Skip to main content

Unsteady skin-friction field estimation based on global luminescent oil-film image analysis


A global luminescent oil-film (GLOF) image analysis method to estimate unsteady skin-friction fields in an unsteady flow field is proposed and demonstrated. A governing equation describing the dynamics of the oil film (the thin-oil-film equation) is employed for the unsteady oil-film images. The frequency response of the oil-film movement is analyzed, and a cutoff frequency is defined as a function of the oil-film thickness and the kinematic oil viscosity. The estimating skin-friction vector is defined along with a spatiotemporal weighted window and obtained by solving the overdetermined system of the thin-oil-film equation. The system can be solved by using the weighted linear least-squares method, and the time-resolved skin-friction field can be estimated. The time-resolved GLOF image analysis method is demonstrated on an experiment of a junction flow on a flat surface with a square cylinder. The GLOF images in the Kármán vortex shedding bounding the flat surface were acquired, and the time-resolved skin-friction fields were obtained. The results showed that fluctuation in the skin-friction vectors corresponds to the shedding frequency, and the vortices bounding the surface were extracted. The averaged skin-friction field is compared with the result of the previous study based on the time-independent model. The normalized skin friction from both methods showed good agreement, which indicates that the quantitative value will be obtained when a calibration process is involved in a future study.

Graphic abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. Asai K, Yorita D (2011) Unsteady PSP measurement in low-speed flow-overview of recent advancement at Tohoku university. In: 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, p 847.

  2. Brown JL, Naughton JW (1999) The thin oil film equation. Technical report NASA/TM-1999-208767, NASA, Washington.

  3. Cedeño FO, Prieto MM, Huidobro JA (2000) Viscosities of binary and ternary mixtures of hexadecanoic, octadecanoic, and cis-9-octadecenoic acids. J Chem Eng Data 45(2):219–224.

    Article  Google Scholar 

  4. Crafton JW, Fonov SD, Jones EG, Goss LP, Forlines RA, Fontaine A (2008) Measurements of skin friction in water using surface stress sensitive films. Meas Sci Technol 19(7):075801.

    Article  Google Scholar 

  5. Diller TE, Telionis DP (1989) Time-resolved heat transfer and skin friction measurements in unsteady flow, chapter 8. Springer, Berlin, pp 323–355.

    Book  Google Scholar 

  6. Husen NM, Liu T, Sullivan JP (2018a) Luminescent oil film flow tagging skin friction meter applied to FAITH hill. AIAA J 56(10):3875–3886.

    Article  Google Scholar 

  7. Husen NM, Liu T, Sullivan JP (2018b) The ratioed image film thickness meter. Meas Sci Technol 29(6):065301.

    Article  Google Scholar 

  8. Kurita M, Iijima H (2017) Hybrid oil film approach to measuring skin friction distribution. Meas Sci Technol 28(5):055301.

    Article  Google Scholar 

  9. Lee T (2017) A least-squares-based optical-flow method for skin-friction field measurement using luminescent oil film. M.S. thesis, Tohoku University, Sendai, Japan

  10. Lee T, Nonomura T, Asai K, Liu T (2018) Linear least-squares method for global luminescent oil film skin friction field analysis. Rev Sci Instrum 89(6):065106.

    Article  Google Scholar 

  11. Lee T, Nonomura T, Asai K, Naughton JW (2020b) Validation and uncertainty analysis of global luminescent oil-film skin-friction field measurement. Meas Sci Technol 31(3):035204.

    Article  Google Scholar 

  12. Lee C, Lee T, Nonomura T, Asai K (2020a) Evaluating the applicability of a phase-averaged processing of skin friction field measurement using an optical flow method, to appear in Journal of Visualization

  13. Liu T (2013) Extraction of skin-friction fields from surface flow visualizations as an inverse problem. Meas Sci Technol 24(12):124004.

    Article  Google Scholar 

  14. Liu T, Sullivan J (1998) Luminescent oil-film skin-friction meter. AIAA J 36(8):1460–1465.

    Article  Google Scholar 

  15. Liu T, Montefort J, Woodiga S, Merati P, Shen L (2008) Global luminescent oil-film skin-friction meter. AIAA J 46(2):476–485.

    Article  Google Scholar 

  16. Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of 7th international joint conference on artificial intelligence, pp 674–679

  17. Menendez AN, Ramaprian BR (1985) The use of flush-mounted hot-film gauges to measure skin friction in unsteady boundary layers. J Fluid Mech 161:139–159.

    Article  MATH  Google Scholar 

  18. Okajima A (1982) Strouhal numbers of rectangular cylinders. J Fluid Mech 123:379–398.

    Article  Google Scholar 

  19. Squire LC (1961) The motion of a thin oil sheet under the steady boundary layer on a body. J Fluid Mech 11(2):161–179.

    MathSciNet  Article  MATH  Google Scholar 

  20. Sugioka Y, Koike S, Nakakita K, Numata D, Nonomura T, Asai K (2018) Experimental analysis of transonic buffet on a 3D swept wing using fast-response pressure-sensitive paint. Exp Fluids 59(6):108

    Article  Google Scholar 

  21. Sugioka Y, Hiura K, Chen L, Matsui A, Morita K, Nonomura T, Asai K (2019) Unsteady pressure-sensitive-paint (PSP) measurement in low-speed flow: characteristic mode decomposition and noise floor analysis. Exp Fluids 60(7):108.

    Article  Google Scholar 

  22. Yorita D, Nagai H, Asai K, Narumi T (2010) Unsteady PSP technique for measuring naturally-disturbed periodic phenomena. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, p 307.

Download references


The present study was supported in part by JSPS KAKENHI Grant Number 19H00800 and JST Presto Grant Number JPMJPR1678.

Author information



Corresponding author

Correspondence to Taku Nonomura.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lee, T., Lee, C., Nonomura, T. et al. Unsteady skin-friction field estimation based on global luminescent oil-film image analysis. J Vis 23, 763–772 (2020).

Download citation


  • Skin friction
  • Wall shear stress
  • Image-based measurement
  • Oil film
  • Unsteady flow
  • Kármán vortex shedding