Numerical Simulation of a Battery Thermal Management System Under Uncertainty for a Racing Electric Car

Texte intégral

(1)Numerical Simulation of a Battery Thermal Management System Under Uncertainty for a Racing Electric Car Elie Solai, Heloise Beaugendre, Pietro Marco Congedo, Rémi Daccord, Maxime Guadagnini. To cite this version: Elie Solai, Heloise Beaugendre, Pietro Marco Congedo, Rémi Daccord, Maxime Guadagnini. Numerical Simulation of a Battery Thermal Management System Under Uncertainty for a Racing Electric Car. Journée d’étude NAFEMS - La simulation pour la mobilité électrique, Nov 2019, Paris, France. �hal-02477939�. HAL Id: hal-02477939 https://hal.inria.fr/hal-02477939 Submitted on 13 Feb 2020. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Numerical Simulation of a Battery Thermal Management System Under Uncertainty for a Racing Electric Car. crédit : Jaguar MENA. E. Solaï*, H. Beaugendre,* P-M Congedo** R. Daccord***, M. Guadagnini***. La simulation pour la mobilité électrique, NAFEMS * INRIA Bordeaux Sud-Ouest, Team CARDAMOM. November 13, 2019. ** INRIA, Centre de Mathématiques Appliquées, Ecole Polytechnique, IPP *** EXOES, France. [email protected].

(3) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. 1 Industrial and Research Objectives. 2 Battery Thermal Management System. 3 Low-Fidelity Numerical Model. 4 Numerical Simulation Under Uncertainty. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 2 / 23.

(4) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. 1 Industrial and Research Objectives 2 Battery Thermal Management System 3 Low-Fidelity Numerical Model 4 Numerical Simulation Under Uncertainty. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 3 / 23.

(5) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Battery Thermal Management for Electric Vehicles. E-racing Car requirements Several charge/discharge cycles in small time intervals High Power from the Electrical Engine and Fast recharging : increased heat loads on Battery Pack. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 4 / 23.

(6) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Battery Thermal Management for Electric Vehicles Immersion Cooling System by EXOES Electric Cells immersed in dielectric cooling fluid. Heat exchanged directly from cells to the fluid. Good thermal homogeneity within the Battery Pack.. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 4 / 23.

(7) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Multi-Fidelity Simulation and Uncertainty Quantification Main PhD project overview (2018-2021) Numerical Simulation of Battery Thermal Management Systems (BTM) : High-Fidelity Model (HF) : based on Computational Fluid Dynamics (CFD) Low-Fidelity Model (LF) : "0D Model" based on energy balance equations. Uncertainty Quantification Methods to take into account uncertainties related to BTM Systems. Multi-Fidelity numerical tool : coupling LF and HF models Reduce computational costs Perform UQ methods including High-Fidelity simulations. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 5 / 23.

(8) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Multi-Fidelity Simulation and Uncertainty Quantification Main PhD project overview (2018-2021) Numerical Simulation of Battery Thermal Management Systems (BTM) : High-Fidelity Model (HF) : based on Computational Fluid Dynamics (CFD) Low-Fidelity Model (LF) : "0D Model" based on energy balance equations. Uncertainty Quantification Methods to take into account uncertainties related to BTM Systems. Multi-Fidelity numerical tool : coupling LF and HF models Reduce of computational costs Perform UQ methods including High-Fidelity simulations. Today’s focus : Performances Analysis of the LF Model with Uncertainty Quantification methods.. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 5 / 23.


(10) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. The Exoes Battery Thermal Management System (BTMS). Cooling Circuit. Battery Module. Modules. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 7 / 23.


(12) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. The Low-Fidelity Model. Time Loop Cooling Fluid. UNCERTAIN INPUTS. RADIATOR. QUANTITIES OF INTEREST. PUMP EXPANSION VESSEL. BATTERY PACK. ELECTRICAL SET UP. RACE PARAMETERS. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 9 / 23.

(13) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Case Study : Race. Race duration : 20 minutes Maximal Power required by the electrical engine : 180 kW More than 70 accelerations and braking sequences.. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 10 / 23.

(14) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. What the LF model computes Tamb=20.12 Mass Flow Rate=1.1 h wfluid=312.88 ESR=0.0224 SOH=101.94. 1 State of Charge. 0.8. SOC. 0.6 0.4 0.2 0 0. 200. 400. 600. 800. 1000. 600. 800. 1000. 600. 800. 1000. Time [s]. Temperatures [C]. 80 Tcore Trad-ex. 70 60 50 40 30 20 0. 200. 400. Time [s] 120 Pressure. Pressure [kPa]. 100 80 60 40 20 0. 200. 400. Time [s]. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 11 / 23.


(16) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Take Uncertainties Into Account. Choice of 4 uncertain parameters : lack of knowledge to set an exact value.. E. SOLAI - INRIA. x1. Massic Flow Rate. ṁ. [1.08; 1.3]. kg.s−1. x2. Heat Transfer Coefficient. hcond. [250; 360]. W.m−2 .K−1. x3. Equivalent Serie Resistance. ESR. [0.01; 0.025]. Ω. x4. State Of Health. SOH. [98; 102]. %. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 13 / 23.

(17) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Take Uncertainties Into Account Choice of 4 uncertain parameters : lack of knowledge to set an exact value.. x1. Massic Flow Rate. ṁ. [1.08; 1.3]. kg.s−1. x2. Heat Transfer Coefficient. hcond. [250; 360]. W.m−2 .K−1. x3. Equivalent Serie Resistance. ESR. [0.01; 0.025]. Ω. x4. State Of Health. SOH. [98; 102]. %. Goals of Uncertainty Propagation : Estimate the variability of the QOI with respect to the input parameters uncertainties. (Statistical moments, Quantiles, Sensitivity analysis, ...). E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 13 / 23.

(18) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Uncertainty Characterization. STEP 1 : Sampling of the 4 uncertain inputs. NS sample points following uniform distribution.. E. SOLAI - INRIA. x1. Massic Flow Rate. ṁ. [1.08; 1.3]. kg.s−1. x2. Heat Transfer Coefficient. hcond. [250; 360]. W.m−2 .K−1. x3. Equivalent Serie Resistance. ESR. [0.01; 0.025]. Ω. x4. State Of Health. SOH. [98; 102]. %. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 14 / 23.

(19) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Uncertainty Propagation. STEP 2 : Perform NS simulations with the Numerical Model, seen as a Black Box. Time Loop Cooling Fluid. RADIATOR. UNCERTAIN INPUTS. QUANTITIES OF INTEREST. PUMP BATTERY PACK. ELECTRICAL SET UP. RACE PARAMETERS. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 15 / 23.

(20) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Uncertainty Propagation. STEP 3 : Compute the variability of the QOI with respect to the input uncertainties of the system. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 16 / 23.

(21) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Uncertainty Propagation. STEP 3 : Compute the variability of the QOI with respect to the input uncertainties of the system Distribution of the QOI. max (Tcenter (t)) , with 115 sampled points. t∈[0,TFIN ] 0.01. 70. 0.009. 0.03. 60 0.008 50. 0.007 0.006. 40. 0.025. 0.005 30. 0.004 0.003. 20. 0.002. Cooling Fluid. 0 150. 200. 250. 300. 350. 400. 0. 450. 0.02. Time Loop. 10 0.001. 0. 0.005. 0.01. 0.015. 0.02. 0.025. 0.03. 0.035. RADIATOR. UNCERTAIN INPUTS. QUANTITIES OF INTEREST. 0.015. PUMP BATTERY PACK. 0.3. 5 4.5. ELECTRICAL SET UP. 0.25. 4 3.5. RACE PARAMETERS. 0.01. 0.2. 3. 0.005. 0.15. 2.5 2. 0.1. 1.5 1. 0 10. 0.05. 0.5 0 0.95. E. SOLAI - INRIA. 1. 1.05. 1.1. 1.15. 1.2. 1.25. 1.3. 1.35. 1.4. 1.45. [email protected]. 0 96. 97. 98. 99. 100. 101. 102. 103. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 104. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 16 / 23.

(22) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Uncertainty Propagation STEP 3 : Compute the variability of the QOI with respect to the input uncertainties of the system Distribution of the QOI. max (Tcenter (t)) , with 115 sampled points. t∈[0,TFIN ] 0.01. 70. 0.009. 0.03. 60 0.008 50. 0.007 0.006. 40. 0.025. 0.005 30. 0.004 0.003. 20. 0.002. Cooling Fluid. 0 150. 200. 250. 300. 350. 400. 0. 450. 0.02. Time Loop. 10 0.001. 0. 0.005. 0.01. 0.015. 0.02. 0.025. 0.03. 0.035. RADIATOR. UNCERTAIN INPUTS. QUANTITIES OF INTEREST. 0.015. PUMP BATTERY PACK. 0.3. 5 4.5. ELECTRICAL SET UP. 0.25. 4 3.5. RACE PARAMETERS. 0.01. 0.2. 3. 0.005. 0.15. 2.5 2. 0.1. 1.5 1. 0 10. 0.05. 0.5 0 0.95. 1. 1.05. 1.1. 1.15. 1.2. 1.25. 1.3. 1.35. 1.4. 1.45. 0 96. 97. 98. 99. 100. 101. 102. 103. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 104. But 115 points is not enough to get accurate distribution. Monte Carlo method too expensive with computational model f (x). Need to replace f (x) by a fast-to-compute surrogate model. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 16 / 23.

(23) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Kriging Surrogate Model Need to replace f (x) by a fast-to-compute surrogate model Time Loop Cooling Fluid. RADIATOR. UNCERTAIN INPUTS. QUANTITIES OF INTEREST. PUMP BATTERY PACK. ELECTRICAL SET UP. RACE PARAMETERS. Kriging Based Surrogate Model Based on Gaussian Process Regression Compute an estimation Ŷ = fˆ(x) of the QOI, built on the 115 training samples from the numerical model f (x). E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 17 / 23.

(24) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Distributions of the QOI Computation of the PDF for each QOI at Tamb = 15o C estimated with surrogate model. min. (SOC(t)). min. t∈[0,TFIN ]. COV = 11.99% E. SOLAI - INRIA. [email protected]. (V(t)). t∈[0,TFIN ]. COV = 4.54% La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 18 / 23.

(25) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Distributions of the QOI Computation of the PDF for each QOI at Tamb = 15o C estimated with surrogate model. max (Tcenter (t)). max (Twf-out (t)). t∈[0,TFIN ]. t∈[0,TFIN ]. COV = 21.49% E. SOLAI - INRIA. [email protected]. COV = 20.21% La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 18 / 23.

(26) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Distributions of the QOI Computation of the PDF for each QOI at Tamb = 15o C estimated with surrogate model. max (δT(t)) t∈[0,TFIN ]. COV = 28.37%. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 18 / 23.

(27) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Results for 2 different Texterior scenarios Comparison of the variability of some QOI for Texterior = 5o C and Texterior = 15o C. min. (SOC(t)). t∈[0,TFIN ] E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 19 / 23.

(28) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Results for 2 different Texterior scenarios Comparison of the variability of some QOI for Texterior = 5o C and Texterior = 15o C. min. (V(t)). t∈[0,TFIN ] E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 19 / 23.

(29) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Results for 2 different Texterior scenarios Comparison of the variability of some QOI for Texterior = 5o C and Texterior = 15o C. max (Tcenter (t)). t∈[0,TFIN ] E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 19 / 23.

(30) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Results for 2 different Texterior scenarios Comparison of the variability of some QOI for Texterior = 5o C and Texterior = 15o C. max (Twf-out (t)). t∈[0,TFIN ] E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 19 / 23.

(31) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Uncertainty Propagation. Results for 2 different Texterior scenarios Comparison of the variability of some QOI for Texterior = 5o C and Texterior = 15o C. max (δT(t)) t∈[0,TFIN ] E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 19 / 23.

(32) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Sensitivity Analysis. Sensitivity Analysis Study. Goal of Sensitivity Analysis : Show which uncertain input parameter has the most influence on the variability of our quantity of interest. → Gain more knowledge about the behavior of a complex model.. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 20 / 23.

(33) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Sensitivity Analysis. Sensitivity Analysis Study. Show which uncertain input parameter has the most influence on the variability of our quantity of interest. Mathematical Framework : ANOVA Decomposition Analysis Of Variance Input x = (x1 , x2 , x3 , x4 ) Black-box numerical model f seen as : f (x) = f0 + |{z} mean. 4 X. fi (xi ) +. fi1 i2 (xi1 , xi2 ) + · · · + f1,...,4 (x1 , ..., x4 ) | {z } fourth order {z }. i1 =1 i2 =i1 +1. i=1. |. 4 4 X X. {z. }. first order. |. second order. Sobol Index for a QOI : YQOI = f (x). E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 20 / 23.

(34) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Sensitivity Analysis. Sensitivity Analysis Study. Show which uncertain input parameter has the most influence on the variability of our quantity of interest. Mathematical Framework : ANOVA Decomposition. Sobol Index for a QOI : YQOI = f (x) First Order Sobol Index for input xi : Si =. Var(E[YQOI |xi ]) Var(YQOI ). Var(E[YQOI |xi ]) = variance of the mean value QOI "knowing" the input xi Var(YQOI ) = main variance of the QOI Si quantifies the main effect of xi on the contribution to the variance of YQOI. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 20 / 23.

(35) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Sensitivity Analysis. First Order Sobol Indices Results. First Order Sobol Indices for each QOI (case Texterior = 15 o C ) E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 21 / 23.

(36) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. What we learned from UQ Analysis. Set up of a Low-Fidelity Model : gives an insight of the system behaviour with low computational costs Predicting the behaviour of the system while taking into account uncertainties on the physical input parameters Sensitivity Analysis gave robust estimation of the impact of some parameters on the Quantities Of Interest ESR is the most determinant parameter for all QOI related to the temperature of the cells or the cooling fluid SOH must not be neglected for minimal voltage of the cell. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 22 / 23.

(37) Industrial and Research Objectives. Battery Thermal Management System. Low-Fidelity Numerical Model. Numerical Simulation Under Uncertainty. Perspectives From the results of Sensitivity Analysis : reduce the number of inputs, set-up simpler models example : for max(Tcenter (t)), get direct relationship between this QOI and ESR parameter. Set up a High-Fidelity Model : based on CFD (Navier-Stokes + Energy Conservation 3D equations). Improve current simulations (influence of the geometry, find local heat spots on battery cells etc...). Represent the same physical case with HF model and LF model to perform multi-fidelity simulation of BTM Systems. Thank you for listening [email protected]. E. SOLAI - INRIA. [email protected]. La simulation pour la mobilité électrique, NAFEMS. November 13, 2019. 23 / 23.

(38)