Linear stability analysis reveals exclusion zone for sliding bed transport

Talmon, Arnold M.

doi:10.1515/johh-2015-0018

Abstract

A bend or any another pipe component disturbs solids transport in pipes. Longitudinal pressure profiles downstream of such a component may show a stationary transient harmonic wave, as revealed by a recent settling slurry laboratory experiment. Therefore the fundamental transient response of the two-layer model for fully stratified flow is investigated as a first approach. A linear stability analysis of the sliding bed configuration is conducted. No stationary transient harmonic waves are found in this analysis, but adaptation lengths for exponential recovery are quantified. An example calculation is given for a 0.1 m diameter pipeline.

Also consequences for long stretches of pipe line emerged. A so far undiscovered exclusion zone is found in the I-V diagram. This exclusion zone is situated adjacent to the deposit limit velocity locus curve. This simplified physical system reveals that flow velocities should be taken about 10% greater than the calculated maximum deposit limit velocity for stable converging flow.

References

Colwell, J.M., Shook, C.A., 1988. The entry length for slurries in horizontal pipeline flows. Canadian J. Chemical Engineering, 66, 714-720.10.1002/cjce.5450660503
Search in Google Scholar
Jones, T.F., 2011. A spreadsheet version of the two-layer model for solid-liquid pipeflow. In: Proc. 15th Int. Conf. Transport & Sedimentation of Solid Particles, Wroclaw, Poland, pp. 101-114.
Search in Google Scholar
Kaushal, D.R., Tomita, Y., 2013. Prediction of concentration distribution in pipeline flow of highly concentrated slurry. Particulate Science and Technology, 31, 1, 28-34.10.1080/02726351.2011.639045
Search in Google Scholar
Kaushal, D.R., Sato, K., Toyota, T., Funatsu, K., Tomita, Y., 2005. Effect of particle size distribution on pressure drop and concentration profile in pipeline flow of highly concentrated slurry. Int. J. Multiphase Flow, 31, 7, 809-823.10.1016/j.ijmultiphaseflow.2005.03.003
Search in Google Scholar
Krupička, J., Matoušek, V., 2010. Modeling of settling-slurry around deposition-limit velocity. In: Proc. Hydrotransport 18, 22-24 September, Rio de Janeiro, Brazil, pp. 143-154.
Search in Google Scholar
Matoušek, V., 2004. Dredge pumps and slurry transport. Lecture notes OE4625, Delft University of Technology.
Search in Google Scholar
Matoušek, V., 2009. Predictive model for frictional pressure drop in settling-slurry pipe with stationary deposit. Powder Technology, 192, 367-374.10.1016/j.powtec.2009.01.017
Search in Google Scholar
Matoušek, V., 2014. Personal communication.
Search in Google Scholar
Matoušek, V., Krupička, J., 2013. Different types of unsteady flow of solids generated in laboratory slurry loop. In: Proc. 16th Int. conf. Transport & Sedimentation of Solid Particles, Rostock, Germany, pp.19-32.
Search in Google Scholar
Matoušek, V., Krupička, J., 2014. One-dimensional modeling of concentration distribution in pipe flow of combined-load slurry. Powder Technology, 260, 42-51.10.1016/j.powtec.2014.03.070
Search in Google Scholar
Matoušek, V., Krupička, J., Penik, V., 2014. Distribution of medium-to-coarse glass beads in slurry pipe flow: evaluation of measured concentration profiles. Particulate Science and Technology, 32, 2, 186-196.10.1080/02726351.2013.840706
Search in Google Scholar
Talmon, A.M., 1999. Mathematical analysis of the amplification of density variations in long-distance sand transport pipelines. In: Proc. Hydrotransport 14, BHRG, Cranfield, UK. BHRG Cranfield UK, Maastricht, the Netherlands, pp. 3-20.
Search in Google Scholar
Wilson, K.C., 1979. Deposit-limit nomograms for particles of various densities in pipeline flow. In: Proc. Hydrotransport 6, BHRG, Cranfield, UK. BHRG Cranfield UK, Canterbury, UK, pp. A1-A12.
Search in Google Scholar

Linear stability analysis reveals exclusion zone for sliding bed transport

Abstract

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