University of Wisconsin –Fusion Technology Institute

Review and Analysis of Condensation Experiments at UW-Madison

University of Wisconsin–MadisonDepartment of Engineering Physics

Fusion Technology InstituteM.H. Anderson, J.G. Murphy and M.L. Corradini

Idaho National Engineering and Environmental Laboratory

Fusion Safety ProgramB.J. Merrill

International Energy Agency Task 2 MeetingMarch 22, 2001

University of Wisconsin –Fusion Technology Institute

• Condensation of water vapor on cold/cryogenic surfaces is an important consideration for future fusion magnet designs

• Structural limitations may be an issue because of ice formation on the magnet systems

• An accurate assessment of the quantity of condensate/ice and subsequent loading to the magnet system is essential

• Experiments have been conducted (with analyses) at UW-Madison to determine the atmospheric moisture content effect on condensation rate and subsequent freezing on a stainless steel surface

• Modelling is utilized to determine frost conductance

University of Wisconsin –Fusion Technology Institute

• Simple first principle models have been employed to test against preliminary experiments

• Test and Analysis sequence• Preliminary analyses performed (large ice formation rates seen)

• Experiments Run• Determining ice properties (frost conductance i.e., hfrost)

• MELCOR simulations will be used when ice porosity isdetermined and code updated with ice properties as modelparameters

• This presentation reviews the experiments and analysis performed

University of Wisconsin –Fusion Technology Institute

UW- Madison has been working in Fusion Safety over 20 yrs with our current activities focused on:

• Liquid metal compatibility tests with fusion blanket coolants

• Cryogenic liquid interactions (LHe, LN2) with water and structures

• Experimental analysis and MELCOR model development

University of Wisconsin –Fusion Technology Institute

• Simplified heat transfer model to determine ice production rate

• Heat conducted through stainless steel and frost layer, and thenconvected through the steam/gas mixture

• This heat removal rate drives ice formation

• Thickness of frost is changing with time• This is accounted for in the heat transfer equation• Added resistance via increase in frost layer

• Appropriate frost thicknesses and porosities will be matched to empirically determine a frost formation modeling methodology

• In the later stages, MELCOR will be utilized with its ice formation models to match the test data

University of Wisconsin –Fusion Technology Institute

• Modeled as resistances in series (stainless, ice and steam/gas)

Heat transfer through material:

q=DT/[1/hsteam/gas + 1/hfrost + dss/kss]A

Mass rate of ice produced:

mr=q/[DHvap + DHfus + CpsteamDTsteam + CpwaterDTwater]

Thickness of ice produced:

thickness=[Dtime mr]/[rice A]

Variables:A = surface areaCp = specific heatK = thermal conduc.Dtime = time stepDT = temp gradientH = heat transfer coeffr = densityDH = heat of formationNote: hfrost ~ (1-porosity)2 kice/dice

University of Wisconsin –Fusion Technology Institute

•With a known hconvection we can eventually fit the test data to the model and determine the appropriate kice from the porosity of the ice

• Natural convection HTC (hconvection)

Heat transfer coefficient = k/[L NuL]

NuL=0.54 RaL0.25

RaL=gB[Ts-Tinf]L3/[an]

•Representative value: hconvection ~ 7 - 13 W/m2-K (small)

VariablesNuL = nusselt numberRaL = Rayleigh numberL = length scaleK = thermal conductivityg = gravityB = 1/TfTbulk = bulk tempa = thermal diffusivityn = viscosity

University of Wisconsin –Fusion Technology Institute

•Calculation of “gas” heat transfer coefficient (HTC)

• hsteam/gas (total HTC)= hconv+hcond

• hconv=0.13(kg/L)Gr1/3Pr1/3

• hcond=Sh[(DhfgCMw)/(LRvTiTb)]F

Representative values:

hcond ~ 47.9 W/m2-K ; for Tboiler = 81.5oC, Pv = 0.5, Pair = 0.5

hconv ~ 8.9 W/m2-K ; for Tboiler = 81.5oC, Pv = 0.5, Pair =0.5

Pr = Cpk/mC = P/(RTavg)Sh = 0.13(GrSc)1/3FMw = molecular weight H2OSc = m/rDoRv = 8314/18Gr = grgb(rgi-rgb)L3/m2

L = lengthq = ln(R+1)/R Suction termkg = thermal conduct.R = (Xvi-Xvb)/(1-Xvi)D = diffusion coeff.F = ln[Xnc,b/Xnc,i]/ln[(1-Xnc,b)/(1-Xnc,I)]X = mole fractions

University of Wisconsin –Fusion Technology Institute

• Plot of Ice Formation versus Time (no porosity)

• Ice formation rates are quite high (hcondensation drives ice formation)

ICE Thickness (m) vs. Time (s)

0.000

0.004

0.008

0.012

0.016

0.020

0 2000 4000 6000 8000 10000Time (s)

ICE

Thi

ckn

ess

(m)

University of Wisconsin –Fusion Technology Institute

• Schematic of vacuum vessel and stainless steel pedestal

Flange

Lines Plate

6.040

3.75

1.0750.50

Interface Plate

9.0

18.0

Fla n

ge

Cap

Pla

te

Inte

rfac

e Pl

ate

Win

dow

Fla

nge

0.875

Flange

Top Plate

0.2000.260

0.945 0.040

0.3500.150

Hygrometer &Temperature

Pressure

University of Wisconsin –Fusion Technology Institute

• Vacuum vessel with stainless steel condensation pedestal

University of Wisconsin –Fusion Technology Institute

• 316 SS Cryogenic Condensation structure withinstrumentation (heat flux sensor, thermocouples)

University of Wisconsin –Fusion Technology Institute

• Water vapor/air mixture is heated to desired conditions in the pressure tank (i.e., temperature/partial pressure)

• The vacuum test chamber is pumped down to a low (~ 200 mTorr)pressure

• Liquid nitrogen cools the stainless steel pedestal in the testvolume, cooling the condensing surface to near 77 K

• When the stainless steel pedestal has reached an equilibrium thermal condition the gas is injected into the vacuum vessel

•A valve is opened on the pressure tank and the water vapor/air contents are slowly released into the vacuum test chamber

• The condensation/freezing event is filmed and data (temperatures, pressures and heat flux) are measured

• The system is allowed to reach pressure equilibrium

University of Wisconsin –Fusion Technology Institute

Test 7Boiler at 81.5o CPv = 0.5 barPair = 0.5 barPlate at ~80 K

University of Wisconsin –Fusion Technology Institute

• Pedestal iced up after 81.5 C boiler experiment Pv = 0.5 , Pair = 0.5

0 200 400 600 800 1000 1200 1400-0.0001

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007Test 7: Boiler conditions 81.5oC, P

v = 0.5,P

air =0 .5

Heat Flux

Hea

t Flu

x [W

/cm

2 ]

Time [s]

0

200

400

600

800

Test Section Pressure

University of Wisconsin –Fusion Technology Institute

0 200 400 600 800 1000 1200 140050

100

150

200

250

300

Test 7: Boiler conditions 81.5oC,Pv = 0.5, Pair = 0.5

Center plate temperature Side plate temperature Top right side plate temp Top left side plate temp

Tem

pert

are

[K]

Time [s]

0 200 400 600 800 1000 1200 140020

25

30

35Test 7: Boiler conditions 81.5oC, P

v = 0.5, P

air = 0.5

Relative hum

idity [%]

Test section Temperature

Tem

pera

ture

[o C]

Time [s]

-20

0

20

40

60

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180

Relative humidity in test section [%]

0 200 400 600 800 1000 1200 14008081828384858687888990

Temperature of gas in boiler

Boi

ler

Tem

pera

ture

[o C]

Time [s]

56789101112131415

Test 7: Boiler conditions 81.5oC, Pv = 0.5, P

air = 0.5

Boiler Pressure [psig]

University of Wisconsin –Fusion Technology Institute

• The high heat transfer coefficient results in a sharp increase in plate temperature

• Uneven cooling of pedestal causes frost and clear ice together. The solid iceforms on the portion of the plate that is at a higher temperature.

0 400 800 1200 1600

-0.0015

-0.0010

-0.0005

0.0000

0.0005Test 4: Boiler conditions 100oC, Pv = 1.0, Pair = 0.0

Pressure [torr]

Heat Flux

Hea

t Flu

x [W

/cm

2 ]

Time [s]

0

200

400

600

800

Test Section Pressure

University of Wisconsin –Fusion Technology Institute

0 200 400 600 800 1000 1200 140050

100

150

200

250

300

350

Center plate temperature Side plate temperature Top left side plate temp Top right side plate temp

Tem

pera

ture

[K]

Time [s]0 200 400 600 800 1000 1200 1400

10

20

30

40

50

60

70

80

90

100Test 4: Boiler conditions 100oC, Pv = 1.0, Pair =0.0

Relative hum

idity [%]

Test section TemperatureT

empe

ratu

re [o C

]

Time [s]

0

20

40

60

80

100

120

Relitive humidity in test section

0 500 1000 150090

92

94

96

98

100

102

104 Test 4: Boiler conditions 100o C, Pv = 1.0, Pair = 0.0

Temperature of gas in boilerB

oile

r T

empe

ratu

re [o C

]

Time [s]

10

11

12

13

14

15

Boiler Pressure [psia]

University of Wisconsin –Fusion Technology Institute

• Heavy ice formation after injection of pure water vapor from the boiler. The injection rate was controlled to main to keep a more uniform plate temperature.

0 500 1000 1500 2000

0.000

0.001

0.002

0.003Test 3: Boiler conditions 100oC, Pv = 1, Pair = 0

Test section Pressure [torr]

Heat Flux

Hea

t Flu

x [W

/cm

2 ]

Time [s]

0

200

400

600

800

Test Section Pressure

University of Wisconsin –Fusion Technology Institute

0 500 1000 1500 200050

100

150

200

250

300

350

Test 3: Boiler conditions 81.5oC, Pv = 1, Pair = 0

Center plate temperature Side plate temperature Top left side temperature Top right side temperature

Tem

pera

ture

[K]

Time [s]

0 500 1000 1500 200020

25

30

35

40

45

50

55

60

Relative humidity in test section [%]

Tem

pera

ture

[o C]

Time [s]

-20

0

20

40

60

80

100

120

140

160

Test 3: Boiler conditions 100 oC, Pv = 1.0, Pair = 0.0

humidity

0 500 1000 1500 200099

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104

105

Test 3: boiler conditions 100 oC, Pv = 1.0, Pair = 0.0

Temperature of gas in boiler

Boi

ler

Tem

pera

ture

[o C]

Time [s]

10

12

14

16

18

20

Boiler Pressure [psia]

University of Wisconsin –Fusion Technology Institute

• Control-volume systems code for thermal-hydraulic analysis (SANDIA National Lab)

• Control volumes connected via orificed flow paths

• Experimental condensation/freezing rate can be modeled by MELCOR

• Benchmark the code against selected UW experiments

• Determine MELCOR utility in predicting ice formation on cryogenic structures used in fusion system designs

University of Wisconsin –Fusion Technology Institute

• MELCOR simulations have been run with “hard-wired” constant values for the ice thermal conductivity and porosity

• An updated version is being modified to allow easy input of these parameters

• Parametric analyses will be run with MELCOR utilizing various ice thermal conductivities and porosities

• This updated version of MELCOR will be used to match test results from the UW experiments

• Ice thermal conductivity and porosity will be varied to produce the desired output (i.e., matching the heat flux and temperatures from the experiment). This will be used to get the correct hfrost = kfrost/d.

University of Wisconsin –Fusion Technology Institute

1. Experiments were run to determine frost formation rates and heat fluxes on a cryo-cooled stainless steel pedestal in a vapor/air environment similar to accident conditions

2. First principle models were employed to determine characteristics of the frost formation on the cold structure

3. The model comparison to the test data will provide porosity behavior as a function of pressure and temperature for use in MELCOR for parametric analyses of the system design

4. MELCOR needs to be modified to allow easy input of these parameters to assist in comprehensive parametric analyses