Modelling of Solidification and Melting in a Latent Heat Storage

Transcription

1 Modelling of Solidification and Melting in a Latent Heat Storage A Quasi-Stationary Approach Felix Eckl, Simon Maranda, Anastasia Stamatiou, Ludger Fischer, Jörg Worlitschek Lucerne University of Applied Science & Arts felix.eckl@hslu.ch joerg.worlitschek@hslu.ch energie-cluster - Innovationsgruppe Speicher / Wärmetauscher 2016, April 12 th, HSLU Horw (Lu)

2 Motivation Latent TES in Buildings High thermal capacity 100 kwh/m 3 range Need for thermal power optimization IRES,

3 Models Solidification Stefan Problem (1905) TT PPPP λ ss + αα TT dddd nn = ρρh PPPP dddd Analytical Numerical 1-dimensional transient Only for simple geometries Instationary IRES, ,3-dimensional Energy and Momentum Balance are solved Complex geometries Commercial softwares available (Ansys, Comsol) Huge computing effort Quasi-stationary 1,2-dimensional Only Energy Balance is solved No commercial software available Small computing effort 3

4 Quasi -Stationary Approach PPP = h PPPP cc pp,ss (TT PPPP TT WW ) > 6,2 Quasi stationary approach Assumption: crystallization kinetics not limiting Assumption: Sensible heat capacity << Latent heat capacity Ph > Heat flux per time step is calculated stationary No need for a high spatial resolution of the computational domain Ability to model large storage systems System integration dynamic modelling including large time simulation are possible IRES,

5 Quasi stationary approach: Solidification Heat flux from the PCM to the HTF: QQ HHHHHH = (TT PPPP TT HHHHHH )/RR (ss) ss Resistance depends on solid layer Equation needed Balance at the solid/liquid interface: HH PPPP = QQ HHHHHH QQ PPPPPP dddd ρρh PPPP = λ TT PPPP dddd ss αα TT ss nn 5

6 Two-Dimensional Model Input Storage System: Volume, Geometry of HEX) Material properties: PCM, HTF) Operational parameters: inlet temperature of HTF, massflow of HTF Simulation Output Heat flux Storage capacity Duration for charging/disscharging 6

7 Results: Model validation - 10 liter set-up Solidification T PC = 10 C T in = -5 C TT PPPP 10 CC AA HHHH 0,1 mm 2 - Computational time (standard PC)< 20s 7

8 Scale Up - Quasi stationary approach Correction Factor AAAA = AA rrrrrrrrrrrrrr = AA uuuuuuuuuuuuuuuuuuuu nn ttttttttt bb AA uuuuuuuuuuuuuuuuuuuu AA uuuuuuuuuuuuuuuuuuuu AArr aaaaaa = AA uuuuuuuuuuuuuuuuuuuu nn ttttttttt,aaaaaa bb AA uuuuuuuuuuuuuuuuuuuu ff AArr aaaaaa = 1.44 AArr aaaaaa AArr aaaaaa AArr aaaaaa AArr aaaaaa rr aa rr cccccccc Quelle: Jekel T.B.; Mitchell J.W.; Klein S.A.: Modeling of ice-storage tanks. ASHRAE Transactions; Vol. 99 (1) (1993), S

9 Results: Validation Scale Up 300 Liter Solidification T PC = 62 C T in = 37 C TT PPPP 62 CC AA HHHH 10 mm 2 - Computational time (standard PC)< 30s 9

10 Observation of Melting t: 0 h Loading = 0 t: 2 h Loading = 0.2 t: 4 h Loading = 0.8 Beginning: Homogeneous growth of liquid PCM layer around the HEX surface. After t: Convection becomes dominant 10

11 Observation of Melting II HSLU&CSEM Beginning: Homogeneous growth of liquid PCM layer around the HEX surface. After t: Convection becomes dominant 11

12 Quasi stationary approach: Melting Phase I melting in circular orifice Heat flux from the PCM to the HTF: QQ HHHHHH = (TT PPPP TT HHHHHH )/RR (ss) ll Resistance depends on growing liquid layer TT HHHHHH (tt kk, ll ii ) TT WW (tt kk, ll ii ) TT PPPP TT aaaaaa (tt kk ) Phase II melting in broken parts Defining a critical radius VV QQ HHHHHH(tt kk, ll ii ) QQ llllllll (tt kk, ll ii )

13 Results: Model validation - 10 liter set-up Melting T PC = 10 C T in = 25 C TT PPPP 10 CC AA HHHH 0,1 mm 2 - Computational time (standard PC)< 20s 13

14 Summary Strengths: Acceptable accuracy for solidification and melting Very small computational effort (seconds to minutes) Applicable for large storages and different PCM Applicable for system dynamic simulation Weaknesses/Outlook Homogenous growth of solid layer (not applicable for all PCM) HEX with horizontal tubes Less accurate for melting process Crystallization kinetics not yet considered 14

15 Thank you for your attention Acknowledgements: 15