Hi,

I am playing low-reynolds-number models on my cases. My question is this is a dimensionless number R(k)=f(y), where y is the distance from wall. My question is that y is for the whole domain or only for the viscous layer? For closed flow, how to determine y? I really appreciate your help.

(1). It is a good question. (2). But you have to remember that all of these turbulence models are derived from the turbulent boundary layer flow over a simple flat plate or through a pipe. (3). By the time you are worrying about the exact definition of y or y+, you will be doing the turbulence modeling research. (4). You can sort of cover it up by converting the y or y+ dependency into other variables other than y itself. Then there is no guarantee that it will work properly either. Internal turbulent flow modeling is a very difficult field.

For most lower Reynolds number turbulence model, you need to calculate turbulence Reynolds number based on distance from the wall for all cells. For Structured mesh, it is relatively easy because you normally know which wall a cell is attached to (for a channel flow having more than two walls, take the minimum distance).

For unstructured mesh, it's a bit more involved - you can store all wall boundary faces and for each cell calculate the distance from all walls, and then take the minimum distance.

(1). I think, the turbulence model is always associated with the boundary layer on a wall. Therefore, it will have to be computed on the per wall basis. (2). In other words, each wall has its own boundary layer, and thus each wall will have its own y or y+. (3). This will be another "black art" in CFD. (4). The principle is very simple. If one take the classical viscous/inviscid interaction approach, we can compute the inviscid pressure and velocity field first. Then with the pressure field, one can use it as the boundary layer edge condition to compute each boundary layer flow on its wall. And it does make sense to do so from physical point of view. (5). I don't think that the boundary layer development is a function of the minimum distance to a wall. For simple external flow, it is probably all right to use such distance, because there is only one wall there. In that case, the normal to the wall distance measured from the wall is a good definition of y or y+. (6). In flows with more than one object or wall, such minimum distance approach can not take care of the physics of the flow. This has been an important issue for the advanced CFD users, and the development of the so-called distance independent turbulence modelling research is still out there. (7). The suggestion here is: one has to study the problem individually, and define the y or y+ for each boundary layer on each wall. (8). By the way, wall boundary layer is not the only type of boundary layer flow, jet or wake mixing layers are also boundary layer type.

I am not sure whether it is the best choice to select the minimum length from the wall. Since all the wall may have effect on the flow, especially lengths from more then one walls are of the same magnititude order. What may be lucky is that wall effect is significant in a small region within the viscous (sub)layer. Hopefully, determination of y far from the wall is in-significant. I am reading more references. I give my newest choice here for discussion. Thanks