Dilution of aircraft exhaust plumes at cruise altitudes
Introduction
Aircraft cruising in the upper troposphere or lower stratosphere may impact the ozone concentration and the climatic state of the atmosphere by gaseous or particulate emissions causing a plume of exhaust species behind the aircraft (Schumann, 1994, Schumann, 1997; Friedl, 1997). The impact depends on the rate of mixing of the emitted species between the plume and the ambient air. This is the case, in particular, if several simultaneously emitted species interact with each other, such as hydroxyl radicals with nitrogen and sulphuric oxides (Kärcher et al., 1996), hydroxyl radicals, oxygen radicals, soot and sulphuric gases (Arnold et al., 1994; Brown et al., 1996), and heat, water vapour, and particles causing contrails (Schumann, 1996a).
The mixing process proceeds differently in the early jet regime (Miake-Lye et al., 1993; Kärcher and Fabian, 1994), the vortex regime (Anderson et al., 1996; Schilling et al., 1996), the vortex-breakup regime (Lewellen and Lewellen, 1996; Gerz and Ehret, 1997), and the final atmospheric dispersion regime (Schumann et al., 1995; Dürbeck and Gerz, 1996). For consistent impact analysis one needs to know the mixing rate from the engine combuster until the plume concentration reaches the natural level of concentration fluctuations in the ambient air. For modern large subsonic aircraft, the regimes typically extend to plume ages of 10 s, 100 s, 3 min, and 3 h, for the jet, vortex, break-up, and dispersion regimes, respectively (Schumann et al., 1995; Gerz and Ehret, 1997).
The details of the mixing process are complex and result in a three-dimensional and time-dependent exhaust plume field. However, the plume properties may be approximated, e.g. in a box model (Karol et al., 1997), in terms of the bulk mean properties of the plume. The dilution ratio N as used in this study, measures the amount of air mass with which the exhaust resulting from a unit mass of burned fuel mixes per unit flight distance within the bulk of the plume. Alternatively, one may define a dilution factor d measuring the bulk plume concentration relative to the concentration at the engine exit. This value depends, however, on the air/fuel ratio within the engine and on the split of air streams in core and bypass ducts of the turbofan engines (see, e.g., Schumann, 1995).
This paper deduces the dilution ratio N for a set of previous measurements. The data include measurements of conservative tracers such as carbon dioxide (CO2) and the sum of all odd nitrogen oxides (NOy), but also data of less conservative tracers, such as reactive nitrogen oxides (NOx, sum of NO and NO2), and sulphur dioxide (SO2).
Section snippets
Plume dilution relationships
The increase in the mass specific concentration of an inert passive tracer in the plume above its ambient concentration is Δci=mi/mplume for any exhaust species i. It depends on the mass of exhaust per unit flight distance mi and the mass of plume gases mplume per unit distance over which the exhaust gets dispersed within the plume. The mass of exhaust equals the mass of fuel burned per flight distance times the emission index of species i, mi=mfuelEIi. The dilution ratio is defined by
Measured dilution ratio values
The dilution ratio N can be determined from measured concentration, temperature, and plume diameter values using the above relationships. Table 1 collects data of such measurements from previous experiments. The data originate from various sources:
(1) CO2 from Schulte and Schlager (1996)(in ppmv=μmol mol-1 ): The data given in Table 1 (No. 1.1–1.6) are the peak CO2 concentration increases as measured with a differential non-dispersive infrared instrument in-situ in the plumes of various mid-sized
Discussion
Fig. 1 compiles data from more than 70 plume encounters with the DLR research aircraft Falcon and the NASA aircraft ER-2. The in-situ concentration measured depends on the flight path of the measuring aircraft relative to the plume axis and the temporal resolution of the instrument. Hence, the measurements give only a rough estimate of the bulk mean concentration. In most cases, the measuring aircraft will have missed the peak concentration positions. This may cause a possibly large
Conclusions
The dilution of aircraft exhaust has been analysed from measurements in more than 70 plume encounters for plume ages of milliseconds to 95 min. It is found that the bulk dilution ratio for a wide range of conditions can be approximated by Eq. (6)within a factor of about 3. The concentration on the plume axis stays about constant until 0.02 s, and then approaches the bulk mean after about 0.3 s, with details depending on engine and flight conditions. Future measurements should try to extend the
Acknowledgements
The authors are grateful for support by the Deutsche Forschungsgemeinschaft (Schwerpunkt-programm: “Grundlagen der Auswirkungen der Luft- und Raumfahrt auf die Atmosphäre”), the German “Bundesministerium für Bildung, Wissenschaft, Forschung und echnologie (BMBF)” (project “Schadstoffe in der Luftfahrt”) and the Commission of the European Union (projects AERO-NOX, POLINAT, and POLINAT-2).
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Max-Planck-Institut für Kernphysik, Atmospheric Physics Division, 69117 Heidelberg, Germany.
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DLR, Institut für Optoelektronik, Oberpfaffenhofen, 82230 Wessling, Germany.
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Fraunhofer Gesellschaft, Institut für Atmosphärische Umweltforschung, Garmisch-Partenkirchen; now at University of Bayreuth, BITOEK Klimatologie, 95440 Bayreuth, Germany.