Abstract
Pressure-sensitive paint (PSP) measurement for turbine blades and vanes is often limited by the optical window and occlusion of the complex blade structure. Endoscopic PSP imaging systems have been designed for the pressure measurement of integrated inter-turbine duct (IITD) guide vanes. Notably, the objective lens of the endoscope leads to severe and dynamic image distortion. The classical direct linear transformation (DLT) algorithm does not consider nonlinear distortion, which reduces the accuracy of three-dimensional (3D) pressure field reconstruction. Therefore, in this study, a dynamic distortion correction endoscopic (DDCE) PSP technique is proposed. Real-time endoscopic images are registered to the post-calibration images through affine transform. Next, the distortion was compensated using the post-calibrated distortion and intrinsic matrix, and the relationship between the pixels on the distorted two-dimensional (2D) PSP images and 3D points on the vanes can be reliably acquired. Reprojection errors are used to evaluate the performance of the proposed technique. The maximum and average errors decrease from 30 to 4 pixels and from 4.8 pixels to 0.8 pixels, respectively. Subsequently, the DDCE PSP technique is applied for the pressure measurement on turbine guide vanes with outlet Mach number ranging from 0.65 to 0.95. Endoscopic PSP images of a structural vane and two aero-vanes are recorded, and the 2D pressure fields of the three vanes are defined through in situ calibration of the PSP. Finally, the 3D pressure fields are reconstructed by mapping the 2D pressure field to the 3D point cloud using the DDCE PSP technique.
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Abbreviations
- a :
-
Coefficient of line equation
- A(T):
-
Stern–Volmer coefficient
- b :
-
Coefficient of line equation
- B(T):
-
Stern–Volmer coefficient
- c :
-
Coefficient of line equation
- f :
-
Focal length
- H :
-
Homography matrix
- I :
-
Wind-on intensity
- I ref :
-
Reference intensity
- k 1 :
-
Radial distortion coefficient
- k 2 :
-
Radial distortion coefficient
- l :
-
Line in homogeneous coordinates
- L :
-
Projection matrix
- m :
-
Homogeneous coordinate of a line
- Ma :
-
Mach number
- n :
-
Homogeneous coordinate of a line
- N :
-
Intrinsic matrix
- p :
-
2D point on the image plane
- p 1 :
-
Tangential distortion coefficient
- p 2 :
-
Tangential distortion coefficient
- p n :
-
2D point on the normalized plane
- P :
-
Pressure in the wind-on condition
- P ref :
-
Pressure in the wind-off condition
- P w :
-
3D point in the world coordinates
- P c :
-
3D point in the camera coordinates
- r :
-
Distance from a point to the origin of the normalized plane
- R :
-
Rotation matrix
- t :
-
Translation vector
- u :
-
Pixel coordinate in the u direction
- u′ :
-
Pixel coordinate in the u direction after affine transformation
- uʺ :
-
Pixel coordinate in the u direction after distortion correction
- v :
-
Pixel coordinate in the v direction
- v′ :
-
Pixel coordinate in the v direction after affine transformation
- vʺ :
-
Pixel coordinate in the v direction after distortion correction
- x n :
-
x Coordinate of a point on the normalized plane
- y n :
-
y coordinate of a point on the normalized plane
- δ :
-
Distortion vector
- δr :
-
Radial distortion
- δr u :
-
Component of the radial distortion in the u direction
- δr v :
-
Component of the radial distortion in the v direction
- δt :
-
Tangential distortion
- δt u :
-
Component of the tangential distortion in the u direction
- δt v :
-
Component of the tangential distortion in the v direction
- δ u :
-
Component of the tangential distortion in the u direction
- δ v :
-
Component of the tangential distortion in the v direction
- α :
-
Scale factor in the x direction of the normalized plane
- β :
-
Scale factor in the y direction of the normalized plane
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (NSFC Nos. 12022202 & 12227803) and the Gas Turbine Research Institute of Shanghai Jiao Tong University.
Funding
This work was supported by the National Natural Science Foundation of China (NSFC Nos. 12022202 & 12227803) and the Gas Turbine Research Institute of Shanghai Jiao Tong University.
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Dong conducted the experiments, processed the data and wrote the main manuscript. Gu, Chen and Yang conducted the experiments. Zhou, Liu and Peng supervised the experiments and revised the manuscript. All authors reviewed the manuscript.
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Dong, Z., Gu, F., Chen, R. et al. Three-dimensional pressure field measurement on turbine guide vanes using a dynamic distortion correction endoscopic pressure-sensitive paint technique. Exp Fluids 64, 97 (2023). https://doi.org/10.1007/s00348-023-03643-6
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DOI: https://doi.org/10.1007/s00348-023-03643-6