Accurate Contrail Simulation In the Jet and Vortex Phases by Combining Space- and Time-Developing Paradigms

Accurate simulation of contrail formation requires to capture the crucial nucleation of ice crystals in the jet phase and their evolution through the vortex phase. During these phases, the dynamics are largely dominated by the engine exhaust jets and the aircraft wake vortices, with turbulent fluctuations that drive the mixing of the hot gases with ambient air. The mixing influences the history of the thermodynamic quantities seen by all ice crystals and may therefore affect their final number concentration and size distribution after the demise of the aircraft wake.
 
A challenge in the simulation of spatially developing aircraft plumes lies in their extremely high aspect ratios, with a length of up to hundreds of kilometers and a cross-sectional dimension of hundreds of meters at most. To bring the computational expenses within a reasonable range, it is customary to simulate the jet and vortex phases separately. The former can be done in a space-developing paradigm. In contrast, the latter usually exploits a space-time analogy to limit the extent of the computational domain, allowing the plume to be aged in a time-developing manner. As a potential limitation of such a segregated approach, the initial condition of the vortex simulations often involves arbitrary assumptions on the velocity field and on the particle distribution. We propose to reconcile the two approaches using a technique to carefully transfer information between space- and time-developing paradigms while maintaining consistency in the momentum balance and particle distributions.
 
This study relies on Large Eddy Simulation performed with the Vortex Particle-Mesh method augmented with a simple ice microphysics model that tracks Lagrangian ice tracers and accounts for condensational growth and sublimation. We present the method itself together with the technique to transform space-developing results into a time-developing initial condition. We then consider a notional twin-engine aircraft with regular Jet fuel. The plume is first simulated in a space-developing manner in a domain of 100 wingspans in length. This case, considered the reference, is compared to time-developing simulations with various initial conditions, using either the presented technique or arbitrary assumptions. We assess the variability in ice crystal properties at the end of the vortex phase from these time-developing simulations and discuss the possible implications for the propagation of uncertainty into the contrail diffusion and dispersion phases.