CN110276109B - Simulation method for electromagnetic property of plasma sheath of hypersonic aircraft - Google Patents

Simulation method for electromagnetic property of plasma sheath of hypersonic aircraft Download PDF

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CN110276109B
CN110276109B CN201910472857.6A CN201910472857A CN110276109B CN 110276109 B CN110276109 B CN 110276109B CN 201910472857 A CN201910472857 A CN 201910472857A CN 110276109 B CN110276109 B CN 110276109B
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李猛猛
胡燕萌
陈如山
周仕浩
李帅帅
周全恩
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Nanjing University of Science and Technology
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Abstract

The invention discloses a method for simulating the electromagnetic property of a plasma sheath of a hypersonic aircraft. The method comprises the following steps: firstly, fluid simulation is carried out according to the geometric shape and flight parameters of the hypersonic aerocraft, and plasma collision frequency, plasma oscillation frequency and electron cyclotron frequency parameters at each position of a space under the condition of applying an electromagnetic field are determined according to simulation information; then extracting a grid file of the plasma target, and setting incident electromagnetic wave parameters; then, calculating the current density of a plasma medium part in the region by using a plasma iterative method, calculating the current density at the interface of the plasma medium and the air by using a magnetic field boundary condition, and performing iterative updating by using a current density vector single-step updating formula; and finally, obtaining the electromagnetic characteristics of the plasma by analyzing the time domain waveform. The method has the advantages of simple programming and high calculation efficiency, and realizes the high-efficiency analysis of the plasma sheath of the hypersonic aircraft.

Description

Simulation method for electromagnetic property of plasma sheath of hypersonic aircraft
Technical Field
The invention relates to the technical field of electromagnetic simulation, in particular to a method for simulating the electromagnetic property of a plasma sheath of a hypersonic aircraft.
Background
When the aircraft flies at ultrahigh speed, the surface of the aircraft generates intense friction with air and extrudes surrounding air, the air near the aircraft is in a viscous state to form a high-temperature region with the temperature of thousands of Kelvin, so that the surrounding air is ionized to form a high-temperature high-pressure plasma sheathAnd (4) sleeving. Typically, the electron density in the plasma sheath can reach 1016～1018m-3. The high electron number density can cause serious negative effects on the communication of the aircraft, so that the propagation characteristics of electromagnetic waves in a plasma sheath need to be analyzed by a numerical method, and a technical basis is provided for realizing the communication under the condition of a hypersonic aircraft black barrier.
At present, the finite difference time domain method is used for analyzing the electromagnetic property of a plasma sheath of a hypersonic aircraft, and two problems exist: (1) the high-efficiency simulation of the high cyclotron frequency magnetized plasma is difficult to realize: the Nyquist sampling theorem requires that the current density, the electric field and the magnetic field time step length in the existing finite difference method are small enough, so that the electromagnetic simulation of the plasma is difficult to realize efficiently; (2) the plasma medium and air interface is difficult to process, and the numerical value at the boundary is easy to be unstable, so that the simulation of the electromagnetic property of the plasma medium is difficult to realize.
Disclosure of Invention
The invention aims to provide a simulation method for the electromagnetic property of a plasma sheath of a hypersonic aircraft, which has good adaptability and high calculation efficiency.
The technical solution for realizing the purpose of the invention is as follows: a simulation method for the electromagnetic property of a plasma sheath of a hypersonic aircraft comprises the following steps:
step 1, performing fluid simulation according to the geometric shape and flight parameters of the hypersonic aerocraft and an applied electromagnetic field, and determining plasma collision frequency, plasma oscillation frequency parameters and electron cyclotron frequency parameter distribution at each position of a space according to simulation information;
step 2, extracting a grid file of the plasma target, and setting incident electromagnetic wave parameters;
step 3, calculating the current density of a plasma medium part in the region by using a plasma iterative method, calculating the current density at the interface of the plasma medium and the air by using a magnetic field boundary condition, and then performing iterative update by using a current density vector single-step update formula;
and 4, analyzing the time domain waveform to obtain the electromagnetic property of the plasma sheath.
Compared with the prior art, the invention has the following remarkable advantages: (1) the time step of the current density vector is different from the time steps of the electric field and the magnetic field, so that the current density vector is differentiated by adopting the time steps smaller than the time steps of the electric field and the magnetic field, so that the iteration steps of the electric field and the magnetic field are reduced, the calculation time is further reduced, and the high-efficiency analysis on the electromagnetic characteristics of the plasma target is realized; (2) for the treatment of the plasma medium and air interface, the numerical stability of the interface is improved, and the accuracy of the electromagnetic property analysis of the plasma target is improved.
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FIG. 1 is a schematic flow chart of a simulation method of the electromagnetic properties of the plasma sheath of the hypersonic aerocraft.
Fig. 2 is a schematic diagram of the current density vector space distribution in the present invention.
Fig. 3 is a schematic diagram of the time step distribution in the present invention.
FIG. 4 is a schematic illustration of a plasma target structure verified using the method of the present invention in an embodiment of the present invention.
FIG. 5 is a comparison graph of the results of analyzing the scattering cross section of the magnetized plasma radar by using the method of the present invention and commercial software CST and the Longge Kutta exponential time-varying differential time-domain finite difference method in the embodiment of the present invention.
FIG. 6 is a graph showing the comparison between the current density time step and the distribution of the electric field and magnetic field time steps varying with the electron cyclotron frequency under the condition of high electron cyclotron frequency of magnetized plasma in the method of the present invention in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
For an ultra-high-speed aircraft, a plasma sheath is formed around the aircraft in the high-speed flight process, the interaction mechanism of the plasma sheath and electromagnetic waves is complex, and the existing time domain finite difference method is difficult to analyze efficiently.
The invention discloses a method for simulating the electromagnetic property of a plasma sheath of a hypersonic aircraft, which comprises the following steps:
step 1, performing fluid simulation according to the geometric shape and flight parameters of the hypersonic aerocraft and an applied electromagnetic field, and determining plasma collision frequency, plasma oscillation frequency parameters and electron cyclotron frequency parameter distribution at each position of a space according to simulation information;
step 2, extracting a grid file of the plasma target, and setting incident electromagnetic wave parameters;
step 3, calculating the current density of a plasma medium part in the region by using a plasma iterative method, calculating the current density at the interface of the plasma medium and the air by using a magnetic field boundary condition, and then performing iterative update by using a current density vector single-step update formula;
and 4, analyzing the time domain waveform to obtain the electromagnetic property of the plasma sheath.
Further, the iterative method using plasma described in step 3 calculates the current density of the plasma medium portion in the region, specifically as follows:
and calculating the current density of the plasma medium part in the region by using an iterative formula of the plasma, wherein the formula is as follows:
Figure BDA0002081271910000031
in the formula
Figure BDA0002081271910000032
C＝A-1B，A-1Is the inverse of the matrix a and is,
Figure BDA0002081271910000033
are all three-order matrixes; Δ tcThe time step for updating the current density vector is a dielectric constant in vacuum, n is the time step, M is the total step for updating the current density vector in one step, k is the kth step in the process of updating the current density vector in one step, and omegapFor the plasma oscillation frequency, I is a third-order unit square matrix, and J ═ JxJyJz]TIs the current density vector in the plasma; e ═ ExEyEz]TIs the electric field strength in the plasma; v is the plasma collision frequency, ωx、ωy、ωzThe x, y and z direction components of the electron cyclotron frequency.
Further, the current density at the interface between the plasma medium and the air is calculated by using the magnetic field boundary conditions in step 3, which is as follows:
the current density vector of the plasma region is positioned in the center of a Yee grid, and the formula for calculating the current density at the boundary is as follows:
Figure BDA0002081271910000034
wherein Δ Hx＝H1x-H2x、ΔHy＝H1y-H2y、ΔHz＝H1z-H2zThe components in the x, y and z directions of the magnetic field variation on both sides of the boundary surface, H1x、H1y、H1zIs the component of the magnetic field in the medium 1 in the x, y, z directions, H2x、H2y、H2zIs a component of the magnitude of the magnetic field in the medium 2 in the x, y, z directions, nx、ny、nzThe components of the outside unit normal vectors x, y and z of the boundary respectively, and the discrete format of formula (2) is as follows:
for an interface with a normal vector in the x direction, the discrete formats of the tangential current densities at the boundary in the y direction and the z direction are as follows:
Figure BDA0002081271910000035
Figure BDA0002081271910000036
for an interface with a normal vector in the y-direction, the discrete format of the tangential current density at the boundary in the x-direction and the z-direction is as follows:
Figure BDA0002081271910000041
Figure BDA0002081271910000042
for a boundary surface with a normal vector in the z direction, the discrete format of the tangential current density at the boundary in the x direction and the y direction is as follows:
Figure BDA0002081271910000043
Figure BDA0002081271910000044
wherein i, j and k are space nodes in the directions of x, y and z respectively,
Figure BDA0002081271910000045
Figure BDA0002081271910000046
i, j, k space nodes in x, y, z directions respectively are translated forwards or backwards
Figure BDA0002081271910000047
In the x direction, the spatial nodes are
Figure BDA0002081271910000048
The current density of (a) is,
Figure BDA0002081271910000049
in the y direction, the spatial nodes are
Figure BDA00020812719100000410
The current density of (a) is,
Figure BDA00020812719100000411
as spatial nodes in the z direction of
Figure BDA00020812719100000412
The current density of (1).
Example 1
In this embodiment, a simulation method for analyzing electromagnetic characteristics of a plasma sheath of a hypersonic aircraft is provided, which is based on a finite difference time domain method, and is implemented by performing simulation on electromagnetic characteristics of a plasma by using a current density vector single-step updating formula method, and includes the following specific steps:
step 1, performing fluid simulation according to the geometric shape and flight parameters of the hypersonic aerocraft and an applied electromagnetic field, and determining plasma collision frequency, plasma oscillation frequency parameters and electron cyclotron frequency parameter distribution at each position of a space according to simulation information;
step 2, extracting a grid file of the plasma target, and setting incident electromagnetic wave parameters;
step 3, calculating the current density of the plasma medium part in the area by using a plasma iterative method, calculating the current density at the interface of the plasma medium and the air by using a magnetic field boundary condition, and then performing iterative update by using a current density vector single-step update formula, wherein the iterative update formula comprises the following specific steps:
the current density of the plasma medium part in the area is updated by iteration through a current density vector single-step updating formula, and the method is specifically as follows with reference to fig. 1:
step 3.1: calculating an n +1/2 moment magnetic field H at the center of the surface by an n moment electric field E at the edge;
step 3.2: the process of solving the electric field E at the n time at the center from the electric field E at the n time at the edge is as follows:
the current density vector spatial distribution is shown in FIG. 2, at the center of the Yee grid. The electric field has three directional components in the Yee cell, which are respectively defined at the edge position non-central position of the Yee cell, so that the electric field vector at the central position can not be directly obtained, but needs to be subjected to spatial interpolation, and the formula is as follows:
Figure BDA0002081271910000051
Figure BDA0002081271910000052
Figure BDA0002081271910000053
step 3.3: current density J at Yee center position n +1/2n+1/2Electric field E at time n from center YeenThe calculation was carried out as follows:
the current density vector, the electric field and the magnetic field adopt different time steps, as shown in fig. 3, the formula is as follows:
Figure BDA0002081271910000054
in the formula
Figure BDA0002081271910000055
C＝A-1B，A-1Is the inverse of the matrix a and is,
Figure BDA0002081271910000056
are all three-order matrixes; Δ tcThe time step for updating the current density vector is a dielectric constant in vacuum, n is the time step, M is the total step for updating the current density vector in one step, k is the kth step in the process of updating the current density vector in one step, and omegapFor the plasma oscillation frequency, I is a third-order unit square matrix, and J ═ JxJyJz]TIs the current density vector in the plasma; e ═ ExEyEz]TIs the electric field strength in the plasma; v is the plasma collision frequency, ωx、ωy、ωzThe x, y and z direction components of the electron cyclotron frequency.
Step 3.4: the current density J at the edge of the Yee grid is determined by the current density J at the center of the Yee gridn+1/2Calculating, and if the currently calculated edge is not positioned at the boundary of the calculation region, calculating by using the formulas (5a) to (5 c); if the current calculation position is in the calculation areaAt the domain boundary, calculating by using the formulas (7a) to (7 f); the method comprises the following specific steps:
the obtained current density vector is located at the center of the Yee cell, and when the vector participates in the electric field update, the electric field and the current density are located at different spatial positions. The electric field position is defined on the edge, and is different from the current density vector at the central position of a Yee cell, and then spatial interpolation is needed to obtain a current density vector J at the edge position, and the formula is as follows:
Figure BDA0002081271910000061
Figure BDA0002081271910000062
Figure BDA0002081271910000063
the current density at the boundary is calculated by the formula:
Figure BDA0002081271910000064
wherein Δ Hx＝H1x-H2x、ΔHy＝H1y-H2y、ΔHz＝H1z-H2zThe components in the x, y and z directions of the magnetic field variation on both sides of the boundary surface, H1x、H1y、H1zIs the component of the magnetic field in the medium 1 in the x, y, z directions, H2x、H2y、H2zFor the x, y, z directional components of the magnetic field magnitude in the medium 2, the current density at the boundary is in the discrete format of equation (6) as follows:
for an interface with a normal vector in the x-direction, the discrete format of the tangential current density at the boundary in the y-direction and the z-direction, respectively, is as follows:
Figure BDA0002081271910000065
Figure BDA00020812719100000714
for an interface with a normal vector in the y-direction, the discrete format of the tangential current density at the boundary in the x-direction and the z-direction, respectively, is as follows:
Figure BDA0002081271910000071
Figure BDA0002081271910000072
for the z-plane with the normal vector as the direction, the discrete format of the tangential current density at the boundary in the x-direction and the y-direction, respectively, is as follows:
Figure BDA0002081271910000073
Figure BDA0002081271910000074
wherein i, j and k are space nodes in the directions of x, y and z respectively,
Figure BDA0002081271910000075
Figure BDA0002081271910000076
i, j, k space nodes in x, y, z directions respectively are translated forwards or backwards
Figure BDA0002081271910000077
In the x direction, the spatial nodes are
Figure BDA0002081271910000078
The current density of (a) is,
Figure BDA0002081271910000079
in the y direction, the spatial nodes are
Figure BDA00020812719100000710
The current density of (a) is,
Figure BDA00020812719100000711
as spatial nodes in the z direction of
Figure BDA00020812719100000712
Figure BDA00020812719100000713
The current density of (1).
The iterative formula of the magnetic field is the same as the common time domain finite difference method
Step 3.5: and the electric field value E at the moment n +1 is obtained by calculating a magnetic field H at the moment n +1/2 at the center of the Yee cell surface and a current density J at the moment n +1/2 at the edge, the electric field value E is used as an initial value for calculating the electric field E at the moment n +2, the step 3.1 is returned until n is equal to the iteration step number within the specified time, and the iteration is finished.
And 4, analyzing the time domain waveform to obtain the electromagnetic property of the plasma sheath.
With reference to fig. 4 and 5, the method according to the invention simulates a magnetized plasma medium cube, the magnetized plasma cube has the spatial dimension of length, width and height of 0.6m × 0.6.6 m × 0.6.6 m, a magnetic field is applied along the positive direction of the Z axis, and the angular frequency omega of the plasma isp＝2π×28.7×108rad/s, collision frequency vc＝2×108Hz, electron cyclotron frequency omegace＝2π×108rad/s, satisfying the stability condition; the plane wave is incident along the + Z axis, and the polarization direction is the X direction; the mesh subdivision size is 0.005m, and the observation frequency is 300 MHz; the total number of iteration steps is 2000 steps. The calculation result is shown in fig. 5, and the correctness of the method of the invention is verified.
FIG. 6 is a graph showing the comparison between the current density time step and the distribution of the electric field and magnetic field time steps along with the change of the electron cyclotron frequency under the condition of high electron cyclotron frequency of magnetized plasma. Aiming at the magnetized plasma under the condition of high electron cyclotron frequency, the difference of an electric field, a magnetic field and current density in the conventional Longge Kutta exponential time-interval differential time-domain finite difference method (RKE-FDTD) adopts the same time step, the time step of a current density vector is different from the time step of the electric field and the time step of the magnetic field, the former is smaller than the latter, and the current density vector adopts the time step smaller than the electric field and the magnetic field to carry out difference, so that the iteration steps of the electric field and the magnetic field are reduced, and the calculation time is further reduced.
In conclusion, in the invention, the current density vector single-step updating formula is adopted for iterative updating during calculation of the hypersonic aircraft plasma region, and the rest is iterated by adopting the traditional time domain finite difference method, so that the electromagnetic property of the sheath of the plasma with the high electron cyclotron frequency can be accurately simulated and calculated.

Claims (2)

1. A simulation method for the electromagnetic property of a plasma sheath of a hypersonic aerocraft is characterized by comprising the following steps:
step 1, performing fluid simulation according to the geometric shape and flight parameters of the hypersonic aerocraft and an applied electromagnetic field, and determining plasma collision frequency, plasma oscillation frequency parameters and electron cyclotron frequency parameter distribution at each position of a space according to simulation information;
step 2, extracting a grid file of the plasma target, and setting incident electromagnetic wave parameters;
step 3, calculating the current density of a plasma medium part in the region by using a plasma iterative method, calculating the current density at the interface of the plasma medium and the air by using a magnetic field boundary condition, and then performing iterative update by using a current density vector single-step update formula;
step 4, obtaining the electromagnetic property of the plasma sheath by analyzing the time domain waveform;
in step 3, the current density of the plasma medium part in the region is calculated by using the iterative method of the plasma, which specifically comprises the following steps:
and calculating the current density of the plasma medium part in the region by using an iterative formula of the plasma, wherein the formula is as follows:
Figure FDA0002535223440000011
in the formula
Figure FDA0002535223440000012
C＝A-1B，A-1Is the inverse of the matrix a and is,
Figure FDA0002535223440000013
are all three-order matrixes; Δ tcThe time step for updating the current density vector is a dielectric constant in vacuum, n is the time step, M is the total step for updating the current density vector in one step, k is the kth step in the process of updating the current density vector in one step, and omegapFor the plasma oscillation frequency, I is a third-order unit square matrix, and J ═ JxJyJz]TIs the current density vector in the plasma; e ═ ExEyEz]TIs the electric field strength in the plasma; v is the plasma collision frequency, ωx、ωy、ωzThe x, y and z direction components of the electron cyclotron frequency.
2. The method for simulating the electromagnetic property of the plasma sheath of the hypersonic flight vehicle as claimed in claim 1, wherein the step 3 of calculating the current density at the interface between the plasma medium and the air by using the boundary condition of the magnetic field is as follows:
the current density vector of the plasma region is positioned in the center of a Yee grid, and the formula for calculating the current density at the boundary is as follows:
Figure FDA0002535223440000021
wherein Δ Hx＝H1x-H2x、ΔHy＝H1y-H2y、ΔHz＝H1z-H2zThe components in the x, y and z directions of the magnetic field variation on both sides of the boundary surface, H1x、H1y、H1zIs the component of the magnetic field in the medium 1 in the x, y, z directions, H2x、H2y、H2zIs a component of the magnitude of the magnetic field in the medium 2 in the x, y, z directions, nx、ny、nzThe components of the outside unit normal vectors x, y and z of the boundary respectively, and the discrete format of formula (2) is as follows:
for an interface with a normal vector in the x direction, the discrete formats of the tangential current densities at the boundary in the y direction and the z direction are as follows:
Figure FDA0002535223440000022
Figure FDA0002535223440000023
for an interface with a normal vector in the y-direction, the discrete format of the tangential current density at the boundary in the x-direction and the z-direction is as follows:
Figure FDA0002535223440000024
Figure FDA0002535223440000025
for a boundary surface with a normal vector in the z direction, the discrete format of the tangential current density at the boundary in the x direction and the y direction is as follows:
Figure FDA0002535223440000026
Figure FDA0002535223440000027
wherein i, j and k are space nodes in the directions of x, y and z respectively,
Figure FDA0002535223440000028
Figure FDA0002535223440000029
i, j, k space nodes in x, y, z directions respectively are translated forwards or backwards
Figure FDA00025352234400000210
In the x direction, the spatial nodes are
Figure FDA00025352234400000211
The current density of (a) is,
Figure FDA00025352234400000212
in the y direction, the spatial nodes are
Figure FDA00025352234400000213
The current density of (a) is,
Figure FDA00025352234400000214
as spatial nodes in the z direction of
Figure FDA00025352234400000215
The current density of (1).
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