Granted Patent B2

US 12,644,409 · App. 18/339,286 · Granted Jun 2, 2026

Inventor: Russell Stratton (Toronto, CA)

Assignee: PRATT & WHITNEY CANADA CORP.

F02C3/30G01W1/08F05D2270/083

Abstract

Claims (54)

1 . 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 required for formation and persistence of contrails produced by an engine of an aircraft, the operations comprising:

determining engine performance model parameters of the engine at desired operating conditions with zero humidity;

determining additional energy flow out of the engine;

determining an exhaust plume temperature scaling factor;

determining a contrail engine efficiency parameter (noverall_λ) based on additional energy flow out of the engine and the exhaust plume temperature scaling factor;

generating an improved Schmidt-Appleman equation (Gλ) based on the contrail engine efficiency parameter (noverall_λ);

determining an improved mixing line slope based on the improved Schmidt-Appleman equation (Gλ); and

determining the minimum humidity required for formation and persistence of contrails produced by the engine based on the improved mixing line slope;

controlling the engine to output exhaust that produces the formation and persistence of the contrails according to the improved mixing line slope.

2 . The computer system of claim 1 , wherein the engine performance model parameters include a residual fuel energy in the aircraft engine.

3 . The computer system of claim 2 , wherein the controller determines the residual fuel energy in the aircraft engine based on the contrail engine efficiency parameter (noverall_λ).

4 . The computer system of claim 3 , wherein the exhaust plume temperature scaling factor is 0.5.

5 . The computer system of claim 4 , wherein the additional energy flow includes power extraction and bleed offtakes used by an aircraft air management system and an electrical system of the aircraft.

6 . 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.

7 . The computer system of claim 6 , wherein the engine performance model parameters include a residual fuel energy in the aircraft engine.

8 . The computer system of claim 7 , wherein the controller determines the residual fuel energy in the aircraft engine based on the contrail engine efficiency parameter (noverall_λ).

9 . The computer system of claim 8 , wherein the exhaust plume temperature scaling factor is 0.5.

10 . The computer system of claim 9 , wherein the additional energy flow includes power extraction and bleed offtakes used by an aircraft air management system and an electrical system of the aircraft.

11 . The computer system of claim 10 , wherein determining the first partial pressure of water value is based on the improved Schmidt-Appleman mixing line slope starting from an ambient temperature and zero humidity.

12 . The computer system of claim 11 , wherein determining the difference (Δ) is set to zero when the difference (Δ) is negative.

13 . The computer system of claim 6 , wherein the processor computes the tangency temperature value is analytically.

14 . The computer system m of claim 6 , wherein the processor computes the tangency temperature value is numerically.

15 . 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.

16 . The computer system 15 , wherein determining the temperature at the partial pressure of water includes determining the temperature at the partial pressure of water starting from the desired operating conditions.

17 . The computer system 16 , wherein the contrail engine efficiency parameter (noverall_λ) comprises:

determining an exhaust plume temperature scaling factor that scales a kinetic energy of the engine by a factor 0.5; and

applying the exhaust plume temperature scaling factor to the contrail engine efficiency parameter (noverall_λ).

18 . The computer system 16 , wherein the minimum temperature margin with respect to dew point is a difference between the temperature at the partial pressure and the tangency temperature.

19 . The computer system of claim 15 , wherein the processor computes the tangency temperature value analytically.

20 . The computer system of claim 15 , wherein the processor computes the tangency temperature value is numerically.

Assignments (1)

Continuity (1)

References Cited (26)