# 8.17: Conclusions and Discussion

- Page ID
- 32341

The DHLLDV Framework is explained for determining head losses and the Limit Deposit Velocity based on uniform sands and gravels and a spatial volumetric concentration. Using a holdup function, the delivered concentration head loss curve(s) can be determined and from there the bed height. By means of superposition, after some adjustments of the liquid properties, the head loss curve(s) for graded sands and gravels can also be determined. The full DHLLDV Framework is more complicated and detailed as described here and would require a multiple of pages. On the website www.dhlldv.com many additional graphs can be found and the latest developments will be shown after being published, including a list of papers about this subject.

The choice of basing the model on spatial volumetric concentration and uniform sands or gravels enables an explicit formulation for the different sub-models.

The criteria determining heterogeneous flow or sliding flow still require more investigation, although they match the Doron & Barnea (1993) experiments and the SCR model. Concentrations of 4.2% and 5% of their experiments clearly show heterogeneous behavior, while all higher concentrations show sliding flow behavior.

The method for graded sands is promising, but may need some fine tuning. Unfortunately there is not much experimental data available, while only Wasp (1963), Kaushal & Tomita (2002C) and Sellgren & Wilson (2007) developed models for graded PSD’s.

The DHLLDV Framework has been compared with the Wasp (1963), the Wilson et al. (1992), the Kaushal & Tomita (2002C) and the SCR model, as well as many more from literature, with good results. In addition the model compares well to a wide range of experimental data from literature. These comparisons are also available on the website.

The DHLLDV Framework enables the user to implement user defined sub models for the different flow regimes, for the holdup function, for the bed height function and for the concentration distribution function.

The DHLLDV Framework gives a reference Framework for slurry flow in horizontal pipes and inclined pipes.