Microsoft Word - ISPIVabstMurai.docx


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Color contamination matrix property assessment 1 

for improvement of colored smoke PIV 2 

 3 

Yuichi Murai, Yasufumi Horimoto, Hyun Jin Park, and Yuji Tasaka 4 

 5 

Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, N13 W8, Sapporo 060-8628, Japan 6 

* Corresponding author. Tel./fax: +81(Japan) 11 706 6372. E-mail: murai@eng.hokudai.ac.jp. 7 

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A single-camera color PIV system that can acquire PIV data of three separated layers has been re-9 

designed, purposing improvement of wind tunnel applicability. We target smoke image that has 10 

particle-per-pixel values higher than unity. The system constitutes of a high-power color-coding 11 

illuminator and a digital color high-speed video camera. RGB values in recorded image involves 12 

severe color contaminations due to five optical and digital sequences (Fig. 1). To quantify this, a 13 

snapshot calibration is proposed to describe the contamination matrix equation (Eq. (1)). Taking the 14 

inverse matrix (Eq. (2)) allows in-plane PIV in each color layer to be accurately implemented. We 15 

also derive mathematical limits to operate the colored smoke PIV, which is explained by the matrix 16 

property (Eq (3)). Feasibility of the proposed method has been demonstrated by application to a 17 

turbulent wake behind a Delta wing (Fig. 2) and also to a boundary layer flow along heated chocolate. 18 
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Fig. 1  Color contamination property for a water mist in air projected by a sheet of color light 21 
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Color contamination matrix equation: 23 

3 5 1

1 6 2

2 4 3

1

1

1

L

L

L

R a a R b

G a a G b

B a a B b

       
               
              

,            (1) 24 



2 
 

   Inverse matrix equation for estimating smoke density in three colored layers 1 

3 6 3 5 4 4 6 5 1

2 6 1 2 5 1 5 6 2

1 3 2 2 4 3 1 4 3

1
1

1

1

L

L

L

R a a a a a a a a R b

G a a a a a a a a G b
K

B a a a a a a a a B b

        
              
             

,         (2) 2 

Determinant of the inverse matrix 3 

 1 3 5 2 4 6 1 4 2 5 3 61K a a a a a a a a a a a a      .           (3) 4 

 5 

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Fig. 2 Flow velocity vector distribution obtained by inter-color 3-D cross correlation for a wake 7 

behind a delta wing of 25 degree in angle of attack at which periodic stall occurred. 8 

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References 10 

Pick S, Lehmann F (2009) Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in 11 

flapping robotic insect wings. Exp Fluids 47: 1009-1023. 12 

Watamura T, Tasaka Y, Murai Y (2013) LCD-projector based 3D color PTV. Exp Thermal Fluid Sci 47: 68–80. 13 

Charonko J, Antoine E, Vlachos PP (2014) Multispectral processing for color particle image velocimetry. Microfluid 14 

Nanofluid 17: 729-743. 15 

Aguirre-Palbo AA, Alarfaj, MK, Li EQ, Hernandez-Sanchez JF, Thoroddsen ST (2017) Tomographic particle image 16 

velocimetry using smartphones and colored shadows. Sci Reports 7: 3714-3722. 17 

Xiong J, Aguirre-Pablo AA, Idoughi R, Thoroddsen ST, Heidrich W (2021) Rainbow PIV with improved depth 18 

resolution – design and comparative study with Tomo PIV. Meas Sci Tech 32: 025401. 19