Abstract
The effects of material and design modifications on the temperature distribution of Li-ion cells are simulated numerically. A two-dimensional anisotropic cylindrical coordinate model with linear triangular finite elements is used to simulate the steady-state temperature distribution within the cell. The cell’s material and geometry are changed. New cell materials are investigated for thermal performance: a negative electrode of variously-oriented carbon nanotubes, as well as separators made of Separion, of Al2O3 containing Cr particles or of BeO containing Be and Si particles. The cell’s diameter and length are varied. A new cell design with an internal cooling tube is proposed. The effect of cooling tube diameter upon cell temperature and the energy efficiency of cooling are investigated. This simple design change significantly improves the temperature distribution at marginal cost.
Zusammenfassung
Der Einfluss neuer Batteriematerialien und konstruktiver Änderungen auf die Temperaturverteilung in Li-Ionen-Zellen wird numerisch simuliert. Ein zweidi-mensionales, anisotropes Modell mit linearen dreieckigen Finiten-Elementen wird zur Simulation der stationären Temperaturverteilung in der Zelle eingesetzt. Als neue Batteriematerialien werden eine negative Elektrode aus Kohlenstoff-Nanoröhrchen verschiedener Orientierungen sowie Separatoren aus Separion, Al2O3 mit Cr-Praktikeln und BeO mit Be- und Si-Partikeln untersucht. Zelldurchmesser und -länge werden variiert. Eine neue Zellkonstruktion mit einem inneren Kühlrohr wird vorgestellt. Der Einfluss des Kühlrohrdurchmessers auf die Temperaturverteilung in der Zelle und die Energieeffizienz der Kühlung werden untersucht. Diese einfache konstruktive Änderung verbessert die Temperaturverteilung signifikant bei geringen Mehrkosten.
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Abbreviations
- A :
-
area (m2)
- A cross :
-
cross-sectional area (m2)
- A s :
-
heat transfer surface area (m2)
- c p :
-
specific heat capacity at constant pressure (kJ kg−1 K−1)
- D s :
-
internal cooling tube diameter (m)
- G l :
-
constant in infinite eigenvalue series (–)
- g :
-
heat generation (W m−3)
- h :
-
heat transfer coefficient (W m−2 K−1)
- I :
-
electric current (A)
- k :
-
thermal conductivity (W m−1 K−1)
- L :
-
length, length of the cell, characteristic length (m)
- n :
-
number of elements in axial direction (–)
- \(\dot{q}\) :
-
heat flow (W)
- \(\dot{q}_{s}''\) :
-
heat flux at surface (W m−2)
- r :
-
radius, radial coordinate (m)
- r s :
-
internal cooling tube radius (m)
- r 1 :
-
outer radius of cell winding (m)
- r 2 :
-
outer radius of cell casing (m)
- r + :
-
dimensionless radial coordinate (–)
- T :
-
Celsius temperature (°C)
- T :
-
thermodynamic temperature in (6) (K)
- T m :
-
mean mixed temperature (°C)
- \(\overline{T}\) :
-
(volume-weighted) mean temperature (°C)
- U :
-
voltage (V)
- u :
-
flow velocity (m s−1)
- u ref :
-
reference flow velocity (m s−1)
- V :
-
volume (m3)
- x :
-
axial coordinate (m)
- x + :
-
dimensionless axial coordinate (–)
- Δ:
-
difference (–)
- Θ:
-
dimensionless fluid temperature (–)
- λ l :
-
eigenvalue in (10) (–)
- ν:
-
kinematic viscosity (m2 s−1)
- ρ :
-
mass density (kg m−3)
- ξ :
-
axial coordinate for step change in wall temperature (m)
- ξ + :
-
dimensionless axial coordinate for step change in wall temperature (–)
- cond:
-
due to conduction
- conv:
-
due to convection
- crit:
-
critical radius
- e:
-
electrolyte, inlet
- f:
-
fluid
- max:
-
maximum
- OC:
-
open circuit
- s:
-
surface
- se:
-
surface at inlet
- step:
-
for a step change
- 1:
-
inner cylinder, cell winding
- 2:
-
outer cylinder, cell casing
- ∞:
-
state of surroundings
- Nu=hL/k:
-
Nußelt number
- Pe=uLρc p /k:
-
Péclet number
- Pr=νρc p /k:
-
Prandtl number
- Re=uL/ν:
-
Reynolds number
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Sievers, M., Sievers, U. & Mao, S.S. Thermal modelling of new Li-ion cell design modifications. Forsch Ingenieurwes 74, 215–231 (2010). https://doi.org/10.1007/s10010-010-0127-y
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DOI: https://doi.org/10.1007/s10010-010-0127-y