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Carbon dioxide vibrational relaxation times and O and N rotational collision numbers at high temperatures measured ultrasonically
The Ti(3+)-doped Al2O3 has been recently demonstrated to be a tunable solid-state laser system with Ti(3+) as the laser-active ion. In this paper, the kinetics of vibrational transitions in the 2E(g)E(3/2) electronic state of Ti(3+):Al2O3a (crucial for characterizing new host materials for the Ti ion) was investigated. A 527-nm 5-ps pulse was used to excite a band of higher vibrational levels of the 2E(g)E(3/2) state, and the subsequent growth of population in the zero vibrational level and lower vibrational levels was monitored by a 3.9-micron picosecond probe pulse. The time evolution curve in the excited 2E(g)E(3/2) state at room temperature was found to be characterized by a sharp rise followed by a long decay, the long lifetime decay reflecting the depopulation of the zero and the lower vibrational levels of the 2E(g)E(3/2) state via radiative transitions. An upper limit of 3.5 ps was estimated for intra-2E(g)E(3/2)-state vibrational relaxation time.
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New N2 vibrational temperature data, obtained in expanding N2 and air using the electron beam technique, are analyzed permitting the vibrational relaxation times to be determined as a function of temperature. In addition, the effects on N2 vibrational relaxation times of direct vibrational energy transfer between N2 and H2O, between N2 and O2, and between N2 and free electrons introduced from arc contaminants are analyzed. The vibrational relaxation times determined from the present measurements agree with those measured in the expanding flows of shock tunnels and impact tubes. These expanding data also agree with relaxation times observed in acoustical resonant cavities where alternating compressions and expansions take place. The relaxation times in expanding flows (vib-tran exchange process) are found to be approximately 50 times faster than those measured in the compressing flow of shock tubes (tran-vib exchange process). This evidence strongly supports the concept that one relaxation time distribution cannot be applied to both exchange processes.
An approach to estimate the effective vibrational relaxation time for polyatomic molecules under the context of two-temperature thermochecmial state model is proposed. Landau-Teller vibrational relaxation equation is used as a basis, and vibrational energies are estimated with partition energy functions assuming harmonic oscillator model. A special weighting procedure is presented, and effective vibrational relaxation time is derived. A series of numerical experiments with CO2 and NH3 mixtures is performed, and the aeroheating results are presented. The results of CO2 environment simulations are compared with the vibrational relaxation model of Park et al. [JTHT, 8(1994), pp. 9–23]. The simulations are also conducted with a modified Landau-Teller expression.
Correlation of nitrogen vibrational-translational relaxation times for various measuring methods, noting temperature distribution of rate
Dissociational rate constants and vibrational relaxation times modifications, considering coupling of vibrational and dissociational nonequilibrium of expanding gas in nozzle
High speed flowing gas system provides uniform mixing in short times compared to flow transit times and carbon dioxide vibrational relaxation times. This system minimizes the effects of surrounding surfaces and provides a uniformly high gain that is independent of dimensions transverse to the flow direction.
Dissociational rate constants and vibrational relaxation times modifications, considering coupling of vibrational and dissociational nonequilibrium of expanding gas in nozzle
A new model is proposed for the computation of vibrational nonequilibrium in the direct simulation Monte Carlo method (DSMC). This model permits level to level vibrational transitions for the first time in a Monte Carlo flowfield simulation. The model follows the Landau-Teller theory for a harmonic oscillator in which the rates of transition are related to an experimental correlation for the vibrational relaxation time. The usual method for simulating such processes in the DSMC technique applies a constant exchange probability to each collision and the vibrational energy is treated as a continuum. A comparison of these two methods is made for the flow of nitrogen over a wedge. Significant differences exist for the vibrational temperatures computed. These arise as a consequence of the incorrect application of a constant exchange probability in the old method. It is found that the numerical performances of the two vibrational relaxation models are equal.
Thermal disturbance radiative decay time in carbon dioxide at low pressures and for nonzero vibrational relaxation times
Results are reported for an investigation into the methods by which energy transfer is calculated in the Direct Simulation Monte Carlo method. Description is made of a recently developed energy exchange model that deals with the translational and rotational modes. A new model for simulating the transfer of energy between the translational and vibrational modes is also explained. This model allows the vibrational relaxation time to follow the temperature dependence predicted by the Landau-Teller theory at moderate temperatures. For temperatures in excess of about 8000K the vibrational model is extended to include an empirical result for the relaxation time. The effect of introducing these temperature dependent collision numbers into the DSMC technique is assessed by making calculations representative of the stagnation streamline of a hypersonic space vehicle. Both thermal and chemical nonequilibrium effects are included while the flow conditions have been chosen such that ionization and radiation may be neglected. The introduction of these new models is found to significantly affect the degree of thermal nonequilibrium observed in the flowfield. Larger, and more widely ranging, differences in the results obtained with the different energy exchange probabilities are found when a significant amount of internal energy is included in the calculation of chemical nonequilibrium.
Study of the vibrational relaxation characteristics of shock-heated CO2 using a tuned CO2 laser absorption technique. Absorption-coefficient histories were obtained for a single rotational state in each of the -10 0- and -02 0- levels over the temperature range from 500 to 2000 K, and for 21 rotational states of the -10 0- level at 1000 K. These histories have been combined with translational-rotational temperature histories based on interferometer measurements to calculate vibrational relaxation times for the bending mode. The results verify the mutual equilibrium of the bending and symmetric-stretch modes due to Fermi resonance. The bending mode relaxation times are approximately 10% shorter than predicted from interferometer results using the ratio of specific heats. Furthermore, relaxation times based on measurements of different rotational states at 1000 K show a variation with quantum number J, indicating a possible rotational nonequilibrium during the vibration relaxation process.
A new model is proposed for energy transfer between the vibrational and translational modes for use in the direct simulation Monte Carlo method (DSMC). The model modifies the Landau-Teller theory for a harmonic oscillator and the rate transition is related to an experimental correlation for the vibrational relaxation time. Assessment of the model is made with respect to three different computations: relaxation in a heat bath, a one-dimensional shock wave, and hypersonic flow over a two-dimensional wedge. These studies verify that the model achieves detailed balance, and excellent agreement with experimental data is obtained in the shock wave calculation. The wedge flow computation reveals that the usual phenomenological method for simulating vibrational nonequilibrium in the DSMC technique predicts much higher vibrational temperatures in the wake region.
Vibrational relaxation times in pure O and in O with methane impurity determined with acoustic absorption measurements
Comparisons between experimental and theoretical values of the thermal conductivity for a series of nonpolar polyatomic gases show large discrepancies at higher temperatures where the vibrational contribution becomes increasingly important. Examination of various theoretical approaches indicates that the discrepancies can be attributed to approximating the coefficient characterizing the diffusion of vibrational energy, D sub vib, by the self-diffusion coefficient. The present theories cannot accurately predict D sub vib, and its measurement is extremely difficult. Consequently, the approach adopted by the author is to obtain D sub vib by using experimental values of the thermal conductivity. An attempt is made to correlate these values of D sub vib with vibrational relaxation time, so that values of D sub vib can be obtained for all nonpolar polyatomic gases.
Best current expressions for the vibrational relaxation times of oxygen and nitrogen in the atmosphere are used to compute total absorption. The resulting graphs of total absorption as a function of frequency for different humidities should be used in lieu of the graph published earlier by Evans et al (1972).
In this study numerical solutions have been obtained for two-dimensional axisymmetric hypersonic nonequilibrium CO2 flow over a high angle blunt cone with appropriate surface boundary conditions to account for energy and mass conservation at the body surface. The flowfield is described by the Navier-Stokes equations and multicomponent conservation laws which account for both translational and internal vibrational nonequilibrium effects. Complete forebody solutions have been obtained for the peak heating point of the Mars entry trajectory specified in the proposed NASA MESUR (Mars Environmental Survey) project. In these solutions, radiative equilibrium wall temperature and surface heating distributions are determined over the MESUR aeroshell forebody for entry velocity equal to 7 km/sec with varying degrees of surface catalysis. The effects of gas kinetics, surface catalysis, transport properties, and vibrational relaxation times on the surface heating are examined. The results identify some important issues in the prediction of surface heating for flows in thermochemical nonequilibrium and show that the Navier-Stokes code used herein is effective for thermal protection system design and materials selection.