circular pipe with a series of equidistant ring like obstructions is calculated. Two assumptions can be made, especially if our interest is in the mean (average) state of a turbulent flow: that the flow is axially symmetric and that its structure is periodic, repeating itself in every groove between the obstructions

Relying on the first assumption allows us to consider a two-dimensional solution with all variables depending on the axial z and radial r coordinates of the cylindrical coordinate system instead of the general three dimensional solution. The computational domain lies in the r -z plane and is limited by the solid walls and the symmetry axis. Special boundary conditions that guarantee regularity of solution have to be imposed at r = 0. The engineering CFD codes usually provide such conditions as an option.

The assumptions should, however, be used with caution. The actual flow structure does not necessarily follow the symmetries suggested by the geometry. For example, hydrodynamic instabilities and other effects would, in many cases, transform the flow