Physical fundamentals of contrail formation the Schmidt-Appleman criterion and the role of particles

Transcription

1 Physical fundamentals of contrail formation the Schmidt-Appleman criterion and the role of particles Klaus Gierens, DLR Oberpfaffenhofen

2 Motivation Schumann et al., 2000

3 Contents Derivation of the Schmidt-Appleman criterion in terms of water vapour and enthalpy budgets The role of particles Contrails from biofuels

4 Simple explanation Contrail formation is like breathing on cold air; the condensation that becomes visible is due to isobaric mixing of two air masses of different temperature and different moisture content. Mixing of air masses can lead to condensation because the saturation pressure of water vapour decreases almost exponentially with decreasing temperature. Isobaric mixing thus can end up in a supersaturated state even if none of the two mixed air masses was saturated before. This mixing trajectory and the saturation pressure curves of water vapour are displayed in a Schmidt-Appleman diagram. Isobaric mixing is represented by a straight line in such a diagram (pressure vs. temperature). t

5 Schmidt-Appleman diagram Isobaric mixing i of hot exhaust gases of high absolute humidity with cold ambient air of low absolute humidity. Schmidt (1941), Appleman (1953), Schumann (1996)

6 Derivation of the Schmidt-Appleman theory in terms of engine mass and enthalpy flows (1)

7 Derivation of the Schmidt-Appleman theory (2): Water mass budget

8 Derivation of the Schmidt-Appleman theory (3): Overall propulsion efficiency i

9 Derivation of the Schmidt-Appleman theory (4): Conservation of momentum

10 Derivation of the Schmidt-Appleman theory (5): Conservation of energy

11 Derivation of the Schmidt-Appleman theory (6): Enthalpy budget

12 Derivation of the Schmidt-Appleman theory (7) Slope factor

13 The role of particles Note that particles are not even mentioned in the Schmidt- Appleman theory. However, particles are necessary for droplet and crystal formation as nucleation centres. How does this fit together? Without any particles, neither in the air nor in the exhaust, the SAC would not work at all, because then nucleation would need several 100% of supersaturation ti to commence. If soot were perfect ice nuclei, ice saturation would probably suffice instead of water saturation for contrail formation. Sulfuric acid covered soot is bad ice nuclei, but there are plenty of these particles such that contrail formation is never constrained by lack of nucleation sites. Therefore particles need not to be mentioned in the SAC.

14 Contrail properties depend on particle emission, contrail formation does not results of AAFEX campaigns and calculations l by Kärcher and Yu, 2009 ice crys stal numb ber concentration n soot emission index by number Fischer-Tropsch blends Kerosene

15 Conclusion Dynamic and thermodynamic aspects of contrail formation are very good understood, as these follow straightforward from basic physical conservation principles of mass, momentum and energy. Microphysical details of contrail formation are less well understood, for instance what excactly happens on soot surfaces, how many soot particles contribute to ice formation, etc. However, initial number of ice crystals is known up to a factor of 2-3. Contrail formation and persistence conditions are fairly well known. Contrail and contrail cirrus properties depend on initial conditions at formation and on many other ambient parameters. Large variability.