Overlay Method for Calculating Excited State Species Properties in Hypersonic Flows

Abstract

In many hypersonicows, the excited states of some chemical species are the dominant radiators. Often, those electronically excited particles are present in small concentrations and the chemical kinetics mechanisms for their formation are very complicated and costly to implement in a fully coupled computationaluid dynamics method. An ef® cient computational method is presented for the calculation of chemical species present in trace amounts, including excited state species. The usefulness of this overlay method is demonstrated with several examples: OH(A) formation from water vaporin a hypersonicshocklayer, state-speci® cCO vibrational relaxation and CO( a) formation in a rocket motor nozzle, and CO( a) kinetics in an expandingow. The overlay calculations allow a careful sensitivity analysis of the kinetics modeling and permit comparison with radiance data obtained inight. HEREhas been a general interest within the hypersonics com- munity to study optical emissions from chemically reacting ¯ ows in nonequilibrium. Such radiation can be measured in both ground-based andight experiments with well-established instru- mentation techniques. These measurements provide data to validate the modeling of species concentrations and temperatures in hyper- sonicows. The approach commonly used today to model thespectral radiant intensity for differentow conditions is to ® rst obtain a solution to the conservation equations for species concentrations and tempera- tures as a function of their location in theow. An important aspect of theow modeling is that the chemical kinetics model applies to the ground-state species only. Then a separate radiation model uses theowsolutiontocomputethespectralradianceateachpointinthe ¯ ow. The radiation model generally consists of two parts: computa- tion of the excited state species concentrations and the line-by-line spectral distribution of the radiation. Usually, the ® rst part of the model has the greater degree of uncertainty. To calculate the excited state populations, one typically assumes a master set of rate equations for populating the excited state levels. For the calculation of radiation in the ultraviolet to visible spectral region, these equations represent the distribution of excited states in the atomic or molecular vibrational, rotational, and electronic lev- els. When the collision rate is suf® ciently high, it is also assumed thattheexcitedstatepopulationdistributionisthequasi-steady-state (QSS) solution of the master set of equations. This condition occurs if two criteria are met. First, the time constants for the population excitation equations must be fast compared with the average gas ¯ ow residence time. Second, the production and destruction rates are closely balanced. 1 The QSS condition has been found to hold for the population of the electronic states of NO for stagnation re- gionows for 10-cm-radius spheres at a speed of 5 km/s and up to altitudes of 80 km (Ref. 2). However, there are other situations where it is expected to fail. The second assumption usually made in the solution of the mas- ter equations for the excited state populations is that the primary creation mechanism is by electron or neutral collisions with the ground-state species. As theow density decreases, collisions be- tween two ground-state species that directly produce the excited state species become important. These chemiluminescent reactions are known to be potentially important for the two cases that we present here. The addition of excited state mechanisms to the reaction set in- creases the computational cost of theow solution. In rare® ed con- ditions, many reaction paths are possible and must be included. Often the rate constants and branching ratios are not well known. Forthese reasons,multiplecomputationsareoften required toquan- tify the sensitivityof theinclusionorexclusion ofspeci® cprocesses and the uncertainty in the rate constants. Hence, an ef® cient computational method is required to calculate the electronically excited states in both compressed and expanding ¯ ows. A method is presented, based on the key assumption that the excited electronic state species concentrations are suf® ciently small such that they are trace species compared with the bulkow. Then, anexamplecalculationoftheconcentrationofelectronicallyexcited hydroxylradicals, OH( A),in a stagnation regionowisconsidered. This calculation can be compared directly with the conventional, uncoupled approach. This comparison provides the validation of the method. The second example corresponds to the calculation of the excited stateCO(a)populationinanexpandingowfromasolidrocketmo- tor.Thisproblemcannotbesolvedintheuncoupledmannerbecause the long lifetime of the CO( a) state and the low collision frequency in the expandingowmake the use ofthe QSSapproximation ques- tionable. The large number of reactions and processes that need to beconsideredwillillustratethe ef® ciency and usefulnessof thepro-