Chapter III: Numerical and Experimental Setup
3.1 Numerical Setup
3.1.1 Reacting Flow Simulations: LAURA
The NASA Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is a high-fidelity, structured grid, CFD flow solver specialized for hypersonic reentry physics [1, 28]. LAURA employs a multidimensional Navier-Stokes solver capable of simulating two temperature reacting flows with vibrational and chemical nonequi- librium. The solver uses shock capturing methods such as Roe’s averaging [93] and Yee’s symmetric total variational diminishing formulation of second-order inviscid flux [123]. LAURA allows for grid adaptation to the shock as shown in a simulation in Figure 3.1.
The energy exchange between the translational-rotational and vibrational-electronic modes is modeled using a Landau-Teller formulation [122] with relaxation times specified for O2[75], CO [86], and CO2[12]. The relaxation model for CO2assumes all of the vibrational modes relax at the same rate.
CO2Chemical Nonequilibrium Modeling
Mars entry CO2chemical kinetic models have been under development dating back to the mid-1960s McKenzie model [74]. In the early 1990s, Park [86] developed a two-temperature model that more accurately matched the slow vibrational relaxation and observed time to peak radiation by assuming the rate coefficients for dissociation are a function of the square root ofT andTV. Rock et al. compared these models to interferometric measurements of the bow shock in high enthalpy CO2flow,h0= 10 MJ/kg, and found good agreement with the Park model [92].
More recently, in 2014 Johnston and Brandis, developed a CO2 chemical kinetic model with the dissociation reactions based on measurements in the Electric Arc Shock Tube (EAST) facility [54]. In the Johnston model, three dissociation reactions are functions of the geometric average temperature√
TTV and the exchange reactions
Y X Z
Body Uniform
Freestream Shock
70o
Sphere-cone
Figure 3.1: Density flow field from a LAURA simulation of CO2 flow at MSL1 condition.
are functions of the translational temperature,T. In 2018, Cruden et al. presented an analysis of CO radiation and diode laser absorption measurements in a velocity range of 3-9 km/s and suggested two sets of kinetic rates, one for above and below 6.6 km/s [19]. The Cruden rates are fit using a single temperature. All of the experiments in this work are conducted with a freestream velocity of less than 4 km/s where ionization is negligible. The relevant neutral species are CO2, CO, O2, O, and C as identified by recent LENS-XX shock tunnel testing [41]. The corresponding five relevant reactions are
CO2+M↔ CO+O+M (3.1)
CO+M↔C+O+M (3.2)
O2+M↔ O+O+M (3.3)
CO2+O↔O2+CO (3.4)
CO+O↔O2+C (3.5)
The Johnston rates are the default CO2 kinetic rates implemented in the 2016 LAURA version used in this work. We also implement the rates specified in Cruden
for below 6.6 km/s as well as the Fridman model rates that were developed in the the context of CO2 decomposition in plasma [27]. The Fridman model is a 4 species (CO2, O2, CO, and O), 16 reaction mechanism. The forward dissociation reactions are controlled byTV while the backwards dissociation reactions are dependent on T. Only the CO2+ O -> CO + O2exchange reaction is a function of√
TTV. Cruden et al. compared these three models to CO2 EAST radiation measurements noting that the key difference in the models is in the rate in which they equilibrate, with the equilibration rates ranked as Fridman> Johnston>Cruden [17]. Each kinetic model agreed with EAST measurements at select conditions, but no individual model provided a universal match to the experimental data.
3.1.2 HARA
The High-Temperature Aerothermodynamic RAdiation (HARA) model detailed in Johnston [55, 56] calculates the radiative properties for species in a known flow field and solves the radiative transport equation. Recall from Section 1.3.3, the solution to the radiative transport along a single ray of distancexin a slab of constant properties is given by
Iλ = Iλ,0e−αλx+ λ
αλ
1−e−αλx
. (3.6)
If the ray passes throughN regions, the solution is given by Iλ =
N
Õ
i=1
λ,i
αλ,iexp©
«
−
N
Õ
j=i+1
αjxjª
®
¬
(1−e−αλ,ixi) (3.7) where the body is the Nth region.
CO2Radiation Modeling
The radiative heating from carbon dioxide during entry is due to emission of rovi- brational lines in the IR spectral ranges of 2.3, 2.7, 4.3, and 15 µm regions [97, 109].
The most extensive line list (630 million) for CO2 presently available is the Car- bon Dioxide Spectroscopic Databank (CDSD-4000) which was an extension of the CDSD-1000 model up to 5000 K [113, 114]. The database is implemented in HARA and used to calculate the spectral emission and absorption coefficients for radiative transfer calculations. To improve the efficiency of HARA, the CO2IR spec- trum is tabulated for a range of temperatures and pressures reducing the number of spectral points to 500,000. A code-to-code comparison with the NASA Ames Non- EQuilibrium Air (NEQAIR) radiation code found agreement within 3% in spectral
Shock Layer Surface
Normal Ray Obliquely
Incident Ray
Constant Property Slabs Freestream
Figure 3.2: Schematic of the tangent slab approximation.
radiance when inputting the same CO2 flow field [9]. For optically thin cases, the smeared band model [14] can be effectively used as opposed to a line-by-line approach. NEQAIR mid-wave infrared CO2radiation simulations have previously been validated using equilibrium shock tube and plasma torch experiments [84].
Tangent Slab Approximation
A common simplification to avoid having to compute radiative properties on mul- tiple obliquely incident rays is to use the tangent slab approximation [57]. This approach calculates radiative properties in N regions only along the ray normal to the surface. These regions are extended tangentially to the surface into slabs of constant properties as shown in Figure 3.2. For an obliquely incident ray at angleθ from the normal, the properties in the slabs remain the same but the distance traveled through a given slab increases fromxi(0)to xi(θ)= xi(0)/cosθ.
In the optically thin limit,αλx→ 0, the radiative transport equation simplifies to Iλ,thin(0)=
N
Õ
i=1
λ,ixi(0). (3.8)
Using the tangent slab approximation, the radiative transfer equation for an obliquely incident ray can be written as
Iλ,thin(θ)=
N
Õ
i=1
λ,ixi,0
cosθ = 1 cosθ
N
Õ
i=1
λ,ixi(0). (3.9) Relating Equations 3.8 and 3.9, the radiance from an obliquely incident ray in the optically thin limit is related to the radiance from the normal ray by
Iλ,thin(θ)= Iλ,thin(0)
cos(θ) . (3.10)
In the optically thick limit,αλx → ∞, the radiative transfer equation simplifies to Iλ,thick = λ,N
αλ,N = Bλ,N. (3.11)
Thus, the optically thick spectral radiance is independent of θ as expected from a Lambertian source such as a black body.