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   The Delft Head Loss & Limit Deposit Velocity Framework (DHLLDV)

In August 2012 I was approached by a dredging company with the question which head loss model to use for a project with a cutter dredge and a discharge length of 35 km.

What did the company want to know?

  1. How many booster stations to use.
  2. What should be the locations of the booster stations.

What were the real issues?

  1. What should be the total pump pressure to avoid plugging the line.
  2. Where to locate the booster stations to avoid cavitation at the entrance of each pump.
  3. How does this depend on the particle size distribution.

These questions trigerred a study in to the existing head loss models. With the knowledge that the main Dutch and Belgium dredging contractors use the Durand & Condolios (1952) and Fuhrboter (1961) models in a modified form, while companies in the USA often use the Wilson (1992) model in a modified form and in Canada the Saskatchewan Research Council model (SRC), the study started with a comparison of these models. Other models that were investigated were the Newitt et al. (1955) model, the Doron & Barnea (1987) model, the Matousek (1997) model and others. Also later models like the 4 component Sellgren & Wilson (2012) model and the 2LM and 3LM models of Wilson (1979-2014) and Matousek (1997-2014) are investigated.

Usually the models perform well in the neighbourhood of the parameters used during the experiments, especially the pipe diameter (small) and the particle diameter, but for real life conditions (large pipe diameters) the models deviate and it's not clear which model matches these conditions. Another issue is that most models are derived for transport volumetric concentrations as input and not the spatial volumetric concentrations. The research into the existing models did not give a satisfactory result.

Reason to develop a new model from scratch, the Delft Head Loss & Limit Deposit Velocity Framework. This DHLLDV Framework is based on the spatial volumetric concentration in the pipe and uniform sands or gravels and consists of a framework containing 12 sub-models.

  1. The fixed or stationary bed model (FB).
  2. The sliding bed model (SB).
  3. The heterogeneous transport model (He).
  4. The homogeneous transport model (Ho).
  5. The sliding flow model (SF).
  6. The limit deposit velocity model (LDV).
  7. The holdup or slip factor model.
  8. The concentration distribution in the pipe.
  9. The transition heterogeneous-homogeneous flow.
  10. The bed height model.
  11. Graded sands & gravels.
  12. Inclined pipes.

The Limit Deposit Velocity divides particles into 5 regions. For each region different physics is used.

The 7th model transforms constant spatial volumetric concentration curves into constant transport volumetric concentration curves.

The concentration distribution is based on the LDV, since at the LDV the bottom concentration has to be the bed concentration.

The transition heterogeneous-homogeneous is at operational conditions for medium sands and requires special attention.

The bed height is also based on the LDV (bedheight zero) and on the holdup function.

The curves for graded sands or gravels are constructed by proportional summation of the curves of the different fractions after adjusting the liquid properties for the fines content.

A last addition is the influence of pipe inclination.

If you like to know more about the DHLLDV Framework, go to DHLLDV in the menu. Over time more information will be added to this website and more publications will follow.

The model is published in a book and is available on ResearchGate.

Constant spatial and delivered concentration curves for uniform and graded sands

Pipe diameters ranging from 1 inch to 1.2 m, particles of 0.5 mm 

Grading d50/d15=d85/d50=4

Now with Excel Workbook, see Publications.

For questions, remarks and requests contact S.A. Miedema, email:

Delft University of Technology (Top-Right)

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We noticed that many visitors like to view and/or download the many papers we show on this site. We will try to put more interesting publications on this website whenever we encounter it.


 Last articles added
06A The Relative Excess Hydraulic Gradient, Graded Sands & Gravels, Cvs
10 Comparing Heterogeneous Models based on the Relative Excess Hydraulic Gradient
11: Dp=1.1000 m, Wasp, Wilson & SRC versus DHLLDV
10: Dp=1.1000 m, A Comparison Of Different Models
06: Dp=1.1000 m, The Transition Heterogeneous-Homogeneous Flow Regimes

 Last pages
Dp=0.0254 m (1 inch)
Dp=0.0508 m (2 inch)
Dp=0.1016 m (4 inch)
Dp=0.1524 m (6 inch)
Dp=0.2032 m (8 inch)

 Top pages
1. 1976 Thomas
71577 Hits
2. Summary with 6 pipe diameters
53439 Hits
3. 1978 Kazanskij
51339 Hits
4. 1955 Newitt et al.
49713 Hits
5. 1960 Gibert
44654 Hits
6. 1952 Durand & Condolios
44580 Hits
7. 1958 Silin et al.
41849 Hits
8. 3 Layer Model + Download Excel Workbook
39973 Hits
9. Dp=1.1000 m (about 44 inch)
38555 Hits
10. 2 Layer Model
38317 Hits

The Delft Sand, Clay & Rock Cutting Model (DSCRC) 
The Delft Head Loss & Limit Deposit Velocity Framework (DHLLDV) 

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