Применение параллельных вычислительных технологий для моделирования процесса отрыва течения за обратным уступом в канале с учетом сил плавучести
DOI:
https://doi.org/10.26577/jmmcs-2018-1-493Ключевые слова:
метод декомпозиции области, обратный уступ, метод расщепления по физическим параметрам, разделение и воссоединение потоков, отрывное течение, силы плавучестиАннотация
В работе приводятся численные решения двумерного ламинарного течения за обратным
уступом в канале с учетом сил плавучести. Для описания данного процесса используется
двумерное несжимаемое уравнение Навье-Стокса. Данная система численно решается
методом расщепления по физическим параметрам, который аппроксимируется с помощью
метода контрольного объема. Полученное уравнение Пуассона, удовлетворяющее
дискретному уравнению неразрывности, решается итерационным методом Якоби на
каждом шаге по времени. Полученные численные решения ламинарного течения за
обратным уступом сравниваются с численными результатами других авторов. Данный
численный алгоритм полностью распараллеливается с помощью различных геометрических
декомпозиций (1D, 2D и 3D). В работе были сделаны предварительный теоретический
анализ эффективности различных методов декомпозиции расчетной области и реальные
вычислительные эксперименты для данной задачи, и был определен лучший метод
декомпозиции области. В дальнейшем проверенная математическая модель и численный
алгоритм с лучшим методом декомпозиции можно будет применить для различных сложных
течении с учетом сил плавучести.
Библиографические ссылки
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ASME, New York.
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heat transfer."Int. J. Hear Muss Transfer. 28(1985): 1757-1771.
[6] Aung, W. and Worku, G. "Theory of fully developed. combined convection including flow reversal."J. Hear Transfer. 108
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[7] Chiang, T.P., Tony, W.H. and Sheu Fang, C.C. "Numerical investigation of vortical evolution in backward-facing step
expansion flow."Appl. Math. 23(1999): 915-932.
[8] Chorin, A.J. "Numerical solution of the Navier-Stokes equations."Math. Comp. 22 (1968):745-762.
[9] Chung, T.J. "Computational fluid dynamics."2002. 1034 p.
[10] Durst, F. and Whitelawj, H. "Aerodynamic properties of separated gas flows: existing measurements techniques and new
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[11] Eaton, J. K. and Johnson, J. P. "A review of research on subsonic turbulent flow reattachment."AIAA J. 19 (1981):
1093-1100.
[12] Fletcher, C.A.J. "Computational techniques for fluid dynamics 2."Springer-Verlag New York. 1 (1988): 387.
[13] Goldsteinr, J., Eriksenv, L., Olsonr, M. and Eckerte, R.G. "Laminar separation, reattachment and transition of flow over
a downstream-facing step."J. Basic Engng. 92 (1970):732.
[14] Gosmana, D. and Punw, M. "Lecture notes for course entitled: ’Calculation of recirculating flow’."Heat Transfer Rep.
74 (1974):2.
[15] Kumara, Yajnikk S. "Internal separated flows at large Reynolds number."J. Fluid Mech. 97 (1980):27.
[16] Issakhov, A. "Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power
plant."International Journal of Nonlinear Science and Numerical Simulation. 16(5) (2015): 229-238. doi:10.1515/ijnsns-
2015-0047.
[17] Issakhov, A. "Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal
power plant under various operational capacities."Applied Mathematical Modelling. 40(2) (2016): 1082-1096.
http://dx.doi.org/10.1016/j.apm.2015.06.024.
[18] Issakhov, A. "Large eddy simulation of turbulent mixing by using 3D decomposition method."J. Phys.: Conf. Ser. 318(4)
(2011): 1282-1288. doi:10.1088/1742-6596/318/4/042051.
[19] Karniadakis, G. E. and Kirby II, R. M. "Parallel Scientific Computing in C++ and MPI: A Seamless Approach to
Parallel Algorithms and their Implementation."Cambridge University Press, 2000. 630 p.
[20] Lin, J.T., Armaly, B.F. and Chen, T.S. "Mixed convection in buoyancy-assisting, vertical backward-facing step
flows."International Journal of Heat and Mass Transfer. 33(10) (1990): 2121-2132.
[21] Ngo, I. and Byon, C. "Effects of heater location and heater size on the natural convection heat transfer in a square cavity
using finite element method."J. Mech. Sci. Technol. 29 (7) (2015): 2995.
[22] Oztop, H. F. and Abu-Nada, E. "Numerical study of natural convection in partially heated rectangular enclosures filled
with nanofluids"Int. J. Heat. Fluid Fl. 29(5) (2008):1326-1336.
[23] Sebanr, A. "Heat transfer to the turbulent separated flows of air downstream of a step in the surface of a plate,"J. Heat
Transfer. 86 (1964):259.
[24] Simpson, R. L. "A review of some phenomena in turbulent flow separation,"J. Fluid Engng. 103 (1981): 520-533.
[25] Sparrow, E. M., Chrysler, G. M. and Azevedo, L. F. "Observed flow reversals and measured-predicted Nusselt numbers
for natural convection in a one-sided heated vertical channel."J. Heat Transfer. 106 (1984): 325-332.
[26] Sparrow, E. M., Kang, S. S. and Chuck, W. "Relation between the points of flow reattachment and maximum heat transfer
for regions of flow separation."Int. J. Heat Mass Transfer. 30 (1987): 1237-1246.
[27] Sparrow, E. M. and Chuck, W. "PC solutions for heat transfer and fluid flow downstream of an abrupt, asymmetric
enlargement in a channel,"Numer. Hear Transfer. 12(1987):1940.
steps."J. Basic Engng. 84 (1962): p. 317.
[2] Armaly, B. F. and Durst, F. "Reattachment length and recirculation regions downstream of two dimensional single
backward facing step In Momentum and Heat Transfer Process in Recirculating Flows."ASME HTDVol. 13 (1980): l-7.
ASME, New York.
[3] Aung, W. "An experimental study of laminar heat transfer downstream of backsteps."J. Heat Transfer. 105 (1983):
23-829.
[4] Aung, W. "Separated forced convection."Proc. ASMEIJSME Thermal Enana Joint Conf. 2(1983): 499-515. ASME. New
York.
[5] Aung, W., Baron, A. and Tsou, F. K. "Wall independency and effect of initial shear-layer thickness in separated flow and
heat transfer."Int. J. Hear Muss Transfer. 28(1985): 1757-1771.
[6] Aung, W. and Worku, G. "Theory of fully developed. combined convection including flow reversal."J. Hear Transfer. 108
(1986): 485-488.
[7] Chiang, T.P., Tony, W.H. and Sheu Fang, C.C. "Numerical investigation of vortical evolution in backward-facing step
expansion flow."Appl. Math. 23(1999): 915-932.
[8] Chorin, A.J. "Numerical solution of the Navier-Stokes equations."Math. Comp. 22 (1968):745-762.
[9] Chung, T.J. "Computational fluid dynamics."2002. 1034 p.
[10] Durst, F. and Whitelawj, H. "Aerodynamic properties of separated gas flows: existing measurements techniques and new
optical geometry for the laser-Doppler anemometer."Prog. Heat Mass Transfer. 4(1971): 311.
[11] Eaton, J. K. and Johnson, J. P. "A review of research on subsonic turbulent flow reattachment."AIAA J. 19 (1981):
1093-1100.
[12] Fletcher, C.A.J. "Computational techniques for fluid dynamics 2."Springer-Verlag New York. 1 (1988): 387.
[13] Goldsteinr, J., Eriksenv, L., Olsonr, M. and Eckerte, R.G. "Laminar separation, reattachment and transition of flow over
a downstream-facing step."J. Basic Engng. 92 (1970):732.
[14] Gosmana, D. and Punw, M. "Lecture notes for course entitled: ’Calculation of recirculating flow’."Heat Transfer Rep.
74 (1974):2.
[15] Kumara, Yajnikk S. "Internal separated flows at large Reynolds number."J. Fluid Mech. 97 (1980):27.
[16] Issakhov, A. "Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power
plant."International Journal of Nonlinear Science and Numerical Simulation. 16(5) (2015): 229-238. doi:10.1515/ijnsns-
2015-0047.
[17] Issakhov, A. "Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal
power plant under various operational capacities."Applied Mathematical Modelling. 40(2) (2016): 1082-1096.
http://dx.doi.org/10.1016/j.apm.2015.06.024.
[18] Issakhov, A. "Large eddy simulation of turbulent mixing by using 3D decomposition method."J. Phys.: Conf. Ser. 318(4)
(2011): 1282-1288. doi:10.1088/1742-6596/318/4/042051.
[19] Karniadakis, G. E. and Kirby II, R. M. "Parallel Scientific Computing in C++ and MPI: A Seamless Approach to
Parallel Algorithms and their Implementation."Cambridge University Press, 2000. 630 p.
[20] Lin, J.T., Armaly, B.F. and Chen, T.S. "Mixed convection in buoyancy-assisting, vertical backward-facing step
flows."International Journal of Heat and Mass Transfer. 33(10) (1990): 2121-2132.
[21] Ngo, I. and Byon, C. "Effects of heater location and heater size on the natural convection heat transfer in a square cavity
using finite element method."J. Mech. Sci. Technol. 29 (7) (2015): 2995.
[22] Oztop, H. F. and Abu-Nada, E. "Numerical study of natural convection in partially heated rectangular enclosures filled
with nanofluids"Int. J. Heat. Fluid Fl. 29(5) (2008):1326-1336.
[23] Sebanr, A. "Heat transfer to the turbulent separated flows of air downstream of a step in the surface of a plate,"J. Heat
Transfer. 86 (1964):259.
[24] Simpson, R. L. "A review of some phenomena in turbulent flow separation,"J. Fluid Engng. 103 (1981): 520-533.
[25] Sparrow, E. M., Chrysler, G. M. and Azevedo, L. F. "Observed flow reversals and measured-predicted Nusselt numbers
for natural convection in a one-sided heated vertical channel."J. Heat Transfer. 106 (1984): 325-332.
[26] Sparrow, E. M., Kang, S. S. and Chuck, W. "Relation between the points of flow reattachment and maximum heat transfer
for regions of flow separation."Int. J. Heat Mass Transfer. 30 (1987): 1237-1246.
[27] Sparrow, E. M. and Chuck, W. "PC solutions for heat transfer and fluid flow downstream of an abrupt, asymmetric
enlargement in a channel,"Numer. Hear Transfer. 12(1987):1940.
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Как цитировать
Issakhov, A. A., Abylkassymova, A., & Sakypbekova, M. (2018). Применение параллельных вычислительных технологий для моделирования процесса отрыва течения за обратным уступом в канале с учетом сил плавучести. Вестник КазНУ. Серия математика, механика, информатика, 97(1), 143–158. https://doi.org/10.26577/jmmcs-2018-1-493
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Прикладная математика
