{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:24:44Z","timestamp":1760235884671,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,2]],"date-time":"2021-10-02T00:00:00Z","timestamp":1633132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Science and Technology Project of ENERGY CHINA","award":["GSKJ2-W01-201"],"award-info":[{"award-number":["GSKJ2-W01-201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A two-dimensional numerical model for solving the Navier\u2013Stokes equations was developed to investigate the local scour around a submarine pipeline with a spoiler. Both the suspended load and the bed load were considered in the present numerical model. The focus of the present study is to investigate the effects of the spoiler length on the hydrodynamic forces on the pipeline and the spoiler as well as the local scour around the submarine pipeline. The corresponding numerical results show that the mean drag coefficients of the pipeline and the spoiler increase with the increase of the spoiler length. As for the mean lift coefficient, a general decreasing trend with the increasing spoiler length is observed for the pipeline. However, the mean lift coefficient of the spoiler first increases and then decreases with the increasing spoiler length. In addition, it is found that a larger spoiler length leads to a deeper scour depth, and an empirical equation was proposed for predicting the non-dimensional scour depth of submarine pipelines with non-dimensional spoiler length based on the numerical results.<\/jats:p>","DOI":"10.3390\/sym13101847","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1847","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Numerical Study of Local Scour around a Submarine Pipeline with a Spoiler Using a Symmetry Boundary Condition"],"prefix":"10.3390","volume":"13","author":[{"given":"Chuan","family":"Zhou","sequence":"first","affiliation":[{"name":"China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou 510663, China"},{"name":"Guangdong Kenuo Surveying Engineering Co., Ltd., Guangzhou 510663, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianhua","family":"Li","sequence":"additional","affiliation":[{"name":"China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou 510663, China"},{"name":"Guangdong Kenuo Surveying Engineering Co., Ltd., Guangzhou 510663, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou 510663, China"},{"name":"Guangdong Kenuo Surveying Engineering Co., Ltd., Guangzhou 510663, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoqiang","family":"Tang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,2]]},"reference":[{"key":"ref_1","unstructured":"Breusers, H.N.C. (1972). Local Scour Near Offshore Structures, Delft Hydraulics Laboratory. Publication No. 105."},{"key":"ref_2","unstructured":"Kjeldsen, S.P., Gjorsvik, C., Bringaker, K.G., and Jacobsen, J. (1973, January 27\u201330). Local scour near offshore pipelines. Proceedings of the Second International Conference on Port and Ocean Engineering Under Arctic Conditions (POAC), Reykjavik, Iceland."},{"key":"ref_3","unstructured":"Denness, B. (1984). Interaction between pipelines and the seabed under the influence of waves and currents. Seabed Mechanics, Springer Science and Business M edia LLC."},{"key":"ref_4","unstructured":"Ibrahim, A., and Nalluri, C. (1986, January 13\u201318). Scour prediction around marine pipelines. Proceedings of the 5th International Symposium on Offshore Mechanics and Arctic Engineering, Tokyo, Japan."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sumer, B.M., and Freds\u00f8e, J. (2002). The mechanics of Scour in the Marine Environment, World Scientific.","DOI":"10.1142\/4942"},{"key":"ref_6","unstructured":"Hansen, E.A., Freds\u00f8e, J., and Mao, Y. (1986, January 13\u201318). Two dimensional scour below pipelines. Proceedings of the 5th International Symposium on Offshore Mechanics and Arctic Engineering, Tokyo, Japan."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1061\/(ASCE)0733-9429(1999)125:4(400)","article-title":"Numerical model for local scour under offshore pipelines","volume":"125","author":"Li","year":"1999","journal-title":"J. Hydraul. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1061\/(ASCE)0733-950X(2001)127:2(106)","article-title":"Prediction of lee-wake scouring of pipelines in currents","volume":"127","author":"Li","year":"2001","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1142\/S0578563403000737","article-title":"Modelling of local scour below a sagging pipeline","volume":"45","author":"Li","year":"2003","journal-title":"Coast. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108546","DOI":"10.1016\/j.oceaneng.2020.108546","article-title":"Numerical investigation of local scour around a vibrating pipeline under steady currents","volume":"221","author":"Liu","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.coastaleng.2009.11.008","article-title":"Numerical investigation of local scour below a vibrating pipeline under steady currents","volume":"57","author":"Zhao","year":"2010","journal-title":"Coast. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1061\/(ASCE)0733-950X(2005)131:5(193)","article-title":"Numerical model for wave-induced scour below a submarine pipeline","volume":"131","author":"Liang","year":"2005","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1061\/(ASCE)0733-950X(1990)116:3(307)","article-title":"Scour below pipelines in waves","volume":"116","author":"Sumer","year":"1990","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.coastaleng.2016.05.003","article-title":"Numerical modeling of local scour and forces for submarine pipeline under surface waves","volume":"116","author":"Liu","year":"2016","journal-title":"Coast. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"109258","DOI":"10.1016\/j.oceaneng.2021.109258","article-title":"Numerical investigation of local scour around submerged pipeline in shoaling conditions","volume":"234","author":"Liu","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_16","first-page":"1","article-title":"Numerical investigation of flow around a pipeline with a spoiler near a rigid bed","volume":"8","year":"2016","journal-title":"Adv. Mech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.oceaneng.2012.07.031","article-title":"Calculation and experiment on scour depth for submarine pipeline with a spoiler","volume":"55","author":"Yang","year":"2012","journal-title":"Ocean Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lee, W.D., Jo, H.J., Kim, H.S., Kang, M.J., Jung, K.H., and Hur, D.S. (2019). Experimental and numerical investigation of self-burial mechanism of pipeline with spoiler under steady flow conditions. J. Mar. Sci. Eng., 7.","DOI":"10.3390\/jmse7120456"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.2514\/3.12149","article-title":"Two-equation eddy-viscosity turbulence models for engineering applications","volume":"32","author":"Menter","year":"1994","journal-title":"AIAA J."},{"key":"ref_20","first-page":"625","article-title":"Ten years of industrial experience with the SST turbulence model","volume":"4","author":"Menter","year":"2003","journal-title":"Turbul. Heat Mass Transf."},{"key":"ref_21","first-page":"35","article-title":"Sedimentation and fluidization: Part I","volume":"32","author":"Richardson","year":"1954","journal-title":"Trans. Inst. Chem. Eng."},{"key":"ref_22","unstructured":"Soulsby, R. (1997). Dynamics of Marine Sands, Tomas Telford."},{"key":"ref_23","unstructured":"Van Rijn, L.C. (1978). Mathematical Modeling of Morphological Processes in the Case of Suspended Sediment Transport. [Ph.D. Thesis, Delft University of Technology]."},{"key":"ref_24","unstructured":"Soulsby, R., and Whitehouse, R. Threshold of sediment motion in coastal environments. Proceedings of the Combined Australasian Coastal Engineering and Ports Conference, Christchurch, New Zealand. Available online: https:\/\/search.informit.org\/doi\/abs\/10.3316\/INFORMIT.929741720399033."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.jfluidstructs.2006.07.003","article-title":"Hydrodynamic forces on dual cylinders of different diameters in steady currents","volume":"23","author":"Zhao","year":"2007","journal-title":"J. Fluids Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.wse.2015.06.002","article-title":"Numerical simulation of flow past twin near-wall circular cylinders in tandem arrangement at low Reynolds number","volume":"8","author":"Tang","year":"2015","journal-title":"Water Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Draper, S., Yao, W.D., Cheng, L., Tom, J., and An, H.W. (2018, January 17\u201322). Estimating the rate of scour propagation along a submarine pipeline in time-varying currents and in fine grained sediment. Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering, Madrid, Spain.","DOI":"10.1115\/OMAE2018-77981"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.coastaleng.2015.12.010","article-title":"Predicting the rate of scour beneath subsea pipelines in marine sediments under steady flow conditions","volume":"110","author":"Mohr","year":"2016","journal-title":"Coast. Eng."},{"key":"ref_29","first-page":"13","article-title":"Time scale for wave\/current scour below pipelines","volume":"2","author":"Sumer","year":"1992","journal-title":"Int. J. Offshore Polar Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1847\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:08:51Z","timestamp":1760166531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1847"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,2]]},"references-count":29,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101847"],"URL":"https:\/\/doi.org\/10.3390\/sym13101847","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,2]]}}}