Developing turbulent flow in a 90 deg. curved duct of rectangular cross-section.
Duct with two straight and one curved sections.
Rectangular cross-section of the duct with a width of H=20.3 cm and a height of 6×H.
Inner radius of curvature of the bend:
R
=3×H.
Straight upstream section with a length of 7.5×H=1.52 m.
Straight downstream section with a length of 25.5×H=5.18 m.
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.
Air with a kinematic viscosity:
=1.45× 10
m²/s.
Freestream velocity at station U1 (x=-4.5×H): U
=16 m/s.
Reynolds number: UH/=224,000.
At station U1 (x=-4.5×H), 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 
=0.08×H and a friction coefficient of C
=.0038. The 2D wind-tunnel contraction
located 3×H 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.
/U
, 
/U 
/U 
/U² , 
/U²
, 
/U² 
/U² , 
/U²
² (deduced) (files su1in.dat, su1out.dat and su1up.dat) 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
diametre 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 C=2/
U².
Static pressure measurements using wall taps. The pressure coefficient is defined as 
=2(
-p)/U², where p is the static pressure at (0,0,3×H).
| () |
1.5% |
| (), () |
3% |
| () |
5% |
| (other
Reynolds stresses) |
10% |
The following measurements are available at 1 station upstream of the bend: U2 (x=-0.5×H); 3 stations along it: 15, 45, 75 and 2 stations downstream of it: D1 (x=0.5×H), D2 (x=4.5×H).
/U , /U /U /U² , /U²
, /U² /U² , /U²
² (deduced) (files s$in.dat,
sout.dat and s$up.dat) 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
30×H) 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:
mean secondary velocity vectors mean streamwise velocity, Reynolds
stress and k contour maps, normalized by U circumferential distribution of C In the symmetry plane, along the lateral walls:
distributions 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.
