# UFR 3-18 Test Case

# 2D Boundary layers with pressure gradients (B)

Underlying Flow Regime 3-18 © copyright ERCOFTAC 2004

# Test Case

## Brief description of the study test case

The geometry is illustrated in Figure 1, comprising a straight inlet channel in which the flow is incompressible turbulent and fully developed.

Based on the inlet channel height, H, and centreline velocity , the Reynolds Number is 20,000.

The quality of the predictions are assessed by the

- Profiles of streamwise mean velocity U and Reynolds stresses u
^{2}, v^{2}and uv, normalised by the bulk velocity U_{b}and U_{b}^{2}, respectively, at axial stations x/H = -5.87, 5.98, 13.56, 16.93, 20.32, 27.09, 30.48 and 53.39, relative to the start of the 10^{o}inclined wall,

HH

- Pressure coefficient and skin-friction curves along the inclined (bottom) and straight (top) walls, indicating that separation occurs at approximately 7.4H, reattachment at approximately 30H,

Figure 1: 2D Plane Diffuser Geometry

## Test Case Experiments

Details descriptions of the test facility and measurement techniques are contained in [2,3].

The assessment parameters datasets summarized in section 3, above, are downloadable from

http://tmdb.ws.tn.tudelft.nl/workshop8.html

These data contain sectional mass flow information, indicating local errors of up to 10% in the re-circulation and downstream in the recovery region. The error is confirmed by the measured stream-wise velocity profiles, which are “fuller” than most of the computations. The latter are by definition are mass conservative. This could be an indication of significant flow unsteadiness in re-circulation bubble and near reattachment.

The measured pressure and skin-friction coefficients do not seem to suffer similar inconsistencies.

One study from [1] allays doubts as to any inconsistency in the assumed fully developed inflow, by varying the inlet Reynolds number between 5,000 and 100,000, reporting that this had “almost no effect on the separation and reattachment locations” predicted.

## CFD Methods

A complete overview of the CFD methods is contained in [1], and is summarized here for completeness.

Turbulence modeling was characterized in six groups, totaling 26 studies;

- Group A: linear k-ε models (Launder-Sharma, Chien, modified Chien, Launder-Spalding, Abe)

- Group B: linear baseline k-ω models (Menter-BSL, Wilcox (1988 and 1998)

- Group C: advanced linear models (new Wilcox 1998, Menter-SST, Gibson-Dafa q-z)

- Group D: non-linear k-ε models (modified Gatski-Speziale, Craft-Launder.Suga, Aspley-Leschziner, Speziale)

- Group E: non-linear k-ω models (modified and low-Re BSL)

- Group F: Reynolds stress closure, LES and spectral models (Gibson-Launder, Hanjalic-Jakirlic, dynamic SGS, S.C.I.T1)

All contributors followed the stated recommendations. The upstream boundary was placed at x/H < -5.87 with either a fully developed profile imposed, or computed directly by adding an inlet channel of 110H upstream. The outflow was placed at x/H > 74 in all cases except for the LES calculation, placed at x/H=39. The subsequent LES calculation reported [5] used an extended downstream domain, with inlet conditions imposed from a separate LES fully developed channel flow pre-cursor calculation.

All groups used 2D structured meshes, with the exception of the LES and spectral method studies, which adopted 3D structured and unstructured (tetrahedral) meshes, respectively. The near-wall spacing was carefully controlled to be suitable for the appropriate near-wall model adopted (low-Reynolds number or wall-function). Mesh dependency studies were carried out in 19 out of 26 cases.

Finite volume methods were used in all but one case, together with second-order or higher, centered or upwinded, spatial discretisation. The LES and Sprectral studies used 3^{rd} order Runge-Kutta and semi-implicit 1^{st} order temporal discretisation, respectively.

All calculations are clearly of high quality. Good cross correspondence between similar turbulence models was achieved. Many of the studies reported the use of CFD best practices and demonstrated insensitivities to uncertainties, particularly in boundary conditions.

In [4] a later study documents the performance of the V2F turbulence model, as implemented in commercial CFD codes, and using the SIMPLE-based algorithms for incompressible flows with 3^{rd} order spatial discretisation (QUICK) used on the momentum variables. Mesh structures and boundary conditions were consistent with those reported above.

© copyright ERCOFTAC 2004

Contributors: Fred Mendonca - Computational Dynamics Ltd