Analysis of flow changes in a diffuser boundary layer in terms of the maximum stability of averaged turbulent flows

Abstract

Changes in velocity profiles were investigated experimentally in a turbulent boundary layer at a diverging wall in a flat asymmetrical diffuser duct.For attached flow in the duct, it is shown that the velocity distribution follows the same universal logarithmic function as for a flow with a zero pressure gradient; as the divergence angle of the duct is increased, the value of the constant in this function decreases downstream.It is also shown that flow separation is a transition to a new stable state, when the classic flow at the wall boundary layer cannot adequately counteract the positive pressure gradient which is determined by the duct geometry.1. Depending on the nature of the reaction to the positive pressure gradient, the turbulent boundary layer can separate into two flow regions: an inner wall region (Y = y/~ < 0.2) and an external region (Y > 0.2). Here y is the distance from the wall, and ~ is the physical thickness of the boundary layer. Three main flow zones are distinguished near the wall [I]: a viscous sublayer next to the wall; a transition zone, where viscous friction forces are on the same order as the turbulent stresses of Reynolds friction; and an inner turbulent region, which occupies 10 to 20% of the thickness of the boundary layer according to various estimates, where the velocity distribution follows a universal logarithmic law u-5,751g(~-) +C.(1.1)Here U is the longitudinal component of the average velocity at a distance y from the wall; u~ = (~,/p)I/2 is the dynamic velocity; r~ is the tangential stress at the wall; p is the density; v is the kinematic viscosity; and the constant C depends on the surface state (C = 5.5 for hydraulically smooth surfaces).The time for the outer part of the layer to react to a local pressure gradient dP/dx is finite and corresponds to the displacement of the flow by tens of boundary-layer thicknesses. Therefore the velocity distribution in this region depends both on local conditions and on previous flow developments, so there is no fixed relationship between the shape of the velocity profile and the local value of dP/dx. The so-called equilibrium boundary layers are an exception; their existence under positive pressure gradients was first observed by Clauser [2].For a given pressure distribution, the velocity distribution for equilibrium layers corresponds to the functionwhere U~ is the velocity at the outer edge of the boundary layer and ~1 is the thickness of the displacement. The part of the layer next to the wall reacts very quickly to flow perturbations on the wall side [3], but returns to the conditions of unperturbed flow just a short distance into the flow from the origin of the perturbation. At the same time, external perturbations, including a positive pressure gradient, have no effect on the wall flow within limits. The proof of this is that the velocity distribution at the wall maintains universal conditions of similitude for large positive pressure gradients [4].Moscow.