A method for measuring three-dimensional vorticity of fluid based on rotational Doppler effect

Abstract

The invention discloses a method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect, and relates to the technical field of fluid vorticity measurement; the method of the invention obtains the rotational Doppler frequency shift in at least three independent directions through light beam scanning and heterodyne detection technology, obtains vorticity information in each direction according to the frequency shift information, and then performs vector synthesis to obtain three-dimensional vorticity distribution information in the light beam irradiation area. The method of the invention can avoid the operation of adding probe particles while ensuring spatial resolution, and has important application prospects in fluid vorticity measurement.

Description

Technical Field

[0001] The invention relates to the technical field of fluid vortex measurement, in particular to a method for measuring three-dimensional fluid vortex based on rotational Doppler effect. Background Art

[0002] In fluid mechanics, the curl ▽×υ of the velocity vector field υ is usually called vorticity. Vorticity plays a vital role in fluid mechanics. The precise measurement of vorticity plays an extremely important role in many fields such as bio-microfluidics technology, complex motion of the ocean and atmospheric boundary layer, and fluid aerodynamics. However, it is very difficult to accurately measure the vorticity of fluids.

[0003] Traditional optical vorticity measurement methods mainly include particle image velocimetry (PIV) and laser Doppler velocimetry (LDV). The idea is to obtain real-time velocity field components and differentiate the velocity components to obtain vorticity field components. This type of method requires simultaneous measurement of velocity vectors at different positions in a certain closed space, and obtains spatial gradients through the finite difference method. However, in the actual measurement process, fluid measurement needs to be integrated in a certain area, so the above method can only obtain the average vorticity in a certain area, and the accuracy of the vorticity is limited by the accuracy of the velocity differential.

[0004] In order to overcome the shortcomings of the above methods, researchers use imaging technology to observe the local rotation of the fluid, such as the vortex optical probe method (VOP). The probe particles are embedded in the fluid, and the probe particles move with the rotation of the fluid. The particles are illuminated by a Gaussian beam, and the vorticity of the fluid is indirectly obtained by measuring the angular momentum of the probe particles. This type of method has high measurement accuracy, but it is not convenient to add probe particles to the fluid to be measured in all cases. Summary of the invention

[0005] In order to overcome the above defects in the prior art, the present invention provides a method for measuring the three-dimensional vorticity of a fluid based on the rotational Doppler effect, which has the characteristics of high spatial resolution and simple operation.

[0006] To achieve the above object, the present invention adopts the following technical solutions, including:

[0007] A method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect comprises the following steps:

[0008] S1, using a laser to generate laser light, dividing the laser light generated by the laser into two beams, one of which is used as a local oscillator light, and the other is modulated to obtain a vortex light beam, and then adjusting the divergence angle of the vortex light beam to obtain a focused vortex light beam;

[0009] S2, irradiate the measured area with the focused vortex beam at a certain angle to obtain scattered light;

[0010] S3, interfering the obtained scattered light with the local oscillation light, using a photodetector to receive the interfered light beam to obtain an intermediate frequency photocurrent, and analyzing and processing the intermediate frequency photocurrent signal to obtain the corresponding vorticity under the irradiation angle;

[0011] S4, changing the irradiation angle of the focused vortex light beam, and performing measurements at three irradiation angles in total according to the method of steps S2 to S3, respectively obtaining the corresponding vorticities at the three irradiation angles, and using the corresponding vorticities at the three irradiation angles to perform vector synthesis to obtain the three-dimensional vorticity field distribution in the area to be measured.

[0012] Preferably, in step S3, the vorticity is calculated as follows:

[0013] ω=(4π / m) <f ⊥ >

[0014] Where ω is the fluid vorticity; m is the topological charge of the focused vortex beam; <f ⊥ > is the frequency shift centroid of the intermediate frequency photocurrent signal, i.e. the echo signal, i.e. the weighted average of the signal spectrum.

[0015] Preferably, the frequency shift centroid of the echo signal <f ⊥ The measurement method of > is as follows:

[0016]

[0017] Among them, F S is the sampling frequency, f ⊥ is the frequency shift of the echo signal, I(f ⊥ ) is the power spectrum of the rotational Doppler effect, M is the total number of samples, k is the serial number of the sample, and f ⊥k is the frequency channel value of the kth sample, I k is the power value corresponding to the kth sample.

[0018] Preferably, step S3 obtains vorticity based on heterodyne detection technology.

[0019] Preferably, in step S4, the three irradiation angles are θ 1 ,θ 2 ,θ 3 The corresponding vorticity under these three illumination angles is ω Z ,ω N ,ω E ; At the irradiation angle θ 1 The irradiation direction is the z axis, and the irradiation angle is θ 2 The irradiation direction and irradiation angle θ 1 The angle between the irradiation directions is γ 21 , irradiation angle θ 3The irradiation direction and irradiation angle θ 1 The angle between the irradiation directions is γ 31 , and γ 21 =γ 31 =γ;

[0020] The three-dimensional vorticity field distribution ω in this area is obtained as follows:

[0021] ω x =(ω E -ω Z cosγ) / sinγ

[0022] ω y =(ω N -ω Z cosγ) / sinγ

[0023] ω z =ω Z

[0024] ω=(ω x ,ω y ,ω z )

[0025] Among them, ω z is the component of the three-dimensional vorticity along the z axis, ω x is the component of the three-dimensional vorticity along the x-axis, ω y is the component of the three-dimensional vorticity along the y-axis.

[0026] Preferably, in step S4, the irradiation angle of the focused vortex light beam is changed using a beam scanning technique.

[0027] Preferably, in step S1, a laser is used to generate a fundamental mode Gaussian beam, and a beam splitter is used to split the fundamental mode Gaussian beam into two laser beams with a ratio of 1:1.

[0028] Preferably, in step S1, another laser beam is modulated by a liquid crystal spatial light modulator loaded with a fork-shaped diffraction grating to obtain a vortex light beam.

[0029] Preferably, in step S1, a focused vortex beam is obtained by adjusting the divergence angle of the vortex beam through a lens; the vortex beam type is a Laguerre-Gaussian beam.

[0030] Preferably, in step S2, the focusing radius and the emission aperture of the focused vortex light beam are adjusted so that the area to be measured is completely within the annular spot of the focused vortex light beam.

[0031] The advantages of the present invention are:

[0032] (1) The present invention provides a method for measuring three-dimensional vorticity of a fluid with high spatial resolution and simple operation.

[0033] (2) The present invention obtains the rotational Doppler frequency shift in at least three independent directions through beam scanning and heterodyne detection technology, obtains the vorticity information in each direction based on the frequency shift information, and then performs vector synthesis to obtain the three-dimensional vorticity distribution information in the beam irradiation area. This technology can avoid the operation of adding probe particles while ensuring spatial resolution, and has important application prospects in fluid vorticity measurement.

[0034] (3) The vorticity measurement method provided by the present invention can further improve the measurement accuracy of vorticity by increasing the topological charge of the measuring light beam and increasing the rotational Doppler frequency shift. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect of the present invention.

[0036] Figure 2 Schematic diagram of the vorticity synthesis principle using the beam scanning method.

[0037] Figure 3 This is the optical path principle of the fluid three-dimensional vortex measurement experiment. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The present invention provides a method for measuring the three-dimensional vorticity of a fluid based on the rotational Doppler effect. The rotational Doppler frequency shift in at least three independent directions is obtained by light beam scanning and heterodyne detection technology. The vorticity information in each direction is obtained according to the frequency shift information. Then, vector synthesis is performed to obtain the three-dimensional vorticity information in the area irradiated by the light beam. This technology can avoid the operation of adding probe particles while ensuring spatial resolution, and has important application prospects in fluid vorticity measurement.

[0040] Depend on Figure 1 As shown, a method for measuring the three-dimensional vorticity of a fluid based on the rotational Doppler effect, the specific steps are as follows:

[0041] S1, using a laser to generate laser light, the laser light generated by the laser is divided into two beams, one of which is used as the local oscillator light, and the other is first modulated to obtain a vortex beam, and then the divergence angle of the vortex beam is adjusted by a lens to obtain a focused vortex beam;

[0042] In this embodiment, a laser is used to generate a fundamental mode Gaussian beam, and a beam splitter is used to split the fundamental mode Gaussian beam into two beams of light with a 1:1 ratio. The modulation method of the other beam of light can be a liquid crystal spatial light modulator loaded with a fork-type diffraction grating, a spiral phase plate, etc. The vortex beam takes a Laguerre-Gaussian beam as an example.

[0043] S2, irradiate the measured area with the focused vortex beam at a certain angle to obtain scattered light.

[0044] In step S2, the focusing radius and the emission aperture of the focused vortex beam are adjusted so that the area to be measured is completely within the annular spot of the focused vortex beam, thereby obtaining the strongest possible scattered light;

[0045] The topological charge of the focused vortex beam is m. For a Laguerre-Gaussian beam, the annular spot radius of the focused vortex beam is Among them, w 0 is the waist radius of the Laguerre-Gaussian beam.

[0046] S3, based on heterodyne detection technology, interferes the scattered light with the local oscillator light, uses a photodetector to receive the interfered light beam, obtains the intermediate frequency photocurrent, and analyzes and processes the intermediate frequency photocurrent signal to obtain the corresponding rotational Doppler frequency shift under the illumination angle.

[0047] Furthermore, the relationship between vorticity and rotational Doppler shift is shown below:

[0048] ω=(4π / m) <f ⊥ >

[0049] Where ω is the fluid vorticity, m is the topological charge of the focused vortex beam, <f ⊥ > is the frequency shift centroid of the intermediate frequency photocurrent signal, i.e. the echo signal, i.e. the weighted average of the echo signal spectrum, <f ⊥ >Usually tens of Hz to hundreds of Hz, <f ⊥ The measurement method of > is as follows:

[0050]

[0051] Among them, F S is the sampling frequency, f ⊥ is the frequency shift of the echo signal, I(f ⊥ ) is the power spectrum of the rotational Doppler effect, M is the total number of samples, k is the serial number of the sample, and f ⊥k is the frequency channel value of the kth sample, I k is the power value corresponding to the kth sample.

[0052] S4, using a beam scanning technology to change the irradiation angle of the focused vortex beam, and performing measurements at three irradiation angles in total according to steps S2 to S3, respectively obtaining vorticities corresponding to the three irradiation angles, and performing vector synthesis using the vorticities corresponding to the three irradiation angles to obtain a three-dimensional vorticity distribution in the area;

[0053] In this embodiment, Figure 2 As shown, the three irradiation angles are θ 1 ,θ 2 ,θ 3 The corresponding vorticity under these three illumination angles is ω Z ,ω N ,ω E ; At the irradiation angle θ 1 The irradiation direction is the z axis, and the irradiation angle is θ 2 The irradiation direction and irradiation angle θ 1 The angle between the irradiation directions is γ 21 , irradiation angle θ 3 The irradiation direction and irradiation angle θ 1 The angle between the irradiation directions is γ 31 , and γ 21 =γ 31 =γ; the three-dimensional vorticity field distribution ω in the area is obtained by vector synthesis using the corresponding vorticity at three irradiation angles as shown below:

[0054] ω x =(ω E -ω Z cosγ) / sinγ

[0055] ω y =(ω N -ω Z cosγ) / sinγ

[0056] ω z =ω Z

[0057] ω=(ω x ,ω y ,ω z )

[0058] Among them, γ is the cone apex angle of the beam scanning, that is, the complementary angle of the pitch angle of the focused vortex beam.

[0059] In this embodiment, the optical path principle of the fluid three-dimensional vortex measurement experiment is as follows: Figure 3 As shown, a specific fork-shaped diffraction grating is loaded on the liquid crystal spatial light modulator, and a helium-neon laser is used to generate laser light.

[0060] In addition, in order to verify the effectiveness of the method of the present invention, after obtaining the wind speed field distribution in the atmospheric turbulence simulation pool by a hot wire anemometer, the three-dimensional vorticity distribution is calculated using the following formula:

[0061]

[0062] Among them, the atmospheric turbulence simulation pool can provide a local stable wind speed field, and the wind speed field distribution in the area can be measured by a hot wire anemometer.

[0063] Finally, the three-dimensional vorticity distribution result measured by the rotational Doppler effect was compared with this result. The preliminary experimental results showed that the error between the two methods was within 10%, thus verifying the effectiveness of the method of the present invention.

[0064] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect, characterized in that: The following steps are involved: S1, using a laser to generate laser light, dividing the laser light generated by the laser into two beams, one of which is used as a local oscillator light, and the other is modulated to obtain a vortex light beam, and then adjusting the divergence angle of the vortex light beam to obtain a focused vortex light beam; S2, irradiate the measured area with the focused vortex beam at a certain angle to obtain scattered light; S3, interfering the obtained scattered light with the local oscillation light, using a photodetector to receive the interfered light beam to obtain an intermediate frequency photocurrent, and analyzing and processing the intermediate frequency photocurrent signal to obtain the corresponding vorticity at the current irradiation angle; S4, changing the irradiation angle of the focused vortex light beam, and performing measurements at three irradiation angles in total according to the method of steps S2 to S3, respectively obtaining the corresponding vorticities at the three irradiation angles, and using the corresponding vorticities at the three irradiation angles to perform vector synthesis to obtain the three-dimensional vorticity field distribution in the measured area.

2. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: In step S3, the vorticity is calculated as follows: ω=(4π / m) <f ⊥ > Where ω is the fluid vorticity; m is the topological charge of the focused vortex beam; <f ⊥ > is the intermediate frequency photocurrent signal, that is, the frequency shift centroid of the echo signal, and also the weighted average of the signal spectrum.

3. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 2, characterized in that: Frequency shift centroid of echo signal <f ⊥ The measurement method of > is as follows: Among them, F S is the sampling frequency, f ⊥ is the frequency shift of the echo signal, I(f ⊥ ) is the power spectrum of the rotational Doppler effect, M is the total number of samples, k is the serial number of the sample, and f ⊥k is the frequency channel value of the kth sample, I k is the power value corresponding to the kth sample.

4. A method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, 2 or 3, characterized in that: Step S3 obtains the vorticity based on heterodyne detection technology.

5. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: The three irradiation angles in step S4 are θ1, θ2, and θ3, respectively, and the corresponding vorticity at these three irradiation angles is ω Z ,ω N ,ω E ; The irradiation direction of the irradiation angle θ1 is the z axis, and the angle between the irradiation direction of the irradiation angle θ2 and the irradiation direction of the irradiation angle θ1 is γ 21 The angle between the irradiation direction of the irradiation angle θ3 and the irradiation direction of the irradiation angle θ1 is γ 31 , and γ 21 =γ 31 =γ; The three-dimensional vorticity field distribution ω in this area is obtained as follows: oh x =(ω E -oh Z cosγ) / sinγ oh y =(ω N -oh Z cosγ) / sinγ oh z =ω Z ω=(ω x ,oh y ,oh z ) Among them, ω z is the component of the three-dimensional vorticity along the z axis, ω x is the component of the three-dimensional vorticity along the x-axis, ω y is the component of the three-dimensional vorticity along the y-axis.

6. A method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1 or 5, characterized in that: In step S4, the irradiation angle of the focused vortex beam is changed by using the beam scanning technology.

7. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: In step S1, a laser is used to generate a fundamental mode Gaussian beam, and a beam splitter is used to split the fundamental mode Gaussian beam into two laser beams with a ratio of 1:

1.

8. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: In step S1, another laser beam is modulated by a liquid crystal spatial light modulator loaded with a fork-shaped diffraction grating to obtain a vortex beam.

9. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: In step S1, a focused vortex beam is obtained by adjusting the divergence angle of the vortex beam through a lens; the vortex beam type is a Laguerre-Gaussian beam.

10. The method for measuring three-dimensional vorticity of a fluid based on the rotational Doppler effect according to claim 1, characterized in that: Step S2, adjusting the focusing radius and the emission aperture of the focused vortex beam so that the area to be measured is completely within the annular spot of the focused vortex beam.

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