## Turbulence near-wall flow modelling

Team leaders: А. Аleksin (DSc), F.А. Mаximov (DSc)

Using the methods of computational aerodynamics applied to the Euler, boundary layer and Navier-Stokes equations the approaches to the design of flying vehicles are presented. Influence of the free-stream parameters, flow regime, separation and vortex structures on the aerodynamical properties of the flying vehicles is investigated. The calculations are carried out on multi-processor machines.

In order to solve certain aerodynamical problems the development of mathematical methods of near-wall turbulence flow modelling is carried out. For a closure of the sets of the averaged boundary layer and RANS equations the semi-empirical turbulent models are considered. The one- and two-parametric differential models, foundational turbulence hypothesis, systems of the equations complemented by the initial and boundary conditions are introduced. To describe the laminar-turbulent transition the various approaches to account for laminar and turbulent transfer interaction near hard surface as applied to turbulent models for compressible viscous media. The problems of differential model modification for the supersonic flows under intensive heat transfer with the surfac, the limits of their applicability defined by the free-stream parameters and wall conditions are investigated.

Under high-free-stream turbulence intensity conditions the dynamics and heat characteristics of the steady-state and unsteady near-wall flows are computed on the basis of available differential turbulent models. Under longitudinal pressure gradient influence of the free-stream parameters on the development of the flow and heat processes in the steady-state fully turbulent boundary layer is analyzed. For the oscillating time-periodic external flow velocity the possibility of theoretical description of the turbulent flow regime by a quasi-stationary turbulence model is shown.

Supersonic flow around the sharp cone at the moderate incidence is modelled on the basis of Navier-Stokes equations in the thin-layer approximation using the relaxation method on time. The computations are carried out using parallel computers and mutil-grid/multi-mesh methods. Influence of the free-stream parameters on the flow pattern at turbulent regime is researched. For different Reynolds numbers the details of flow character and valuation of the aerodynamics characteristics are obtained on the basis numerical computations.

Pictures 1, 2. The flow on the leeward side of a cone for its half-angle 10о at an angle of incidence 20^{о} (М=3, Re=1.5*10^{5} and 1.5*10^{6}) in terms of density isolines and streamlines of transverse flow.

pic. 1 | pic. 2 |