CN116738889A - Rapid prediction method for near-field acoustic explosion of all-circumferential angle of supersonic civil aircraft - Google Patents
Rapid prediction method for near-field acoustic explosion of all-circumferential angle of supersonic civil aircraft Download PDFInfo
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Abstract
The invention provides a rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft, which comprises the following steps: solving an aircraft flow field by adopting a supersonic velocity surface element method to obtain pressure coefficient distribution of a sound explosion signal monitoring position line; converting the pressure coefficient distribution into linear overpressure signal distribution of the acoustic explosion signal monitoring position line by utilizing a conversion formula; nonlinear correction is carried out on the linear overpressure signal distribution by utilizing a plane nonlinear wave characteristic line correction equation, so that the distorted overpressure signal distribution with multiple values is obtained; and determining the shock wave position in the distorted overpressure signal distribution by using an area balance principle and a potential function method, and correcting the distorted overpressure signal distribution according to the shock wave position to obtain the acoustic explosion signal distribution. The method avoids solving of two equivalent sectional area distributions of volume distribution and lift force distribution of the aircraft, considers nonlinear effect in the shock wave propagation process, and can rapidly predict near-field acoustic explosion of all circumferential angles of any supersonic civil aircraft with complex appearance.
Description
Technical Field
The invention belongs to the technical field of aerodynamics, and particularly relates to a rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft.
Background
Faster travel speeds are a constant pursuit of humans. Compared with the traditional high subsonic speed civil aircraft, the flight speed of the supersonic speed civil aircraft can be 2 times or more than that of the traditional civil aircraft, the flight time in the air can be shortened in a multiplied way, and the travel efficiency is greatly improved. The supersonic civil aircraft plays a role similar to that of a highway in a highway system and a high-speed railway in a railway system in the civil aviation transportation field, becomes one of the main directions of the next generation and the development of the future civil aircraft, and is a new strategic high point in the aviation technology field. The development of supersonic civil engineering has important leading and pushing effects on the development of human society science, technical progress and industrial innovation. However, shock waves and expansion waves generated by the supersonic civil aircraft during supersonic flight propagate to the ground through the atmosphere to form acoustic explosions. The acoustic explosion has the characteristics of strong pressure pulsation, short rising time and wide influence area, and seriously influences the normal production and life of the ground. Thus, acoustic explosion is a primary bottleneck that limits its development. Taking the ultrasonic civil aircraft with harmony numbers, which are put into commercial operation, as an example, the ground sonic boom is as high as 108PLdB when the civil aircraft cruises, and the civil aircraft is forbidden to carry out ultrasonic flight above the land, which is also one of the major reasons for the failure of the commercial operation. Eventually, the "harmony" number exits the historic stage.
The method solves the problem of acoustic explosion, and firstly, the core key technology of acoustic explosion prediction is to be burst. Currently, the most practical acoustic explosion prediction method in engineering is a method combining 'near field prediction' and 'far field propagation'. Firstly, a near-field signal at the position of several times of the aircraft is obtained, and then the near-field signal is transmitted to the ground through a far-field transmission equation. The near-field acoustic explosion prediction is divided into a CFD-based high-reliability prediction method and a linear theory-based rapid prediction method. Numerical simulation of near-field acoustic explosion by CFD requires tens or even hundreds of millions of grid quantities, which is very computationally intensive, which severely affects design efficiency. The rapid prediction method can evaluate a large number of configurations in a short time, so that the method has important significance for the conceptual design of the low-acoustic-explosion supersonic civil aircraft. The near-field acoustic explosion rapid prediction method is established based on a linearization theory, wherein two main methods are used for solving a supersonic linearization small disturbance velocity potential equation. A disturbance of the volume and the lift force of an aircraft on air is equivalent to the disturbance of an equivalent rotation body through theoretical analysis and solution, an F function is constructed by utilizing analysis solutions of some basic flows to represent disturbance characteristics of the aircraft, and a nonlinear plane wave correction formula is considered to correct parallel characteristic lines, so that the calculated space pressure signal has second-order precision. However, the method needs to calculate the volume and lift equivalent sectional area distribution and the second derivative thereof of the aircraft, and the calculation process is complex. The other is to directly obtain the pressure signal in the space through the numerical solution of the bin method. Although this approach avoids the solution of equivalent cross-sectional area, nonlinear effects during shock propagation cannot be considered.
In addition, as the understanding of acoustic explosion has been deepened in recent years, studies have found that a low acoustic explosion design with only a single circumferential angle is likely to cause deterioration of acoustic explosion performance in other directions. Therefore, in order to ensure that the whole acoustic blanket has lower acoustic explosion level in the flying process, the design of the supersonic civil aircraft is not limited to only considering the acoustic explosion characteristics under the track (under-track), but also considering the full circumferential angle design of the track lateral (off-track) acoustic explosion. This requires that the fast prediction requires some accuracy over the prediction of the full circumferential angle. The traditional near-field acoustic explosion prediction method based on the linearization theory is low in prediction accuracy due to the fact that more assumptions are made in the lateral direction. Therefore, a fast near-field acoustic explosion prediction method capable of predicting the full circumferential angle is urgently needed in the prior art, and the prediction precision meets the requirements of conceptual design, so that support is provided for the low acoustic explosion design of the full acoustic explosion blanket in the conceptual design stage.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides a rapid prediction method for near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft, which can effectively solve the problems and provide a prediction means for developing the low acoustic explosion design of the full acoustic explosion blanket.
The technical scheme adopted by the invention is as follows:
the invention provides a rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft, which comprises the following steps:
step 1, obtaining an airplane geometric shape of near-field acoustic explosion of a full circumferential angle to be predicted, and determining an airplane object plane according to the airplane geometric shape; acquiring flight state parameters of an aircraft; determining an acoustic explosion signal monitoring position line for fast prediction of near-field acoustic explosion; the acoustic explosion signal monitoring position line passes through a specified circumferential angle theta in the full circumferential angles 0 Distance r to aircraft 0 Acoustic explosion signal monitoring position line length l 0 Determining three parameters;
step 2, setting corresponding boundary conditions according to the plane object plane;
step 3, under the constraint of the boundary condition, taking the flight state parameter as input, and solving an aircraft flow field by adopting a supersonic velocity surface element method to obtain the pressure coefficient distribution of a sound explosion signal monitoring position line;
step 4, converting the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line by using a conversion formula;
step 5, utilizing a plane nonlinear wave characteristic line correction equation to carry out nonlinear correction on linear overpressure signal distribution of the acoustic explosion signal monitoring position line, and obtaining distorted overpressure signal distribution with multiple values;
and 6, determining a shock wave position in the distorted overpressure signal distribution by using an area balance principle and a potential function method, and correcting the distorted overpressure signal distribution according to the shock wave position to obtain corrected distorted overpressure signal distribution, namely acoustic explosion signal distribution predicted at an acoustic explosion signal monitoring position line.
Preferably, in step 1, the acoustic explosion signal monitoring position line is:
taking an aircraft nose as a coordinate origin o, taking an axis of the aircraft body as an x axis, taking an axis system vertical to the pointing space of the x axis as an r axis, and taking an included angle formed by the r axis and a symmetry plane right below the aircraft body as a circumferential angle theta;
at circumferential angle θ, designated as designated circumferential angle θ 0 The distance from the aircraft is designated as distance r 0 When the position point determined in space is denoted as a (x 0 ,r 0 ,θ 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein x is 0 Is the x-coordinate of the location point;
with position point A (x 0 ,r 0 ,θ 0 ) For starting point, parallel to the x-axis and pointing in the positive x-direction by a length l 0 The line segment is the acoustic explosion signal monitoring position line.
Preferably, the flight state parameters include: free incoming stream Mach number M ∞ Free incoming flow velocity vectorFree-flowing pressure q at fly height ∞ Atmospheric pressure p of cruising altitude free inflow ∞ The specific heat ratio of air and the local mach number Ma.
Preferably, the step 3 specifically comprises:
step 3.1, equidistant m monitoring points are taken from the acoustic explosion signal monitoring position line, and the coordinate of the kth monitoring point in the m monitoring points is (x) k ,r 0 ,θ 0 ) Wherein k=1, 2,3, …, m;
step 3.2, obtaining the kth monitoring point (x) by adopting the following method k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )：
3.2.1, taking an aircraft nose as a coordinate origin o, taking an axis of a machine body as an x axis, taking an axis which passes through the origin o on a symmetrical plane of the machine body, is perpendicular to the x axis and points to the right upper side of the machine body as a z axis, and taking an axis which is perpendicular to a xoz plane and passes through an o point as a y axis, and establishing an xyz coordinate system;
step 3.2.2, coordinates (x k ,r 0 ,θ 0 ) Conversion to xyz coordinatesThe rectangular coordinates of the kth monitoring point in the xyz coordinate system are obtained as (x k ,y 0 ,z 0 )；
Step 3.2.3, constructing a pressure coefficient C in the xyz coordinate system shown in formula (1) P General expression for (x, y, z):
wherein:
u (x, y, z) represents a general expression of the disturbance speed in the x direction in the xyz coordinate system;
v (x, y, z) represents a general expression of the disturbance speed in the y direction in the xyz coordinate system;
representing a general expression of the disturbance speed along the z direction in the xyz coordinate system;
M ∞ mach number for free incoming stream;
step 3.2.4, coordinates (x k ,y 0 ,z 0 ) Substituting the pressure coefficient C into the formula (1) to obtain the pressure coefficient C of the kth monitoring point P (x k ,y 0 ,z 0 ) Due to C P (x k ,y 0 ,z 0 )＝C p (x k ,r 0 ,θ 0 ) Thus, the kth monitoring point (x k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )；
And 3.3, obtaining the pressure coefficient of each monitoring point in the m monitoring points by adopting the method of the step 3.2, and forming the pressure coefficient distribution of the acoustic explosion signal monitoring position line.
Preferably, in step 3.2.3, the formula (1) is obtained by the following method:
step 3.2.3.1, structuring the plane object surface into n grids, respectively expressed as: grid 1, grid 2, grid …, grid n, the coordinates of each grid are: (x) 1 ,y 1 ,z 1 )，(x 2 ,y 2 ,z 2 ),...,(x n ,y n ,z n )；
Step 3.2.3.2, distributing flow basic solutions with unknown intensity in each grid; wherein the flow base solution of unknown intensity comprises a point source of unknown intensity and a dipole of unknown intensity;
step 3.2.3.3, determining the point source intensity of each grid arrangement by:
for any ith grid (x i ,y i ,z i ) I=1, 2,..n, the point source intensity σ (x) of which is determined using formula (2) i ,y i ,z i )：
Wherein:
is a free incoming flow velocity vector;
for the ith grid (x i ,y i ,z i ) Is a unit normal vector of (2);
step 3.2.3.4, determining the dipole strength of each grid arrangement by:
1) For n grids, when the 1 st grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,1 Is 0;
for n grids, when the 2 nd grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,2 Is 0;
and so on;
for n grids, when the nth grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the nth grid in,n Is 0;
thereby establishing the following set of n-ary equations:
wherein: the meaning of j is: of the n meshes, an arbitrary ith mesh (x i ,y i ,z i ) For the induction point, i=1, 2,..any of n, other n-1 grids is denoted as the j-th grid (x j ,y j ,z j )，x j ,y j ,z j Rectangular coordinates representing a j-th grid; mu (x) j ,y j ,z j ) Represents the jth grid (x j ,y j ,z j ) Dipole intensity of (2);
2) Solving an n-element equation set to obtain the dipole intensity of each grid arrangement; wherein for the ith grid (x i ,y i ,z i ) The dipole strength is expressed as mu (x i ,y i ,z i )；
Step 3.2.3.5, substituting the point source intensity and the dipole intensity of each grid into formula (4) to obtain a general expression of the disturbance velocity potential phi (x, y, z) in the xyz coordinate system:
the meaning is as follows: in the plane of the aircraft, the sum of disturbance velocity potentials induced by the point sources of each grid and any point (x, y, z) of the dipole in the flow field is the disturbance velocity potential of any point (x, y, z) in the flow field;
step 3.2.3.6, according to equation (5), solving the first derivative of the disturbance velocity potential phi (x, y, z) along the xyz method to obtain a general expression u (x, y, z) of the disturbance velocity along the x-direction, a general expression v (x, y, z) along the y-direction, and a general expression along the z-direction in the xyz coordinate system:
step 3.2.3.7, obtaining the pressure coefficient C in the xyz coordinate system shown in the formula (1) by perturbing the velocity P General expression of (x, y, z).
Preferably, the step 4 specifically comprises:
according to a transformation formula shown in formula (6), transforming the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line:
wherein:
q ∞ dynamic pressure for free inflow at fly height;
p infinity is the atmospheric pressure of the cruise altitude free inflow;
C p (x k ,r 0 ,θ 0 ) When m monitoring points are equidistantly taken for the acoustic explosion signal monitoring position line, the pressure coefficient of any kth monitoring point, k=1, 2,3, … and m;
is a linearised overpressure value; wherein Δp L (x k ,r 0 ,θ 0 )＝p-p ∞ The pressure difference between the pressure p representing the position of the monitoring point and the atmospheric pressure p infinity of the free incoming flow of cruising altitude.
Preferably, in step 5, nonlinear correction is performed on the linearized overpressure signal distribution of the acoustic explosion signal monitoring position line, specifically, adjustment correction is performed on the value of the abscissa of each monitoring point in the acoustic explosion signal monitoring position line, so as to simulate nonlinear effects in the shock wave propagation process, specifically, for the kth monitoring point (x k ,r 0 ,θ 0 ) K=1, 2,3, …, m, x is calculated using equation (7) k Correcting to obtain corrected x k Expressed as: x' k ：
Wherein:
gamma is the specific heat ratio of air;
ma is the local mach number;
b is a pluronic-glaber compressibility correction factor;
F(x k ) The function value of the F function of the ith point on the position line is monitored for the acoustic explosion signal,
wherein F (x) i ) For the function value of the F function of the kth monitoring point on the acoustic explosion signal monitoring line, the F function characterizes the characteristic of the aircraft as a disturbance source, and the calculation formula is as follows:
nonlinear correction of linear overpressure signal distribution of acoustic explosion signal monitoring position line, namely x k After correction, a distorted overpressure signal distribution with multiple points is obtained, expressed as:
preferably, the step 6 specifically comprises:
since the distorted overpressure signal has multiple points, namely: monitoring a certain abscissa of a position line for the acoustic explosion signal, and corresponding to a plurality of distorted overpressure signals with the same value;
assume for the abscissa x1 that a plurality of distorted overpressure signals of the same value correspond; for another abscissa x2, a plurality of distorted overpressure signals of the same value are likewise corresponding;
x=x1 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s1;
x=x2 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s2;
when the area s1 and the area s2 are equal, the area balance phenomenon is the phenomenon that the positions of x=x1 and x=x2 are shock wave positions;
and in the distortion overpressure signal distribution, removing the distortion points at the inner sides of x=x1 and x=x2 to obtain corrected distortion overpressure signal distribution, namely the acoustic explosion signal distribution predicted at the acoustic explosion signal monitoring position line.
The method for rapidly predicting the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft has the following advantages:
1. the near-field acoustic explosion rapid prediction method can realize near-field acoustic explosion rapid prediction of the full circumferential angle of the supersonic civil aircraft, and can calculate the acoustic explosion level in the whole ground acoustic explosion blanket by combining a far-field acoustic explosion propagation equation.
2. Compared with the traditional near-field acoustic explosion rapid prediction method based on the correction linearization theory, the near-field acoustic explosion rapid prediction method avoids solving two equivalent sectional area distributions of the volume distribution and the lift force distribution of an airplane, reduces the calculated amount and simplifies the acoustic explosion prediction flow; compared with the near-field acoustic explosion directly predicted by the traditional bin method, the nonlinear effect in shock wave propagation is considered, so that the prediction result is more accurate.
Drawings
FIG. 1 is a flow chart of a rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft;
FIG. 2 is a schematic diagram of the positional relationship between the acoustic explosion signal monitoring position line and the aircraft according to the present invention;
FIG. 3 is a diagram showing the relationship between rectangular coordinate system and cylindrical coordinate system according to the present invention;
FIG. 4 is a schematic diagram of the area balance principle and potential function method for determining the shock wave position according to the embodiment of the present invention;
FIG. 5 is a schematic diagram of the geometry of a JWB example for performing acoustic explosion prediction according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a grid and boundary condition setup of a supersonic surface method according to an embodiment of the present invention;
FIG. 7 is a graph showing the prediction of acoustic explosion at a circumferential angle of 0℃for a 2.55-fold body length in an embodiment of the present invention;
FIG. 8 is a graph showing the predicted sonic boom at 30℃circumferential angle for a 2.55-fold body length in an embodiment of the present invention;
FIG. 9 is a graph showing the prediction of acoustic explosion at a circumferential angle of 50℃for a 2.55-fold body length in an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects solved by the invention more clear, the invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention aims to complement the short plates of the existing near-field acoustic explosion rapid prediction method and provides a rapid prediction technology capable of calculating the full circumferential angle acoustic explosion of a near-field space. Compared with the traditional rapid prediction method, the method avoids the solution of the equivalent sectional area distribution and the second derivative thereof, and can provide a prediction tool for developing the low acoustic explosion design of the full acoustic explosion blanket in the conceptual design stage. According to the method, according to the geometric shape and surface grid, incoming flow Mach number, flight height, corresponding atmospheric parameters and other conditions of an airplane, boundary conditions are set according to the specific shape of the airplane, and a supersonic velocity surface element method is adopted to solve disturbance pressure coefficients in a space. And then a linear acoustic explosion signal in the space is obtained through a transformation formula. Because the linear acoustic explosion signal cannot consider nonlinear effects in the shock wave propagation process, a planar nonlinear wave characteristic line correction formula is adopted to correct the linear signal. And for the non-physical multi-value phenomenon of the corrected waveform, determining the shock wave position in the distorted waveform by utilizing an area balance principle and a potential function method in the weak shock wave theory, so as to obtain a final near-field acoustic explosion signal. The method avoids solving two equivalent sectional areas of volume distribution and lift force distribution, considers nonlinear effects in the shock wave propagation process, and can rapidly predict near-field acoustic explosion of the full circumferential angle of any complicated-appearance supersonic civil aircraft.
The invention provides a rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft, which comprises the following steps with reference to fig. 1:
step 1, early-stage preparation work for rapidly predicting near-field acoustic explosion of all-circumferential angle of supersonic civil aircraft comprises the following steps:
acquiring the geometrical shape of an airplane to be predicted of near-field acoustic explosion of a full circumferential angle, and determining an airplane object plane according to the geometrical shape of the airplane; acquiring flight state parameters of an aircraft; determining an acoustic explosion signal monitoring position line for fast prediction of near-field acoustic explosion; the acoustic explosion signal monitoring position line passes through a specified circumferential angle theta in the full circumferential angles 0 Distance r to aircraft 0 Acoustic explosion signal monitoring position line length l 0 Determining three parameters; in the present invention, any specified circumferential angle θ among the full circumferential angles can be specified 0 Therefore, near-field acoustic explosion prediction at full circumferential angles can be achieved.
In step 1, the acoustic explosion signal monitoring position line is as follows:
referring to fig. 2, taking an aircraft nose as a coordinate origin o, taking an axis of the aircraft body as an x axis, taking an axis system vertical to the pointing space of the x axis as an r axis, and taking an included angle formed by the r axis and a symmetry plane right below the aircraft body as a circumferential angle theta, thereby establishing a cylindrical coordinate system;
at circumferential angle θ, designated as designated circumferential angle θ 0 The distance from the aircraft is designated as distance r 0 When the position point determined in space is denoted as a (x 0 ,r 0 ,θ 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein x is 0 Is the x-coordinate of the location point;
with position point A (x 0 ,r 0 ,θ 0 ) For starting point, parallel to the x-axis and pointing in the positive x-direction by a length l 0 The line segment is the acoustic explosion signal monitoring position line.
The invention aims to conduct near-field acoustic explosion prediction. After the acoustic explosion signal monitoring position line is determined, the near-field acoustic explosion prediction result is the acoustic explosion signal distribution of the acoustic explosion signal monitoring position line.
In this step, the flight status parameters include: free incoming stream Mach number M ∞ Free incoming flow velocity vectorFree-flowing pressure q at fly height ∞ Atmospheric pressure p of cruising altitude free inflow ∞ The specific heat ratio of air and the local mach number Ma.
Step 2, setting corresponding boundary conditions according to the plane object plane; the specific boundary condition type is set according to the layout of different supersonic civil aircrafts.
Step 3, under the constraint of the boundary condition, taking the flight state parameter as input, and solving an aircraft flow field by adopting a supersonic velocity surface element method to obtain the pressure coefficient distribution of a sound explosion signal monitoring position line;
the step 3 is specifically as follows:
step 3.1, equidistant m monitoring points are taken from the acoustic explosion signal monitoring position line, and the coordinate of the kth monitoring point in the m monitoring points is (x) k ,r 0 ,θ 0 ) Wherein k=1, 2,3, …, m;
step 3.2, obtaining the kth monitoring point (x) by adopting the following method k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )：
3.2.1, taking an aircraft nose as a coordinate origin o, taking an axis of a machine body as an x axis, taking an axis which passes through the origin o on a symmetrical plane of the machine body, is perpendicular to the x axis and points to the right upper side of the machine body as a z axis, and taking an axis which is perpendicular to a xoz plane and passes through an o point as a y axis, and establishing an xyz coordinate system;
step 3.2.2, coordinates (x k ,r 0 ,θ 0 ) Converting to an xyz coordinate system, thereby obtaining rectangular coordinates (x) of the kth monitoring point in the xyz coordinate system k ,y0,z 0 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate conversion formula is shown in fig. 3:
the coordinate transformation formula is:
step 3.2.3, construct a MalePressure coefficient C in xyz coordinate system represented by formula (1) P General expression for (x, y, z):
wherein:
u (x, y, z) represents a general expression of the disturbance speed in the x direction in the xyz coordinate system;
v (x, y, z) represents a general expression of the disturbance speed in the y direction in the xyz coordinate system;
representing a general expression of the disturbance speed along the z direction in the xyz coordinate system;
M ∞ mach number for free incoming stream;
in this step, the formula (1) is obtained by the following method:
step 3.2.3.1, structuring the plane object surface into n grids, respectively expressed as: grid 1, grid 2, grid …, grid n, the coordinates of each grid are: (x) 1 ,y 1 ,z 1 )，(x 2 ,y 2 ,z 2 ),...,(x n ,y n ,z n )；
In practice, the aircraft geometry may first be rotated to calculate the angle of attack and then structured into n grids.
Step 3.2.3.2, distributing flow basic solutions with unknown intensity in each grid; wherein the flow base solution of unknown intensity comprises a point source of unknown intensity and a dipole of unknown intensity;
step 3.2.3.3, determining the point source intensity of each grid arrangement by:
for any ith grid (x i ,y i ,z i ) I=1, 2,..n, the point source intensity σ (x) of which is determined using formula (2) i ,y i ,z i )：
Wherein:
is a free incoming flow velocity vector;
for the ith grid (x i ,y i ,z i ) Is a unit normal vector of (2);
step 3.2.3.4, determining the dipole strength of each grid arrangement by:
1) For n grids, when the 1 st grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,1 Is 0;
specifically, firstly, the disturbance velocity potential phi induced by the 2 nd grid on one side of the object plane interior of the 1 st grid is calculated respectively in,1,2 The 3 rd grid induces a disturbance velocity potential phi at one side of the object plane interior of the 1 st grid in,1,3 … the nth grid induces a disturbance velocity potential phi on the in-plane side of the 1 st grid in,1,n The method comprises the steps of carrying out a first treatment on the surface of the Then to phi in,1,2 ，φ in,1,3 ,…,φ in,1,n The result is 0.
The calculation method is the same and only phi is introduced in,1,2 The calculation formula of (2) is as follows:
for n grids, when the 2 nd grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,2 Is 0;
and so on;
for n grids, when the nth grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the nth grid in,n Is 0;
thereby establishing the following set of n-ary equations:
wherein: the meaning of j is: of the n meshes, an arbitrary ith mesh (x i ,y i ,z i ) For the induction point, i=1, 2,..any of n, other n-1 grids is denoted as the j-th grid (x j ,y j ,z j )，x j ,y j ,z j Rectangular coordinates representing a j-th grid; mu (x) j ,y j ,z j ) Represents the jth grid (x j ,y j ,z j ) Dipole intensity of (2);
2) Solving an n-element equation set to obtain the dipole intensity of each grid arrangement; wherein for the ith grid (x i ,yi,z i ) The dipole strength is expressed as mu (x i ,y i ,z i )；
Step 3.2.3.5, substituting the point source intensity and the dipole intensity of each grid into formula (4) to obtain a general expression of the disturbance velocity potential phi (x, y, z) in the xyz coordinate system:
the meaning is as follows: in the plane of the aircraft, the sum of disturbance velocity potentials induced by the point sources of each grid and any point (x, y, z) of the dipole in the flow field is the disturbance velocity potential of any point (x, y, z) in the flow field;
step 3.2.3.6, according to equation (5), solving the first derivative of the disturbance velocity potential phi (x, y, z) along the xyz method to obtain a general expression u (x, y, z) of the disturbance velocity along the x-direction, a general expression v (x, y, z) along the y-direction, and a general expression along the z-direction in the xyz coordinate system:
step 3.2.3.7, obtaining the pressure coefficient C in the xyz coordinate system shown in the formula (1) by perturbing the velocity P General expression of (x, y, z).
Step 3.2.4, coordinates (x k ,y 0 ,z 0 ) Substituting the pressure coefficient C into the formula (1) to obtain the pressure coefficient C of the kth monitoring point P (x k ,y 0 ,z 0 ) Due to C P (x k ,y 0 ,z 0 )＝C p (x k ,r 0 ,θ 0 ) Thus, the kth monitoring point (x k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )；
And 3.3, obtaining the pressure coefficient of each monitoring point in the m monitoring points by adopting the method of the step 3.2, and forming the pressure coefficient distribution of the acoustic explosion signal monitoring position line.
Step 4, converting the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line by using a conversion formula;
the step 4 is specifically as follows:
according to a transformation formula shown in formula (6), transforming the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line:
wherein:
q ∞ dynamic pressure for free inflow at fly height;
p infinity is the atmospheric pressure of the cruise altitude free inflow;
C p (x k ,r 0 ,θ 0 ) When m monitoring points are equidistantly taken for the acoustic explosion signal monitoring position line, the pressure coefficient of any kth monitoring point, k=1, 2,3, … and m;
is a linearised overpressure value; wherein Δp L (x k ,r 0 ,θ 0 )＝p-p ∞ Pressure p representing the position of the monitoring point and atmospheric pressure p of the free incoming flow of cruising altitude ∞ Is a pressure difference of (a).
Step 5, utilizing a plane nonlinear wave characteristic line correction equation to carry out nonlinear correction on linear overpressure signal distribution of the acoustic explosion signal monitoring position line, and obtaining distorted overpressure signal distribution with multiple values;
in step 5, nonlinear correction is performed on the linear overpressure signal distribution of the acoustic explosion signal monitoring position line, specifically, the value of the abscissa of each monitoring point in the acoustic explosion signal monitoring position line is adjusted and corrected to simulate the nonlinear effect in the shock wave propagation process, specifically, the value of the abscissa of the kth monitoring point (x k ,r 0 ,θ 0 ) K=1, 2,3, …, m, x is calculated using equation (7) k Correcting to obtain corrected x k Expressed as: x' k ：
Wherein:
gamma is the specific heat ratio of air, e.g., 1.4;
ma is the local mach number;
b is a pluronic-glaber compressibility correction factor;
F(x k ) The function value of the F function of the ith point on the position line is monitored for the acoustic explosion signal,
wherein F (x) i ) For the function value of the F function of the kth monitoring point on the acoustic explosion signal monitoring line, the F function characterizes the characteristic of the aircraft as a disturbance source, and the calculation formula is as follows:
at the opposite soundNonlinear correction of linear overpressure signal distribution of explosion signal monitoring position line, namely, x k After correction, a distorted overpressure signal distribution with multiple points is obtained, expressed as:
and 6, determining a shock wave position in the distorted overpressure signal distribution by using an area balance principle and a potential function method, and correcting the distorted overpressure signal distribution according to the shock wave position to obtain corrected distorted overpressure signal distribution, namely acoustic explosion signal distribution predicted at an acoustic explosion signal monitoring position line.
The step 6 is specifically as follows:
since the distorted overpressure signal has multiple points, namely: monitoring a certain abscissa of a position line for the acoustic explosion signal, and corresponding to a plurality of distorted overpressure signals with the same value;
as shown in fig. 4, assume that for the abscissa x1, there are a plurality of distorted overpressure signals of the same value; for another abscissa x2, a plurality of distorted overpressure signals of the same value are likewise corresponding;
x=x1 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s1;
x=x2 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s2;
when the area s1 and the area s2 are equal, the area balance phenomenon is the phenomenon that the positions of x=x1 and x=x2 are shock wave positions;
and in the distortion overpressure signal distribution, removing the distortion points at the inner sides of x=x1 and x=x2 to obtain corrected distortion overpressure signal distribution, namely the acoustic explosion signal distribution predicted at the acoustic explosion signal monitoring position line.
In particular, a potential function method may be employed at the location where the area balance is determined. First, for a twisted overvoltage signal lineAnd (3) integrating:
the integral may be calculated using a trapezoidal formula. After the integration is completed, the x coordinate of the intersection point of the potential function S obtained by integration along with the x change curve and the potential function S is the position of area balance, and the distortion points around the position are removed from the distortion overpressure signal, so that the final acoustic explosion signal can be obtained
Examples:
the invention provides a rapid prediction method for near-field acoustic explosion of the full-circumferential angle of a supersonic civil aircraft, which is further described by a specific application example:
in this embodiment, a low acoustic explosion standard model JAXA Wing Body (JWB) issued by the second acoustic explosion prediction seminar (SBPW 2) of AIAA in the united states was selected, the geometric shape is shown in fig. 5, and near-field acoustic explosion predictions of different circumferential angles are performed. The relevant calculated parameters for JWB are shown in table 1:
TABLE 1 calculation parameter Table for JWB calculation example
| Related parameters | Numerical value |
| Aircraft length | 38.7m |
| Cruise Mach number | 1.6 |
| Cruising altitude | 15760m |
| Atmospheric density | 0.172859kg/m 3 |
| Atmospheric pressure | 10750.1Pa |
| Wing reference area (half) | 32.8m 2 |
And under the current flight parameter condition, predicting near-field acoustic explosion at spatial positions of 0 degree, 30 degrees and 50 degrees respectively taken by 2.55 times of the length and the circumferential angle of the airframe just below the standard model.
The method for rapidly predicting the near-field full-circumferential angular sonic boom mainly comprises the following steps:
(1) Relevant calculation parameters are prepared according to the conditions and calculated positions in table 1, while a binning calculation grid as shown in fig. 6 is prepared according to the geometry of JWB.
(2) The boundary conditions used in this example are also identified in fig. 6, with corresponding boundary conditions set based on the JWB profile characteristics.
(3) After the boundary condition is set, solving the flow field of the aircraft by adopting a supersonic velocity surface element method, and obtaining the pressure coefficient of the specified space position of any circumferential angle.
(4) And (3) converting the pressure coefficient of the designated position obtained in the step (3) into a near-field linear overpressure signal by using a conversion formula.
(5) And (3) carrying out nonlinear correction on the linear overpressure signal in the step (3) by using a plane nonlinear wave characteristic line correction equation to obtain twisted overpressure signal distribution with multiple values.
(6) And determining the shock wave position in the distorted overpressure signal by using an area balance principle and a potential function method, and correcting the distribution of the distorted overpressure signal according to the shock wave position to obtain a final near-field acoustic explosion waveform.
The calculated single core run times for the three circumferential angles were 36.229 seconds, 33.373, 35.103 seconds, respectively. It can be seen that the calculated results, such as waveforms of 0 degree (fig. 7), 30 degrees (fig. 8) and 50 degrees (fig. 9), are quite close to the high-reliability CFD calculation results submitted by the acoustic explosion seminar on the premise of saving a large amount of calculation time, and the accuracy meets the requirements of conceptual design.
The beneficial effects of the invention are as follows:
1. the near-field acoustic explosion rapid prediction method can realize near-field acoustic explosion rapid prediction of the full circumferential angle of the supersonic civil aircraft, and can calculate the acoustic explosion level in the whole ground acoustic explosion blanket by combining a far-field acoustic explosion propagation equation.
2. Compared with the traditional near-field acoustic explosion rapid prediction method based on the correction linearization theory, the near-field acoustic explosion rapid prediction method avoids solving two equivalent sectional area distributions of the volume distribution and the lift force distribution of an airplane, reduces the calculated amount and simplifies the acoustic explosion prediction flow; compared with the near-field acoustic explosion directly predicted by the traditional bin method, the nonlinear effect in shock wave propagation is considered, so that the prediction result is more accurate.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which is also intended to be covered by the present invention.
Claims (8)
1. A rapid prediction method for near-field acoustic explosion of a full-circumferential angle of a supersonic civil aircraft is characterized by comprising the following steps:
step 1, obtaining an airplane geometric shape of near-field acoustic explosion of a full circumferential angle to be predicted, and determining an airplane object plane according to the airplane geometric shape; acquiring flight state parameters of an aircraft; determining an acoustic explosion signal monitoring position line for fast prediction of near-field acoustic explosion; the acoustic explosion signal monitoring position lineBy a specified circumferential angle theta of the full circumferential angles 0 Distance r to aircraft 0 Acoustic explosion signal monitoring position line length l 0 Determining three parameters;
step 2, setting corresponding boundary conditions according to the plane object plane;
step 3, under the constraint of the boundary condition, taking the flight state parameter as input, and solving an aircraft flow field by adopting a supersonic velocity surface element method to obtain the pressure coefficient distribution of a sound explosion signal monitoring position line;
step 4, converting the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line by using a conversion formula;
step 5, utilizing a plane nonlinear wave characteristic line correction equation to carry out nonlinear correction on linear overpressure signal distribution of the acoustic explosion signal monitoring position line, and obtaining distorted overpressure signal distribution with multiple values;
and 6, determining a shock wave position in the distorted overpressure signal distribution by using an area balance principle and a potential function method, and correcting the distorted overpressure signal distribution according to the shock wave position to obtain corrected distorted overpressure signal distribution, namely acoustic explosion signal distribution predicted at an acoustic explosion signal monitoring position line.
2. The method for rapidly predicting the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 1, wherein in step 1, the acoustic explosion signal monitoring position line is as follows:
taking an aircraft nose as a coordinate origin o, taking an axis of the aircraft body as an x axis, taking an axis system vertical to the pointing space of the x axis as an r axis, and taking an included angle formed by the r axis and a symmetry plane right below the aircraft body as a circumferential angle theta;
at circumferential angle θ, designated as designated circumferential angle θ 0 The distance from the aircraft is designated as distance r 0 When the position point determined in space is denoted as a (x 0 ,r 0 ,θ 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein x is 0 Is the x-coordinate of the location point;
with position point A (x 0 ,r 0 ,θ 0 ) To start withA point parallel to the x-axis and pointing in the positive x-direction for a length l 0 The line segment is the acoustic explosion signal monitoring position line.
3. The rapid prediction method for near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 1, wherein the flight state parameters comprise: free incoming stream Mach number M ∞ Free incoming flow velocity vectorFree-flowing pressure q at fly height ∞ Atmospheric pressure p of cruising altitude free inflow ∞ The specific heat ratio of air and the local mach number Ma.
4. The method for rapidly predicting the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 1, wherein the step 3 is specifically as follows:
step 3.1, equidistant m monitoring points are taken from the acoustic explosion signal monitoring position line, and the coordinate of the kth monitoring point in the m monitoring points is (x) k ,r 0 ,θ 0 ) Wherein k=1, 2,3, …, m;
step 3.2, obtaining the kth monitoring point (x) by adopting the following method k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )：
3.2.1, taking an aircraft nose as a coordinate origin o, taking an axis of a machine body as an x axis, taking an axis which passes through the origin o on a symmetrical plane of the machine body, is perpendicular to the x axis and points to the right upper side of the machine body as a z axis, and taking an axis which is perpendicular to a xoz plane and passes through an o point as a y axis, and establishing an xyz coordinate system;
step 3.2.2, coordinates (x k ,r 0 ,θ 0 ) Converting to an xyz coordinate system, thereby obtaining rectangular coordinates (x) of the kth monitoring point in the xyz coordinate system k ,y 0 ,z 0 )；
Step 3.2.3, constructing a pressure coefficient C in the xyz coordinate system shown in formula (1) P General expression for (x, y, z):
wherein:
u (x, y, z) represents a general expression of the disturbance speed in the x direction in the xyz coordinate system;
v (x, y, z) represents a general expression of the disturbance speed in the y direction in the xyz coordinate system;
representing a general expression of the disturbance speed along the z direction in the xyz coordinate system;
M ∞ mach number for free incoming stream;
step 3.2.4, coordinates (x k ,y 0 ,z 0 ) Substituting the pressure coefficient C into the formula (1) to obtain the pressure coefficient C of the kth monitoring point P (x k ,y 0 ,z 0 ) Due to C P (x k ,y 0 ,z 0 )＝C p (x k ,r 0 ,θ 0 ) Thus, the kth monitoring point (x k ,r 0 ,θ 0 ) Pressure coefficient C of (2) p (x k ,r 0 ,θ 0 )；
And 3.3, obtaining the pressure coefficient of each monitoring point in the m monitoring points by adopting the method of the step 3.2, and forming the pressure coefficient distribution of the acoustic explosion signal monitoring position line.
5. The rapid prediction method for the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 4, wherein in step 3.2.3, the formula (1) is obtained by adopting the following method:
step 3.2.3.1, structuring the plane object surface into n grids, respectively expressed as: grid 1, grid 2, grid …, grid n, the coordinates of each grid are: (x) 1 ,y 1 ,z 1 )，(x 2 ,y 2 ,z 2 ),...,(x n ,y n ,z n )；
Step 3.2.3.2, distributing flow basic solutions with unknown intensity in each grid; wherein the flow base solution of unknown intensity comprises a point source of unknown intensity and a dipole of unknown intensity;
step 3.2.3.3, determining the point source intensity of each grid arrangement by:
for any ith grid (x i ,y i ,z i ) I=1, 2,..n, the point source intensity σ (x) of which is determined using formula (2) i ,y i ,z i )：
Wherein:
is a free incoming flow velocity vector;
for the ith grid (x i ,y i ,z i ) Is a unit normal vector of (2);
step 3.2.3.4, determining the dipole strength of each grid arrangement by:
1) For n grids, when the 1 st grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,1 Is 0;
for n grids, when the 2 nd grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the 1 st grid in,2 Is 0;
and so on;
for n grids, when the nth grid is selected as an induction point, the dipoles of other n-1 grids induce the sum phi of disturbance velocity potentials on the side of the object plane interior of the nth grid in,n Is 0;
thereby establishing the following set of n-ary equations:
wherein: the meaning of j is: of the n meshes, an arbitrary ith mesh (x i ,y i ,z i ) For the induction point, i=1, 2,..any of n, other n-1 grids is denoted as the j-th grid (x j ,y j ,z j )，x j ,y j ,z j Rectangular coordinates representing a j-th grid; mu (x) j ,y j ,z j ) Represents the jth grid (x j ,y j ,z j ) Dipole intensity of (2);
2) Solving an n-element equation set to obtain the dipole intensity of each grid arrangement; wherein for the ith grid (x i ,y i ,z i ) The dipole strength is expressed as mu (x i ,y i ,z i )；
Step 3.2.3.5, substituting the point source intensity and the dipole intensity of each grid into formula (4) to obtain a general expression of the disturbance velocity potential phi (x, y, z) in the xyz coordinate system:
the meaning is as follows: in the plane of the aircraft, the sum of disturbance velocity potentials induced by the point sources of each grid and any point (x, y, z) of the dipole in the flow field is the disturbance velocity potential of any point (x, y, z) in the flow field;
step 3.2.3.6, according to equation (5), solving the first derivative of the disturbance velocity potential phi (x, y, z) along the xyz method to obtain a general expression u (x, y, z) of the disturbance velocity along the x-direction, a general expression v (x, y, z) along the y-direction, and a general expression along the z-direction in the xyz coordinate system:
in step 3.2.3.7 the process steps are performed,by the disturbance speed, the pressure coefficient C in the xyz coordinate system shown in the formula (1) is obtained P General expression of (x, y, z).
6. The method for rapidly predicting the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 1, wherein the step 4 is specifically as follows:
according to a transformation formula shown in formula (6), transforming the pressure coefficient distribution of the acoustic explosion signal monitoring position line into linear overpressure signal distribution of the acoustic explosion signal monitoring position line:
wherein:
q ∞ dynamic pressure for free inflow at fly height;
p ∞ atmospheric pressure for cruising high free inflow;
C p (x k ,r 0 ,θ 0 ) When m monitoring points are equidistantly taken for the acoustic explosion signal monitoring position line, the pressure coefficient of any kth monitoring point, k=1, 2,3, … and m;
is a linearised overpressure value; wherein Δp L (x k ,r 0 ,θ 0 )＝p-p ∞ Pressure p representing the position of the monitoring point and atmospheric pressure p of the free incoming flow of cruising altitude ∞ Is a pressure difference of (a).
7. The method for rapidly predicting full-circumferential angle near-field acoustic explosion of supersonic civil aircraft according to claim 1, wherein in step 5, nonlinear correction is performed on linear overpressure signal distribution of acoustic explosion signal monitoring position lines, specifically, adjustment correction is performed on values of abscissa of each monitoring point in acoustic explosion signal monitoring position lines, so as to simulate nonlinear effects in the propagation process of shock waves, specifically, acoustic explosion signalsMonitoring the kth monitoring point (x k ,r 0 ,θ 0 ) K=1, 2,3, …, m, x is calculated using equation (7) k Correcting to obtain corrected x k Expressed as: x' k ：
Wherein:
gamma is the specific heat ratio of air;
ma is the local mach number;
b is a pluronic-glaber compressibility correction factor;
F(x k ) The function value of the F function of the ith point on the position line is monitored for the acoustic explosion signal,
wherein F (x) i ) For the function value of the F function of the kth monitoring point on the acoustic explosion signal monitoring line, the F function characterizes the characteristic of the aircraft as a disturbance source, and the calculation formula is as follows:
nonlinear correction of linear overpressure signal distribution of acoustic explosion signal monitoring position line, namely x k After correction, a distorted overpressure signal distribution with multiple points is obtained, expressed as:
8. the method for rapidly predicting the near-field acoustic explosion of the full-circumferential angle of the supersonic civil aircraft according to claim 1, wherein the step 6 is specifically as follows:
since the distorted overpressure signal has multiple points, namely: monitoring a certain abscissa of a position line for the acoustic explosion signal, and corresponding to a plurality of distorted overpressure signals with the same value;
assume for the abscissa x1 that a plurality of distorted overpressure signals of the same value correspond; for another abscissa x2, a plurality of distorted overpressure signals of the same value are likewise corresponding;
x=x1 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s1;
x=x2 is a straight line perpendicular to the x axis, the straight line intersects the twisted overpressure signal distribution line at a plurality of points, and the area of a region surrounded by the straight line and the twisted overpressure signal distribution line is s2;
when the area s1 and the area s2 are equal, the area balance phenomenon is the phenomenon that the positions of x=x1 and x=x2 are shock wave positions;
and in the distortion overpressure signal distribution, removing the distortion points at the inner sides of x=x1 and x=x2 to obtain corrected distortion overpressure signal distribution, namely the acoustic explosion signal distribution predicted at the acoustic explosion signal monitoring position line.
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