CN109740288A - A method of the aero-optical effect of simulation High Speed Flow Field culminant star optical transport - Google Patents
A method of the aero-optical effect of simulation High Speed Flow Field culminant star optical transport Download PDFInfo
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Abstract
The invention discloses a kind of methods of aero-optical effect for simulating High Speed Flow Field culminant star optical transport, belong to Pneumatic optical field.Set the regional scope of turbulent boundary lamellar field to be simulated and the control parameter of gas ellipsoid；The probability density that opsition dependent control parameter defines in the regional scope of setting generates several spheroids at random, according still further to the spatial dimension assigning density value that remaining control parameter of gas ellipsoid gives each ellipsoid to be included, forms artificial density field；Optical path difference after passing through artificial density field using the incident light that ray tracing method calculates a certain angle, obtains a distorted wavefront snapshot.Aforesaid operations n times are repeated, N distorted wavefront snapshots are obtained, equal wavefront distortion passes through the aero-optical effect after turbulent boundary layer to get the light for arriving simulation when obtained N distorted wavefront snapshots are averaging to obtain.The present invention is smaller to experience dependence, and the operability of method is stronger, and cost is lower, and required time is less.
Description
Technical field
The invention belongs to Pneumatic optical fields, are related to transmission analogy method of the light in aircraft high speed Flow Field, tool
Body is a kind of method of aero-optical effect for simulating High Speed Flow Field culminant star optical transport.
Background technique
With the fast development of high speed and hypersonic aircraft, high-precision optical guidance and guidance technology become concern
Hot spot, wherein celestial navigation and infrared guidance are typically to represent.But optical device is receiving incidence in High Speed Flow Field
The interference that will receive aero-optical effect when light makes imaging generate blur effect.This gas is simulated in ground experiment
Dynamic optical effect simultaneously studies corresponding image compensation and restored method is promote high-speed aircraft navigation and guidance precision effective
Approach.
The accurate simulation of aero-optical effect needs flight test, wind tunnel test or high-precision Fluid Mechanics Computation at present
(CFD) it emulates, these methods require high experimentation cost.Therefore, it is pneumatic to simulate to develop a kind of computation model of simplification
Optical effect can reduce cost.
Turbulent flow is to cause the principal element of aero-optical effect.Current Hydrodynamics Theory and experiment shows that turbulent flow is
It is made of the whirlpool of different scale.Therefore, the vortex structure for simulating turbulent flow is the key that simulation aero-optical effect.Manually place
Gas vortex structure come the vortex structure simulated in turbulent flow be a kind of reduction aero-optical effect simulation complexity method.
American scholar proposes a kind of gaseous sphere whirlpool with randomly placing earliest come the method for simulating turbulent density fluctuation, sees
Document [1]: a kind of test and diagnostic emulation technology of aero-optical effect, author: James Trolinger, David
Weber, William Rose, publication date: in January, 2002；Domestic scholars then also proposed similar analogy method.These
The process of method is: the parameters such as placement location first in the size in setting gaseous sphere whirlpool, inside and outside density contrast and artificial flow field；So
The optical path difference after light beam passes through artificial ball vortex field is calculated by ray tracing method afterwards；It is assessed finally by analysis optical path difference
The power of aero-optical effect.
What the vortex structure analogue technique in above-mentioned document was all made of is the method for placing gaseous sphere whirlpool, the space scale of sphere
It is isotropic, cannot reflects difference of the light of incidence angles degree on aero-optical effect, and the equal table of many experiments
Bright aero-optical effect to incident light angle have apparent dependence, see document [2]: the physical principle of aero-optical effect with
Measurement: reviews and prospects, author: Eric J.Jumper, Stanislav Gordeyev, issuing date: 2017.In addition, existing
The parameter setting of artificial vortex structure all relies on experience in some vortex structure analogue techniques, and the design cycle not standardized can be grasped
The property made is not strong.
Summary of the invention
The present invention is directed to above-mentioned two problems, proposes a kind of method with gas ellipsoid whirlpool simulation aero-optical effect,
Aero-optical effect can not only be simulated to the dependence of incident light angle, but also establish a kind of gas dependent on notional result
Body ellipsoid whirlpool Parameters design, operability are stronger；The Pneumatic optical of specifically a kind of simulation High Speed Flow Field culminant star optical transport
The method of effect.
Specific step is as follows:
Step 1: setting the regional scope of turbulent boundary lamellar field to be simulated；
Optical window the coordinate system OXYZ, coordinate origin O for defining turbulent boundary lamellar field region to be simulated are located at light
The center of window upper surface is learned, X-axis forward direction is flow direction, and Z axis is directed toward on the outside of aircraft casing perpendicular to optical window surface, Y-axis and X-axis
Right-handed coordinate system is constituted with Z axis；Regional scope includes length, width and the thickness in boundary layer.
Step 2: the control parameter of setting gas ellipsoid；
Control parameter includes the quantity k of ellipsoidnum, position, scale, inclination angle, ellipticity and interior outer density.
knumRule of thumb value；In the case where other parameters are constant, increase knumIt can make the corrugated upper ripple peak/trough that distorts
Quantity increase；
Position distribution of the position control gas ellipsoid of ellipsoid in region, distribution rule are as follows: the quantity in whirlpool is with leaving wall
The distance in face increases；
The scale of ellipsoid is indicated with the long axis length of gas ellipsoid；Quadratic function with vertex near wall height indicates
Ellipsoid scale Λ is with height znVariation tendency, expression formula is defined as follows:
Wherein, klenIt is the control parameter of ellipsoid scale, znThe ellipsoid centre of sphere after indicating normalization leaves the distance of wall surface,
That is normalization height；It is the normalization height that smallest dimension gas ellipsoid occurs, the i.e. vertex of quadratic function, ΛminIt is most
Small ellipsoid scale.
The inclination angle theta of gas ellipsoid is defined as the angle of the long axis of spheroid and the OXY plane of optical window coordinate system OXYZ；
The ellipticity α of gas ellipsoid is defined as α=(a-b)/a；A is the long axis length of gas ellipsoid, and b is the short of gas ellipsoid
Shaft length；
Outer density is uniform in gas ellipsoid, and only there are the mutation of density on ellipsoid.
Step 3: the probability density that opsition dependent control parameter defines in the regional scope of setting generates several ellipsoids at random
Body forms people according still further to the spatial dimension assigning density value that remaining control parameter of gas ellipsoid gives each ellipsoid to be included
Work density field；
Specific step is as follows:
Step 301 randomly selects an integer in gas ellipsoid quantity section, as putting in the regional scope of setting
Set total spheroid quantity；
Step 302, the random number generated according to the probability distribution of gas ellipsoid position coordinates, distribute one to each ellipsoid
Sphere center position coordinate；
The probability distribution of gas ellipsoid position X and Y coordinates is being uniformly distributed within the scope of setting regions, the probability of Z coordinate
Distribution meets following formula:
P(zn) indicate znThe probability of position placement spheroid；K is probability normalization coefficient；Indicate that placement spheroid is most
Height；σ is the standard deviation of distribution, for controlling gas ellipsoid in the intensity of z directional spreding.
Step 303 included according to the sphere center position coordinate of spheroid, long axis size and each ellipsoid of Dip countion
Spatial dimension；
Specifically: setting centre coordinate as the positive ellipsoid equation of origin is
Then meet inequalityCoordinate points be all contained in positive spheroid.
It is [x for centre coordinate0 y0 z0] and inclination angle be the oblique ellipsoid of θ, chosen in it using the method for coordinate rotation
The point in portion, if tiltedly the coordinate of the point on ellipsoid is [x ' y ' z '], according to coordinate Principle of Rotating, [x ' y ' z '] and positive ellipsoid
Point [x y z] on face meets following relationship:
Formula (4) right-hand vector is brought into equation (3), replacing [x y z] respectively can be obtained oblique ellipsoid equation, similarly
Choose the intracorporal all coordinate points of oblique ellipsoid.
Step 304 is assigned according to the space coordinate set that the density expression formula in gas ellipsoid is included to each ellipsoid
Give density value.
Density p in gas ellipsoidinIt is expressed as
ρin=(- 1)NkρF(M,z)Λρ∞+ρ∞ (5)
Wherein, (- 1)NThe random number for taking 1 or -1, indicate gas ellipsoid in density could possibly be higher than or lower than incoming flow it is close
Degree.kρIt is the density domination parameter of gas ellipsoid, F (M, z) is the mach number effect factor, ρ∞For the density outside gas ellipsoid.
Step 4: the optical path difference after artificial density field is passed through using the incident light that ray tracing method calculates a certain angle,
Obtain a distorted wavefront snapshot.
Optical path difference is defined as the product of the propagation distance s and the refractive index n on propagation path of light.For entire optical path,
The light path in every section of path of optical path difference is cumulative to be obtained, i.e.,
ΔsiIndicate the geometrical length in i-th section of path, propagation distance is k sections shared.niIndicate the refractive index in i-th section of path, and
niWith the density p on i-th section of pathiRelationship be ni=1+KGDρi, wherein KGDFor the Gladstone-Dale coefficient of light, only
It is related with the wavelength of light.
Step 5: repetition step 3 and step 4 are total to n times, N distorted wavefront snapshots are obtained, by obtained N distortional waves
Preceding snapshot when being averaging to obtain equal wavefront distortion to get to simulation light pass through turbulent boundary layer after aero-optical effect.
N is the frame number of snapshot superposition.
The present invention has the advantages that
1) a kind of, method for the aero-optical effect for simulating High Speed Flow Field culminant star optical transport, simulates rapids with gas ellipsoid
Vortex structure in laminar boundary layer can simulate aero-optical effect to the dependence of incident light angle, and compared to Physical Experiment and
Fluid Mechanics Computation simulation experiment method, cost is lower, and required time is less.
2) a kind of, method for the aero-optical effect for simulating High Speed Flow Field culminant star optical transport, the control parameter of gas ellipsoid
It is the theoretical result studied based on current Pneumatic optical, there is the display expression-form of formulation, it is smaller to experience dependence,
The operability of method is stronger.
Detailed description of the invention
Fig. 1 is the schematic diagram that gas ellipsoid is placed in artificial flow field of the present invention；
Fig. 2 is a kind of flow chart of the method for the aero-optical effect for simulating High Speed Flow Field culminant star optical transport of the present invention；
Fig. 3 is gas ellipsoid scale k of the present inventionlenWith reynolds number RexPower function relationship；
Fig. 4 is the schematic diagram of gas ellipsoid of the present invention
Fig. 5 (a) is the quantity N and average distortion wavefront rms OPD of present invention superposition snapshotrmsBetween relationship.
Fig. 5 (b) is the every variable quantity summation for increasing average optical path difference caused by a snapshot of the present invention；
Fig. 6 is the normalization wavefront distortion contrast schematic diagram of different angle incident light of the present invention；
Fig. 7 is distorted wavefront (optical path difference) curved surface for the vertical incidence directional light that present invention simulation obtains.
Fig. 8 is the image planes intensity profile after the vertical incidence directional light imaging that present invention simulation obtains.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention is a kind of method of aero-optical effect for simulating High Speed Flow Field culminant star optical transport, the gas manually placed
Body ellipsoid generates artificial density field to simulate light across disturbed effect after turbulent boundary.With gas ellipsoid whirlpool simulated person's work stream
Such as Fig. 1, using the method for gas ellipsoid whirlpool simulation aero-optical effect, by random in artificial flow field by certain rule
Gas ellipsoid is placed, so that different angle incident light is produced blur effect related with incidence angle, has reached simulation turbulent boundary
The effect of layer aero-optical effect, has calculation amount small, parameter is easy to determining advantage.
As shown in Figure 2, the specific steps are as follows:
Step 1: setting the regional scope of turbulent boundary lamellar field to be simulated；
Optical window the coordinate system OXYZ, coordinate origin O for defining turbulent boundary lamellar field region to be simulated are located at light
The center of window upper surface is learned, X-axis forward direction is flow direction, and Z axis (indicating wall face height) is directed toward aircraft shell perpendicular to optical window surface
External side, Y-axis and X-axis and Z axis constitute right-handed coordinate system；Simulate the geofence of turbulent boundary lamellar field are as follows: long (X-axis)
200mm, wide (Y-axis) 100mm, thickness (Z axis) 30mm.
Step 2: the control parameter of setting gas ellipsoid；
Control parameter includes the quantity k of ellipsoidnum, position, scale, inclination angle, ellipticity and interior outer density.
(1) the quantity k of gas ellipsoidnum
knumThe shape that will affect the distortion corrugated of this method output increases k in the case where other parameters are constantnumMeeting
Make corrugated upper ripple peak/trough quantity increase that distorts.knumValue depend on experience, universal experience value is several hundred to thousands of.?
Under the flow field regions size of setting, k is takennum=1000 can make to export relatively reasonable distortion corrugated shape.When practical operation,
The gas ellipsoid number placed when simulating every frame wavefront snapshots is in [0.9knum, 1.1knum] random integers, such energy are taken in range
Enough embody the randomness of turbulent flow.
(2) position of gas ellipsoid
Current Pneumatic optical experiment shows: the outskirt in boundary layer is optics active regions, plays main tribute to wavefront distortion
It offers；Large-scale structure plays a leading role to the distortion of the light beam passed through in turbulent boundary layer.Therefore, the present invention sets gas ellipsoid
Position distribution of the position control gas ellipsoid in region, distribution rule are as follows: the quantity in whirlpool has increasing with the distance for leaving wall surface
The trend added；It is defined with following expression:
Wherein, P (zn) indicate znThe probability of position placement spheroid.zn=z/ δ indicates the ball of the gas ellipsoid after normalization
The heart leaves the distance of wall surface, i.e. normalization height；δ indicates the boundary layer thickness of simulated domain,Indicate that placement spheroid is most
Height.Current Pneumatic optical test result shows the flow field structure at 0.8 δ of wall face height to the contribution of optical distortion most
Greatly, it therefore takesσ is that the standard deviation of this distribution is pressed for controlling gas ellipsoid in the intensity of z directional spreding
Empirical value takes the δ of σ=0.5.K is probability normalization coefficient, is met
zn iIndicate that the centre of sphere of i-th of gas ellipsoid leaves the distance of wall surface.
(3) scale of gas ellipsoid
The present invention indicates the characteristic dimension of spheroid with the long axis length of gas ellipsoid.Current Pneumatic optical tests knot
Fruit shows the density correlation length Λ (z of turbulent boundary layer outskirtn) with znIt is incremented by, it is significant near wall areal concentration correlation length
Increase.In view of the terseness of rule design, the present invention indicates ellipsoid body characteristics in the quadratic function of near wall height with vertex
Scale Λ is with height znVariation tendency, defined with following expression:
Wherein,It is the normalization height that smallest dimension gas ellipsoid occurs, the i.e. vertex of quadratic function, is taken as 0.05
δ。ΛminIt is the smallest spheroid scale, according to the setting in the prior art to boundary layer gaseous sphere whirlpool scale lower bound, it is known that rapid
The vortex structure of smallest dimension is within the scope of the δ of 0.05 δ~0.1 in laminar boundary layer, therefore takes Λmin=0.05 δ.klenIt is spheroid ruler
The control parameter of degree, Pneumatic optical experiment show reynolds number RexIt will affect the density scale dependent in turbulent boundary layer, and Reynolds
The bigger scale dependent of number and OPDrmsIt is smaller, therefore, the reynolds number Re that the present invention passes through explicit physical meaningxTo set klen.?
The Typical Reynolds Numbers range Re of high-speed aircraftx∈[1×106, 9 × 108] in pass through empiric observation distortion corrugated degree of crushing
Relative size gives klenValue rangeEstablish k as shown in Figure 3lenWith RexPower function
Relationship, expression formula are as follows
klen=g1(Rex(the Re of)=242.7x)-0.1883 (4)
(4) inclination angle of gas ellipsoid and ellipticity
Structure inclination angle in turbulent boundary layer is confirmed in test and fluid mechanical emulation.This structure inclination angle
Size be difficult directly to recognize from flow field, pass through measurement different angle incident ray optical path difference root mean square OPDrmsSize
It can reflect structure inclination angle indirectly.Spheroid scale has the characteristics that space anisotropic, the knot being suitble in performance turbulent boundary layer
Structure inclination angle.
Rotational ellipsoid is obtained after the oval rotation around its long axis that long axis length is a by the present invention, minor axis length is b, then
This spheroid is rotated into the angle θ, as shown in Figure 4.The density correlation knot in turbulent boundary layer is indicated with this postrotational spheroid
Structure.
The inclination angle theta of gas ellipsoid is defined as the angle of the long axis of spheroid and the OXY plane of optical window coordinate system OXYZ, takes
θ=24.17 °, the ellipticity α of gas ellipsoid are defined as α=(a-b)/a；Take ellipticity α=0.447.
With the angle γ injection/injection light (angle that the angle γ is defined as light Yu upstream direction of flow), OPDrmsWith hang down
The OPD of straight incident lightrmsWith similar proportionate relationship:
Wherein c (γ) is proportionality coefficient related with light beam inclination angle, according to experimental result, the upper boundProbably 1.4
In~2 ranges, the present invention takes 1.7, lower boundc(γ)About 0.94.This optical beam ratio for being namely directed toward downstream is directed toward upstream
The distortion of light beam is more serious, and it is longer that this can be explained as referring to light path of the light beam in turbulence structure downstream.
Entire flow field is equivalent to a gas ellipsoid as shown in Figure 4 by the present invention, then along long axis a and along the direction short axle b
Light beam be respectively provided with minimum and maximum distortion.Due to density having the same everywhere in gas ellipsoid, so light path can be by several
What length replaces, and can obtain
Wherein, LvDefinition see Fig. 4.
Inclination angle theta=24.17 ° of gas ellipsoid, ellipticity α=(a-b)/a=0.447, for manually flowing can be solved by above formula
All gas ellipsoid in field areas is all made of identical inclination angle and ellipticity setting.
(5) density in gas ellipsoid
It is consecutive variations different from density in true flow field, for ease of calculation, the present invention is set inside and outside gas ellipsoid
Density is all uniformly that only there are the mutation of density on ellipsoid.
By the way that the OPD of obtained distorted wavefront will be simulatedrmsWith the turbulent boundary layer in the prior art with theoretical generally acknowledged property
Aero-optical effect prediction model (hereinafter referred to as BLPM) anchoring, to design the density parameter of gas ellipsoid.Since BLPM is to horse
Conspicuous several M have dependence, so joined the mach number effect factor in the density expression formula of gas ellipsoid.Due to current gas
Dynamic optical test shows that large-scale structure plays main contributions to wavefront distortion, so the scale Λ of gas ellipsoid is also added to ellipse
In ball density expression formula, then the density p in gas ellipsoidinIt is expressed as
ρin=(- 1)NkρF(M,z)Λρ∞+ρ∞ (6)
Wherein, ρ∞For the density outside gas ellipsoid, it is set as carrying out current density.(-1)NIt is the random number for taking 1 or -1, indicates gas
Density in body ellipsoid, which could possibly be higher than or be lower than, carrys out current density.F (M, z) is the mach number effect factor, and expression formula is
Wherein, κ is specific heat ratio.F (z/ δ)=Uz/δ/U∞It is average speed profile；Uz/δIt is the average speed at height z/ δ,
U∞It is speed of incoming flow.According to Hydrodynamics Theory, the average speed of boundary layer inner region and outskirt is respectively provided with linearly and to number form
Formula
Wherein, coefficient c1,c21And c22It can be solved with it in the condition of continuity of interior outskirt by the boundary condition of average speed.
kρIt is the density domination parameter of gas ellipsoid, the present invention passes through calibration kρBy the OPD on the distortion corrugated simulatedrmsWith
BLPM anchoring, demarcates kρThe step of it is as follows:
1) in a given reynolds number Rex0Under, fitting obtains OPD under different Mach numberrmsAbout kρFunction
OPDrms(kρ)；
2) by the anchoring condition (OPD on distortion corrugatedrms=BLPM calculated value) and fitting function OPDrms(kρ) determine kρ
Scatterplot set { the k of value under different Mach numberρ(M,Rex0)i}；
3) different Re is chosenx0, step 1) is repeated with 2), obtains k under different Mach number and different Reynolds numberρValue dissipates
Point set { kρ(M,Rex)i, k is obtained using surface fitting technologyρAbout Mach number M and reynolds number RexFunction expression kρ
(M,Rex)。
Step 3: the probability density that opsition dependent control parameter defines in the regional scope of setting generates several ellipsoids at random
Body forms people according still further to the spatial dimension assigning density value that remaining control parameter of gas ellipsoid gives each ellipsoid to be included
Work density field；
An integer is randomly selected in gas ellipsoid quantity section first, as placing total spheroid quantity；Then
Random number is generated according to the position distribution probability of gas ellipsoid, distributes a sphere center position coordinate to each ellipsoid；Then according to
Sphere center position, long axis size, inclination angle and the ellipticity of spheroid calculate the spatial dimension that each ellipsoid is included；Finally according to gas
The space coordinate set assigning density value that density expression formula in body ellipsoid gives each ellipsoid to be included.
Specific step is as follows:
Step 301 randomly selects an integer in gas ellipsoid quantity section, as putting in the regional scope of setting
Set total spheroid quantity；
Step 302, the random number generated according to the probability distribution of gas ellipsoid position coordinates, distribute one to each ellipsoid
Sphere center position coordinate；
The probability distribution of gas ellipsoid position X and Y coordinates is being uniformly distributed within the scope of setting regions, the probability of Z coordinate
Distribution meets formula (1).
Step 303 included according to the sphere center position coordinate of spheroid, long axis size and each ellipsoid of Dip countion
Spatial dimension；
Specifically: setting centre coordinate as the positive ellipsoid equation of origin is
Then meet inequalityCoordinate points be all contained in positive spheroid.
It is [x for centre coordinate0 y0 z0] and inclination angle be the oblique ellipsoid of θ, chosen in it using the method for coordinate rotation
The point in portion, if tiltedly the coordinate of the point on ellipsoid is [x ' y ' z '], according to coordinate Principle of Rotating, [x ' y ' z '] and positive ellipsoid
Point [x y z] on face meets following relationship:
Formula (10) right-hand vector is brought into equation (9), replacing [x y z] respectively can be obtained oblique ellipsoid equation, together
Reason chooses the oblique intracorporal all coordinate points of ellipsoid.
Step 304, the space coordinate set for giving each ellipsoid to be included according to the density expression formula (6) in gas ellipsoid
Assigning density value.
Step 4: the optical path difference after artificial density field is passed through using the incident light that ray tracing method calculates a certain angle,
Obtain a distorted wavefront snapshot.
Optical path difference is defined as the product of the propagation distance s and the refractive index n on propagation path of light.For entire optical path,
The light path in every section of path of optical path difference is cumulative to be obtained, i.e.,
ΔsiIndicate the geometrical length in i-th section of path, propagation distance is k sections shared.niIndicate the refractive index in i-th section of path, and
niWith the density p on i-th section of pathiRelationship be ni=1+KGDρi, wherein KGDFor the Gladstone-Dale coefficient of light, only
It is related with the wavelength of light.
Step 5: repetition step 3 and step 4 are total to n times, N distorted wavefront snapshots are obtained, by obtained N distortional waves
Preceding snapshot when being averaging to obtain equal wavefront distortion to get to simulation light pass through turbulent boundary layer after aero-optical effect.
N is the frame number of snapshot superposition, belongs to the control parameter of this method.
One is represented instantaneously with the distorted wavefront that the boundary layer flow field that vortex structure analogue technique generates is simulated
As a result, by a certain number of transient distortion wavefront snapshots it is average after can be with the average wave in the analogue exposure time before.In order to true
Fixed suitable superposition snapshot quantity N, considers both sides factor: being on the one hand the stability that average distortion wavefront changes with N, when
Average distortion wavefront thinks that output is stablized when little with the increase variation of N.It on the other hand is calculation amount, the snapshot number of superposition is fewer
It is time-consuming shorter.
Average distortion wavefront with N variation as shown in figure 5, in Fig. 5 (a) average distortion wavefront rms with N increase and subtract
Small but reduced speed is more than that reduce rapidly and gradually tend to 0, Fig. 5 (b) after 20 be caused by one snapshot of every superposition in N
The variable quantity summation of optical path difference before average wave, it can be seen that in N be more than to be further added by snapshot quantity to the shadow of corrugated optical path difference after 25
Very little is rung, illustrates that the output of emulator has reached stabilization.Comprehensively consider output stability and calculation amount, this method is by the fast of superposition
25 are taken as according to quantity N.
Simulated conditions are as shown in table 1:
Table 1
The present invention is to different angle incident beam aero-optical effect (with the optical path difference root mean square OPD of distorted wavefrontrmsCome
Measure) simulation result it is as shown in Figure 6.Horizontal axis indicates that the angle of outgoing/incident ray and upstream, the longitudinal axis are indicated to vertical in Fig. 6
OPD after straight incident light normalizationrms, analogy method of the invention with emulated in the prior art by Fluid Mechanics Computation (CFD)
Obtained experimental result is compared, and simulator indicates analogy method of the invention；White&Visbal (2012) and
Wang&Wang (2012) is to emulate obtained experimental result by Fluid Mechanics Computation (CFD) in the prior art；It can be seen that
Analogy method of the invention is very close with data in literature, illustrates that Pneumatic optical analogy method of the invention can effectively simulate rapids
The anisotropic character of aero-optical effect in laminar boundary layer.
The present invention to the simulation result of the distorted wavefront of the aero-optical effect of vertical incidence directional light and imaging effect such as
Shown in Fig. 7 and Fig. 8.Fig. 7 has very high with the distorted wavefront shape obtained in the prior art by Fluid Mechanics Computation method
Similarity, but under the conditions of listed in table 1 simulation hardware, analogy method time-consuming of the invention about 2400~2600 seconds, and count
Fluid operator mechanics method usually require on large server run tens hours could obtain similar simulation result.Fig. 8
It is middle using effect of the starlight by image blur after aero-optical effect disturbance in method simulation celestial navigation of the invention, can be with
Find out that the effect of image planes asterism energy dissipation has been truly reflected to come out.
Claims (4)
1. a kind of method for the aero-optical effect for simulating High Speed Flow Field culminant star optical transport, which is characterized in that specific step is as follows:
Step 1: setting the regional scope of turbulent boundary lamellar field to be simulated；
Optical window the coordinate system OXYZ, coordinate origin O for defining turbulent boundary lamellar field region to be simulated are located at optical window
The center of upper surface, X-axis forward direction are flow direction, and Z axis is directed toward on the outside of aircraft casing perpendicular to optical window surface, Y-axis and X-axis and Z
Axis constitutes right-handed coordinate system；
Step 2: the control parameter of setting gas ellipsoid；
Control parameter includes the quantity k of ellipsoidnum, position, scale, inclination angle, ellipticity and interior outer density；
Step 3: the probability density that opsition dependent control parameter defines in the regional scope of setting generates several spheroids at random,
According still further to the spatial dimension assigning density value that remaining control parameter of gas ellipsoid gives each ellipsoid to be included, formed artificial close
Spend field；
Specific step is as follows:
Step 301 randomly selects an integer in gas ellipsoid quantity section, total as to place in the regional scope of setting
Spheroid quantity；
Step 302, the random number generated according to the probability distribution of gas ellipsoid position coordinates, distribute a centre of sphere to each ellipsoid
Position coordinates；
The probability distribution of gas ellipsoid position X and Y coordinates is being uniformly distributed within the scope of setting regions, the probability distribution of Z coordinate
Meet following formula:
P(zn) indicate znThe probability of position placement spheroid；K is probability normalization coefficient；It indicates to place the most height of spheroid
Degree；σ is the standard deviation of distribution, for controlling gas ellipsoid in the intensity of z directional spreding；
Step 303, the space for being included according to the sphere center position coordinate of spheroid, long axis size and each ellipsoid of Dip countion
Range；
Step 304, the space coordinate set for being included to each ellipsoid according to the density expression formula in gas ellipsoid assign close
Angle value；
Density p in gas ellipsoidinIt is expressed as
ρin=(- 1)NkρF(M,z)Λρ∞+ρ∞ (2)
Wherein, (- 1)NIt is the random number for taking 1 or -1, indicates that the density in gas ellipsoid could possibly be higher than or be lower than and carry out current density；kρ
It is the density domination parameter of gas ellipsoid, F (M, z) is the mach number effect factor, ρ∞For the density outside gas ellipsoid；
Step 4: passing through the optical path difference after artificial density field using the incident light that ray tracing method calculates a certain angle, obtain
One distorted wavefront snapshot；
Optical path difference is defined as the product of the propagation distance s and the refractive index n on propagation path of light；For entire optical path, light path
The light path in every section of path of difference is cumulative to be obtained, i.e.,
ΔsiIndicate the geometrical length in i-th section of path, propagation distance is k sections shared；niIndicate the refractive index in i-th section of path, and niWith
Density p on i-th section of pathiRelationship be ni=1+KGDρi, wherein KGDFor the Gladstone-Dale coefficient of light, only with light
The wavelength of line is related；
Step 5: repetition step 3 and step 4 are total to n times, N distorted wavefront snapshots are obtained, obtained N distorted wavefronts are fast
Equal wavefront distortion is when obtaining according to averaging to get the aero-optical effect to the light of simulation after turbulent boundary layer；
N is the frame number of snapshot superposition.
2. a kind of method of aero-optical effect for simulating High Speed Flow Field culminant star optical transport as described in claim 1, feature
It is, regional scope described in step 1 includes length, width and the thickness in boundary layer.
3. a kind of method of aero-optical effect for simulating High Speed Flow Field culminant star optical transport as described in claim 1, feature
It is, k described in step 2numRule of thumb value；In the case where other parameters are constant, increase knumIt can make corrugated of distorting
The quantity of upper wave crest/trough increases；
Position distribution of the position control gas ellipsoid of ellipsoid in region, distribution rule are as follows: the quantity in whirlpool is with leaving wall surface
Distance increases；
The scale of ellipsoid is indicated with the long axis length of gas ellipsoid；Quadratic function with vertex near wall height indicates ellipsoid
Scale Λ is with height znVariation tendency, expression formula is defined as follows:
Wherein, klenIt is the control parameter of ellipsoid scale, znThe ellipsoid centre of sphere after indicating normalization leaves the distance of wall surface, i.e. normalizing
Change height；It is the normalization height that smallest dimension gas ellipsoid occurs, the i.e. vertex of quadratic function, ΛminIt is the smallest ellipse
Ball scale；
The inclination angle theta of gas ellipsoid is defined as the angle of the long axis of spheroid and the OXY plane of optical window coordinate system OXYZ；
The ellipticity α of gas ellipsoid is defined as α=(a-b)/a；A is the long axis length of gas ellipsoid, and b is that the short axle of gas ellipsoid is long
Degree；
Outer density is uniform in gas ellipsoid, and only there are the mutation of density on ellipsoid.
4. a kind of method of aero-optical effect for simulating High Speed Flow Field culminant star optical transport as described in claim 1, feature
It is, the step 303 specifically:
If the positive ellipsoid equation that centre coordinate is origin is
Then meet inequalityCoordinate points be all contained in positive spheroid；
It is [x for centre coordinate0 y0 z0] and inclination angle be the oblique ellipsoid of θ, it is internal that it is chosen using the method for coordinate rotation
Point, if tiltedly the coordinate of the point on ellipsoid is [x ' y ' z '], according to coordinate Principle of Rotating, on [x ' y ' z '] and positive ellipsoid
Point [x y z] meet following relationship:
Formula (6) right-hand vector is brought into equation (5), replacing [x y z] respectively can be obtained oblique ellipsoid equation, similarly choose
The intracorporal all coordinate points of oblique ellipsoid.
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