Coupled Two-Dimensional Computer Analysis of CW Chemical Mixing Lasers

Abstract

The advantages of utilizing chemical reactions to support laser emission have been recognized for several years. However, a central problem identified in a variety of cw chemical mixing lasers is the dominance of gas-dynamics on the character of the flowing active medium, pointing to the need for a theoretical model that couples the effects of fluid mechanics of mixing with the nonequilibrium kinetics and the cascade of vibrational-rotational laser transitions. As one of the efforts to meet this need, a two-dimensional, rate equation model has been developed. A detailed discussion of the computer model is presented, as well as sample calculations for a representative "cold reaction" HF laser. Comparisons are made with experiment where appropriate. Nomenclature C k= mass fraction of species k c p = specific heat at constant pressure D k = laminar diffusion coefficient for species k A£y = activation energy for reaction j E r = rotational-state energy-specific total enthalpy including heats of formation h k = specific enthalpy of species k A/i k = heat of formation for species k AHj = heat of reaction for reaction j k = Boltzmann's constant, chemical rate coefficient, thermal conductivity K =V-TorV-V rate coefficient L = active optical path length Le -Lewis number = (D k + e d )/(/c + K) m -velocity ratio between primary and secondary m -mass flow rate m k -mass of one molecule of species k M -Mach number n -density ratio between primary and secondary n k *= number density of species k n v = number density of emitter molecules in vibrational state v n v>J -number density of emitter molecules in vibrational state v and rotational state J p = pressure p 0 = total pressure •p, -Prandtl number = c p (n + e)/(/c + /c) q = volumetric rate of heat addition to the gas mixture g rad = volumetric rate of radiative energy emission g rot = rotational partition function R = specific gas constant t R v , v +1 = matrix element for the radiative transition v +1 -> v r^r 2 = reflectivities of left and right mirrors i -time T = static temperaturePresented as Paper 74-224 at the AIAA 12th Aerospace Sciences = total temperature u = velocity in x (flow) direction <w> = average relative velocity between molecules v -velocity in z (transverse) direction w k = mass rate of production of species k per unit volume W v = intracavity flux (sum of right and left running fluxes) for the radiative transition v +1 -»t; Xi -dummy symbol for chemical species i x = coordinate in flow direction z = coordinate transverse to flow in optical direction OL P = pressure-broadened half width OD = Doppler-broadened half width oiij, a-j = stoichiometric coefficients for species i in reaction ; e = eddy viscositŷ d = eddy diffusion coefficient r\ = efficiency K = eddy thermal conductivity /z = coefficient of viscosity v = frequency of emitted radiation £ = line shape parameter = oi p (ln2) ll2 /tx D p = gas density a = specific power (f > = line shape factor