## Numerical simulation of turbulent flows based on RANS with intermediate boundary conditions

Responsible: I.V.Egorov, A.V.Novikov, P.V.Chuvahov

Scientific interest of DAFE (Department of aerodynamics and flight engineering) team that is managed by professor Ivan V. Egorov splits into two closely coupled fields in the network of Flowmodellium laboratory of Moscow Institute of Physics and Technology (State University, MIPT). First of all the team is involved in turbulent flows modeling based on numerical solution of Reynolds Avaraged Navier – Stokes equations (RANS). Secondly, the team test a new concept of intermediate boundary conditions on the base of RANS modeling, which make it possible to considerably simplify calculating process.

It’s common knowledge that near-wall turbulent flows arise in a great deal of applications concerning viscous gas flows. In order to investigate those flows one can make use of both experimental and theoretical ways which enable to obtain liquid and gas flow regularities and, in particular, heat flux pattern. Unfortunately, there aquires rather small amount of information in aerodynamic experiment. That is why necessary for the profound understanding and realizing of a phenomenon under consideration is the calculating accompaniment to an experiment.

The most known approach is solving RANS. Here the mean values of calculated parameters are realized while fluctuations influence is taken into account by closing RANS equations with semiempirical turbulence closure. The models based on the concept of Reynolds averaging are widely used in applications. This approach possesses a number of advantages. It’s important to note the ability to catch phenomena physical points among them.

Egorov’s scientific group use their own software having developed previously and met the collaborate verification, that is for solving both full Navier – Stokes and RANS equations with (q – ω) closure by Coakley T.J. A great variety of problems have been studied so far by using this software, which are from simple fundamental problems (e.g. flow over a flat plate, a cone, ets.) up to sophisticated applications (e.g. numerical investigations of models in wind tunnels, movement of rockets and re-entry space vehicles, ets.). However concerning all those problems numerically one has to deal with very thin near-wall regions, which affect the outer flow to a considerable degree. This circumstance imposes dramatic restrictions on spatial and temporal resolution of numerical problems and often drastically impedes to gain the solution.

It’s well known that turbulent Reynolds number *Re _{t}* in near wall region is so low that turbulent effects turn out to be small compared with viscous effects. One of the most widespread ways to simplify turbulent near wall flow modeling is related with the use of so called wall functions. Firstly, this approach considerably reduces computing requirements owing to near-wall region resolution being coarser, which results in reducing the stiffness of the differential equations set. Secondly, wall function treatment is based on some empirical data, what let one take into account various flow aspects (e.g. roughness of the streamed surface). Nevertheless semiempirical formulation conceals different shortcomings because of the absence of universality in wall function concept.

However there exist models which are free from restrictions mentioned – Robin type near wall boundary conditions.

Rather effective is a method based on the computational domain decomposition into near-wall (inner) and outer subregions. On the base of the Calderon-Ryaben’kii potential theory it is possible to consider the near-wall problem independently on the outer one. The influence of the inner problem can exactly be represented by a pseudo-differential equation formulated on the intermediate boundary. In a 1D case, it leads to the wall function represented by Robin boundary condition, which can be determined either analytically or numerically. It is important that the wall functions (or boundary conditions) are mesh independent and can be implemented in a separate routine. Thus, the original problem can only be solved in the outer domain with some specific nonlocal boundary conditions called nonlocal wall functions.