Continuum breakdown assessment and state-based transport modeling for non-equilibrium hypersonic flows

Subramaniam, Sharanya

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https://hdl.handle.net/2142/109549 Copy

Description

Title

Continuum breakdown assessment and state-based transport modeling for non-equilibrium hypersonic flows

Author(s)

Subramaniam, Sharanya

Issue Date

2020-08-05

Director of Research (if dissertation) or Advisor (if thesis)

Stephani, Kelly A

Doctoral Committee Chair(s)

Stephani, Kelly A

Committee Member(s)

• Glumac, Nick
• Lee, Tonghun
• Bodony, Daniel
• Jaffe, Richard L

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• hypersonic reentry
• aerothermodynamics
• non-equilibrium flows
• state-to-state models
• non-continuum flows
• transport collision integrals
• chemically reacting flows
• continuum breakdown
• coarse-grained models

Abstract

The work presented in this dissertation is motivated by the need for improving the fidelity of physical and chemical models used for predicting flowfield properties during hypersonic (re)entry of space vehicles into planetary atmospheres. Commonly employed numerical approaches for simulating the thermal and chemical non-equilibrium encountered in these high speed flows are multi-temperature computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and hybrid CFD/DSMC solvers that capitalize on the advantages of both methodologies. Improving the kinetics and transport models used in these solution techniques as well as developing accurate reduced order frameworks allow for reliable yet efficient estimation of flowfield parameters, thus optimizing thermal protection system (TPS) design. Informed by these objectives, the first aspect of this work is directed towards the advancement of hybrid CFD/DSMC solvers. This involves formulating `breakdown parameters' that are used to identify locations where the continuum assumption fails within a hypersonic, chemically reacting flowfield, necessitating a transition from CFD to DSMC within these non-continuum zones. The breakdown parameter formulation is then extended to the rovibrationally resolved and reduced order state-to-state (StS) frameworks. However, in order to perform a continuum breakdown assessment within these rovibrationally resolved and reduced order StS frameworks, a consistent transport methodology is required. Therefore, the second aspect of this dissertation aims to: (i) develop a rovibrationally resolved transport methodology and compute vibrationally as well as rovibrationally resolved transport collision integrals for the O+O2 (atom-diatom) system; (ii) develop a reduced order/coarse-grained StS transport methodology. The generalized Chapman-Enskog (GCE) approach serves as the primary underlying principle of this work. The first aspect of this dissertation involves the assessment of continuum breakdown within flowfields computed using multi-temperature CFD solvers. Using the `mechanism-based' GCE breakdown parameters developed for chemically reacting flows, locations of non-continuum along with the physical processes that lead to breakdown - translational, rotational and vibrational heat fluxes, mass diffusion fluxes and stress tensor components - are identified within the forebody region of a Mach 24 airflow past a sphere. Regions of non-continuum were observed in the shock, and close to the sphere surface. The flowfield near the surface was found to be characterized by sharp species concentration gradients due to gas-phase and surface reactions. Thus, chemical reactions were found to indirectly distort the underlying equilibrium distribution function, providing a new pathway to continuum breakdown as indicated by the GCE species-wise diffusion breakdown parameter. Next, a `species-wise' perturbation parameter based on the 2-norm in Hilbert space of the first order GCE perturbation expression is developed for assessing the extent to which the underlying equilibrium Maxwell-Boltzmann (MB) distribution of a given species has been perturbed. All transport mechanisms that can lead to distortion of the species-wise equilibrium MB distribution function are simultaneously incorporated into this perturbation parameter that can be computed for each species as an indication of local non-continuum. This parameter, along with the mechanism based GCE breakdown parameters were used to assess continuum breakdown in the forebody and wake region of a cylinder subjected to hypersonic flow. Additionally, the influence of altitude, freestream velocity and cylinder surface chemistry on continuum breakdown was analyzed. Regions of continuum breakdown were observed in the shock, boundary layer, and the wake. Most notably, the surface chemistry at the cylinder wall forebody led to the formation of breakdown regions in the wake that were detached from the cylinder surface. It was also found that the rigorously formulated species-wise perturbation parameter captured larger regions of local non-continuum than the traditionally used phenomenological gradient length local Knudsen number. Next, the GCE breakdown parameter formulations are extended to the rovibrationally resolved and reduced order StS system, highlighting the need for transport models for these frameworks. As a first step towards improving transport models employed in CFD, vibrationally resolved transport collisional quantities including scattering angles, cross-sections and collision integrals are computed for the O+O2 system by extending conventional `non-trajectory based' calculation methods to include StS effects. These calculations were performed using the set of nine ab initio potential energy surfaces (PES) by Varga et al., specifically constructed to capture high energy collisions that dominate hypersonic flows. The `surface-averaged' state-based collision integral values computed from the Varga et al. set of surfaces generally increased with vibrational excitation for temperatures up to 6000 K, and decreased with vibrational excitation at higher temperatures. Additionally, due to this non-trivial dependence of the collision integrals on the vibrational state of O2, state-of-the-art empirical models were found to be unable to correctly estimate vibrational state-based collision integrals. Differences as high as 80 % in StS collision integral values were obtained between the model predictions and those computed directly from the PES. Next, rovibrational transport cross-sections and collision integrals are computed for the O+O2 system by carrying out `trajectory-based' calculations that incorporate dynamical details of the collision process. It was found that molecular rotation can influence the collision integral values by ~30 %, depending on the vibrational state of the molecule and the gas temperature. Further, comparison with the vibrationally resolved collision integrals calculated earlier revealed that conventional `non-trajectory based' calculations for an atom-diatom system that employ a number of simplifying assumptions tend to overestimate StS collision integral values. With the view to decrease the computational expense associated with full StS-CFD calculations, physics-based reduced order/coarse-grained models are constructed by grouping together rovibrational levels connected by processes occurring on similar timescales. As part of this dissertation, a framework for the calculation of transport coefficients for such reduced order models is developed. Finally, the `group/bin collision integrals' for the O+O2 system are calculated for use in reduced order StS-CFD calculations.

Graduation Semester

2020-12

Type of Resource

Thesis

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http://hdl.handle.net/2142/109549

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Copyright 2020 Sharanya Subramaniam

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