CN113705117B - Optimized analysis method for flight performance of hypersonic cruise aircraft - Google Patents
Optimized analysis method for flight performance of hypersonic cruise aircraft Download PDFInfo
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Abstract
The application belongs to the field of flight mechanics of hypersonic cruise aircrafts, and particularly relates to a method for optimizing and analyzing flight performance of a hypersonic cruise aircraft. The method comprises the following steps: determining a flight performance measurement index, wherein the flight performance measurement index is the ratio of the total mass of an airplane at the takeoff time to the mass of the airplane except fuel; constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of the airplane and a second balance equation of engine thrust and aerodynamic resistance; and step three, determining a first constraint condition of the hypersonic cruise of the airplane and a second constraint condition of rocket boosting, and solving the optimal speed of the hypersonic cruise. The optimization analysis method for the flight performance of the hypersonic cruise aircraft can achieve optimization calculation of optimal cruise of the rocket-powered hypersonic cruise aircraft, can quickly obtain rules of optimal cruise speed and flight distance, and improves the speed of scheme convergence of the rocket-powered hypersonic cruise aircraft.
Description
Technical Field
The application belongs to the field of flight mechanics of hypersonic cruise aircrafts, and particularly relates to a method for optimizing and analyzing flight performance of a hypersonic cruise aircraft.
Background
Rocket-powered hypersonic cruise flight is the fusion of aviation and aerospace technologies. On the one hand, its speed is between that of the aircraft and that of the remote missile; on the other hand, the actual way of obtaining the hypersonic cruising speed by rocket power is the same as that of a ballistic missile by means of rocket boosting, and the method of using the aerodynamic lift force to balance the weight force for hypersonic flight is the same as that of an airplane. As a transportation route, flying has 3 elements: quality, distance and time of transport. Given the distance of flight, the time of flight depends on the speed, which is usually obtained and maintained at the expense of fuel consumption. For ballistic missiles, from the potential energy point of view, the rocket is accelerated near the earth surface, so that the rocket jet is left at the place with low gravitational potential energy, the consumed fuel is minimum, and therefore, the booster rocket mainly works in an active section, about 100km from the ground to the height, and depends on inertial motion in the long middle section of flight. In contrast to ballistic missiles, aircraft fuel is used more to overcome air drag during flight.
The fuel use of hypersonic flight is between that of an airplane and a ballistic missile, the necessary fuel consumption needs to be obtained and maintained at the hypersonic cruise speed, and how to realize better hypersonic flight performance is a difficult problem of current research.
Accordingly, a technical solution is desired to overcome or at least alleviate at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The application aims to provide a hypersonic cruise aircraft flight performance optimization analysis method to solve at least one problem in the prior art.
The technical scheme of the application is as follows:
a hypersonic cruise aircraft flight performance optimization analysis method comprises the following steps:
determining a flight performance measurement index, wherein the flight performance measurement index is the ratio of the total mass of an airplane at the takeoff time to the mass of the airplane except fuel;
constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of the airplane and a second balance equation of engine thrust and aerodynamic resistance;
and step three, determining a first constraint condition of the hypersonic cruise of the airplane and a second constraint condition of rocket boosting, and solving the optimal speed of the hypersonic cruise.
In at least one embodiment of the present application, the first step specifically includes:
total mass of aircraft at takeoff time:
wherein, the first and the second end of the pipe are connected with each other,
as total mass of the aircraft, M p For payload quality, M f As mass of fuel, M e Other aircraft masses besides payload and fuel;
will M p And M e Merging:
to be provided with
As a measure of flight performance.
In at least one embodiment of the present application, step two specifically includes:
constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of an airplane:
constructing a second balance equation of the engine thrust and the aerodynamic drag of the hypersonic cruising flight of the airplane:
F jet ＝F D ＝F L /C L/D
wherein, F L For aerodynamic lift, M f，c Mass of fuel consumed for cruising, F jet As engine thrust, F D For aerodynamic drag, C L/D Is the lift-drag ratio of cruising flight.
In at least one embodiment of the present application, step three specifically includes:
when the cruise engine specific impulse Ic is constant, the engine thrust is proportional to the fuel flow:
and substituting the first balance equation and the above formula into the second balance equation to obtain:
suppose that
Keeping the cruise time constant, integrating the two ends of the formula, and keeping the cruise time delta t constant during the cruise process c ＝t c，2 -t c，1 At cruise start time, the fuel mass is
Cruise end time spent fuel M f，c (t c，2 ) When the value is 0, then:
will cruise time
Substituting the equation to obtain a first constraint equation:
wherein, L is the flight distance, Lc is the cruising flight distance, and Vc is the cruising speed;
for N-stage booster rockets, total mass initially launched
Mass from cruise start
There is the following relationship, i.e. the second constraint equation:
wherein, c R，i ＝I R，i Xg is the jet speed of the I-th rocket engine, I R，i To a corresponding specific impulse, α R，i Is the structural mass ratio of the i-th rocket, Δ v i For the ith stage rocketA speed increment supplied;
multiplying the two ends of the first constraint equation and the second constraint equation respectively by:
order to
The above formula is substituted into the above formula to obtain the optimal speed V of the hypersonic cruise c，o 。
In at least one embodiment of the present application, the velocity increment provided by the ith stage rocket is:
V r related to the mode of transmission;
if transmitting from the ground:
V r ＝V air +V g
V air additional velocity increment, V, required to overcome aerodynamic drag rockets during boost g An additional velocity increment is required to be provided for overcoming the gravity rocket in the boosting process;
if transmitting from the air:
V r ≈-V m
V m is the speed of the aircraft.
In at least one embodiment of the present application,
optimum speed V of hypersonic cruise under the condition of first-stage booster rocket c，o The relation of (A) is as follows:
optimum speed V for hypersonic cruise under the condition of two-stage booster rocket c，o Is onThe series formula is:
the invention has at least the following beneficial technical effects:
the optimization analysis method for the flight performance of the hypersonic cruise aircraft can achieve optimization calculation of optimal cruise of the rocket-powered hypersonic cruise aircraft, can quickly obtain rules of optimal cruise speed and flight distance, and improves the speed of scheme convergence of the rocket-powered hypersonic cruise aircraft.
Drawings
FIG. 1 is a variation rule of an optimal cruise speed and a flight distance under the condition that a first-stage rocket boosting and a second-stage rocket boosting are respectively adopted under the condition that a lift-drag ratio is 4 according to an embodiment of the application;
fig. 2 is a change rule of flight performance index and flight distance under the condition of respectively adopting first-stage rocket boosting and second-stage rocket boosting according to an embodiment of the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are a subset of the embodiments in the present application and not all embodiments in the present application. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
In the description of the present application, it is to be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience in describing the present application and for simplifying the description, and do not indicate or imply that the referenced device or element must have a particular orientation, be constructed in a particular orientation, and be operated, and therefore should not be construed as limiting the scope of the present application.
The present application is described in further detail below with reference to fig. 1-2.
The application provides a hypersonic cruise aircraft flight performance optimization analysis method, which comprises the following steps:
determining a flight performance measurement index, wherein the flight performance measurement index is the ratio of the total mass of an airplane at the takeoff time to the mass of the airplane except fuel;
constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of the airplane and a second balance equation of engine thrust and aerodynamic resistance;
and step three, determining a first constraint condition of the hypersonic cruise of the airplane and a second constraint condition of rocket boosting, and solving the optimal speed of the hypersonic cruise.
The hypersonic cruise aircraft flight performance optimization analysis method comprises the following steps of firstly, taking the ratio of the total mass of an aircraft at the takeoff time to the mass of the aircraft except fuel as a flight performance measurement index, and specifically comprising the following steps:
total mass of aircraft at takeoff time:
wherein the content of the first and second substances,
as total mass of the aircraft, M p For payload quality, M f As mass of fuel, M e Other aircraft masses besides payload and fuel;
M p and M e The division of (1) has certain arbitrariness, and the two can be combined to be regarded as generalized load;
will M p And M e Merging:
to be provided with
As a measure of flight performance.
The method for optimizing and analyzing the flight performance of the hypersonic cruise aircraft comprises the following steps of constructing two balance equations of hypersonic cruise flight of the aircraft, specifically:
the basic requirements of cruising flight are that the aerodynamic lift force is balanced with the gravity, and the thrust force of an engine is balanced with the aerodynamic resistance, namely:
constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of an airplane:
constructing a second balance equation of the engine thrust and the aerodynamic drag of the hypersonic cruising flight of the airplane:
F jet ＝F D ＝F L /C L/D (3)
wherein, F L For aerodynamic lift, M f，c Fuel mass consumed for cruising, F jet As engine thrust, F D For aerodynamic drag, C L/D The lift-drag ratio of cruising flight.
Further, the hypersonic cruise aircraft flight performance optimization analysis method determines a first constraint condition of the hypersonic cruise of the aircraft and a second constraint condition of rocket boosting, and comprises the following steps:
when the cruise engine specific impulse Ic is constant, the engine thrust is proportional to the fuel flow:
substituting the first balance equation (2) and the above equation (4) into the second balance equation (3) to obtain:
suppose that
Keeping the cruise time constant, integrating the two ends of the above formula (5) and keeping the cruise time delta t constant c ＝t c，2 -t c，1 At cruise start time, the fuel mass is
Cruise end time spent fuel M f，c (t c，2 ) When the value is 0, then:
will cruise time
Substituting equation (6) above yields a first constraint equation:
wherein L is the flight distance, Lc is the cruising flight distance, and Vc is the cruising speed;
rocket boosting is a realistic way to obtain hypersonic cruise speed.
For N-stage booster rockets, total mass initially launched
Mass from cruise start time
There is the following relationship, i.e. the second constraint equation:
wherein, c R，i ＝I R，i Xg is the jet speed of the I-th rocket engine, I R，i To a corresponding specific impulse, α R，i Is the structural mass ratio of the i-th rocket, Δ v i The velocity increment provided for the ith stage rocket.
Wherein, the speed increment provided by the ith stage rocket is as follows:
V r related to the mode of transmission;
if transmitting from the ground:
V r ＝V air +V g (10)
V air additional velocity increment, V, required to overcome aerodynamic drag rockets during boost g An additional speed increment is required to be provided for overcoming the gravity rocket in the boosting process;
if transmitting from the air:
V r ≈-V m (11)
V m is the speed of the aircraft.
Multiplying the first constraint equation (7) by the second constraint equation (8) at both ends respectively by:
order to
Substituting the formula (12) into the formula, simplifying and tidying to obtain the optimal speed V of the hypersonic cruise c，o 。
Optimum speed V of hypersonic cruise under the condition of first-stage booster rocket c，o The relation of (A) is as follows:
optimum speed V for hypersonic cruise under the condition of two-stage booster rocket c，o The relation of (A) is as follows:
high cruise optimum speed versus flight distance. From the equation (12), the optimal speed for high-speed cruising depends on the flight distance, the cruising lift-drag ratio and the specific impulse of the engine and the boosting rocket, and the specific impulse and the structural mass ratio of each stage.
In a preferred embodiment of the present application, assuming a 250s specific impulse for the first stage of boosted rockets, the second stage of boosted rockets, and hypersonic cruise powered rockets, the specific impulse is approximately 20% higher than for the first stage rockets operating at ground or low altitude, taking 290s for operation at high altitude. The structural mass ratio of the rocket is set to be 7 percent. V in hypersonic cruise flight if launched from the ground air And V g The sum is approximately at several hundred meters per second, and as an estimate, in this embodiment, 500m/s is taken.
In the case where a secondary booster rocket is required, assume:
Δv 1 ＝Δv 2 ＝(v c +v r )/2
if launched from the air, assume the speed with the aircraft is:
V m ＝270m/s
the cruise power adopts a rocket engine, the lift-drag ratio of an aircraft is generally reduced along with the increase of the flying speed, and under the condition of hypersonic speed, Kuchemann summarizes various flightsMaximum lift-drag ratio of device and Mach number (M) of incoming flow ∞ ) The following empirical formula is given for the relationship between:
C L/D，max ＝4(M ∞ +3)/M ∞
in this embodiment:
(1) optimum cruising speed V c，o The optimal cruising speed V under the condition of two-stage rocket power boosting is increased along with the increase of the flying distance under the same flying distance c，o Is higher than the optimal cruising speed V under the condition of power boosting of a first-stage rocket c，o ；
(2) When the flying distance is below 3000km, the booster rocket is one-stage or two-stage for the optimal cruising speed V c，o The influence of the speed is small, namely, the first-stage boosting rocket can economically obtain the optimal speed of super cruise; the flight distance exceeds 5000km, and a secondary boosting rocket is needed to be adopted for economically obtaining the optimal speed of super cruise;
(3) from flight performance indicators
When the flight distance is less than 3000km, the rocket-powered hypersonic cruise aircraft adopts a first-stage rocket to boost better, and when the flight distance is more than 3000km, the rocket-powered hypersonic cruise aircraft adopts a second-stage rocket to boost better.
The hypersonic cruise aircraft flight performance optimization analysis method can achieve optimization calculation of optimal cruise of the rocket-powered hypersonic cruise aircraft, can quickly obtain rules of optimal cruise speed and flight distance, the optimal speed of the hypersonic cruise depends on the flight distance, cruise lift-drag ratio and engine specific impulse, the number of stages of boosting rocket and the specific impulse and structural mass ratio of each stage, and the hypersonic cruise speed is selected according to the flight distance, the cruise lift-drag ratio, the engine performance, the performance of the boosting rocket and the like, so that fuel consumed in the whole flight process is minimum, and the speed of scheme convergence of the rocket-powered hypersonic cruise aircraft is improved.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (3)
1. A hypersonic cruise aircraft flight performance optimization analysis method is characterized by comprising the following steps:
the method comprises the following steps of determining a flight performance measurement index, wherein the flight performance measurement index is the ratio of the total mass of an airplane at the takeoff time to the mass of the airplane except fuel, and specifically comprises the following steps:
total mass of aircraft at takeoff time:
wherein the content of the first and second substances,
as total mass of the aircraft, M p For payload quality, M f As mass of fuel, M e Other aircraft masses besides payload and fuel;
will M p And M e Merging:
to be provided with
As a measure of flight performance;
step two, constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of the airplane and a second balance equation of engine thrust and aerodynamic resistance, and specifically comprising the following steps of:
constructing a first balance equation of aerodynamic lift and gravity of hypersonic cruising flight of an airplane:
constructing a second balance equation of the engine thrust and the aerodynamic drag of the hypersonic cruising flight of the airplane:
F jet ＝F D ＝F L /C L/D
wherein, F L For aerodynamic lift, M f,c Fuel mass consumed for cruising, F jet As engine thrust, F D For aerodynamic drag, C L/D The cruise flight lift-drag ratio;
determining a first constraint condition of the hypersonic cruise of the airplane and a second constraint condition of rocket boosting, and solving the optimal speed of the hypersonic cruise, wherein the method specifically comprises the following steps of:
when the cruise engine specific impulse Ic is constant, the engine thrust is proportional to the fuel flow:
and substituting the first balance equation and the above formula into the second balance equation to obtain:
suppose that
Keeping the cruise time constant, integrating the two ends of the formula, and keeping the cruise time delta t constant during the cruise process c ＝t c,2 -t c,1 At cruise start time, the fuel mass is
Cruise end time spent fuel M f,c (t c,2 ) When the value is 0, then:
will cruise time
Substituting the equation to obtain a first constraint equation:
wherein, L is the flight distance, Lc is the cruising flight distance, and Vc is the cruising speed;
for N-stage booster rockets, total mass initially launched
Mass from cruise start
There is the following relationship, i.e. the second constraint equation:
wherein, c R,i ＝I R,i Xg is the jet speed of the I-th rocket engine, I R,i To a corresponding specific impulse, α R,i Is the structural mass ratio of the i-th rocket, Δ v i A velocity increment provided for an ith stage rocket;
multiplying the two ends of the first constraint equation and the second constraint equation respectively by:
order to
The above formula is substituted into the above formula to obtain the optimal speed V of the hypersonic cruise c,o 。
2. The hypersonic cruise aircraft flight performance optimization analysis method of claim 1, characterized in that the velocity increment provided by the ith stage rocket is:
V r related to the mode of transmission;
if transmitting from the ground:
V r ＝V air +V g
V air additional velocity increment, V, required to overcome aerodynamic drag rockets during boost g An additional velocity increment is required to be provided for overcoming the gravity rocket in the boosting process;
if transmitting from the air:
V r ≈-V m
V m is the speed of the aircraft.
3. The hypersonic cruise aircraft flight performance optimization analysis method of claim 2,
optimum speed V of hypersonic cruise under the condition of first-stage booster rocket c，o The relation of (A) is as follows:
optimum speed V for hypersonic cruise under the condition of two-stage booster rocket c,o The relation of (A) is as follows:
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| CN107908109A (en) * | 2017-11-13 | 2018-04-13 | 浙江大学 | A kind of hypersonic aircraft reentry stage track optimizing controller based on orthogonal configuration optimization |
| CN111045447A (en) * | 2019-11-21 | 2020-04-21 | 浙江大学 | High-precision hypersonic aircraft trajectory optimization multi-scale optimal control system |
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Application publication date: 20211126 Assignee: Shenyang Aircraft Design Institute Yangzhou Collaborative Innovation Research Institute Co.,Ltd. Assignor: AVIC SHENYANG AIRCRAFT DESIGN & Research Institute Contract record no.: X2023990000057 Denomination of invention: An Optimal Analysis Method for Flight Performance of Hypersonic Cruise Aircraft Granted publication date: 20220920 License type: Common License Record date: 20230109 |