anthony servonet stefano nebuloni bruno agostini - supervisor

Micro-channel flow boiling correlations and 3-zone model plus comparison to recent published resultsAnthony ServonetStefano NebuloniBruno Agostini - supervisor08 February 2007

Contents of the presentationintroduction to micro-channel featuresheat transfer prediction modelsKandlikar and Balasubramanian (2004)Zhang at al. (2004)3 zone model Thome-Dupont-Jacobi (2004)comparison with experimental dataconclusions

General considerations on micro-scale flow boiling trends (from experiments)h is not dependent on mass velocityh is not dependent on vapor quality (x>0.1)h is dependent on heat fluxh is dependent on saturation temperature

Macro to micro-scale transition

Kandlikar and Grande : 3 mm

Mehandal et al. : micro-channels (1 100 m)meso-channels (100 m 1mm)macro-channels (1 6 mm)conventional (Dh > 6 mm)

Kew and Cornwell :

Kandlikar and Balasubramanian model (1/2)this model is an extension of their macro-scale correlation to tube diameter

Kandlikar and Balasubramanian model (2/2)The model predicts that nucleate boiling becomes dominant for low Reynolds numbersconvective boiling contribution becomes dominant to high vapor quality

The model has been implemented in a MATLAB code (Excel compatible)

Zhang modified Chen model (1/3)this model (2004) is a modification of the macro-scale flow boiling correlation proposed by Chen (1966) where the correlation proposed by Foster and Zuber for nucleate boiling heat transfer is usedChen model was developed to determine flow boiling heat transfer coefficients when both liquid and vapor phases were both in turbulent flows (Rek>2300)S: suppression factorF: Reynolds number factorMartinelli parameterC is a function of flow conditions (Re)

Zhang modified Chen model (2/3)friction factors for circular channelsfor 1000

Zhang modified Chen model (3/3)A clear transition zone is identifiable in correspondence of sharp variation of heat transfer coefficient (subordinated to Reynolds number range)At high vapor quality (x1-) the heat transfer coefficient diverges, due to the big contribution of convective boiling component

3-Zone model - Thome-Jacobi-Dupont (2004) (1/6)A three zone flow boiling model of the evaporation of elongated bubbles in micro-channelsthe sequential passages of a liquid slug, an evaporating bubble and a vapor slug are assumed as a qualitative description of the flow patternlocal heat transfer coefficient is then obtained by a time average (over the period of the passage of the triple):

3-Zone model - Thome-Jacobi-Dupont (2004) (2/6)Major hypothesis:liquid film remains attached to the wall (shear stresses are assumed negligible) and is assumed very small compared to channel radiushomogeneous flow (vapor and liquid velocities are the same)heat flux is uniform and constant in timeneither liquid or the vapor phases are superheatedBubble departure frequency:bubbles are assumed to grow until r= R where the fluid reaches saturation temperature (x=0)from bubble departures frequency f =1/ it is possible to evaluate the length of the liquid slug and the residence time of vapor and liquidmass and volume conservation

3-Zone model - Thome-Jacobi-Dupont (2004) (3/6)Local heat transfer coefficient: liquid slug and dry zoneResidence time:The flow is assumed to be hydrodynamically and thermally developingif Re 2300:London and Shah correlationif Re> 2300:Gnielinski correlation(homogeneous flow)Asymptotic method (Churchill and Usagi)

3-Zone model - Thome-Jacobi-Dupont (2004) (4/6)Thin film evaporation modelEnergy balance across the liquid layer gives the following evolution with timeof the layer:Since h tends to infinity if end tends to zero(and the choice of end is quite complicate)mean heat transfer coefficientLiquid film thicknessThe prediction of initial liquid film thickness is based on the work done by doneby Moriyama and Inoue (a correlation including a further constant C0)

3-Zone model - Thome-Jacobi-Dupont (2004) (5/6)The constant C0. the bubble departure frequency and the end constitute the 3parameter of the model that can be optimized on a specific databaseperiodic heat transfer coefficient(vapor quality 8%)

3-Zone model - Thome-Jacobi-Dupont (2004) (6/6)The two models (basic version logarithm and modified version) have beenprovided for the project development

Graph 1

7.92453265867.7212731727.77553289077.9247534145

7.69431955087.4508695637.4760510837.6007458575

7.49024108957.22195525167.22601567797.3328452159

7.31204570387.02457038477.01243588027.1054603405

7.1553390086.85160662426.82653706446.9084498885

7.01533225346.69797656476.66225494046.7349553995

6.88881764426.55996837126.51526758726.5801573271

6.77349068726.43481302876.38240348586.4405538746

6.66759460376.32039985646.26127425486.3135273466

6.56975089656.21508798856.1500403116.1970730774

6.47885736396.11757914266.04725681986.0896238092

6.39401952466.02682991385.95176952975.9899322256

6.31450217595.94199002715.86264250795.8969901463

6.23969420435.86235798925.7791068375.8099715485

6.16908250785.78734864415.7005234355.7281915028

6.10223235245.71646903435.62635560595.6510759982

6.0387723635.64930016295.55614843675.5781393823

5.97838290825.58548302015.48951309915.5089672311

5.92078700535.5247077385.42611472485.4432031585

5.86574312235.46670507655.36566292675.3805385304

5.81303942585.41123966465.30790430265.3207043501

5.76248914045.35810458455.25261644845.2634647905

5.71392677565.30711699085.19960312925.2086119879

5.66720503155.25811453755.1486903525.1559618147

5.62219224435.21095244125.09972314535.1053504183

5.57877026255.16550104955.05256289895.0566313669

5.53683266955.12164381495.00708515115.0096732774

5.49628328835.0792755954.96317773674.9643578336

5.45703491515.03830121864.92073922654.9205781177

5.41900824264.99863426974.87967760684.8782371996

5.38213093934.96019605024.83990915434.8372469372

5.34633685774.92291469164.80135747414.7975269501

5.31156535274.88672439044.76395267234.7590037392

5.277760694.8515647474.72763064244.7216099267

5.24487153174.81738019254.69233244594.6852835981

5.21285048794.78411948824.6580037744.6499677295

5.18165372314.75173528944.62459447664.6156096883

5.15124061044.72018376154.59205815044.5821607954

5.12157342714.68942424244.56035177564.5495759406

5.0926170854.65941894484.52943539624.5178132434

5.0643388914.63013269194.49927183644.4868337528

5.03670833474.60153268314.46982644964.4566011814

5.00969689844.57358828494.44106689424.4270816688

4.98327788764.54627084454.41296293464.39824357

4.95742627914.51955352274.38548626174.3700572672

4.93211858414.49341114444.35861033354.342495

4.90733272544.46782006354.33231023094.3155307138

4.88304792624.44275804164.30656252774.2891399229

4.85924461024.41820413824.28134517394.2632995867

4.835904314.39413861124.25663738984.2379879982

4.8130095854.37054282724.23241956944.2131846827

4.79054394634.34739917944.20867319414.1888703058

4.76849178794.32469101294.18538075254.1650265899

4.74683832464.3024025574.16252566854.1416362382

4.7255695354.28051886294.1400922354.1186828648

4.70467210874.2590257474.11806555374.0961509311

4.68413339854.23790973854.09643147944.0740256877

4.66394137644.21715803184.07517656954.0522931209

4.64408459314.19675844224.05428803664.0309399033

4.624552144.17669936544.0337537064.0099533486

4.6053336154.15696973994.01356197573.9893213697

4.58641909084.13755901273.99370177933.9690324405

4.56779908424.11845710653.97416255263.9490755593

4.54946452984.09965439043.95493420123.9294402162

4.53140675324.08114165193.93600707153.9101163622

4.51361744794.06291007123.91737192333.8910943798

4.49608865254.04495119653.89901990393.8723650568

4.47881272984.02725692193.88094252423.8539195607

4.46178234724.00981946563.86313163593.8357494149

4.44499045793.99263134983.84557941033.8178464763

4.42843028333.97568538193.82827831783.8002029143

4.41209529653.95897463563.81122110893.7828111901

4.39597920573.94249243383.79440079513.7656640373

4.38007593923.92623233173.77781063143.7487544433

4.36437962973.91018813.76144409853.7320756306

4.34888460023.89435370873.74529488533.7156210388

4.33358534853.87872331083.7293568723.6993843059

4.31847653283.86329122583.71362411183.6833592507

4.30355295613.84805192243.69809081343.6675398525

4.28880955043.83300000063.68275132113.6519202317

4.27424135913.81813017223.66760009393.6364946274

4.25984351863.80343723953.65263168313.621257373

4.24561123653.78891607013.63784070483.6062028687

4.23153976683.77456156923.62322181013.5913255487

4.21762438053.76036864423.60876964683.5766198418

4.20386032793.74633216273.59447881353.5620801222

4.1902427923.73244689673.58034380013.547700647

4.17676682593.7187074513.56635890873.5334754727

4.16342726723.70510816413.55251814663.5193983415

4.15021861733.6916429693.53881507443.5054625212

4.13713486233.67830518883.52524258383.4916605694

4.1241691973.66508722563.51179255843.4779839747

4.11131357633.65198005953.49845532923.4644225797

4.09855793723.63897239653.4852187493.4509636009

4.08588874013.62604910433.47206649683.4375898331

4.07328593393.61318804043.45897465453.4242760269

4.06071566363.60035266063.44590377993.4109805116

4.04810849313.58747066363.43277624393.3976213158

4.03526359163.57434238423.41938070143.3839761673

G = 200

G = 400

G = 600

G = 800

Vapor quality [-]

Heat transfer coefficient [kW/m^2K]

R22 ; Tsat = 15 [C] ; Q = 10 [kW/m^2] ; DH = 1.4 [mm]

Graph2

1.26190406811.29512319761.28608548641.2618689159

1.29966008481.34212522651.33760455741.3156603559

1.33507051121.3846665691.38388850041.3637271353

1.36760633141.42357460351.42603799461.4073683507

1.3975578221.45951169541.46487156021.4475027193

1.42544923591.49298820371.50099329571.4847908274

1.45162791591.52439759371.53485637641.5197205026

1.47634365531.55404670741.56680786831.5526614938

1.49979124321.58217837911.59711898781.5839006392

1.52212772711.60898767941.62600560231.6136650117

1.54348204291.63463353181.65364235351.6421375627

1.56396144271.65924709061.68017258571.6694679712

1.58365611751.68293786331.70571546651.6957803476

1.60264264121.70579825021.73037119441.7211788245

1.62098658711.72790695961.75422487321.7457516906

1.63874454831.74933161361.77734944261.7695745028

1.6559657161.77013076161.7998079271.7927124646

1.67269312681.79035545611.8216551851.8152222695

1.68896465811.81005049931.84293928661.8371535489

1.70481383031.829255441.86370260991.8585500212

1.72027045881.84800537771.88398272271.8794504152

1.73536118791.86633161831.90381309931.8998892171

1.75010993191.88426221191.9232237061.9198972823

1.76453824141.90182239821.9422414861.9395023391

1.77866561041.91903497741.96089076111.9587294075

1.79250973411.93592062111.97919356971.9776011488

1.80608672811.95249813571.99716994981.9961381604

1.81941131411.96878468452.01483818042.0143592253

1.83249697971.98479597912.03221498632.0322815248

1.84535611542.00054644142.04931571422.0499208199

1.85800013282.01604934542.06615448372.0672916082

1.87043956752.03131693852.08274431852.084407259

1.88268416862.04636054772.09909725982.1012801309

1.89474297672.06119067182.11522446582.117921674

1.90662439292.07581706252.13113629852.1343425196

1.91833623912.0902487962.14684239972.150552559

1.92988581142.10449433542.16235175872.1665610126

1.94127992782.11856158692.17767277162.1823764914

1.95252496962.13245794862.19281329422.1980070518

1.96362691972.14619035522.2077806892.2134602431

1.97459139592.15976531682.22258186742.2287431519

1.98542368062.17318895432.23722332692.2438624398

1.99612874852.18646703142.25171118522.2588243787

2.00671129042.19960498222.26605121052.2736348819

2.01717573542.21260793792.28024884892.2882995322

2.02752627082.22548074922.29430924882.3028236072

2.03776686032.23822800782.30823728382.3172121028

2.04790125982.25085406552.32203757312.3314697538

2.05793303332.26336305142.33571449952.345601053

2.06786556542.27575888812.3492722272.3596102689

2.07770207462.28804530592.36271471582.373501461

2.08744562462.30022585632.37604573672.3872784952

2.09709913432.31230392422.38926888412.4009450562

2.10666538782.32428273912.40238758782.4145046607

2.11614704342.33616538562.41540512442.4279606681

2.12554664152.34795481272.42832462712.4413162914

2.13486661232.35965384282.44114909532.4545746067

2.14410928292.37126518012.45388140352.4677385623

2.15327688372.38279141812.46652430952.480810987

2.16237155462.39423504672.47908046172.4937945983

2.17139535072.40559845892.49155240672.5066920093

2.18035024762.41688395732.50394259582.519505736

2.18923814632.42809375972.51625339122.5322382036

2.19806087832.43923000522.52848707242.5448917529

2.20682020942.45029475892.54064584192.5574686464

2.21551784472.46129001752.55273183042.5699710734

2.22415543222.4722177142.56474710222.5824011562

2.23273456682.48307972252.57669366082.594760955

2.24125679422.49387786312.58857345352.6070524736

2.24972361472.50461390592.60038837672.619277664

2.25813648632.51528957642.61214028082.6314384325

2.26649682932.52590655932.62383097552.6435366444

2.27480602892.53646650382.6354622352.6555741301

2.28306543972.54697102852.64703580342.6675526901

2.29127638942.55742172612.65855340082.6794741023

2.29944018282.56782016942.67001672932.6913401274

2.30755810622.57816791732.68142748022.7031525175

2.31563143252.58846652132.69278734162.7149130235

2.32366142632.59871753342.70409800752.7266234048

2.33164934992.60892251462.71536118742.7382854404

2.3395964712.61908304562.72657861922.7499009416

2.34750407062.62920073882.73775208332.761471768

2.35537345342.63927725372.74888342052.7729998461

2.36320596072.64931431552.75997455422.784487194

2.3710029862.65931373922.77102751872.7959359514

2.3787659962.66927746012.78204449622.8073484192

2.38649655792.67920757532.7930278652.8187271123

2.39419637652.68910639832.80398026562.8300748307

2.40186734592.69897653652.81490469222.8413947583

2.40951162392.70882100032.82580462382.8526906049

2.41713174282.71864336612.83668421742.863966815

2.42473078152.72844802442.84754860482.8752288891

2.43231264522.7382405812.85840436962.8864839002

2.43988255212.74802853952.86926035932.8977413721

2.44744794492.75782255352.88012917072.909014887

2.45502038462.76763896262.89103014592.9203253246

2.46262009672.77750568982.90199629432.9317083361

2.47028952342.78747924032.91309403512.9432355965

2.47815285742.79771743312.9245061822.9551035544

G = 200

G = 400

G = 600

G = 800

Vapor qualitiy [-]

Wall superheat [K] l

R22 ; Tsat = 15 [C] ; Q = 10 [kW/m^2] ; DH = 1.4 [mm]

Feuil1

xh_200h_400h_600h_800T_200T_400T_600T_800

0.017.92457.72137.77557.92481.26191.29511.28608548641.2619

0.027.69437.45097.47617.60071.29971.34211.33760455741.3157

0.037.49027.22207.22607.33281.33511.38471.38388850041.3637

0.047.31207.02467.01247.10551.36761.42361.42603799461.4074

0.057.15536.85166.82656.90841.39761.45951.46487156021.4475

0.067.01536.69806.66236.73501.42541.49301.50099329571.4848

0.076.88886.56006.51536.58021.45161.52441.53485637641.5197

0.086.77356.43486.38246.44061.47631.55401.56680786831.5527

0.096.66766.32046.26136.31351.49981.58221.59711898781.5839

0.106.56986.21516.15006.19711.52211.60901.62600560231.6137

0.116.47896.11766.04736.08961.54351.63461.65364235351.6421

0.126.39406.02685.95185.98991.56401.65921.68017258571.6695

0.136.31455.94205.86265.89701.58371.68291.70571546651.6958

0.146.23975.86245.77915.81001.60261.70581.73037119441.7212

0.156.16915.78735.70055.72821.62101.72791.75422487321.7458

0.166.10225.71655.62645.65111.63871.74931.77734944261.7696

0.176.03885.64935.55615.57811.65601.77011.7998079271.7927

0.185.97845.58555.48955.50901.67271.79041.8216551851.8152

0.195.92085.52475.42615.44321.68901.81011.84293928661.8372

0.205.86575.46675.36575.38051.70481.82931.86370260991.8586

0.215.81305.41125.30795.32071.72031.84801.88398272271.8795

0.225.76255.35815.25265.26351.73541.86631.90381309931.8999

0.235.71395.30715.19965.20861.75011.88431.9232237061.9199

0.245.66725.25815.14875.15601.76451.90181.9422414861.9395

0.255.62225.21105.09975.10541.77871.91901.96089076111.9587

0.265.57885.16555.05265.05661.79251.93591.97919356971.9776

0.275.53685.12165.00715.00971.80611.95251.99716994981.9961

0.285.49635.07934.96324.96441.81941.96882.01483818042.0144

0.295.45705.03834.92074.92061.83251.98482.03221498632.0323

0.305.41904.99864.87974.87821.84542.00052.04931571422.0499

0.315.38214.96024.83994.83721.85802.01602.06615448372.0673

0.325.34634.92294.80144.79751.87042.03132.08274431852.0844

0.335.31164.88674.76404.75901.88272.04642.09909725982.1013

0.345.27784.85164.72764.72161.89472.06122.11522446582.1179

0.355.24494.81744.69234.68531.90662.07582.13113629852.1343

0.365.21294.78414.65804.65001.91832.09022.14684239972.1506

0.375.18174.75174.62464.61561.92992.10452.16235175872.1666

0.385.15124.72024.59214.58221.94132.11862.17767277162.1824

0.395.12164.68944.56044.54961.95252.13252.19281329422.1980

0.405.09264.65944.52944.51781.96362.14622.2077806892.2135

0.415.06434.63014.49934.48681.97462.15982.22258186742.2287

0.425.03674.60154.46984.45661.98542.17322.23722332692.2439

0.435.00974.57364.44114.42711.99612.18652.25171118522.2588

0.444.98334.54634.41304.39822.00672.19962.26605121052.2736

0.454.95744.51964.38554.37012.01722.21262.28024884892.2883

0.464.93214.49344.35864.34252.02752.22552.29430924882.3028

0.474.90734.46784.33234.31552.03782.23822.30823728382.3172

0.484.88304.44284.30664.28912.04792.25092.32203757312.3315

0.494.85924.41824.28134.26332.05792.26342.33571449952.3456

0.504.83594.39414.25664.23802.06792.27582.3492722272.3596

0.514.81304.37054.23244.21322.07772.28802.36271471582.3735

0.524.79054.34744.20874.18892.08742.30022.37604573672.3873

0.534.76854.32474.18544.16502.09712.31232.38926888412.4009

0.544.74684.30244.16254.14162.10672.32432.40238758782.4145

0.554.72564.28054.14014.11872.11612.33622.41540512442.4280

0.564.70474.25904.11814.09622.12552.34802.42832462712.4413

0.574.68414.23794.09644.07402.13492.35972.44114909532.4546

0.584.66394.21724.07524.05232.14412.37132.45388140352.4677

0.594.64414.19684.05434.03092.15332.38282.46652430952.4808

0.604.62464.17674.03384.01002.16242.39422.47908046172.4938

0.614.60534.15704.01363.98932.17142.40562.49155240672.5067

0.624.58644.13763.99373.96902.18042.41692.50394259582.5195

0.634.56784.11853.97423.94912.18922.42812.51625339122.5322

0.644.54954.09973.95493.92942.19812.43922.52848707242.5449

0.654.53144.08113.93603.91012.20682.45032.54064584192.5575

0.664.51364.06293.91743.89112.21552.46132.55273183042.5700

0.674.49614.04503.89903.87242.22422.47222.56474710222.5824

0.684.47884.02733.88093.85392.23272.48312.57669366082.5948

0.694.46184.00983.86313.83572.24132.49392.58857345352.6071

0.704.44503.99263.84563.81782.24972.50462.60038837672.6193

0.714.42843.97573.82833.80022.25812.51532.61214028082.6314

0.724.41213.95903.81123.78282.26652.52592.62383097552.6435

0.734.39603.94253.79443.76572.27482.53652.6354622352.6556

0.744.38013.92623.77783.74882.28312.54702.64703580342.6676

0.754.36443.91023.76143.73212.29132.55742.65855340082.6795

0.764.34893.89443.74533.71562.29942.56782.67001672932.6913

0.774.33363.87873.72943.69942.30762.57822.68142748022.7032

0.784.31853.86333.71363.68342.31562.58852.69278734162.7149

0.794.30363.84813.69813.66752.32372.59872.70409800752.7266

0.804.28883.83303.68283.65192.33162.60892.71536118742.7383

0.814.27423.81813.66763.63652.33962.61912.72657861922.7499

0.824.25983.80343.65263.62132.34752.62922.73775208332.7615

0.834.24563.78893.63783.60622.35542.63932.74888342052.7730

0.844.23153.77463.62323.59132.36322.64932.75997455422.7845

0.854.21763.76043.60883.57662.37102.65932.77102751872.7959

0.864.20393.74633.59453.56212.37882.66932.78204449622.8073

0.874.19023.73243.58033.54772.38652.67922.7930278652.8187

0.884.17683.71873.56643.53352.39422.68912.80398026562.8301

0.894.16343.70513.55253.51942.40192.69902.81490469222.8414

0.904.15023.69163.53883.50552.40952.70882.82580462382.8527

0.914.13713.67833.52523.49172.41712.71862.83668421742.8640

0.924.12423.66513.51183.47802.42472.72842.84754860482.8752

0.934.11133.65203.49853.46442.43232.73822.85840436962.8865

0.944.09863.63903.48523.45102.43992.74802.86926035932.8977

0.954.08593.62603.47213.43762.44742.75782.88012917072.9090

0.964.07333.61323.45903.42432.45502.76762.89103014592.9203

0.974.06073.60043.44593.41102.46262.77752.90199629432.9317

0.984.04813.58753.43283.39762.47032.78752.91309403512.9432

0.994.03533.57433.41943.38402.47822.79772.9245061822.9551

Feuil2

Feuil3

Graph 1

7.92453265867.7212731727.77553289077.9247534145

7.69431955087.4508695637.4760510837.6007458575

7.49024108957.22195525167.22601567797.3328452159

7.31204570387.02457038477.01243588027.1054603405

7.1553390086.85160662426.82653706446.9084498885

7.01533225346.69797656476.66225494046.7349553995

6.88881764426.55996837126.51526758726.5801573271

6.77349068726.43481302876.38240348586.4405538746

6.66759460376.32039985646.26127425486.3135273466

6.56975089656.21508798856.1500403116.1970730774

6.47885736396.11757914266.04725681986.0896238092

6.39401952466.02682991385.95176952975.9899322256

6.31450217595.94199002715.86264250795.8969901463

6.23969420435.86235798925.7791068375.8099715485

6.16908250785.78734864415.7005234355.7281915028

6.10223235245.71646903435.62635560595.6510759982

6.0387723635.64930016295.55614843675.5781393823

5.97838290825.58548302015.48951309915.5089672311

5.92078700535.5247077385.42611472485.4432031585

5.86574312235.46670507655.36566292675.3805385304

5.81303942585.41123966465.30790430265.3207043501

5.76248914045.35810458455.25261644845.2634647905

5.71392677565.30711699085.19960312925.2086119879

5.66720503155.25811453755.1486903525.1559618147

5.62219224435.21095244125.09972314535.1053504183

5.57877026255.16550104955.05256289895.0566313669

5.53683266955.12164381495.00708515115.0096732774

5.49628328835.0792755954.96317773674.9643578336

5.45703491515.03830121864.92073922654.9205781177

5.41900824264.99863426974.87967760684.8782371996

5.38213093934.96019605024.83990915434.8372469372

5.34633685774.92291469164.80135747414.7975269501

5.31156535274.88672439044.76395267234.7590037392

5.277760694.8515647474.72763064244.7216099267

5.24487153174.81738019254.69233244594.6852835981

5.21285048794.78411948824.6580037744.6499677295

5.18165372314.75173528944.62459447664.6156096883

5.15124061044.72018376154.59205815044.5821607954

5.12157342714.68942424244.56035177564.5495759406

5.0926170854.65941894484.52943539624.5178132434

5.0643388914.63013269194.49927183644.4868337528

5.03670833474.60153268314.46982644964.4566011814

5.00969689844.57358828494.44106689424.4270816688

4.98327788764.54627084454.41296293464.39824357

4.95742627914.51955352274.38548626174.3700572672

4.93211858414.49341114444.35861033354.342495

4.90733272544.46782006354.33231023094.3155307138

4.88304792624.44275804164.30656252774.2891399229

4.85924461024.41820413824.28134517394.2632995867

4.835904314.39413861124.25663738984.2379879982

4.8130095854.37054282724.23241956944.2131846827

4.79054394634.34739917944.20867319414.1888703058

4.76849178794.32469101294.18538075254.1650265899

4.74683832464.3024025574.16252566854.1416362382

4.7255695354.28051886294.1400922354.1186828648

4.70467210874.2590257474.11806555374.0961509311

4.68413339854.23790973854.09643147944.0740256877

4.66394137644.21715803184.07517656954.0522931209

4.64408459314.19675844224.05428803664.0309399033

4.624552144.17669936544.0337537064.0099533486

4.6053336154.15696973994.01356197573.9893213697

4.58641909084.13755901273.99370177933.9690324405

4.56779908424.11845710653.97416255263.9490755593

4.54946452984.09965439043.95493420123.9294402162

4.53140675324.08114165193.93600707153.9101163622

4.51361744794.06291007123.91737192333.8910943798

4.49608865254.04495119653.89901990393.8723650568

4.47881272984.02725692193.88094252423.8539195607

4.46178234724.00981946563.86313163593.8357494149

4.44499045793.99263134983.84557941033.8178464763

4.42843028333.97568538193.82827831783.8002029143

4.41209529653.95897463563.81122110893.7828111901

4.39597920573.94249243383.79440079513.7656640373

4.38007593923.92623233173.77781063143.7487544433

4.36437962973.91018813.76144409853.7320756306

4.34888460023.89435370873.74529488533.7156210388

4.33358534853.87872331083.7293568723.6993843059

4.31847653283.86329122583.71362411183.6833592507

4.30355295613.84805192243.69809081343.6675398525

4.28880955043.83300000063.68275132113.6519202317

4.27424135913.81813017223.66760009393.6364946274

4.25984351863.80343723953.65263168313.621257373

4.24561123653.78891607013.63784070483.6062028687

4.23153976683.77456156923.62322181013.5913255487

4.21762438053.76036864423.60876964683.5766198418

4.20386032793.74633216273.59447881353.5620801222

4.1902427923.73244689673.58034380013.547700647

4.17676682593.7187074513.56635890873.5334754727

4.16342726723.70510816413.55251814663.5193983415

4.15021861733.6916429693.53881507443.5054625212

4.13713486233.67830518883.52524258383.4916605694

4.1241691973.66508722563.51179255843.4779839747

4.11131357633.65198005953.49845532923.4644225797

4.09855793723.63897239653.4852187493.4509636009

4.08588874013.62604910433.47206649683.4375898331

4.07328593393.61318804043.45897465453.4242760269

4.06071566363.60035266063.44590377993.4109805116

4.04810849313.58747066363.43277624393.3976213158

4.03526359163.57434238423.41938070143.3839761673

G = 200

G = 400

G = 600

G = 800

Vapor quality [-]

Heat transfer coefficient [kW/m^2K]

R22 ; Tsat = 15 [C] ; Q = 10 [kW/m^2] ; DH = 1.4 [mm]

Graph2

1.26190406811.29512319761.28608548641.2618689159

1.29966008481.34212522651.33760455741.3156603559

1.33507051121.3846665691.38388850041.3637271353

1.36760633141.42357460351.42603799461.4073683507

1.3975578221.45951169541.46487156021.4475027193

1.42544923591.49298820371.50099329571.4847908274

1.45162791591.52439759371.53485637641.5197205026

1.47634365531.55404670741.56680786831.5526614938

1.49979124321.58217837911.59711898781.5839006392

1.52212772711.60898767941.62600560231.6136650117

1.54348204291.63463353181.65364235351.6421375627

1.56396144271.65924709061.68017258571.6694679712

1.58365611751.68293786331.70571546651.6957803476

1.60264264121.70579825021.73037119441.7211788245

1.62098658711.72790695961.75422487321.7457516906

1.63874454831.74933161361.77734944261.7695745028

1.6559657161.77013076161.7998079271.7927124646

1.67269312681.79035545611.8216551851.8152222695

1.68896465811.81005049931.84293928661.8371535489

1.70481383031.829255441.86370260991.8585500212

1.72027045881.84800537771.88398272271.8794504152

1.73536118791.86633161831.90381309931.8998892171

1.75010993191.88426221191.9232237061.9198972823

1.76453824141.90182239821.9422414861.9395023391

1.77866561041.91903497741.96089076111.9587294075

1.79250973411.93592062111.97919356971.9776011488

1.80608672811.95249813571.99716994981.9961381604

1.81941131411.96878468452.01483818042.0143592253

1.83249697971.98479597912.03221498632.0322815248

1.84535611542.00054644142.04931571422.0499208199

1.85800013282.01604934542.06615448372.0672916082

1.87043956752.03131693852.08274431852.084407259

1.88268416862.04636054772.09909725982.1012801309

1.89474297672.06119067182.11522446582.117921674

1.90662439292.07581706252.13113629852.1343425196

1.91833623912.0902487962.14684239972.150552559

1.92988581142.10449433542.16235175872.1665610126

1.94127992782.11856158692.17767277162.1823764914

1.95252496962.13245794862.19281329422.1980070518

1.96362691972.14619035522.2077806892.2134602431

1.97459139592.15976531682.22258186742.2287431519

1.98542368062.17318895432.23722332692.2438624398

1.99612874852.18646703142.25171118522.2588243787

2.00671129042.19960498222.26605121052.2736348819

2.01717573542.21260793792.28024884892.2882995322

2.02752627082.22548074922.29430924882.3028236072

2.03776686032.23822800782.30823728382.3172121028

2.04790125982.25085406552.32203757312.3314697538

2.05793303332.26336305142.33571449952.345601053

2.06786556542.27575888812.3492722272.3596102689

2.07770207462.28804530592.36271471582.373501461

2.08744562462.30022585632.37604573672.3872784952

2.09709913432.31230392422.38926888412.4009450562

2.10666538782.32428273912.40238758782.4145046607

2.11614704342.33616538562.41540512442.4279606681

2.12554664152.34795481272.42832462712.4413162914

2.13486661232.35965384282.44114909532.4545746067

2.14410928292.37126518012.45388140352.4677385623

2.15327688372.38279141812.46652430952.480810987

2.16237155462.39423504672.47908046172.4937945983

2.17139535072.40559845892.49155240672.5066920093

2.18035024762.41688395732.50394259582.519505736

2.18923814632.42809375972.51625339122.5322382036

2.19806087832.43923000522.52848707242.5448917529

2.20682020942.45029475892.54064584192.5574686464

2.21551784472.46129001752.55273183042.5699710734

2.22415543222.4722177142.56474710222.5824011562

2.23273456682.48307972252.57669366082.594760955

2.24125679422.49387786312.58857345352.6070524736

2.24972361472.50461390592.60038837672.619277664

2.25813648632.51528957642.61214028082.6314384325

2.26649682932.52590655932.62383097552.6435366444

2.27480602892.53646650382.6354622352.6555741301

2.28306543972.54697102852.64703580342.6675526901

2.29127638942.55742172612.65855340082.6794741023

2.29944018282.56782016942.67001672932.6913401274

2.30755810622.57816791732.68142748022.7031525175

2.31563143252.58846652132.69278734162.7149130235

2.32366142632.59871753342.70409800752.7266234048

2.33164934992.60892251462.71536118742.7382854404

2.3395964712.61908304562.72657861922.7499009416

2.34750407062.62920073882.73775208332.761471768

2.35537345342.63927725372.74888342052.7729998461

2.36320596072.64931431552.75997455422.784487194

2.3710029862.65931373922.77102751872.7959359514

2.3787659962.66927746012.78204449622.8073484192

2.38649655792.67920757532.7930278652.8187271123

2.39419637652.68910639832.80398026562.8300748307

2.40186734592.69897653652.81490469222.8413947583

2.40951162392.70882100032.82580462382.8526906049

2.41713174282.71864336612.83668421742.863966815

2.42473078152.72844802442.84754860482.8752288891

2.43231264522.7382405812.85840436962.8864839002

2.43988255212.74802853952.86926035932.8977413721

2.44744794492.75782255352.88012917072.909014887

2.45502038462.76763896262.89103014592.9203253246

2.46262009672.77750568982.90199629432.9317083361

2.47028952342.78747924032.91309403512.9432355965

2.47815285742.79771743312.9245061822.9551035544

G = 200

G = 400

G = 600

G = 800

Vapor qualitiy [-]

Wall superheat [K] l

R22 ; Tsat = 15 [C] ; Q = 10 [kW/m^2] ; DH = 1.4 [mm]

Feuil1

xh_200h_400h_600h_800T_200T_400T_600T_800

0.017.92457.72137.77557.92481.26191.29511.28608548641.2619

0.027.69437.45097.47617.60071.29971.34211.33760455741.3157

0.037.49027.22207.22607.33281.33511.38471.38388850041.3637

0.047.31207.02467.01247.10551.36761.42361.42603799461.4074

0.057.15536.85166.82656.90841.39761.45951.46487156021.4475

0.067.01536.69806.66236.73501.42541.49301.50099329571.4848

0.076.88886.56006.51536.58021.45161.52441.53485637641.5197

0.086.77356.43486.38246.44061.47631.55401.56680786831.5527

0.096.66766.32046.26136.31351.49981.58221.59711898781.5839

0.106.56986.21516.15006.19711.52211.60901.62600560231.6137

0.116.47896.11766.04736.08961.54351.63461.65364235351.6421

0.126.39406.02685.95185.98991.56401.65921.68017258571.6695

0.136.31455.94205.86265.89701.58371.68291.70571546651.6958

0.146.23975.86245.77915.81001.60261.70581.73037119441.7212

0.156.16915.78735.70055.72821.62101.72791.75422487321.7458

0.166.10225.71655.62645.65111.63871.74931.77734944261.7696

0.176.03885.64935.55615.57811.65601.77011.7998079271.7927

0.185.97845.58555.48955.50901.67271.79041.8216551851.8152

0.195.92085.52475.42615.44321.68901.81011.84293928661.8372

0.205.86575.46675.36575.38051.70481.82931.86370260991.8586

0.215.81305.41125.30795.32071.72031.84801.88398272271.8795

0.225.76255.35815.25265.26351.73541.86631.90381309931.8999

0.235.71395.30715.19965.20861.75011.88431.9232237061.9199

0.245.66725.25815.14875.15601.76451.90181.9422414861.9395

0.255.62225.21105.09975.10541.77871.91901.96089076111.9587

0.265.57885.16555.05265.05661.79251.93591.97919356971.9776

0.275.53685.12165.00715.00971.80611.95251.99716994981.9961

0.285.49635.07934.96324.96441.81941.96882.01483818042.0144

0.295.45705.03834.92074.92061.83251.98482.03221498632.0323

0.305.41904.99864.87974.87821.84542.00052.04931571422.0499

0.315.38214.96024.83994.83721.85802.01602.06615448372.0673

0.325.34634.92294.80144.79751.87042.03132.08274431852.0844

0.335.31164.88674.76404.75901.88272.04642.09909725982.1013

0.345.27784.85164.72764.72161.89472.06122.11522446582.1179

0.355.24494.81744.69234.68531.90662.07582.13113629852.1343

0.365.21294.78414.65804.65001.91832.09022.14684239972.1506

0.375.18174.75174.62464.61561.92992.10452.16235175872.1666

0.385.15124.72024.59214.58221.94132.11862.17767277162.1824

0.395.12164.68944.56044.54961.95252.13252.19281329422.1980

0.405.09264.65944.52944.51781.96362.14622.2077806892.2135

0.415.06434.63014.49934.48681.97462.15982.22258186742.2287

0.425.03674.60154.46984.45661.98542.17322.23722332692.2439

0.435.00974.57364.44114.42711.99612.18652.25171118522.2588

0.444.98334.54634.41304.39822.00672.19962.26605121052.2736

0.454.95744.51964.38554.37012.01722.21262.28024884892.2883

0.464.93214.49344.35864.34252.02752.22552.29430924882.3028

0.474.90734.46784.33234.31552.03782.23822.30823728382.3172

0.484.88304.44284.30664.28912.04792.25092.32203757312.3315

0.494.85924.41824.28134.26332.05792.26342.33571449952.3456

0.504.83594.39414.25664.23802.06792.27582.3492722272.3596

0.514.81304.37054.23244.21322.07772.28802.36271471582.3735

0.524.79054.34744.20874.18892.08742.30022.37604573672.3873

0.534.76854.32474.18544.16502.09712.31232.38926888412.4009

0.544.74684.30244.16254.14162.10672.32432.40238758782.4145

0.554.72564.28054.14014.11872.11612.33622.41540512442.4280

0.564.70474.25904.11814.09622.12552.34802.42832462712.4413

0.574.68414.23794.09644.07402.13492.35972.44114909532.4546

0.584.66394.21724.07524.05232.14412.37132.45388140352.4677

0.594.64414.19684.05434.03092.15332.38282.46652430952.4808

0.604.62464.17674.03384.01002.16242.39422.47908046172.4938

0.614.60534.15704.01363.98932.17142.40562.49155240672.5067

0.624.58644.13763.99373.96902.18042.41692.50394259582.5195

0.634.56784.11853.97423.94912.18922.42812.51625339122.5322

0.644.54954.09973.95493.92942.19812.43922.52848707242.5449

0.654.53144.08113.93603.91012.20682.45032.54064584192.5575

0.664.51364.06293.91743.89112.21552.46132.55273183042.5700

0.674.49614.04503.89903.87242.22422.47222.56474710222.5824

0.684.47884.02733.88093.85392.23272.48312.57669366082.5948

0.694.46184.00983.86313.83572.24132.49392.58857345352.6071

0.704.44503.99263.84563.81782.24972.50462.60038837672.6193

0.714.42843.97573.82833.80022.25812.51532.61214028082.6314

0.724.41213.95903.81123.78282.26652.52592.62383097552.6435

0.734.39603.94253.79443.76572.27482.53652.6354622352.6556

0.744.38013.92623.77783.74882.28312.54702.64703580342.6676

0.754.36443.91023.76143.73212.29132.55742.65855340082.6795

0.764.34893.89443.74533.71562.29942.56782.67001672932.6913

0.774.33363.87873.72943.69942.30762.57822.68142748022.7032

0.784.31853.86333.71363.68342.31562.58852.69278734162.7149

0.794.30363.84813.69813.66752.32372.59872.70409800752.7266

0.804.28883.83303.68283.65192.33162.60892.71536118742.7383

0.814.27423.81813.66763.63652.33962.61912.72657861922.7499

0.824.25983.80343.65263.62132.34752.62922.73775208332.7615

0.834.24563.78893.63783.60622.35542.63932.74888342052.7730

0.844.23153.77463.62323.59132.36322.64932.75997455422.7845

0.854.21763.76043.60883.57662.37102.65932.77102751872.7959

0.864.20393.74633.59453.56212.37882.66932.78204449622.8073

0.874.19023.73243.58033.54772.38652.67922.7930278652.8187

0.884.17683.71873.56643.53352.39422.68912.80398026562.8301

0.894.16343.70513.55253.51942.40192.69902.81490469222.8414

0.904.15023.69163.53883.50552.40952.70882.82580462382.8527

0.914.13713.67833.52523.49172.41712.71862.83668421742.8640

0.924.12423.66513.51183.47802.42472.72842.84754860482.8752

0.934.11133.65203.49853.46442.43232.73822.85840436962.8865

0.944.09863.63903.48523.45102.43992.74802.86926035932.8977

0.954.08593.62603.47213.43762.44742.75782.88012917072.9090

0.964.07333.61323.45903.42432.45502.76762.89103014592.9203

0.974.06073.60043.44593.41102.46262.77752.90199629432.9317

0.984.04813.58753.43283.39762.47032.78752.91309403512.9432

0.994.03533.57433.41943.38402.47822.79772.9245061822.9551

Feuil2

Feuil3

Threshold diameter criteriaTransitional diameter depends on the refrigerant properties

Original data

Authordiameter according Ken and cornewell [mm]Dh/Dthmicro-scaleXhRefrigerantdiameter [mm]GTsatqnumber of channelschannel formatdirectiontube materialtube lengthheating process3 zones modelKandikar modelValidityChen modelExist in modelChen +- 30%Kandikar +- 30%

Huai et al (2004)1.3720.95510.0109255568.2carbondioxide1.313105.21136010circularhorizontalaluminum500mmhot water848.5-12890.2100Chen model :19.2164179104

Huai et al (2004)1.3720.95510.0259477631.4carbondioxide1.313105.21136010circularhorizontalaluminum500mmhot water856.0-12872.3100

Huai et al (2004)1.3720.95510.0430925220.2carbondioxide1.313105.21277710circularhorizontalaluminum500mmhot water916.6-13086.7100Kadimar model :13.8059701493

Huai et al (2004)1.3720.95510.0620594375carbondioxide1.313105.21277710circularhorizontalaluminum500mmhot water911.1-13463.9110

Huai et al (2004)1.3720.95510.0820887308.2carbondioxide1.313105.29495.710circularhorizontalaluminum500mmhot water763.1-13575.5100














Koyama(2001)1.2171.47900.01306222476carbondioxide1.826011.031320581circularhorizontalstainless stell type316340mmdirect DC1297.2-13570.8100




































Pettersen(2004)1.2460.64210.103688139.9carbondioxide0.828010500025circularhorizontalaluminum540mmhot water897.6-13324.9100





Pettersen(2004)1.2460.64210.2005511245carbondioxide0.8280101000025circularhorizontalaluminum540mmhot water1222.6-14541.4100























Pettersen(2004)1.4960.53510.276569171.7carbondioxide0.819001000025circularhorizontalaluminum540mmhot water1516.913343.5100

Pettersen(2004)1.4960.53510.490549171.7carbondioxide0.819001000025circularhorizontalaluminum540mmhot water1527.613497.0100

Pettersen(2004)1.4960.53510.650669375carbondioxide0.819001000025circularhorizontalaluminum540mmhot water1554.713387.6100
































Yun et al (2005)1.3770.82810.2329257.1carbondioxide1.1430051000010rectangularhorizontalnot specifiednot specifieddirect Dc831.9-14742.5100





Yun et al (2005)1.3770.82810.26411152carbondioxide1.1430051500010rectangularhorizontalnot specifiednot specifieddirect Dc1012.5-15124.2100




Yun et al (2005)1.3770.82811326313263carbondioxide1.1430052000010rectangularhorizontalnot specifiednot specifieddirect Dc-1.0-1-1.0000

Yun et al (2005)1.3770.82811264112641carbondioxide1.1430052000010rectangularhorizontalnot specifiednot specifieddirect Dc-1.0-1-1.0000

Yun et al (2005)1.3770.82819121.89121.8carbondioxide1.1430052000010rectangularhorizontalnot specifiednot specifieddirect Dc-1.0-1-1.0000
























Bao et al (2000)1.881.0370-0.254651078.2R111.9544675.9550001circularhorizontalcopper270 mmelectrical heating-1.0-1-1.0000






Bao et al (2000)1.881.0370-0.00766975817R111.9544675.9550001circularhorizontalcopper270 mmelectrical heating-1.0-1-1.0000

Bao et al (2000)1.881.03700.0328446921.8R111.9544675.9550001circularhorizontalcopper270 mmelectrical heating1202.2-12568.7100











Bao et al (2000)1.881.03700.189846203R111.9533575.9550001circularhorizontalcopper270 mmelectrical heating1286.0-13187.7100













Bao et al (2000)1.881.03700.00781555990R111.9516775.9550001circularhorizontalcopper270 mmelectrical heating2328.511965.9100

Bao et al (2000)1.881.03700.127047281.2R111.9516775.9550001circularhorizontalcopper270 mmelectrical heating2141.612215.2100



Bao et al (2000)1.881.03700.478477015R111.9516775.9550001circularhorizontalcopper270 mmelectrical heating1469.112448.7100


Bao et al (2000)1.8871.0330-0.225722618.7R111.95446751250001circularhorizontalcopper270 mmelectrical heating-1.0-1-1.0000



Bao et al (2000)1.8871.03300.06523612864R111.95446751250001circularhorizontalcopper270 mmelectrical heating2023.3-13752.9100










Bao et al (2000)1.8871.03300.00829279951.3R111.95446751050001circularhorizontalcopper270 mmelectrical heating1859.4-12938.3100



















Bao et al (2000)1.8871.0330-0.142672299R111.9544675660001circularhorizontalcopper270 mmelectrical heating-1.0-1-1.0000

Bao et al (2000)1.8871.0330-0.0898662960R111.9544675660001circularhorizontalcopper270 mmelectrical heating-1.0-1-1.0000


































































Wambsganss et al (1993)1.9191.52200.013823108.8R1132.925060.1388031circularhorizontalstainless stell (type 304)368mm (diameter outside 4.75mm)direct DC-1.0-1-1.0000






Wambsganss et al (1993)1.9481.49900.295181431R1132.925055.3100541circularhorizontalstainless stell (type 304)368mm (diameter outside 4.75mm)direct DC-1.0-1-1.0000


























































Wambsganss et al (1993)1.911.52900.0538182519.5R1132.9224261.6252931circularhorizontalstainless stell (type 304)368mm (diameter outside

anthony servonet stefano nebuloni bruno agostini - supervisor

Documents

boiling model

balasubramanian model

usedchen model

zone model thomedupont

high vapor qualitythe

vapor slug

liquid slug

nucleate boiling