Two-Layer Model for the Heat Transfer to Supercritical CO 2
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1 5th International CO 2 Poer Cycles Symposium March 28-31, 2016, San Antonio, USA To-Layer Model for the Heat Transfer to Supercritical CO 2 E. Laurien, S. Pandey Institute of Nuclear Technology and Energy Systems University of Stuttgart, Germany D.M. McEligot* Nuclear Engineering Division University of Idaho, USA
2 Outline Introduction To-Layer Model for a Supercritical Fluid Extension to Take Account of Buoyancy Application to the Lo-Temperature Recuperator Application to the Reject Heat Exchanger Conclusion Starflinger Institutsversammlung
3 Temperature T [ C] Supercritical CO 2 -Loop for Energy Conversion MIT-Study 800 ~77 ar HighTemp Recuparator Lo Temp Recuparator % ar 78 ar advanced design 5 4 Input HX Reject HX Alternator 1 Turine Re-Compressor Main Compressor V. Dostal, M.J. Driscoll, P. Hejzlar: A Supercritical Caron Dioxide Cycle for Next Generation Nuclear Reactors, MIT- ANP-TR-100 (2004) 3 ~200 ar 60% Lo-Temp Recuperator ar ar 6 critical point 8 0 1,0 1 1,5 2,0 2,5 3,0 entropy s [kj/kg] [entropy s kj/kgk]
4 Fluid Properties oc CO2 Dichte dyn. Zähigkeit Wärmeleitfähigkeit Temperatur vs. Enthalpie "S-Kurve" T pc h pc W. Lemmon, Marcia L. Huer, and Mark O. McLinden Thermophysical Properties Division National Institute of Standards and Technology Program. REFPROP (2014)
5 Starflinger Institutsversammlung
6 Experiments y Kim et al ar heated all Starflinger Institutsversammlung
7 Integration Domain an Governing Equations Su-Headline pipe axis all T (x) Theoretical Description Methods: Lookup Tale D/2 CFD (RANS and DNS) dx x, u G y, y + (x) r, R q g 1-dimensional theory y Laurien 2012 Explicit or implicit formulas (model equations), correlations e Nu a Re 1 Pr e2 e3 e4 e5 c c p e6
8 u u To-Layer Method Constant Properties u Re Velocity la of the all 1 u ( y ) ln y D u C u Re 8 c f C ( T q W W T ) u c p T Temperature la of the all PrT T ( y ) ln y (Pr) Pr T u y T Pr y y y u y u y laminar (viscous) su-layer y vs turulent all layer 11.6 laminar (conducting) su-layer y cs turulent all layer y Pr vs 1 3
9 Heat Transfer Friction temperature increase all shear stress Headline Su-Headline y Scaling ith ulk quantities y u u y Scaling ith all quantities y u u created at the all Re 1 c f um D 2 log 10 D Re c f c f c f c f 8 u 2 m turulent Layer (tur) T tur T tur T q W PrT tur u c ln R ln y cs conducting sulayer (cs) T cs Tcs u q c W 2/3 T cs Pr yvs T T cs T T cs T T tur cs
10 Temperature T Result of the Original Method Experiment Li et al Bulk fluid enthalpy h (kj/kg) deterioration can e predicted, ut some iaccuracies remain
11 Headline Su-Headline Recycle inlet r z g q L 1 =5D L 2 =30D/60D Re Autor: Xu Chu, IKE Code: OpenFoam Cray XC-40 'HazelHen' des HLRS ca CPU-cores L 2 30D 60D + r z (R θ) no of cells Mio. 150 Mio.
12 Re = 5400 Vertikales eheiztes Rohr Ref.: DNS: Xu Chu, IKE, 2015 aufärts thermisch stail aärts thermisch instail g Visualisierung der Turulenzstrukturen mit dem λ 2 Kriterium g
13 Caliration of the Method Starflinger Institutsversammlung
14 Extension of the Method to take account of acceleration and uoyancy Implementation in the method Acceleration Parameter 4q u K h m v ; 2 GD h c p y 11.8 c vs v K v Parameter for the 'structural' effect of uoyancy Gr Ri 2 Re y cs 11.8 Pr 1 3 cs c uoyin, Ri Parameter for the 'external' effect of uoyancy Gr 2 3 g D T T 7 z 5D 2, mod c uoyex, 10 Gr 1 e
15 Lo-Temperature Recuperator, Secondary Side 200 ar upard flo all shear stress all temperature
16 Lo-Temperature Recuperator, Secondary Side 200 ar donard flo all shear stress all temperature
17 Lo-Temperature Recuperator, Primary Side 80 ar cooling all shear stress all temperature
18 Reject-Heat Exchanger 80 ar cooling all shear stress all temperature
19 Conclusion The to-layer model has een modified to take account of uoyancy and acceleration in a vertical (upeard or donard) supercritical pipe flo at lo Reynolds numers (Re < 10000) Wall temperature and all shear stress are determined as a function of pressure, pipe diameter, all heat flux (heating or cooling), mass flux, and ulk enthalpy Empirical model parameters have een determined using to results of Direct Numerical Simulations must e extended y further ork (in progress) Model is applied to flos in the lo-temperature recuperator and the reject-heat exchanger
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