Notice: Undefined index: linkPowrot in C:\wwwroot\wwwroot\publikacje\publikacje.php on line 1275
Abstract: The experimental purpose of the study was to simultaneously measure and record two-dimensional temperature distributions on the heating surface and the images of the corresponding two-phase flow structures. The study was conducted for FC-72 flow boiling in rectangular, vertical and asymmetrically heated minichannels with a high aspect ratio of 40, 20 and 13.3 (0.5, 1.0, 1.5 mm deep, 20 mm wide) and 360 mm long, for heat fluxes ranging from 58 to 132 kWm-2, absolute pressure from 1.16 to 1.84 bar and the mass flux from 185 to 1139 kg m-2 s-1.The flat heating surface was made of a thin rolled plate. The inlet temperature of the liquid was kept constant at 288 K. The CCD camera, mounted on the heated side of the channel, produced color images
of liquid crystals. High-speed camera images, taken through the glass window on the opposite side of the channel, were used to measure void fraction for selected cross-sections as a function of variable thermal and flow parameters.
The theoretical part of the study focused on the development of flow boiling heat transfer model based on the Trefftz method. The model was formulated to include the minimum number of experimental constants. The procedure included solving two sequential inverse problems (in the heating foil and in the flowing liquid) and the accompanying direct problem (in the protecting glass pane). To obtain two-dimensional temperature distributions in the boiling liquid for bubbly and bubbly – slug flows, a triple coupled inverse problem was solved using the Trefftz method. The numerical solution was compared with the simplified one, assuming that the entire heat generated in the foil was transferred to the flowing refrigerant. Both solutions gave similar results.
B I B L I O G R A F I A[1] Z. Guo, D.F. Fletcher, B.S. Haynes, A Review of Computational Modelling of Flow Boiling
in Microchannels, Journal of Computational Multiphase Flows 6(2) (2014) 79–110.
[2] A. Rasmus, Heat transfer flow boiling –theoretical model, Recent Advances in Heat Transfer, ed.
B. Sunden and A. Żukauskas, Elsevier, (1992) 176–188.
[3] R.T. Lahey Jr., A CFD Analysis of Multidimensional Two-Phase Flow and Heat Transfer Phenomena: Process, Enhanced and Multiphase Heat Transfer, Begel House, Inc., New York, 1996.
[4] R.T. Lahey Jr., D.A. Drew, An analysis of two-phase flow and heat transfer using
a multidimensional, multi-field, two-fluid computational fluid dynamics (CFD) model, Proc. of the Japan/US Seminar on Two-Phase Flow Dynamics, Santa Barbara, USA, 2000, 36 pages.
[5] R.T. Lahey Jr., D.A. Drew, The analysis of two-phase flow and heat transfer using
a multidimensional, four field, two-fluid model, Nuclear Engineering and Design 204 (2001) 29–44.
[6] A. Alajbegovic, D.A. Drew, R.T. Lahey Jr., An Analysis of Phase Distribution and Turbulence
in Dispersed Particle/Liquid Flows, Chemical Engineering Communications 174 (1999) 85–133.
[7] M.Z. Podowski, Multidimensional modeling of two-phase flow and heat transfer, International Journal of Numerical Methods for Heat & Fluid Flow 18 (2008) 491–513.
[8] M.Z. Podowski, R.M. Podowski, Mechanistic multidimensional modeling of forced convection boiling heat transfer, Science and Technology of Nuclear Installations, article ID 387020, http://dx.doi.org/10.1155/2009/387020 (2009) 10 pages.
[9] P. Tiwari, S.P. Antal, M.Z. Podowski, On the Modeling of Dispersed Particulate Flows using
a Multifield Model, Computational Fluid and Solid Mechanics, ed. K.J. Bathe, I (2003) 1160–1165.
[10] J.R. Thome, Boiling in microchannels: a review of experiment and theory, International Jouranl of Heat and Fluid Flow 25 (2004) 128–139.
[11] B. Agostini, J.R. Thome, Comparison of an Extended Database for Flow Boiling Heat Transfer Coefficients in Multi-Microchannels Elements with the Three-Zone Model, ECI Heat Transfer and Fluid Flow in Microscale, Castelvecchio Pascoli, Italy (2005).
[12] M. Magnini, B. Pulvirenti, J.R. Thome, Numerical investigation of the influence of leading and sequential bubbles on slug flow boiling within a microchannel, International Journal of Thermal Sciences 71 (2012) 36–52.
[13] V. Dupont, J.R. Thome, Evaporation in microchannels
influence of the channel diameter on heat transfer, Proceedings of the IInd International Conference on Microchannels and Minichannels, Rochester, USA (2004) 461– 468.
[14] R. Kaniowski, M.E. Poniewski, Measurement of void fraction distribution and heating surface local temperature in a rectangular, vertical minichannel heated asymmetrically, Proceedings for 6th International Conference on Transport Phenomena in Multiphase System - HEAT, Ryn, Poland (2011) 263–270.
[15] R. Kaniowski, M.E. Poniewski, Two-phase flow structures and boiling heat transfer
in asymmetrically heated minichannels, Proceedings of the ECI VIIIth International Conference on Boiling and Condensation Heat Transfer, Lausanne, Switzerland (2012) pendrive: paper - o_s1_1509 10 pages.
[16] S.G. Kandlikar, Fundamental issues related to flow boiling in minichannels and microchannels, Experimental Thermal and Fluid Science 26 (2002) 389–407.
[17] J.W. Hwang, M.S. Kim, Two-phase flow heat transfer of R-134a in microtubes, Journal of Mechanical Science and Technology 23 (2003) 3095–3104.
[18] Y.M. Lie, F.Q. Su, R.L. Lai, T.F. Lin, Experimental study of evaporation heat transfer characteristics of refrigerants R-134a and R-407C in horizontal small tubes, International Journal of Heat and Mass Transfer 49 (2006) 207–221.
[19] S. Saisorn, J. Kaew-On, S. Wongwises, Flow pattern and heat transfer characteristics of R-134a refrigerant during flow boiling in a horizontal circular mini-channel, International Journal of Heat and Mass Transfer 53 (2010) 4023–4038.
[20] S.G. Kandlikar, Scale effects on flow boiling heat transfer in microchannels: A fundamental perspective, International Journal of Thermal Sciences 49 (2009) 1073–1085.
[21] C.L. Ong, J.R. Thome, Macro-to-microchannel transition in two-phase flow: Part 1 -Two-phase flow patterns and film thickness measurements, Experimental Thermal and Fluid Science 35 (2011) 37–47.
[22] M. Piasecka, B. Maciejewska, Enhanced heating surface application in a minichannel flow and use the FEM and Trefftz functions to the solution of inverse heat transfer problem, Experimental Thermal and Fluid Science 44 (2013) 23–33.
[23] M. Piasecka, An application of enhanced heating surface with mini-recesses for flow boiling research in minichannels, Heat and Mass Transfer 49 (2013) 261–271.
[24] E. Sobierska, R. Kulenovic, R. Mertz, Heat transfer mechanism and flow pattern during flow boiling of water in a vertical narrow channel - experimental results, International Journal of Thermal Science 46 (2007) 1172–1181.
[25] S. Su, S. Huang, X. Wang, Study of boiling incipience and heat transfer enhancement in forced flow through narrow channels, International Journal of Multiphase Flow 31 (2005) 253–260.
[26] T. Bohdal, Causes of phase change instability of heat transferring liquids, Koszalin University
of Technology Publishing House, Monograph in Mechanical Engineering (in Polish), no.130, Koszalin, Poland, 2006.
[27] G.E. Thorncroft, J.F. Klausner, R. Mei, An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling, International Journal of Heat and Mass Transfer 41 (1998) 3857–3871.
[28] Y. Wang, K. Sefiane, S. Harmand, Flow boiling in high aspect ratio mini- and micro-channels with FC72 and ethanol: Experimental results and heat transfer correlation assessments, Experimental Thermal and Fluid Science 36 (2012) 93–106.
[29] Y. Wang, K. Sefiane, Effects of heat flux, vapor quality, channel hydraulic diameter on flow boiling heat transfer in variable aspect ratio micro-channels using transparent heating, International Journal on Heat and Mass Transfer 55 (2012) 2235–2243.
[30] Y. Wang, K. Sefiane, Z. Wang, S. Harmand, Analysis of two-phase pressure drop fluctuations during micro-channel flow boiling, International Journal on Heat and Mass Transfer 70 (2014) 353–362.
[31] T. Trefftz, Ein Gegenstäuk zum Ritz'schen Verfahren, Proceedings of the IInd International Congress of Applied Mechanics, Zurich, Switzerland, (1926) 131–137.
[32] R. Pastuszko, T. M. Wójcik, Experimental investigations and a simplified model for pool boiling on micro-fins with sintered perforated foil, Experimental Thermal and Fluid Science 63 (2015) 34–44.
[33] R. Kaniowski, M.E. Poniewski, Measurements of two-phase flow patterns and local void fraction
in vertical rectangular minichannel, Archives of Thermodynamics 34 (2) (2012) 3–22.
[34] M. Piasecka, S. Hożejowska, M.E. Poniewski, Experimental evaluation of flow boiling incipience
of subcooled fluid in a narrow channel, International Journal of Heat and Fluid Flow 25 (2004) 159–172.
[35] S. Hożejowska, M. Piasecka, M.E. Poniewski, Boiling heat transfer in vertical minichannels. Liquid crystal experiments and numerical investigations, International Journal of Thermal Sciences 48 (2009) 1049–1059.
[36] M. Piasecka, S. Hożejowska, M.E. Poniewski, Experimental error analysis and heat polynomial method improvement for boiling heat transfer numerical calculations in minichannels, Proceedings of the IIIrd International Conference Microchannels and Minichannels, Toronto, Canada (2005) CD–ICMM2005–75142.
[37] S. Hożejowska, R. Kaniowski, M.E. Poniewski, Application of adjustment calculus to the Trefftz method for calculating temperature field of the boiling liquid flowing in a minichannel, International Journal of Numerical Methods for Heat & Fluid Flow 24(4) (2014) 811–824.
[38] T. Bohdal, Modelling the process of bubble boiling in flows, Archives of Thermodynamics 21 (3-4) (2000) 34–75.
[39] L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon Press, London, 1959.
[40] R.K. Shah, A.L. London, Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data, Academic Press, New York, 1978.
[41] I. Herrera, Trefftz method: A general theory, Numerical Methods for Partial Differential Equations 16 (2000) 561-580.
[42] J. Jirousek, Variational formulation of two complementary hybrid Trefftz models, Communications in Numerical Methods in Engineering 9 (1993) 837–845.
[43] Q-H. Qin, H. Wang, MATLAB and C Programming for Trefftz Finite Element Methods, CRC Press, 2008.
[44] A.P. Zieliński, I. Herrera, Trefftz method: Fitting boundary conditions, International Journal Numerical Methods in Engineering 24 (1987) 871–891.
[45] K. Grysa, A. Maciag, A. Pawińska, Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions, International Journal of Heat and Mass Transfer 55 (2012) 7336–7340.
[46] P.L. Spedding, D.R. Spence, Prediction of holdup in two phase flow, International Journal of Engineering Fluid Mechanics 2 (1989) 109–118.
[47] S. Dalkilic, S. Laohalertdecha, S. Wongwises, Effect of void fraction models on the film thickness
of R134a during downward condensation in a vertical smooth tube, International Communications in Heat and Mass Transfer 36 (2009) 172–179.
[48] R. Srisomba, O. Mahian, A.S. Dalkilic, S. Wongwises, Measurements of the void fraction of R-134a flowing through a horizontal tube, International Communications in Heat and Mass Transfer 56 (2014) 8–14.
[49] R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal two-phase, two-component flow in pipes, Chemical Engineering Progress 45 (1949) 39–48.
[50] C.J. Baroczy, Correlation of liquid fraction in two-phase flow with application to liquid metals, Chemical Engineering Progress Symposium Series 61 (57) (1965) 179–191.
[51] D. Chisholm, Pressure gradients due to friction during the flow of evaporating twophase mixtures in smooth tubes and channels, International Journal of Heat and Mass Transfer 16 (1973) 347–358.
[52] D. Steiner D, Heat transfer to boiling saturated liquids, VDI-Warmeatlas (VDI Heat Atlas), Editor: Verein Deutscher Ingenieure, VDI-Gessellschaft Verfahrenstechnik und Chemie-ingenieurwesen (GCV), Translator: J.W. Fullarton, Dusseldorf, 1993.
[53] S. Hożejowska, Homotopy Perturbation Method Combined with Trefftz Method in Numerical Identification of Temperature Fields in Flow Boiling, Journal of Theoretical and Applied Mechanics 53 (2015) 969–980.
[54] K. Grysa, S. Hożejowska, B. Maciejewska, Adjustment calculus and Trefftz functions applied to local heat transfer coefficient determination in a minichannel, Journal of Theoretical and Applied Mechanics 50 (2012) 1087–1096.