Thermal abuse

Syntax

Defined in an fvModels dictionary in the constant folder of the CFD case. Can only be applied if a solver can handle fvModels.source.

heatSource
{
    type            heatSourceTR_4eq;

    selectionMode   all;

    // SEI Decomposition reaction
    Asei      dimensionedScalar;
    Hsei      dimensionedScalar ;
    Esei      dimensionedScalar;
    Wc        dimensionedScalar;
    c_sei     scalar;

    //Negative-solvent reaction
    Ane       dimensionedScalar;
    Hne       dimensionedScalar;
    Ene       dimensionedScalar;
    // here W = Wc
    c_ne     scalar;
    z        scalar;

    // Positvive-solvent reaction
    Ape       dimensionedScalar;
    Hpe       dimensionedScalar ;
    Epe       dimensionedScalar;
    Wp        dimensionedScalar;
    alpha     scalar;

    // Electolyte Decomposition Reaction
    Ae        dimensionedScalar;
    Ee        dimensionedScalar;
    He        dimensionedScalar;
    We        dimensionedScalar;
    c_e       scalar;

    R        dimensionedScalar;


    //ODE solver details

    relTol  scalar;
    absTol  scalar;
    dxEst   scalar;
    solver   word;
    maxSteps scalar;
}

selectionMode = selection mode (all or cellSet)
cellSet = cellSet on which to apply the burner.

Abuse model parameters

Asei = SEI-decomposition frequency factor (s-1).
Hsei = SEI-decomposition heat release (J/g).
Esei = SEI-decomposition activation energy (J/mol)
Wc = Specific carbon content in jellyroll (g/m3)
c_sei = Initial value of $c_{sei}$
Ane = Negative-solvent frequency factor (s-1).
Hne = Negative-solvent heat release (J/g).
Ene = Negative-solvent activation energy (J/mol)
c_ne = Initial value of $c_{ne}$
z = Initial value of $z$
Ape = Positive-solvent frequency factor (s-1).
Hpe = Positive-solvent heat release (J/g).
Epe = Positive-solvent activation energy (J/mol)
Wp = Specific positive active content in jellyroll (g/m3)
alpha = Initial value of $\alpha$
Ae = Electrolyte decomposition frequency factor (s-1).
He = Electrolyte decomposition heat release (J/g).
Ee = Electrolyte decomposition activation energy (J/mol)
We = Specific electrolyte content in jellyroll (g/m3)
c_e = Initial value of $c_{e}$

ODE solver parameters

relTol = Relative convergence tolerance per step.
absTol = Absolute convergence tolerance per step.
dxEst = Max allowed time step.
solver = Name of the solver. Here you can find a list of the available solvers (https://cpp.openfoam.org/v10/classFoam_1_1ODESolver.html).
maxSteps = The maximum number of sub-steps allowed for the integration step.

Examples

heatSource
{
    type            heatSourceTR_4eq;

    selectionMode   all;

    // SEI Decomposition reaction
    Asei      Asei  [0 0 -1 0 0 0 0] 1.667e15;
    Hsei      Hsei [0 2 -2 0 0 0 0] 257e3 ;
    Esei      Esei  [1 2 -2 0 -1 0 0] 1.3508e5;
    Wc        Wc [1 -3 0 0 0 0 0] 610.4;
    c_sei    0.15;

    //Negative-solvent reaction
    Ane       Ane   [0 0 -1 0 0 0 0] 2.5e13;
    Hne       Hne [0 2 -2 0 0 0 0] 1714e3;
    Ene       Ene   [1 2 -2 0 -1 0 0] 1.3508e5;
    // here W = Wc
    c_ne     0.75;
    z        0.033;

    // Positvive-solvent reaction
    Ape       Ape   [0 0 -1 0 0 0 0] 2.25e14;
    Hpe       Hpe [0 2 -2 0 0 0 0] 790e3 ;
    Epe       Epe   [1 2 -2 0 -1 0 0] 1.54e5;
    Wp        Wp [1 -3 0 0 0 0 0] 1293;
    alpha     0.04;

    // Electolyte Decomposition Reaction
    Ae        Ae    [0 0 -1 0 0 0 0] 5.14e25;
    Ee        Ee    [1 2 -2 0 -1 0 0] 2.74e5;
    He        He [0 2 -2 0 0 0 0] 155e3;
    We        We [1 -3 0 0 0 0 0] 406.9;
    c_e       1;

    R        R  [1 2 -2 -1 -1 0 0] 8.314;


    //ODE solver details

    relTol  1e-5;
    absTol 1e-5;
    dxEst   1e-5;
    solver "seulex";
    maxSteps 100000;
}

Description

Li-ion battery thermal abuse reactions are modeled for three-dimensional battery simulation by listing component reactions that occur at elevated temperatures:

The volumetric heat generation that originated from Li-ion battery component reactions at increasing temperatures is decomposed as [1]

$S_{abuse} = S_{sei} + S_{ne} + S_{pe} + S_{ele}$

where $S_{sei}$ is the heat from the SEI (solid electrolyte interphase) decomposition reaction, $S_{ne}$ the reaction between the negative active material and electrolyte, $S_{pe}$ the reaction between the positive active material and electrolyte, $S_{ele}$ the electrolyte decomposition, and $S_{nb}$ is the reaction between the negative active and binder.

The four contributions can be computed using Arrhenius-like equations

$S_{sei}$ is the heat from the SEI decomposition reaction

$\frac{\mathrm{d} c_{sei}}{dt} = - R_{sei}$

$R_{sei} = A_{sei}\exp\left[-\frac{E_{a,sei}}{R T}\right]c^{m_s}_{sei}$

$S_{sei} = H_{sei} W_{c} R_{sei}$

where $c_{sei}$ is the dimensionless amount of lithium-containing meta-stable species in the SEI. $R_{sei}$ , $A_{sei}$ , $E_{a,sei}$ are reaction parameters. Specific heat release $H_{sei}$ is evaluated as Joule per gram of carbon, and $W_{c}$ is the volume-specific carbon content in the jellyroll.

$S_{ne}$ is the heat from the negative-solvent reaction

$\frac{\mathrm{d} c_{ne}}{dt} = - R_{ne}$

$R_{ne} = A_{ne} \exp\left[-\frac{z}{z_{ref}}\right] \exp\left[-\frac{E_{a,ne}}{R T}\right]c^{m_n}_{ne}$

$S_{ne} = H_{ne} W_{c} R_{ne}$

where $c_{ne}$ is the dimensionless amount of lithium intercalated between the carbon. $R_{ne}$ , $A_{ne}$ , $E_{a,ne}$ are reaction parameters. Specific heat release $H_{ne}$ is evaluated as Joule per gram of carbon, and $W_{c}$ is the volume-specific carbon content in the jellyroll. $z$ is a dimensionless measure of the SEI layer thickness and it is computed by [2]

$\frac{\mathrm{d} z}{dt} = A_{ne} \exp\left[-\frac{z}{z_{ref}}\right] \exp\left[-\frac{E_{a,ne}}{R T}\right]c^{m_n}_{ne}$

$S_{pe}$ is the heat from the positive-solvent reaction

$\frac{\mathrm{d} \alpha}{dt} = R_{pe}$

$S_{pe} = H_{pe} W_{p} R_{pe}$

where $\alpha$ is the degree of conversion. $R_{ne}$ , $A_{ne}$ , $E_{a,ne}$ are reaction parameters. Specific heat release $H_{pe}$ is evaluated as Joule per gram of carbon and $W_{p}$ is the volume-specific, positive-active content in the jellyroll.
$S_{ele}$ is the heat from the electrolyte decomposition reaction

$\frac{\mathrm{d} c_{e}}{dt} = - R_{e}$

$R_{e} = A_{e}\exp\left[-\frac{E_{a,e}}{R T}\right]c^{m_e}_{e}$

$S_{ele} = H_{e} W_{e} R_{e}$

where $c_{e}$ is the dimensionless concentration of electrolyte. $R_{e}$ , $A_{e}$ , $E_{a,e}$ are reaction parameters. Specific heat release $H_{e}`is evaluated as Joule per gram of carbon, and :math:`W_{e}$ is the volume-specific electrolyte content in the jellyroll.

In the end, we have to solve the following ODE system

$\begin{eqnarray} \frac{\mathrm{d} c_{e}}{dt} & = & - A_{e}\exp\left[-\frac{E_{a,e}}{R T}\right]c^{m_e}_{e} \\ \frac{\mathrm{d} \alpha}{dt} & = & A_{pe} \alpha(1-\alpha) \exp\left[-\frac{E_{a,pe}}{R T}\right]\\ \frac{\mathrm{d} c_{ne}}{dt} & = & - A_{ne} \exp\left[-\frac{z}{z_{ref}}\right] \exp\left[-\frac{E_{a,ne}}{R T}\right]c^{m_n}_{ne}\\ \frac{\mathrm{d} z}{dt} & = & A_{ne} \exp\left[-\frac{z}{z_{ref}}\right] \exp\left[-\frac{E_{a,ne}}{R T}\right]c^{m_n}_{ne}\\ \frac{\mathrm{d} c_{sei}}{dt} & = & - A_{sei}\exp\left[-\frac{E_{a,sei}}{R T}\right]c^{m_s}_{sei} \end{eqnarray}$

Physical and kinetic parameters used in the model
Symbol	Description	Units
$A_{sei}$	SEI-decomposition frequency factor	$s^{-1}$
$A_{ne}$	Negative-solvent frequency factor	$s^{-1}$
$A_{pe}$	Positive-solvent frequency factor	$s^{-1}$
$A_{e}$	Electrolyte decomposition frequency factor	$s^{-1}$
$E_{a,sei}$	SEI-decomposition activation energy	$J \mathrm{mol}^{-1}$
$E_{a,ne}$	Negative-solvent activation energy	$J \mathrm{mol}^{-1}$
$E_{a,pe}$	Positive-solvent activation energy	$J \mathrm{mol}^{-1}$
$E_{a,e}$	Electrolyte decomposition activation energy	$J \mathrm{mol}^{-1}$
$H_{sei}$	SEI-decomposition heat release	$J \mathrm{g}^{-1}$
$H_{ne}$	Negative-solvent heat release	$J \mathrm{g}^{-1}$
$H_{pe}$	Positive-solvent heat release	$J \mathrm{g}^{-1}$
$H_{e}$	Electrolyte decomposition heat release	$J \mathrm{g}^{-1}$
$W_{c}$	Specific carbon content in jellyroll	$\mathrm{g} \mathrm{m}^{-3}$
$W_{p}$	Specific positive active content in jellyroll	$\mathrm{g} \mathrm{m}^{-3}$
$W_{e}$	Specific electrolyte content in jellyroll	$\mathrm{g } \mathrm{m}^{-3}$

Literature

[1] Kim, Gi-Heon, Ahmad Pesaran, and Robert Spotnitz. “A three-dimensional thermal abuse model for lithium-ion cells.” Journal of power sources 170.2 (2007): 476-489.

[2] Hatchard, T. D., et al. “Thermal model of cylindrical and prismatic lithium-ion cells.” Journal of The Electrochemical Society 148.7 (2001): A755.

Thermal abuse

Syntax

Examples

Description

Literature

Related commands