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1 Thermophysical properties of molten and -Bi eutectic (review) V. Sobolev SCK CEN, Boeretang 200, Mol, Belgium 1

2 Contents 1. Introduction 2. Physical parameters of interest 3. Thermodynamic properties 4. Transport properties 5. Conclusions 6. Annex 2

3 1. Introduction (1) 1. The second part of 1940 s: Liquid, Bi, Hg and their alloys were considered as the promising coolants for future nuclear reactors -> Heavy Liquid Metal Collants (HLMC) s: Possibility of utilisation of HLMC in nuclear reactors was studied in USA and Canada: a) Liquid Metal Fuel Reactor Program (U-Bi fuel, ). b) A few small special installations cooled by liquid Hg and -Bi eutectic were constructed. These programs were closed because of serious difficulties related to intensive corrosion at operation 3

4 1. Introduction (2) s: the intensive studies of HLMC were performed in the former USSR: a) Few loops was constructed and used for the tests of components of the nuclear power installations cooled by and -Bi eutectic. b) 8 submarines were constructed with 150 MW propulsion reactors cooled by -Bi eutectic s: studies in Europe and other countries on -Li eutectic (coolant and T-breeder in a fusion reactor). 4

5 1. Introduction (3) 5. Since middle 1990 s until now: growing interest and intensive studies of -Bi eutectic,, and Hg, aiming at application in spallation neutron sources and in fast reactors (subcritical and critical) of new generation: a) SNS with Hg target of 1 MW and 1.3 GeV LINAC in USA (started at low power of 0.1 MW in May 2006). b) MEGAPIE with -Bi target of 1 MW (started in 2006) c) MYRRHA ADS (-Bi) design at SCK CEN in Belgium. EDT ADS conceptual design in EU (). ADS studies in Japan, Korea, USA (, -Bi). d) -Bi and -cooled fast reactor projects in GEN-IV, FP6 (ELSY) and in Russia (BREST, SVBR). e) OECD/NEA Handbook on HLMC Properties and Technology. 5

6 2. Properties of interest: General Requirements Metallic coolants of a nuclear reactor should have the following properties: a) Low melting temperature and high boiling temperature. b) Low neutron absorption cross-section. c) Radiation stability. d) Low viscosity and density. e) High heat capacity and thermal conductivity. f) High thermal expansion coefficient. g) Low chemical activity 6

7 2. Properties of interest: Design impact Heat removal in channels: Q& ~ C p Heat transfer from surfaces: h ~ λ + A C p Power for circulation: P ~ n pump ν ρ Natural convection capacity: p α nc ~ p Evaporation: ps, σ, Q 7

8 2. Properties of interest: Comparison (*T = 700 K) Parameter -Bi (e) Na H 2 O (PWR conditions) M a (g mol -1 ) T melt (K) Q melt (J mol -1 ) T boil (K) Q boil (J mol -1 ) T crit (K) (calculated) *Σ tot fast (cm -1 ) Radiation stability yes yes yes no *Chemical activity low low high medium Metal dissolution high high medium low 8

9 2. Properties of interest: Comparison (T = 700 K) Parameter -Bi (e) Na H 2 O (PWR conditions) ρ (kg m -3 ) α vol (10-5 K -1 ) C p (J mol -1 K -1 ) σ (10-3 N m -1 ) λ (W m -1 K -1 ) a p (10-6 m²/s) η (10-4 Pa s) ν (10-7 m²/s) Pr

10 3. Thermodynamic properties: -Bi system phase-diagram T melt T melt Bi Liquidus line Liquid -Bi e-point Liquidus line Solidus line Solid solution of in Bi Bi Solid -Bi N.A. Gokcen, J.Phase Equilibria 13 (1992) 21 Solid solution of Bi in Intermediate incongruent melting phase 10

11 3. Thermodynamic properties: Density Density (kg m -3 ) ρ T kgm T = =± 3 ( ) ε 0.6% -Bi(e) ρ T kgm T LBE = =± 3 ( ) ε 0.6% Lyons 1954 Kutateladze 1959 Kirshenbaum 1961 Ruppersberg 1976 Lucas 1984 Iida 1988 from Onistchenco 1999 Kirillov 2000 Alchagirov 2002 Khairulin 2004 recommended -Bi(e) recommended Temperature (K) 11

12 3. Thermodynamic properties: Isobaric thermal expansion 1.8E-04 α ( T, p ) - p p 1 ρ( T, p ) 0 0 ρ( T, p0) T 0 0 p ρ( T, p0 ) T p α ( T, p ) - 1 ρ( T, p ) Isobaric volumetric CTE (K -1 ) 1.6E E-04 α ( ) 1 K T T 1 -Bi(e) ( ) = Bi(e) LBE 1.2E-04 α ( ) 1 T K T 1 ( ) = Temperature (K) due to a weaker interatomic attraction in -Bi(e) system 12

13 3. Thermodynamic properties: Sound velocity Sound velocity (m s -1 ) = + 1 <± 0.5% G.M. Mustafin, G.F. Shaikhiev, Russ. J. Phys. Chem. 45 (1983) usound ms T T ε -Bi (e) -Bi(e) u ms = T ε <± 1 sound -Bi(e) % Kleppa 1950 Kutateladze 1959 Gordon 1959 Konyuchenko 1969 Mustafin 1983 Kazys 2002 recommended -Bi(e) recommended Temperature (K) 13

14 3. Thermodynamic properties: Isentropic compressibility Elasticity modulus (GPa) p ρ BS = V = = ρ u K V p ( ρ / ) S S S 2 sound LBE -Bi (e) Temperature (K) The lower bulk elasticity modulus (the higher compressibility) of -Bi is due to the lower density and weaker interatomic forces. 14

15 3. Thermodynamic properties: HLM s heat capacity Onistchenko et al. (HT-HP, 1999, 31, ), using PP and PT methods showed that Cp of HLM decrises with T after melting and then increases. Relative heat capacity Old recommendations (calculated by Onistchenko 1999) -Li Sn Hg Bi ( ) ( ) ρ ( T ) T B T T 2 ( kinetic) ( potential ) p( ) = V + V ( ) + p T c T c c T T-T m (K) α 15

16 3. Thermodynamic properties: isobaric heat capacity R.N. Lyon 1952 S.S. Kutateladze 1959 Isobaric specific heat (J kg -1 K -1 ) A.J. Freeland 1966 R. Hultgren 1973 L.V. Gurvich 1991 B. Cheynet 1996 Onistchenko 1999 (calc) Smithells 2004 Recommended ( ) = H T a b T c T d T e T f T p Temperature (K) + 0 =± 7% L.V. Gurvich, I. V. Veyts, Thermodynamic Properties of Individual Substances (translated in 1991) c p J kg K = T T T T ε 16

17 3. Thermodynamic properties: -Bi(e) isobaric heat capacity Specific heat (J kg -1 K -1 ) Bi(e) LBE Kutateladze 1959 Lyon 1952 Hultgren et al 1973 Kopp's law Recommended 130 c ( T) = T T plbe Temperature (K) 17

18 3. Thermodynamic properties: Simplified EOS for low pressures ρ ρ pt = p0 T + dp p p (, ) ρ(, ) Taking into account that ρ ρ cp = p p c T s V one can obtain ρ p S p 0 = u 1 2 sound T 2 cp α p T = 1+ c c ρ K V p s α T α T 2 2 ρ 1 p 1 p = = + 2 p u T sound cp ρ K s usound c p Then at pressures close to p 0 : K S 1 ρ ρ p S ρ 1 T α usound ( T) cp T ( pt, ) ρ( p, T) ( p p) 2 p ( T) ( ) 18

19 3. Thermodynamic properties: Surface tension 2/3 ' : σ σ a c ( ) Eotvos && && s law k V T T Surface tension (10-3 N m -1 ) σ 1-4 Nm = T ε =± σ 5% U. Jauch and B. Schulz, KfK-4144, Karlsruhe (1986) -Bi(e) = =± 1 5 -Bi(e) Nm T ε 3% Temperature (K) Skapski ' s correlation : σ melt H Va Miller 1951 Lyon 1954 Semenchenko 1961 Friedland 1966 Lucas 1984 Kazakova 1984 Jauch 1986 Iida 1988 Keene 1993 Kyrillov 2000 Novacovic 2002 vap IAEA TECDOC Pastor Torres 2003 Smithells 2004 recommended -Bi (e) recommended -2/ 3 19

20 3. Thermodynamic properties: -vapour pressure Pressure (Pa) 1.0E E E E E E E E RT sat [ ] = e =± 12% p Pa ε /Temperature (K -1 ) Lyon 1954 Friland 1966 Hultgren 1974 Iida 1988 Cheynet 1996 Recommended Clapeiron Clausius : dp Hvap H = dt T V V sat liq ( vap liq ) if vapour is ideal gas : ln p sat H A RT evap 20

21 3. Thermodynamic properties: -Bi vapour pressure 1.0E E+05 ps RT e ε 50% = =± Tupper 1991 Orlov 1997 Vapour pressure (Pa) 1.0E E E E-03 -Bi(e) Michelato 2003 Schuurmans 2005 Sh. Ohno 2005 Recommended 1.0E E /T (1/K) Temperature (K) 21

22 4. Transport properties: Dynamic viscosity 1.0E-02 Dynamic viscosity (Pa s) 1.0E-03 recommended LBE -Bi(e) recommended 1.0E /T (K -1 ) Lyons et al Kutateladze et al McLainet al Hollman et al Hofmann 1970 Kaplun et al Lucas 1984 Iida Bi(e) LBE Kyrillov et al Smithells Hb 2004 Arrhenius law: exp Eη η = η0 R T ln Eη 1 = 0 + R T ( η) ln ( η ) 22

23 4. Transport properties: Dynamic viscosity Dynamic viscosity (Pa s) 3.5E E E-03 η RT LBE [ Pa s] = e ε =± 6% -Bi(e) Lyons et al Kutateladze et al McLainet al Hollman et al Hofmann 1970 Kaplun et al Lucas 1984 Iida 1988 Kyrillov et al Smithells Hb 2004 recommended -Bi(e) recommended 5.0E-04 η RT [ Pa s ] = e ε=± 4% Temperature (K) 23

24 4. Transport properties: Electric resistivity Electrical resistivity (10-8 Η m) [ m] ( ) r Ω = T 10 ε =± 3% LBE -Bi (e) [ ] ( ) -8 r Ω m= T 10 ε =± 1% Temperature (K) Lyon1952 Hofmann 1970 Iida 1988 Kyrillov 2002 Smithells Hb 2004 recommended -Bi(e) recommended 24

25 4. Transport properties: thermal conductivity 26 ( ) ( ) Wiedemann Frantz law simple metals : λ T =L T /r T e 0 Thermal conductivity (W m -1 K -1 ) λ Wm K = + T ε =± % Temperature (K) Lyon 1952 Kutateladze 1959 Hofmann 1970 Iida 1988 Ziniviev 1989 Kyrillov 2000 Yamasue 2003 Smithells Hb 2004 Wiedemann-Franz law Recommended 25

26 4. Transport properties: -Bi(e) thermal conductivity 20 Thermal conductivity (W m -1 K -1 ) Bi(e) Lyon 1952 Kutateladze 1959 Iida 1988 Kirillov 2000 Widemann-Franz law Recommended λ Temperature (K) = + =± Bi(e) Wm K T T ε 15% 26

27 4. Transport properties: Thermal diffusivity and kinematic viscosity Thermal diffusivity (10-6 m 2 s -1 ) Bi(e) a p = λ ρ c p Kinematic viscosity (10-6 m 2 s -1 ) Bi(e) ν = µ ρ Temperature (K) Temperature (K) 27

28 4. Transport properties: Prandtl number Prandtl Number Bi(e) Pr = ν a p Temperature (K) 28

29 5. CONCLUSIONS For the molten and -Bi eutectic, the experimental data are available for most of thermophysical parameters of interest in the temperature region of normal operation of nuclear installations of interest, but at atmospheric pressure. However, some of the parameters (the heat capacity, the thermal conductivity, the saturated vapour pressure, the sound velocity, the electrical resistivity and the critical point parameters) are not yet determined with the needed accuracy and reliability, especially for -Bi(e). International and national R&D program (experimental and theoretical) are needed to develop a more reliable and complete properties database for and -Bi(e) and to extend it to the higher pressures and temperatures required for safety studies of nuclear installations and reactors. 29

30 6. ANNEX 1: melt properties Property, parameter SI unit Correlation Temperature range (K) Melting temperature K T = melt n/a 0.1 Latent heat of melting kj kg -1 Q =23.8 melt n/a 0.7 Boiling temperature K T =2016 boil n/a 10 Latent heat of boiling kj kg -1 Q =858.2 boil n/a 1.9 Estimated error ± Saturated vapour pressure Pa ps 9 = exp( / T) % Surface tension N m -1-4 σ = T % Density kg m -3 ρ = T % Sound velocity m s u = sound T T % Bulk modulus Pa Bs ( T T ) = % Isobaric specific heat J kg -1 K c 2 p = T T T T % -4 Dynamic viscosity Pa s = exp( 1069/ T) Electric resistivity Ω m = ( + T) η % r % Thermal conductivity W m -1 K -1 λ = T % 30

31 6. ANNEX 2: -Bi(e) melt properties Property, parameter SI unit Correlation Temperature range (K) Melting temperature K T melt = n/a 0.6 Latent heat of melting kj kg -1 Q = 38.6 melt n/a 0.2 Boiling temperature K T boil = 1943 n/a 10 Latent heat of boiling kj kg -1 Q = 854 boil n/a Saturated vapour pressure Pa p exp( / T) Surface tension N m -1 ( ) -3 s Estimated error ± = % σ = T % Density kg m -3 ρ = T % Sound velocity m s -1 u = T % Bulk modulus Pa Bs ( T T ) sound = % Isobaric specific heat J kg -1 K -1 2 c = T T % 4 Dynamic viscosity Pa s η exp( 754.1/T ) 8 Electric resistivity Ω m ( ) p = % r = T % Thermal conductivity W m -1 K λ = T T % 31

32 Acknowledgement to Dr. H. Aït Abderrahim (SCK CEN), Dr. G. Benamati (ENEA), Dr. A. Gessi (ENEA) for the help and contributions in Chapter 2 of the OECD Handbook on HLMC Technology. to Dr. H.U. Borgstedt ( Germany), Prof. R. Ballinger (MIT), Dr. C. Latgé (CEA), Dr. N. Li (LANL), Dr. H. Katsuta (Japan) and Dr. W. Pfrang (FZK) for useful suggestions, and some important remarks on Chapter 2 of the OECD Handbook. 32

School on Physics, Technology and Applications of Accelerator Driven Systems (ADS) November 2007

1858-36 School on Physics, Technology and Applications of Accelerator Driven Systems (ADS) 19-30 November 2007 Thermal Hydraulics of Heavy Liquid Metal Target for ADS. Part I Polepalle SATYAMURTHY BARC