The initially 2D boundary layers developing on the vertical lateral walls are subjected to strong streamwise curvatures and associated pressure gradients along the bend. On the other hand, the pressure-driven secondary motion in the corner regions eventually leads to the formation of a longitudinal vortex on the convex wall. The duct aspect ratio is such that these two features of the flow develop more or less independently, without interaction.
At station U1 (x = -4.5H), the velocity is uniform in the core flow, outside the boundary layers, within a deviation less than 1%. On the vertical lateral walls, the boundary layers are of flat-plate type with a momentum thickness Reynolds number of 1650, a boundary layer thickness of = 0.08H and a friction coefficient of Cf = 0.0038. The 2D wind-tunnel contraction located 3H upstream of U1 introduces a secondary motion in the boundary layers on top and bottom flat walls but its magnitude reaches only 5% of the freestream velocity. The following measurements are then provided for a slightly three-dimensional duct flow but are sufficiently detailed to be used as inlet conditions.
Hot-wire velocity measurements have been carried out using a miniature X-wire probe for the turbulence quantities.
Mean velocity measurements have been carried out using a five-hole pressure probe of a diameter of 3 mm.
All velocity measurements have been made in the upper half of the duct divided into 5 different domains, namely in1, up1, ou1, in2, ou2 (see file readme).
Wall stress measurements using two pressure probes in combination (only the magnitude is actually measured). The friction coefficient is defined as Cf = 2/(Uo2).
Static pressure measurements using wall taps. The pressure coefficient is defined as Cp = 2(p - po)/(Uo2), where po is the static pressure at (0,0,3H).
|(other Reynolds stresses)||10%|
The following measurements are available at 1 station upstream of the bend: U2 (x=-0.5H); 3 stations along it: 15, 45, 75 and 2 stations downstream of it: D1 (x=0.5H), D2 (x=4.5H).
The following measurements are available along the inner and the outer walls, in the plane of symmetry.
The calculation of the duct flow should be started at station U1 using the experimental values provided as inlet conditions. The non-measured quantity may be assumed as negligible.
Due to geometric symmetry with respect to the z=0 plane, one can use a computational domain including only the upper half of the duct.
The outlet should be placed sufficiently far away (x > 30H) so that zero gradients may be assumed for the flow variables.
The following results should be plotted and compared with the data:
At all locations:
In the symmetry plane, along the lateral walls:
Sotiropoulos and Patel (ref 3.) have performed calculations of this case with the two-layer k- model using two different numerical methods: the "finite-analytic" and a finite-difference method. In both cases, the overall structure of the flow is well predicted but both the strength of the secondary motion, and consequently its effect on the streamwise flow development, and the effects of wall curvature on the turbulence within the lateral boundary layers are underestimated.
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