Method for mapping contrail formation to engine performance characteristics

A computer system including a processor having memory storing instruction, which when executed by the processor, controls the computer system to perform operations to generate contrail formation and persistence maps by evaluating the minimum humidity required for formation and persistence over the engine operating envelope of a given aircraft engine, the operations comprising:

• determining engine performance model parameters of the aircraft engine at desired operating conditions with zero humidity;
• determining a contrail engine efficiency parameter (noverall_λ);
• determining an improved Schmidt-Appleman equation (Gλ) based on the contrail engine efficiency parameter (noverall_λ);
• determining an improved mixing line slope based on the contrail engine efficiency parameter (noverall_λ) and the improved Schmidt-Appleman equation (Gλ);
• determining a tangency temperature value at which the slope of a first saturation limit with respect to water vs temperature is the same as the improved mixing line slope;
• determining a first partial pressure of water value at the tangency temperature based on the improved Schmidt-Appleman mixing line slope;
• determining a second partial pressure of water value at a second saturation limit with respect to water at the tangency temperature;
• determining a difference (Δ) between the second partial pressure of water and the first partial pressure of water value;
• determining a third partial pressure of water at a third saturation limit with respect to water at the ambient temperature;
• determining a minimum relative humidity for a contrail to form as a first ratio of the difference (Δ) with respect to water;
• determine a fourth saturation limit with respect to ice at the ambient temperature;
• determining a minimum relative humidity for the contrail to persist as a second ratio of the fourth saturation limit to the third saturation limit;
• determining the minimum relative humidity for the contrail to form and persist as the greater of the first ratio and the second ratio;
• and
• generating exhaust from the aircraft engine that produces the formation and persistence of the contrail based on the minimum relative humidity.

A computer system including a processor having memory storing instruction, which when executed by the processor, controls the computer system to perform operations of determining a minimum humidity necessary to form contrails by an engine of an aircraft, the operations comprising:

• determining engine performance model parameters of the engine at desired operating conditions;
• determining a contrail engine efficiency parameter (noverall_λ);
• determining an improved Schmidt-Appleman equation (Gλ) based on the contrail engine efficiency parameter (noverall_λ);
• determining an improved mixing line slope based on the contrail engine efficiency parameter (noverall_λ) and the improved Schmidt-Appleman equation (Gλ);
• determining a tangency temperature value at which the slope of a first saturation limit with respect to water vs temperature is the same as the improved mixing line slope;
• determining a partial pressure of water at the first saturation limit with respect to water at the tangency temperature;
• determining a first temperature at the partial pressure of water based on the improved mixing line slope;
• determining a minimum temperature margin with respect to dew point based on the temperature at the partial pressure and the tangency temperature value;
• determining the minimum humidity necessary to form contrails by the engine based on the minimum temperature margin with respect to the dew point;
• and
• generating exhaust from the aircraft engine that produces the formation and persistence of the contrail based on the minimum humidity.