Mechanistic Modelling of Water Vapour ... condensation of vapor in binary and ternary mixtures with

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  • Mechanistic Modelling of Water Vapour

    Condensation in Presence of Noncondensable Gases

    Doctoral Thesis

    by

    Krzysztof Karkoszka

    School of Engineering Sciences Department of Physics

    Div. of Nuclear Reactor Technology Stockholm, 2007

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    Abstract This thesis concerns the analytical and numerical analysis of the water vapour condensation from the multicomponent mixture of condensable and noncondensable gases in the area of the nuclear reactor thermal-hydraulic safety. Following an extensive literature review in this field three aspects of the condensation phenomenon have been taken into consideration: a surface condensation, a liquid condensate interaction with gaseous mixtures and a spontaneous condensation in supersaturated mixtures. In all these cases condensation heat and mass transfer rates are significantly dependent on the local mixture intensive parameters like for example the noncondensable species concentration. In order to analyze the multicomponent mixture distribution in the above-mentioned conditions, appropriate simplified physical and mathematical models have been formulated. Two mixture compositions have been taken into account: a binary mixture of water vapour with heavy noncondensable gas and a ternary mixture with two noncondensable gases with different molecular weights. For the binary mixture a special attention has been focused on the heavy gas accumulation in the near- interface region and the influence of liquid film instabilities on the interface heat and mass transfer phenomena. For the ternary mixture of gases a special attention has been paid to the influence of the light gas and induced buoyancy forces on the condensation heat and mass transfer processes. Both analytical and numerical methods have been used in order to find solutions to these problems. The analytical part has been performed applying the boundary layer approximation and the similarity method to the system of film and mixture conservation equations. The numerical analysis has been performed with the in- house developed code and commercial CFD software. Performing analytical and CFD calculations it has been found that most important processes which govern the multicomponent gas distribution and condensation heat transfer degradation are directly related to the interaction between interface mass balances and buoyancy forces. It has been observed that if the influence of the liquid film instabilities is taken into consideration the heat transfer enhancement due to the presence of different types of waves is directly related to the internal film hydrodynamics and shows up in the mixture-side heat transfer coefficient. The model developed for the dispersed phase growth shows that degradation of the condensation heat transfer rate, which is a consequence of degradation of the convective mass flux, should be taken into account for highly supersaturated gaseous mixtures and can be captured by combination with the mechanistic CFD surface condensation model. Keywords: condensation, noncondensable gases, CFD simulation, boundary-layer approximation, binary and ternary mixtures

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    List of papers and publications Publications and papers included

    I. Karkoszka K., Anglart H., 2006. CFD modeling of laminar film and spontaneous condensation in presence of noncondesable gas. Archives of Thermodynamics, Vol. 27, No. 2, 23 – 36.

    II. Karkoszka K., Anglart H., 2005. Multidimensional multicomponent

    model of consensation in presence of noncondensable gases. 11th International Topical Meeting on Nuclear Reactor Thermohydraulics, October 2-6, Avignon, France.

    III. Karkoszka K., Anglart H., 2006. Numerical analysis of solitary wave

    influence on the filmwise condensation in presence of noncondensable gases. 14th International Conference on Nuclear Engineering, July 17-20, Miami, Florida, USA.

    IV. Karkoszka K., Anglart H., 2007. Laminar filmwise condensation of vapor

    in presence of multi-component mixture of non-condensable gases. 12-th International Topical Meeting on Nuclear Reactor Thermohydraulics, September 30 – October 4, Pittsburgh, Pennsylvania, USA, to be presented.

    V. Karkoszka K., Anglart H. Multidimensional effects in laminar filmwise

    condensation of vapor in binary and ternary mixtures with non- condensable gases. Submited to the Nuclear Engineering and Design.

    Publications and papers not included

    VI. Karkoszka K., Anglart H., 2004. CFD Modelling of Direct-Contact Condensation in Presence of Non-Condensable Gases on Liquid Film Surface. 42nd European Two-Phase Flow Group Meeting, Genoa, Italy.

    VII. Karkoszka K., Anglart H., 2005. CFD modelling of wall condensation

    in presence of noncondensable gas. HEAT2005, Gdansk, Poland.

    VIII. Karkoszka K., 2005. Theoretical Investigation of Water Vapour Condesation in Presence of Noncondesable Gases. Royal Institute of Technology, Stockholm, Sweden, licentiate thesis.

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    Contribution to papers All papers, included and not included in the present thesis, have been written under supervision of Assoc. Prof. Henryk Anglart. All calculations, models and results have been developed, implemented and analyzed by the author. Summary of included papers Paper I describes the mechanistic modelling of forced convection water vapour condensation from the binary mixture with air. The filmwise condensation is investigated as well as effects of the direct-contact condensation and influence of the spontaneous water droplets nucleation. In all cases modelling is based on the resolution of the gaseous boundary layer in the vicinity of the liquid condensate. Paper II is mainly focused on the forced convection direct-contact and spontaneous condensation effects. It contains detailed discussion of the applied models as well as discussion about the noncondesable mass fraction distribution in the vicinity of the interface boundary layer. The most important conclusion from both Paper I and Paper II is that a proper mechanistic CFD model is able to predict the heat transfer degradation due to the presence of noncondensable gas. Paper III is focused on the liquid film structure influence on the heat transfer between gaseous and liquid phases. All calculations are performed with a two- dimensional in-house code which has been developed in order to give required flexibility in the film geometry modelling. This paper discuses how the film structure disturbances in forms of sinusoidal and soliton-shaped waves influence the local condensation heat transfer rate. It has been found that the internal vortex present inside the wave and interface boundary conditions are directly responsible for the enhancement of the heat transfer process. Paper IV presents the mechanistic modelling of water vapour free convection condensation from the ternary mixture of gases with the boundary layer approximation. Fully coupled, through interface balances, boundary layer equations for liquid and gaseous phases, are solved with the similarity method. Results show how resistance to the interface heat transfer process is influenced by the presence of noncondensable species with different molecular weights and what relations between those species are. Paper V is an extension of Paper IV, where also the free convection condensation from ternary mixture of gases has been investigated. As an extension to Paper IV both the boundary layer approximation and mechanistic modelling with the commercial CFD code have been applied. The main conclusion from this article is that mechanistic CFD modelling with carefully implemented interface balances shows local physical relations between noncondensable components and local

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    noncondensable distribution fields. Both solutions of the boundary layer equations and mechanistic CFD model converge to each other for the binary mixture of gases.

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    Contents

    Abstract III

    List of papers and publications V Contents IX

    List of figures XI Nomenclature XV

    Chapter 1 Introduction 1 1.1 Condensation process and its applications……………………………………....1 1.2 Review of research approaches….……………………………..……...………...3 1.3 Review of modelling approaches………………………………………..………3 1.3.1 Empirical correlations ………………………………………………………...3 1.3.2 Analogy between heat and mass transfer……………………………………...4 1.3.3 Diffusion layer model…………………………………………………………4 1.3.4 Boundary layer approximation and fully mechanistic model…………………4 Chapter 2 Literature review 7 2.1 Empirical and theoretic