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Research Papers: Fundamental Issues and Canonical Flows

Experimental Investigation Into the Relationship Between the Roughness Height in Use With Nikuradse or Colebrook Roughness Functions and the Internal Wall Roughness Profile for Commercial Steel Pipes

[+] Author and Article Information
K. K. Botros

Fluid Dynamics Department,
Centre for Applied Research,
NOVA Chemicals,
2928-16 Street NE,
Calgary, AB T2E 7K7, Canada
e-mail: kamal.botros@novachem.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 24, 2015; final manuscript received January 18, 2016; published online April 22, 2016. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 138(8), 081202 (Apr 22, 2016) (8 pages) Paper No: FE-15-1763; doi: 10.1115/1.4032601 History: Received October 24, 2015; Revised January 18, 2016

The relationships between the sand grain roughness height (ks) in use with Nikuradse or Colebrook correlations for the roughness function (RF) and the internal pipe wall roughness element described by the root-mean-square (RMS) of the roughness profile (Rq) for turbulent flow in pipes are experimentally examined. Flow tests were conducted on a total of 13 commercial steel pipes of two sizes: 168.3 mm and 114.3 mm outer diameter (OD). The aim was to provide further insight into relationship between ks and Rq, for use with either RF correlations. The tests were conducted on high-pressure pipeline quality natural gas in the range of Reynolds number (based on pipe internal diameter) of 9 × 106–16 × 106. For commercial carbon steel pipes, the relationship between ks and Rq was found in the form ks=1.306Rq+0.078Rq2 and ks=2.294Rq (both ks and Rq in μm), for use with Colebrook and Nikuradse RF correlations, respectively. These correlations cover a wide range of Rq from 2.7 μm to 12.5 μm which is typically found in commercial carbon steel pipes. For stainless steel (SS) pipes, preliminary results indicate that other surface roughness profile parameters need to be employed to better define the values of ks for these types of commercial steel pipes.

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Figures

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Fig. 1

Nikuradse and Colebrook RFs versus roughness Reynolds number (ks+)

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Fig. 2

Schematic of the test setup for the 114.3 mm OD pipes (top) and the 168.3 mm OD pipes (bottom). The test section is the part between the two indicated differential pressure measurement ports shown with two circles and marked A (upstream) and B (downstream). All dimensions are in millimeter.

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Fig. 3

Measured roughness parameters of the 13 pipes tested in the present work—error bars represent ±95% confidence intervals

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Fig. 4

Plot of friction factor versus Re for the example pipe #1 test data

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Fig. 6

Results of the measured friction factor (λ) and corresponding Colebrook curves passing through each data point of the 13 tested pipes

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Fig. 7

Results of the experimentally extracted Colebrook equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq), based on the present test data on the 11 commercial steel pipes, and comparison with Langelandsvik et al. [2] and Shockling et al. [5] data points

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Fig. 8

Results of the experimentally extracted Nikuradse equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq) based on the present test data on 11 commercial steel pipes

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Fig. 9

Results of the experimentally extracted Colebrook equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq), based on the present test data on the two SS pipes #6 and #13

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Fig. 10

Comparison between the roughness elements of pipe #6 (SS) to pipe #11 (carbon steel); both have the same Rq but pipe #6 has much lower RSm than pipe #11

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Fig. 5

Experimental results of the RF, ΔU+, superimposed on Colebrook and Nikuradse RF (labels indicate pipe #)

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