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Electronic component cooling inside switch cabinets: combined radiation and natural convection heat transfer

  • Alexander Frank
  • Wolfgang Heidemann
  • Klaus Spindler
Original
  • 40 Downloads

Abstract

The thermal conditions inside switch cabinets for industrial applications without cooling devices are equally influenced by natural convection and radiation heat transfer. In this work the open source library OpenFOAM is applied and enhanced, in order to simulate the temperature field of the air inside the cabinet. Turbulent natural convection heat transfer is modeled using Menter’s SST model. Radiation heat transfer is modeled using a surface-to-surface model, whereas the view factors are computed based on a Monte Carlo algorithm. Numerical results obtained with different flow models are compared with measurements and correlations from literature for a cavity and a Rayleigh-Bénard test case. The Radiation model is validated against comparative numerical data. Finally, the models are applied to calculate the temperature field of a switch cabinet test rig. These numerical results are compared with experimental data.

List of symbols

Latin symbols

a1

Bradshaw’s structural parameter ()

A

surface area (m2)

B

Turbulence production due to buoyancy (kg m−1 s−3)

cp

Specific heat capacity at constant pressure (J kg−1 K−1)

C

Weights (−)

CBVG

Constant in buoyant vorticity generation term CBVG = 0.35 (−)

F1,F2

Blending function (−)

\( \overline{\overline{F}} \)

View factor matrix (−)

\( {\overline{\overline{F}}}^{\ast } \)

View factor matrix after the first smoothing step (−)

\( {\overline{\overline{F}}}_{ij}^{\ast \ast } \)

View factor matrix after the second smoothing step (−)

\( \overrightarrow{\boldsymbol{g}} \)

Gravitational acceleration (m s−2)

h

Specific enthalpy (J kg−1)

H

Height (m)

\( \overline{\overline{I}} \)

Identity matrix (−)

k

Specific turbulence kinetic energy (m2 s−2)

K

Specific kinetic energy (m2 s−2)

L

Length (m)

nwall

Wall distance of the midpoint of the first cell (m)

N

Number of radiating surfaces inside the switch cabinet (−)

Ni

Number of photons emitted from surface i (−)

Nij

Number of photons emitted from surface i, that hit surface j (−)

NP

Number of photons emitted per subarea (−)

Nsub

Number of subareas (−)

Nu

Local Nusselt number (−)

\( \overline{\boldsymbol{Nu}} \)

Average Nusselt number (−)

p

Pressure (Pa)

ptot

Total pressure \( {p}_{tot}=p+\frac{\rho }{2}\ {\left|\overrightarrow{\mathrm{U}}\right|}^2+\rho \overrightarrow{g}\bullet \overrightarrow{r} \) (Pa)

Pk

Production of specific turbulence kinetic energy \( {P}_k={\mu}_t\frac{\partial {U}_i}{\partial {x}_j}\left(\frac{\partial {U}_i}{\partial {x}_j}+\frac{\partial {U}_j}{\partial {x}_i}\right)\left( kg\ {m}^{-1}\ {s}^{-3}\right) \)

\( {\overset{\sim }{\boldsymbol{P}}}_{\boldsymbol{k}} \)

Limiter function of Pk, \( {\overset{\sim }{P}}_k=\min \left({P}_k,10\ {\beta}^{\ast }\ \rho\ k\ \omega \right) \) (kg m−1 s−3)

Pr

Prandtl number (−)

Prt

Turbulent Prandtl number (−)

\( \dot{\boldsymbol{Q}} \)

Heat flow (W)

\( \dot{\boldsymbol{q}} \)

Heat flux (W m−2)

R

Specific gas constant (J kg−1 K−1)

Ra

Rayleigh number (−)

S

Absolute value of the strain rate \( S=\sqrt{2\ {S}_{ij}} \) (s−1)

\( \overline{\overline{S}} \)

Strain rate tensor \( \overline{\overline{S}}=\frac{1}{2}\left(\frac{\partial {U}_i}{\partial {x}_j}+\frac{\partial {U}_j}{\partial {x}_i}\right) \) (s−1)

t

Time (s)

T

Temperature (K)

\( \overrightarrow{\boldsymbol{U}} \)

Velocity (m s−1)

Greek symbols

β,β

Turbulence model coefficients ()

γ

Turbulence model coefficient (−)

\( \overline{\overline{\delta}} \)

Kronecker symbol (−)

ε

Total hemispherical emissivity (−)

λ

Molecular thermal conductivity (W m−1 K−1)

λt

Turbulent thermal conductivity (W m−1 K−1)

μ

Molecular viscosity (kg m−1 s−1)

μt

Eddy viscosity (kg m−1 s−1)

ρ

Density (kg m−3)

σ

Stefan-Boltzmann constant (W m−2 K−4)

σkωω2

Turbulence model coefficients (−)

\( \overline{\overline{\tau}} \)

Stress tensor (N m−2)

ω

Specific dissipation rate (s−1)

Abbreviations

air

Air

amb

Ambient

BVG

Buoyant vorticity generation

c

Cold

con

Convection

h

Hot

PISO

Pressure-Implicit with Splitting of Operators

PIMPLE

Combined PISO and SIMPLE

PLC

Programmable logic controller

RANS

Reynolds averaged Navier-Stokes

rad

Radiation

SGDH

Simple gradient diffusion hypothesis

SIMPLE

Semi-implicit Method for Pressure Linked Equations

SST

Shear stress transport

URANS

Unsteady Reynolds averaged Navier-Stokes

wall

Wall

Notes

Acknowledgments

This research was supported by a foundation of Friedrich Lütze GmbH. The authors gratefully acknowledge this support.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Frank
    • 1
  • Wolfgang Heidemann
    • 1
  • Klaus Spindler
    • 1
  1. 1.University of StuttgartInstitute of Thermodynamics and Thermal Engineering (ITW)StuttgartGermany

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