Modeling of high enthalpy flows for hypersonic re-entry and ground-based arc-jet testing

This work presents a simulation framework for modeling high enthalpy ionized gas flows during planetary entry flights and ground-based arc-jet testing. The system of Favre-averaged Navier-Stokes equations in thermo-chemical non-equilibrium with Spalart-Allmaras turbulence closure is outlined, along with models for thermodynamics, chemical kinetics, transport properties, and the applied electric field. The electric field and the Joule heating term are computed using a Poisson equation and the generalized Ohm's law. A standard two-temperature model is implemented to account for non-equilibrium effects. A numerical method based on the streamline upwind Petrov-Galerkin (SUPG) finite element formulation is utilized. A two-way loose coupling strategy between the flow solver and the electric field is introduced to achieve convergence. The methodology is first tested by modeling hypersonic axisymmetric flows over a blunt body for a range of increasingly complex flight conditions. We then apply it to simulate the flow-field and electrical discharge inside the 20 MW NASA Ames Aerodynamic Heating facility (AHF) to further confirm the capabilities and robustness of the developed framework

Extension of Multiband Opacity-Binning to Molecular, Non-Boltzmann Shock Layer Radiation

For accurate predictions of shock layer radiative heating to reentry vehicles, the smeared rotational band (SRB) model is appropriate for molecular band systems with negligible self absorption, meaning they are optically-thin. However, for band systems with noticeable self absorption, the orders-of-magnitude more computationally expensive line-by-line (LBL) approach is required. Considering past and proposed NASA missions, the molecular band systems most likely to require the LBL approach are the CO 4th-Positive, CN Violet, and CO2 IR bands. The CO 4th- Positive and CN Violet bands are required for Mars entry at velocities greater than 6 km/s, with the CN Violet band also required for Titan entry. These two bands typically emit strongly in flow regimes with non-Boltzmann upper electronic state populations. The CO2 IR band is required for Mars entry at velocities below 5 km/s. This ro-vibrational band system is typically assumed to contain Boltzmann populations of radiating levels (the quality of this assumption is the subject of other studies)

Reduced-order modeling of non-Boltzmann thermochemistry and radiation for hypersonic flows

The non-equilibrium aerothermal environment during hypersonic flows is determined by the interaction between a multitude of disparate physical phenomena with varying characteristic time scales. The multi-physics nature of this flight regime renders the task of accurately estimating vehicular characteristics both theoretically and computationally challenging. The rapid dissipation of flow velocity into thermal energy in the post-shock region drives collisional-radiative processes that alter the chemical and energy composition of the flowfield. Traditional thermochemical and radiative models often introduce ad-hoc simplifications and rely on model parameters calibrated for a limited range of experimental conditions. Recent advances in computing power have allowed non-equilibrium internal state population distributions of gaseous species to be precisely determined using ab-initio quantum-chemistry calculations, referred to as the state-to-state (StS) approach. Similarly, first-principles based databases for different chemical species are now available that can characterize radiative behavior by accounting for millions of individual radiative transitions, referred to as line-by-line (LBL) modeling. Although exceedingly accurate, both StS and LBL approaches are computationally expensive and cannot be viably applied for solving practical physical problems. This thesis is aimed at developing a unified reduced-order framework for describing non-equilibrium thermochemistry and radiative heating which retains the physical fidelity of the aforementioned approaches but at dramatically lowered computational costs. A computationally tractable description of non-Boltzmann thermochemistry is obtained using the multi-group maximum-entropy (MGME) framework. This involves dividing individual internal states into bins and then reconstructing the state population distribution using the maximum entropy principle. The current work introduces an adaptive grouping methodology that incorporates state-specific kinetics for further improving the MGME method. Two strategies are considered —Modified Island Algorithm and Spectral Clustering Method — for identifying clusters of states that are likely to equilibrate faster with respect to each other and then lumping them together into bins. The efficacy of MGME-based model reduction is assessed by studying non-equilibrium characteristics of two chemical systems, molecular nitrogen and carbon-dioxide, in a homogeneous chemical reactor. The introduction of adaptive binning which correctly accounts for localized thermalization due to preferential transition pathways allows the complex dynamics of about 9,000 internal states to be modeled using only 10-30 bins. The multi-variate nature of radiative transfer is tackled by breaking it down into two components: geometric transfer and spectral modeling. A combination of discrete-ordinate method and finite-volume discretization with mesh sweeping is used to resolve generalized three-dimensional radiation fields in the angular and spatial domains. A reduced-order representation of the spectral variation in absorption/emission behavior is obtained through multi-group Planck-averaging. A formal interpretation for Planck-averaging is obtained based on maximum entropy closure in frequency space which allows a direct equivalence to be drawn with the MGME framework. Furthermore, a new generalized grouping strategy for non-equilibrium radiation is proposed that considers both absorption and emission coefficients while defining reduced-order groups. A detailed line-of-sight analysis for various Earth and Jovian entry problems indicates that Planck-averaging combined with the new grouping procedure allows reliable predictions while achieving a two orders-of-magnitude speed-up with respect to narrow-band methods (and three to four orders with respect to full LBL modeling). The new simulation framework, with its focus on minimizing computational outlays, is ideally suited for realizing flow-radiation coupled simulations on large computational meshes. This is demonstrated by investigating, in conjunction with the US3D flow solver, the impact of vibrational non-equilibrium on carbon dioxide wake flows and resultant infrared radiation around NASA's Mars 2020 vehicle. Predictions for flowfield properties and radiative transfer are obtained using the conventional two-temperature model, bin-based StS model, and for decoupled/coupled flow-radiation calculations. Conventional two-temperature models overestimate the rate of thermal equilibration in the near-wake region resulting in the population of mid-lying and upper carbon dioxide vibrational levels being underpredicted by multiple orders of magnitude. Additionally, the two-temperature approach (in comparison to bin-based StS) overpredicts the rate of carbon dioxide dissociation thereby leading to erroneous estimates for flow properties in the post-shock region (primary source of afterbody radiative emission). This results in inflated values for surface radiative heat flux with conventional two-temperature modeling, although overall differences in radiative behavior are moderated by factors such as fast characteristic relaxation times for ground vibrational levels

Reduced-order modeling of non-Boltzmann thermochemistry and radiation for hypersonic flows

The non-equilibrium aerothermal environment during hypersonic flows is determined by the interaction between a multitude of disparate physical phenomena with varying characteristic time scales. The multi-physics nature of this flight regime renders the task of accurately estimating vehicular characteristics both theoretically and computationally challenging. The rapid dissipation of flow velocity into thermal energy in the post-shock region drives collisional-radiative processes that alter the chemical and energy composition of the flowfield. Traditional thermochemical and radiative models often introduce ad-hoc simplifications and rely on model parameters calibrated for a limited range of experimental conditions. Recent advances in computing power have allowed non-equilibrium internal state population distributions of gaseous species to be precisely determined using ab-initio quantum-chemistry calculations, referred to as the state-to-state (StS) approach. Similarly, first-principles based databases for different chemical species are now available that can characterize radiative behavior by accounting for millions of individual radiative transitions, referred to as line-by-line (LBL) modeling. Although exceedingly accurate, both StS and LBL approaches are computationally expensive and cannot be viably applied for solving practical physical problems. This thesis is aimed at developing a unified reduced-order framework for describing non-equilibrium thermochemistry and radiative heating which retains the physical fidelity of the aforementioned approaches but at dramatically lowered computational costs. A computationally tractable description of non-Boltzmann thermochemistry is obtained using the multi-group maximum-entropy (MGME) framework. This involves dividing individual internal states into bins and then reconstructing the state population distribution using the maximum entropy principle. The current work introduces an adaptive grouping methodology that incorporates state-specific kinetics for further improving the MGME method. Two strategies are considered —Modified Island Algorithm and Spectral Clustering Method — for identifying clusters of states that are likely to equilibrate faster with respect to each other and then lumping them together into bins. The efficacy of MGME-based model reduction is assessed by studying non-equilibrium characteristics of two chemical systems, molecular nitrogen and carbon-dioxide, in a homogeneous chemical reactor. The introduction of adaptive binning which correctly accounts for localized thermalization due to preferential transition pathways allows the complex dynamics of about 9,000 internal states to be modeled using only 10-30 bins. The multi-variate nature of radiative transfer is tackled by breaking it down into two components: geometric transfer and spectral modeling. A combination of discrete-ordinate method and finite-volume discretization with mesh sweeping is used to resolve generalized three-dimensional radiation fields in the angular and spatial domains. A reduced-order representation of the spectral variation in absorption/emission behavior is obtained through multi-group Planck-averaging. A formal interpretation for Planck-averaging is obtained based on maximum entropy closure in frequency space which allows a direct equivalence to be drawn with the MGME framework. Furthermore, a new generalized grouping strategy for non-equilibrium radiation is proposed that considers both absorption and emission coefficients while defining reduced-order groups. A detailed line-of-sight analysis for various Earth and Jovian entry problems indicates that Planck-averaging combined with the new grouping procedure allows reliable predictions while achieving a two orders-of-magnitude speed-up with respect to narrow-band methods (and three to four orders with respect to full LBL modeling). The new simulation framework, with its focus on minimizing computational outlays, is ideally suited for realizing flow-radiation coupled simulations on large computational meshes. This is demonstrated by investigating, in conjunction with the US3D flow solver, the impact of vibrational non-equilibrium on carbon dioxide wake flows and resultant infrared radiation around NASA's Mars 2020 vehicle. Predictions for flowfield properties and radiative transfer are obtained using the conventional two-temperature model, bin-based StS model, and for decoupled/coupled flow-radiation calculations. Conventional two-temperature models overestimate the rate of thermal equilibration in the near-wake region resulting in the population of mid-lying and upper carbon dioxide vibrational levels being underpredicted by multiple orders of magnitude. Additionally, the two-temperature approach (in comparison to bin-based StS) overpredicts the rate of carbon dioxide dissociation thereby leading to erroneous estimates for flow properties in the post-shock region (primary source of afterbody radiative emission). This results in inflated values for surface radiative heat flux with conventional two-temperature modeling, although overall differences in radiative behavior are moderated by factors such as fast characteristic relaxation times for ground vibrational levels

Measurement and Analysis of Dust-Laden Flow Experiments in the DLR GBK Facility

The analysis of dust-laden flows can be an important element of spacecraft design. For example, a spacecraft entering the Martian atmosphere will encounter dust particles suspended in the atmosphere. If the entry occurs during a major regional or global dust storm, dust particle impacts on the heatshield of the spacecraft can cause erosion of the vehicle thermal protection system (TPS) that can be equivalent to that caused by thermochemical ablation [1]. There is also a possibility of particulate matter in the atmosphere of Titan that may impact the Dragonfly project capsule during its atmospheric entry. Vehicles landing on the surface of Mars or on the Earth’s moon may also liberate surface dust or regolith due to plume-surface interaction (PSI) effects [2]. Developing a simulation capability to model dust-laden flows requires the ability to accurately predict the velocity of a particle as it travels through a shock layer, nozzle plume, or the flow of an experimental facility. The primary mechanism that determines the particle velocity is the drag force acting on the particle. The drag force is typically expressed in terms of the frontal area of the particle, its velocity relative to the surrounding fluid, the density of the surrounding fluid, and a non-dimensional drag coefficient. Substantial effort has been devoted over many decades to developing models or correlations to estimate the drag coefficient for spherical bodies over a wide range of flow conditions [3] – [8]. The correlations have historically been based on experimental data, but more recently computational simulations have been used to augment the experimental data [3]. Since 2017 there has been a successful partnership between the NASA Entry Systems Modeling (ESM) project under the NASA Game Changing Development (GCD) program and the German Aerospace Center (DLR). Dusty flow experiments have been performed in the DLR GBK facility [9]. DLR has developed advanced diagnostic techniques in the GBK facility that allow simultaneous measurement of particle size, velocity, and mass flow rate [9]. This new high-precision experimental data is well-suited to drag model validation efforts. An additional element of the ESM project is the development of an integrated CFD-particle trajectory code, named US3D-DUST [10], that uses a Lagrangian-based framework to compute particle trajectories in a dust-laden flow. The GBK experimental data will be used to validate the US3D-DUST code as well as to assess the ability of existing particle drag models to accurately simulate particle trajectories in the GBK experiments