519.6:532.529.5 Hybrid methods of computer diagnosis of two-phase flow in the circulation loop

Sulimov V. D. (Bauman Moscow State Technical University), Shkapov P. M. (Bauman Moscow State Technical University)

TWO-PHASE FLOW, INVERSE PROBLEM, REGULARIZATION, GLOBAL OPTIMIZATION, METROPOLIS ALGORITHM, HYBRID ALGORITHM


doi: 10.18698/2309-3684-2015-3-6888


The article considers the problems of coolant flow computational diagnostics in a closed circulation loop. The mathematical models of acoustic waves in two-phase flow are developed. Indirect diagnostic information, contained in the flow vibrational spectra recorded by regular systems is used. The inverse eigenvalue problem is formulated. Solving it the optimization approach is implemented. It is supposed that partial criteria are presented by continuous, Lipschitz, not everywhere differentiable, multi-extremal functions. Search of global solutions was performed using a new hybrid algorithms integrating stochastic algorithm of variable space viewing and deterministic methods of local search. A numerical example of model diagnosing the phase composition of the coolant in the circulation loop of nuclear reactor plant is presented.


[1] Romenski E., Drikakis D., Toro E. Conservative models and numerical methods for compressible two-phase flow. J. of Scientific Computing, 2010, vol. 42, no. 1, pp. 68 −95.
[2] Yao L., Zhu C. Free boundary value problem for a viscous two-phase model with mass-dependent viscosity. J. of Differential Equations, 2009, vol. 247, no. 10, pp. 2705−2739.
[3] Bonilla J., Yebra L.J., Dormido S. Chattering in dynamic mathematical two-phase flow models. Applied Mathematical Modelling, 2012, vol. 36, no. 5, pp. 2067−2081.
[4] Khatri S., Tornberg A.-K. An imbedded boundary method for soluble surfactants with interface tracking for two-phase flows. J. of Computational Physics, 2014, vol. 256, pp. 768−790.
[5] Evje S. Global weak solutions for a compressible gas-liquid model with wellformation interaction. J. of Differential Equations, 2011, vol. 251, no. 8, pp. 2352−2386.
[6] Yao L., Zhu C.J. Existence and uniqueness of global weak solution to a two-phase flow model with vacuum. Mathematische Annalen, 2011, vol. 349, no. 4, pp. 903−928.
[7] Vallée C., Höhne T., Prasser H.-M., Sühnel T. Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena. Nuclear Engineering and Design, 2008, vol. 238, no. 3, pp. 637−646.
[8] Poullikas A. Effects of two-phase flow on the performance of nuclear reactor cooling pumps. Progress in Nuclear Energy, 2003, vol. 42, no. 1, pp. 3−10.
[9] Yang X., Schiegel J.P., Liu Y., Paranjape S., Hibiki T., Ishii M. Experimen-tal study of interfacial area transport in air-water two phase flow in a scaled 8×8 BWR rod bundle. J. of Multiphase Flow, 2013, vol. 50, pp. 16−32.
[10] Semchenkov Yu.M., Milto V.A., Shumskiy B.E. Atomnaya energiya – Nuclear Power, 2008, vol. 105, no. 2, pp. 79−82.
[11] Kornyushin Yu.P., Egupov N.D., Kornyushin P.Yu. Matematicheskoe modelirovanie i chislennye menody – Mathematical Modeling and Numerical Methods, 2015, no. 2(6), pp. 73–86.
[12] [Kumbaro A. Simplified eigenstruture decomposition solver for the simula-tion of two-phase flow systems. Computers and Fluids, 2012, vol. 64, pp. 19−33.
[13] Zeidan D., Slaouti A. Validation of hyperbolic model for two-phase flow in conservative form. International J. Computational Fluid Dynamics, 2009, vol. 23, no. 9, pp. 623−641.
[14] Oberkampf W.L., Barone M.F. Measures of agreement between computation and experiment: Validation metrics. J. of Computational Physics, 2006, vol. 217, no. 1, pp. 5−36.
[15] Mañes J.P., Espinoza V.H.S., Vicent S.C., Böttcher M., Stieglitz R. Validation of NEPTUNE-CFD two-phase flow models using experimental data. Science and Technology of Nuclear Installations, 2014, vol. 2014, article ID 185950, 19 p.
[16] Lippert R.A. Fixing multiple eigenvalues by a minimal perturbation. Linear Algebra and its Applications, 2010, vol. 432, pp. 1785−1817.
[17] Kirsch A. An introduction to the mathematical theory of inverse problems. 2nd edition. New York et al., Springer, 2011, 308 p.
[18] [Chu D., Lin L., Tan R.C.E., Wei Y. Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems. Numerical Linear Algebra with Applications, 2011, vol. 18, no. 1, pp. 87−103.
[19] Goncharskiy A.V., Romanov S.Yu. Zhurnal vychislitelnoy matematiki i matematicheskoi fiziki – Journal of Computational Mathematics and Mathematical Physics, 2012, vol. 52, no. 2, pp. 263−269.
[20] Glikman B.F. Matematicheskie modeli pnevmogidravlicheskikh system [Mathematical Models of Pneumohydraulic Systems]. Moscow, Nauka Publ., 986, 386 p.
[21] Kinelev V.G., Sulimov V.D., Shkapov P.M. Izvestiya RAN.Energetika – Proceedings of the RAS. Power Engineering, 1998, no. 6, pp. 112−119.
[22] Bai Z.-J., Ching W.-K. A smoothing Newton’s method for the construction of a damped vibrating system from noisy test eigendata. Numerical Linear Algebra with Applications, 2009, vol. 16, no. 2, pp. 109−128.
[23] Kinelev V.G., Shkapov P.M., Sulimov V.D. Application of global optimization to VVER-1000 reactor diagnostics. Progress in Nuclear Energy, 2003, vol. 43, no. 1−4, pp. 51−56.
[24] Medeiros J.A.C., Schirru R. Identification of nuclear power plant transients using the Particle Swarm Optimization algorithm. Annals of Nuclear Energy, 2008, vol. 35, no. 4, pp. 576−582.
[25] Chen X. Smoothing methods for nonsmooth, nonconvex minimization. Mathematical Programming, 2012, vol. 134, no. 1, pp. 71−99.
[26] Bagirov A.M., Al Nuaimat A, Sultanova N. Hyperbolic smoothing function method for minimax problems. Optimization: A Journal of Mathematical Programming and Operations Research, 2013, vol. 62, no. 6, pp. 759−782.
[27] Sulimov V.D. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2010, no. 3, pp. 3−14.
[28] Karpenko A.P. Sovremennye algoritmy poiskovoy optimizatsii. Algoritmy, vdokhnovlennye prirodoy [Modern Algorithms of Search Optimization. Algorithms Inspired by Nature]. Moscow, BMSTU Publ., 2014, 446 p.
[29] Wang Y., Garcia A. Interactive model-based search for global optimization. J. of Global Optimization, 2015, vol. 61, no. 3, pp. 479−495.
[30] Luz E.F.P., Becceneri J.C., de Campos Velho H.F. A new multi-particle collision algorithm for optimization in a high performance environment. J. of Computational Interdisciplinary Sciences, 2008, vol. 1, pp. 3−10.
[31] Voglis C., Parsopoulos K.E., Papageorgiou D.G., Lagaris I.E., Vrahatis M.N. MEMPSODE: A global optimization software based on hybridization of population- based algorithms and local searches. Computer Physics Communications, 2012, vol. 183, no. 2, pp. 1139−1154.
[32] Izmailov A.F., Solodov M.V. Chislennye metody optimizatsii [Numerical Optimization Techniques]. Moscow, Fismatlit Publ., 2005, 304 p.
[33] Sulimov V.D., Shkapov P.M. Application of hybrid algorithms to computational diagnostic problems for hydromechanical systems. J. of Mechanics Engineering and Automation, 2012, vol. 2, no. 12, pp. 734−741.


Sulimov V., Shkapov P. Hybrid methods of computer diagnosis of two-phase flow in the circulation loop. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 68-88



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