Glaciation and thawing models of the outer surface of an offshore gas pipeline in the northern seas. (Russian. English summary) Zbl 1458.76117
Summary: The models of glaciation and thawing of the outer surface of an offshore gas pipeline are presented. In the glaciation model the modification of Stefan condition is proposed which allows accounting for the special features of a sea ice growing in salt water. The algorithm of numerical solution to unsteady problem of glaciation (thawing) of the multilayer cylindrical area by the explicit front tracking method and some numerical simulation results of different variants of these problems, which are of practical interest, are given. The quantitative estimates of a shift to a quasi-stationary version of the glaciation (thawing) model of multilayer areas are obtained. The qualitative condition for the admissibility of using a quasi-stationary approximation for numerical simulation of glaciation of the multilayer area is found. These estimates are very important for the developing effective numerical algorithms for simulation of the unsteady regimes of gas transportation through the offshore gas pipelines. For the problems of thawing of the outer surface pipelines the equation is proposed, which allows finding the minimal ice layer thickness under researched conditions.
MSC:
| 76T99 | Multiphase and multicomponent flows |
| 76M99 | Basic methods in fluid mechanics |
| 80A22 | Stefan problems, phase changes, etc. |
| 86A40 | Glaciology |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
Stefan problem; numerical solution; explicit front-tracking method; quasi-stationary approximationReferences:
| [1] | G.I. Kurbatova, E.A. Popova, B.V. Filippov i dr., Modeli morskikh gazoprovodov, St.-Petersburg State University, St.-Petersburg, 2005, 156 pp. |
| [2] | V. Malkov, G. Kurbatova, N. Ermolaeva, Y. Malkova, R. Petrukhin, “Analysis of the strength of sea gas pipelines of positive buoyancy conditioned by glaciation”, AIP Conference Proceedings, 1959 (2018), 050019 · doi:10.1063/1.5034647 |
| [3] | D.A. Medvedev, A.P. Ershov, “Modelirovanie namerzaniia lda na podvodnoy trube gazoprovoda”, Vestnik NGU. Seriia: Matematika, Mekhanika, informatika, 13:4 (2013), 96-101 · Zbl 1349.82039 |
| [4] | I.A. Gishkeluk, Y.V. Stanilovskaia, D.V. Evlanov, “Prognozirovanie ottaivaniia mnogoletnemerzlykh gruntov vokrug podzemnogo truboprovoda bolshoy protiazhennosti”, Nauka i tekhnologii truboprovodnogo transporta nefti i neftiproduktov, 2015, no. 1, 20-25 |
| [5] | M. Vitel, A. Rouabhi, M. Tijana, F. Guerin, “Modelling Heat and Mass Transfer During Ground Freezing Subjected to High Seepage Velocities”, Comput. Geotech., 73 (2015), 1-15 · doi:10.1016/j.compgeo.2015.11.014 |
| [6] | N.N. Ermolaeva, G.I. Kurbatova, “Parametricheskaia identifikatsia modeli ustanovivshegosia neizotermicheskogo techenia gaza po morskomu gazoprovodu”, Morskie intellectualnye tekhnologii, 1:1(35) (2017), 8-13 |
| [7] | N.N. Ermolaeva, G.I. Kurbatova, “Nestatsionarnaia model narastaniia morskogo lda”, Vestnik Sankt-Peterburgskogo Universiteta Tekhnologii i dizaina. Seriia 1. Estestvennye i tekhnicheskie nauki, 2017, no. 1, 3-8 |
| [8] | A.A. Samarskii, P. N. Vabishevich, Computentional Heat Transfer, Wiley, cop., Chichester, 1996, 418 pp. |
| [9] | F.P. Vasilev, “O metode konechnykh raznostei dlia resheniia odnofaznoi zadzchi Stefana”, Zh.V.M. i M.F., 3:5 (1963), 861-873 |
| [10] | J. Douglas, T.M. Gallie, “On the numerical integration of a parabolic differential equations subject to a moving boundary condition”, Duke Math. J., 22:4 (1955), 557-572 · Zbl 0066.10503 · doi:10.1215/S0012-7094-55-02262-6 |
| [11] | G.I. Kurbatova, N.N. Ermolaeva, V.V. Mikova, “Analytical and numerical solutions to Stefan problem in model of the glaciation dynamics of the multilayer cylinder in sea water”, Journal of Physics: Conference Series, 2017 · doi:10.1088/1742-6596/929/1/012103 |
| [12] | Yu.P. Doronin, D.E. Kheysin, Morskoi led, Gidrometeoizdat, L., 1975, 320 pp. |
| [13] | G.I. Kurbatova, N.N. Ermolaeva, B.Y. Nikitchuk, “Calculation of the Flow Characteristics in the Offshore Gas Pipelines in the Northern Seas with Accounting for Growing and Ice Melting on its Outer Surface”, WSEAS Transactions on Heat and Mass Transfer, 13 (2018), 29-34 |
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