{"title":"An Implicit Numerical Method for Integration of the Conservation Equations Incorporated into the KORSAR Code Two-Fluid Model","authors":"Yu. V. Yudov, I. G. Danilov","doi":"10.1134/s0040601524040074","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A noniterative implicit method for solving the discrete conservation equations of the KORSAR/GP computer code (hereinafter referred to as KORSAR) two-fluid model is presented. The KORSAR/GP code has been developed jointly by specialists of the Federal State Unitary Enterprise Aleksandrov Research Institute of Technology (NITI) and the special design bureau OKB Gidropress. In 2009, the code was certified at the Federal Service for Environmental, Technological, and Nuclear Supervision (Rostekhnadzor) as applied to numerical safety assessment of VVER-type power reactor plants. The code uses the semi-implicit numerical scheme, which limits the integration time step by the Courant condition with respect to the velocity of a two-phase flow. To cut down the time it takes to calculate prolonged transients in reactor plants, an implicit numerical method, which does not limit the time step by the Courant condition, has been developed on the basis of the SETS (stability-enhancing two-step) method. It is based on the semi-implicit scheme. Prior to its application, discrete phase momentum conservation equations with the convective terms written in implicit form are solved at each time step. After the semi-implicit step, the specific (per unit volume) mass and energy of the phases, which are donor quantities in the convective terms of the transport equations, are calculated at the new time layer. Unlike the SETS method, the implicit method developed for the KORSAR code employs a semi-implicit scheme with linearization of unsteady terms describing the change in the specific mass and energy of a two-phase flow. This approach enables us to solve discrete equations in a noniterative manner. However, the implementation of this procedure requires that the unknown scalar variables, such as the phase specific enthalpies, the vapor volume fraction, and the pressure, be determined in the computational cells. Therefore, the semi-implicit scheme with linearization of unsteady terms with recalculated donor quantities at the end of the time step is reused. The performance and effectiveness of the developed implicit method have been confirmed by solving, using the KORSAR code, a test problem of a two-phase flow in a heated horizontal tube driven by a pressure difference.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thermal Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s0040601524040074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENERGY & FUELS","Score":null,"Total":0}
引用次数: 0
Abstract
A noniterative implicit method for solving the discrete conservation equations of the KORSAR/GP computer code (hereinafter referred to as KORSAR) two-fluid model is presented. The KORSAR/GP code has been developed jointly by specialists of the Federal State Unitary Enterprise Aleksandrov Research Institute of Technology (NITI) and the special design bureau OKB Gidropress. In 2009, the code was certified at the Federal Service for Environmental, Technological, and Nuclear Supervision (Rostekhnadzor) as applied to numerical safety assessment of VVER-type power reactor plants. The code uses the semi-implicit numerical scheme, which limits the integration time step by the Courant condition with respect to the velocity of a two-phase flow. To cut down the time it takes to calculate prolonged transients in reactor plants, an implicit numerical method, which does not limit the time step by the Courant condition, has been developed on the basis of the SETS (stability-enhancing two-step) method. It is based on the semi-implicit scheme. Prior to its application, discrete phase momentum conservation equations with the convective terms written in implicit form are solved at each time step. After the semi-implicit step, the specific (per unit volume) mass and energy of the phases, which are donor quantities in the convective terms of the transport equations, are calculated at the new time layer. Unlike the SETS method, the implicit method developed for the KORSAR code employs a semi-implicit scheme with linearization of unsteady terms describing the change in the specific mass and energy of a two-phase flow. This approach enables us to solve discrete equations in a noniterative manner. However, the implementation of this procedure requires that the unknown scalar variables, such as the phase specific enthalpies, the vapor volume fraction, and the pressure, be determined in the computational cells. Therefore, the semi-implicit scheme with linearization of unsteady terms with recalculated donor quantities at the end of the time step is reused. The performance and effectiveness of the developed implicit method have been confirmed by solving, using the KORSAR code, a test problem of a two-phase flow in a heated horizontal tube driven by a pressure difference.
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