numerical simulation of steam condensation in a parallel plate … · 2011-05-25 · numerical...

Energy Science, Lund University, 2011 / Presented by Zhenyu Liu

Numerical Simulation of Steam Condensation in a Parallel Plate Passage

Dr. Zhenyu [email protected]


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


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)


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.


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


• 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


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


• 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.


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


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


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.


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:


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


∆

0.5,

For the cases where only two phases are present in a cell, and , :

2

Geometric Reconstruction Scheme

Wall Adhesion

Surface Tension


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 )


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


′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)


Y directional velocity distribution (m/s)

Liquid boundary layer

Vapor boundary layer

Laminar

Wavy


Temperature distribution (oC) Liquid volume fraction factor distribution

2mm

1.5mm

10 mm

10 mm


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


Liquid volume fraction

Temperature

velocity


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


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


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)


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)


-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)


-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)


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


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.


Numerical Test (A Three Dimensional Model)

Temperature Velocity

Condensation Rate Liquid Volume Fraction


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


LUND UNIVERSITY

Thanks

numerical simulation of steam condensation in a parallel plate … · 2011-05-25 · numerical...

Documents