530
A. del Val et al.
For the energy exchange rate, different models must be adopted for each
individual internal energy mode. In general, energy transfer mechanisms fall
into two categories: energy relaxation processes and chemical energy exchange
processes. Energy relaxation is the process in which two distributions of energy
states exchange energy through elastic and inelastic collisions and relax to a final
equilibrium distribution: Vibration-translation, free electron-vibration, vibrationvibration, elastic energy exchange between free electrons and heavy particles,
etc. Chemical energy exchange processes result from reactive collisions between
particles in which energy is transferred in order to promote the reaction. Important
coupling mechanisms and energy relaxation processes are described in detail in [8].
16.3.3 Radiative Heating: A Coupled Phenomenon
Each radiative mechanism discussed in the previous section contributes to the net
emission and absorption of photons. The energy carried by a photon at wavenumber
σ is given by hcσ . Therefore, emission and absorption of photons results in a net
energy transfer between points in the flowfield or from the flowfield to the vehicle
surface, heating it up.
The radiant intensity I σ (x, ˆ
s) is defined as the photon energy flux per unit area,
per elementary solid angle, per wavenumber, in the direction ˆ
s at wavenumber
σ and position x. In the absence of scattering, the steady Radiative Transport
Equation (RTE) describes the variation of spectral intensity I σ along a ray with
length parameter s as:
dI σ
ds
= ˆ
s · ∇I σ (ˆ s) = η σ − κ σ I σ (ˆ s)
(16.31)
where η σ and κ σ are the local emission and absorption coefficients at point s along
the ray.
Photons may be emitted in any direction. Therefore, the spectral emission
coefficient is independent of direction and represents the total photon energy
emitted per volume, per time, per wavenumber, and per elementary solid angle.
The absorption coefficient represents the fraction of photon energy absorbed by the
gas over a unit distance, and is independent of direction as well. In general, these
coefficients are functions of the local energy level populations of the participating
gaseous species. More details about boundary conditions for this equation and
modeling can be found in [39].
Once the intensity field is known, the solution must be coupled back to the mass
and energy transport equations previously depicted via the radiative surface heat
flux, power, and species mass production rates due to photochemical processes.
A. del Val et al.
For the energy exchange rate, different models must be adopted for each
individual internal energy mode. In general, energy transfer mechanisms fall
into two categories: energy relaxation processes and chemical energy exchange
processes. Energy relaxation is the process in which two distributions of energy
states exchange energy through elastic and inelastic collisions and relax to a final
equilibrium distribution: Vibration-translation, free electron-vibration, vibrationvibration, elastic energy exchange between free electrons and heavy particles,
etc. Chemical energy exchange processes result from reactive collisions between
particles in which energy is transferred in order to promote the reaction. Important
coupling mechanisms and energy relaxation processes are described in detail in [8].
16.3.3 Radiative Heating: A Coupled Phenomenon
Each radiative mechanism discussed in the previous section contributes to the net
emission and absorption of photons. The energy carried by a photon at wavenumber
σ is given by hcσ . Therefore, emission and absorption of photons results in a net
energy transfer between points in the flowfield or from the flowfield to the vehicle
surface, heating it up.
The radiant intensity I σ (x, ˆ
s) is defined as the photon energy flux per unit area,
per elementary solid angle, per wavenumber, in the direction ˆ
s at wavenumber
σ and position x. In the absence of scattering, the steady Radiative Transport
Equation (RTE) describes the variation of spectral intensity I σ along a ray with
length parameter s as:
dI σ
ds
= ˆ
s · ∇I σ (ˆ s) = η σ − κ σ I σ (ˆ s)
(16.31)
where η σ and κ σ are the local emission and absorption coefficients at point s along
the ray.
Photons may be emitted in any direction. Therefore, the spectral emission
coefficient is independent of direction and represents the total photon energy
emitted per volume, per time, per wavenumber, and per elementary solid angle.
The absorption coefficient represents the fraction of photon energy absorbed by the
gas over a unit distance, and is independent of direction as well. In general, these
coefficients are functions of the local energy level populations of the participating
gaseous species. More details about boundary conditions for this equation and
modeling can be found in [39].
Once the intensity field is known, the solution must be coupled back to the mass
and energy transport equations previously depicted via the radiative surface heat
flux, power, and species mass production rates due to photochemical processes.