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CN111176329B - Formation flight mixing performance function construction method based on wind tunnel test data - Google Patents

Formation flight mixing performance function construction method based on wind tunnel test data Download PDF

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CN111176329B
CN111176329B CN202010087855.8A CN202010087855A CN111176329B CN 111176329 B CN111176329 B CN 111176329B CN 202010087855 A CN202010087855 A CN 202010087855A CN 111176329 B CN111176329 B CN 111176329B
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performance function
wind tunnel
formation
mixing performance
formation flight
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陶洋
杜钰锋
吴军强
赵忠良
熊能
林俊
马上
王晓冰
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
    • G—PHYSICS
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Abstract

The invention discloses a formation flight mixing performance function construction method based on wind tunnel test data. The method comprises the following steps: (1) acquiring pneumatic force and moment parameters of a rear machine in different formation flying forms of the formation through wind tunnel tests or numerical calculation; (2) selecting a prior function to establish a mixed function model; (3) solving a mixed function weight vector by using a least square method; (4) acquiring a hybrid performance function based on prior aerodynamic moment in the formation flight process; (5) and estimating the position of the aerodynamic extreme value by utilizing the position of the extreme value of the mixing performance function. The formation flight mixing performance function construction method based on wind tunnel test data predicts the minimum resistance position of the rear aircraft during the flight of the dual-aircraft formation by using the experimental data obtained by developing the dual-aircraft formation flight test in the high-speed wind tunnel and combining the mixing performance function, can guide flight practice, and has the advantages of high reliability and good economy.

Description

Formation flight mixing performance function construction method based on wind tunnel test data
Technical Field
The invention belongs to the field of airplane formation flight research, and particularly relates to a formation flight mixed performance function construction method based on wind tunnel test data.
Background
The lift-increasing drag reduction is a constant pursuit target of fluid mechanics researchers and aircraft designers, and meanwhile, the drag reduction is consistent with the current pursuit of flight targets such as green environmental protection, fuel economy and the like. Drag directly affects the aircraft's load capacity and fuel carrying capacity, thereby affecting aircraft performance and economy. For example, for a U.S. C-5 aircraft, a reduction in the drag coefficient of 0.0001 (one unit of drag) would increase the C-5 aircraft payload by 454 kilograms. Over the course of over 70 years, the performance of the latest aircraft based on the existing layout (e.g. a380 for airbus or B787 for boeing) has improved considerably, with great progress being made both in terms of increasing aerodynamic efficiency and in terms of reducing fuel consumption. From another perspective, it is a great challenge to reduce each resistance unit based on the existing profile without substantial breakthrough.
Bionic is one of the directions of scientific progress, American journal of nature issues research results on the formation flying of the distant migrations of the goose down, and researches show that the energy can be saved by 11-14% by adopting the formation flying mode, and meanwhile, the goose down flying in the formation can fly for a longer distance than the goose down flying alone.
Similar to bird flight, a pair of counter-rotating wake vortexes also appear at the wingtips of the aircraft during flight. The wake vortexes of aircraft have long been known to adversely affect the aircraft itself and the aircraft following it. In fact, the aircraft wake vortex can wash up the airflow in a certain area behind the aircraft, and researchers have started the research on the aerodynamic characteristics of aircraft formation flying by means of bird long-distance migration, and introduced a concept of vortex surfing (SurfingAircraft Vortices for Energy). The concept involves two or more aircraft flying in formation, with the effect of significantly reducing drag.
In the actual formation flying process, the position with the minimum resistance needs to be searched to realize the optimal formation shape so as to save energy consumption, and the flight distance is increased.
Disclosure of Invention
The invention aims to provide a formation flight mixing performance function construction method based on wind tunnel test data.
The invention discloses a formation flight mixing performance function construction method based on wind tunnel test data, which comprises the following steps of:
a. a double-machine formation flight test is developed in a high-speed wind tunnel, a front machine is fixed in the test process, the relative flow direction position, the relative spread direction position and the vertical relative position of the rear machine and the front machine are changed, the resistance, the rolling moment, the pitching moment and the yawing moment of the rear machine are measured, and D (X), P (P) and D (X) are obtained1(X)、P2(X) and P3(X) matrix, wherein D (X) is a resistance matrix, P1(X) is the roll moment matrix, P2(X) is the pitching moment matrix, P3(X) is a yaw moment matrix, and X is the relative position of the rear machine; by D (X) to obtain DminRelative position X ofmin；
b. Defining a discrete set P ═ P1(X)T,P2(X)T,P3(X)T]TMixing performance function
B＝wP (1)
In the formula, w ∈ RmIs a weight vector;
c. determining optimal weight vectors by solving the following generalized least squares problem
Figure BDA0002382637320000021
Minimizing the error between D (X) and B:
Figure BDA0002382637320000022
in the formula, V is a nonsingular weight vector;
d. by passing
Figure BDA0002382637320000023
To obtain
Figure BDA0002382637320000024
Computing
Figure BDA0002382637320000025
Minimum value of
Figure BDA0002382637320000026
To obtain
Figure BDA0002382637320000027
Relative position X ofBmin；
e.△X＝|Xmin-XBminIf the delta X is less than or equal to 10 percent L (L is the span length of the rear wing), the calculation is finished; otherwise, changing the non-singular weight vector of the V, and repeating the step c and the step d until the required data is obtained to finish the calculation.
Further, V is an identity matrix.
The method for constructing the formation flight mixed performance function based on the wind tunnel test data is suitable for the condition that the target performance function cannot be measured in real time (such as an extremum search control system).
The formation flight mixing performance function construction method based on wind tunnel test data approximates a pre-measured or estimated target performance function by combining related parameters which can be measured in real time, and completes the combination of the related parameters by using a weight vector obtained by a least square optimization method to form a mixing performance function which can better approximate the target performance function.
The formation flight mixing performance function construction method based on wind tunnel test data utilizes a weighted least square method to linearly combine related parameters which can be measured in real time to form a mixing performance function to approximate a target performance function, and the approximation degree of the extreme value of the mixing performance function to the extreme value of the target performance function is far superior to that of other independent related parameters.
The formation flight mixing performance function construction method based on wind tunnel test data adopts a prior weight method, namely, the optimal weight vector obtained by pre-calculation is utilized to carry out linear combination on the measured related parameters to construct a mixing performance function.
The formation flight mixing performance function construction method based on wind tunnel test data predicts the minimum resistance position of the rear aircraft during the flight of the dual-aircraft formation by using the experimental data obtained by developing the dual-aircraft formation flight test in the high-speed wind tunnel and combining the mixing performance function, can guide flight practice, and has the advantages of high reliability and good economy.
Drawings
FIG. 1 is a flow chart of a method for constructing a formation flight mixing performance function based on wind tunnel test data according to the present invention;
FIG. 2 is a relative position diagram of the minimum value of the mixing performance function obtained by the method for constructing the formation flight mixing performance function based on wind tunnel test data and the minimum value of the post-aircraft resistance obtained by wind tunnel test measurement.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
The formation flight mixing performance function construction method based on wind tunnel test data of the embodiment carries out validity check through a double-machine formation flight test carried out in the FL-26 wind tunnel.
Test data obtained by the FL-26 wind tunnel dual-machine formation flight test comprise resistance, lift force, lateral force, rolling moment, pitching moment and yawing moment of rear machines under different formation forms (different relative flow direction relative positions, different spreading direction relative positions and different vertical relative positions).
As shown in fig. 1, the method for constructing a formation flight mixing performance function based on wind tunnel test data in this embodiment includes the following steps:
a. the double-machine formation flight test is developed in a high-speed wind tunnel, the front machine is fixed in the test process, the relative position of the flow direction, the relative position of the spread direction and the vertical direction of the rear machine and the front machine are changed, the resistance, the rolling moment, the pitching moment and the yawing moment of the rear machine are measured,obtaining D (X), P1(X)、P2(X) and P3(X) matrix, wherein D (X) is a resistance matrix, P1(X) is the roll moment matrix, P2(X) is the pitching moment matrix, P3(X) is a yaw moment matrix, and X is the relative position of the rear machine; by D (X) to obtain DminRelative position X ofmin；
b. Defining a discrete set P ═ P1(X)T,P2(X)T,P3(X)T]TMixing performance function
B＝wP (3)
In the formula, w ∈ RmIs a weight vector;
c. determining optimal weight vectors by solving the following generalized least squares problem
Figure BDA0002382637320000031
Minimizing the error between D (X) and B:
Figure BDA0002382637320000032
in the formula, V is a nonsingular weight vector; taking V as I, the weight vector of the linear mixing function based on the three directional moments is:
Figure BDA0002382637320000033
d. by passing
Figure BDA0002382637320000034
To obtain
Figure BDA0002382637320000035
Computing
Figure BDA0002382637320000036
Minimum value of
Figure BDA0002382637320000037
To obtain
Figure BDA0002382637320000038
Relative position X ofBminDrawing a contour diagram 2, wherein o in FIG. 2 is XBminD obtained for wind tunnel testminRelative position X ofmin；
e.△X＝|Xmin-XBminL | ═ 7% L (L is the rear wing span length)
As can be seen from FIG. 2, the formation flight mixing performance function construction method based on wind tunnel test data can well approach the optimal position of the drag reduction effect, and the obtained result can guide the dual-locomotive formation flight.

Claims (2)

1. A formation flight mixing performance function construction method based on wind tunnel test data is characterized by comprising the following steps:
a. a double-machine formation flight test is developed in a high-speed wind tunnel, a front machine is fixed in the test process, the relative flow direction position, the relative spread direction position and the vertical relative position of the rear machine and the front machine are changed, the resistance, the rolling moment, the pitching moment and the yawing moment of the rear machine are measured, and D (X), P (P) and D (X) are obtained1(X)、P2(X) and P3(X) matrix, wherein D (X) is a resistance matrix, P1(X) is the roll moment matrix, P2(X) is the pitching moment matrix, P3(X) is a yaw moment matrix, and X is the relative position of the rear machine; by D (X) to obtain DminRelative position X ofmin；
b. Defining a discrete set P ═ P1(X)T,P2(X)T,P3(X)T]TMixing performance function
B＝wP (1)
In the formula, w ∈ RmIs a weight vector;
c. determining optimal weight vectors by solving the following generalized least squares problem
Figure FDA0002595984220000016
Minimizing the error between D (X) and B:
Figure FDA0002595984220000011
in the formula, V is a nonsingular weight vector;
d. by passing
Figure FDA0002595984220000012
To obtain
Figure FDA0002595984220000013
Computing
Figure FDA0002595984220000014
Minimum value of
Figure FDA0002595984220000017
To obtain
Figure FDA0002595984220000015
Relative position X ofBmin；
e.ΔX＝|Xmin-XBminIf the delta X is less than or equal to 10 percent L and L is the span length of the rear wing, the calculation is finished; otherwise, changing the non-singular weight vector of the V, and repeating the step c and the step d until the required data is obtained to finish the calculation.
2. The method for constructing a formation flight mixing performance function based on wind tunnel test data according to claim 1, wherein V is an identity matrix.
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CN111506114B (en) * 2020-05-25 2021-05-04 北京理工大学 Aircraft formation control method
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