Numerical Simulation of Steam Condensation in a Parallel Plate Passage

Transcription

1 Numerical Simulation of Steam Condensation in a Parallel Plate Passage Dr. Zhenyu Liu Zhenyu.Liu@energy.lth.se

2 Introduction Shell-Tube Exchanger (from Southwest Thermal Technology ) Plate Heat Exchanger (from Alfa Laval) PHEs can serve as an alternative to shell-tube heat exchanger for most applications Temperature limit: 160 o C Pressure limit: 25 bar

3 Various types of PHEs Temperature limit: 400 o C Pressure limit: 40 bar More fluids permitted A brazed PHE A semi-welded PHE (from Alfa Laval) A fully-welded PHE

4 Common condensation applications are involved with steam, refrigerants, hydrocarbons, etc. A Combined Heat and Power Plant A Distillation Unit A Typical HVAC System L. Wang, Bengt Sundén, Thermal and hydraulic performance of plate heat exchangers as condensers. Compact Heat Exchangers and Enhancement Technology for the Process Industries,2003:

5 Condensation Liquid droplet nucleation Homogeneous condensation --Liquid droplet nucleation occurring entirely within a supercooled vapor Heterogeneous condensation --Liquid droplet nucleation occurring at the interface of a metastable vapor and another phase at a low temperature Dropwise Filmwise Tobias Seidel, Helmholtz-Zentrum Dresden-Rossendorf, Germany

6 Review of Previous Work --Film Condensation on a Vertical Plate Nusselt Analysis for Laminar Flow A pure vapor at T sat. Negligible shear stress at liquid/vapor interface. u y y 0 Negligible advection in the film. Hence, the steady-state x- momentum and energy equations for the film are 2 u 1 p X 2 y x 2 T 0 2 y l l p / y 0, The boundary layer approximation, may be applied to the film. p dp vg x dx Film thickness: x 4kll Tsat Ts x gl l vhfg 1/ 4 Nusselt, W., 1916, Die Oberflächenkondensation des Wasserdampfes, Z. Vereins deutscher Ininuere, Vol. 60, pp No shear stress No vapor motion No subcooling of liquid Interface is smooth

7 Filmwise Condensation in a Stagnant Pure Vapor Reservoir: Amir Faghri, Yuwen Zhang, Transport Phenomena in Multiphase Systems, Academic Press,2006 Transition may occur in the film and three flow regimes may be identified and delineated in terms of a Reynolds number, as defined as Re 4ρ μ δ μ 2 13 / hl l / g -1/3 147Re. k l (Analytical result) No vapor motion h h L L 2 13 / l / g 2 l k k l l 13 / (Numerical result) / g (Experimental result) Re Re 5. 2 Re Pr Re 253

8 Previous Experimental Studies Bum-Jin, C., K. Sin, et al. (2004). "An experimental investigation of film condensation of flowing mixtures of steam and air on a vertical flat plate." International Communications in Heat and Mass Transfer 31(Copyright 2004, IEE):

9 Large amplitude waves S, K. P., H. K. M, et al. (1996). "Condensation of pure steam and steam-air mixture with surface waves of condensate film on a vertical wall." International Journal of Multiphase Flow 22(5):

10 B. Qi., Z. Li, et al. (2011). "Experimental study on condensation heat transfer of steam on vertical titanium plates with different surface energies." Experimental Thermal and Fluid Science 35(Compendex): # Dropwise +Filmwise q= W/m 2, T=11.0 o C q= W/m 2, T=16.3 o C 2# Filmwise q= W/m 2, T=3.5 o C q= W/m 2, T=10.4 o C 3# Dropwise q= W/m 2, T=3.9 o C q= W/m 2, T=10.9 o C Surface Energy: 2# >1 # >3 # Contact Angle(H2O): 2 # <1 # <3 #

11 Some Related Numerical Works Liu, Q. M., Z. X. Zhong, et al. (2010). "The CFD Simulation Study on the Fluid-State of a Wavy Plate of Evaporative Condenser." AIP Conference Proceedings 1207(1): Gu, F., C. J. Liu, et al. (2004). "CFD simulation of liquid film flow on inclined plates." Chemical Engineering and Technology 27(Compendex): Sun, J., Y.-L. He, et al. (2011). "A molecular dynamics study on heat and mass transfer in condensation over smooth/rough surface." International Journal of Numerical Methods for Heat and Fluid Flow 21(Compendex): Nebuloni, S. and J. R. Thome (2010). "Numerical modeling of laminar annular film condensation for different channel shapes." International Journal of Heat and Mass Transfer 53(Compendex):

12 CFD Simulation of Filmwise Condensation with VOF method The VOF model is designed to track the location and motion of a free surface between two or more immiscible fluids. VOF model applicability: Flow regime Slug flow, stratified/free-surface flow Assumes that each control volume contains just one phase (or the interface between phases). For volume fraction of k th fluid, three conditions are possible: F k = 0 if cell is empty (of the k th fluid) F k = 1 if cell is full (of the k th fluid) 0 < F k < 1 if cell contains the interface between the fluids Tracking of interface(s) between phases is accomplished by solution of a volume fraction continuity equation for each phase:

13 Governing Equations Continuity Equation div ρu 0 Momentum Equation ρuu P μ u u ρgf Energy Equation ρc T div ρc t Tu div k grad T Q VOF Equation F t div F u m ρ Physical Properties kf k 1F k ρf ρ 1F ρ μf μ 1F μ c F ρ c 1F ρ c Boundary Condition Inlet: V in =1 m/s or 3 m/s, T SAT =373K, F v =1 Wall: T w =353K or 300K Outlet: outflow / pressure outlet Middle plane of Channel: symmetry Physical model

14 Geometric Reconstruction Scheme 0.5, For the cases where only two phases are present in a cell, and, : 2 Surface Tension Wall Adhesion

15 Numerical Technique/Assumptions Viscous Model: Laminar Pressure-Velocity Coupling Scheme: PISO Spatial Discretization of Variables Gradient: Least Squares Cell Based Pressure : PRESTO! Volume Fraction: Geo-Reconstruction Others: QUICK Transient formulation: First order implicit (non-iterative Time Advancement) UDF: source terms for energy and VOF equations Surface Tension & Wall Adhesion Mesh: uniform quad mesh (0.1mm*0.5mm), total cells=0.16m Convergence Criteria: All variables < 10e -5 Time Step Method: Variable (Global Courant Number< 0.1) A Calculation time of 200 hours is necessary to obtain a steady-state result for each case (A parallel simulation using 4 processors, 3 GHz, 8 GB )

16 Various Source Terms for VOF and Energy Equation Based on the concept that Q is a function of the latent heat L C. Wilhelmsson et al.,2007 m ρ 1F, Q ABh A10 c T T, B 10 Based on the energy equation. The temperatures at the interface are assumed to be the saturation temperature and Q is calculated based on the newly updated temperature field A. Faghri et al, 2006 div ρc Tu div k grad T /, 10 T T The direct calculation of the normal component of the heat flux vector to the liquid vapor interface based on the last time step explicit procedure. L. Wang et al.,2004 m k /L, Q k is the temperature gradient at the interface, A is the area of the interface and V is the cell volume. Linear temperature distribution in the liquid layer in Nusselt theoryw. Nusselt, 1916 m k /L, Q k In NEPTUNE CFD documentation Lavieville et al., m,,q L, where HTC stands for the liquid heat transfer coefficient, h for the liquid enthalpy, h, for the saturation enthalpy liquid temperature and T T p for the saturation temperature Hertz Knudsen equation based on kinetic gas theory Knudsen,1934, 2 2 Use energy balance in the interface region Samuel et al., 2000 k F T k F T F / Q k F T k F T F A B

17 Numerical results ---Source terms based on Hertz-Knudsen equation (A) Hertz-Knudsen equation: 6 2 Causius-Clapeyon equation (Lide,1998) : p p T T The accommodation coefficient as a function of the condensation coefficient (Knudsen, 1934): 1 The volumetric interfacial surface area is related to the mean Sauter diameter 6 Hertz-Knudsen equation could be expressed as β β 6 2 In order to numerically maintain the interface temperature close to saturation temperature β 200 Excessively a large β causes a numerical convergence problem, while too small value leads to a significant deviation between the interfacial temperature and the saturation temperature(schepper,2009)

18 Laminar Liquid boundary layer Wavy Vapor boundary layer Y directional velocity distribution (m/s)

19 10 mm 2mm 1.5mm 10 mm Temperature distribution ( o C) Liquid volume fraction factor distribution

20 1mm 5mm a) b) c) d) Distribution of: a) liquid volume fraction factor, b) temperature[oc], c) Condensation rate [kg/s/m2], and d) velocity[m/s]

21 Liquid volume fraction Temperature velocity

22 Due to variations in Interfacial area and film thickness for wavy flow q (W) q (W) q Condensate Time (s) T w ( o C) q Condensate Total wall heat flux and amount of condensate for different simulating time Total wall heat flux and amount of condensate for different wall temperature Condensate (kg/s) Condensate (kg/s) Nu Nu Nu Nu Nu Time=25s Time=20s Time=15s Time=10s Time=5s Y (m) Nusselt number along the Y axis

23 F l Interface Temperature ( o C) Interface X position (m) 12 X position (m) Velocity (m/s) Interface Condesate Rate (kg/(sm 3 )) Interface X position (m) X position (m) Liquid volume factor, temperature, velocity and condensate rate along x axis (at outlet)

24 The interface mass flux in energy and volume fraction equations is determined using energy balance in the interface Here and are rates of heat transfer conduction from liquid to interface and vapor to interface respectively and is the unit normal vector of the interface, therefore: and Numerical results ---Source terms based on energy balance in the interfacial region (B) k F T k F T F /

25 Liquid volume fraction (Inlet velocity=1m/s, Tw=353K) Liquid volume fraction (Inlet velocity=3m/s, Tw=353K) Y velocity (Inlet velocity=1m/s, Tw=353K) Y velocity (Inlet velocity=3m/s, Tw=353K)

26 4.0x10 5 Velociy 1m/s 3.5x x10 5 Velocity 3m/s Nusselt Film Theory Boyko Kruzhilin Formula 2.5x10 5 q (w/m 2 ) 2.0x x x x Y (m) Wall heat flux along the Y-axis (T w =353K)

27 Tw=300K Tw=353K q (w/m 2 ) Y (m) Wall heat flux along the y-axis (V in =3m/s)

28 Larger amplitude waves Larger amplitude waves a) surface tension= 0.1 N/m b) surface tension= N/m Liquid volume fraction factor distribution for different surface tension (Tw=353K, Inlet velocity=1m/s)

29 Brief Summary Source term A The sharpness of interface depends on β a large β leads to a sharp interface, but bad convergence) The condensation rate depends on β ( it should be specified according to experiment results) and temperatures at interfacial cells Source term B The interface is sharp The condensation rate depends on gradients of temperature and volume fraction factor at interfacial cells.

30 Numerical Test (A Three Dimensional Model) Temperature Velocity Condensation Rate Liquid Volume Fraction

31 Future Work Mesh should be modified to simulate thin film flow more accurately 0.1mm 0.01mm ; Dynamic Mesh Adaptation Adopt different turbulence models to simulate wavy or turbulent flows

32 Thanks LUND UNIVERSITY