Abstract

This paper presents results from experimental measurements on radiative transfer in FeCrAlY (a steel based high temperature alloy) foams having high porosity (95%) and different cell sizes, manufactured at low cost from the sintering route. The spectral transmittance and reflectance are measured at different infrared wavelengths ranging from 2.5 to 50 μm, which are subsequently used to determine the extinction coefficient and foam emissivity. The results show that the spectral quantities are strongly dependent on the wavelength, particularly in the short wavelength regime (<25 μm). Whilst the extinction coefficient decreases with increasing cell size, the effect of cell size on foam reflectance is not significant. When the temperature is increased, the total extinction coefficient increases but the total reflectance decreases. An analytical model based on geometric optics laws, diffraction theory and metal foam morphology is developed to predict the radiative transfer, with cell size (or cell ligament diameter) and porosity identified as the two key parameters that dictate the foam radiative properties. Close agreement between the predicted effective foam conductivity due to radiation alone and that measured is observed. At fixed porosity, the radiative conductivity of the metal foam increases with increasing cell size and temperature.

Author Keywords: Metal foams; Thermal radiation; Transmittance; Reflectance; Extinction coefficient; Emissivity; Experimental measurement; Modelling

Nomenclature

C, C₁, C₂

constants

C_s

correction scan of source with sample

C_e

correction scan of source without sample

d_i

inner diameter of cell ligament, m

d_o

outer diameter of cell ligament, m

d_p

cell size, m

D₀

dark sample scan for zero offset

E

emissive power

f

influence function, Eq. (24)

I, I_λ

total intensity and spectral intensity of radiant energy

K, K_λ

total and spectral extinction coefficient, 1/m

K_R

Rosseland mean extinction coefficient, 1/m

K_λ^*

weighted spectral extinction coefficient, 1/m

k_c

effective thermal conductivity due to conduction, W/mK

k_e

effective thermal conductivity of metal foam, W/mK

k_r

effective radiative thermal conductivity, W/mK

L

sample height, m

m

complex refractive index

n

constant

q

heat flux, W/m²

R_f

reference scan (hemisphere radiance)

S

sample scan (sample radiance)

T

temperature, K

α, α_λ

absorption coefficient and spectral volume absorption coefficient

χ

non-dimensional size parameter

_eff

total emissivity

_λ,eff

spectral emissivity

λ

wavelength, m

ρ_eff

total reflectance

ρ_λ,eff

spectral reflectance

σ

Stefan–Boltzman constant

σ_s

scattering coefficient

τ, τ_λ

total transmittance and spectral transmittance

φ

porosity of foam

Φ_λ

spectral volumetric phase function of scattering

Article Outline

Nomenclature

1. Introduction

2. Metal foam samples

3. Experimental equipment and measurement procedures

4. Experimental results

4.1. Spectral transmittance, τ_λ

4.2. Extinction coefficient

4.3. Reflectance

4.4. Emissivity

4.5. Effective radiative conductivity k_r

5. Modeling based on the effective medium approach

5.1. Rosseland diffusion

5.2. Spectral absorption and scattering coefficients

5.3. Phase function

5.4. Prediction versus measurement

6. Conclusions

Acknowledgements

References