Vibrational Energy Accommodation Research Articles

Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition

In hypersonic shock tunnel experiments, the high-temperature reservoir gas expands and accelerates so rapidly that there is not enough time for vibrational energy relaxation. As a result, thermal nonequilibrium gas flow is frequently encountered in the test section, and this significantly affects the measured heat flux. In this paper, hypersonic compression-ramp flows are studied numerically to investigate the effect of incomplete vibrational energy accommodation on the separation flow structure and peak heat flux in the reattachment region under low-to-medium Reynolds number and high Mach number conditions. Numerical results and theoretical analysis suggest that the vibrational energy accommodation has no noticeable impact on the length scale of the separation zone, but strongly influences the peak heat flux of the separated ramp flows. Decomposing the peak heat flux into translational–rotational energy and vibrational energy components, qtr and qv, respectively, we find that qv/qtr characterizes the nonequilibrium degree of the vibrational energy accommodation. A formula for predicting the peak heat flux is then proposed, taking the effect of incomplete vibrational energy accommodation into consideration. Finally, surface heat flux measurements in a hypersonic shock tunnel indicate that a deviation of up to 13% in total peak heat flux could arise if vibrational energy accommodation is not considered under the vibrationally excited free-stream condition.

Particle Modeling of Reflected Shock Waves

A direct simulation Monte Carlo based approach is proposed to model the planar shock-wave reflection in a shock tube. The approach is validated through comparisons with available time-dependent pressure and absorbance measurements of gas relaxation behind a reflected shock in an argon–oxygen gas mixture for incident shock velocities of . It is then used to model reacting airflows for velocities , with the primary focus on the flow evolution inside the boundary layer. The feasibility of using the reflected shock configuration for the evaluation of vibrational energy accommodation, as well as the gas-phase recombination reaction rate constants, is studied. Finally, low- and high- fidelity real gas effect models are used to assess the model impact on gas macroparameters under nonequilibrium conditions.

Theoretical modeling of heat transfer to flat plate under vibrational excitation freestream conditions

In the hypersonic shock tunnel experiment, the high temperature reservoir gas expands so drastically that the vibrational energy of the gas is frozen at a high level in the test section, which could significantly affect the aero-heating measurement and ground-to-flight extrapolation. In this paper, theoretical modeling and direct simulation Monte Carlo methods are employed to study the effects of vibrational accommodation incompleteness on heat transfer to a flat plate under vibrational excitation freestream conditions. The microscopic process of the energy transfer by the gas molecule-surface collision is analyzed, and a criterion is introduced to characterize the nonequilibrium degree of the vibrational energy accommodation. Based on this criterion, an analytical formula is derived for prediction of the heat transfer performance, and its reasonability and effectiveness are also shown by the numerical results. It is found that the heat flux reduction could be as high as 18% compared to the vibrational equilibrium or complete accommodation cases. A further discussion of the heat flux measurement by coaxial thermocouple shows that a measurement deviation up to 62% could be induced by the difference between the sensor and test model’s material properties.

Influence of Molecular Vibrational Energy Accommodation Modeling on Cone Surface Heat FLUX at Mach 10

Influence of Molecular Vibrational Energy Accommodation Modeling on Cone Surface Heat FLUX at Mach 10

Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments

Recent numerical simulations of hypersonic double-cone experiments overpredict the heat-transfer rate to the model by about 20%. We present a systematic analysis of the experimental facility and the physical modeling to explainthisdiscrepancy.Nozzlee owe eldsimulationsareusedtoinvestigatetheeffectofvibrationalnonequilibrium in the test section. These simulations show that the vibrational modes of the nitrogen gas freeze near the nozzle throatconditions, resulting inanelevated vibrationaltemperatureinthetestsection. Thislowersthekineticenergy e ux, reducing the heat transfer to the model. The effect of slip boundary conditions is also studied, and it is shown that weak accommodation of vibrational energy at the surface further reduces the heat-transfer rate to the model. The combination of these two effects brings the predicted heat-transfer rate into agreement with the experiments. In addition, weak e ow nonuniformity in the test section is shown to slightly modify the predicted separation zone, further improving the agreement.

Modeling of Infrared Radiation in a Space Transportation System Environment

An approach for modeling the infrared (IR) glow radiation about the space shuttle at low-Earth-orbit flight altitudes is examined. The study builds on the modeling and numerical techniques developed for understanding the visible glow of the Atmospheric Explorer. Because of the rarefied nature of the flow, a direct simulation Monte Carlo method is used. The study extends the earlier gas-phase reaction model to include NO vibrational-state-specific formation using cross sections derived from quasi-classical trajectory calculations. IR spectra are computed using the state-specific NO vibrational levels and an accurate line-by-line spectral model. The effect of internal and translational energy accommodation coefficients in the Maxwell gas-surface interaction model was studied. The translational energy accommodation coefficient affects the width of the NO overtone transition (Δν= 2) spectral peak, and a value less than unity is required to give good agreement between modeling and experiment. The vibrational energy accommodation coefficient significantly impacts the magnitude of the NO infrared spectra. The influence of surface reactions on the IR spectra was also examined and shown to be small. Finally, simulated spectra are compared with IR data obtained from shuttle space flight experiments. The comparison shows that the postulated gas and gas-surface phase models used in particle simulation enable one to predict quantitatively IR spectra at high altitudes.

Numerical investigation of thermal and chemical nonequilibrium flows past slender blunted cones

A steady laminar axisymmetric flow of viscous, heat conducting, nonequilibrium, partially dissociated, and ionized air past a thin slender sphere-cone is considered. The flowfield characteristics with the interplay between reactions and vibrational relaxation taken into account are investigated. An adiabatic dissociation model accounting for both nonequilibrium excitation of vibrational modes and equilibrium excitation of rotational modes of the air molecules is used to calculate thermal nonequilibrium dissociation rate constants. In the case of thermal equilibrium, the model yields a good agreement of dissociation constants with experimental data widely used in hypersonic calculations. The combined effect of the multicomponent diffusion with real binary diffusion coefficients on the heat transfer rates has been evaluated. Quantitative assessments of the influence of thermal nonequilibrium on the flow parameters have been obtained at various freestream conditions. The influence of the body surface activity with respect to accommodation of vibrational energy on the heat transfer rate has been evaluated.

Some further extensions of the Cercignani–Lampis gas–surface interaction model

A recent paper has described extensions of the Cercignani–Lampis scattering kernel to cover (i) diffuse scattering with partial accommodation of translational kinetic energy and (ii) accommodation of vibrational energy of a diatomic molecule modelled as a rigid rotor/harmonic oscillator. The models are here further extended to cover the cases of partially diffuse scattering and of the anharmonic oscillator model of molecular vibration. The new models, like the old, satisfy detailed balance or reciprocity, thereby ensuring the preservation of an equilibrium distribution, and can be conveniently implemented in direct simulation Monte Carlo calculations. The results of some calculations are presented.

Some extensions to the Cercignani–Lampis gas–surface scattering kernel

The Cercignani–Lampis gas–surface scattering kernel is extended to include two important cases not covered by the basic model. These are (a) diffuse scattering with partial energy accommodation, and (b) accommodation of vibrational energy of a diatomic molecule with equally spaced energy levels. Both extensions are easily implemented in direct simulation Monte Carlo (DSMC) calculations. The results of some test calculations are presented.

Vibrational energy transfer at a liquid gallium surface. Activation of unimolecular cyclobutene isomerization

Abstract : Single collision vibrational energy transfer for a canonical ensemble (T=300K) of cyclobutene molecules at a heated liquid gallium surface has been studied from 450K to 700K. Transport above the reaction threshold for iosmerization to butadiene (E sub o = 32.4 kcal/mole) was used as the criterion for efficiency of vibrational energy accommodation. The efficiency was found to fall below strong collider behavior above 625K. Evidence of surface catalysis became important below 525K. The observed behavior is reminiscent of that found previously for other liquid (Sn) and solid (Au) metal surfaces.

Study of vibrational energy transfer at a liquid tin surface

Abstract : Single collision vibrational energy transfer for a canonical ensemble (T=300K) of cyclobutene molecules at a liquid tin surface was studied at temperatures from 500K to 775K. Transport above the reaction threshold for isomerization to butadiene was used as the criterion for efficiency of vibrational energy accommodation. The surface was found to function as a strong collider below 550 K. Experiments both above and below the freezing point revealed no discontinuity in the vibrational accommodation efficiency.

Low-level vibrational relaxation in single gas-surface encounters. Molecular structure, surface, and temperature effects

Direct measurement of the vibrational temperatures attained by different gases after single encounters with hot silica or platinum surfaces at T_S have been obtained by modulated-beam mass spectrometry. Vibrational energy accommodation coefficients a, for n-butane, n-octane, and 1-chlorobutane are smaller than one over both surfaces, slightly increase with molecular size or polarity, and are nearly independent of T_S between 350 and 700 K. Relaxation is more efficient on platinum.

Trajectory studies of vibrational energy transfer in gas–surface collisions

We have applied the stochastic trajectory method to the scattering of NO from the (001) surface of an LiF crystal. The surface was represented by a 32 atom primary zone and the effects of the rest of the surface atoms were included using the Generalized Langevin Equation method. The forces between the surface atoms were treated using a shell model and the gas–surface interactions included short-range repulsions, attractive dispersion forces, and the interaction of the dipole moment of NO and the surface ions. The dependence of the dipole moment and the dependence of the molecular polarizability on the internuclear separation of NO were also included. The calculated vibrational energy accommodation coefficient was less than 1% when trapping of the gas diatom was negligible. By modifying the vibrational frequency of the scattered diatom we have examined the dependence of vibrational energy transfer on frequency. An exponential dependence on the ratio of the molecular frequency to the surface Debye frequency was found, similar to behavior observed for vibrational relaxation in condensed phases. We have also examined the relative efficiency of the coupling of the vibrational mode to the translational and rotational modes of the gas diatom and to the phonon modes of the surface. We found that the vibrational mode is most strongly coupled to the surface phonons with a much weaker coupling to the rotational and translational modes.

Direct evidence of inefficient vibrational energy transfer in gas-surface collisions

Vibrational energy equilibration between n-octane and hot seasoned silica surfaces at T, has been studied at low pressures (≤10^-4) torr) by modulated beam mass spectrometry in the range 350 ≤ T_S ≤ 800 K. The sensitive temperature dependence of the dissociative ionization of n-octane at 15 eV was used to monitor the temperatures attained by the gas after undergoing a few nonreactive collisions with the surface. In this system, the low-lying vibrational levels of n-octane, whose relative populations account for the mass spectral changes, never reach T_S in a single collision: the vibrational energy accommodation coefficient has a value of 0.66 at 350 K and decreases with temperature.

Energy accommodation coefficients of internally excited molecules

A method for determining partial energy accommodation coefficients is described. Laser radiation is used to excite absorbing molecules in the gas phase, which subsequently strike a solid surface depositing energy. This energy transfer is monitored by observing the temperature rise of the solid. Measurement of this temperature rise as a function of gas pressure is used to determine the vibrational energy accommodation coefficient. This method is applied to the interaction of CH3F, SF6, methanol, and cyclopropane with a seasoned molybdenum surface. Values of the vibrational energy accommodation coefficient are found to correlate well with the heat of vaporization of the absorbing molecule.

Single-collision gas-surface vibrational energy transfer in a reacting system

Abstract : Gas-surface vibrational energy accommodation in a reactive system has been studied under single collision conditions. The reaction system is the isomerization of cyclobutene to 1,3-butadiene. Both seasoned pyrex and silica surfaces were used over the temperature ranges 400-775 K and 500-975 K, respectively. Strong collider behavior was observed below about 425 K. The vibrational energy accommodation coefficient was found to decrease with rise of temperature from about 1.0 to 0.2, while the relative collisional efficiency Beta sub 1 declined from about 1.0 to 0.008. A stochastic model was used to fit the data. (Author)

Vibrational Energy Exchange between Diatomic Molecules and a Surface

The problem of the steady-state vibrational energy distribution of diatomic molecules that temporarily reside on a surface during exposure to a molecular beam is examined according to the rate equations proposed by Klemperer and Herschbach. It is shown that it is possible to obtain explicitly the steady-state vibrational energy distribution for different vibrational energy distributions in the incident beam and that the vibrational energy accommodation coefficient suitably defined is of a very simple form.