DNS 1-3 Description

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Introduction

The 3D (Stanford) Diffuser is a well documented case with complex internal corner flow and 3D separation while having a relatively simple geometry. It has an inlet section, an expansion section and an outlet section (see Figure 1). The flow at the inlet is assumed to be a fully developed rectangular channel flow. At the outlet, standard Dirichlet condition for the pressure is prescribed. An inflow Reynolds number of 10000 is considered based on the duct height and the flow is considered to be incompressible. The following DNS data has been obtained using the in-house Finite Element Method (FEM) code Alya developed at BSC.

Review of previous studies

The only high-fidelity data available is the DNS performed by Ohlsson et al. (2010). This DNS had a Re=10000 and a simplified diffuser and was solved using a spectral element code with 11th order polynomials. Their calculations were performed on the Blue Gene/P at ALCF, using 32768 cores and 8 million core hours. Another computation was performed on the cluster “Ekman” at PDC, Stockholm, Sweden, using 2048 cores and a total of 4 million core hours, also at the reduced Reynolds number 10000 and with the simplified geometry. The flow was computed for 13 flow-through-times (based on the bulk inlet velocity and diffuser length) before gathering statistics. The statistics were gathered over an additional 21 flowthrough-times.

Description of the test case

The diffuser studied is the UFR_4-16_Test_Case, Diffuser 1 provided in the ERCOFTAC database.

Geometry and flow parameters

The diffuser shape, dimensions and the coordinate system are shown in Fig. 1 (reproduced from UFR 4-16 Test Case).

Figure 1: Geometry of the 3-D diffuser 1 considered (not to scale), Cherry et al. (2008); see also Jakirlić et al. (2010a)

For the current diffuser, the upper-wall expansion angle is 11.3° and the side-wall expansion angle is 2.56°. The flow in the inlet duct (height h=1 cm, width B=3.33 cm) corresponds to fully-developed turbulent channel flow. The L=15h long diffuser section is followed by a straight outlet part (12.5h long). Downstream of this the flow goes through a 10h long contraction into a 1 inch diameter tube. The curvature radius at the walls transitioning between diffuser and the straight duct parts are 6 cm. The bulk velocity in the inflow duct is ${U_{\textrm {bulk}}=U_{\textrm {inflow}}=1m/s}$ in the x-direction resulting in the Reynolds number based on the inlet channel height of 10000. The origin of the coordinates (y=0, z=0) coincides with the intersection of the two non-expanding walls at the beginning of the diffuser's expansion (x=0).

Boundary conditions

The inflow is set to $U=1$. Turbulence is triggered by creating a small discontinuity in the form of a small chevron in the channel. The exit is set to $dU/dn=0$ while the walls of the channel and the diffuser are set to no slip.

References

1. Ohlsson, J., Schlatter, P., Fischer P.F. and Henningson, D.S. (2009): DNS of three-dimensional separation in turbulent diffuser flows. In Advances in Turbulence XII, Proceedings of the 12th EUROMECH European Turbulence Conference, Marburg. Springer Proceedings in Physics, Vol. 132, ISBN 978-3-642-03084-0
2. Ohlsson, J., Schlatter, P., Fischer P.F. and Henningson, D.S. (2010): DNS of separated flow in a three-dimensional diffuser by the spectral-element method. J. Fluid Mech., Vol. 650, pp. 307–318

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Contributed by: Oriol Lehmkuhl, Arnau Miro — Barcelona Supercomputing Center (BSC)

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