ABSTRACT. MCCORKLE, EVAN REID. Comparisons between Computation and Experiment for Shock-Layer Radiation. (Under the direction of Hassan Hassan.

Transcription

1 ABSTRACT MCCORKLE, EVAN REID. Comparisons between Computation and Experiment for Shock-Layer Radiation. (Under the direction of Hassan Hassan.) In attempts to validate NEQAIR, a tool used by NASA Ames Research Center for the calculation of radiative heating, a study was undertaken that ventured to understand and explain the discrepancies between computations and the experimental spectroscopy of the NASA Ames Electric Arc Shock Tube facility. A method is described by which the spatially-spectrally resolved spectrographic data of shock-layer radiation can be reduced to spectrally-only resolved data representative of the radiation behind the shockwave. Workflows are created to allow the linking of different computational flowfields to NEQAIR. These include Chemical Equilibrium with Applications (CEA), producing a simple post-shock equilibrium flowfield with no spatial variation, and the Data-Parallel Line Relaxation computational fluids code (DPLR), producing a complex thermochemical nonequilibrium flowfield with both axial and radial spatial variations. In an attempt to resolve discrepancies through radiation modeling changes, updates to the NEQAIR codebase and databases were undertaken. These included the addition of new molecular bands, changes in atomic Stark broadening, a sync of atomic bound-bound transitions from the NIST Atomic Spectra database, and an application of atomic bound-free cross-sections from The Opacity Project. Another attempt was made to resolve discrepancies through flowfield modeling changes, i.e. by using DPLR and allowing for spatial variation and nonequilibrium effects. In this way, the effect of the boundary-layer on calculated radiation was studied. While the update of NEQAIR did little, the DPLR flowfield method had some effect in closing the gap between computation and experiment. However, none of the attempts were able to completely resolve discrepancies.

2 c Copyright 2010 by Evan Reid McCorkle All Rights Reserved

3 Comparisons between Computation and Experiment for Shock-Layer Radiation by Evan Reid McCorkle A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Aerospace Engineering Raleigh, North Carolina 2010 APPROVED BY: Stephen Campbell Hong Luo Hassan Hassan Chair of Advisory Committee

4 BIOGRAPHY Evan McCorkle was born in 1985 to Gary and Leslie McCorkle in Charlotte, North Carolina. After his pastoral youth, he moved to the City of Oaks (Raleigh, North Carolina) to study Aerospace Engineering at North Carolina State University. After finishing his undergraduate degree, he enrolled in the graduate program under the direction of Professor Hassan Hassan. During this program, several fruitful summers were spent interning at NASA Ames Research Center under Dr. David Hash. The culmination of this work is represented here. ii

5 TABLE OF CONTENTS List of Figures iv Chapter 1 Introduction Motivation Methodology Chapter 2 Equilibrium Comparisons Workflow Chapter 3 Updated Computational Models Updates Chapter 4 Nonequilbrium Comparisons Workflow Chapter 5 Results & Discussion Nomenclature Sample EAST Spectroscopy Updated NEQAIR DPLR Conclusions References iii

6 LIST OF FIGURES Figure 1.1 Shocktube setup/nomenclature Figure 1.2 Shock structure after diaphragm bursts Figure 1.3 Spectroscopy setup Figure 1.4 Spectrographs record spectral and axial variation Figure 2.1 Equilibrium (CEA) workflow Figure 4.1 Nonequilibrium (DPLR) workflow Figure 4.2 Variation of Computational (DPLR) Shock-Front Speed Figure 5.1 Shock structure after diaphragm bursts Figure 5.2 Spectroscopy setup Figure 5.3 Example of EAST Spectroscopy with Annotated Spatial-Averaging Region 25 Figure 5.4 Example of EAST Radiance Profile Figure 5.5 Example of EAST Spatial-Averaged Spectral Radiance Figure 5.6 Example of EAST Spectroscopy with Annotated Spatial-Averaging Region 28 Figure 5.7 Example of EAST Radiance Profile Figure 5.8 Example of EAST Spatial-Averaged Spectral Radiance Figure 5.9 Spectral Radiance from CEA-NEQAIR in the Vacuum Ultraviolet Spectrum 31 Figure 5.10 Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum Figure 5.11 Spectral Radiance from CEA-NEQAIR in the Visible Spectrum Figure 5.12 Spectral Radiance from CEA-NEQAIR in the Infrared Spectrum Figure 5.13 Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum Figure 5.14 Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum Figure 5.15 Spectral Radiance from CEA-NEQAIR in the Visible Spectrum Figure 5.16 Spectral Radiance from CEA-NEQAIR in the Infrared Spectrum Figure 5.17 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIR (large artificial impurity addition) in the Ultraviolet Spectrum. 39 Figure 5.18 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIR (large artificial impurity addition) in the Ultraviolet Spectrum. 40 Figure 5.19 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIR (large artificial impurity addition) in the Visible Spectrum Figure 5.20 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIR (large artificial impurity addition) in the Near-Infrared Spectrum 42 Figure 5.21 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIR (large artificial impurity addition) in the Infrared Spectrum.. 43 Figure 5.22 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIRup (bound-free updates only) in the Ultraviolet Spectrum Figure 5.23 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIRup (bound-free updates only) in the Visible Spectrum Figure 5.24 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIRup (bound-free updates only) in the Near-Infrared Spectrum.. 46 iv

7 Figure 5.25 Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA- NEQAIRup (bound-free updates only) in the Infrared Spectrum Figure 5.26 Translational Temperature Snapshot of DPLR Flowfield showing Shock- Front Curvature and Viscous Effects Figure 5.27 Axial Velocity Snapshot of DPLR Flowfield showing Shock-Front Curvature and Viscous Effects Figure 5.28 Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.29 Vibrational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.30 Axial Velocity Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.31 Pressure Snapshot of DPLR Flowfield showing both Axial and Radial Variation 53 Figure 5.32 Density Snapshot of DPLR Flowfield showing both Axial and Radial Variation 54 Figure 5.33 Helium Density Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.34 Degree of Ionization Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.35 Helium Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.36 Atomic Nitrogen Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.37 Atomic Nitrogen Ion Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.38 Atomic Oxygen Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.39 Atomic Oxygen Ion Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.40 Electron Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.41 Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Vacuum Ultraviolet Spectrum Figure 5.42 Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Ultraviolet Spectrum Figure 5.43 Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Visible Spectrum Figure 5.44 Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Infrared Spectrum Figure 5.45 Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.46 Vibrational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.47 Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation v

8 Figure 5.48 Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.49 Vibrational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation Figure 5.50 Spectral Radiance from DPLR-NEQAIR (Boltzmann) in the Ultraviolet Spectrum Figure 5.51 Spectral Radiance from DPLR-NEQAIR (Boltzmann) in the Visible Spectrum 73 Figure 5.52 Spectral Radiance from DPLR-NEQAIR (Boltzmann) in the Infrared Spectrum 74 vi

9 CHAPTER 1 Introduction The design of a thermal protection system (TPS) for atmospheric reentry vehicles depends almost solely on the ability to accurately predict heat transfer. This involves predicting both the aerothermal environment and the heating resulting from this environment. The aerothermal environment is relatively well, though by no means completely, understood. Convective heat transfer is also relatively well understood. Unfortunately, this is not the only method of heat transfer. Radiative heat transfer also occurs due to the extreme conditions encountered during planetary entry and uncertainties are high in its prediction. Until now, its effect has been relatively small but as we design more ambitious vehicles and missions, we require the ability to accurately model and predict radiative heating. 1.1 Motivation One such ambitious vehicle/mission combination is the NASA Orion Capsule for Lunar or Mars return trajectory. It is estimated that the thermal protection system (hereafter abbreviated as TPS) on Orion for the Lunar trajectory will encounter radiative heating comparable to convective heating. An efficient design requires a good understanding of this radiative heating so as not to use more TPS materials than necessary. High uncertainties in radiative heating will, in the best case, will lead to a heavy and overbuilt TPS with less mass/space for science and cargo. In the worst case, they could lead to the loss of the mission. Because of this, understanding and decreasing the uncertainties in our predictions of radiative heating is a high priority for the Orion TPS design. To show the relative importance of convective and radiative heat transfer for atmospheric 1

10 entry applications, engineering correlations can be used. Two correlations of interest are the Sutton-Graves[13] formula for convective heating and the Tauber-Sutton[14] formula for radiative heating. These are given in Equation 1.1 and Equation 1.2 respectively. q c r 1/2 ρ 1 /2 V 3 (1.1) q r r a ρ b f(v ) (1.2) For these equations, r, ρ, V, q c, and q r represent blunt-body nose radius, freestream density, freestream velocity, convective heat flux, and radiative heat flux, respectively. For Tauber-Sutton, f(v ) is a nonlinear function of velocity. Often, for comparison with Sutton-Graves, it is approximated as V 7. For Earth entry, the exponents in Tauber-Sutton are given as 0 a 1 and b = For Mars entry, they are a = and b = The important differences to note here are the exponents on r (the body nose radius) and V (the freestream velocity). Convective heating decreases with increasing nose radius while radiative heating does the opposite. Radiative heating increases much faster with velocity than convective heating. These two results imply that as entry-vehicles becomes larger and/or faster, such as Orion, radiative heating will begin to dominate. The desire to accommodate larger science payloads or fly novel mission profiles will necessitate our understanding of this phenomenon and how to model it for TPS design purposes. Increasingly, computation models are being used as engineering design tools. To be considered useful, these models must be validated against experimental data. For estimating radiative heating, one of the primary tools is the Nonequilibrium Air (NEQAIR) code created by Whiting et al. [15] and used by NASA Ames Research Center. Lacking a flight experiment, attention has been focused on validating NEQAIR against the recent experiments of Grinstead et al. [7] and Cruden et al. [3] using the NASA Ames Electric Arc Shock Tube (EAST) facility. These experiments measured spectral radiance at flow conditions similar to those for an Orion Lunar return trajectory. The following work focuses on improving agreement and understanding disagreement between NEQAIR and EAST by adjusting computational models and methods. 1.2 Methodology The EAST facility uses a a diaphragm-based shock tube. A schematic of the shock tube and associated nomenclature is given in Figure 1.1. For the experiments of concern, Grinstead et al. [7] and Cruden et al. [3], the driver gas was Helium at 100 psi (689 kpa or torr). The driven gas was synthetic (no trace chemical species) Earth or Mars atmosphere at between 0.1 torr and 2

11 1.0 torr. This work will focus on the Earth atmosphere cases (Lunar return trajectory). The EAST facility operates as follows. The driver and driven gas chambers are separated by an aluminum diaphragm. Energy is added to the driver gas by way of an electricial discharge from a large capacitor bank. This results in an increase of both pressure and temperature. Eventually, the diaphragm ruptures and a shockwave moves through the driven gas. A schematic of the resulting flow structure is given in Figure 1.2. The region denoted as 2 is similar to the shock layer for an atomospheric entry-vehicle and is the region of interest for this work. As the shockwave travels down the tube, a series of pressure sensors note the shockwave s passing. This information is used post-experiment to calculate the shockwave s travel speed. After the shockwave has traveled some distance down the tube, several spectrographs are used to record spatially (axially) resolved spectra from the hot, radiating gas behind the shockwave. A schematic of this process is given in Figure 1.3 and Figure 1.4. NEQAIR was originally developed for the calculation of spectral radiance in nonequilibirum air. This is very close to its use in this case. It is a line-by-line radiation code, which means atomic, and in particular, molecular radiation is computed on a very fine scale. Molecular band radiation is made up of many individual lines instead of simplifying approximate band shape/radiance. Meaning, these features can be more accurately simulated, albeit at a significantly higher computational cost. NEQAIR solves the radiative transport equation allowing for both emission and absorption. NEQAIR also uses the tangent slab assumption to reduce the radiative transport equation to an extent that it becomes feasible to solve. Under this assumption, gas composition varies along a one dimensional line, known as a line-of-sight. The slab normal to this line has this same composition. This assumption allows for a reduction of the radiative transport equation to one spatial variable and simplifies the handling of solid angle dependence. NEQAIR allows for separate translational, vibrational, and rotational temperatures when specifing gas conditions (mixture temperatures, not species specific). NEQAIR incorporates many different line broadening mechanisms, including Natural, Stark, van de Waals, and Resonance, using a Voigt line shape (combination Gaussian and Lorentzian shape). Finally, as mentioned above NEQAIR handles convolution of spectral radiance with a slit-function in order to compare with experimental data. Using the NEQAIR code to predict these EAST spectrography measurements requires first predicting the flowfield behind the shock (region 2) in the EAST facility. The following work involves two different types of flowfield predictions and one NEQAIR model update to understand and improve discrepancies between computation and experiment. The simplest flowfield model producing good agreement is desirable. Because of this, the first flowfield model attempted assumes that the flow behind the shockwave has reached thermochemical equilibrium. This method and results are given in chapter 2. The NEQAIR code is updated and the update is described in chapter 3. Finally, a higher fidelity flowfield model (thermochemical nonequilibrium) 3

12 is used in chapter 4. Throughout this work, attempts will be made to describe the current state of agreement and to understand any disagreements/discrepancies between NEQAIR and EAST. Driver Gas Diaphragm r,y x Driven Gas Centerline Figure 1.1: Shocktube setup/nomenclature 4 3a r,y x 3b 2 1 Centerline Figure 1.2: Shock structure after diaphragm bursts 4

13 Spectrograph Top View 4 3a r,y x 3b 2 1 Centerline Figure 1.3: Spectroscopy setup Figure 1.4: Spectrographs record spectral and axial variation 5

14 CHAPTER 2 Equilibrium Comparisons Accuracy of the NEQAIR predictions of EAST measurements depends on prediction of the flowfield behind the shockwave (region 2). In particular, NEQAIR requires knowledge of the mixture temperatures (translational, vibrational, rotational, etc) and the number densities (particles/volume) of each component species. The simplest possible accurate flowfield is desirable. For this reason, we begin by assuming the flowfield is in thermochemical equilibrium. If this is the case, the experiment and computational models (and methods) are more directly traceable to the Orion Lunar return design. This is because the shock-layer for this entry-vehicle is dominated by flow in thermochemical equilibrium, as discovered by Bose et al. [1]. 2.1 Workflow The assumption of thermochemical equilibrium behind the shockwave precludes any spatial variation of the flowfield. The flowfield is constant in region 2, both in axial and radial directions. The conditions behind the shockwave can then be found by a relatively simple equilibrium calculation using the pre-shock conditions (driven gas temperature, pressure, and composition) and the shockwave speed. The former is known as it is controlled directly by the experimental setup in the EAST facility. And as mentioned earlier, the latter is calculated from pressure sensors in shocktube. This equilibrium calculation is done using the Chemical Equilibrium with Applications (CEA) code of Gordon and McBride [5]. This NASA developed code provides the capability to simulate many different processes, including a shockwave, using arbitrary input and output chemical species. After the post-shock composition is found, it can be used as input to NEQAIR. The results of NEQAIR (spectral radiance) can then be compared to the EAST 6

15 spectroscopy, though not directly. The NEQAIR spectral radiance must be convolved with a slit function for direct comparison. The slit function is dependent on the EAST spectrograph setup (changes between experiments and spectrographs). However, the convolution does not change the integrated spectral radiance (radiance). Thus, a first check of computational prediction valid for all experiments and spectrographs is to compare NEQAIR and EAST radiance (not spectral radiance). A schematic of this process is show in Figure 2.1. Shock Conditions CEA Generate Line-of-Sight NEQAIR (Boltzmann) Integrate Figure 2.1: Equilibrium (CEA) workflow 7

16 CHAPTER 3 Updated Computational Models To address deficiencies with the CEA-NEQAIR model, either the flowfield or the radiation model must be improved. The latter is presented first. It is applicable to more than just EAST predictions. Also, as mentioned earlier, the Orion shocklayer was found to be dominated by equilibrium flow so a CEA flowfield would be directly applicable. Improving the radiation model involves updating the radiation database. Much of this database has not been updated since In order to address concerns about the baseline radiance seen in the EAST facility, several improvements were made. The first involve the addition of atomic bound-bound transitions involving energy levels with higher principal quantum numbers (n > 5). Secondly, attempts were made to update Stark broadening. This, according to Bose et al. [1], is the dominant broadening mechanism in highly ionized shocklayers such as the one for Orion Lunar return. Thirdly, the bound-free atomic radiation database was updated. Finally, several molecular radiation bands were added. 3.1 Updates The first update was the addition of atomic bound-bound transitions involving energy levels with higher principal quantum numbers (n > 5). The species of concern are Nitrogen, Oxygen, and Carbon. Allowed transitions for these species were found using the NIST Atomic Spectra database[12] and converted for use in NEQAIR. Most of the new transitions where due to Carbon. In using the NIST database, no preference was given towards the accuracy of the transitions. Transitions were added down to the NEQAIR lower wavelength limit and up to 50000Å. The second update involved the calculation of Stark broadening widths. The half-width at 8

17 half-height in NEQAIR is given by ( ) n ( ) Te Ne λ s = λ s, (3.1) where T e is the electron temperature in Kelvin, N e is the electron number density in particles per cubic centimeter, n is a transition dependent temperature dependence exponent, and λ s,0 is transition dependent and given by experimental data or curvefit. For strong/important atomic transitions, λ s,0 and n are given by experimental data. For others, they are found using the following curvefit [8, 9]: λ s,0 = C s λ 2 cl (E i Eu) ms (3.2) n = 1/3 (3.3) where C s and m s are constants, λ cl is the center-line wavelength for the transition, E i is the ionization energy for the species, and E u is the energy of the upper state of the transition in inverse centimeters. The term E i E u is limited so as not to create unrealistic line widths. This work begins by updating the experimentally found values, n and λ s,0, using data from Griem[6] and Wilson and Nicolet[16]. The λ s,0 is a straightforward lookup while the update of n involves a least-squares fitting of λ s against T e using Equation 3.1 with N e equal to part/cm 3. Another method of Stark broadening calculation was also tried. For Nitrogen and Oxygen, a curvefit form developed by Page, et al.[11] was used. This fit calculates the Stark half-width directly, without having need for λ s,0. The fit is as follows for Nitrogen and Oxygen respectively: λ s = ( )N e T 0.25 n 6 u(l 2 l + 1), Å (3.4) λ s = ( )N e T 0.46 n 6 u(l 2 l + 1), Å (3.5) where n u and l are the principal and azimuthal quantum numbers of the upper transition state. The above fits are valid between 3947Å and 13164Å and should not be used for high values of principal quantum numbers. The third update was to the atomic bound-free transition database. Atomic bound-free (photoionization) transitions happen when a photon transfers enough energy to an atom to dislodge an electron (or an electron is captured by an atom, emitting a photon). This process can be described as follows: A n + hν A + + e (3.6) 9

18 The spectral absorption coefficient (κ ν ) for the bound-free transition is calculated using: κ ν = n N n σ νn (3.7) where N n is the number density, σ νn is the cross-section, for the atomic energy level n, and n denotes the lowest energy level for which a photon of frequency ν can detach an electron. The cross-section is the key term in this expression and is what needs updating. NEQAIR originally assumed that all atoms are hydrogen-like in their cross-section and then correct it using a Gaunt factor (function of energy). This can cause significant error, especially for states near the gound state. Instead of using a Gaunt factor approach, we tabulate the cross-section directly against energy. No assumption of a hydrogen-like atom is made. Also, this allows for much more detail in the cross-section profile as each Gaunt factor was interpolated over a large energy/wavelength range. The tabulated cross-sections were obtained from the TOPbase atomic database[4]. This database is the online atomic database for the Opacity Project. The information contained within was determined solely using theoretical computation with L-S coupling. Finally, four molecular electronic transition bands were added by Dinesh Prabhu. These are Birge-Hopefield (b 1 Π u X 1 Σ + g ), Lyman-Birge-Hopefield (a 1 Π g X 1 Σ + g ), Carroll-Yoshino (c + 4 Σ+ u X 1 Σ + g ), and Worley-Jenkins (c + 3 Π u X 1 Σ + g ). The above bands are usually small contributers to the intensity. 10

19 CHAPTER 4 Nonequilbrium Comparisons Updates to the radiation model in NEQAIR did not account for the discrepancies seen between computation and experiment. Therefore, another avenue of exploration must be attempted. Now, it is supposed that NEQAIR is accurately predicting the radiation emitted from a slab of gas with given conditions. If this is the case, it must be that the conditions given to NEQAIR do not match those present in the EAST facility. Thus, an update to the computation flowfield must be undertaken. This can be accomplished by eschewing CEA (equilibrium) calculations and adopting a higher-fidelity approach. The Data-Parallel Line Relaxation code[17] (hereafter referred to as DPLR) in use at NASA Ames Research Center provides the desired calculations. DPLR is a Navier-Stokes CFD code that allows for thermal and chemical nonequilibrium. The use of this tool for simulating EAST facility experiments provides two capabilities that are lacking when using CEA. Firstly, thermochemical relaxation of the flowfield behind the shockwave allows for axial variation in computed radiance (similiar to that seen in experimental spectroscopy). Secondly, the ability to calculate axisymmetric flowfields allows for a study of the effect of the boundary-layer on radiation in the EAST facility. Both of these capabilities enable the calculation of flowfields which more closely match the characteristics of shocktube flow, when compared with CEA. Unfortunately, this advantage comes with a significant cost in terms of time and complexity. 4.1 Workflow As mentioned above, the use of DPLR to calculate a higher fidelity flowfield comes at a cost in time and complexity. Firstly, a spatial mesh (albeit simple) must be constructed on which to solve the Navier-Stokes equations. Although the geometry of the shock tube is by no means complex, 11

20 the requirement of a mesh brings with it the questions of grid refinement and grid convergence. Secondly, the various models available in DPLR provide many capabilities not possible with a CEA flowfield. Finally, the use of DPLR requires specification of initial and boundary conditions that may be unknown. As mentioned above, a spatial mesh is required on which to find the flowfield. For this work, a two-part axisymmetric mesh is used. The two parts being the individual meshes for the driver and driven gas. These are joined together at the diaphragm location. The radial dimensions and spacings are the same for both mesh parts. A stretched (constant stretching ratio) is used in the radial direction, with the finest spacing at the shocktube wall. This fine spacing is required to resolve the viscous effects in the shocktube. In the axial dimension, the driven gas mesh is much larger than the driver gas mesh. Also, the axial spacing of the driven gas mesh is much more fine that that of the driver gas mesh. The region of concern (directly being the shockwave) exists solely in the driven gas mesh and as such, this mesh needs to be of higher quality than that of the driver gas. As long as attention is paid to the left-running rarefaction, no problems should arise from a coarse driver gas mesh. The use of DPLR requires specification of initial and boundary conditions. The boundary conditions are simplest and will begin the discussion. As the shocktube is axisymmetric, there is a natural axisymmetric boundary condition along the centerline of the tube (the bottom edge of the mesh). The shocktube wall is considered to be at room temperature. This gives the upper edge of the mesh a viscous, isothermal boundary condition. Finally, the left and right edges of the mesh are set to always hold the initial conditions of the driver and driven gas, respectively. This is the simplest boundary condition for these edges and causes no problems as long as the important flow features do not reach these boundaries (a condition which is held in all results). The initial conditions are more complicated. The initial conditions in the driven gas are known. This is because the composition and pressure are specified, the temperature can be assumed to be room temperature, and the gas mixture can be assumed to follow the ideal gas law. Unfortunately, the driver gas inital conditions are not so easily found. As the name implies, the Electric Arc Shock Tube (EAST) facility works by adding a large amount of electrical energy into the driver gas. This results in a large increase in both pressure and temperature of the driver gas and is terminated with the rupture of the diaphragm seperating the driver and driven gases. This point of rupture is the initial condition of the flowfield computation. There is not sufficient instrumentation in the driver gas section of the shocktube to determine the conditions at rupture. There is however, some information that is known. Namely, the conditions before the energy addition and the amount of energy stored for addition into the shocktube. The conditions before the energy addition are 100% He at 100 psia and room temperature. This information can be used to construct an estimate of the conditions after energy addition. It is assumed that the addition of energy via electric arc does nothing to change the composition of the gas in the driver chamber. 12

21 Conservation of mass implies that the density of the driver gas can not change, due to a closed and rigid driver gas chamber. This, coupled with the ideal gas law, means only temperature is needed to find the conditions at rupture. Assuming no energy is lost before being added into the driver gas, this temperature can be found using the first law of thermodynamics. For simplicity, assume also that the driver gas specific heat (at constant volume) is taken to be an average value (for a quick/uncomplicated estimate). Equation 4.1 can then be used to calculate the temperature rise caused by the addition of the electric energy. The symbols are as follows: E is the electric energy added, m the mass of the driver gas, C v the specific heat at constant volume, and T the temperature rise. The temperature at rupture can then be found by solving for T and realizing that the temperature before energy addition was room temperature. Many assumptions went into the creation of this rupture temperature and thus rupture conditions estimate. In order to validate these conditions, another piece of EAST experimental information is used. The EAST facility measures shock speed at the spectrographs location using a series of pressure sensors. For each experimental shot, the shock speed is calculated and can be compared with the speed calculated from DPLR. A small amount of code was added to DPLR to track the shock front as it traveled across the mesh. This information can be used to refine the initial rupture temperature estimate in an iterative process until the computational shock speed matches that of the experiment. However, the shock speed (experimental or computational) is not constant but rather begins relatively high and drops quickly until its deceleration becomes small and almost constant. An example of this can be seen in Figure 4.2 Obtaining this situation requires the computational flowfield to be run out for some time. Because of this, the iterative procedure is listed here is very slow. This process was done only for the nominal shock velocity of 10 km/s. The temperature found was around K for the 0.2 torr case (around K to K for all cases). These temperatures are much lower than the estimates found using thermodynamic arguments. This points to problems with shock speed accuracy in DPLR and/or to large losses when energy is added to the driver gas in experiment. Even with no losses, it is also very possible that the diaphragm ruptures before all the energy is released, resulting in the same issue. E = mc v T (4.1) Even with access to a parallel computating tool such as DPLR, a solution on a relatively short mesh ( m long) took several days on processors using the Columbia supercomputer at NASA Ames Research Center (SGI Altix system using 1.6 GHz Intel Itanium 2 Montecito CPUs). Attempts were made to work around this short mesh limitation by coarsening the grid in both axial and radial directions or in the axial direction only. However, running such a case to the 7 meters necessary to simulate the actual size of the EAST shock tube caused anomalies in the computation. As such, it was decided to continue work with a short mesh and attempt to 13

22 trace this computational flowfield to that of the EAST facility. modify Initial Conditions DPLR Generate Lines-of-Sight NEQAIR (QSS) Integrate NEQAIR (Boltzmann) Integrate Figure 4.1: Nonequilibrium (DPLR) workflow 14

23 13 shock speed (km/s) shock location (cm) Figure 4.2: Variation of Computational (DPLR) Shock-Front Speed 15

24 CHAPTER 5 Results & Discussion Results shown here consist primarily of spectral radiance or radiance comparisons over various spectral ranges. Comparisons involving computations, experiments, or both are shown. Not all results involve direct comparision with EAST spectroscopy. For example, comparisons and discussion involving early CEA results can be found in Bose et al. [2] and are not listed here; Though the CEA results themselves are listed for comparison with later results. Other comparisons may only involve the differences between different flowfield models, with no concern for experiment. Still others may show the similarities/differences present in the EAST spectroscopy with no interest in computation. Dispite this, most comparisions involve both EAST spectroscopy and some sort of computation. These results are divided into several wavelength regions, vacuum ultraviolet, ultraviolet, visible, near-infrared, and infrared. The intervals involved are completely determined by the EAST spectroscopy, as it is the more limited of the two data sets. The computational results include both convolved and raw spectral radiance. For the latter, spectral line shapes and sizes are not directly comparable between computation and experiment. However, it is possible to compare the integral (radiance) over these spectral lines. Midway through this project, the preferred nomenclature for radiation in the EAST facility changed and the results here reflect that change. In plots, spectral radiance is referred to both as intensity and as spectral radiance. The integral over wavelength is referred to both as integrated intensity and as radiance. As the latter set of terms is more widely accepted and the former set is often ambiguous, spectral radiance and radiance will always be used in the text of this document. 16

25 5.1 Nomenclature In undertaking a discussion of the results obtained through this research, some nomenclature is used to simplify the description of the workflows/methods used. This nomenclature consists of the flowfield calculation method followed by the radiation calculation method. These two terms will be hyphenated and appear as a single identifier, e.g. CEA-NEQAIR. Any other pertinent information is listed in parentheses and follows this identifier. Possible flowfield calculations methods are CEA and DPLR. Possible radiation calculation methods are NEQAIR and NEQAIRup corresponding to NEQAIR verision 99d and the updated version described here, respectively. Information to be listed in parentheses includes the addition of impurities into the flowfield and nonstandard options in either the flowfield or radiation calculations. One specified nonstandard option to note is the use of Boltzmann vs non-boltzmann (quasi-steady-state) assumptions when modeling the distribution of excited states in NEQAIR. Unless otherwise noted, a Boltzmann distribution was used. 5.2 Sample EAST Spectroscopy Experimental data was taken from two test series at the EAST facility. The first of these was under the direction of Grinstead[7]. The second was under the direction of Cruden[3]. Both test series used a driven gas tube with an interior diameter of cm. The total length of the tube was 8.4 m with spectrographs at about 7 m from the diaphragm rupture point. The driver gas was Helium while the driven gas contained either synthetic Earth or Martian atmosphere. Only the Earth atmosphere cases were considered in this work. Data is available for velocities ranging from 9.5 km/s to 10.8 km/s at various driven gas pressures. These velocities and pressures are representative of some of the typical environments seen by atmospheric entry vehicles at maximum heating. In both test series, the spectrographs measure spatially (axial only) and spectrally resolved shock-layer radiation as the shock wave passes by windows in the shock tube. These spectrographs used intensified charged-coupled device (ICCD) cameras to record the data. The work of Grinstead et al. [7] used two spectrographs to simultaneously capture images in two different wavelength regions during the course of a single shockwave s passing. The work of Cruden et al. [3] extended this capability to allow for the use of four spectrographs simultaneously, greatly improving the amount of useful data obtained from a single test shot. This work and others (Bose et al. [2]) noticed some issues with contamination and baseline radiation in the data from Grinstead[7]. Because of this, an EAST facility update was undertaken to address these issues. This was done by the introduction of a shock-tube heater blanket, oil-free vacuum pumps, and most importantly, a oxygen plasma cleaning system for the tube walls. The data from Cruden[3] includes these updates. Because of contamination issues, this work primarily compares with the results from the updated EAST facility. 17

26 In other to elucidate the results that follow, examples of EAST spectroscopy and its associated/derived plots are given. For convenience, the shock structure and EAST camera setup schematics are repeated here in Figure 5.1 and Figure 5.2, respectively. Almost always, the EAST spectrograph images will include a small portion of region 1 followed by a large portion of region 2. Occasionally, region 3b will be shown as well. All computational work focuses solely on region 2. The sample plots here follow the methodology laid out in section 2.1. Begin with the two-dimensional spectrographic image (spectral radiance over axial distance and wavelength). From this, a radiance profile can be generated against axial distance. This profile is invaluable in selecting the spatial region over which to average spectral radiance, reducing the two-dimensional image to a single plot of spectral radiance against wavelength. As mentioned earlier, the experimental flowfield posseses both axial and radial variation, though only the axial is seen directly by spectroscopy. Therefore, a method was devised to reduce the experimental data so that it could easily be compared with that of computation. This procedure involves selecting a small axial slice from each spectrographic image and averaging spectra over this portion. Even with almost exactly the same integrated radiance, adjacent axial (wavelength varying) lines from the spectroscopy can have slightly different spectral radiances. The averaging within an axial slice is done to reduce the effects of this noise and further reduce the data. Unfortunately, there is no way to remove the effects of radial variation from the experiment. However, proper selection of the axial slice size and location can be used to reduce the experimental data as consistently as possible with the assumptions of the computation models. This is done by examining a plot of integrated radiance against axial location for each spectrographic image in question. Many of these images, as expected, show a spike of radiance at the shock front, followed by a trough, then a rise and subsequent plateau. A final change in radiance is seen at the location of the contact surface where the driven gas meets the driver gas. In spectrograph images such as this, it is assumed that the plateau region represents an equilibrium region and this plateau is taken as the axial slice for data reduction. Unfortunately, not all experimental images follow this expected trend. In these cases, the axial slice is taken to be small and located just forward of the contact surface. This portion of the flowfield has had the most time to equilibrate and therefore will be closest to equilibrium. Using this data reduction technique on all the EAST facility spectroscopy allows for simple and direct comparison with the computation spectral radiance obtained via CEA and NEQAIR or via DPLR and NEQAIR. The first example comes from the infrared region of the spectrum. A calibrated spectroscopic image is given by Figure 5.3. The shock front in this image is at approximately 6.5 cm and moving towards 7 cm. In other words, the datum line for these two example images corresponds to end of the spectrograph s field-of-view closest to the shocktube diaphragm. It does not, however, correspond to the actual location of the diaphragm (as the spectrograph is several meters down the shocktube). The horizontal lines at 2 cm and 5 cm mark the limits of the spatial region over 18

27 which averaging will be done. To see how these locations were chosen, one needs to look at the radiance profile given by Figure 5.4. The radiance is found by integrating spectral radiance across the entire wavelength region captured by the spectrograph. If this is done for each axial location, a radiance profile is obtained. This profile does not show the overshoot in intensity predicted by theory but could still hold useful radiation data behind the shock front. The region between 2 cm and 5 cm is relatively flat and is chosen to represent region 2 of Figure 5.1. Again, looking at the spectrographic image in Figure 5.3 confirms that this region appears reasonable. Noise is apparent in both the 2d image and profile, justifying the spatial averaging procedure. The result of this averaging is given by Figure 5.5. The two-dimensional spectrographic image has been reduced to spectral radiance against wavelength, removing all axial distance dependence while still representing the region of interest (region 2). This process is repeated for all EAST spectrographic images. All EAST results/comparisons that follow have gone through this process of data reduction. The second example comes from the ultraviolet region of the spectrum. The image is given by Figure 5.6. The corresponding radiance profile is given by Figure 5.7. In this profile, the overshoot predicted by theory is present. The noise is also much higher for this image. This is due to calibration issues and the smaller wavelength window seen by the spectrograph. The maximum wavelength recorded in this image changes with axial distance. Because of this, a smaller averaging region (closer to the shockfront) was chosen in order to obtain the largest wavelength region. The result of averaging between 4 cm and 7 cm is given by Figure 5.8. This is the representative plot for this spectrographic image and is what most, if not all, computational results are be compared against. 5.3 Updated NEQAIR The most simple flowfield used in this work is the equilibrium flowfield of CEA. Unfortunately, discrepancies were found by Bose et al. [2] between these CEA-NEQAIR results and the EAST data of Grinstead et al. [7]. However, samples of these results are still presented here for comparison with CEA-NEQAIRup calculations. For 0.2 torr and 0.7 torr, the nominal shock speed of 10 km/s is used and no comparisons with EAST data are visually shown. For 0.3 torr, the experimental shock speed is used and EAST (reduced) spectroscopy is overlayed onto the computational results. Also, for the 0.3 torr cases, 12% Carbon by mole was added to investigate the effects of impurities. This percentage was suggested by Bose et al. [2]. All results are convolved with Voigt shapes consistent with the instrumentation of EAST and shown covering wavelength ranges representative of all spectrograph images in each spectral region. First, consider the lowest pressure of 0.2 torr. These experiments should contain the most nonequilibrium effects and thus be matched relatively poorly with the equilibrium flowfield of 19

28 CEA. Results for the vacuum ultraviolet, ultraviolet, visible, and infrared spectra are given by Figure 5.9, Figure 5.10, Figure 5.11, and Figure 5.12, respectively. As mentioned earlier, it was shown in Bose et al. [2] that 0.2 torr CEA-NEQAIR results matched poorly with EAST facility spectroscopy. These figures are shown solely for the purpose of comparison with updated NEQAIR results. Secondly, consider the highest pressure of 0.7 torr. Results for the vacuum ultraviolet, ultraviolet, visible, and infrared spectra are given by Figure 5.13, Figure 5.14, Figure 5.15, and Figure 5.16, respectively. Finally, consider the intermediate pressure of 0.3 torr. Results for ultraviolet spectrum are given by Figure 5.17 and Figure Results for the visible, near-infrared, and infrared spectra are given by Figure 5.19, Figure 5.20, and Figure 5.21, respectively. As mentioned earlier, the results for 0.3 torr were obtained by using the experimental shock speed instead of the nominal shock speed as input to CEA. The effects of this can be seen in the differences between Figure 5.17 and Figure CEA-NEQAIR results transition from underprediction to overprediction as wavelength increases from the ultraviolet to the visible spectrum. Some agreement may be fortuitious, due only to high baseline radiation in EAST not present in NEQAIR. The first attempt to improve the agreement between computation and experiment involved updating NEQAIR[10]. Firstly, the NEQAIR atomic bound-bound transition database (for C, N, O) was updated to contain all lines in the NIST Atomic Spectra database. Very few lines were added and their effects are not studied here. Secondly, Stark broadening curve fit expressions were changed for N and O. Thirdly, several new molecular transition bands were added. Both of these effects are also small and not studied. Finally, atomic bound-free transition cross-sections were updated to supplant the Gaunt factor method. The new method directly uses tabulated cross-sections from TOPbase. The effect of this new bound-free update can be seen in the results that follow. The results for the ultraviolet, visible, near-infrared, and infrared spectra are given by Figure 5.22, Figure 5.23, Figure 5.24, Figure At least in these regions, the bound-free update has almost no effect. Computations were repeated with all NEQAIR updated features present and again produced no significant effects. The updating of NEQAIR done in this work does very little to explain or solve the discrepencies between computation and experiment that were noted in Bose et al. [2]. 5.4 DPLR The final attempt to improve the agreement between computation and experiment involved the introduction of a higher fidelity flowfield. As discussed in chapter 4, it is assumed that NEQAIR was accurating predicting spectral radiance and the discrepencies seen between computationa 20

29 and experiment exist because of the simplifying assumptions made in the modeling of the computational flowfield. DPLR-NEQAIR results are shown here for 0.2 torr and 0.7 torr cases with shock velocities of approximately 10 km/s. Two different cases of 0.2 torr are shown, comparisions are made to EAST spectroscopy, and a cursory analysis is done of boundary-layer effects. First, consider a 0.2 torr case on a relatively short mesh of 20 cm beyond intial driver/driven gas discontinuity (diaphragm). The shock speed at this point is approximately 10 km/s. The translational temperature and axial velocity are shown in Figure 5.26 and Figure 5.27, respectively. Notice the shock-front curvature and viscous effects evident in both figures. The radial axis begins at the centerline of the tube and goes to the viscous/isothermal wall. The axial axis datum line is the diaphragm location. As the subtle variation of flowfield in both axial and radial directions is difficult to discern on a contour plot, most of the other results that follow will be over axial distance with radial slices (constant radius) to show radial variation. Such a plot for translational temperature can be found in Figure The theoretical nonequilibrium overshoot is seen as expected. Again, notice the shock-front curvature that can be seen by the location of the overshoot in different radial slices. Very close to the wall, hot gas remains long after the shock has passed; while in the interior of the shock tube, the arrival of the cold driver gas can clearly be seen at around cm. The vibrational temperature is shown in Figure Again, the boundary-layer temperature is colder than the interior. The hump centered on 16 cm for the 97% radial slice most likely corresponds to a bulge in the boundary-layer, though the lack of molecules in the post-shock flow make the vibrational temperature a less reliable measure than others. Axial velocity shown in Figure 5.30 follows expected trends. That is, the velocity is mostly constant (around 10 km/s) behind the shock except for near the wall. Figure 5.31 and Figure 5.32 shown pressure and density, respectively. These follow, to a degree, the theoretical results for a ideal inviscid shocktube. The only exceptions to this being, near the wall, and around an axial distance of 16 cm. For example, in mixture density plot, the shock front and contact surface is clearly visible. The region between 18 cm and cm is the region of interest for radiation calculations and the region modeled previously by CEA. The arrival of the Helium driver gas can clearly be seen in Figure Finally, the effects of chemistry are clearly shown in Figure The percentage of the flow that is ionized increases away from the shock-front, never reaching a plateau. The peak value, directly in front of the contact surface, is around 12%. Interestingly, this trend is reversed in the boundary layer. That is, the flow becomes less ionized away from the shock-front. Looking at the individual chemcial constituents of the flow may help to elucidate these issues. The profiles for He, N, N +, O, O +, and electrons can be seen in Figure 5.35, Figure 5.36, Figure 5.37, Figure 5.38, Figure 5.39, and Figure 5.40 respectively. Molecular species exist almost solely in the boundary-layer. Nitrogen ions are mostly responsible for the rise in degree of ionization away from the shock-front. The interior of the shocktube is 21

30 highly dissociated and highly ionized while the boundary layer contains colder less ionized gas. A axial slice of the flowfield was halfway between the shock-front and contact surface. This slice was then mirrored about the centerline to ensure that a line-of-sight could be constructed for NEQAIR which began at one wall, went through the interior of the flow, and then ended at another wall. In this way, all physically relevant portions of the flowfield can be included in the simulation (rather than just an interior as modeled by CEA). NEQAIR was run using this flowfield, both with atomic species only and with atomic/molecular species. This was done to indirectly study the effect of the boundary-layer on calculated radiance (as most molecules exist in the boundary layer) in hopes to understand this in the experimental data. The results are given by 5.41(a), 5.42(a), 5.43(a), and 5.44(a). These can be compared with reduced EAST data given by 5.41(b), 5.42(b), 5.43(b), and 5.44(b). The computational results are not convolved, so comparisons should only be done with radiance (not spectral radiance). Almost no difference between atomic only and atomic/molecular is seen in the vacuum ultraviolet spectrum. However, molecular species contribute much in the ultraviolet spectrum while they cause significant absorption in the visible and infrared spectra. This could explain some overprediction in high wavelengths when using CEA-NEQAIR as this boundary-layer effect is not modeled. In the vacuum ultraviolet spectrum, the primary reason for disagreement is the size of the atomic line at around Å. In the ultraviolet spectrum, the agreement is relatively good, with the majority of the differences due to Å to Å. For the visible spectrum, the differences are due to the high baseline in the EAST spectroscopy. Notice that the NEQAIR radiance has has flat regions while EAST radiance is always rising due to the baseline. Also, note that the NEQAIR atomic and molecular case fits much better with the EAST data than the atomic-only case. This can be seen especially well by looking at the rise in radiance across the lines at Å and Å. These rises are much smaller than those seen in the atomic-only case and are consistent with EAST. This alone gives credence to the importance of the boundary layer in these cases. The disagreement in the infrared spectrum is due to the relative high strength of several NEQAIR lines. The features at Å and Å are much much stronger in NEQAIR than in EAST. Again, these observations are consistent with the trend of agreement discussed earlier for CEA-NEQAIR. NEQAIR transitions from underprediction to overprediction as wavelength increases. The use of DPLR has improved this agreement but the trend still exists. Next, consider another 0.2 torr DPLR case. This case was produced on a longer mesh with a different CFL schedule and a snapshot at 10 km/s can be seen in Figure The features in this flowfield are very similar to those in the previous. The translational and vibrational temperature profiles are qualitatively and quantitatively similar. This is shown in Figure 5.45 and Figure However, the shock-front curvature is reduced significantly. Again, an axial slice of the flowfield was chosen halfway between the shock-front and contact surface. This was used as input to NEQAIR in the way discussed earlier. Unlike the previous results, these are convolved and can be 22

31 compared directly to EAST data. Results for the ultraviolet, visible, and infrared sectra are given by Figure 5.50, Figure 5.51, and Figure 5.52, respectively. Again, these can be compared with the reduced EAST data. However, it is important to note that these figures do not have the same size wavelength interval. Being as these are convolved results, we can compare spectral radiance and features directly. In the ultraviolet spectrum, the bands at Å and Å match between NEQAIR and EASt. However, the NEQAIR feature at Å is much weaker in EAST and the EAST features between Å and Å are missing from NEQAIR. Again, for the visible spectrum differences are primarily due to the EAST baseline. Finally, in the infrared spectrum, NEQAIR relative spectral radiance between lines do not match those in EAST. This points to a difference in distribution of excited states for computation versus reality. 5.5 Conclusions This work was done in attempts to close the gap between computation and experiment, and to explain discrepancies seen between these. All comparisons were made against EAST spectroscopy and all radiation computations done using NEQAIR. Workflows were developed to link CEA or DPLR flowfields to NEQAIR radiation calculations. Several updates were made to NEQAIR including atomic lines, Stark broadening, bound-free cross-sections, and new molecular bands. It was found that these updates did little to resolve discrepancies with the EAST facility. Finally, DPLR was used to provide a high fidelity flowfield simulating both axial and radial variation in a shock-tube. This flowfield, linked with NEQAIR, was used to try to improve or at least explain the discrepancies between computation and experiment. Some improvement was found though the trends of disagreement discovered with CEA still apply. NEQAIR underpredicts in the ultraviolet spectrum and overpredicts in the infrared spectrum. The DPLR method could prove promising in the study of the boundary layer in EAST and how its presence affects experimental spectroscopy. Overall, major discrepancies still remain between NEQAIR computations and EAST spectroscopy. More study will be required to determine the validity and source of these differences. 4 3a r,y x 3b 2 1 Centerline Figure 5.1: Shock structure after diaphragm bursts 23

32 Spectrograph Top View 4 3a r,y x 3b 2 1 Centerline Figure 5.2: Spectroscopy setup 24

33 Figure 5.3: Example of EAST Spectroscopy with Annotated Spatial-Averaging Region 25

34 Figure 5.4: Example of EAST Radiance Profile 26

35 Figure 5.5: Example of EAST Spatial-Averaged Spectral Radiance 27

36 Figure 5.6: Example of EAST Spectroscopy with Annotated Spatial-Averaging Region 28

37 5 4 Intensity (W/cm 3 -micron-sr) Distance (cm) Figure 5.7: Example of EAST Radiance Profile 29

38 75 60 Intensity (W/cm 2 -micron-sr) Wavelength (Angstroms) Figure 5.8: Example of EAST Spatial-Averaged Spectral Radiance 30

39 Figure 5.9: Spectral Radiance from CEA-NEQAIR in the Vacuum Ultraviolet Spectrum 31

40 Figure 5.10: Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum 32

41 Figure 5.11: Spectral Radiance from CEA-NEQAIR in the Visible Spectrum 33

42 Figure 5.12: Spectral Radiance from CEA-NEQAIR in the Infrared Spectrum 34

43 Figure 5.13: Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum 35

44 Figure 5.14: Spectral Radiance from CEA-NEQAIR in the Ultraviolet Spectrum 36

45 Figure 5.15: Spectral Radiance from CEA-NEQAIR in the Visible Spectrum 37

46 Figure 5.16: Spectral Radiance from CEA-NEQAIR in the Infrared Spectrum 38

47 Figure 5.17: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIR (large artificial impurity addition) in the Ultraviolet Spectrum 39

48 Figure 5.18: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIR (large artificial impurity addition) in the Ultraviolet Spectrum 40

49 Figure 5.19: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIR (large artificial impurity addition) in the Visible Spectrum 41

50 Figure 5.20: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIR (large artificial impurity addition) in the Near-Infrared Spectrum 42

51 Figure 5.21: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIR (large artificial impurity addition) in the Infrared Spectrum 43

52 Figure 5.22: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIRup (bound-free updates only) in the Ultraviolet Spectrum 44

53 Figure 5.23: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIRup (bound-free updates only) in the Visible Spectrum 45

54 Figure 5.24: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIRup (bound-free updates only) in the Near-Infrared Spectrum 46

55 Figure 5.25: Comparison of Spectral Radiance from EAST, CEA-NEQAIR, and CEA-NEQAIRup (bound-free updates only) in the Infrared Spectrum 47

56 Figure 5.26: Translational Temperature Snapshot of DPLR Flowfield showing Shock-Front Curvature and Viscous Effects 48

57 Figure 5.27: Axial Velocity Snapshot of DPLR Flowfield showing Shock-Front Curvature and Viscous Effects 49

58 20000 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% T (K) axial (cm) Figure 5.28: Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation 50

59 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% 8000 T vib (K) axial (cm) Figure 5.29: Vibrational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation 51

60 axial velocity (m/s) r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% axial (cm) Figure 5.30: Axial Velocity Snapshot of DPLR Flowfield showing both Axial and Radial Variation 52

61 Pressure (kpa) r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% axial (cm) Figure 5.31: Pressure Snapshot of DPLR Flowfield showing both Axial and Radial Variation 53

62 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% density (kg/m 3 ) axial (cm) Figure 5.32: Density Snapshot of DPLR Flowfield showing both Axial and Radial Variation 54

63 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% He density (kg/m 3 ) axial (cm) Figure 5.33: Helium Density Snapshot of DPLR Flowfield showing both Axial and Radial Variation 55

64 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% Degree of Ionization axial (cm) Figure 5.34: Degree of Ionization Snapshot of DPLR Flowfield showing both Axial and Radial Variation 56

65 1 0.8 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% He Mole Fraction axial (cm) Figure 5.35: Helium Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 57

66 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% 0.5 N Mole Fraction axial (cm) Figure 5.36: Atomic Nitrogen Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 58

67 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% N+ Mole Fraction axial (cm) Figure 5.37: Atomic Nitrogen Ion Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 59

68 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% O Mole Fraction axial (cm) Figure 5.38: Atomic Oxygen Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 60

69 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% O+ Mole Fraction axial (cm) Figure 5.39: Atomic Oxygen Ion Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 61

70 r/r = 99.6% r/r = 97.0% r/r = 50.0% r/r = 0.0% Electron Mole Fraction axial (cm) Figure 5.40: Electron Mole Fraction Snapshot of DPLR Flowfield showing both Axial and Radial Variation 62

71 500 Atomic Atomic & Molecular 3 Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] 0 (a) DPLR-NEQAIR Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] 0 (b) EAST Figure 5.41: Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Vacuum Ultraviolet Spectrum 63

72 300 Atomic Atomic & Molecular 3 Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] 0 (a) DPLR-NEQAIR Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] 0 (b) EAST Figure 5.42: Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Ultraviolet Spectrum 64

73 1000 Atomic Atomic & Molecular 10 Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] (a) DPLR-NEQAIR Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] (b) EAST Figure 5.43: Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Visible Spectrum 65

74 1000 Atomic Atomic & Molecular 7 Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] (a) DPLR-NEQAIR Spectral Radiance [W/cm 2 -mi-sr] Radiance [W/cm 2 -sr] Wavelength [Angstroms] (b) EAST Figure 5.44: Effect of Boundary-Layer Molecular Species on Spectral Radiance in the Infrared Spectrum 66

75 cm cm cm cm cm T[K] axial distance [cm] Figure 5.45: Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation 67

76 cm cm cm cm cm Tv [K] axial distance [cm] Figure 5.46: Vibrational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation 68

77 Figure 5.47: Translational Temperature Snapshot of DPLR Flowfield showing both Axial and Radial Variation 69