Li Peng，Ming Xiao

(1.College of Automation Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China;2.College of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China)

0 Introduction

Skin friction is one of the most importantand difficult quantities in boundary layer research.Although various indirect and non-global techniques have been developed and great efforts have been made for measuring skin friction［1-3］，global skin friction diagnostics techniques are highly desirable.Recently，a global fluorescence oil-film skin friction meter has been developed and applied to diagnostics of skin friction fields in complexseparated flows by Liu，et al［4-5］.This is a more rigorous method for quantitative global high-spatial-resolution diagnostics of skin friction，which result from luminescent oil images.

Fukagata，et al［6］analytically derived a direct relationship between the Reynolds stress and the skin friction coefficient under the condition of constant flow rate.The relationship indicates the connection between local skin friction and Reynolds shear stress.It is reconfirmed that the near-wall Reynolds stress is primarily important for the prediction and control of wall turbulence.Consequently，the skin friction can be used to valuate quantitatively the effectiveness of flow control.

The aim of the present work is to investigate the technique of fluorescence oil-film technique and its application in flow control.At first，the theory of the fluorescence oil-film technique is briefiy described，and its optimization solution algorithm is proposed.Then two flow control experiments are carried out，including a passive control for boundary layer transition and an active control of flow over a backward-facing step(BFS).The technique is used to measure the global skin friction on the surface downstream.The results presented in this paper are useful for better understanding of the flow physics and assessing the flow control strategies.

1 Theory and optimization solution algorithm

Consider a thin film of viscous liquid，such assilicone oil，initially placed on a test surface as shown in Fig.1 .The oil film will move in response to the skin friction and to the body force，e.g.gravity，acting on the oil.Additionally，the oil film will experience surface tension effects related to the curvature of the oil film surface.The thickness of the film，h(x，y，t)，will vary with position(x，y)on the surface and with time(t).Assuming the 3D aerodynamic flow is steady，Squire［7］and Tanner［8］gave respectively different form of the thin oil film equation，and the equivalence of the two forms of the thin oil film equation is demonstrated through a metric transformation.Liu and Sullivan［4］doped silicone oil with luminescent molecules and made fluorescence oil that can emit the radiation at a longer wavelength due to the Stokes shift when illuminated by an appropriate light source，Iex，like UV lamp.Since the luminescent intensity，I(x，y，t)，is proportional to the oil film thickness，h(x，y，t)，thickness measurement is converted to luminescence measurement that is much easier.When the oil film thickness is transformed to the image intensity，the thin oil film equation can be projected onto the image plane to provide a relationship between skin friction and the temporal and spatial derivatives of the image intensity.For the case where the pressure，gravity and surface tension terms are negligible compared to the shear stress term，the measurement model of fluorescence oil film can be derived from the thin oil film equation

Where g=I/Iexis the normalized luminescent intensity，=τg(λ/2μa)is the equivalent skin friction(ESF)，μ is the dynamical viscosity of the oil，a is a coefficient proportional to the quantum efficiency of seeded luminescent molecules，λ is a scaling factor which is an oneto-one mapping factor between the image plane and the surface，▽ is the gradient operator in the image plane.To solve the problem for skin friction，a variational formulation is given with a regularization term for the smoothness of a skin friction field［9-10］.The corresponding Euler-Lagrange equations are derived and numerically solved with the Neumann condition for a snapshot solution of a skin friction field.The detailed solution method is given by Liu et al［4］.

Fig.1 Measurement system for luminescent oil film skin friction measurement

In order to accelerate convergence and improve the accuracy of solution，the pyramid iterative evolution method is proposed.There are two critical steps in the optimization algorithm.First，the original image of fluorescence oil-film is decomposed into a series of image pyramids for accelerating convergence.The image pyra-mids［11-13］are often used in a wide variety of vision applications.An image pyramid is a collection of images—all arising from a single original image—that are successively down sampled until some desired stopping point is reached.The sizes of down sampled images decrease exponentially with the pyramid layer.On the other hand，the down sampled images also reduce the space rate of the original image of fluorescence oil-film.The second critical step is the iterative evolution of the original image of fluorescence oil-film.This step can improve the accuracy of solution.As we know，the intensity of fluorescence oil-film will vary in response to these wall stresses，thus we can use the solution of the measurement model to simulate the evolution process，and in turn to evaluate the accuracy of solution.If the desired accuracy of solution is not reached，the solution process can be done repeatedly based on the recent image of similar evolution.The following scheme is its implement strategy as shown in Fig.2 .Without a priori calibration，this method is able to give a relative or normalized skin friction field.Fig.3 shows that the laminar boundary layer on a flat plate is tripped by a wire.The global skin friction field obtained by present technique indicates the details of the transition quantitatively.The original image of fluorescence oil-film is decomposed into three layers image pyramids and the global relative skin friction field of measured region by averaging the 70 snapshots.Particularly，the skin friction downstream the tripping wire has increased dramatically comparing with upstream flow which is laminar.The case verifies the measurement method and the solution strategy.

Fig.2 Implement strategy of the pyramid iterative evolution method

Fig.3 Result of trip wire(a:Original oil film b:One minute evolution c:Skin friction distribution)

2 Experimental details

Experiments were conducted in aopen-loop wind tunnel，with a test section of 0.3m(width)× 0.5m(height)×4m(length).The flow speed in the test section is 28m/s.Two flow control experiments are carried out in the wind tunnel，which include a passive control of zigzag trip and an active control of flow over a backward-facing step.The basic setup is shown in figures 4.There is the physical diagram of two flow control experiments at the fig.4(a).At the fig.4(b)a detail of the zigzag trip experiment is given.In this case a 300mm(width)×2mm(height)×10mm(length)transition trip can be placed on a 0.3m(width)×0.01m(height)× 1m(length)Plexiglas plate at 50mm from leading edge.There are three types of the angle of zigzag top，including 30°，60°and 90°.At the fig.4(c)a schematic of BFSexperiment is given.The step height(H)is 30mm.Zero mass jet through a slot at the corner is affected by a piston system，allowing for modulation of actuation frequency.It is used to excite faster shear layer growth to enhance mixing and reduce detaches.In the experiment，three actuation frequency(namely:0Hz，35Hz and 50Hz)are done in order to comparing the control effect of different actuation frequency.

3 Results and discussion

The figure 5 presents the global relative skin friction field of measured region by averaging the 70 snapshots without and with zigzag trip.For comparison，the natural transition(without control)is also demonstrated at the left side of the figure.Comparing to the natural transition，the skin friction patterns for controlled cases are more complicated and greater in magnitude.The pattern reveals streak-like structures behind the trip，extending downstream.The images appear to be three dimensional.The streak-like structures come from a pair of vortices which builds up along each tooth of the tripand will separate at the end of the tooth.The vortices cause more mixing downstream.The result is in qualitative agreement with the PIV measurements in［14］and Tomographic-PIV measurements in［15］， which tested only the 60°angle of zigzag top.Comparing the different case of zigzag top angle，the case of 30°has greater magnitude than the case of 90°，and has less magnitude than the case of 60°.

Fig.4 Setup of flow control experiments

Fig.5 Magnitude figure of the global ESF

It is of great benefit to mixing and increase energy in viscous sublayer，which explain why the case of 30°has greater magnitude than the case of 90°.There must is an optimum angle nearby 60°in order to achieve artificial boundary layer transition.

Figure 6 depicts the experimental results on the BFS，with and without control.It shows skin friction distribution along stream-wise.Figure 6(a～c)show that the reattachment will move significantly upstream when the actuator is acting.The red line in Fig 6 are separation line which are deliberately added.The different frequency results in different effectiveness.The results indicate that the flow separation can be effectively restrained by manipulation frequency of zero mass jet.Close inspection of figure 6(d)reveals a regularity that the greater the skin friction is，the more effective the control.The main reason is that zero mass jet enhancesthe Reynolds stress in the free stress layer and the flow gets greater energy to overcome flow separation.According the Fukagata’s［6］study，the Reynolds stress is direct relevance to skin friction，thus the measurement of skin friction can be using to evaluate the control effect of manipulation Reynolds Stress.

Fig.6 Result of the BFS control

4 Conclusions

(1)The global measuring technique based on fluorescence oil-film is verified as anovel method that can quantify the skin friction fields on a surface.

(2)The proposed pyramid iterative evolution method can accelerate convergence and improve the accuracy.

(3)Two experiments of flow control have demonstrated that the fluorescence oil-film method is promising in the research of flow control.

［1］Winter K G.An outline of the techniques available for measurement of skin friction in turbulent boundary layer［J］.Progress in Aerospace Sciences，1979，18:1-57.DOI:10.2514/6.1986-1099

［2］Settles G S.Recent skin-friction techniques for compressible flows［C］//AIAA/ASME 4thFluid Mechanics，Plasma Dynamics and Lasers Conference，Atlanta GA，1986:1086-1099.

［3］Plesniak M，Peterson S.Wall shear stress measurements for conventional applications and biomedical flows［C］//24thAIAA Aerodynamic Measurement Technology and Ground Testing Conference，Portland Oregon，2004:33-36.DOI:10.2514/6.2004-2301

［4］Liu T，Sullivan J P.Luminescent oil-film skin friction meter［J］.AIAA Journal，1998，36(8):1460-1465.DOI:10.2514/2.538

［5］Liu T，Woodiga S，Montefort J，et al.Global skin friction diagnostics in separated flows using luminescent oil［J］.J.Flow Vis.Image Process，2009，16(1):19-39.

［6］Fukagata K，Iwamoto K，Kasagi N.Contribution of reynolds stress distribution to the skin friction in wall-bounded flows［J］.Phys.Fluids，2002，14(11):73-76.

［7］Squire L C.The motion of a thin oil sheet under the boundary layer on a body［J］.J.Fluid Mech.，1961，11(2):161-179.

［8］Tanner L H，Blows L G.A study of the motion of oil films on surfaces in air flow，with application to the measurement of skin friction［J］.J.Physics E:Scientific Instruments，1976，9(3):194-202.

［9］Weickert J，Schnorr C.Variational optic flow computation with a spatio-temporal smoothness constraint［J］.Journal of Mathematical Imaging and Vision，2001，14(3):245-255.

［10］Nagel H H.Extending the’oriented smoothness constraint’into the temporal domain and the estimation of derivatives of optical flow［C］//O.Faugeras，editor，Computer Vision-ECCV’90，volume 427 of Lecture Notes in Computer Science，Berlin，1990:139-148.

［11］Adelson E H，Anderson CH，Bergen JR，et al.Pyramid methods in image processing［J］.RCA Engineer，1984，29:33-41.

［12］Lucas B，Kanade T.An iterative image registration technique with an application to stereo vision［C］//In Proc.Seventh International Joint Conference on Artificial Intelligence，Vancouver，Canada，1981:674-679.

［13］M'emin E，P'erez P.Hierarchical estimation and segmentation of dense motion fields［J］.International Journal of Computer Vision，2002，46(2):129-155

［14］Slangen R A C M.Experimental investigation of artificial boundary layer transition［D］.［Master of Science Thesis］.Delft University of Technology，2009.

［15］Elsinga G E，Westerweel J.Tomographic-PIV measurement of the flow around a zigzag boundary layer trip［J］.Exp.Fluids，2012，52:865-876.