We need to specify additional boundary conditions for our new transport equations. Unfortunately k and are not always measured quantities, so we may have to estimate them.
For laminar (incompressible) flow, we specify at the inlet. For turbulence modelled with the k - model we specify , k, at the inlet. However k, values are not always known. We have to estimate the values to use as b.c. and it is always worth checking to see that the calculated result is not sensitive to the inlet conditions. Conventionally : k ~ 5 - 10% of the inlet kinetic energy. We can also guess the turbulent length scale to be
For laminar flow, we usually specify p. For turbulent flow, specify
Treatment of solid walls is quite complex. Near-wall turbulent flow is not like that in free stream - instead have a boundary layer consisting of laminar sublayer, transition region and log-law region. We could make the mesh fine enough to resolve all the detail in this region, but this would be very expensive. Hence we need to treat this region of the flow differently. Luckly near-wall flow is universal and we can introduce a separate wall model to describe the flow in the layer of cells close to the wall.
Wall functions of the form
However such functions have been derived under the assumption that we do indeed have turbulent flow in the near-wall cell, i.e. the cell centre needs to be within the transition region. This provides a restriction on the y+ value for the first cell yp+ :