FLists. F.1 Nomenclature

Transcription

1 FLit Appendix F F.1 Noenclature In the following ubection the ybol ued in thi thei are given, with their dienion if applicable, followed by a hort decription. F.1.1 A A B c x d D D c D D T E F g g n G h I j k Sybol - critical power-law aplitude for the iochoric pecific heat K W -1 apparent aplitude (ee ection 2.2.2) - critical power-law aplitude for the ayptotic hape of the coexitence curve J ol-1 K-1 pecific heat at contant x - dienionality of the yte - critical power-law aplitude for the variation of the preure with denity along the critical iother diaeter of a cylinder (ee ection 5.3) diaeter of the circular arker (ee ection 5.3) 2-1 theral diffuivity -1/2 yte dependent contant (ee ection 2.3.2) ditance between iage plane and fil plane (ee ection 4.3.1) -2 acceleration of gravity -1 average gradient (ee ection 4.3.1) -1/2 yte dependent contant (ee ection 2.3.1) height - noralized teperature integral (ee ection 2.3) W -2 heat flux - interference order 113

2 F Lit K y K 1 K 2 L M M ' M n N p P P P q f q l Q Q Q 0 R a R D S t t c t T T et v V x y z Z 0 2 N-1 copreibility at contant y ol -4 fluid dependent paraeter (ee ection 4.3.2) ol -5 optic dependent paraeter (ee ection 4.3.2) path length of light in the aple kg ol -1 olar a - linear agnification (ee ection 4.3.1) - linear agnification in the fil plane (ee ection 4.3.1) - refractive index - angular agnification (ee ection 4.3.1) N -2 preure W power - reduced enicu poition (ee ection 5.3) - reduced enicu poition (ee ection 5.3) W generated heat W heat flow into the fluid (ee ection 2.2.2) W heat loe to the cell wall (ee ection 2.2.2) J aount of heat 3 kg-1 Lorentz-Lorenz contant (ee ection 5.1) - yte dependent contant in the power-law decription for the vicoity - Rayleigh nuber - univeral aplitude (ee ection 2.1.3) J ol-1 K-1 entropy 2 urface area tie characteritic tie for ientropic equilibration (ee ection 2.2.2) tie after which the behaviour of the hadow change fro type II into type I (ee ection 4.3.2) K teperature K et teperature of the therotat (ee ection 3.1.2) 3 ol-1 olar volue 3 fixed volue patial coordinate (in interferoetry along the optical axi) patial coordinate (in interferoetry perpendicular to the optical axi and parallel to the urface of the heater) patial coordinate along the direction of gravity (in interferoetry perpendicular to the optical axi and to the urface of the heater) axiu ize of the hadow (ee ection 4.3.2) x reduced value of x x Laplace tranfored value of x xˆ difference fro the initial value of x x reduced value of x x average value of x 114

3 Noenclature F.1.2 Greek ybol α α z β γ Γ δ T ρ ζ η ϑ λ Λ µ ν ξ ξ 0 ρ K -1 theral expanion coefficient at contant z - critical power-law aplitude for the iotheral copreibility - reduced teperature lag (ee ection 2.3.1) - reduced exce denity (ee ection 2.3.2) N -2 vicoity rad angle between light ray and heater urface (ee ection 4.2.2) W -1 K-1 theral conductivity laer light wavelength - paraeter (ee ection 2.3.1) correlation length critical power-law aplitude for the correlation length ol -3 denity ol -3 average of and - rule of Cailletet-Mathia (ee ection 5.3) ol -3 liquid denity ol -3 vapour denity - theral ipedance ratio of a wall and the fluid (ee ection 2.2.2) - reduced teperature difference - reduced denity difference - reduced preure difference ρ CM ρ l ρ v ρ l ρ v σ τ φ ψ F.1.3 a b c eff f h i p tot T v w Indice apparent value (ee ection 6.2.3) in the bulk of the fluid critical value effective value of the fluid of the heater of the ith wall at contant preure at contant entropy the u of all value at contant teperature at contant volue of the wall 115

4 F Lit F.2 Lit of acrony AE Adiabatic Effect BPE Botto Peltier Eleent BPL Bae Plate CP Critical Point CPF Critical Point Facility CRESCENDO Center for Reote SCience ENhanceent by DUC Operation CSS Current Source Syte DHS Data Handling Syte DUC Dutch Utilization Center EDE Experient Dedicated Equipent EGSE Electrical Ground Support Equipent EOS Equation of State EPT Experient Paraeter Table ESA European Space Agency HEX Heat Exchanger IF Interferoetry IFU Interferoeter Unit IML-2 International Microgravity Laboratory #2 LDC Linear Diode Caera LED Light Eitting Diode NASA National Aeronautic & Space Adinitration NLR Nationaal Lucht- en Ruitevaartlaboratoriu (National Aeropace Laboratory) OIO Optical Input and Output yte OTS Outer Theral Shield PA Parabolic Approxiation PCB Printed Circuit Board PE Piton Effect PMT Photo Multiplier Tube PWM PuleWidth Modulated SALS Sall Angle Light Scattering SAMS Space Acceleration Meaureent Syte SC Saple Cell SCU Saple Cell Unit SCU Saple Cell Unit onitoring theritor SCUr Saple Cell Unit regulating theritor TCS Theral Control Syte THU Therotat Unit TNO Nederlande Organiatie voor Toegepat Natuurwetenchappelijk Onderzoek TNO TPD TNO Technich Phyiche Dient TPE Top Peltier Eleent TPL Top Plate VSS Voltage Source Syte 116

5 Lit of table VWZI WALS Van der Waal-Zeean Intituut Wide Angle Light Scattering F.3 Lit of table Table 2.1 Univeral critical exponent. page 10 Table 3.1 Lit of optical coponent. page 31 Table 5.1 Critical value for SF 6. page 56 Table 5.2 Experiental reult. page 60 Table 6.1 Invere theral ipedance and urface area of wall aterial. page 71 Table 6.2 Meaured theral diffuivitie. page 80 Table 6.3 Meaured value of (-ρα ). page 86 Table E.1 Optical layout for the CPF. page 111 Table E.2 CPF Optical diagnotic ethod. page 112 F.4 Lit of figure Figure 1.1 The (P,T) Phae Diagra. page 2 Figure 2.1 Illutration of the denity-teperature phae diagra. page 9 Figure 2.2 The teperature profile after the onet of heating. page 13 Figure 2.3 Teperature profile at the heater. page 17 Figure 2.4 Teperature change near a cold wall. page 19 Figure 2.5 I a a function of µ. παγε 21 Figure 2.6 Denity change near a cold wall. page 21 Figure 2.7 The critical dependence of E. page 23 Figure 2.8 Gravity induced denity gradient. page 24 Figure 3.1 A iplified cro-ection of the THU and HEX. page 28 Figure 3.2 CPF therotat and optical yte block diagra. page 30 Figure 3.3 THU and ground optical arrangeent. page 35 Figure 3.4 The optical et up for the IFU. page 36 Figure 3.5 Scheatic of the interferoetry chaber. page 38 Figure 3.6 Top view of the cattering chaber including the arrangeent of the WALS optical fibre. page 39 Figure 3.7 The Spaceflight SCU. page 40 Figure 3.8 The denity-refractive index SCU. page 41 Figure 4.1 An exaple of an interferogra. page 44 Figure 4.2 Geoetry of a light ray paing through an optically inhoogeneou aple. page 45 Figure 4.3 Gravity induced deviation of a bea of light in a critical aple at variou teperature; the dahed line indicate the level at which ρ=ρ c (the enicu). page 46 Figure 4.4 Scheatic repreentation of the path of a ray through the aple. page 47 Figure 4.5 Scheatic repreentation of the path of ray through the aple and the optic to the iage plane and caera-fil. page 49 Figure 4.6 An exaple of a hadow adjacent to the heater. page 50 Figure 4.7 Deviation w.r.t. to a parallel bea of a bea paing through a denity field following heating at one ide. page 51 Figure 4.8 Z0 and t veru the ditance to Tc for SF 6 and CPF-optic. page

6 F Lit Figure 4.9 zf in tie for variou teperature. page 54 Figure 5.1 Denity v enicu poition. page 61 Figure 5.2 Denity v enicu poition. page 61 Figure 5.3 P at Tc-110 K v P at Tc-30 K. page 62 Figure 5.4 A unified plot of ρc veru P. page 63 Figure 5.5 Refractive index (n) v denity (ρ). page 63 Figure 6.1 WALS at 22, 30 and 38 during croing of Tc. Each curve i labelled by it correponding fibre. page 66 Figure 6.2 Coexiting phae at 10 K below Tc in µg viualized. page 67 Figure 6.3 Scheatic diplay of heat flow during heating with the plate heater. page 67 Figure 6.4 Interferoetry fringe (a) before heating (t=0 ), and (b) at tie t=57 after the onet of heating. page 68 Figure 6.5 Fraction of total delivered energy that enter the heater ubtrate. page 70 Figure 6.6 Coparion between the invere theral ipedance of the fluid and the wall aterial. page 73 Figure 6.7 Variation of the characteritic tie, tc, with the ditance to Tc. page 73 Figure 6.8 Theoretical prediction of ientropic teperature rie in our aple fluid accounting for heat loe to the heater ubtrate and through the other urrounding wall. page 74 Figure 6.9 Theritor reading relatively far fro CP during heat pule of contant power and prediction by eq. (2.34), (2.36) and (2.37). page 75 Figure 6.10 Theritor reading relatively cloe to CP during heat pule of contant power and prediction by eq. (2.34), (2.36) and (2.37). page 76 Figure 6.11 Experiental data of ientropic teperature rie per Watt of diipated power at everal tie during heating run veru the ditance to Tc. page 77 Figure 6.12 Coparion between prediction and experient a regard the aplitude A. page 77 Figure 6.13 Shadow front oveent in the PA. page 79 Figure 6.14 The hadow front cloe to Tc. page 81 Figure 6.15 The hadow front far fro Tc. page 82 Figure 6.16 The theral diffuivity veru teperature difference to Tc. In the iddle the teperature range tudied by the variou author are indicated. page 83 Figure 6.17 A ketch of the denity change veru the iultaneouly eaured teperature change during local heating. page 85 Figure 6.18 Meaureent of bulk teperature and denity change. page 87 Figure 6.19 A plot of <ρ(t)> veru Tb(t)(1+E t). page 88 Figure 6.20 A double logarithic plot of cv veru T-Tc. page 89 Figure 6.21 Illutration of the ientropic character of the T-ρ repone and it break down due to gravity jitter. The dahed vertical line indicate the tart of the gravity jitter. The actual ize of the diturbance in the gravity level i diplayed in the upper part. page 90 Figure B.1 R within xeff. page 99 Figure B.2 R at x=0. page 99 Figure E.1 C 1 v teperature for two different power denitie. page 106 Figure E.2 A contour plot of C 2. page 107 Figure E.3 C 1 and C 2 in tie for zf at variou teperature. page 108 Figure E.4 Scheatic repreentation of the real path of a ray through the fluid copared to the path in the PA. page 109 Figure E.5 A contour plot of z /z PA veru z and t. page 110 Figure E.6 The effect of the departure fro the PA to zf in tie. page