CN105740530A - Simulation method for electromagnetic wave propagation in hypersonic turbulence - Google Patents

Abstract

The present invention discloses a simulation method for electromagnetic wave propagation in hypersonic turbulence, in order to mainly solve problems that a method in the prior art cannot obtain hypersonic turbulence refractive index fluctuation power spectrum and cannot carry out simulation on a diffraction field and an average diffraction intensity after electromagnetic waves pass through a phase screen. The implementation steps comprises: according to a fractal theory and non kolmogorov power spectrum in the hypersonic turbulence, solving the hypersonic turbulence refractive index fluctuation power spectrum and converting the fluctuation power spectrum to two parameter forms containing a refractive index fluctuation variance and an outer scale; using a band-limited fractal function to stimulate a hypersonic turbulence refractive index fluctuation function, and solving the diffraction field and the average diffraction intensity behind a fractal phase screen; and finally carrying out simulation on an average diffraction intensity distribution curve. The method disclosed by the present invention compensates for vacancy of the hypersonic turbulence refractive index fluctuation power spectrum, so that a fractal phase screen method is no longer limited to the research field of atmospheric turbulence, and can be used to calculate diffraction by the fractal phase screen to the electromagnetic waves in the hypersonic turbulence.

Description

Electromagnetic wave propagation emulation mode in hypersonic turbulent flow

Technical field

The invention belongs to electromagnetic wave technology field, be specifically related to radio wave propagation characteristic numerical value emulation method, be used for obtaining electromagnetic wave propagation characteristic parameter in hypersonic turbulent flow.

Background technology

Along with the development of Aero-Space science and technology, the hypersonic turbulent flow formed around aircraft in high-speed aircraft flight course becomes the focus of current field of fluid mechanics.Meanwhile, electromagnetic wave propagation is had obvious disturbance effect by hypersonic turbulence structure, can cause observing and controlling communication signal amplitude, phase place random fluctuation time serious, and this multipath fading even can cause communication to interrupt completely, i.e. " black barrier effect ".Therefore, the electromagnetic wave propagation Study on Problems in hypersonic turbulent flow has significant learning value in national defence and civil area and is widely applied prospect.

Phase screen theory is a kind of effectively approximation method processing random medium to ripple propagation effect, and in the past few decades, fractal phase screen theory is widely used in the middle of the research of atmospheric turbulance electromagnetic wave propagation problem.Turbulence effect on transmission path is equivalent to the fractal phase screen meeting the statistical theory of turbulence by fractal phase screen method, the electric wave passed through only is played phase-modulation effect by this thin screen simultaneously, namely only producing the phase change of ripple on medium exit plane, wave-amplitude remains unchanged.Ripple modulated in this phase place is propagated in free space again.To fractal phase screen method is applied in hypersonic turbulent flow, it is necessary first to solve the fractal image code problem of hypersonic Turbulence Media.Zhao Yuxins etc. propose and achieve a nanometer planar laser scattering method, it is called for short NPLS, the fractal dimension of hypersonic turbulent flow has been measured, but the refractive index fluctuation power spectrum that hypersonic turbulent flow meets is not solved, cause that fractal phase screen method cannot be applied to hypersonic turbulent flow, rest on always and solve the research field of electromagnetic wave propagation problem in atmospheric turbulance.

In sum, the fractal research of High Speed Flow Field being currently based on experimental image has had lot of research, also more based on radio wave propagation characteristic research in the atmospheric turbulance of fractal phase screen method, but do not combine with fractal Brown motion due to the experiment of hypersonic turbulent flow and atmospheric turbulance refractive index fluctuation power spectrum is not particularly suited for hypersonic turbulent flow, if directly using atmospheric turbulance fractal phase screen theory certainly will cause no small calculating error.

Summary of the invention

Present invention aims to the deficiency of above-mentioned prior art, it is provided that electromagnetic wave propagation emulation mode in a kind of hypersonic turbulent flow, to reduce calculating error, obtain the diffractional field of electromagnetic wave propagation in hypersonic turbulent flow accurately and average diffracted intensity.

For achieving the above object, technical scheme includes as follows:

(1) theoretical according to the fractal characteristic parameter in hypersonic turbulent flow and fractal Brown motion, and the common form of non-kolmogorov turbulence power spectrum, solve the refractive index fluctuation power spectrum V that hypersonic turbulent flow meets_n(κ), and this power spectrum is converted into containing refractive index fluctuation variance and two parameters of turbulent flow external measurement, obtains the refractive index fluctuation power spectrum V containing refractive index fluctuation variance and two parameters of turbulent flow external measurement_n′(κ)；

(2) one-dimensional band limit Weierstrass fractal function W (x) multiplication by constants P is utilized₁Simulate the refractive index fluctuation function n of hypersonic turbulent flow₁(x), and utilize refractive index fluctuation function n₁(x) derive hypersonic turbulent flow meet refractive index fluctuation power spectrum

(3) orderObtain constant P₁Value, it is determined that refractive index fluctuation function n₁The expression formula n of (x)₁(x)=P₁·W(x)；

(4) according to refractive index fluctuation function n₁X (), utilizes the field at the fractal phase screen place of fractal phase screen Algorithm for Solving $\mathrm{\ψ}\left({\stackrel{\→}{x}}^{\′}\right)=\exp \[i\·n_1\left(x\right)\];$

(5) field according to fractal phase screen placeSolve the diffractional field after fractal phase screenWith average diffracted intensity

$\mathrm{\ψ}\left(\stackrel{\→}{x}\right)=(-2ik){\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}\mathrm{\ψ}\left({\stackrel{\→}{x}}^{\′}\right)P\left({\stackrel{\→}{x}}^{\′}\right)G(\stackrel{\→}{x};{\stackrel{\→}{x}}^{\′})d{\stackrel{\→}{x}}^{\′},$

$I\left(\stackrel{\&RightArrow;}{x}\right)=<\mathrm{\&psi;}\left(\stackrel{\&RightArrow;}{x}\right)\&CenterDot;\mathrm{\&psi;}*\left(\stackrel{\&RightArrow;}{x}\right)>,$

Wherein, k ' represents wave number,It is rectangular modulation function,Being Green's function, it is that ancestor is average that * represents that complex conjugate, < > represent；

(6) with the distance x of observation station and yoz coordinate plane for abscissa, with average diffraction intensity I (x) for vertical coordinate, average diffraction intensity after phase screen fractal in hypersonic turbulent flow is emulated, draw the distribution curve of average diffraction intensity, draw the hypersonic micro-structure of turbulence affecting laws to electromagnetic wave propagation by this distribution curve.

The present invention uses for reference the basic thought of the fractal phase screen method of electromagnetic wave propagation in atmospheric turbulance, test according to hypersonic turbulent flow, solve the refractive index fluctuation power spectrum suitable in Hypersonic Flow Field, establish the precondition that fractal phase screen method is applied to hypersonic turbulent flow, and this power spectrum is applied in fractal phase screen method, solve the refractive index fluctuation function in hypersonic turbulent flow, obtain the diffractional field after fractal phase screen and average diffracted intensity further, avoid the calculating error directly using kolmogorov spectrum to replace the refractive index fluctuation power spectrum of Hypersonic Flow Field to cause, ensure that fractal phase screen method calculates the accuracy of electromagnetic wave propagation problem in Hypersonic Flow Field.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the schematic diagram of fractal phase screen diffraction in the present invention；

Fig. 3 emulates the asynchronous fractal phase screen average diffraction intensity distribution of hypersonic turbulent Reynolds number by the present invention；

Fig. 4 emulates the asynchronous average diffraction intensity distribution of fractal phase screen size in hypersonic turbulent flow by the present invention；

Detailed description of the invention

With reference to Fig. 1, the present invention to implement step as follows:

Step 1: theoretical according to the fractal characteristic parameter in hypersonic turbulent flow and fractal Brown motion, and the common form of non-kolmogorov turbulence power spectrum, solve the refractive index fluctuation power spectrum V that hypersonic turbulent flow meets_n(κ)。

(1.1) fractal dimension D=1.6 of hypersonic turbulent flow are obtained by nanometer planar laser scattering experiment, relation further according between turbulent flow fractal dimension D hypersonic in fractal Brown motion, 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 the relation α of spectrum index α and scaling law p=p+3, the scaling law that hypersonic turbulent flow refractive index fluctuation power spectrum meets is obtained

(1.3) by scaling law p and spectrum index α, non-kolmogorov power spectrum formula is substituted into:

$V_n\left(\mathrm{\&kappa;}\right)=A\left(\mathrm{\&alpha;}\right){\tilde{C}}_n^2{\mathrm{\&kappa;}}^{-(p+1)},$

Wherein, $A\left(\mathrm{\&alpha;}\right)=2^{\mathrm{\&alpha;}-6}({\mathrm{\&alpha;}}^2-5\mathrm{\&alpha;}+6){\mathrm{\&pi;}}^{-3/2}\&lsqb;\mathrm{\&Gamma;}\left(\frac{\mathrm{\&alpha;}-2}{2}\right)/\mathrm{\&Gamma;}\left(\frac{5-\mathrm{\&alpha;}}{2}\right)\&rsqb;$ For power spectrum constant, Γ is gamma function, and α=3.8 are brought into the expression formula of A (α), obtains A (α)=0.14, the refractive index fluctuation power spectrum V that therefore hypersonic turbulent flow meets_n(κ) be:

$V_n\left(\mathrm{\&kappa;}\right)=0.14{\tilde{C}}_n^2{\mathrm{\&kappa;}}^{-9/5},$

For refractive index fluctuation structural constant on transmission path, κ=2k ' sin (θ/2), k ' is wave number, and θ is electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, the angle in incident direction and scattering direction.

Step 2: by refractive index fluctuation power spectrum V_n(κ) the form V utilizing Turbulence Media containing refractive index fluctuation variance and two parameters of turbulent flow external measurement it is converted into_n′(κ)。

(2.1) refractive index fluctuation correlation function B in random medium is set_n' (r) is:

$B_n^{\&prime;}\left(r\right)=\frac{<n_1^2>}{2^{\mathrm{\&nu;}-1}\mathrm{\&Gamma;}(p/2)}{\left(\frac{r}{L_0}\right)}^{p/2}{F}_{p/2}\left(\frac{r}{L_0}\right),$

According to random medium refractive index fluctuation structure function D_n' (r) and correlation function B_nThe following relational expression of ' (r): D_n' (r)=2 [B_n′(0)-B_n' (r)], obtain refractive index fluctuation structure function D in random medium_n' (r) is:

$D_n^{\&prime;}\left(r\right)=2<n_1^2>\&lsqb;1-\frac{1}{2^{p/2-1}\mathrm{\&Gamma;}(p/2)}{\left(\frac{r}{L_0}\right)}^{p/2}{F}_{p/2}\left(\frac{r}{L_0}\right)\&rsqb;,$

Wherein, p is scaling law, and Γ is gamma function,For refractive index fluctuation variance, L₀For the external measurement of Hypersonic Flow Field, r is the distance of point-to-point transmission in medium,For Bessel function of imaginary argument；

Due toThen willIt is expressed as:

$F_{p/2}\left(\frac{r}{L_0}\right)=\frac{(\mathrm{\&pi;}/2)}{\sin p\mathrm{\&pi;}/2}\&lsqb;{\left(\frac{r}{2L_0}\right)}^{-p/2}\frac{1}{\mathrm{\&Gamma;}(1-p/2)}-{\left(\frac{r}{2L_0}\right)}^{p/2}\frac{1}{\mathrm{\&Gamma;}(1+p/2)}\&rsqb;;$

(2.2) scaling law p=4/5 is substituted into refractive index fluctuation structure function D in random medium_nThe expression formula of ' (r), obtains

$D_n^{\&prime;}\left(r\right)=1.93<n_1^2>{L_0}^{-4/5}{r}^{-4/5},$

(2.3) order $D_n^{\&prime;}\left(r\right)={\tilde{C}}_n^2{r}^{-p},$ Obtain

${\tilde{C}}_n^2=1.93<n_1^2>{L_0}^{-4/5}$

Wherein,For Turbulence Media refractive index fluctuation structure function；

(2.4) willSubstitute into the refractive index fluctuation power spectrum that hypersonic turbulent flow meetsMake V_n(κ) be converted into containingAnd L₀Form V_n' (κ):

$V_n^{\&prime;}\left(\mathrm{\&kappa;}\right)=0.27<n_1^2>{L_0}^{-4/5}{\mathrm{\&kappa;}}^{-9/5},$

Wherein, κ=2k ' sin (θ/2), θ is electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, the angle in incident direction and scattering direction.

Step 3: utilize refractive index fluctuation function n₁(x) derive hypersonic turbulent flow meet refractive index fluctuation power spectrum

(3.1) refractive index fluctuation function n is set₁(x):

(3.2) according to refractive index fluctuation function n₁(x) derivation refractive index fluctuation correlation function B_n(τ):

$\begin{array}{c}{B}_n\left(\mathrm{\&tau;}\right)=<n_1(x+\mathrm{\&tau;})n_1\left(x\right)>\\ =\frac{P_1^2<n_1^2>\&lsqb;1-b^{(2D-4)}\&rsqb;}{1-b^{(2D-4)(N+1)}}\underset{n=0}{\overset{N}{\&Sigma;}}{b}^{(2D-4)n}\cos (2{\mathrm{\&pi;b}}^n\mathrm{\&tau;}/L_0)\end{array}$

Wherein, P₁For constant to be asked,For refractive index fluctuation variance, D represents fractal dimension, L₀For the external measurement of Hypersonic Flow Field, b representation space fundamental frequency, N represents stacking fold,Being the equally distributed random number on [0,2 π], τ represents independent increment, and τ levels off to 0；

(3.3) according to yardstick l interior in hypersonic turbulent flow₀To external measurement L₀Between all have the situation in rapid whirlpool, make b=1+ τ, and fractal dimension D=1.6 substituted into B_n(τ) expression formula, B_n(τ) abbreviation is

$B_n\left(\mathrm{\&tau;}\right)=\frac{4P_1^2<n_1^2>\mathrm{\&tau;}}{5}\underset{n=0}{\overset{N}{\&Sigma;}}{b}^{-4n/5}cos(2{\mathrm{\&pi;b}}^n\mathrm{\&tau;}/L_0),$

(3.4) according to the refractive index fluctuation correlation function B after abbreviation_n(τ), derivation refractive index fluctuation power spectrum

$\begin{array}{c}{\stackrel{\&OverBar;}{V}}_n\left(\mathrm{\&kappa;}\right)=\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{B}_n\left(\mathrm{\&tau;}\right)\exp \left(i\mathrm{\&kappa;}\mathrm{\&tau;}\right)d\mathrm{\&tau;}\\ =\frac{2P_1^2<n_1^2>\mathrm{\&tau;}}{5}\underset{n=0}{\overset{N}{\&Sigma;}}{b}^{-4n/5}\mathrm{\&delta;}(\mathrm{\&kappa;}-2{\mathrm{\&pi;b}}^n/L_0)\end{array}$

Wherein, δ represents that Descartes's function, κ=2k ' sin (θ/2), θ are electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, and the angle in incident direction and scattering direction, i represents pure imaginary number；

(3.5) Baily method is utilized, rightDo continuous approximation, and at interval [κ-Δ κ/2, κ+Δ κ/2] upper work such as lower integral:

M represents integration variable

ObtainSimplest formula be: ${\stackrel{\&OverBar;}{V}}_n\left(\mathrm{\&kappa;}\right)=1.74P_1^2<n_1^2>L_0^{-4/5}{\mathrm{\&kappa;}}^{-9/5}.$

Step 4: calculate constant P to be asked₁: order containsAnd L₀Power spectrum V_n' (κ) is equal toNamely

$0.27<n_1^2>{L_0}^{-4/5}{\mathrm{\&kappa;}}^{-9/5}=1.74P_1^2<n_1^2>L_0^{-4/5}{\mathrm{\&kappa;}}^{-9/5},$

Thus equation calculates P₁=0.39.

Step 5: solve electromagnetic wave diffractional field after fractal phase screen diffraction in hypersonic turbulent flow

Reference Fig. 2, being implemented as follows of this step:

(5.1) refractive index fluctuation function n is utilized₁X (), solves the electric field at fractal phase screen placeFor:

Wherein,And n=0,1 ... N, N represent that stacking fold, D represent and are divided into number, J_qRepresent Bessel function, q₀,q₁…q_NRepresent the different rank of Bessel function, b^N=Re^3/4, b representation space fundamental frequency, Re represents Reynolds number, and i represents pure imaginary number,And n=0,1 ... N,It is [0,2 π] upper equally distributed random number,Representing the position vector of any in phase screen, x ' represents the abscissa of this point, L₀Represent external measurement；

(5.2) utilize broad sense Fresnel Huygen's principle, solve point of observation after fractal phase screenThe diffractional field at place is:

$\mathrm{\&psi;}\left(\stackrel{\&RightArrow;}{x}\right)=(-2ik){\&Integral;}_{-\mathrm{\&infin;}}^{\mathrm{\&infin;}}{\&Integral;}_{-\mathrm{\&infin;}}^{\mathrm{\&infin;}}\mathrm{\&psi;}\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)P\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)G(\stackrel{\&RightArrow;}{x};{\stackrel{\&RightArrow;}{x}}^{\&prime;})d{\stackrel{\&RightArrow;}{x}}^{\&prime;},$

Wherein, rectangular modulation functionX ', y ' are respectivelyVector along the component of x-axis and y-axis,Represent the position vector of observation station, Green's functionL represents the size of fractal phase screen；

(5.3) to diffractional fieldGreen's function in expression formulaIt is approximated as follows:

$G(\stackrel{\&RightArrow;}{x};{\stackrel{\&RightArrow;}{x}}^{\&prime;})\&ap;\frac{\exp \left({\mathrm{ik}}^{\&prime;}z\right)}{4\mathrm{\&pi;}z}\exp \&lsqb;\frac{{\mathrm{ik}}^{\&prime;}\&lsqb;{(x-x^{\&prime;})}^2+{(y-y^{\&prime;})}^2\&rsqb;}{2z}\&rsqb;,$

Wherein, z is the phase screen distance to observation station, and k ' represents wave number, x, and y represents the transverse and longitudinal coordinate of point of observation；

(5.4) by the field at fractal phase screen placeRectangular modulation functionAnd the Green's function after approximateSubstitute into diffractional fieldExpression formula, obtain:

Wherein, s=1/L₀, sinc represents sampling function.

Step 6: according to diffractional fieldDerivation average diffraction intensity

Utilize diffractional fieldIt is multiplied by the complex conjugate of self, obtains:

$\begin{array}{c}<I\left(\stackrel{\&RightArrow;}{x}\right)>=<\mathrm{\&psi;}\left(\stackrel{\&RightArrow;}{x}\right)\&CenterDot;\mathrm{\&psi;}*\left(\stackrel{\&RightArrow;}{x}\right)>\\ =\frac{1}{4}\left(\left(1-<n_1^2>\right)\right\{{\&lsqb;c\left({\mathrm{\&xi;}}_4\right)-c\left({\mathrm{\&xi;}}_3\right)\&rsqb;}^2+{\&lsqb;s\left({\mathrm{\&xi;}}_4\right)-s\left({\mathrm{\&xi;}}_3\right)\&rsqb;}^2\}\\ +\underset{n=0}{\overset{N}{\&Sigma;}}(C_n^2/4)\{{\&lsqb;c\left({\mathrm{\&xi;}}_6\right)-c\left({\mathrm{\&xi;}}_5\right)\&rsqb;}^2+{\&lsqb;s\left({\mathrm{\&xi;}}_6\right)-s\left({\mathrm{\&xi;}}_5\right)\&rsqb;}^2\})\\ \&times;\{{\&lsqb;c\left({\mathrm{\&eta;}}_2\right)-c\left({\mathrm{\&eta;}}_1\right)\&rsqb;}^2+{\&lsqb;s\left({\mathrm{\&eta;}}_2\right)-s\left({\mathrm{\&eta;}}_1\right)\&rsqb;}^2\}\end{array},$

Wherein, ${\mathrm{\&eta;}}_1=-\sqrt{k^{\&prime;}/\mathrm{\&pi;}z}(L/2+y),{\mathrm{\&eta;}}_2=\sqrt{k^{\&prime;}/\mathrm{\&pi;}z}(L/2-y),$ K ' is wave number, and z is the distance that point of observation arrives phase screen, ${\mathrm{\&xi;}}_3=-\sqrt{k^{\&prime;}/\mathrm{\&pi;}z}(L/2+x),{\mathrm{\&xi;}}_4=\sqrt{k^{\&prime;}/\mathrm{\&pi;}z}(L/2-x),$ Representing the position vector of observation station, x, y represents the transverse and longitudinal coordinate of point of observation,λ represents wavelength, and c and s represents two class fresnel integrals respectively,D represents fractal dimension,Represent refractive index fluctuation variance, $C_n=\frac{0.39\&CenterDot;{\{2<n_1^2>\&lsqb;1-b^{(2D-4)}\&rsqb;\}}^{1/2}{b}^{(D-2)n}}{{\&lsqb;1-b^{(2D-4)(N+1)}\&rsqb;}^{1/2}},$ * representing that complex conjugate, < > represent is that ancestor is average, b^N=Re^3/4, Re represents that Reynolds number, L represent phase screen size, L₀Represent external measurement.

Step 7: the average diffraction strength distribution curve after phase screen fractal in hypersonic turbulent flow is emulated.

In average diffraction intensityExpression formula in take y=0, thenThe simply function of the distance x of observation station and yoz coordinate plane, then with x for abscissa, with average diffraction intensity I (x) for vertical coordinate, the average diffraction intensity after phase screen fractal in hypersonic turbulent flow is emulated, draws the distribution curve of average diffraction intensity；

In order to make distribution curve variation tendency become apparent from, average diffraction intensity is carried out normalization with its maximum, draw the hypersonic micro-structure of turbulence affecting laws to electromagnetic wave propagation again through this distribution curve.

The simulated effect of the present invention can be further illustrated by tests below

(1) test simulation condition

The parameter of fractal phase screen diffraction model selects as follows: the size L=0.1m of fractal phase screen, incidence wave wavelength is λ=10^-4M, wave number k '=2 π/λ, fractal dimension D=1.6, N=9 in band limit fractal function, point of observation is z=0.4m to the distance of fractal phase screen, external measurement L₀=0.01m, Reynolds number R_e=8.63 × 10⁶/ m,

(2) test simulation interpretation of result

L-G simulation test 1, utilizes the present invention that the asynchronous fractal phase screen average diffraction intensity distributions of hypersonic turbulent Reynolds number has been carried out test simulation, and result is Fig. 3 such as.Wherein Fig. 3 (a) gives Reynolds number R_e=8.63 × 10⁶Average diffraction intensity distributions during/m, Fig. 3 (b) gives Reynolds number R_e=3.63 × 10⁵Average diffraction intensity distributions during/m, Fig. 3 (c) gives Reynolds number R_e=1.23 × 10⁴Average diffraction intensity distributions during/m.

Can be seen that from the contrast of Fig. 3 (a), Fig. 3 (b) He Fig. 3 (c) three width figure, average diffraction intensity is staged distribution, and along with the reduction of Reynolds number, diffracted intensity principal maximum is always positioned at x=0 place, but phase screen geometrical shadow district there will be more and more brighter many diffracted intensity secondary maximum values, and the position of these diffracted intensity secondary maximum values and amplitude all there occurs change.This phenomenon shows that hypersonic turbulent Reynolds number is more little, and its turbulent flow is more faint, and the impact of electromagnetic wave propagation is more little.

L-G simulation test 2, utilizes the present invention that the asynchronous average diffraction intensity distributions of phase screen size fractal in hypersonic turbulent flow has been carried out test simulation, and result is Fig. 4 such as.Wherein Fig. 4 (a) gives average diffraction intensity distributions during phase screen size L=0.1m, Fig. 4 (b) gives average diffraction intensity distributions during phase screen size L=0.06m, and Fig. 4 (c) gives average diffraction intensity distributions during phase screen size L=0.03m.

Can be seen that from the contrast of Fig. 4 (a), Fig. 4 (b) He Fig. 4 (c) three width figure, average diffraction intensity is staged distribution, and along with the reduction of phase screen size L, diffracted intensity principal maximum is always positioned at x=0 place, but there will be more and more and close diffracted intensity secondary maximum values in the geometrical shadow district of phase screen, and the position of these diffracted intensity secondary maximum values and amplitude all do not change.This phenomenon shows that hypersonic turbulent flow phase screen size is more little, and the diffraction that electromagnetic wave propagation is subject to is more strong.

Above description is only example of the present invention; obviously for the professional in this area; after having understood present invention and principle; can carry out the various corrections in form and in details and change, but these based on the correction of inventive concept and change still within the claims of the present invention.

Claims (6)

1. electromagnetic wave propagation emulation mode in hypersonic turbulent flow, comprises the following steps that

(1) theoretical according to the fractal characteristic parameter in hypersonic turbulent flow and fractal Brown motion, and the common form of non-kolmogorov turbulence power spectrum, solve the refractive index fluctuation power spectrum V that hypersonic turbulent flow meets_n(κ), and this power spectrum is converted into containing refractive index fluctuation variance and two parameters of turbulent flow external measurement, obtains the refractive index fluctuation power spectrum V containing refractive index fluctuation variance and two parameters of turbulent flow external measurement_n′(κ)；

(2) one-dimensional band limit Weierstrass fractal function W (x) multiplication by constants P is utilized₁Simulate the refractive index fluctuation function n of hypersonic turbulent flow₁(x), and utilize refractive index fluctuation function n₁(x) derive hypersonic turbulent flow meet refractive index fluctuation power spectrum

(3) orderObtain constant P₁Value, it is determined that refractive index fluctuation function n₁The expression formula n of (x)₁(x)=P₁·W(x)；

(4) according to refractive index fluctuation function n₁X (), utilizes the field at the fractal phase screen place of fractal phase screen Algorithm for Solving $\mathrm{\&psi;}\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)=\exp \&lsqb;i\&CenterDot;n_1\left(x\right)\&rsqb;;$

(5) field according to fractal phase screen placeSolve the diffractional field after fractal phase screenWith average diffracted intensity

$\mathrm{\&psi;}\left(\stackrel{\&RightArrow;}{x}\right)=(-2ik){\&Integral;}_{-\mathrm{\&infin;}}^{\mathrm{\&infin;}}{\&Integral;}_{-\mathrm{\&infin;}}^{\mathrm{\&infin;}}\mathrm{\&psi;}\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)P\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)G(\stackrel{\&RightArrow;}{x};{\stackrel{\&RightArrow;}{x}}^{\&prime;})d{\stackrel{\&RightArrow;}{x}}^{\&prime;},$

$I\left(\stackrel{\&RightArrow;}{x}\right)=<\mathrm{\&psi;}\left(\stackrel{\&RightArrow;}{x}\right)\&CenterDot;\mathrm{\&psi;}*\left(\stackrel{\&RightArrow;}{x}\right)>,$

Wherein, i represents pure imaginary number, and k ' represents wave number,It is rectangular modulation function,Being Green's function, it is that ancestor is average that * represents that complex conjugate, < > represent；

(6) with the distance x of observation station and yoz coordinate plane for abscissa, with average diffraction intensityFor vertical coordinate, the average diffraction intensity after phase screen fractal in hypersonic turbulent flow is emulated, draws the distribution curve of average diffraction intensity, draw the hypersonic micro-structure of turbulence affecting laws to electromagnetic wave propagation by this distribution curve.

2. the method according to claims 1, wherein fractal characteristic according to hypersonic turbulent flow and non-kolmogorov power spectrum in step (1), solve hypersonic turbulent flow refractive index fluctuation power spectrum V_n(κ), carry out as follows:

(1a) fractal dimension D of hypersonic turbulent flow is obtained by experiment；Relation further according between turbulent flow fractal dimension D hypersonic in fractal Brown motion, fractal index H and spectrum index α: H=2-D and α=2H+3, solves the spectrum index α that hypersonic turbulent flow refractive index fluctuation power spectrum meets；

By the relation α=p+3 of spectrum index α Yu scaling law p, obtain the scaling law p that hypersonic turbulent flow refractive index fluctuation power spectrum meets；

(1b) by scaling law p and spectrum index α, non-kolmogorov power spectrum formula is substituted into:

$V_n\left(\mathrm{\&kappa;}\right)=A\left(\mathrm{\&alpha;}\right){\tilde{C}}_n^2{\mathrm{\&kappa;}}^{-(p+1)},$

Obtain the refractive index fluctuation power spectrum that hypersonic turbulent flow meets.

$V_n\left(\mathrm{\&kappa;}\right)=0.14{\tilde{C}}^2{\mathrm{\&kappa;}}^{-9/5},$

Wherein, $A\left(\mathrm{\&alpha;}\right)=2^{\mathrm{\&alpha;}-6}({\mathrm{\&alpha;}}^2-5\mathrm{\&alpha;}+6){\mathrm{\&pi;}}^{-3/2}\&lsqb;\mathrm{\&Gamma;}\left(\frac{\mathrm{\&alpha;}-2}{2}\right)/\mathrm{\&Gamma;}\left(\frac{5-\mathrm{\&alpha;}}{2}\right)\&rsqb;$ For power spectrum constant, Γ is gamma function,For refractive index fluctuation structural constant on transmission path, κ=2k ' sin (θ/2), θ is electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, the angle in incident direction and scattering direction.

3. the method according to claims 1, wherein by V in step (1)_n(κ) the form V containing refractive index fluctuation variance and two parameters of external measurement it is converted into_n' (κ), carries out as follows:

(1a) the refractive index fluctuation structure function D ' of random medium is made_nThe refractive index fluctuation structure function D of (r) and Turbulence Media_nR () is equal, even D '_n(r)=D_nR (), obtains

Wherein D '_n(r) and D_nR () is expressed as:

$D_n^{\&prime;}\left(r\right)=2<n_1^2>\&lsqb;1-\frac{1}{2^{p/2-1}\mathrm{\&Gamma;}(p/2)}{\left(\frac{r}{L_0}\right)}^{p/2}{F}_{p/2}\left(\frac{r}{L_0}\right)\&rsqb;,$

$D_n\left(r\right)={\tilde{C}}_n^2{r}^{-p},$

Wherein, p is scaling law,For refractive index fluctuation structural constant on transmission path, F is Bessel function of imaginary argument, and r is the distance of point-to-point transmission in medium,For refractive index fluctuation variance, L₀For the external measurement of Hypersonic Flow Field, Γ is gamma function.

(1b) willExpression formula substitute into hypersonic turbulent flow meet refractive index fluctuation power spectrumV_n(κ) be converted into containingAnd L₀Form V '_n(κ)

$V_n^{\&prime;}\left(\mathrm{\&kappa;}\right)=0.27<n_1^2>{L_0}^{-4/5}{\mathrm{\&kappa;}}^{-9/5},$

Wherein, κ=2k ' sin (θ/2), θ is electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, the angle in incident direction and scattering direction.

4. method according to claim 1, wherein utilizes refractive index fluctuation function n in step (2)₁(x) derive hypersonic turbulent flow meet refractive index fluctuation power spectrumCarry out as follows:

(2a) according to refractive index fluctuation function n₁(x), derivation refractive index fluctuation correlation function B_n(τ)

B_n(τ)=< n₁(x)·n₁(x+ τ) >,

Wherein, τ represents independent increment.

(2b) according to refractive index fluctuation correlation function B_n(τ), derivation refractive index fluctuation power spectrum

${\stackrel{\&OverBar;}{V}}_n\left(\mathrm{\&kappa;}\right)=\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&infin;}}^{+\mathrm{\&infin;}}{B}_n\left(\mathrm{\&tau;}\right)\exp \left(i\mathrm{\&kappa;}\mathrm{\&tau;}\right)d\mathrm{\&tau;},$

(2c) Baily method is utilized, rightExpression formula do continuous approximation, and be integrated, obtain

${\stackrel{\&OverBar;}{V}}_n\left(\mathrm{\&kappa;}\right)=1.74P_1^2<n_1^2>{L_0}^{-4/5}{\mathrm{\&kappa;}}^{-9/5}.$

Wherein, κ=2k ' sin (θ/2), θ is electromagnetic wave incident in Turbulence Media during arbitrary scattering unit, the angle in incident direction and scattering direction,For refractive index fluctuation variance, L₀External measurement for Hypersonic Flow Field.

5. the method according to claims 1, wherein refractive index fluctuation function n in step (4)₁X () is expressed as follows:

Wherein,For refractive index fluctuation variance, D represents fractal dimension, L₀For the external measurement of Hypersonic Flow Field, b representation space fundamental frequency, N represents stacking fold,It it is the equally distributed random number on [0,2 π].

6. method according to claims 1, wherein rectangular modulation function in step (5)And Green's functionExpression formula be respectively as follows:

$P\left({\stackrel{\&RightArrow;}{x}}^{\&prime;}\right)=rect(x^{\&prime;}/L)rect(y^{\&prime;}/L),$

$G(\stackrel{\&RightArrow;}{x},{\stackrel{\&RightArrow;}{x}}^{\&prime;})=\frac{\exp \left({\mathrm{ik}}^{\&prime;}\right|\stackrel{\&RightArrow;}{x}-{\stackrel{\&RightArrow;}{x}}^{\&prime;}\left|\right)}{4\mathrm{\&pi;}|\stackrel{\&RightArrow;}{x}-{\stackrel{\&RightArrow;}{x}}^{\&prime;}|},$

Wherein,Representing the position vector of any in fractal phase screen, x ', y ' is respectivelyVector along the component of x-axis and y-axis,Representing the position vector of observation station, L represents the size of fractal phase screen.