Heat exchanger capacity for one or more heat exchangers associated with a power gearbox of a turbofan engine
A turbofan engine having one or more heat exchangers tied to a power gearbox is provided. The power gearbox mechanically couples a low pressure spool and a fan of the turbofan engine. The one or more heat exchangers have a heat exchanger capacity defined by a resultant heat transfer surface area density associated with the one or more heat exchangers multiplied by a heat conductance factor that relates a power gearbox heat load, a fan power consumption function, a fan diameter of the fan, and a bypass ratio of the turbofan engine. The heat exchanger capacity is between 0.77 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 13,000 m 2 /m 3 .
1. A turbofan engine, comprising:
a low pressure spool;
a fan;
a power gearbox mechanically coupling the low pressure spool and the fan; and
one or more heat exchangers tied to the power gearbox, the one or more heat exchangers having a heat exchanger capacity defined by a resultant heat transfer surface area density associated with the one or more heat exchangers multiplied by a heat conductance factor that relates a power gearbox heat load, a fan power consumption function, a fan diameter of the fan, and a bypass ratio of the turbofan engine, and
wherein the heat exchanger capacity is between 0.77 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 13,000 m 2 /m 3 .
2. The turbofan engine of claim 1 , wherein the resultant heat transfer surface area density is determined by taking a product to an Nth root, wherein the product is determined by multiplying together a heat transfer surface area density associated with each of the one or more heat exchangers tied to the power gearbox together, wherein N is a number of heat exchangers tied to the power gearbox.
3. The turbofan engine of claim 2 , wherein the one or more heat exchangers each have one or more exchanger units each having a core defining a plurality of channels.
4. The turbofan engine of claim 3 , wherein the heat transfer surface area density for a given one of the one or more heat exchangers is defined as a quotient determined by dividing a heat exchanger channel surface area associated with the plurality of channels of the given one of the one or more heat exchangers to a heat exchanger channel volume associated with the plurality of channels of the given one of the one or more heat exchangers.
5. The turbofan engine of claim 2 , wherein the heat transfer surface area density for a given one of the one or more heat exchangers is determined by one or more characteristics associated with a control volume defined by a core of the given one of the one or more heat exchangers.
6. The turbofan engine of claim 1 , wherein the heat conductance factor is defined as a product determined by multiplying a first quotient by a second quotient, the first quotient being determined by dividing the power gearbox heat load by the fan power consumption function, the second quotient being determined by dividing the fan diameter of the fan by the bypass ratio of the turbofan engine,
wherein the power gearbox heat load is defined as a product determined by multiplying a maximum continuous thrust associated with the turbofan engine by one minus a power gearbox efficiency of the power gearbox and by a maximum continuous cruise speed associated with the turbofan engine, and
wherein the fan power consumption function is defined as a product determined by multiplying a fan thrust function by a maximum cruise speed associated with the turbofan engine.
7. The turbofan engine of claim 6 , wherein the power gearbox efficiency is between 95 and 99.8.
8. The turbofan engine of claim 6 , wherein the fan thrust function is defined as a product determined by multiplying an air density of air at 11,000 m above sea level by a fan tip speed of the fan, squared, by a fan area of the fan, wherein the fan area is defined as a quotient determined by dividing a product by four,
wherein the product is determined by multiplying pi by the fan diameter of the fan, squared, and
wherein the fan tip speed of the fan is defined as a product determined by multiplying pi by the fan diameter of the fan by a quotient, the quotient being determined by dividing a rotational speed of the low pressure spool by a gear ratio of the power gearbox.
9. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 38.6 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 6,000 m 2 /m 3 and 13,000 m 2 /m 3 .
10. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 0.77 and 137.62 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 6,000 m 2 /m 3 .
11. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 51.46 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 10,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 6,000 m 2 /m 3 and 13,000 m 2 /m 3 .
12. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 38.6 and 111.49 for a rotational speed of the low pressure spool between 10,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 6,000 m 2 /m 3 and 13,000 m 2 /m 3 .
13. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 1.03 and 137.62 for a rotational speed of the low pressure spool between 2,000 and 10,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 6,000 m 2 /m 3 .
14. The turbofan engine of claim 1 , wherein the heat exchanger capacity is between 0.77 and 51.46 for a rotational speed of the low pressure spool between 10,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 6,000 m 2 /m 3 .
15. A method, comprising:
operating a turbofan engine having a low pressure spool, a fan, a power gearbox mechanically coupling the low pressure spool and the fan, and one or more heat exchangers tied to the power gearbox, and
wherein the one or more heat exchangers have a heat exchanger capacity defined by a resultant heat transfer surface area density associated with the one or more heat exchangers multiplied by a heat conductance factor that relates a power gearbox heat load associated with the one or more heat exchangers, a fan power consumption function of the fan, a fan diameter of the fan, and a bypass ratio of the turbofan engine, and
wherein the heat exchanger capacity is between 0.77 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 13,000 m 2 /m 3 .
16. The method of claim 15 , wherein the resultant heat transfer surface area density is determined by taking a product to an Nth root, wherein the product is determined by multiplying together a heat transfer surface area density associated with each of the one or more heat exchangers tied to the power gearbox, wherein N is a number of heat exchangers tied to the power gearbox, the heat transfer surface area density for a given one of the one or more heat exchangers is defined as a quotient determined by dividing a heat exchanger channel surface area associated with a plurality of channels of the given one of the one or more heat exchangers to a heat exchanger channel volume associated with the plurality of channels of the given one of the one or more heat exchangers, and
wherein the heat conductance factor is defined as a product determined by multiplying a first quotient by a second quotient, the first quotient being determined by dividing the power gearbox heat load by the fan power consumption function, the second quotient being determined by dividing the fan diameter by the bypass ratio of the turbofan engine.
17. The method of claim 16 , wherein the heat transfer surface area density for a given one of the one or more heat exchangers is determined based at least in part on one or more characteristics associated with a control volume defined by a core of the given one of the one or more heat exchangers.
18. The method of claim 15 , wherein the heat exchanger capacity is between 38.6 and 298.17 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 6,000 m 2 /m 3 and 13,000 m 2 /m 3 .
19. The method of claim 15 , wherein the heat exchanger capacity is between 0.77 and 137.62 for a rotational speed of the low pressure spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 6,000 m 2 /m 3 .
20. A cooling system for a turbofan engine, comprising:
one or more heat exchangers tied to a power gearbox mechanically coupling a fan with a spool of the turbofan engine, the one or more heat exchangers having a heat exchanger capacity defined by a resultant heat transfer surface area density associated with the one or more heat exchangers multiplied by a heat conductance factor that relates a power gearbox heat load of the one or more heat exchangers, a fan power consumption function associated with the fan, a fan diameter of the fan, and a bypass ratio of the turbofan engine, and
wherein the heat exchanger capacity is between 0.77 and 298.17 for a rotational speed of the spool between 2,000 and 16,000 revolutions per minute at one hundred percent capacity and a resultant heat transfer surface area density being between 3,000 m 2 /m 3 and 13,000 m 2 /m 3 .