A numerical study on non-equilibrium multi-temperature thermo-chemistry
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The accurate computation of hypersonic flowfields is an ongoing endeavor and is important for the accurate prediction of heat transfer and space vehicle design. The governing equations for hypersonic flowfields have been evolving from multi-temperature modeling, state-to-state modeling to the more recent reduced order modeling. Of the various models existing till date of varying levels of complexity, multi-temperature modeling continues to be the most widely implemented and computationally least expensive form of modeling hypersonic flows. This thesis explores the resulting physics from various forms of multi-temperature modeling. The non-equilibrium flows at typical hypersonic re-entry conditions can be modeled by considering varying extents of non-equilibrium: chemical, thermo-chemical with the typical two temperature formalism, and thermo-chemical with more than two temperatures used to represent the gas under consideration. Most initial numerical verification studies examine non-equilibrium relaxation rates using zero-dimensional heat bath systems. Literature abounds with heat bath relaxation rate studies at isothermal conditions, and consequently for very dilute systems with negligible chemical non-equilibrium. Nonetheless, the same verified representative equations, including the Landau-Teller translation-vibration energy exchange, are used to compute multi-dimensional flows involving high degrees of chemical non-equilibrium. Thus, despite a well-established understanding of the temperature limitations of Park's empirical two-temperature model, and the original form of the Landau-Teller formulation, the effects of system dilution levels on the resulting non-equilibrium characteristics have not been well understood. The present work focuses on the effects of such dilution on the thermo-chemical non-equilibrium characteristics of isochoric, finite heat baths represented by varying resolutions of multi-temperature models. The non-equilibrium characteristics for such heating systems reveal non-linear effects in attaining thermal non-equilibrium which are enhanced by the mixing-type Millikan-White relaxation time empirical curve fit. Multi-vibrational, single translational temperature modeling leads to significantly altered time-scales of non-equilibrium chemistry relative to a simple two-temperature model representation for internal energy. This was further confirmed during the two-dimensional flows studied where thermo-chemical modeling with first order effects exhibited altered shock stand-off, near-surface temperatures, and flow field chemistry with multi-vibrational, single translational temperature modeling. The implementation of an increased resolution of thermal non-equilibrium representation for any weakly ionized flows present in the system closely followed the trends exhibited by a system in which electron and heavy particle translational temperatures were assumed to be in equilibrium with each other. However, the shock structure showed an enhanced sensitivity to a more complete representation of the underlying chemical kinetics. For the aerothermodynamics community, this work contributes to understanding the resultant thermo-chemical non-equilibrium rate effects for various forms of representing the effective temperature of a reaction, within a multi-temperature modeling perspective. In particular, it emphasizes the temporal and spatial sensitivity of non-equilibrium energy modeling approaches for various zero-dimensional and two-dimensional flow fields. Such intermediate non-equilibrium chemistry effects could be leveraged for aerodynamic flow control and controlled heat transfer applications.