Energy Science, Lund University, 2011 / Presented by Zhenyu Liu Numerical Simulation of Steam Condensation in a Parallel Plate Passage Dr. Zhenyu Liu [email protected]
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Numerical Simulation of Steam Condensation in a Parallel Plate Passage
Dr. Zhenyu [email protected]
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Various types of PHEs• Temperature limit: 400 o C• Pressure limit: 40 bar• More fluids permitted
A brazed PHE
A semi-welded PHE
A fully-welded PHE(from Alfa Laval)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Common condensation applications are involved with• steam,• refrigerants, • hydrocarbons, • etc.
A Combined Heat and Power Plant
A Typical HVAC SystemA Distillation Unit
L. Wang, Bengt Sundén, Thermal and hydraulic performance of plate heat exchangers as condensers. Compact Heat Exchangers and Enhancement Technology for the Process Industries,2003:461-469.
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
FilmwiseDropwise
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
Tobias Seidel, Helmholtz-Zentrum Dresden-Rossendorf, Germany
Condensation
Liquid droplet nucleation
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
• Nusselt Analysis for Laminar Flow
A pure vapor at .satTNegligible shear stress at liquid/vapor interface.
0y
uy
Negligible advection in the film. Hence, the steady-state x-momentum and energy equations for the film are
2
2
2
2
1
0
l l
pu Xy x
Ty
The boundary layer approximation, may be applied to the film.0/ ,p y
vp dp gx dx
1 44
/l l sat s
l l v fg
k T T xx
g h
Film thickness:
No shear stressNo vapor motionNo subcooling of liquidInterface is smooth
Nusselt, W., 1916, “Die Oberflächenkondensation des Wasserdampfes,” Z. Vereins deutscher Ininuere, Vol. 60, pp. 541-575.
Review of Previous Work--Film Condensation on a Vertical Plate
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Filmwise Condensation in a Stagnant Pure Vapor Reservoir:
Transition may occur in the film and three flow regimes may be identifiedand delineated in terms of a Reynolds number, as defined as
1 32-1/31 47 Re
//
.L l
l
h gk
1 32
1.22Re
1.08 Re 5 2
//
.L l
l
h gk
1 32
-0.5 0 75
Re8750 +58 Pr Re 253
/
.
/L l
l
h gk
(Analytical result)
(Numerical result)
(Experimental result)No vapor motion
Amir Faghri, Yuwen Zhang, Transport Phenomena in Multiphase Systems, Academic Press ,2006
Re4ρ μ δμ
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
• 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): 703-710.
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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): 893-908.
Large amplitude waves
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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): 211-218.
1#
2#
3#
Surface Energy: 2# >1 # >3 # Contact Angle(H2O): 2 # <1 # <3 #
Dropwise+Filmwise
Filmwise
Dropwise
q= 4.2×105 W/m2, ∆T=11.0 oC q= 4.5×105 W/m2, ∆T=16.3 oC
q= 0.96×105 W/m2, ∆T=3.5 oC q= 1.91×105 W/m2, ∆T=10.4 oC
q= 4.15×105 W/m2, ∆T=3.9 oC q= 8.51×105 W/m2, ∆T=10.9 oC
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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): 244-267.
Some Related Numerical Works
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): 2615-2627.
Gu, F., C. J. Liu, et al. (2004). "CFD simulation of liquid film flow on inclined plates." Chemical Engineering and Technology 27(Compendex): 1099-1104.
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): 922-926.
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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 kth fluid, three conditions are possible:
Fk = 0 if cell is empty (of the kth fluid)Fk = 1 if cell is full (of the kth fluid)0 < Fk< 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:
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Continuity Equationdiv ρu 0
Momentum Equation∙ ρuu P ∙ μ u u ρg F
Energy Equationρc Tt div ρc Tu div kgradT Q
VOF EquationFt div F u
mρ
Physical Properties k F k 1 F kρ F ρ 1 F ρμ F μ 1 F μ
c F ρ c 1 F ρ c
Governing Equations
Boundary ConditionInlet: Vin=1 m/s or 3 m/s, TSAT=373K, Fv=1Wall: Tw=353K or 300KOutlet: outflow / pressure outletMiddle plane of Channel: symmetry
Physical model
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
∆
0.5,
For the cases where only two phases are present in a cell, and , :
2
Geometric Reconstruction Scheme
Wall Adhesion
Surface Tension
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Numerical Technique/Assumptions Viscous Model: Laminar
Pressure-Velocity Coupling Scheme: PISO
Spatial Discretization of VariablesGradient: Least Squares Cell BasedPressure : PRESTO!Volume Fraction: Geo-ReconstructionOthers: 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 )
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
BasedontheconceptthatQ isafunctionofthelatentheatL C.Wilhelmsson etal.,2007
m ρ 1 F ,Q A Bh A 10 c T T , B 10
Basedontheenergyequation. ThetemperaturesattheinterfaceareassumedtobethesaturationtemperatureandQ iscalculatedbasedonthenewlyupdatedtemperaturefield A.Faghri etal,2006
div ρc Tu div kgradT / , 10 T T
Thedirectcalculationofthenormalcomponentoftheheatfluxvectortotheliquid‐vaporinterfacebasedonthelasttimestep explicitprocedure . L.Wangetal.,2004
m k| |
/L,Q k| |
| |isthetemperaturegradientattheinterface,AistheareaoftheinterfaceandVisthecellvolume.
LineartemperaturedistributionintheliquidlayerinNusselt theory W. Nusselt,1916
m k /L,Q k
InNEPTUNECFDdocumentation Lavieville etal.,2005 .
m,
, Q,
L
whereHTC standsfortheliquidheattransfercoefficient, h fortheliquidenthalpy, h , forthesaturationenthalpyliquidtemperatureandT T p forthesaturationtemperatureHertz‐Knudsenequationbased onkineticgastheory Knudsen,1934
′ 2 , 2Useenergybalanceintheinterfaceregion Samueletal.,2000
k F T k F T ∙ F /Q k F T k F T ∙ F
Various Source Terms for VOF and Energy Equation
A
B
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
′6
2
Causius-Clapeyon equation (Lide,1998) : p p T T
The accommodation coefficient as a function of the condensation coefficient (Knudsen, 1934): 1
Hertz-Knudsen equation:
Hertz-Knudsen equation could be expressed as
β
β6
2
In order to numerically maintain the interface temperature close to saturation temperature
6The volumetric interfacial surface area is related to the mean Sauter diameter
β 200Excessively a large β causes a numerical convergence problem, while toosmall value leads to a significant deviation between the interfacialtemperature and the saturation temperature(Schepper,2009)
Numerical results ---Source terms based on Hertz-Knudsen equation (A)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Y directional velocity distribution (m/s)
Liquid boundary layer
Vapor boundary layer
Laminar
Wavy
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Temperature distribution (oC) Liquid volume fraction factor distribution
2mm
1.5mm
10 mm
10 mm
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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]
5mm
1mm
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Liquid volume fraction
Temperature
velocity
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
300 310 320 330 340 350 360
500
1000
1500
2000
2500
3000
3500 q Condensate
Tw(oC)
q (W
)
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
Condensate (kg/s)
-0.4 -0.2 0.0
0
20
40
600
20
40
600
20
40
0
20
40
600
20
40
-0.4 -0.2 0.0
Nu
Y (m)
Time=5s
Nu
Time=10s
Nu
Time=15s
Nu
Time=20s
Nu
Time=25s
Nusselt number along the Y axis
Total wall heat flux and amount of condensate for different simulating time
Total wall heat flux and amount of condensate for different wall temperature
0 5 10 15 20 25 30 35 402800
3000
3200
3400
3600
3800
4000
4200
4400
q Condensate
Time (s)
q (W
)
0.00170
0.00172
0.00174
0.00176
0.00178
0.00180
0.00182
0.00184
0.00186
0.00188
0.00190
Condensate (kg/s)
Due to variations in Interfacial area and film thickness for wavy flow
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
0.000 0.005 0.010 0.015 0.020
0.0
0.2
0.4
0.6
0.8
1.0
F l
X position (m)0.000 0.005 0.010 0.015 0.020
290
300
310
320
330
340
350
360
370
380
Tem
pera
ture
(o C)
X position (m)
0.000 0.005 0.010 0.015 0.020
0.0
0.2
0.4
0.6
0.8
1.0
Vel
ocity
(m/s
)
X position (m)0.000 0.005 0.010 0.015 0.020
0
2
4
6
8
10
12
Con
desa
te R
ate
(kg/
(sm
3 ))
X position (m)
Liquid volume factor, temperature, velocity and condensate rate along x axis (at outlet)
Interface
Interface
Interface
Interface
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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
k F T k F T ∙ F /
Numerical results ---Source terms based on energy balance in the interfacial region (B)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Y velocity(Inlet velocity=3m/s , Tw=353K)
Liquid volume fraction (Inlet velocity=3m/s , Tw=353K)
Y velocity (Inlet velocity=1m/s, Tw=353K)
Liquid volume fraction (Inlet velocity=1m/s, Tw=353K)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
-0.4 -0.3 -0.2 -0.1 0.0
0.0
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
3.5x105
4.0x105
Velociy 1m/s Velocity 3m/s Nusselt Film Theory Boyko Kruzhilin Formula
q (w
/m2 )
Y (m)
Wall heat flux along the Y-axis (Tw=353K)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
-0.4 -0.3 -0.2 -0.1 0.0
0
100000
200000
300000
400000
500000
600000 Tw=300K Tw=353K
q (w
/m2 )
Y (m)Wall heat flux along the y-axis (Vin=3m/s)
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Liquid volume fraction factor distribution for different surface tension (Tw=353K, Inlet velocity=1m/s)
a) surface tension= 0.1 N/m b) surface tension= 0.0582 N/m
Larger amplitude wavesLarger amplitude waves
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
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.
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Numerical Test (A Three Dimensional Model)
Temperature Velocity
Condensation Rate Liquid Volume Fraction
Energy Science, Lund University, 2011 / Presented by Zhenyu Liu
Future Work
Mesh should be modified to simulate thin film flow more accurately0.1mm 0.01mm ; Dynamic Mesh Adaptation
Adopt different turbulence models to simulate wavy or turbulent flows