UFR 4-10 Evaluation

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Natural convection in simple closed cavity

Underlying Flow Regime 4-10               © copyright ERCOFTAC 2004

Evaluation

Comparison of CFD calculations with Experiments

There are available a number of useful review articles and comparative studies regarding both the specific test case chosen here [3, 5] and other very similar cases. The complexity and variety of physical phenomena encountered in turbulent buoyant flows and the wide variety of approaches applied make it difficult to draw absolute general conclusions, however some general principles emerge. In general, while mean velocity and temperature fields seem to be quite well predicted even with rather simple models, the prediction of the heat transfer rate (usually expressed as a Nusselt number), which is in general the quantity of most interest, is much more problematic. The fluctuating quantities are usually only well predicted by the more advanced models.

One of the earliest successful simulations of turbulent flow in a tall cavity was that of Ince and Launder [38] in 1988 which consisted of the following main components:

• Launder-Sharma low-Re k-ε model [41];

• Yap length-scale correction in ε equation [41];

• Daly and Harlow GGDH used to calculate turbulent heat flux but only in the buoyancy term of the turbulence production source.

Ince and Launder applied this model to the tall cavity of Betts and Dafa’Alla [4] which has a very similar arrangement (with the same aspect ratio) to the present case and were able to obtain quite reasonable agreement with the experiments, summarised in Table 2. Earlier Betts and Dafa’Alla [4] had applied the Launder-Sharma k – ε model to their own experimental case but without the Yap correction and GGDH treatment, giving much less promising results, which can also be seen in the table.

It can be seen in that the improvement comes mainly from the use of the Yap correction with a small effect from the use of the GGDH. The Yap correction was originally proposed to overcome shortcomings in the ε equation for separated flows and Ince and Launder [38] suggest that the reason for its effectiveness in the tall cavity flow is that the high turbulence levels in the centre of the cavity lead to strong diffusion of turbulence towards the wall, similar to that observed in separated flows.

Table 2: Comparison of predicted values for tall cavity case of Betts and Dafa’Alla (data taken from [38]).

Data	Nu	Max. vertical velocity at mid-height (cm/s)
Experiment [4]	4.9	11.40
LS k-ε model	6.53	8.96
LS k-ε model + Yap correction	4.66	12.40
LS k-ε model + Yap + GGDH	4.74	12.10

Dol et al. [19] applied three different RANS approaches to the simulation of flow at the half-height of the Betts and Bokhari cavity considered here. The calculations were one-dimensional and comparisons were also made with the DNS data of [6] and [63]. The models they applied were as follows:

• Eddy-viscosity model (low-Re k – ε model with Yap-type correction and eddy diffusivity);

• Low-Re four-equation (k, ε, , ε) model with Rodi ASM for Reynolds stresses and anisotropic algebraic flux model for turbulent heat fluxes;

• Reynolds stress transport model.

They found that the mean temperature and vertical velocity were well predicted by all of the models considered however much more variation was observed in the prediction of the turbulence quantities. The EVM, which assumes pure gradient diffusion, gives a reasonable prediction of the horizontal turbulent heat flux but predicts a zero vertical heat flux (there is no vertical mean temperature gradient) and strongly overpredicts the temperature variance (by a factor of more than two). In contrast the two anisotropic approaches gave more realistic levels, though not without significant shortcomings.

Similar conclusions can be drawn from the other studies reviewed in the [U4-10exp.htm#cfd_methods_9 CFD methods] section both for the present case and other simple cavity flows. Simple eddy-viscosity models with low-Re modifications can give surprisingly good results for mean temperature (and therefore Nusselt number) and vertical velocity but this success disguises serious shortcomings which would lead these models to fail in more complex situations. It can also be observed however that the use of a more advanced anisotropic model is no guarantee of an improved prediction of the mean temperature and velocity field and the terms employed in these models should be examined carefully, as discussed for example in [31].

© copyright ERCOFTAC 2004

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Contributors: Nicholas Waterson - Mott MacDonald Ltd

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References