Advertisement

Analysis Model and Numerical Simulation of Thermoelectric Response of CFRP Composites

  • Yueguo Lin
Article
  • 306 Downloads

Abstract

An electric current generates Joule heating, and under steady state conditions, a sample exhibits a balance between the strength dissipated by the Joule effect and the heat exchange with the environment by radiation and convection. In the present paper, theoretical model, numerical FEM and experimental methods have been used to analyze the radiation and free convection properties in CFRP composite samples heated by an electric current. The materials employed in these samples have applications in many aeronautic devices. This study addresses two types of composite materials, UD [0]8 and QI [45/90/−45/0]S, which were prepared for thermoelectric experiments. A DC electric current (ranging from 1A to 8A) was injected through the specimen ends to find the coupling effect between the electric current and temperature. An FE model and simplified thermoelectric analysis model are presented in detail to represent the thermoelectric data. These are compared with the experimental results. All of the test equipments used to obtain the experimental data and the numerical simulations are characterized, and we find that the numerical simulations correspond well with the experiments. The temperature of the surface of the specimen is almost proportional to the electric current. The simplified analysis model was used to calculate the balance time of the temperature, which is consistent throughout all of the experimental investigations.

Keywords

CFRP Thermoelectric Temperature Law joule Aeronautical 

Nomenclature

cp

Specific heat capacity (J/kg.K)

g

Gravity acceleration (g=9.81 m/s2)

Gr

Average Grashof number

Grx

Local Grashof number at height x

hx

Local heat transfer coefficient (W / m2.K)

I

Electric current intensity (A)

k

Thermal conductivity (W/m.K)

Nu

Average Nusselt number

Nux

Local Nusselt number at position x

Pr

Average Prandtl number

Prx

Local Prandtl number at position x

Ra

Average Rayleigh number

Rax

Local Rayleigh number at position x

R

Electric resistance (Ω)

S

Area of plate (m2)

q

Heat flow rate (W)

q'

Heat flow rate per unit length (W/m)

q"

Heat flux (W/m2)

t

Time (s)

T

Temperature (K)

U

Electric voltage (V)

u0

Velocity of air (m/s)

x

Coordinate from the base of the plate (m)

y

Coordinate normal to the plate(m)

Greek Symbols

α

Fluid thermal diffusivity(m2/s)

β

Fluid thermal expansion rate(1/K)

δ

Thickness of air film (m)

ε

Surface emissivity

μ

Dynamic viscosity (kg/m.s)

ρ

Density (kg/m3)

σE

Electrical conductivity(S/m)

σ

Stefan-Boltzmann constant 5.67 × 10–8 W/m2.K4

λ

Thermal conductivity (W/m.K)

Subscripts

elec

Electric

conv

Convection

rad

Radiation

paroi

Surface of plate

amb

Ambient

t

Total

Notes

Acknowledgements

All partners of the research are gratefully acknowledged and some supports from CAUC Tianjin are gratefully acknowledged (Projects of CAUC:2016SYCX04, and MHRD20160105).

References

  1. 1.
    Schulte, K., Baron, C.: Load and failure analysis of CFRP laminates by means of electrical resistively measurements. Comp. Sci. Techno. 36, 63–76 (1989)CrossRefGoogle Scholar
  2. 2.
    Schulte, K., Wittich, H.: The electrical response of strained and or damaged polymer-matrix composites. Proceeding of ICCM-10th. V. Structures; Canada.. pp. 349–356 (1995)Google Scholar
  3. 3.
    Xia, Z.H., Okabe, T., Park, J.B., Curtin, W.A., Takeda, N.: Quantitative damage detection in CFRP composites: coupled mechanical and electrical models. Compo. Sci. Technol. 63, 1411–1422 (2003)CrossRefGoogle Scholar
  4. 4.
    Curtin, W.A.: Stochastic damage evolution and failure in fiber-reinforced composites. Adv. Appl. Mech. 36, 162–253 (2000)Google Scholar
  5. 5.
    Vavouliotis, A.P., Kostopoulos, V.: On the fatigue life prediction of CFRP laminates using the electrical resistance change method. Compos. Sci. Technol. 71, 630–642 (2011)CrossRefGoogle Scholar
  6. 6.
    Sierakowski, R.L., Telitchev, Y.I., Zhupanska, O.I.: On the impact response of electrified carbon fiber polymer matrix composites: effects of electric current intensity and duration. J. Compos. Sci. Technol. 68, 639–649 (2008)CrossRefGoogle Scholar
  7. 7.
    Snyder, D.R., Sierakowski, R.L., Chenette, E.R., Aus, J.W.: Preliminary assessment of electro-thermo-magnetically loaded composite panel impact resistance/crack propagation with high speed digital laser photography. In: 24th International congress on high-speed photography and photonics, Proceedings of SPIE, vol. 4183; p. 488–513 (2001)Google Scholar
  8. 8.
    Lipton, R.: Inequalities for electric and elastic polarization tensors with application to random composites. J. Mech. Phys. Solids. 41, 809–833 (1993)CrossRefGoogle Scholar
  9. 9.
    Gigliotti, M., Lafarie, M.C., Grandidier, J.C.: Development of experimental and modeling tools for the characterization of the thermo-electro-mechanical behavior of composite materials for aircraft applications. Mec. Ind. 12, 87–101 (2011)Google Scholar
  10. 10.
    Gigliotti, M., Grandidier, J.C., Lafarie-Frenot, M.C., Marchand, D.: Development of experimental and modelling tools for electro-mechanical fatigue tests in composite materials for aircraft applications. The 14th European Conference on Composite Materials, (2010)Google Scholar
  11. 11.
    Lin, Y., Gigliotti, M., Lafarie-Frenot, M.C., Bai, J.: Effect of carbon nanotubes on the thermoelectric properties of CFRP laminate for aircraft applications. J. Reinf. Plast. Compos. 34(2), 173–184 (2015)CrossRefGoogle Scholar
  12. 12.
    Lux, F.: Models proposed to explain the electrical conductivity of mixtures made of conductive and insulating materials. J. Mater. Sci. 28, 285–301 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Designs and Manufactures of AircraftsCivil Aviation University of ChinaTianjinChina

Personalised recommendations