A THERMAL STUDY OF POWER CABLES COOLING IN TUNNELS

A THERMAL STUDY OF POWER CABLES COOLING IN TUNNELS F. Boukrouche 1 (PhD), C.Moreau 1, S.Harmand 2, F. Beaubert 2, J.Pellé 2, O.Moreau 3 1 EDF R&D, Moret-sur-Loing, France, 2 LAMIH-UMR CNRS 8201, University of Lille Nord-de-France, France 3 EDF CIST, Paris, France E-mail: fahd.boukrouche@edf.fr 2013 1 1 EDF I Recherche & Développement I I COMSOL - Boston 2016

SOMMAIRE I. INTRODUCTION II.EXPERIMENTAL & SIMULATION SETUP III.CABLE COOLING : RESULTS & DISCUSSION IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS 2 I COMSOL - Boston 2016 2

I. INTRODUCTION I.Power transmission network II.Thermal limiting factor III.Simulation challenges II.EXPERIMENTAL & SIMULATION SETUP III.CABLE COOLING : RESULTS & DISCUSSION IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS

I POWER TRANSMISSION NETWORK From energy production centers to the distribution networks, several solutions are available : Overhead lines : Buried lines : Tunnels : Exemple of London tunnel 4 I COMSOL - Boston 2016 4

I THERMAL LIMITING FACTOR Principal limiting factor : the dielectric insulation temperature. De Conducteur Core Dielectric Isolant insulation diélectrique The Joule heating from the transiting current is dissipated through. Conduction in the cables layers. Convection with the surrounding air. Radiation with other surfaces (tunnel walls, other cables, etc.). Radiation cable / walls Ecran Metallic screen Isolant Outer-sheat extérieur Tunnel Soil Existing rating methods suffer some limitations such as : All cables are considered identicals. Empirical derating coefficients for groups. Cooling laws not proposed for fully developed turbulent flow. Cable Convection cable / air Convection air / walls Ph.D. main objective : Remove the last two issues 5 I COMSOL - Boston 2016 5

h W. m 2. K 1 I SIMULATION CHALLENGES Tunnels are kilometers long Long geometries involved High aspect ratio between the tunnel and the cables High number of elements for a good mesh quality. Need of a Low Reynolds approach for high precision in the computed heat transfer. Even higher number of elements Turbulent flow regime needs a (very) long entrance length. More elements 140 120 100 80 60 40 20 Heat transfer coefficient evolution 0 0 3 6 9 12 15 18 21 z (m) Re = 11600 Re = 26220 6 I COMSOL - Boston 2016 6

I. INTRODUCTION II.EXPERIMENTAL & SIMULATION SETUP I.Ventilated cable tunnel Mock-up II.COMSOL use for data treatment III.3D numerical simulations III.CABLE COOLING : RESULTS & DISCUSSION IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS

II VENTILATED TUNNEL MOCK-UP x y z Measurement section 6.5 m Plexiglas Test cable Inlet Lx = 1De Copper Ceramic Aluminium 8 I COMSOL - Boston 2016 8

II COMSOL USE FOR DATA TREATMENT The experimental data are treated with a coupled MATLAB-COMSOL inverse method. The local Nusselt numbers Nu i are obtained with an optimization script using two parts: Surface Surface radiation The COMSOL heat transfer module for the heat transfer resolution. 2D geometry. Heat conduction in the cables & tunnel walls. Surface-to-surface radiation (hemicube formulation). Heat transfer coefficient at the cable surface controlled by the optimization process in the MATLAB interface. h ambient 10 W. m 2. K 1 The mesh is a very fine one Underconstrained model. Use of an interpolation fonction for the heat transfer coefficient Iterative heat transfer coefficient Control point for the optimization method P 0.029 m 9 9 I COMSOL - Boston 2016

II COMSOL USE FOR DATA TREATMENT The local Nusselt numbers Nu i are obtained with an optimization script using : S = A MATLAB optimization process based on the minimization of the S criterion (1). 10 i=1 A second order regularization is chosen. The regulation coefficient β is optimized for each iterations. θ comsol θ mes 2 + β The mean Nusselt number is obtained by integration on the cable surface. j h j+1 2h j + h j 1 2 (1) Optimization script h φ = h i,opt β = β opt Cooling profile Identification process Initial heat transfer coefficient vector h 0 and β 0 value LiveLink for MATLAB 2D COMSOL simulation with the profil h φ at iteration i 1 Extraction of the θ i and h i simulated data Evaluation of the S criterion (1) D e Nu De = 2πλ( θ s θ ambient 0 2π P conv φ dφ (2) Yes Difference > 0.1 No Final result: h i = h φ 10 I COMSOL - Boston 2016 10

II COMSOL USE FOR DATA TREATMENT The validation case led to a benchmark with the opensource code OpenFOAM and experimental published results. Thermal isolation Cable Connector Similar results obtained. OpenFOAM finite volume formulation preferred to COMSOL for the 3D multi-million mesh elements (cluster availability). Airflow 1.5 100 1 90 0.5 Cp 0-0.5 α ( 0 20 40 60 80 100 120 140 160 180 Nu De 80 70 60 50 40-1 30-1.5 Cpréférence Reference Cp Comsol Cp OpenFoam 20 0 20 40 60 80 100 120 140 160 180 α ( Experimental Expérimental NuDe COMSOL I COMSOL - Boston 2016 11 11

II 3D NUMERICAL SIMULATIONS Simulation RANS using the open source code OpenFOAM. Coupled solver and low Reynolds mesh with a turbulence model k- omega SST. Y+ << 1 Cable 3 m 1De from the tunnel wall 12 I COMSOL - Boston 2016 12

I. INTRODUCTION II.EXPERIMENTAL & SIMULATION SETUP III.CABLE COOLING : RESULTS & DISCUSSION I.Airflow analysis & cable cooling profile II.Mean Nusselt numbers III.New cooling laws IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS

III AIRFLOW ANALYSIS & CABLE COOLING PROFILE As the cable wall spacing decreases, the air flow structure deforms itself. A velocity drop is observed in the gap between cable and wall. Lx = 2De Lx = 1De Lx = 0.5De 14 I COMSOL - Boston 2016 14

III AIRFLOW ANALYSIS & CABLE COOLING PROFILE The observed velocity drop can be down to 50% of the entrance velocity. A threshold wall spacing value of Lx = 2De can be defined. y z x Velocity profile - line plot z = 2.8 m 24 22 Constrained region Cable Unconstrained region U0 Nu De 20 18 16 14 12 10 Experimental Lx = 0.5De Re De = 26220 0 50 100 150 200 250 300 350 α ( ) Lx = 5.7De Lx = 2De Lx = 1De Lx = 0.5De I COMSOL - Boston 2016 15 15

III MEAN NUSSELT NUMBERS The depreciation of mean Nusselt number is clearly obtained, with a 20% drop for very close proximity with a wall (Lx = 0.5De). Heat transfer 2 times less important as regards to the current cooling law [1]. Possible reasons : Turbulence entrance length not reached in [1]. Studies without support elements (brackets). [1] B,M Weedy, H,M El Zaayat, Heat Transfer From Cables In Tunnels And Shafts, IEEE-PES 1972 Nu De 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 10,000 20,000 30,000 40,000 50,000 60,000 R ed e With wall proximity Lx = 5.7De Lx = 2De Lx = 1De Lx = 0.5De 1 câble - 5.7De 1 câble - 2De 1 câble - 1De 1 câble - 0.5De Nu D e 160 140 120 100 80 60 40 20 21% 0 10,000 20,000 30,000 40,000 50,000 60,000 Nu Nu(z De = at 0.2 0.2m) m from inlet Nu De = 0.13 R0.65 ed e 29% R ed e Weedy and El Zayyat 16 I EDF R&D LAMIH, 29 mars 2015 16

I. INTRODUCTION II.EXPERIMENTAL & SIMULATION SETUP III.CABLE COOLING : RESULTS & DISCUSSION IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS

IV IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT Using the design tool for underground power cables with the new laws, the impact on the maximum transmissible current in the power link can be tested. Idealized case (no brackets, no corkscrewing effects, etc.) U = 1 m/s T = 20 C Cable De = 0.122 m D = 3 m Max. operating temperature: 90 C in the core L = 1 km Weedy and El Zayyat Nu De Lx/De Weedy and El Zayyat I = 2354 A T core ( C) 89,96 89,97 79,16 T air ( C) 30,41 28,86 28,8-12% h wall (W/m².K) 2,91 2,91 2,91 h cable (W/m².K) 9,35 3,96 9,37 I max (A) 2526 2354 2354 18-7% I COMSOL - Boston 2016 18

I. INTRODUCTION II.EXPERIMENTAL & SIMULATION SETUP III.CABLE COOLING : RESULTS & DISCUSSION IV.IMPACT ON THE MAXIMUM PERMISSIBLE CURRENT V.CONCLUSIONS

V - CONCLUSION Experimental & numerical studies have highlighted the impacts of the proximity to a tunnel wall and the flow development. The depreciation of the heat transfer can be of 20% for close installations to a wall. On-going work. Cable groups effects on the heat transfer (two cables and trefoil configurations). Effects of the support elements. Wish list Get rid of the OpenFOAM platform for the 3D have COMSOL simulate everything. A mean to simulate details local heat transfer for very long geometries with limited mesh elements (ideas?). Or else, a full COMSOL cluster license 20 I COMSOL - Boston 2016 20

THANK YOU ANY QUESTIONS