UFR 3-14 Test Case

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Flow over surface-mounted cube/rectangular obstacles

Underlying Flow Regime 3-14               © copyright ERCOFTAC 2004

Test Case

Brief description of the study test case

Figure 1 shows the general experimental set-up used by Martinuzzi & Tropea (1993). The rig is described in Section §4.

The experiments used for comparisons in most of the subsequent numerical simulations were obtained at a Reynolds number, based on channel mean velocity and obstacle height, of 40,000. Mean velocities and Reynolds stresses were measured both around the obstacle itself and in the wake, largely on the spanwise centre-line, and it is these which have provided most of the bases of comparison with numerical results. Reynolds stress data was sufficiently detailed to allow deduction of the turbulence kinetic energy - crucial for comparison with the output from many CFD codes - but direct measurements of the energy dissipation rate were not made. However, higher order moments of the fluctuating velocities were obtained, so that the more important turbulent transport terms in the kinetic energy equation could be derived, allowing dissipation to be estimated by difference (Hussein & Martinuzzi, 1996). The detailed velocity data is available as part of the Journal of Fluids Engineering database, and can be accessed at:

http://scholar.lib.vt.edu/ejournals/JFE/data/JFE/DB93-085

Together with the flow visualisation, these data also provided values for x_F and x_R, the location of centre-line separation and attachment points, respectively (Fig. 1). These can be viewed as important global parameters of the mean flow, for even apparently quite minor adjustments to a turbulence model can change them significantly, and thus constitute principle measured quantities which should be used for assessment of CFD calculations. In addition, as suitable characteristics of the flow field, mean velocity and turbulence profiles on the wake centre-line downstream of the obstacle should be used for assessment. Other measured data include the wall skin friction, both with the cube present and in its absence; these would provide further useful test data for CFD comparison. In fact, quantitative comparisons would provide a severe test of the way in which CFD wall boundary conditions are applied, but have thus far not been attempted, to this author's knowledge.

 

Figure 1 Sketch of the experimental arrangement.

Test Case Experiments

The channel shown in Figure 1 was positioned at the contraction outlet of an open, blower type air rig and had dimensions of 390 x 60 x5 cm (with 60 cm the spanwise width). The cube leading edge was placed 52 channel heights (2L) downstream of the inlet and the boundary layer was tripped at the inlet, so fully developed conditions were achieved at least 10 cube heights upstream of its front face. A two-component LDA system was used to obtain velocity and turbulence statistics and all three components were deduced (by orienting the channel either horizontally or vertically with respect to the axis of the three-beam system). Counter processors were used for data acquisition, with data rates typically between 500 and 4000 Hz and sample sizes between 30,000 and 100,000. Various measurements showed the upstream channel flow to be accurately two-dimensional over 85% of the channel width. Flow visualisation was performed (largely in a corresponding water-channel facility) and pressure measurements on the channel surfaces were obtained using 1.0mm diameter pressure taps.

Experimental uncertainties are discussed in Hussein & Martinuzzi (1996). Maximum errors in mean velocity and the Reynolds stresses, normalised by the bulk channel velocity, are quoted as 0.012, 0.00053, 0.0009 and 0.013 for U/U_B, (u² & v²)/U_B², w²/U_B² and uw/U_B², respectively. In terms of the measured quantities themselves these figures suggest that Reynolds normal and shear stresses are measured with an error lower than 1% and 2.6%, respectively, even in regions where the turbulent intensity is very high.

A number of validation experiments were undertaken. In particular, the on-coming fully-developed conditions were verified by comparing data at a number of axial stations well upstream of the cube; these showed no systematic change. The results were closely consistent with others in the literature for similar 2D channels. There were also no significant differences in profiles obtained at different spanwise locations within the range -18<z/H<18, corresponding roughly to 80% of the channel width - maximum variations in all measured quantities (principally mean velocity and Reynolds stress profiles) were within 2%. This is actually a little greater than the uncertainty associated with the LDA system and could be caused, for example, by slight variations in the channel height (which were within the manufacturing tolerance of 50±0.1mm) and/or positioning uncertainty in the traverse system, especially in the y-direction. A further check was provided by determination of the surface skin friction coefficient via the axial pressure gradient in the (far) upstream region; this agreed very closely with classical data. Likewise, symmetry in the cube wake was verified, with sample profiles up to 10h downstream of the cube trailing edge showing differences below 2% at different spanwise locations. We judge these various uncertainties in the data to be easily small enough to allow sensible comparisons with CFD results.

The well-characterised, fully-developed upstream conditions make the preparation of the required inlet conditions for a CFD computation particularly straightforward. Applying appropriate conditions at the other boundaries is also relatively easy. Even in the context of LES, precurser 2D channel flow computations can in principle provide appropriate time-dependent inlet conditions for the cube computations (see later).

CFD Methods

Numerous early RANS computations for this and related flows have been reported by Murakami and his co-workers (e.g. Murakami et al, 1987). These demonstrate many of the features since reported by other authors. Since it has become clear that high-quality LES is generally needed to obtain even adequate computations of flow over sharp-edged bodies, it is appropriate, for this review, to rely heavily on the report of the Rottach-Ergen LES Workshop held in 1995, prepared by Rodi et al (1997) and more recently discussed in Rodi (2002). RANS computations were included in the workshop comparisons and these were predominantly of k-e type, although with modifications in some cases. (The implications of these latter computations were similar in many respects to those of the earlier work of Murakami, noted above). All the major details are contained in the two Rodi papers so it is appropriate here to give only a few of the salient details.

For the RANS computations (originally reported by Lakehal & Rodi, 1997) both standard and two-layer k-ε models were used. The latter employs a one-equation model in the near-wall region, obviating the need to employ wall-functions but requiring a much finer grid there, to allow computation all the way to the wall. Runs were also undertaken for both types of model but with a modification (Kato & Launder, 1993 - the KL modification) which effectively suppresses the well-known, spurious production of too high a turbulent energy in regions of strong axial pressure gradient (e.g. in stagnation regions). The reports make no comment about grid dependency tests but in most computations second-order methods were used for convective terms, so it is likely that numerical errors were small. On the other hand, Rodi et al (1997) comment that 'there is not enough evidence to support the contention that refinement of the grid would not change the results' so some caution is clearly in order.

In the case of the LES, wall functions were applied in all cases. Some computations employed a dynamic sub-grid model (in which the smallest scales in the resolved field are used to determine the parameters of the sub-grid model), or a mixed model, rather than the more straightforward but physically cruder Smagorinsky model.

© copyright ERCOFTAC 2004

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Contributors: Ian Castro - University of Southampton

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