Prediction of Vibrational Relaxation in Hypersonic Expanding Flows Part 2: Results

This article examines the range of applicability and performance of the Landau-Teller vibrational relaxation model and a simplified anharmonic model in expanding flows. The simplified relaxation model allows both non- Boltzmann population distributions and includes anharmonic transition rates and energy transfer. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. The calculations are compared with experimental results obtained in nozzles. The predictions of the detailed master equation solver are in excellent agreement with experimental results. Although the simplified anharmonic model requires significantly less computational time than the master equation solver, it gives good agreement with the detailed solver and with experimental test results. tionally efficient than a detailed master equation solver, while maintaining reasonable accuracy over a wide range of con- ditions. In the present study calculations are performed with the simplified anharmonic model and with the Landau-Teller model. These results are compared with experimental data and with results obtained by solving the vibrational master equation. The vibrational relaxation processes of N2 and CO in cool- ing flows are studied. For the detailed calculations, a coupled set of vibrational master equations and quasi-one-dimensional fluid dynamic equations is solved. Vibration-translation (V- T) transition rates are computed from a modified version of the Schwartz, Slawsky, and Herzfeld2 (SSH) theory, and vi- bration-vibration (V-V) exchange rates are computed by con- sidering both long-range and short-range intermolecular forces. The transition rates are validated with available experimental data and other theoretical models. The reader is referred to a prior study by Ruffin3 for a detailed description of the quasi- one-dimensional solver and the transition rates. The quasi- one-dimensional solver is used to predict the steady-state flow in nozzles and to conduct idealized studies of vibrational re- laxation under isothermal conditions. The present computational schemes are compared with ex- perimental data obtained in expanding nozzles. Relaxation predictions are compared with the most reliable experimental results, which use direct measurement techniques for popu- lation distributions and have very low levels of impurities in the test gas. Anharmonic and harmonic oscillator predictions are also compared in external flows around a blunt re-entry vehicle. The present study also seeks to address three questions related to the simplified anharmonic model: 1) How accurate is the model compared to master equation solutions and experimental data? 2) What is its range of applicability ? 3) Is the computational requirement prohibitive for use in multidimensional flow codes? The accuracy of the model for a wide range of conditions in isothermal relaxations is studied in the next section. The range of applicability is also discussed later in that section. In the subsequent section the model is compared to experimental data and master equation solutions in nonisothermal gasdynamic flows. Both of the next two sections include assessments of the model's computational requirements.