Engineering topics
Publications and source records attributed to Hansen, C. Frederick.
Rate coefficients for ionization produced in collision of N and O atoms and the reverse dissociative recombination of NO(+) and electrons is redeveloped so as to provide the specific rate dependence on translational, vibrational, and free-electron temperatures. At equilibrium, the results compare favorably with experimental data over a wide range of temperature.
Most of the important chemical reactions which occur in the very high temperature air produced around space vehicles as they enter the atmosphere were investigated both experimentally and theoretically, to some extent at least. One remaining reaction about which little is known, and which could be quite important at the extremely high temperatures that will be produced by the class of space vehicles now contemplated - such as the AOTV - is the excitation of bound electron states due to collisions between heavy gas particles. Rates of electronic excitation due to free electron collisions are known to be very rapid, but because these collisions quickly equilibrate the free and bound electron energy, the approach to full equilibrium with the heavy particle kinetic energy will depend primarily on the much slower process of bound electron excitation in heavy particle collisions and the subsequent rapid transfer to free electron energy. This may be the dominant mechanism leading to full equilibrium in the gas once the dissociation process has depleted the molecular states so the transfer between molecular vibrational energy and free electron energy is no longer available as a channel for equilibration of free electron and heavy particle kinetic energies. Two mechanisms seem probable in electronic excitation by heavy particle impact. One of these is the collision excitation and deexcitation of higher electronic states which are Rydberg like. A report, entitled 'Semi-Classical Theory of Electronic Excitation Rates', was submitted previously. This presented analytic expressions for the transition probabilities, assuming that the interaction potential is an exponential repulsion with a perturbation ripple due to the dipole-induced dipole effect in the case of neutral-neutral collisions, and to the ion-dipole interaction in the case of ion-neutral collisions. However the above may be, there is little doubt that excitation of ground state species by collision occurs at the point where the initial and final potentials cross, or at least come very close. Therefore, this mechanism would be applicable to the case where a gas is initially at very low temperature suddenly subjected to high energy heavy particle bombardment. This situation would model the measurement of excitation cross section by molecular beam techniques, for example. The purpose is to report values of cross sections and rate coefficients for collision excitation of ground state atoms estimated with the Landau-Zener transition theory and to compare results with measurement of excitation cross sections for a beam of Hydrogen atoms impacting Argon atom targets. Some very dubious approximations are used, and the comparison with measurement is found less than ideal, but results are at least consistent within order of magnitude. The same model is then applied to the case of N-N atom collisions, even though the approximations then become even more doubtful. Still the rate coefficients obtained are at least plausible in both magnitude and functional form, and as far as I am aware these are the only estimates available for such rate coefficients.
Space vehicles flying through the atmosphere at high speed are known to excite a complex set of chemical reactions in the atmospheric gases, ranging from simple vibrational excitation to dissociation, atom exchange, electronic excitation, ionization, and charge exchange. Simple arguments are developed for the temperature dependence of the reactions leading to ionization of NO, including the effect of vibrational electronic thermal nonequilibrium. NO ionization is the most important source of electrons at intermediate temperatures and at higher temperatures provides the trigger electrons that ionize atoms. Based on these arguments, recommendations are made for formulae which fit observed experimental results, and which include a dependence on both a heavy particle temperature and different vibration electron temperatures. In addition, these expressions will presumably provide the most reliable extrapolation of experimental results to much higher temperatures.
Vibrational relaxation of N2 molecules is considered at temperatures up to 40,000 K in gas mixtures that contain electrons as well as heavy collision partners. The theory of vibrational relaxation due to N2-N2 collisions is fit to experimental data to 10,000 K by choice of the shape of the intermolecular potential and size of the collision cross section. These values are then used to extrapolate the theory to 40,000 K.
The Landau-Zener theory of reactive cross sections was applied to diatomic molecules dissociating from a ladder of vibrational states. The result predicts a dissociation rate that is quite well duplicated by an Arrhenius function having a preexponential temperature dependence of about T(sub -1/2), at least for inert collision partners. This relation fits experimental data reasonably well. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators, the results are about the same as given by Hammerling, Kivel, and Teare in their analytic approximation for harmonic oscillators, though at very high temperature a correction for the partition function limit is included. The empirical correction for vibration nonequilibrium proposed by Park, which is a convenient algorithm for CFD calculations, is modified to prevent a drastic underestimation of dissociation rates that occurs with this method when vibrational temperature is much smaller than the kinetic temperature of the gas.
Approximate analytic solutions for properties of equilibrium air up to 15,000 K have been programmed for machine computation. Temperature, compressibility, enthalpy, specific heats, and speed of sound are tabulated as constant entropy functions of temperature. The reciprocal of acoustic impedance and its integral with respect to pressure are also given for the purpose of evaluating the Riemann constants for one-dimensional, isentropic flow.
The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.
Solutions are presented for the conduction of beat through a semi-infinite gas medium having a uniform initial temperature and a constant boundary temperature. The coefficients of thermal conductivity and diffusivity are treated as variables, and the solutions are extended to the case of air at temperatures where oxygen dissociation occurs. These solutions are used together with shock-tube measurements to evaluate the integral of thermal conductivity for air as a function of temperature.
The thermodynamic and transport properties of high-temperature air are found in closed form starting from approximate partition functions for the major components in air and neglecting all minor components. The compressibility, enthalpy, entropy, the specific heats, the speed of sound, the coefficients of viscosity and of thermal conductivity, and the Prandtl numbers for air are tabulated from 500 degrees to 15,000 degrees Kelvin over a range of pressure from 0.0001 to 100 atmospheres. The energy of air and the mol. fractions of the major components of air can be found from the tabulated values for compressibility and enthalpy. It is predicted that the Prandtl number for fully ionized air, which is in complete equilibrium, will become small compared to unity, the order of 0.01, and this implies that boundary layers in such flow will be very transparent to heat flux.