Concentration Field WU Jing
II. P ROPOSED S CHEME
A. Image Acquisition System
Image acquisition system of PIVC is similar to that of PIV, and it consists of digital video camera, image collector and computer. And the camera determines the resolution, collection rate and digital-signal format of the system.
Optical imaging device is hardware equipment which transforms the signal of electromagnetic energy spectrum into electric signal. The main characteristic parameters of CCD include spectral response, photoelectric transfer characteristic, dynamic range, dark current, resolution and electronic shutter [2].
(a) Red, green and blue component of the response of color CCD
(b) Grey response
Figure.1 Schematic of spectral response sensitivity characteristics charts of BASLER A300 SERIES
When CCD is used to shoot flow fields, the selection of exposure time should satisfy the requirement that the displacement of particle movement couldn’t exceed the minimum resolution of CCD under the control of synchronous generator, or the acquired flow images will have ghost image, which causes measuring error. In addition, in actual experiments, the density of incoming
light is constant, and illumination of image plane of fixed optical system can realize the match of illumination of image plane and spectral response characteristic of CCD by choosing suitable relative aperture or exposure time of electronic shutter. In actual experiment, digital oscilloscope not only can be used to observe CCD signal, but also can be used to rectify the imaging distortion of CCD caused by various factors [3].
Spectral response of CCD has close relationship with wavelengths of light, and the wavelengths of light should correspond to peak response spectral characteristics of CCD. Generally speaking, spectral response range of CCD is 200nm～1100nm,and peak response wavelength is about 550nm. Figure 1 shows color response spectral characteristics and gray response spectral characteristics of array BASLER A300/A301/A302 SERIES. It is obvious that this category of CCD has very sensitive response to green ray (532nm), which must be considered on selecting light source.
CCD used for PIV has four working modes, continuous mode, control mode, triggering mode and double exposure mode. And each working mode and the relevant parameters can be set by software.
B. Image Processing Technique
The main measurement characteristics of images include luminous intensity and color. And the images of luminous intensity which are also called grey images or monochrome images which can be described by exposure and reflection model——two-dimensional intensity function:
( , ) ( , ) ( , )
f x y =I x y r x y (1)
x and y are space coordinates of image, ( , )I x y is incident function of incident light energy component depending on light source, ( , )r x y is the reflection function reflecting reflection characteristics of surface, and 0<I x y( , )< +∞ , 0<r x y( , )< . Incident function 1 reflects external factors or environmental factors of image, and reflection function reflects the internal characteristics of image or the reflection characteristics of object on various lights.
The result of sample and quantization is an actual matrix. It is common that two main methods are used to express digital images. If an image f x y is sampled, ( , ) the generating digital image has M lines and N columns. The value of coordinate ( , )x y is discrete magnitude now. And integers are used to express the discrete magnitudes for convenience. The coordinate value of the origin is ( , )x y =(0, 0). The next coordinate value of the fist line of the image is expressed by ( , )x y =(0,1). And the upper left corner is the origin of the coordinates for coordinate representation of digital image.
In the digital process, M N, and discrete gray level L of each pixel need to be determined. There is no other requirements except for the requirement that M and N must be positive integers. However, for the consideration on process, storage and sampling hardware,
the typical value of gray level should be integral power of 2, L=2k. If discrete gray level is equally spaced and is the integral within the interval[0,L−1]. Sometimes the value range of gray level is called dynamic range of image. And the images of all effective segments with gray level are called high dynamic range images. When a considerable number of pixels have the characteristic, the images have higher contrast. On the contrary, low dynamic range images seem like watered-down gray style. The bit number for storage is formula (2):
b=M× × (2) N k
Table 1 shows the bit number for storing square images when N and k is different common values. The gray level of each k is shown in parentheses. When the gray level of an image is 2k
, the image is called k -byte image. In the present flow visualization, the acquired digital images have 1024 possible gray levels, which is called 10-bit image.
Table 1． Bits for saving square images of common Ns and ks
N /k 1(L =2) 4(L =16) 8(L =256) 10(L =1024) 11(L =2048) 12(L =4096) 32 1,024 4,096 8,192 10,240 11,264 12,288 64 4,096 16,384 32,768 40,960 45,056 49,152 128 16,384 65,536 131,072 163,840 180,224 196,608 256 65,536 262,144 524,288 655,360 720,896 786,432 512 262,144 1,048,576 2,097,152 2,621,440 2,883,584 3,145,728 1024 1,048,576 4,194,304 8,388,608 10,485,760 11,534,336 12,582,912 2048 4,194,304 16,777,216 33,554,432 41,943,040 46,137,344 50,331,648 4096 16,777,216 67,108,864 134,217,728 167,772,160 184,549,376 201,326,592
Measurement of video quality is based on objective criterions of difference between the original signals and the processed signals, which is very important in applying video coding, the reason for which is that it not only can measure the distortion caused by compression, but also is a good criterion for motion estimation finding the best match (many PIV algorithms depend on it). In an ideal world, the measurement should relate to the difference between two video sequences, but it is difficult to find out the method. Although various quality measurements have been proposed, it is complicated for the method to calculating the correlation with visual perception of people. The design of most video processing systems makes the MSE between video sequence ψ and 1 ψ minimal: 2
2 2 1 2 , 1 MSE e ( ( , , ) ( , , )) k m n m n k m n k N σ ψ ψ = =
∑∑
− (3)N is the total number of pixels in each sequence. For color video, MSE of each color component is calculated respectively. PSNR replacing MSE with dB as unit is usually used for quality measurement of video coding, and the definition is:
2 max 10 2 PSNR 10 log e ψ σ = (4) max
ψ is the maximum density value of video signal. For common each color 8-bit video, ψmax is 255. For
fixed peak value, PSNR is completely determined by MSE. As an important criterion, the quality of PSNR images higher than 40dB is very good, which means that it is close to the original image. The quality of PSNR images between 30dB and 40dB is good, and the quality of images less than 30dB is worse. In order to reduce the calculation, the measurement replacing MSE is MAD, and the definition is:
1 2 , 1 MAD ( , , ) ( , , )) k m n m n k m n k N ψ ψ =
∑∑
− (5)For motion estimation, MAD is usually used to find out the best match of the known
3. Overall design of measurement system
Based on the study on light scattering measurement methods of particles in concentration field and the image measurement technique, the paper develops complete image measurement system of instantaneous concentration field. The system not only has the function of instantaneous particle image field obtaining instantaneous concentration field, but also has the function of getting velocity field by calculating the collected PIV images. The system consists of hardware system and software system. And hardware system includes subsystems such as image capture, laser, CCD, particle exploder and control signal. Software system includes the modules such as image bus, concentration field display, velocity field analysis, curl field analysis, flow line analysis, memory management, other after processes and assistance.
Table 2 indicated the allocation of PIVC. The laser and digital camera of the system is the most expensive and the most important device. It's worth mentioning that the system can be as non-contact and solid-distorted measurement tool. The solid-distorted displacement field and velocity field can be obtained without laser, particle exploder and synchronous controller. On the other hand, the system can be expanded as motion estimation or motion monitoring system, which can be used for secure construction of buildings, warehouses and residential areas.
Figure 2 shows the hardware system architecture diagram of PIVC. Air, water and oil enter from the main entrance in the left corner. Some enter the tester through flow meter after branch entrance and particles generator
Legends Parts Parameters
Laboratory table Length × width × height=2200mm×700mm×700mm
Laser
Model: Ambergreen-LFA050121
Name: 532nmpump end PuQuan solid-state green laser
Maximum power: 1.02W (the current is 5.16A, and the stability is less than ±3%) Pumping source: Cw semiconductor
laser medium: Nd:YVO4
Patch light: Beam diameter <1mm; Experimental section thickness:1mm, size: 700×700mm Divergence angle: <4mrad
Cooling model: air cooling (natural cooling) Power input: 220V/50Hz/AC
Overall dimensions: length × width × height =155mm×68mm×85mm
Origin of product: Beijing cubic heaven and earth science and technology development co., LTD
Camera
Model: SONY DSC-F828
Resolution: 640pixel×480pixel(30fps); 3264×2448 = 7990272 pixels( Single frame) Frame rate: 640pixel×480pixel 时 15fps~25 fps
Bit rate: 25 MB/s
Other parameters: Optical zoom 7.1; aperture F2.0-2.8; focal length f=7.1mm-51mm; 2/3 inches CCD; static and dynamic imaging; TIFF ape flac; exposure time 1/2000s
Origin of product: SSGE
Particle exploder
Model: FOGGER-AB-1500
Name: remote-control environmental tobacco oil heat sublimation smoke generator Particle: Particle size1μm ~500μm; environmental tobacco oil,
Origin of produc: Beijing cubic heaven and earth science and technology development co., LTD
Air blower axial-flow fan 1800m3/h, 120w, wind speed of wind tunnel experimental section is 1m/s
Computer PC; CPU 3.0G; Mmory1.0G; Hard disc 80G
PIVC software Development; based on Windows XP; man-machine and dexterity
Other necessary
accessories Auxiliary measuring equipment: camera tripod, laser tripod
Fig. 2 Schematic of the PIVC hardware system
mixes. Meanwhile, the objective of the tester is illuminated by the patch light formulated by the laser on the right side. CCD shoots the flow field from the angle which is perpendicular to patch light, and the obtained information of flow filed is sent to the computer for process.
III.CFDNUMERIC CALCULATION OF CONCENTRATION
FIELD A. Control Equation Continuity equation 0 i i U x ∂ = ∂ (6) Momentum equation:
1 i i i j i j j i j j U U P U U u u t x ρ x x ν x ∂ + ∂ = − ∂ + ∂ ∂ − ∂ ∂ ∂ ∂ ∂ (7) k− equation: ε j t i i j t j j k j j i j U U U k k k U t x x x x x x ν ν ε σ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + = + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ (8) 1 2 j t i i j t j j j j i j U U U U C C t x x ε x k ε x x x ε ν ε ε ε ε ν ε σ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + = + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ (9) In the equations, 2 / 3 ( / / ) i j ij t i j j i u u = kδ ν− U ∂ +x U ∂x , 2 ( / ) t C ku ν = ε ; 0.09 u C = ; Cε1 =1.44 ; Cε2 =1.92 ; σ =k 1.0 ; 1.3 ε
σ = ; ν is dynamic viscosity turbulence t coefficient, and ε is turbulent dissipation term.
If gas and solid two- phase flow has no effect on flow field or the distribution of flow filed has no relation with solid phase (or liquid phase), it is true when the diameter of particle is small. And if there is no reaction and mass exchange between fluid and particle, particle diffusion is the result caused by fluid and particle. And advection-diffusion equation of particle is:
( j i) i i i j j j u C C C K S t x x x ∂ ∂ ∂ ∂ + = + ∂ ∂ ∂ ∂
(10)
In the equation, C is the concentration of particle, i K is turbulent diffusion coefficient, K=ν σt/ ,
0.7 σ = .
B. Numerical Method
The transmission of fluid medium is the transmission of air and CO mixture, so it belongs to two-phase flow of air and CO. Numerical method uses grid computing method. According to the actual situation of wind tunnel experimental table and measurement of flow filed, meshing generation is firstly made, as shown in Figure 3, the size of the dimension of cylindrical radius with 1 is 160, the computational domain uses non-uniform grid, the grids near cylinder wall and CO entrance are very intensive, and other grids are sparse.
Reynolds number is
5
/ / 1 0.16 / (1.512 10 ) 10582
Re=ρvl µ=vl ν = × × − ≈
, and it is the same to Reynolds number in actual measurement experiment, which is good for comparison. The equations from equation (6) to equation (10) use Finite Volume Method for discrete, the discrete format is QUICK and the time step is 0.005s.
In order to prevent the discrete and instability, under-relaxation method is used for momentum equation and scalar transport equation, and SIMPLE algorithm is
used for coupling of pressure and velocity.
Figure 3. Meshes of computation regions
Figure 4. Computational velocity field and concentration field of CO (t=8s) in air and CO two-phase flow
(a) Calculation of correlation dimension
(b) Fitting result of linear segment
Fig. 5 Results of calculating the associated dimensions for pulsating concentrations with different embedded dimensions
Inflow boundary condition: velocity of dimension with 1u= ，1 v= . 0
Outflow boundary condition: derivative of each flow
parameter along the flow line ui k p 0 x x x x ε ∂ ∂ ∂ ∂ = = = = ∂ ∂ ∂ ∂ .
Wall boundary condition: non-slipping condition is used for solid wall, and wall-function method is used nearby the wall.
Span direction boundary method: using free boundary condition, ∂ ∂ = . / n 0
The variables in the process of calculation should use double precision.
IV.CHAOTIC CHARACTERISTICS OF TIME SERIES FOR
CONCENTRATION DISTRIBUTION
According to the judgment if the time sequence is mixed, the quantization calculation with the degree of controllability can be obtained by calculating correlation dimension, Kolmogorov entropy and maximal Lyapuno index of time sequence. Autocorrelation function method is used to select time delay τ = and calculate 5 correlation dimension, which can get ln ( ) ~ lnC r r curve graph in Figure 5(a). The linear segment with
9
m= sequence is selected for fitting, and the result is shown in Figure 5(b), which can get correlation dimensionD=3.218. Through further calculation, we can get Kolmogorov entropy K2 =0.63691and the
maximum Lyapunov indexLmax=0.138541.
The analysis on time sequence of other points in field can get similar results, from which we can see that the concentration system has singular attractors ( D=3.218 is fractal dimension), which is chaotic motion (becauseK2 =0.63691 is positive number) and
instable (because Lmax =0.138541 is positive number).
Figure 6. Computational result of the information entropies of the concentration field
Figure 6 is pseudo-color image of information entropy distribution of Figure 5. We can see from Figure 6 that the information entropy can represent uncertainty of information source for the system.
The time sequence of information entropy of concentration filed shown in Figure 7 can be got by exploring the change of information entropy with the time. And Figure 7 is the result of FFT. Obviously, the sequence has evident controlled composition and has certain ordering [4]. According to the judgment if the former time sequence is chaotic, the quantization calculation with the degree of controllability can be got by calculating the correlation dimension, Kolmogorov
entropy and maximal Lyapuno index of time sequence [5].
Figure 7. Time series of the information entropies of the concentration fields
(a) Calculation of correlation dimension with different embedded dimensions
(b) Fitting result of linear segment (m=5 sequence Figure 8. Non-linear characteristics analysis of the information
entropies of the concentration fields
Autocorrelation function method is used to select time delay τ = and to calculate correlation dimension, 5 which can get ln ( ) ~ lnC r r curve graph in Figure 8(a). The linear segment with m = 5 sequence is selected for fitting, and the result is shown in Figure 8(b), which can get correlation dimensionD=3.209. Through further calculation, we can get Kolmogorov entropy
2 0.511828
K = and the maximum Lyapunov index
max 0.109229
L = .
The analysis on time sequence of other points in field can get similar results, from which we can see that the concentration system has singular attractors (because D=3.209 is fractal dimension), which is chaotic motion (because K2 =0.511828 is positive
number) and instable (because Lmax=0.109229 is
positive number).
V. CONCLUSION
Two-phase flow measurement is a study which is concerned all over the world, and there are still many problems needing to be solved. The quantitative measurement on concentration field not only can provide scientific methods for people measuring environment wind tunnel, but also can provide important data for solving convection--diffusion problem in practical project [6]. The established large environment and wind engineering wind tunnel needs to develop the measurement system of instantaneous concentration field in order to study concentration field of environmental pollution diffusion. Based on collecting, analyzing and selecting a large number of literatures, the paper comprehensively studies the image measurement of instantaneous concentration field, and develops the complete software and hardware system. And the developed measurement system is used to measure the results, and the nonlinear characteristics of instable concentration field are studied [7]. Combined with
experimental fluid mechanics, information technology, optical scattering and imaging theory, the paper develops image measurement study on instantaneous concentration field.
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