Numerical Simulation of the Thermal Resposne Test Within the Comsol Multiphysics Environment

Transcription

1 Presented at the COMSOL Cnference 2008 Hannver University f Parma Department f Industrial Engineering Numerical Simulatin f the Thermal Respsne Test Within the Cmsl Multiphysics Envirnment Authr : C. Crradi, L. Schiavi, S. Rainieri and G. Pagliarini

2 Intrductin The Thermal Respnse test allws in-situ-determinatin f the equivalent r effective grund thermal cnductivity and brehle thermal resistance. In the present wrk the finite element methd, implemented within the Cmsl Multiphysics envirnment, has been adpted t slve the partial differential equatin gverning the heat transfer prblem in a tube-in-tube brehle energy strage system. 2 / 15

3 Mdel Axis f symmetry Fill material Adiabatic surface nn-hmgenus sil Wrking fluid Adiabatic surface Gemetry f the gethermal brehle system 3 / 15

4 Line Surce Mdel Mdel is apprximated by the Line Surce Mdel Analitical slutin T(r,t) = T 0 + Q/(4 π λ H) E 1 [r 2 /(4 α t)] - the thermal prperties f the heat exchanger and sil are the same - the pipe in which the wrking fluid flws is placed n the symmetry axis f the system and it has a negligible diameter - the fluid temperature desn t change alng the axial directin k = Q/(4 π λ H) T f (t) m + k ln(t) m = T 0 + Q/(4 π λ H) (ln(4 α /r b2 ) - γ) + R b Q/H The estimatin prcedure is based n the cmparisn between the temperature f wrking fluid, experimentally acquired and evaluated as the arithmetic mean between the inlet and utlet fluid temperature, and equatin. 4 / 15

5 Gverning equatins Transient heat transfer cnductin is gverned by the Furier equatin T c p div grad T Initial cnditin T r,0 T t 0 Thermal bundary cnditin at r = r 2 T r F rr 2 h T z,tt r,t By assuming that the cnvectin prblem bth in the tube and in the annular sectin f the heat exchanger is ne-dimensinal, and by mdelling the thermal cupling between the tw cunter-current stream thrugh the thermal cnductance per unit length U, the energy equatin fr the tube side fluid flw: Ti Ti Ai f cpf ui UT z,tti z,t Initial cnditin Ti z,0 T 0 t z i, The crrespnding equatin fr the annular sectin is: A c f pf T t u T z U T z, tt z, t h pt r, tt z, t i F Initial cnditin T, 0 T z,0 F 2 5 / 15

6 Gverning equatins The cnditin f cnstant pwer supplied t the wrking fluid is implemented by the cnditin: T i 0,t T 0,t T T cnstant ver the whle tempral dmain The U-tube cnfiguratin has been simulated by impsing that the temperature f the tube-side dwnward flw equals the temperature f the upward annularside flw at the end f the heat transfer sectin. T H,t T H,t i 6 / 15

7 Gverning equatins A 2-D Heat Cnductin mdel in the sil A 1-D mdel, implemented by means f the weak frm frmulatin in the fluid dmain. Gemetry f the gethermal brehle system 7 / 15

8 Sil types Type f sil A B C D Cmpsitin Thermal Cnductivity (W/mK) Vlumetric Thermal Capacity (MJ/m 3 K) H 1 = 0.2 H 2 2 H 2 = 0.8 H 4 2 H 1 = 0.2 H 2 2 H 2 = 0.8 H 4 3 H 1 = 0.5 H 1 2 H 2 = 0.5 H 1 3 H 1 = 0.5 H 1 2,5 H 2 = 0.5 H 1 2,5 8 / 15

9 Results Sil Temperature distributin 9 / 15

10 Results Average fluid temperature versus time fr sil tipe D 10 / 15

11 Results The temperature distributin alng the axial crdinate at the brehle-sil interface is reprted in figure fr cases C and D, describing respectively a nn-hmgenus and a hmgeneus sils with equal mean vlumetric heat capacity fr a given thermal cnductivity value. Temperature axial distributin at the brehle-sil interface 11 / 15

12 Results: Sil thermal cnductivity Case A In case f nn-hmgeneus sil thermal cnductivity, case A, and f bth nnhmgeneus thermal cnductivity and vlumetric heat capacity, case B, the estimated effective λ value appraches the value btained by perfrming a mean, weighted accrding t the cmpsitin, f the values characterizing the single sil layer. 1 H eq H i i i Case B 12 / 15

13 Results: Sil thermal cnductivity When cnsidering the vlumetric heat capacity nn-hmgeneity nly, case C, the thermal cnductivity is recvered exactly already after 10 hurs after the beginning f the transient. Case C 1 H eq H i i i Case D 13 / 15

14 Results: Brehle thermal resistance Case C The brehle thermal resistance estimated accrding t the fitting prcedure fr cases C and D, describing respectively a nn-hmgenus and hmgeneus sils with equal mean vlumetric heat capacity fr a given thermal cnductivity value. 1 H eq H i i i This apprach prvides a gd apprximatin since, when the capacitive effects becmes negligible, the tw asympttic values assumed by the brehle thermal resistance f cases C and D differ by less than 3%. Case D 14 / 15

15 Cnclusins In cnclusin, the analysis cnfirms that, under certain hypthesis, the estimated prperties resulting frm the Thermal Respnse Test can be interpreted as effective values which apprach the mean, weighted accrding t the sil cmpsitin, f the values characterizing the single grund layers. carl.crradi@unipr.it 15 / 15