A design method of special-shaped curved observation window for internal flow field focusing schlieren test

Abstract

The application discloses a design method of a special-shaped curved surface observation window for an internal flow field focusing schlieren test, and relates to the technical field of experimental fluid mechanics. The observation window is composed of left and right glass windows. The inner surfaces of the left and right glass windows are respectively the same as the left and right special-shaped wall surfaces of an internal flow field test area. According to the light path reversibility principle, the Malus law and the design requirement that the converging characteristics of a converging light beam through the observation window remain unchanged in a focusing schlieren system, the outer surfaces of the left and right glass windows are respectively obtained by using an iteration method and a light ray tracing method. The design method solves the problem of the design of the special-shaped wall surface observation window for the visualization test of the internal flow field of the special-shaped wall surface by using the focusing schlieren system. The special-shaped curved surface observation window designed by using the method meets the transmission requirement of the focusing schlieren system for the light beam, ensures the original converging characteristics of the light beam in front of the focusing lens, and thus ensures the distortion-free imaging of the flow field.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of experimental fluid mechanics. More particularly, the present application relates to a design method of a special-shaped curved observation window for an internal flow field focusing schlieren test. BACKGROUND

[0002] The inlet duct is a key component of the ramjet engine, and its performance is crucial to the entire propulsion system. Among various types of inlet ducts, the internal turning inlet duct has the advantages of high flow capture, strong compression capability, small aerodynamic resistance, and easy interfacing with the combustion chamber, and has attracted extensive attention from scholars in the relevant fields at home and abroad. It has become the most promising type of air intake component for the integrated configuration of high-speed aircraft.

[0003] The design method of the internal turning inlet duct generally adopts the streamline tracking method and the streamline correction method to form the flow passage wall. The generated flow passage wall is obviously different from the conventional two-dimensional plane compression and axisymmetric compression. This wall is a spatial special-shaped curved surface. When the internal flow is compressed by this special-shaped curved surface, complex flow phenomena such as mutual interference between the spatial special-shaped curved shock wave and the boundary layer of the special-shaped wall, cross interference between the spatial special-shaped shock waves, and mutual interference between the special-shaped shock wave and the special-shaped expansion wave occur, making the internal flow field structure extremely complex. Obtaining the special-shaped curved internal flow field structure through experiments can provide direct support for verifying the design method of the internal turning inlet duct, revealing the flow mechanism of the internal turning inlet duct, and forming the flow field control technology of the internal turning inlet duct, and has been the direction of efforts of researchers.

[0004] Currently, there are mainly two ways to obtain the internal flow field structure and information of the internal turning inlet duct through experiments. One is contact measurement, such as measuring the flow field pressure or velocity by installing a probe or a wire in the internal flow field. The other is non-contact measurement, such as flow visualization by optical method through the glass window opened on the internal flow wall. As a complement, non-contact measurement is an indispensable measurement method. However, opening a window on the wall of the internal turning inlet duct, or designing a glass window on the wall of the internal turning inlet duct is a primary problem that needs to be solved for non-contact measurement.

[0005] In order to observe the internal flow field of the internal turning inlet duct, two types of glass windows are opened on the wall of the internal turning inlet duct. One is used for conventional schlieren test. However, due to the spatial complexity of the internal flow field of the internal turning inlet duct, the conventional schlieren test obtains the flow field of integral effect, and the display result cannot restore the spatial flow field. The other is used for focusing schlieren test. This method can obtain the slice effect of the spatial flow field, and the display result can be directly used for further research. Obviously, the glass window technology for the internal turning inlet duct adapted to the focusing schlieren test is more practical.

[0006] However, the inner turning inlet wall windowing technology for focusing schlieren test has always been a technical difficulty. This is because: the traditional planar glass window or regular curved glass window design will change the wall shape of the inner flow channel, causing the inner flow simulation distortion; the special-shaped curved glass window (patent application number: 201610458467.X, invention name: aircraft special-shaped curved inner flow channel flow field visualization glass observation window and design method) based on the design of plane wave (parallel light incidence and parallel light emission) can realize the shape preservation of the inner wall of the inner turning inlet, but can only obtain the integral total effect of the three-dimensional space complex flow field along the optical axis direction; the design technology of the special-shaped curved glass of the inner turning inlet wall windowing suitable for the focusing schlieren test is still in the blank of research. SUMMARY

[0007] An object of the present application is to solve at least the above problems and / or defects, and to provide at least the advantages to be described later.

[0008] In order to achieve these objects and other advantages of the present application, a special-shaped curved observation window design method for inner flow field focusing schlieren test is provided, the special-shaped curved observation window comprising: two asymmetric glass windows installed on the left and right side walls of the inner flow field test area, comprising:

[0009] S1, determining the input condition and design requirement according to the optical parameters of the focusing schlieren system and the special-shaped wall of the inner flow field, and taking the special-shaped walls on the left and right sides of the inner flow field test area as the inner surfaces of the glass windows;

[0010] S2, according to the inner surface of the left glass window C 1, using the iterative method and the light ray reverse tracing method to trace the light rays in the converging light beam of the focusing schlieren system, and obtaining the outer surface of the left glass window C 3;

[0011] S3, according to the inner surface of the right glass window C 2, using the iterative method and the light ray forward tracing method to trace the light rays in the converging light beam of the focusing schlieren system, and obtaining the outer surface of the right glass window C 4.

[0012] Preferably, in S1, the optical parameters of the focusing schlieren system include: the object distance of the original grid L , the light passing aperture of the Fresnel lens D F , and the light passing aperture of the imaging lens D L ;

[0013] The determination method of the input condition is:

[0014] S11, establishing a three-dimensional rectangular coordinate system according to the right-hand rule OXYZWith the optical axis of the focused schlieren system as X The axis, from left to right is X The positive direction of the axis is perpendicular to... X The direction of the axis upward is Y The positive direction of the axis, Z Shaft and Z The positive direction of the axis is determined by the right-hand rule, and the origin of the coordinate system is... O It is located at the spatial center of the internal flow field test area;

[0015] S12. Obtain the inner surface of the left glass window based on the irregular wall surface on the left side of the internal flow field. C Discrete points of 1 A i ( a i , b i , c i The set of ) i =1, 2, ..., S , a i For discrete points A i x-coordinate, b i For discrete points A i y-coordinate, c i For discrete points A i The z-coordinate;

[0016] S13. Obtain the inner surface of the right-side glass window based on the irregular wall surface on the right side of the internal flow field. C Discrete points of 2 D j ( u j , v j , w j The set of ) j =1, 2, ..., K , u j For discrete points D j x-coordinate, v j For discrete points D j y-coordinate, w j For discrete points D j The z-coordinate;

[0017] S14, determine the convergence angle of the light beam in the focusing schlieren system based on the following formula β :

[0018]

[0019] In the above formula, is the inverse tangent function, P is the distance between the Fresnel lens and the original grid;

[0020] S15, set the convergence point of the converging light beam of the focusing schlieren system O 1(0, 0, 0), a is the x coordinate of the convergence point a 1, and O is characterized by the following formula: a

[0021]

[0022] In the above formula, is the tangent function, is the distance from the center of the internal flow field to the imaging lens; S16, other known input conditions include: the refractive index of the glass window material

[0023] , the nominal thickness of the glass window n ; d

[0024] In S1, the design requirement is that the addition of the left and right glass windows on the profiled wall surface of the internal flow field does not change the convergence characteristics of the light beam in the optical system.

[0025] Preferably, in S2, the method for obtaining the outer surface C 3 of the left glass window is as follows:

[0026] S21, in the focusing schlieren system, the light beam is incident from the outer surface C 3 of the left glass window, after two refractions, it is emitted from the inner surface C 1 into the internal flow field, since the outer surface C 3 of the left glass window is the surface to be designed, and the inner surface C 1 is a known surface, according to the principle of optical path reversibility, the inner surface C 1 is taken as the incident surface, and the outer surface C 3 is taken as the emitted surface, the incident light beam of the inner surface C 1 is a divergent light beam, and the emitted light beam of the outer surface C 3 is a divergent light beam, and the convergence characteristics of the same light ray at the incident position and the emitted position in the divergent light beam do not change;

[0027] S22, the inner surface C ​​S21, the edge ray of the incident divergent light beam of 1 is ray-traced reversely, and the starting point of the incident divergent light beam is determined by using an iteration method O 2( b C 3 B S ( x S , y S , z S ), b O 2

[0028] S23, the divergent light beam with 2 as the starting point is discretized according to different divergence angles, and the angle between the first ray and the z-axis is denoted as O X β i i C 3 A i ( a i , b i , c i ), λ i i 3 C B i ( x i , y i , z i );

[0029] wherein, β i ∈(0, β ), i =1,……, S -1, S is the number of discrete points on the outer surface C 3;

[0030] S24, the intersection point B S ( x S , y S , z ​​​​​​​​​S ) and intersection B i ( x i , y i , z i The set of ) is used to construct the outer surface of the left glass window. C 3.

[0031] Preferably, in S22, the intersection point B S ( x S , y S , z S The method to obtain ) is:

[0032] S2201, inner surface C The starting point of the incident diverging beam of 1 is located at X On the axis and the starting point is O 2( b (0, 0), at the convergence point O A value to be determined is given around 1. b Assign initial values;

[0033] S2202, with O Starting from 2, and with X The included angle of the axis is β The diverging beam edge rays and the inner surface C 1 intersects at one point A S ( a S , b S , c S Find the edge rays of the diverging beam. O 2 A S vector , will vector Normalization yields vectors Normalized vector From point O 2 pointing points A S ;

[0034] According to the inner surface C 1 on point A S The cross product of the four surrounding points is obtained. A S Normal of a point normal The unit vector is , from A S Pointing to the internal flow field, edge rays O 2 A S angle of incidence α S1 satisfy:

[0035]

[0036] S2203. According to the law of refraction of light, the refracted ray can be obtained through the following formula. A S B S vector , from A S point to B S :

[0037]

[0038] In the above formula, It is refracted light. A S B S The angle of refraction, n It is the refractive index of the glass window material, and , For normal line unit vector, vector The normalized vector is And vector ,vector ,vector In the same plane;

[0039] S2204, Preset scaling factor λ Normalized vector Scale to outer surface C 3. The intersection point is recorded as... B S Then we have:

[0040]

[0041] Let the inner surface C 1 and X The intersection of the axes is A 1. Outer surface C 3 and X The intersection of the axes is B 1;

[0042] Constructing a sphere W 1: Assume a sphere W The center of the ball is 1. O 2( b ,0,0), spherical W Vertex of 1 N 1 and the intersection point A Distance of 1 | N 1 A 1|= d 1. Vertex N 1 is located at the intersection A The right side of 1, edge light O 2 A S With sphere W 1 intersects at point N S ,point A S ,point N S ,point O 2. If they are on the same straight line, then the sphere W The constructive equation for 1 is characterized by the following equation:

[0043]

[0044] In the above equation, x, y, and z are the variables used to construct the equation. R 1 is a sphere W The radius of 1, and R The value of 1 needs to ensure the spherical surface W 1. On the inner surface C The right side of 1;

[0045] Constructing a sphere W 3: Assume a sphere W The center of ball 3 is O 1( a ,0,0), spherical W 3 vertices M 1 and the intersection point B Distance of 1 | B 1 M 1|= d 3. Vertex M 1 is located at the intersection B 1. Left side, edge light B S M S With sphere W 3 intersect at point M S ,point B S ,point M S ,point O1. If they are on the same straight line, then the sphere W The construction equation for 3 is characterized by the following equation:

[0046]

[0047] in, R 3 is a sphere W The radius is 3, and R The value of 3 needs to ensure the spherical surface W 3. On the outer surface C 3 to the left;

[0048] S2205, Regarding the scaling factor λ By iterating, we can obtain ;

[0049] S2206, the starting point of the emitted diverging beam O 1 and B S Connect them to obtain edge rays. O 1 B S corresponding vector Then the edge light O 1 B S and X Angle between axes β S Characterized by the following formula:

[0050]

[0051] in, The direction vector of the X-axis and ;

[0052] If | β S - β |≤ Δ If this is not valid, then at the convergence point... O 1. Search nearby O 2( b (0, 0), repeat steps S2202~S2206 for the given value b Perform iterations;

[0053] If | β L - β |≤ Δ Established, yielding a value to be determined. b The iteration value;

[0054] in, Δ It is a tiny quantity, given Δ =10 -10 ;

[0055] S2207、According to the iteration value of the pending value b , determine the intersection point of the incident divergent light beam of the inner surface C 1 and the exit divergent light beam edge ray of the outer surface O 2 b , 0, 0) C B S x S y S z S

[0056] Preferably, it includes: in S2205, the flow of iterating the scaling factor λ includes:

[0057] S220501, calculate the edge ray O 2 A S from the point W 1 on the sphere N S to the point W 3 on the sphere M S The optical path OPL NS→MS :

[0058]

[0059] In the above formula, the modulus of the vector O 2 A S , is the modulus of the normalized vector , and is the scaling factor of the normalized vector , λ , 1 O B S is the distance from the point B S to the center of the sphere W 3 O 1

[0060] S220502, calculate the optical path X on the axis from the vertex W 1 of the sphere N 1 to the vertex W 1 of the sphere M 3​​​​​​OPL N1→M1 :

[0061]

[0062] In the above formula, d 1 is the vertex of the sphere W 1 and the intersection point N 1 is the distance from the vertex of the sphere A 1 to the intersection point d 3 is the vertex of the sphere W 3 and the intersection point M 1 is the distance from the vertex of the sphere B 3 to the intersection point

[0063] S220503, according to Malus' law, the optical path difference between the corresponding points of the two light rays on the incident sphere W 1 and the exit sphere W 3 is zero;

[0064] Calculate the optical path difference between the corresponding points of the two light rays on the incident sphere W 1 and the exit sphere W 3: OPD :

[0065]

[0066] If OPD ≤ δ is not true, change the scaling factor λ in the interval λ ∈(0, ∞) and repeat S220501-S220503 to iterate the scaling factor λ ;

[0067] If OPD ≤ δ is true, the scaling factor of the normalized vector λ is obtained;

[0068] wherein δ is a small amount, given δ =10 -10 ;

[0069] S220504, according to the scaling factor of the normalized vector λ , obtain .

[0070] Preferably, in S3, the method for obtaining the outer surface C 4 of the right glass window is:

[0071] S31, the convergence point is O 2( b, 0, 0), the edge ray A K D K is the inner surface C 2 is the point D K is the incident ray, the edge ray A K D K is the vector , is the normalized vector , from the point A K to the point D K ;

[0072] According to the four points around the point C 2 on the inner surface D K , the normal of the point D K is obtained by calculating the cross product , the unit vector of the normal is , from D K to the inner flow field, the edge ray A K D K satisfies the following equation:

[0073]

[0074] S32, according to the law of refraction of light, the refracted ray D K E K is obtained by the following equation , from D K to E K :

[0075]

[0076] wherein is the refraction angle of the refracted ray D K E K ;

[0077] the vector ​The normalized vector is ,vector ,vector , In the same plane;

[0078] S33. Preset scaling factor λ to normalize the vector. Zoom to the outer surface of the right-side window C 4. The intersection point is recorded as... E K Then we have:

[0079]

[0080] Let the inner surface C 2 and X The intersection of the axes is D 1. Outer surface C 4 and X The intersection of the axes is E 1;

[0081] Constructing a sphere W 2: spherical W The center of ball 2 is O 2( b ,0,0), spherical W Vertex of 2 P 1 and the intersection point D Distance of 1 | P 1 D 1|= d 2. Vertex of the sphere P 1 is located at the intersection D The left side of 1, edge light A K D K With sphere W 2 intersect at point P K ,point D K ,point P K ,point O 2. On the same straight line, the sphere W The constructive equation for 2 is characterized by the following equation:

[0082]

[0083] in, R 2 is a sphere W The radius of 2, and R The value of 2 needs to ensure the spherical surface W 2. On the inner surface C To the left of 2;

[0084] Constructing a sphere W 4: Spherical W The center of the ball is 4. O 1( a ,0,0), spherical W Vertex of 4 Q 1 and the intersection point E Distance of 1 | E 1 Q 1|= d 4. Vertex of the sphere Q 1 is located at the intersection E The right side of 1, edge light E K Q K With sphere W 4 intersect at point Q K ,point E K ,point Q K ,point O 1. On the same straight line, the sphere W The construction equation for 4 is characterized by the following equation:

[0085]

[0086] in, R 4 is a sphere W The radius is 4, and R The value of 4 needs to ensure the spherical surface W 4. On the outer surface C 4 to the right;

[0087] S34. Adjust the scaling factor according to the methods in S220501~S220504. λ Perform iterations to determine the edge rays of the outgoing converging beam and the outer surface. C The intersection of 4 E K ( x K , y K , z K );

[0088] S35, with O The converging beam at the convergence point is discretized according to different convergence angles, and let it be... X The included angle of the axis is β j The j ray and inner surface C 2 intersect at point D j ( uj , v j , w j Repeat steps S2202 to S2205 to refine the incident converging beam. j The first ray is traced in the forward direction to obtain the first converging beam. j A ray of light and the outer surface C The intersection of 4 E j ( x j , y j , z j );

[0089] in, β j ∈(0, β ), j =1, ..., K -1, K For the outer surface C The number of discrete points on 4;

[0090] S36, Passing through the intersection E K ( x K , y K , z K ) and intersection E j ( x j , y j , z j The set of ) is used to construct the outer surface of the right-side glass window. C 4.

[0091] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0092] The irregular curved glass window designed based on the design method of this invention does not change the focusing characteristics of the converging beam in the focusing schlieren system. It can not only obtain a focused schlieren image with significant schlieren effect on the imaging surface, but also obtain a distortion-free flow field image of any cross section of the three-dimensional spatial flow field inside the irregular wall on the imaging screen. The design method of this invention solves the design problem of the flow field observation window inside the irregular wall under the conditions of converging beam incident or spherical light wave transmission. The technology of this invention fills the gap in the field of three-dimensional spatial flow field visualization technology inside irregular walls at home and abroad. Attached Figure Description

[0093] Figure 1 Flow chart for designing special-shaped curved observation window for internal flow field focusing schlieren test;

[0094] Figure 2 Schematic diagram of focusing schlieren system for internal flow field visualization test of special-shaped wall surface;

[0095] Figure 3 Principle diagram for designing special-shaped curved observation window;

[0096] Figure 4 Principle diagram for designing left glass window;

[0097] Figure 5 Principle diagram for designing right glass window;

[0098] Wherein, the Fresnel lens-1, the imaging lens-2, the left glass window-3, the right glass window-4, the imaging screen-5, the knife-edge grid-6, the internal flow field-7, the original grid-8, the extended light source-9. DETAILED DESCRIPTION

[0099] The application will be further described in detail below with reference to the accompanying drawings, so that those skilled in the art can implement the application according to the description.

[0100] The special-shaped curved observation window design for internal three-dimensional space flow field focusing schlieren visualization test of special-shaped wall surface of internal turning inlet duct in the application, when the special-shaped curved observation window is designed based on the method, in order to prevent the internal surface shape of the glass window from causing internal flow simulation distortion, the internal surface of the observation window is directly conformal with the special-shaped wall surface of the internal flow field, and the external surface of the glass window is used to eliminate the change of light convergence characteristics caused by refraction of the internal surface, so as to ensure that the special-shaped curved observation window does not change the convergence characteristics of the light beam in the focusing schlieren system, the internal three-dimensional space flow field visualization of the special-shaped wall surface is realized through the focusing schlieren system, and the slicing effect of the space flow field is obtained.

[0101] Specifically, the design method of the application takes the optical parameters of the focusing schlieren system for internal flow field visualization test of special-shaped wall surface as input, takes the left and right special-shaped wall surfaces of the internal flow field test area as the internal surfaces of the observation window, adopts the iteration method and the ray tracing method to track the light rays in the converging light beam of the focusing schlieren system based on the optical path reversibility principle, the refraction law of light and the Malus law, designs the external surface of the observation window, the special-shaped curved observation window is composed of two glass windows, each glass window includes two light transmission surfaces, the internal surface is the same as the special-shaped wall surface of the installation position of the glass window, and the external surface is a correction curved surface, which is used to eliminate the change of light convergence characteristics caused by refraction of the internal surface, so as to ensure that the glass window does not change the convergence characteristics of the light beam in the focusing schlieren system, so as to ensure that the flow field structure schlieren image of the internal three-dimensional space flow field focusing surface of the special-shaped wall surface obtained through the focusing schlieren system is not distorted

[0102] Furthermore, this invention proposes a design method for an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments. The design process is as follows: Figure 1 As shown, the specific technical solution includes:

[0103] Step 1: Specify the input conditions and design requirements

[0104] Input conditions include:

[0105] 1. Convergence angle of the light beam β :like Figure 2 As shown, the optical parameters of the focusing schlieren system used for the visualization experiment of the three-dimensional spatial flow field inside the irregular wall are determined based on the scale and spatial location of the flow field inside the irregular wall: the object distance of the original grid 8. L (i.e., the distance from the original grid 8 to the focusing lens 2), the aperture of the Fresnel lens 1 D F The aperture of imaging lens 2 D L The distance between Fresnel lens 1 and the original grid 8 P Under normal circumstances P =15~20mm, calculate the beam convergence angle. β (i.e., the angle between the edge rays of the beam and the optical axis of the optical system):

[0106]

[0107] In the above formula, It is the arctangent function. P This represents the distance between the Fresnel lens and the original grid.

[0108] 2. Inner surface of left-side glass 3 C 1 and the inner surface of the right-side glass window 4 C 2:

[0109] Establish a three-dimensional coordinate system: Establish a three-dimensional rectangular coordinate system according to the right-hand rule. OXYZ Optical axis is X The axis, with positive pointing to the right, is perpendicular to the axis. X The direction of the axis upward is Y The positive direction of the axis, Z Shaft and Z The positive direction of the axis is determined by the right-hand rule, and the origin of the coordinate system is... O Set at the center of the flow field within the irregular wall, such as Figure 3 As shown;

[0110] To ensure accurate simulation of the internal flow, the inner surface of the glass window must be identical to the irregular wall of the internal flow field. The inner surface of the left glass window 3 is obtained based on the irregular wall on the left side of the internal flow field. C Discrete points of 1 Ai ( a i , b i , c i The set of data is used to obtain the inner surface of the right-side glass window 4 based on the irregular wall surface on the right side of the internal flow field. C Discrete points of 2 D j ( u j , v j , w j A set of ).

[0111] 3. The convergence point of the focused schlieren system beam O 1( a ,0,0):

[0112]

[0113] In the above formula, It is the tangent function. , It is the distance from the center of the internal flow field 7 to the imaging lens 2.

[0114] 4. Other known conditions

[0115] Refractive index of glass window material n The nominal thickness of the glass window d .

[0116] Design requirements:

[0117] On the irregular wall surface of the internal flow field, the addition of the left glass window 3 and the right glass window 4 does not change the beam converging characteristics of the optical system; that is, the converging angle of the beam outside the glass windows is... β The converging angle of the light beam between the left glass window 3 and the right glass window 4 is β .

[0118] Step Two, as follows Figure 3 and Figure 4 As shown, based on the inner surface of the left glass window 3 C 1. Design the outer surface of the left-side glass window 3 C 3.

[0119] 1. In a focused schlieren system, the light beam originates from the outer surface of the left-side glass window 3. C 3. Incident light, after two refractions, from the inner surface C 1 exit, inner surface C 1 is a known surface, the outer surface. C 3 is the surface to be designed. According to the principle of reversible light path, the inner surface is...C 1 as an incident surface, the outer surface C 3 as an emergent surface, the inner surface C 1 is a divergent beam, the outer surface C 3 is a divergent beam, the inner surface C 1 and the incident beam of X the axis is the intersection point O 2( b , 0, 0);

[0120] wherein, b is a pending value, the pending value is initialized near the convergent point O 1. b

[0121] 2, ray reverse tracing is performed on the edge rays of the divergent beam

[0122] (1), the edge rays are determined

[0123] A straight line with an angle of O 2( b , 0, 0) as the starting point is drawn to the inner surface C 1, and the straight line intersects the inner surface X 1 at point β C 1, and the straight line is the edge ray of the divergent beam, the edge ray A 2 S ( a S , b S , c S ), the straight line is the edge ray of the divergent beam, the edge ray O 2 A S The vector corresponding to the vector is , the vector is normalized to obtain the vector , and the normalized vector points from point O 2( b , 0, 0) to point A S ( a S , b S , c S );

[0124] (2), the normal line of the incident point C 1 of the edge ray on the inner surface A S

[0125] According to the inner surface​​C 1 on point A S The cross product of the four surrounding points is obtained. A S Normal of a point normal The unit vector is , from A S Pointing to the internal flow field 7;

[0126] (3) Find the refracted ray A S B S

[0127] The edge rays can be calculated using formula (3). O 2 A S angle of incidence α S1 :

[0128]

[0129] According to the law of refraction of light, the refracted ray is obtained. A S B S vector :

[0130]

[0131]

[0132] in, It is refracted light. A S B S angle of refraction n It is the refractive index of the glass window material;

[0133] vector Normalization process yields normalized vectors ,vector ,vector ,vector In the same plane, S inner surface C The first on 1 S The serial number of each discrete point;

[0134] (4) Find the refracted ray A S B S With outer surfaceC The intersection of 3 B S

[0135] Preset scaling factor λ Normalized vector Scale to outer surface C 3. Above, with the outer surface C 3 intersect at B S ( x S , y S , z S Then we have:

[0136]

[0137] Construct two spheres:

[0138] Let the inner surface C 1 and X The intersection of the axes is A 1. Outer surface C 3 and X The intersection of the axes is B 1;

[0139] spherical W 1: spherical W The center of the ball is 1. O 2( b ,0,0), spherical W The point where 1 intersects the optical axis is the vertex of the sphere. N 1 and the intersection point A Distance of 1 | N 1 A 1|= d 1. Vertex of the sphere N 1 is located at the intersection A To the right of 1, the edge rays of the incident diverging beam. O 2 A S With sphere W 1 intersects at point N S ,point A S ,point N S ,point O 2. On the same straight line, the sphere W The equation for 1:

[0140]

[0141] Where x, y, and z are the variables used to construct the equation. RThe value of 1 only needs to ensure the sphere W 1. On the inner surface C It can be found on the right side of 1.

[0142] spherical W 3: Spherical W The center of ball 3 is O 1( a ,0,0), spherical W The point where 3 intersects the optical axis is the vertex of the sphere. M 1 and the intersection point B Distance of 1 | B 1 M 1|= d 3. Vertex of the sphere M 1 is located at the intersection B To the left of 1, the edge of the emanating diverging beam. B S M S With sphere W 3 intersect at point M S ,point B S ,point M S ,point O 1. On the same straight line, the sphere W Equation for 3:

[0143]

[0144] in, R The value of 3 only needs to ensure the sphere W 3. On the outer surface C 3 can be placed to the left;

[0145] (5) Scaling factor λ Perform iterations

[0146] (a) Calculating the optical path OPL NS→MS :

[0147]

[0148] Among them, | O 2 A S |vector model , It is a normalized vector The model, and , | O 1 B S | is a point BS ( x S , y S , z S ) with the distance from the center of the sphere W 3 to the center of the sphere O 1( a , 0, 0);

[0149] (b) calculating the optical path OPL N1→M1 :

[0150]

[0151] wherein, d is the nominal center thickness of the glazing;

[0152] (c) calculating the optical path difference OPD

[0153] According to Malus' law, the optical path between the corresponding points on the incident sphere W 1 and the exit sphere W 3 is a constant value, i.e. the optical path difference between the corresponding points of the two light rays on the incident sphere W 1 and the exit sphere W 3 is zero;

[0154]

[0155] determine whether OPD ≤ δ is true, if the result is false, change the scaling factor λ ∈(0, ∞) and repeat steps (a)-(c) to iterate the scaling factor λ ; otherwise, output the scaling factor λ and obtain λ B S ( x S , y S , z S ) given δ =10 -10 .

[0156] (6) iterate the to-be-determined value b

[0157] connect the exit divergent light beam edge light ray O 1 B S of O 1 B ​​S The corresponding vector is Edge lighting O 1 B S and X Angle between axes β S for:

[0158]

[0159] in, for X The direction vector of the axis and ;

[0160] Judgment | β S - β |≤ Δ Whether it is true or not, if the result is no, then at the convergence point O 1. Search nearby O 2( b ,0,0), repeat (1)~(6) for the given value b Perform iterations; otherwise, output. b And obtained B S ( x S , y S , z S ), given Δ =10 -10 .

[0161] 3. Following the methods in steps 2 (1) to (5) of step two, examine the diverging beam for the components that are in contact with the target beam. X The included angle of the axis is β i The i By performing reverse ray tracing on the first ray, the outgoing diverging beam is obtained. i A ray of light and the outer surface C The intersection of 3 B i ( x i , y i , z i ).

[0162] In summary, the outer surface of the left glass window 3 is obtained. C 3.

[0163] Step 3, as follows Figure 3 and Figure 5 As shown, based on the inner surface of the right-side glass window C2, design the outer surface of the right glass window C 4.

[0164] The incident divergent light beam in step two, whose origin is at point O 2( b , 0, 0), is the incident convergent light beam of the inner surface of the right glass window 4. C 2. By using the method of steps two, 2nd to 3rd, to trace the rays in the convergent light beam forward, the outer surface of the right glass window 4 can be designed. C 4. Since the coordinates of the origin O 2( b , 0, 0) have been determined in step two, the iteration of parameter b is not needed any more. X b The technical effect of the present example is that:

[0165] 1. From the design requirement, the prior art keeps the parallel light unchanged, while the present application keeps the convergent property of the light beam unchanged.

[0166] 2. From the light transmission mode, the prior art is the light transmission along the plane wave, which can only obtain the integral total effect of the complex flow field along the optical axis direction in the three-dimensional space, while the light of the present application is transmitted along the spherical wave, which can obtain the flow field information of any cross section in the complex internal flow field in the three-dimensional space.

[0167] 3. From the use occasion, the glass window designed by the prior art is suitable for the common schlieren optical system, mainly from invisible to visible, i.e. solving the problem that the internal flow visualization of the irregular shaped wall surface is blocked, while the glass window of the present application is suitable for the focusing schlieren optical system, mainly from visible to focusing, i.e. solving the problem of flow visualization of any cross section of the three-dimensional space flow field in the irregular shaped wall surface.

[0168] 4. From the design method, the prior art is basically the design method of the irregular shaped curved glass window based on the plane wave transmission and the distortion correction method of the flow field image, the irregular shaped curved glass only involves the parallel light transmission, not the convergent light, and the two glass windows are left-right symmetrical, so only one glass needs to be solved in the design; while the present application is the design method of the irregular shaped curved observation window based on the spherical wave transmission, the design process involves the iterative solution of the convergent point of the convergent light beam between the glass windows, and since the left glass window and the right glass window of the present application are not symmetrical, the design process needs to be solved respectively.

[0169] 4. From the design method, the prior art is basically the design method of the irregular shaped curved glass window based on the plane wave transmission and the distortion correction method of the flow field image, the irregular shaped curved glass only involves the parallel light transmission, not the convergent light, and the two glass windows are left-right symmetrical, so only one glass needs to be solved in the design; while the present application is the design method of the irregular shaped curved observation window based on the spherical wave transmission, the design process involves the iterative solution of the convergent point of the convergent light beam between the glass windows, and since the left glass window and the right glass window of the present application are not symmetrical, the design process needs to be solved respectively.

[0170] ​The above examples only illustrate the principles of the present application and its efficacy, and are not intended to limit the application. Any modification or change on the above examples made by any person skilled in the art, without departing from the spirit and scope of the present application, shall be covered by the claims of the present application.

Claims

1. A method for designing an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments, wherein the irregularly shaped curved surface observation window comprises: Two asymmetrical glass windows installed on the left and right side walls of the internal flow field test area are characterized by comprising: S1. Based on the optical parameters of the focusing schlieren system and the irregular wall surface of the internal flow field, determine the input conditions and design requirements, and take the irregular wall surfaces on the left and right sides of the internal flow field test area as the inner surfaces of each glass window. S2, based on the inner surface of the left-side glass window C 1. The light rays within the converged beam of the focused schlieren system are traced using an iterative method and a reverse ray tracing method to obtain the outer surface of the left glass window. C 3; S3, based on the inner surface of the right-side glass window C 2. The iterative method and the forward ray tracing method are used to trace the rays within the converged beam of the focused schlieren system to obtain the outer surface of the right-side glass window. C 4; In S2, the outer surface of the left glass window is obtained. C Method 3 is as follows: S21. In a focused schlieren system, the light beam originates from the outer surface of the left-side glass window. C 3. Incident light, after two refractions, from the inner surface C 1. Upon exiting the internal flow field, due to the outer surface of the left-side glass window... C 3 represents the surface to be designed, including the inner surface. C 1 is a known surface. Based on the principle of reversibility of light paths, the inner surface... C 1 is the incident surface, outer surface C 3 serves as the exit surface, inner surface C The incident beam at position 1 is a diverging beam, and the outer surface... C The emitted beam of 3 is a diverging beam, and the converging characteristics of the same ray within the diverging beam remain unchanged at the incident and exit positions. S22, for the inner surface C The starting point of the incident diverging beam is determined by inverse ray tracing of the edge rays of the incident diverging beam using an iterative method. O 2( b (0, 0), obtaining the edge rays of the outgoing diverging beam and the outer surface C The intersection of 3 B S ( x S , y S , z S ), b Starting point O The x-coordinate of 2; S23, with O The diverging beam starting from point 2 is discretized according to different divergence angles, and let it be... X The included angle of the axis is β i The i ray and inner surface C 1 intersects at point A i ( a i , b i , c i ), by scaling factor λ Perform iterations to complete the first step of the incident diverging beam. i By performing reverse ray tracing on the first ray, the outgoing diverging beam is obtained. i A ray of light and the outer surface C The intersection of 3 B i ( x i , y i , z i ); in, β i ∈(0, β ), i =1, ..., S -1, S For the outer surface C The number of discrete points on 3; S24, Passing through the intersection B S ( x S , y S , z S ) and intersection B i ( x i , y i , z i The set of ) is used to construct the outer surface of the left glass window. C 3.

2. The method for designing an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments according to claim 1, characterized in that, In S1, the optical parameters of the focused schlieren system include: the object distance of the original grid. L The aperture of a Fresnel lens D F The aperture of the imaging lens D L ; The input conditions are determined as follows: S11. Establish a three-dimensional rectangular coordinate system according to the right-hand rule. OXYZ With the optical axis of the focused schlieren system as X The axis, from left to right is X The positive direction of the axis is perpendicular to... X The direction of the axis upward is Y The positive direction of the axis, Z Shaft and Z The positive direction of the axis is determined by the right-hand rule, and the origin of the coordinate system is... O It is located at the spatial center of the internal flow field test area; S12. Obtain the inner surface of the left glass window based on the irregular wall surface on the left side of the internal flow field. C Discrete points of 1 A i ( a i , b i , c i The set of ) i =1, 2, ..., S , a i For discrete points A i x-coordinate, b i For discrete points A i y-coordinate, c i For discrete points A i The z-coordinate; S13. Obtain the inner surface of the right-side glass window based on the irregular wall surface on the right side of the internal flow field. C Discrete points of 2 D j ( u j , v j , w j The set of ) j =1, 2, ..., K , u j For discrete points D j x-coordinate, v j For discrete points D j y-coordinate, w j For discrete points D j The z-coordinate; S14. Determine the convergence angle of the beam in the focused schlieren system based on the following formula. β : In the above formula, It is the arctangent function. P This is the distance between the Fresnel lens and the original grid. S15. Define the convergence point of the focusing schlieren system's beam. O 1( a ,0,0), a As a convergence point O The x-coordinate of 1, and a It is characterized by the following formula: In the above formula, It is the tangent function. yes The distance from the center of the internal flow field to the imaging lens; S16. Other known input conditions include: the refractive index of the glass window material. n The nominal thickness of the glass window d ; In S1, the design requirement is that the addition of the left and right glass windows on the irregular wall surface of the internal flow field does not change the beam focusing characteristics of the optical system.

3. The method for designing an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments according to claim 1, characterized in that, In S22, the intersection point B S ( x S , y S , z S The method to obtain ) is: S2201, inner surface C The starting point of the incident diverging beam of 1 is located at X On the axis and the starting point is O 2( b (0, 0), at the convergence point O A value to be determined is given around 1. b Assign initial values; S2202, with O Starting from 2, and with X The included angle of the axis is β The diverging beam edge rays and the inner surface C 1 intersects at one point A S ( a S , b S , c S Find the edge rays of the diverging beam. O 2 A S vector , will vector Normalization yields vectors Normalized vector From point O 2 pointing points A S ; According to the inner surface C 1 on point A S The cross product of the four surrounding points is obtained. A S Normal of a point normal The unit vector is , from A S Pointing to the internal flow field, edge rays O 2 A S angle of incidence α S1 satisfy: S2203. According to the law of refraction of light, the refracted ray can be obtained through the following formula. A S B S vector , from A S point to B S : In the above formula, It is refracted light. A S B S The angle of refraction, n It is the refractive index of the glass window material, and , For normal line unit vector, vector The normalized vector is And vector ,vector ,vector In the same plane; S2204, Preset scaling factor Normalized vector Scale to outer surface C 3. The intersection point is recorded as... B S Then we have: Let the inner surface C 1 and X The intersection of the axes is A 1. Outer surface C 3 and X The intersection of the axes is B 1; Constructing a sphere W 1: Assume a sphere W The center of the ball is 1. O 2( b ,0,0), spherical W Vertex of 1 N 1 and the intersection point A Distance of 1 | N 1 A 1|= d 1. Vertex N 1 is located at the intersection A The right side of 1, edge light O 2 A S With sphere W 1 intersects at point N S ,point A S ,point N S ,point O 2. If they are on the same straight line, then the sphere W The constructive equation for 1 is characterized by the following equation: In the above equation, x, y, and z are the variables used to construct the equation. R 1 is a sphere W The radius of 1, and R The value of 1 needs to ensure the spherical surface W 1. On the inner surface C The right side of 1; Constructing a sphere W 3: Assume a sphere W The center of ball 3 is O 1( a ,0,0), spherical W 3 vertices M 1 and the intersection point B Distance of 1 | B 1 M 1|= d 3. Vertex M 1 is located at the intersection B The left side of 1, edge light B S M S With sphere W 3 intersect at point M S ,point B S ,point M S ,point O 1. If they are on the same straight line, then the sphere W The construction equation for 3 is characterized by the following equation: in, R 3 is a sphere W The radius is 3, and R The value of 3 needs to ensure the spherical surface W 3. On the outer surface C 3 to the left; S2205, Regarding the scaling factor λ By iterating, we can obtain ; S2206, the starting point of the emitted diverging beam O 1 and B S Connect them to obtain edge rays. O 1 B S corresponding vector Then the edge light O 1 B S and X Angle between axes β S Characterized by the following formula: in, The direction vector of the X-axis and ; If | β S - β |≤ Δ If this is not valid, then at the convergence point... O 1. Search nearby O 2( b (0, 0), repeat steps S2202~S2206 for the given value b Perform iterations; If | β L - β |≤ Δ Established, yielding a value to be determined. b The iteration value; in, Δ It is a tiny quantity, given Δ =10 -10 ; S2207, Based on the undetermined value b The iterative value determines the inner surface. C The starting point of the incident diverging beam of 1 O 2( b (0,0) and the edge rays of the outgoing diverging beam and the outer surface C The intersection of 3 B S ( x S , y S , z S ).

4. The method for designing an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments according to claim 3, characterized in that, include: In S2205, the scaling factor... λ The iterative process includes: S220501, Calculate the edge rays using the following formula. O 2 A S From the sphere W 1 on point N S To the sphere W 3 points M S optical path OPL NS→MS : In the above formula, | O 2 A S |vector model , It is a normalized vector The model, and , λ Normalized vector The scaling factor, | O 1 B S | is a point B S With sphere W 3's center O A distance of 1; S220502, calculated using the following formula X From the sphere on the axis W Vertex of 1 N 1 to sphere W 3 vertices M 1 optical path OPL N1→M1 : In the above formula, d 1 is a sphere W Vertex of 1 N 1 and the intersection point A A distance of 1 d 3 is a sphere W 3 vertices M 1 and the intersection point B A distance of 1; S220503, According to Malus's law, the incident sphere... W 1 and the surface of the ball being shot W The optical path difference between corresponding points of the two light rays in step 3 is zero. Calculate the incident sphere W 1 and the surface of the ball being shot W 3. Optical path difference between corresponding points of two rays OPD : if OPD ≤ δ This is not true. λ Change the scaling factor within the interval (0, ∞) λ Repeat steps S220501 to S220503 for scaling factors. λ Perform iterations; if OPD ≤ δ This holds true, resulting in a normalized vector. scaling factor λ ; in, δ It is a tiny quantity, given δ =10 -10 ; S220504, Based on the normalized vector scaling factor λ get .

5. The method for designing an irregularly shaped curved surface observation window for internal flow field focusing schlieren experiments according to claim 2, characterized in that, In S3, the outer surface of the right-side glass window C The method to obtain 4 is as follows: S31, the convergence point is O 2( b In a converging beam of light (0, 0), the edge rays A K D K inner surface C 2 points D K The incident light rays converge at the edge of the beam. A K D K The vector is , The normalized vector is , From point A K Point of view D K ; According to the inner surface C 2 points D K The four surrounding points are obtained by taking their cross product. D K Normal of a point normal The unit vector is , from D K Pointing to the internal flow field, edge rays A K D K angle of incidence Satisfy the following formula: S32. According to the law of refraction of light, the refracted ray can be obtained through the following formula. D K E K vector , from D K point to E K : in, It is refracted light. D K E K The angle of refraction; vector The normalized vector is ,vector ,vector , In the same plane; S33. Preset scaling factor λ to normalize the vector. Zoom to the outer surface of the right-side window C 4. The intersection point is recorded as... E K Then we have: Let the inner surface C 2 and X The intersection of the axes is D 1. Outer surface C 4 and X The intersection of the axes is E 1; Constructing a sphere W 2: spherical W The center of ball 2 is O 2( b ,0,0), spherical W Vertex of 2 P 1 and the intersection point D Distance of 1 | P 1 D 1|= d 2. Vertex of the sphere P 1 is located at the intersection D The left side of 1, edge light A K D K With sphere W 2 intersect at point P K ,point D K ,point P K ,point O 2. On the same straight line, the sphere W The constructive equation for 2 is characterized by the following equation: in, R 2 is a sphere W The radius of 2, and R The value of 2 needs to ensure the spherical surface W 2. On the inner surface C To the left of 2; Constructing a sphere W 4: Spherical W The center of the ball is 4. O 1( a ,0,0), spherical W Vertex of 4 Q 1 and the intersection point E Distance of 1 | E 1 Q 1|= d 4. Vertex of the sphere Q 1 is located at the intersection E The right side of 1, edge light E K Q K With sphere W 4 intersect at point Q K ,point E K ,point Q K ,point O 1. On the same straight line, the sphere W The construction equation for 4 is characterized by the following equation: in, R 4 is a sphere W The radius is 4, and R The value of 4 needs to ensure the spherical surface W 4. On the outer surface C 4 to the right; S34. Adjust the scaling factor according to the methods in S220501~S220504. λ Perform iterations to determine the edge rays of the outgoing converging beam and the outer surface. C The intersection of 4 E K ( x K , y K , z K ); S35, with O The converging beam at the convergence point is discretized according to different convergence angles, and let it be... X The included angle of the axis is β j The j ray and inner surface C 2 intersect at point D j ( u j , v j , w j Repeat steps S2202 to S2205 to refine the incident converging beam. j The first ray is traced in the forward direction to obtain the first converging beam. j A ray of light and the outer surface C The intersection of 4 E j ( x j , y j , z j ); in, β j ∈(0, β ), j =1, ..., K -1, K For the outer surface C The number of discrete points on 4; S36, Passing through the intersection E K ( x K , y K , z K ) and intersection E j ( x j , y j , z j The set of ) is used to construct the outer surface of the right-side glass window. C 4.

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