Method-of-characteristics models for flowfield evaluation of hypervelocity test facilities

Abstract

Ground test facilities are an imperative part of the design and development of flying vehicles. In the case of high-enthalpy facilities, evaluating the gasdynamic and thermochemical state of the test gas poses challenges due to high temperature effects. This study aims to contribute to the development impulse facilities by developing reduced-order models resolving the flowfields of such facilities. Developed as a part of this study are various method-of-characteristics (MoC) algorithms which consider gases under varying levels of thermochemical complexity. The algorithms span from simple calorically perfect gases to full thermochemical nonequilibrium.

The first set of algorithms was limited to unsteady flow of calorically perfect gases with no area variation. The effects of momentum and heat losses were included as appropriate sink terms in the governing equations. Based on ordinary differential equations from MoC, numerical algorithms were developed to solve various gasdynamic phenomena such as weak compressions, rarefactions, shocks and contact surfaces. The momentum losses in the governing equations were estimated using established friction factors. Various empirical methods were explored to determine an appropriate heat-transfer model. In an effort to limit the scope of model development, a detonation-driven shock tube was first modeled based on the expected ideal wave processes utilizing various MoC algorithms.

Subsequently, experiments were carried out in a small-scale detonation-driven shock tube to validate the results from the reduced-order model. The experiments used nitrogen as the high-pressure driver gas, stoichiometric oxyhydrogen as the detonation driver gas and nitrogen or helium as the driven gas. Comparison with experiments showed that the MoC model reasonably replicated detonation tube operation for all the experimental cases. Specifically, the decaying incident shock trajectory in the driven section was replicated well, and so was the peak pressure at the driven endwall. The quasi-steady plateau pressure in the detonation driver was replicated reasonably, with experimental pressure traces showing early decay than MoC pressure traces. The wave system produced by the reflected shock wave--contact surface interaction in the driven section was also predicted accurately by the MoC model.

The second set of algorithms pertained to unsteady, inviscid, quasi-one-dimensional flow of a chemically reacting mixture of gases. Gaseous mixtures were assumed to be in thermal equilibrium but finite-rate chemical reactions were permitted. Initially, the variables associated with chemical composition were evaluated using the open-source toolkit, Cantera. The final results reported here use a stand-alone chemistry solver developed during this study, which evaluates rate constants using Arrhenius equation. A new integration procedure was formulated for flows with finite-rate chemistry. Simple gasdynamic models representing supersonic combustion, normal shock wave and a quasi-one-dimensional flow were developed and validated.

The third set of algorithms deal with thermally perfect gases. These were primarily selected to investigate vectorization of the existing MoC algorithms for nonequilibrium flows. Vectorization was carried out for the interior point solver, which yields the maximum computational impact through parallelization. Thermally perfect algorithms were also developed for other MoC subroutines, but did not have the need to be vectorized. The variation of specific heats (and their ratio) was captured using curvefits constructed within the algorithm utilizing NASA polynomials and Cantera. A thermally perfect expansion tube solver was developed based on these algorithms and validated against analytical solution. Also developed along the thermally perfect algorithms were equilibrium algorithms. These use the same vectorized approach as thermally perfect algorithm, but the thermodynamic curvefits are, or course three-dimensional. Equilibrium MoC subroutines were used to develop expansion tube and detonation-driven shock tube algorithms. The results due to these models were validated against theory and experimental data available in the literature.

The final set of algorithms simulate unsteady, inviscid, quasi-one-dimensional flow gases in thermochemical nonequilibrium. These algorithms are based on the vectorized IMoC approach developed earlier in this work. Previously developed in-house chemistry solver was modified to use Park's two-temperature model for evaluating finite-rate chemistry. While there is no (such) restriction on the chemistry solver, vibrational relaxation is limited to diatomic gases currently. Vibrational relaxation considers both vibration-translation and vibration-vibration exchanges. Validation studies carried out with these subroutines include steady-state nozzle flowfield with vibrational, thermochemical relaxation and an expansion tube flowfield. Comparison of thermochemical nonequilibrium MoC results with state-to-state and computational fluid dynamics results in the literature show that the MoC models can reliably estimate the relevant nonequilibrium phenomena.