CN105740530B - Electromagnetic Wave Propagation emulation mode in hypersonic turbulent flow - Google Patents
Electromagnetic Wave Propagation emulation mode in hypersonic turbulent flow Download PDFInfo
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Abstract
The present invention discloses Electromagnetic Wave Propagation emulation mode in a kind of hypersonic turbulent flow, mainly solves the problems, such as that the prior art cannot obtain hypersonic turbulent flow refractive index fluctuation power spectrum and cannot emulate to diffractional field of the electromagnetic wave after phase screen and average diffracted intensity.Implementation step is：According to the fractal theory and non-kolmogorov power spectrum in hypersonic turbulent flow, hypersonic turbulent flow refractive index fluctuation power spectrum is solved, and is translated into containing two parametric forms of refractive index fluctuation variance and external measurement；Hypersonic turbulent flow refractive index fluctuation function is simulated using band limit fractal function, solution divides diffractional field and average diffracted intensity after shape phase screen；Finally average diffraction strength distribution curve is emulated.The present invention compensates for the vacancy of hypersonic turbulent flow refractive index fluctuation power spectrum, and point shape phase screen method is made to be no longer limited to the research field of atmospheric turbulance, can be used to calculate in hypersonic turbulent flow point shape phase screen to the diffraction of electromagnetic wave.
Description
Technical field
The invention belongs to electromagnetic wave technology fields, and in particular to radio wave propagation characteristic numerical value emulation method, for obtaining height
Electromagnetic Wave Propagation characteristic parameter in supersonic turbulent.
Background technique
With the development of aerospace science and technology, what is formed around aircraft in high-speed aircraft flight course is hypersonic
Turbulent flow becomes the hot spot of current field of fluid mechanics.At the same time, hypersonic turbulence structure has electromagnetic wave propagation bright
Aobvious disturbance effect, can cause observing and controlling communication signal amplitude, phase random fluctuation when serious, this multipath fading even can be with
It causes to communicate complete interruption, i.e. " black barrier effect ".Therefore, the Electromagnetic Wave Propagation Study on Problems in hypersonic turbulent flow is led in national defence
Domain and civil field have significant learning value and broad application prospect.
Phase screen theory is to handle random medium to a kind of effective approximation method of wave propagation effect, in the past few decades
In, a point shape phase screen theory is widely used in the research of atmospheric turbulance Electromagnetic Wave Propagation problem.Divide shape phase screen side
Turbulence effect in transmission path is equivalent to meet point shape phase screen of the statistical theory of turbulence by method, while this thin screen is only to logical
The electric wave crossed plays phase-modulation, i.e., the phase change of wave is only generated on medium exit plane, and wave-amplitude remains unchanged.This
The wave being modulated in kind phase is propagated in free space again.To a point shape phase screen method is applied to hypersonic turbulent flow
In, it is necessary first to solve the problems, such as the fractal image code of hypersonic Turbulence Media.Zhao Yuxin etc. propose and realize nanometer plane swash
Light scattering method, abbreviation NPLS measure the fractal dimension of hypersonic turbulent flow, but the folding that hypersonic turbulent flow meets
It penetrates rate fluctuating power spectrum not to be resolved but, causes a point shape phase screen method that can not be applied to hypersonic turbulent flow, stop always
Stay in the research field for solving the problems, such as Electromagnetic Wave Propagation in atmospheric turbulance.
In conclusion the High Speed Flow Field point shape research currently based on experimental image has lot of research, based on dividing shape
Radio wave propagation characteristic research is also more in the atmospheric turbulance of phase screen method, but not and divides shape cloth due to the experiment of hypersonic turbulent flow
Bright movement combines and atmospheric turbulance refractive index fluctuation power spectrum is not particularly suited for hypersonic turbulent flow, if directly using atmospheric turbulance
Point shape phase screen theory is bound to cause no small calculating error.
Summary of the invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, electromagnetic wave in a kind of hypersonic turbulent flow is provided and is passed
Emulation mode is broadcast, to reduce calculating error, the diffractional field of Electromagnetic Wave Propagation in accurately hypersonic turbulent flow is obtained and averagely spreads out
Penetrate intensity.
To achieve the above object, technical solution of the present invention includes as follows：
(1) according to the fractal characteristic parameter and fractal Brown motion theory in hypersonic turbulent flow, Yi Jifei
The common form of kolmogorov turbulence power spectrum solves the refractive index fluctuation power spectrum V that hypersonic turbulent flow meetsn(κ), and
It converts this power spectrum to containing two parameters of refractive index fluctuation variance and turbulent flow external measurement, obtains containing refractive index fluctuation variance
With the refractive index fluctuation power spectrum V of two parameters of turbulent flow external measurementn′(κ)；
(2) Weierstrass fractal function W (x) multiplication by constants P is limited using one-dimensional band1To simulate hypersonic turbulent flow
Refractive index fluctuation function n1(x), and refractive index fluctuation function n is utilized1(x) refractive index fluctuation that hypersonic turbulent flow meets is derived
Power spectrum
(3) it enablesObtain constant P1Value, determine refractive index fluctuation function n1(x) expression formula n1(x)=
P1·W(x)；
(4) according to refractive index fluctuation function n1(x), divide the field at shape phase screen using a point shape phase screen algorithm solution
(5) basis divides the field at shape phase screenSolution divides the diffractional field after shape phase screenAnd average diffraction
Intensity
Wherein, k ' expression wave number,It is rectangular modulation function,It is Green's function, * indicates complex conjugate, <
> expression is that ancestor is average；
(6) using observation point with yoz coordinate plane distance x as abscissa, with average diffraction intensity I (x) be ordinate, it is right
Average diffraction intensity in hypersonic turbulent flow after point shape phase screen is emulated, and obtains the distribution curve of average diffraction intensity,
Obtain hypersonic micro-structure of turbulence to the affecting laws of Electromagnetic Wave Propagation by this distribution curve.
The present invention uses for reference the basic thought that Electromagnetic Wave Propagation in atmospheric turbulance divides shape phase screen method, according to hypersonic rapids
Stream experiment, solves the refractive index fluctuation power spectrum for being suitable for Hypersonic Flow Field, and a point shape phase screen method is applied to height by establishment
The precondition of supersonic turbulent, and this power spectrum is applied in point shape phase screen method, it solves in hypersonic turbulent flow
Refractive index fluctuation function further obtains and divides diffractional field and average diffracted intensity after shape phase screen, avoids direct use
Kolmogorov spectrum replaces calculating error caused by the refractive index fluctuation power spectrum of Hypersonic Flow Field, ensure that a point shape phase screen
Method calculates the accuracy of Electromagnetic Wave Propagation problem in Hypersonic Flow Field.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is the schematic diagram of point shape phase screen diffraction in the present invention；
Fig. 3 is to emulate hypersonic asynchronous point of shape phase screen average diffraction intensity distribution of turbulent Reynolds number with the present invention
Figure；
Fig. 4 is to emulate point asynchronous average diffraction intensity distribution of shape phase screen dimensions in hypersonic turbulent flow with the present invention
Figure；
Specific embodiment
It is referring to Fig.1, of the invention that the specific implementation steps are as follows：
Step 1：According to the fractal characteristic parameter and fractal Brown motion theory in hypersonic turbulent flow, Yi Jifei
The common form of kolmogorov turbulence power spectrum solves the refractive index fluctuation power spectrum V that hypersonic turbulent flow meetsn(κ)。
(1.1) fractal dimension D=1.6 that hypersonic turbulent flow is obtained by nanometer planar laser scattering experiment, further according to
Relationship in fractal Brown motion between hypersonic turbulent flow fractal dimension D, fractal index H and spectrum index α：H=2-D and α
=2H+3 solves spectrum index α=3.8 that hypersonic turbulent flow refractive index fluctuation power spectrum meets；
(1.2) by relationship α=p+3 of spectrum index α and scaling law p, hypersonic turbulent flow refractive index fluctuation power is obtained
Compose the scaling law met
(1.3) by scaling law p and spectrum index α, non-kolmogorov power spectrum formula is substituted into：
Wherein,For power spectrum constant, Γ is gamma letter
α=3.8, are brought into the expression formula of A (α), obtained A (α)=0.14 by number, therefore the refractive index fluctuation function that hypersonic turbulent flow meets
Rate composes Vn(κ) is：
For refractive index fluctuation structural constant in transmission path, κ=2k ' sin (θ/2), k ' are wave number, and θ enters for electromagnetic wave
When being mapped to any scattering member in Turbulence Media, the angle of incident direction and scattering direction.
Step 2：By refractive index fluctuation power spectrum Vn(κ) is converted into containing refractive index fluctuation variance and turbulent flow external measurement two
Parameter utilizes the form V of Turbulence Median′(κ)。
(2.1) refractive index fluctuation correlation function B in random medium is setn' (r) be：
According to random medium refractive index fluctuation structure function Dn' (r) and correlation function BnThe following relational expression of ' (r)：Dn′
(r)=2 [Bn′(0)-Bn' (r)], obtain refractive index fluctuation structure function D in random mediumn' (r) be：
Wherein, p is scaling law, and Γ is gamma function,For refractive index fluctuation variance, L0For Hypersonic Flow Field
External measurement, r are the distances of point-to-point transmission in medium,For Bessel function of imaginary argument；
Due toThen willIt is expressed as：
(2.2) scaling law p=4/5 is substituted into refractive index fluctuation structure function D in random mediumnThe expression formula of ' (r), obtains
It arrives
(2.3) it enablesIt obtains
Wherein,For Turbulence Media refractive index fluctuation structure function；
(2.4) willSubstitute into the refractive index fluctuation power spectrum that hypersonic turbulent flow meets
Make Vn(κ) be converted into containingAnd L0Form Vn′(κ)：
Wherein, κ=2k ' sin (θ/2), θ are electromagnetic wave incident when into Turbulence Media, any scattering is first, incident direction and
Scatter the angle in direction.
Step 3：Utilize refractive index fluctuation function n1(x) the refractive index fluctuation power spectrum that hypersonic turbulent flow meets is derived
(3.1) refractive index fluctuation function n is set1(x)：
(3.2) according to refractive index fluctuation function n1(x) refractive index fluctuation correlation function B is derivedn(τ)：
Wherein, P1For constant to be asked,For refractive index fluctuation variance, D indicates fractal dimension, L0For hypersonic speed flow
The external measurement of field, b representation space fundamental frequency, N indicate stacking fold,It is the equally distributed random number on [0,2 π], τ indicates only
Vertical increment, and τ levels off to 0；
(3.3) according to scale l interior in hypersonic turbulent flow0To external measurement L0Between the case where there are rapid whirlpools, enable b=1
+ τ, and fractal dimension D=1.6 are substituted into BnThe expression formula of (τ), Bn(τ) abbreviation is
(3.4) according to the refractive index fluctuation correlation function B after abbreviationn(τ) derives refractive index fluctuation power spectrum
Wherein, δ indicates that Descartes's function, κ=2k ' sin (θ/2), θ are electromagnetic wave incident any scattering into Turbulence Media
When first, the angle of incident direction and scattering direction, i indicates pure imaginary number；
(3.5) Baily method is utilized, it is rightMake continuous approximation, and work is as follows on section [κ-Δ κ/2, κ+Δ κ/2]
Integral：
M indicates integration variable
Obtained simplest formula is：
Step 4：Calculate constant P to be asked1：Order containsAnd L0Power spectrum Vn' (κ) is equal toI.e.
Thus equation calculates P1=0.39.
Step 5：Solve diffractional field of the electromagnetic wave after point shape phase screen diffraction in hypersonic turbulent flow
Referring to Fig. 2, this step is implemented as follows：
(5.1) refractive index fluctuation function n is utilized1(x), the electric field divided at shape phase screen is solvedFor：
Wherein,And n=0,1 ... N, N indicate that stacking fold, D indicate to divide
For number, JqIndicate Bessel function, q0,q1…qNIndicate the different rank of Bessel function, bN=Re3/4, b representation space fundamental frequency,
Re indicates that Reynolds number, i indicate pure imaginary number,And n=0,1 ... N,It is equally distributed random on [0,2 π]
Number,The position vector of a bit, x ' indicate the abscissa of the point, L in expression phase screen0Indicate external measurement；
(5.2) broad sense Fresnel-Huygen's principle is utilized, solution divides point of observation after shape phase screenThe diffractional field at place is：
Wherein, rectangular modulation functionX ', y ' are respectivelyVector is along x-axis and y-axis
Component,Indicate the position vector of observation point, Green's functionL expression divides shape phase screen
Size；
(5.3) to diffractional fieldGreen's function in expression formulaIt is approximated as follows：
Wherein, z is distance of the phase screen to observation point, and k ' expression wave number, x, y indicate the transverse and longitudinal coordinate of point of observation；
(5.4) field at shape phase screen will be dividedRectangular modulation functionAnd the Green's function after approximationSubstitute into diffractional fieldExpression formula, obtain：
Wherein, s=1/L0, sinc expression sampling function.
Step 6：According to diffractional fieldDerive average diffraction intensity
Utilize diffractional fieldMultiplied by the complex conjugate of itself, obtain：
Wherein,K ' is wave number, and z is point of observation to phase
The distance of screen,Indicate the position vector of observation point, x, y table
Show the transverse and longitudinal coordinate of point of observation, λ indicates that wavelength, c and s respectively indicate two classes phenanthrene
Nie Er integral, D indicate fractal dimension, indicate refractive index fluctuation variance,* complex conjugate is indicated, < > expression is that ancestor is average, bN=Re3/4, Re table
Show that Reynolds number, L indicate phase screen dimensions, L0Indicate external measurement.
Step 7：Average diffraction strength distribution curve after in hypersonic turbulent flow points of shape phase screen is emulated.
In average diffraction intensityExpression formula in take y=0, thenOnly observation point and yoz coordinate are flat
The function of the distance x in face, then using x as abscissa, with average diffraction intensity I (x) for ordinate, in hypersonic turbulent flow points
Average diffraction intensity after shape phase screen is emulated, and obtains the distribution curve of average diffraction intensity；
In order to keep distribution curve variation tendency more obvious, average diffraction intensity is normalized with its maximum value,
Obtain hypersonic micro-structure of turbulence to the affecting laws of Electromagnetic Wave Propagation by this distribution curve again.
Simulated effect of the invention can be further illustrated by following tests
(1) test simulation condition
Divide the parameter selection of shape phase screen diffraction model as follows：Divide the size L=0.1m of shape phase screen, incidence wave wavelength is
λ=10-4M, wave number k '=2 π/λ, fractal dimension D=1.6, band limit fractal function in N=9, point of observation to divide shape phase screen away from
From for z=0.4m, external measurement L0=0.01m, Reynolds number Re=8.63 × 106/ m,
(2) test simulation interpretation of result
L-G simulation test 1 is strong to asynchronous point of shape phase screen average diffraction of hypersonic turbulent Reynolds number using the present invention
Degree distribution has carried out test simulation, as a result such as Fig. 3.Wherein Fig. 3 (a) gives Reynolds number Re=8.63 × 106Being averaged when/m is spread out
Intensity distribution is penetrated, Fig. 3 (b) gives Reynolds number Re=3.63 × 105Average diffraction intensity distribution, Fig. 3 (c) give thunder when/m
Promise number Re=1.23 × 104Average diffraction intensity distribution when/m.
It can be seen that average diffraction intensity from the comparison of Fig. 3 (a), Fig. 3 (b) and three width figure of Fig. 3 (c) to be distributed in staged,
And with the reduction of Reynolds number, diffracted intensity principal maximum is always positioned at x=0, but phase screen geometrical shadow area will appear
More and more brighter more diffracted intensity secondary maximum value, and the position of these diffracted intensity secondary maximum values and amplitude are become
Change.This phenomenon shows that hypersonic turbulent Reynolds number is smaller, and turbulent flow is fainter, and the influence to Electromagnetic Wave Propagation is got over
It is small.
L-G simulation test 2, using the present invention to dividing the asynchronous average diffraction of shape phase screen dimensions strong in hypersonic turbulent flow
Degree distribution has carried out test simulation, as a result such as Fig. 4.Average diffraction is strong when wherein Fig. 4 (a) gives phase screen dimensions L=0.1m
Degree distribution, average diffraction intensity distribution when Fig. 4 (b) gives phase screen dimensions L=0.06m, Fig. 4 (c) give phase screen ruler
Average diffraction intensity distribution when very little L=0.03m.
It can be seen that average diffraction intensity from the comparison of Fig. 4 (a), Fig. 4 (b) and three width figure of Fig. 4 (c) to be distributed in staged,
And with the reduction of phase screen dimensions L, diffracted intensity principal maximum is always positioned at x=0, but in the geometrical shadow of phase screen
Area will appear more and more and close diffracted intensity secondary maximum values, and the position of these diffracted intensity secondary maximum values and amplitude are equal
It does not change.This phenomenon shows that hypersonic turbulent flow phase screen dimensions are smaller, and the diffraction that Electromagnetic Wave Propagation is subject to is got over
By force.
Above description is only example of the present invention, it is clear that for professional in the art,
After having solved the content of present invention and principle, the various modifications and variations in formal and details can be carried out, but these are based on this
The modifications and variations of invention thought are still within the scope of the claims of the present invention.
Claims (6)
1. Electromagnetic Wave Propagation emulation mode in hypersonic turbulent flow, including steps are as follows：
(1) according to the fractal characteristic parameter and fractal Brown motion theory and non-kolmogorov rapids in hypersonic turbulent flow
The common form for flowing power spectrum solves the refractive index fluctuation power spectrum V that hypersonic turbulent flow meetsn(κ), and this power spectrum is turned
It turns to containing two parameters of refractive index fluctuation variance and turbulent flow external measurement, obtains containing refractive index fluctuation variance and turbulent flow external measurement
The refractive index fluctuation power spectrum V of two parametersn′(κ)；
(2) Weierstrass fractal function W (x) multiplication by constants P is limited using one-dimensional band1To simulate the refractive index of hypersonic turbulent flow
Fluctuating function n1(x), and refractive index fluctuation function n is utilized1(x) the refractive index fluctuation power spectrum that hypersonic turbulent flow meets is derived
(3) it enablesObtain constant P1Value, determine refractive index fluctuation function n1(x) expression formula n1(x)=P1·W
(x)；
(4) according to refractive index fluctuation function n1(x), divide the field at shape phase screen using a point shape phase screen algorithm solution
(5) basis divides the field at shape phase screenSolution divides the diffractional field after shape phase screenWith average diffracted intensity
Wherein, i expression pure imaginary number, k ' expression wave number,It is rectangular modulation function,It is Green's function, * indicates multiple total
Yoke, < > expression are that ancestor is average；
(6) using observation point with yoz coordinate plane distance x as abscissa, with average diffraction intensityFor ordinate, to superb
Average diffraction intensity in velocity of sound turbulent flow after point shape phase screen is emulated, and is obtained the distribution curve of average diffraction intensity, is passed through
This distribution curve obtains hypersonic micro-structure of turbulence to the affecting laws of Electromagnetic Wave Propagation.
2. method according to claim 1, wherein according to the fractal characteristic of hypersonic turbulent flow and non-in step (1)
Kolmogorov power spectrum solves hypersonic turbulent flow refractive index fluctuation power spectrum Vn(κ) is carried out as follows：
(1a) obtains the fractal dimension D of hypersonic turbulent flow by experiment；Further according to turbulent flow hypersonic in fractal Brown motion
Relationship between fractal dimension D, fractal index H and spectrum index α：H=2-D and α=2H+3 solves hypersonic turbulent flow refraction
The spectrum index α that rate fluctuating power spectrum meets；
By relationship α=p+3 of spectrum index α and scaling law p, the mark that hypersonic turbulent flow refractive index fluctuation power spectrum meets is obtained
Degree rule p；
Scaling law p and spectrum index α are substituted into non-kolmogorov power spectrum formula by (1b)：
Obtain the refractive index fluctuation power spectrum that hypersonic turbulent flow meets：
Wherein,For power spectrum constant, Γ is gamma function,
For refractive index fluctuation structural constant in transmission path, κ=2k ' sin (θ/2), θ, which are that electromagnetic wave incident is any into Turbulence Media, to be dissipated
When penetrating member, the angle of incident direction and scattering direction.
3. method according to claim 1, wherein by V in step (1)n(κ) be converted into containing refractive index fluctuation variance and
The form V of two parameters of external measurementn' (κ), carries out as follows：
(1a) enables the refractive index fluctuation structure function D ' of random mediumn(r) with the refractive index fluctuation structure function D of Turbulence Median
(r) equal, even D 'n(r)=Dn(r), it obtains
Wherein D 'n(r) and Dn(r) it is expressed as：
Wherein, p is scaling law,For refractive index fluctuation structural constant in transmission path, F is Bessel function of imaginary argument, and r is to be situated between
The distance of point-to-point transmission in matter,For refractive index fluctuation variance, L0For the external measurement of Hypersonic Flow Field, Γ is gamma function；
(1b) willExpression formula substitute into the refractive index fluctuation power spectrum that hypersonic turbulent flow meets?
Vn(κ) be converted into containingAnd L0Form Vn′(κ)
Wherein, κ=2k ' sin (θ/2), θ are electromagnetic wave incident when into Turbulence Media, any scattering is first, incident direction with scatter
The angle in direction.
4. according to the method described in claim 1, wherein utilizing refractive index fluctuation function n in step (2)1(x) it derives hypersonic
The refractive index fluctuation power spectrum that turbulent flow meetsIt carries out as follows：
(2a) is according to refractive index fluctuation function n1(x), refractive index fluctuation correlation function B is derivedn(τ)
Bn(τ)=< n1(x)·n1(x+ τ) >,
Wherein, τ indicates independent increment；
(2b) is according to refractive index fluctuation correlation function Bn(τ) derives refractive index fluctuation power spectrum
(2c) utilizes Baily method, rightExpression formula do continuous approximation, and integrated, obtained
Wherein, κ=2k ' sin (θ/2), θ are electromagnetic wave incident when into Turbulence Media, any scattering is first, incident direction with scatter
The angle in direction,For refractive index fluctuation variance, L0For the external measurement of Hypersonic Flow Field.
5. method according to claim 1, wherein refractive index fluctuation function n in step (4)1(x) it is expressed as follows：
Wherein,For refractive index fluctuation variance, D indicates fractal dimension, L0For the external measurement of Hypersonic Flow Field, b indicates empty
Between fundamental frequency, N indicate stacking fold,It is the equally distributed random number on [0,2 π].
6. according to 1 the method for claims, wherein rectangular modulation function in step (5)And Green's function
Expression formula be respectively：
Wherein,The position vector of any is indicated to divide in shape phase screen, x ', y ' are respectivelyVector along x-axis and y-axis component,
Indicate that the position vector of observation point, L indicate the size for dividing shape phase screen.
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