Flow over surface-mounted cube/rectangular obstacles

Underlying Flow Regime 3-14 © copyright ERCOFTAC 2004

Evaluation

Comparison of CFD calculations with Experiments

Detailed comparisons are contained in the Rodi reports. These include centre-plane streamline plots, some velocity profiles both above and downstream of the cube and some of the global parameters like x_F and x_R (separation and attachment locations). Figures 2 and 3 are taken from Rodi (2002) and Rodi et al (1997), respectively, and compare streamline patterns and velocity profiles with different models.

The LES solutions are generally significantly closer to the experimental results than k-ε solutions. The point is emphasised in Table 1, which shows separation and attachment locations. X_T is the location of shear layer attachment on the roof of the cube; the experimental evidence suggests that this does not occur so models which produce it are in that sense deficient. Notice that k-ε models, even those which use the KL modification, produce much too long a downstream separation region. In fact, the modified model actually leads to a worse prediction in this sense than the standard k-ε model.

It is unfortunate that no comparisons between surface pressures are available from this workshop. However, in a paper from Murakami's group, Tsuchiya et al (1997) compared measured cube surface pressure distributions from another experiment (see §2 above) with various RANS computations and it appears that KL type modifications lead to quite good agreement between computation and experiment, see figure 4. But only minimal flow field data is shown and there is evidence that the computed length of the downwind separation region is no closer to the experimental result than was reported by Rodi for RANS computations. This seems not inconsistent with the 'inverse' of the point made by Shah & Ferziger (1997) (noted in §2 above), i.e. that adequate computation of the surface pressure field does not necessarily imply adequate computation of the velocity field. We repeat again here their statement that 'to validate a method solely by its ability to predict the velocity distribution about a single object is dangerous; relying on the pressure distribution alone is surely of no value whatever'. From a Wind Engineering perspective, one might sometimes be quite satisfied with adequate surface pressure computation (if one is only interested in forces) but clearly, if processes like pollutant dispersion in the wake or pedestrian winds around the building are of interest, then being confident about the surface pressure computations is evidently not enough to engender confidence about the flow field results.

MODEL	COMMENT	x_F	x_T	x_R
Experiment	Martinuzzi & Tropea (1993)	1.040		1.612
LES (UKAHY3)	Smagorinsky sub-grid model	1.287		1.696
LES (UKAHY4)	Dynamic sub-grid model	0.998		1.432
LES (UBWM2)	Samgorinsky	0.808	0.837	1.722
LES (IIS-KOBA)	Smagorinsky (short averaging)	0.835	0.814	1.652
RANS (k-ε)	Standard model	0.651	0.432	2.182
RANS (k-ε)	KL modification	0.650		2.728
RANS (k-ε)	Two-layer model	0.950		2.731
RANS (v²-f)	Unsteady computation (Durbin)	0.732		1.876
RANS (v²-f)	Steady (Durbin)	0.640		3.315

Table 1. Upstream separation point (x_F), top attachment point (x_T) and rear attachment point (x_R) from various turbulence models and compared with the experimental values.

Figure 2. Mean flow streamlines on the centre-plane (left) and near the channel floor (right). Model notation as in Table 1.

Figure 3. Mean (centre-plane) velocity profiles over the centre of the cube (a) and in the wake (b). Notation as in Table 1.

Figure 4. Comparison of mean cube surface pressures on the centre-plane, from Tsuchiya & Murakami (1997). Note that the MMK model is a variant of the LK modification to the standard k-'ε model and has very similar effects. The experiment is reported (very briefly) in Murakami et al (1990).

It is worth mentioning that a few workers have been able to employ unsteady RANS methods to obtain more satisfactory results. Iaccarino & Durbin (2000), for example, have used Durbin's (1995) turbulence model in an unsteady computation of the cube-in-a-channel problem and obtained very good agreement with the steady flow field found in the experiments. Data for this calculation are included in Table 1. No pressure comparisons were made, however. Note that a steady computation with the same model yielded results as bad as found in the other (k-ε-based) RANS computations. One of the reasons that LES does so much better for this problem is that some quasi-periodic shedding of vorticity from the side walls of the cube is observed in experiments. This enhances the exchange of momentum in the wake, thus reducing the length of the separated region. Steady RANS methods cannot account for this process, but this feature of the flow may be one of the reasons why the unsteady RANS solution of Iaccarino & Durbin does so much better. As might be expected from this argument, it should be noted that higher order (steady) RANS closures, like algebraic stress closures or full differential second-moment closures, fare no better than the simpler eddy-viscosity closures in predicting the downwind flow field (as shown by Murakami & Mochida, 1999, for example).

It should also be noted that it is unclear to what extent the fairly ubiquitous use of standard wall functions in nearly all the computations may have degraded the accuracy of the computations. It is well known that in strongly adverse pressure gradient regions (i.e. near separation) and certainly within separated regions, the 'classic' log-law relationship for mean velocity does not hold. Wall functions cannot, therefore, capture the appropriate physics of the near-wall region. But in flows, like this one, where the global parameters are dominated by the influence of the unsteady, large eddy motions, it could be argued that the precise nature of the wall condition is not likely to be too critical. As yet, however, there is little proof of this assertion.

Contributors: Ian Castro - University of Southampton