MODELING OF THE NON-AZEOTROPIC MIXTURE CONDENSATION ON A VERTICAL ISOTHERMAL PLATE

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1 Proeedings of the Asian Conferene on Therma Sienes 07, st ACTS Marh 6-30, 07, Jeju Isand, Korea ACTS-P00605 MODELING OF THE NON-AZEOTROPIC MIXTURE CONDENSATION ON A VERTICAL ISOTHERMAL PLATE Li-i Zhang, Guan-min Zhang, Mao-heng Tian, Wen-ong Mao Shoo of Energy and Power Engineering, Shandong University, Jingshi Road No. 793, Jinan 5006, Shandong, PR China Presenting Author: ii.essentia@gmai.om * Corresponding Author: zhang_guan_min@39.om ABSTRACT This paper mainy fous on the anaytia and numeria anaysis of the non-azeotropi mixture ondensation proess on an infinite vertia pate. Based on the simpified natura gas omponents (methane, ethane, propane and nitrogen), modes the vapor ondensation in presene of non-ondensabe gases. Considering the mutiomponent mixture, the physia and mathematia modes are simpified appropriatey. The numeria soution of iquid and gaseous domains are soved separatey by the finite eement method in COMSOL Mutiphysis, then inked by the simpified iquid-gas interfaia equations soved by the subroutines written in MATLAB. The moving iquid-gas interfae oation and update of interfaia vaues are traked by the Arbitrary Lagrange-Euer method. This paper mainy researhes the infuene of onentration of non-ondensabe gas, iquid fim instabiities and buoyany fores on the heat and mass transfer proesses, whih is the mainy resistane of heat transfer. By finding out the mainy therma resistane, we oud take measure to enhane the heat transfer effiieny effetivey. KEYWORDS: Condensation, non-azeotropi mixture, heat and mass transfer, finite eement method, CFD simuation. INTRODUCTION In the proess of iquefation of Nature Gas (NG), there are many kinds of non-azeotropi mediums. Beause of the arge differene of the boiing point, there is just one materia ondensates whie others pay as the non-ondensabe gases in the different ondensation setions. So that the segmented ondensation is neessary in the nature gas iquefation proess to avoid the freeze.[] The infuene of non-ondensabe gas in the heat transfer proess is reevant to many industria appiations, suh as the air separation, biomass syngas and oi pyroysis. In this paper, numerous investigations were arried out for the ondensation in an infinite isotherma vertia pate. The ondensabe gas is propane in presene of methane, ethane and nitrogen as non-ondensabe gases.. MATHEMATICAL MODEL When the non-azeotropi mixture fow in the ooing hanne, the ondensation wi our on the od wa ausing iquid fim aong the wa and inrease with distane. If the medium is the pure vapor, the main therma resistane is the ondution resistane of the iquid fim aording to the Nusset mode[]. In the non-azeotropi mixture system, the mass fration of vapor dereases with the ondensate going on, at the same time the non-ondensabe omponents onentrate in the iquid-gas interfae hoding bak the diffusion of the vapor from the gas buk to iquid-gas interfae. Aording to the previous researh[3], with the absent of non-ondensabe gas the heat transfer resistane is mainy in the gas boundary ayer. Aso in ase of the fored onvetion, the iquid fim wi be disturbed by the mixture resuting the redution of thikness and inrease of veoity and transform to turbuent fow in a ow Reynods number. The turbuent fow an redue the heat transfer resistane of iquid fim. So in the ondensation proess, there are mainy three therma resistanes: the iquid fim, iquid-gas interfae, and gas mixture fim.

2 The physia mehanism of the heat and mass transfer proess is shown in the figure.. Figure. Physia mode of the ondensation in a vertia pate in presene of non-ondensabe gases.. Governing equations In this physi mode, the The basi onservation equations as foows: t u u 0 t uu g p T p Tu p q t In the CFD mode, some assumptions and simpifiations have been appied. There is no sip between iquid and gaseous phases. The iquid propane is onsidered to have onstant properties beause of the ow temperature differene. There is no spontaneous reation of the iquid dropets in the gaseous phase. The veoity and temperature is known and uniform in the gaseous buk. The fim interfae is impermeabe to non-ondensabe omponent. Based on the assumptions, the onservation is simpified as foows: The iquid fim: u x v y 0 u u u u v g x y y y () () (3) (4) (5)

3 T T T u v a (6) x y y Assuming that the gaseous mixture have uniform veoity and temperatures. Using the Maxwe-Stefan equation to desribe the mass transfer rather than Fik s aw. The onservation equations of ontinuity, momentum, energy, and gas omponent for the gaseous phase are: mum mvm 0 (7) x y um mumum mumvm m g m x y y y t m W mump T m m mvmp t m m k m md p g p t v m x y y y y y WA WB WC mumwa mvmwa md md md3 x y y y y y y y WA WB WC mumwb mvmwb md md md3 x y y y y y y y WA WB WC mumwc mvmwc md3 md3 md33 x y y y y y y y W W W W. The interfaia ondition.3 Boundary onditions: At the pate wa y 0 At the fow free domain y At the iquid-mixture interfae y um D A B C (8) (9) (0) u v 0, T Twa () u,t T,W W () u u u um, i m y y d dm mi u v m um vm (3) dx dx n T Tm K Km mih fg Ni Hi y y i The effet of mass transfer on the heat transfer is mainy in two aspets. The speies transport between two phase may bring additiona enthapy to the tota heat transfer. Another is aed Dofour effet, referring to the heat transfer aused by the diffusion of omponents. The atter is desribed as the ast item in the ontinuous heat fux equation, whih an be ignored in the hemia engineering proess inuding ondensation[4]..4 Dimensiona anaysis and simpify. m 3

4 To ose the system of onservation equations before, the iquid-gas interfae an be express as foows: (x, y,t) y (x,t) (4) The interfae tangent vetor is, the interfae norma vetor is n, the, y, n, x (5) x y The harateristi quantities is defined as foows: d L, U u 0, T Tsat pin T w (6) Dimensioness quantities: x X L, y Y L, L, U t L, u * u U, v * v U, 0 p p U, TT, m m * U The non-dimensiona differentia forms of the simpified iquid-gas interfae equations: * * * * u u ( v v ) (7) m X m * * * m = u v X t (8) X * m * * mm = um vm X t X Ja * km m mi = Re Pr Y i k Y i C T Where p Ja, Pr, Re v, and Fr U hfg a gl..5 The basi properties of the modeing omponents Tabe. Physia parameter of the modeing omponents Name Moar 分子沸点偏心临界温度临界压力 fration 量 M Tb / K 因子 T/K P / MPa 临界体积 V / (L mo ) 临界压缩 因子 Z CH CH CH N (9) (0) 3. THE NUMERICAL SOLUTION PROCEDURES 3. The modeing proedure 4

5 COMSOL Mutiphysis is based on the Finite Eement Method (FEM) to sove the physia mode in the form of differentia equations. Seet the turbuent ow k-ɛ mode to mode the fowing of iquid and gaseous phase separatey. At the same time, the iquid-gas interfae is aught by the Moving Mesh Interfae using the arbitrary Lagrangian-Euerian method (ALE).The interfaia traking equation is: V eff 0 t k T k T where V i i m m i eff v is the modified veoity reated to the interfae veoity of the iquid fim, h fg the temperature gradients of iquid and mixture in the interfae, the therma ondutivity of iquid and mixture, and the atent heat of vaporization. Aording to the order of magnitude anaysis, the initia iquid-gas interfae is x x. The body fore is Fx 0, Fy g ( ). desribed as /4 The mass transfer mode is defined by the Transport of Conentrated Speies Interfae based on the Maxwe-Stefan equation. To find out the heat and mass transfer aw, this paper take the pure propane ondensation proess as a ontro group to ompare with the mixture gas (propane, ethane, methane and nitrogen). 3. The modeing resut of the propane ondensation proess. g Figure3. The veoity fieds of pure propane fow Figure3. The temperature fieds of pure propane fow Figure3.3 The veoity fieds of mixture fow Figure3.4 The temperature fieds of mixture fow 5

6 Figure3.5 The partia temperature fieds of pure fow Figure3.6 The partia temperature fieds of mixture fow Figure3.7 The partia mass fration fieds of gaseous propane As shown in the figure 3. and 3., the turbuent fow shows up in the y=-0.4m for pure propane fow and y=0.m for the mixture fow. The presene of non-ondensabe gas may disturb the gas fim. We an see partia temperature fied in the same position of two ondition from the figure 3.3 and 3.4 indiating that the non-ondensabe ause a arge temperature gradient. In the non-azeotropi mixture ondensation proess, there is a arge heat transfer resistane at the gas boundary ayer. The figure3.7 shows the mass fration of gaseous propane in the mixture. In the iquid-gas interfae beause of the non-ondensabe gases, the distribution of propane is non-uniform. The presene of non-ondensabe gases resist the propane moeue diffusion to the interfae. 6

7 REFERENCE [] N.G. Kiriov, Anaysis of Modern Natura Gas Liquefation Tehnoogies, Chemia and Petroeum Engineering, 40(7) (004) [] W. Rohsenow, Heat transfer and temperature distribution in aminar fim ondensation, Trans. Asme, 78 (956) [3] S.B. A-Shammari, D.R. Webb, P. Heggs, Condensation of steam with and without the presene of nonondensabe gases in a vertia tube, Desaination, 69() (004) [4] V. Srzi, H.M. Soiman, S.J. Ormiston, Anaysis of aminar mixed-onvetion ondensation on isotherma pates using the fu boundary-ayer equations: mixtures of a vapor and a ighter gas, Internationa Journa of Heat and Mass Transfer, 4(4) (999)