CN103940779A - Measurement method of gas injection flow field - Google Patents

Abstract

The invention discloses a measurement method of a gas injection flow field. A differential interferometry system is formed by Wollaston prism optical elements; the center section of a spatial flow field of a test section is imaged, and differential interference fringe charts with carrier wave fringes are collected at any moment before air flow injection and during air flow injection, so that the fringe order distribution and the fluid optical refractive index gradient in a whole field are obtained, and the density gradient field, the density field, the temperature field and the temperature gradient field of a fluid also can be obtained synchronously. The analyzing and treating method of fringe charts, which is disclosed by the invention, can be used for basically eliminating experiment errors caused by the differential interferometry system, has a low shock-resistant requirement, is convenient to apply, and overcomes problems caused by flow field instability.

Description

A kind of gas sprays the measuring method in flow field

Technical field

The present invention relates to the measuring method that a kind of gas sprays flow field.

Background technology

Spray being determined at of flow field and in the association area such as process industry, aviation, have very important application, compare with the detection technique of pointwise, contact, the mobile display technique of optics has many advantages: 1) can provide whole audience information in the mode of image, not only information capacity is large, and information intuitive display; 2) light transmition is very rapid, can be used for the kinetic measurement in flow field; 3) there is no mechanical probe, flow field to be measured is not had to interference effect.

The optical interference techniques such as classical interferometric method and Electronic Speckle Pattern Interferometry, change by measurement of optical path difference, and then measure fluid refractive index, thereby obtain the space distribution of fluid density or temperature.But Through Optical Interference Spectra need to could be realized by reference beam, therefore optical system is had to very high shockproof requirement.In addition, utilize optical interference techniques to carry out flow field transient state detection, must analyze and process a large amount of interference fringe pictures, but due to the instability in flow field, common phase shift detection system is difficult to utilize, and Phase Shifting System is not only complicated in real time, and expensive.

Wollaston prism can produce two bundles are separated from each other, the mutually perpendicular linearly polarized light of direction of vibration, utilize the optical element composition differential interferometry measuring systems such as Wollaston prism, polarization adjuster, collimating mirror, beam expanding lens, in test section space, the flow field section imaging that needs are detected, in as plane, form two width light fields of a slight distance of mutual dislocation, and interfere with each other formation interference fringe picture.This system does not need reference beam, optical system compactness, shockproof require low.The fluid optical refractive index gradient reflecting according to bar graph, can further obtain the isoparametric space distribution of density gradient, density, temperature of gas jet.

Summary of the invention

In order to overcome the deficiencies in the prior art, the invention provides the measuring method in a kind of gas injection flow field.

Gas sprays the measuring method in flow field, and step is as follows:

1) utilize the optical element such as Wollaston prism composition differential interferometry measuring system, to the centre section imaging of flow field, test section space, the differential interferometry bar graph with carrier fringe of any time before gathering jet-impingement and when jet-impingement;

2), according to the differential interferometry bar graph with carrier fringe described in step 1), utilize following formula to calculate the relative drift value △ of differential interferometry striped S/S:

$\frac{\mathrm{\ΔS}}{S}=\frac{d}{\mathrm{\λ}}\∫\frac{\∂n(x,y,z)}{\∂x}\mathrm{dz}---\left(1\right)$

Wherein, the interval S of carrier fringe, striped absolute drift amount △ S, d is object space shearing displacement, and λ is optical maser wavelength, and n is the spatially distributed functions of fluid refractive index, and △ S/S=△ N (x, y) is the relative drift value of striped, x, y, z is volume coordinate;

3) for two-dimensional flow field,

Obtain following formula according to formula (1)

$\frac{\∂n(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.L}---\left(3\right)$

In formula, L is the length of spraying flow field along light transmition direction;

For gas, utilize Gladstone-Dell relational expression, obtain the relational expression between following refractive index gradient and density gradient:

$\frac{\∂n(x,y)}{\∂x}=K\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}---\left(4\right)$

In formula, K is Gladstone-Dell constant, while measuring the density of air with helium-neon laser, and K=2.256 × 10 ^-4m ³/ kg; ρ (x, y) is Density Distribution; By (4) formula substitution (3 formula), obtain following density gradient field:

$\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.K.L}---\left(5\right)$

Integration (5) formula, obtains following formula:

$\mathrm{\ρ}(x,y)={\mathrm{\ρ}}_{\∞}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(6\right)$

In formula, ρ _∞it is environmental density;

If stream pressure is constant, utilize the Ideal-Gas Equation, obtain environmental density ρ _∞:

${\mathrm{\ρ}}_{\∞}=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}---\left(7\right)$

In formula, p _∞for environmental pressure; T _∞for the absolute temperature of environment; M is molecular weight gas;

R=0.0823latm/molK is gas law constant;

By (7) formula substitution (6) formula, try to achieve the density calculation formula of gas:

$\mathrm{\ρ}(x,y)=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(8\right)$

For two-dimensional gas temperature field, utilize the Ideal-Gas Equation, obtain gas temperature distribution T (x, y) by gas density field:

$(x,y)=\frac{\mathrm{MP}}{R_{\mathrm{\ρ}}(x,y)}---\left(9\right)$

By (9) formula, can lead to obtain temperature gradient distribution:

$\frac{\∂T}{\∂x}=-\frac{\mathrm{MP}}{{\mathrm{R\ρ}}^2(x,y)}\frac{\∂\mathrm{\ρ}}{\∂x}---\left(10\right)$

Like this, by (8) formula and (4) formula substitution (10) formula, just can be in the hope of the temperature gradient distribution of gas.

Collection described in step 1) is specific as follows:

1.1) striped before flow field centre section interference fringe picture-the be called disturbance before recording gas and spraying;

1.2), after gas starts to spray, record striped after the flow field centre section interference fringe picture in arbitrary moment-be called disturbance.

Step 2) △ N in described formula (1) obtains as follows:

2.1) extract every stripe center line of bar graph before disturbance and after disturbance;

2.2) set fringe order corresponding to stripe centerline, use numerical interpolation method to determine fringe order corresponding to the each pixel of image, thereby obtain carrier wave curved surface and disturbance curved surface;

2.3) carrier wave curved surface and disturbance curved surface are subtracted each other, obtain the actual fringe order distribution of whole audience △ N.

The invention has the beneficial effects as follows, the fringe order that can obtain the whole audience distributes and fluid optical refractive index gradient, can also obtain the density gradient field of fluid, density field, temperature field, temperature gradient field simultaneously; Analysis and the disposal route of the bar graph proposing, can eliminate the experimental error that differential interferometry system itself is introduced substantially; Shockproofly require lowly, application is convenient, has overcome the unstable problem of bringing in flow field.

Brief description of the drawings

Below in conjunction with drawings and Examples, the present invention is further described.

Fig. 1 gathers the schematic diagram with the differential interferometry bar graph of carrier fringe in the present invention;

Fig. 2 a is the front bar graph of disturbance in the embodiment of the present invention;

Fig. 2 b is bar graph after disturbance in the embodiment of the present invention.

Embodiment

Fig. 1 has shown and utilizes Wollaston prism differential interferometer to gather before jet-impingement and the schematic diagram of the differential interferometry bar graph with carrier fringe of any time when jet-impingement.The linearly polarized light that laser instrument sends, is adjusted to Wollaston prism optical axis to become in the direction of 45o through polarization direction regulator; Beam expanding lens and collimating mirror lens 1 become laser beam the directional light expanding, and pass through flow field; Lens 2 and lens 3 dwindle light beam visual field, and the centre section in flow field is imaged on frosted glass.

Wollaston prism is placed near the back focus of lens 2, and incident light is divided into two bundles are separated from each other, the mutually perpendicular linearly polarized light of direction of vibration.By regulating the distance of back focus of Wollaston prism center and lens 2, make two bundle polarized lights at vertical direction dislocation slight distance d, after the polaroid that becomes 45o direction through a polarization direction with Wollaston prism optical axis again, interfere with each other, on frosted glass, form with the differential interferometry bar graph of carrier fringe, finally by CCD cameras record and store in computer processing system.

One, the test philosophy of differential interferometry

The relative drift value of differential interferometry striped can calculate with following formula:

$\frac{\mathrm{\ΔS}}{S}=\frac{d}{\mathrm{\λ}}\∫\frac{\∂n(x,y,z)}{\∂x}\mathrm{dz}---\left(1\right)$

In formula, △ S is striped absolute drift amount; S is the spacing of carrier fringe; △ S/S=△ N (x, y) is the relative drift value of striped, and d is object space shearing displacement, and λ is optical maser wavelength, and n is the spatially distributed functions of fluid refractive index.

△ N can obtain by the following method:

1, image pre-service:

As shown in Fig. 2 a, 2b, the differential interferometry bar graph before and after disturbance is carried out respectively to gray-scale statistical, Threshold, binaryzation and thinning processing.

2, advanced processes:

(1) the refinement striped before and after disturbance is taken out respectively to skeleton and calculate, determine 1 fringe center position that pixel is wide;

(2) specify the initial progression of striped (being defaulted as 1) and upgrading direction, carry out whole audience striped and automatically define the level, the integer level that obtains fringe order distributes;

(3) utilize striped integer level distributed data, by numerical interpolation, obtain the fringe order distribution △ N in the each pixel of the whole audience.

(4) fringe order after disturbance is deducted to the fringe order before disturbance, calculate the fringe order only being caused by jet-impingement disturbance and distribute.

Also formula (1) can be expressed as to following form:

$\∫=\frac{\∂n(x,y,z)}{\∂x}\mathrm{dz}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d}---\left(2\right)$

Two, the measuring principle of two-dimensional gas density field

For two-dimensional flow field, can be in the hope of by (2) formula:

$\frac{\∂n(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.L}---\left(3\right)$

In formula, L is the length along light transmition direction flow field.

For gas, utilize Gladstone-Dell relational expression, can obtain the relational expression between following refractive index gradient and density gradient:

$\frac{\∂n(x,y)}{\∂x}=K\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}---\left(4\right)$

In formula, K is Gladstone-Dell constant, while measuring the density of air with helium-neon laser, and K=2.256 × 10-4m3/kg; ρ (x, y) is Density Distribution.

By (4) formula substitution (3 formula), can obtain following density gradient field:

$\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.K.L}---\left(5\right)$

Integration (5) formula, can obtain following formula:

$\mathrm{\ρ}(x,y)={\mathrm{\ρ}}_{\∞}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(6\right)$

In formula, ρ _∞it is environmental density.

If stream pressure is constant, utilize the Ideal-Gas Equation, can obtain environmental density ρ _∞:

${\mathrm{\ρ}}_{\∞}=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}---\left(7\right)$

In formula, p _∞for environmental pressure, be generally 1atm; T _∞for the absolute temperature of environment; M is molecular weight gas, the M=28.97g/mol of air; R=0.0823latm/molK is gas law constant.

By (7) formula substitution (6) formula, can be in the hope of the density calculation formula of gas:

$\mathrm{\ρ}(x,y)=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(8\right)$

Three, the measuring principle in two-dimensional gas temperature field

Utilize the Ideal-Gas Equation, can obtain gas temperature distribution T (x, y) by gas density field:

$(x,y)=\frac{\mathrm{MP}}{R_{\mathrm{\ρ}}(x,y)}---\left(9\right)$

By (9) formula, can lead to obtain temperature gradient distribution:

$\frac{\∂T}{\∂x}=-\frac{\mathrm{MP}}{{\mathrm{R\ρ}}^2(x,y)}\frac{\∂\mathrm{\ρ}}{\∂x}---\left(10\right)$

Like this, by (8) formula and (4) formula substitution (10) formula, just can be in the hope of the temperature gradient distribution of gas.

Claims (3)

1. gas sprays the measuring method in flow field, it is characterized in that, step is as follows:

1) utilize Wollaston prism optical element composition differential interferometry measuring system, to the centre section imaging of flow field, test section space, before gathering jet-impingement and the differential interferometry bar graph with carrier fringe in a former moment of jet-impingement;

2), according to the differential interferometry bar graph with carrier fringe described in step 1), utilize following formula to calculate the relative drift value △ of differential interferometry striped S/S:

$\frac{\mathrm{\ΔS}}{S}=\frac{d}{\mathrm{\λ}}\∫\frac{\∂n(x,y,z)}{\∂x}\mathrm{dz}---\left(1\right)$

Wherein, the interval S of carrier fringe, striped absolute drift amount △ S, d is object space shearing displacement, and λ is optical maser wavelength, and n is the spatially distributed functions of fluid refractive index, and △ S/S=△ N (x, y) is the relative drift value of striped, x, y, z is volume coordinate;

3) for two-dimensional flow field,

Obtain following formula according to formula (1)

$\frac{\∂n(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.L}---\left(3\right)$

In formula, L is the length of spraying flow field along light transmition direction;

For gas, utilize Gladstone-Dell relational expression, obtain the relational expression between following refractive index gradient and density gradient:

$\frac{\∂n(x,y)}{\∂x}=K\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}---\left(4\right)$

In formula, K is Gladstone-Dell constant, in the time using helium-neon laser to measure the density of air, and K=2.256 × 10 ^-4m ³/ kg; ρ (x, y) is Density Distribution; By (4) formula substitution (3 formula), obtain following density gradient field:

$\frac{\∂\mathrm{\ρ}(x,y)}{\∂x}=\frac{\mathrm{\ΔN}(x,y).\mathrm{\λ}}{d.K.L}---\left(5\right)$

Integration (5) formula, obtains following formula:

$\mathrm{\ρ}(x,y)={\mathrm{\ρ}}_{\∞}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(6\right)$

In formula, ρ _∞it is environmental density;

If stream pressure is constant, utilize the Ideal-Gas Equation, obtain environmental density ρ _∞:

${\mathrm{\ρ}}_{\∞}=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}---\left(7\right)$

In formula, p _∞for environmental pressure; T _∞for the absolute temperature of environment; M is molecular weight gas; R=0.0823latm/molK is gas law constant;

By (7) formula substitution (6) formula, try to achieve the density calculation formula of gas:

$\mathrm{\ρ}(x,y)=\frac{{\mathrm{MP}}_{\∞}}{{\mathrm{RT}}_{\∞}}-\left(\frac{\mathrm{\λ}}{d.K.L}\right){\∫}_{x_{\∞}}^x\mathrm{\ΔN}(x,y)\mathrm{dx}---\left(8\right)$

For two-dimensional gas temperature field, utilize the Ideal-Gas Equation, obtain gas temperature distribution T (x, y) by gas density field:

$(x,y)=\frac{\mathrm{MP}}{R_{\mathrm{\ρ}}(x,y)}---\left(9\right)$

By (9) formula, can lead to obtain temperature gradient distribution:

$\frac{\∂T}{\∂x}=-\frac{\mathrm{MP}}{{\mathrm{R\ρ}}^2(x,y)}\frac{\∂\mathrm{\ρ}}{\∂x}---\left(10\right)$

Like this, by (8) formula and (4) formula substitution (10) formula, just can be in the hope of the temperature gradient distribution of gas.

2. gas according to claim 1 sprays the measuring method in flow field, it is characterized in that, the collection described in step 1) is specific as follows:

1.1) striped before flow field centre section interference fringe picture-the be called disturbance before recording gas and spraying;

1.2), after gas starts to spray, record striped after the flow field centre section interference fringe picture in arbitrary moment-be called disturbance.

3. gas according to claim 1 sprays the measuring method in flow field, it is characterized in that step 2) △ N in described formula (1) obtains as follows:

2.1) extract every stripe center line of bar graph before disturbance and after disturbance;

2.2) set fringe order corresponding to stripe centerline, use numerical interpolation method to determine fringe order corresponding to the each pixel of image, thereby obtain carrier wave curved surface and disturbance curved surface;

2.3) carrier wave curved surface and disturbance curved surface are subtracted each other, obtain the actual fringe order distribution of whole audience △ N.