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AUTHOR PROOF

TsAGI Science Journal, 46 (6): 1–9 (2015)

NEW METHOD OF OPTICALINVESTIGATIONS OF BOUNDARY LAYERSTATE IN AERODYNAMIC EXPERIMENT

M. A. Brutyan,∗ A. V. Petrov, & A. V. Potapchik

Central Aerohydrodynamic Institute (TsAGI), 1 Zhukovsky St.,Zhukovsky, Moscow region, 140180 Russia

∗Address all correspondence to: M. A. Brutyan, E-mail: uzts@tsagi.ru

The optical method of transonic flow investigation around airfoils is offered based on the effect ofboundary layer state influence on light scattering effect of a parallel beam passing through it. Someexamples of the new method practical application are given.

KEY WORDS: non-contact measurements, boundary layer, transition trips, aero-dynamic experiment

1. INTRODUCTIONThe phenomenon of optical refraction (deflection) of light rays in media with a variablerefraction index is well known. In particular, air is such a medium, which flows overdifferent bodies with boundary layer generation. A rigorous theory of refraction phe-nomenon in media with a variable-in-space refraction index was developed by Newtonat the end of the 17th century. It is well known that only the refraction index gradientcomponent that is perpendicular to the direction of propagation of light rays affects therefraction of light rays. The component along the direction of propagation of light raysdoes not affect the light refraction, which takes place, in particular, in the case of orthog-onal passing of the rays through the optical windows and boundary layer on the windtunnel walls.

Air refraction index n is related to its density ρ by the well-known relationship [1]

n− 1 = K ρ, (1)

where K is the Gladstone–Dale constant, which is equal to 0.2264 cm3/g for air.The light beam deflection in the perpendicular direction Y from the direction of its

propagation is characterized by derivative d2Y/dX2, which is proportional to the re-fraction index gradient: ∂2Y/∂X2 ∼ ∂n/∂Y . According to Eq. (1), the refraction indexgradient is proportional to the density ρ gradient; therefore, the light beam propagationis determined by the following equation:

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d2Y/dX2 = K∂ρ/∂Y. (2)

The phenomenon of light refraction opens a possibility in principle for performing bothquantitative and qualitative optical investigations of gas flows using shadow instruments[2, 3]. The first attempt at application of optical methods using the light refraction phe-nomenon to investigate the boundary layer state was made in 1950 in the NPL high-speedwind tunnel [4]. At TsAGI, the optical shadow methods were applied starting from theforties of the 20th century to study the critical region of near-sonic flow over airfoilsand wings. Later, the optical methods were widely applied for different purposes, in par-ticular, to analyze comprehensively the physics of flow over airfoils and other aircraftelements (for example, see [5, 6] and their references). The possibility of obtaining thedata about the state of the boundary layer on the bodies in flow is an important elementof experimental investigations, because viscosity (Reynolds number and boundary-layerlaminar–turbulent transition) significantly affects the parameters of airfoils in the near-sonic flow [7].

2. METHOD DESCRIPTION

The proposed method of optical investigations is based on the phenomenon of light re-fraction in the boundary layer. Figure 1(a) shows schematically the direction of light rays

FIG. 1: Scheme of refraction of light rays: a, conventional method; b, new method: 1,airfoil surface; 2, optical windows; 3, plane of focusing of shadow instrument, 4, barndoor.

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New Method of Optical Investigations of Boundary Layer State 3

near the surface of an airfoil model located between the wind-tunnel optical windows.The shadow pattern is fixed in the plane of focusing using the schlieren system.

Affected by the transverse density gradients, the parallel light beams are “ejected”from the boundary-layer region and scatter. According to [4], the main problem of quali-tative registering of light refraction phenomenon in the boundary-layer region is that thepattern observed is not sufficiently contrast, because the effect of refraction of rays isdifficult to distinguish against a background of the main light flux that passes above theboundary layer region [see Fig. 1(a)].

For a more clear visualization of the pattern of light refraction in the boundary layer,the authors of the present study propose a simple and sufficiently efficient method—to limit the light flux width near the model surface to a dimension of the refractionzone of light beams. The width of this zone is comparable by its value to the boundary-layer characteristic thickness on the model surface. In the experiments, the characteristicthickness was taken to be equal to the boundary-layer thickness upon a correspondingReynolds number at a distance of approximately 0.5 chord from the leading edge of theairfoil under study.

The proposed new scheme of observation of the light refraction pattern in the bound-ary layer is shown in Fig. 1(b) and differs from the conventional scheme [Fig. 1(a)]by the installation of an additional barn door 4 that limits the light beam height nearthe airfoil model surface. This method allows elimination of the effect of the mainlight flux that propagates over the boundary-layer region on the pattern of refractionof beams.

3. EXPERIMENTAL INVESTIGATIONS

Experimental investigations of the light scattering in the boundary layer were carried outin the ejector-type wind tunnel T-112 based at TsAGI with test section lateral dimensionsof 0.6 × 0.6 m and a range of possible variation of Mach number M∞ from 0.6 to1.25. The upper and lower walls of the wind-tunnel test section are perforated; the sidewalls, which are not perforated, have transparent 265 mm diameter optical windows. Theinvestigations were performed with the models of different-type airfoils with thicknessratios of 9, 12, and 15% within the range of angle of attack α from zero to 6° upon M∞= 0.6–0.8. At a chord of the models of 200 mm, the Reynolds number was varied withina range of Re = (2.4–3.0) × 106. The tested airfoils were fixed between the opticalwindows of the wind-tunnel test section on a special suspension connected with thewind-tunnel balance and the mechanism of continuous variation of the angle of attack.

A photograph of a restricted-in-width light beam near the airfoil model upper sur-face, which was taken without the incoming flow and the boundary layer on the model,is shown in Fig. 2. The light beam width restriction was performed using a barn doormade by the shape of the upper surface of the airfoil under study. The model sample wasused for this purpose.

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FIG. 2: Light beam restricted in height over the airfoil upper surface without the flow.

Comparison of the photographs of the light scattering pattern in the boundary layerat M∞ = 0.6 and angle of attack α = 0 on the airfoil model upper surface, which wereobtained by conventional direct shadow method (a) and new method (b), is given inFig. 3.

It is well seen in the given photographs that the application of the conventional directshadow method does not allow obtaining a clear picture of light scattering owing to theaforementioned reason [Fig. 3(a)].

The new method allows obtaining a contrast pattern of light scattering, which makesit possible to consider the boundary-layer state. In Fig. 3(b), the refraction scattering of alight beam is observed on a considerable part of the airfoil upper surface, where the flowis laminar (1). In the rear part of the airfoil model upper surface, where the turbulentflow without separation takes place (2), the light beam scattering is hardly observed. Azone of a gradual attenuation of light scattering (3) is located between the regions oflaminar and turbulent flow. This zone corresponds to the laminar–turbulent transitionregion (intermittency region).

The laminar state of the boundary layer in the regions where the refraction lightscattering was observed was confirmed by investigations using kaolinic coating. For thispurpose, a layer of kaoline with a thickness of approximately 0.1 mm was applied on theairfoil upper surface. The boundary-layer state was determined simultaneously by the

FIG. 3: Light scattering in the boundary layer: a, conventional approach; b, new method;1, laminar boundary layer; 2, turbulent boundary layer; 3, intermittency region.

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method of kaolinic coating and by the proposed new optical method at different anglesof attack and free-stream velocities.

As a result of the experiments it was found that the results obtained by the twostudied methods are in a satisfactory correlation. The location of the laminar–turbulentboundary-layer transition x̄t, determined by the method of kaoline coating, dependingon M∞ and angle of attack, is within a region from the beginning to the middle of thetransition region observed in the pattern of light scattering (Fig. 4).

Numerous investigations of light refraction, performed by the new method on diffe-rent-type airfoil models, show that the effect of light beam refraction scattering in theboundary layer is clearly observed in the case of the boundary-layer laminar state andis hardly observed in the case of the turbulent state. Because the refraction of light raysis proportional to the density transverse gradient (2), the conclusion can be drawn basedon the optical pattern of light scattering in the boundary layer that the values of densitytransverse gradients in the laminar boundary layer are considerably higher than those inthe turbulent boundary layer.

It is known that the pressure across the boundary layer is almost constant; therefore,the air density gradient in the boundary layer is determined by the temperature gradient.In the case of the turbulent flow, owing to an intense mixing of the layers, the temperatureacross the boundary layer is equalized; the density gradients become insignificant anddo not generate observable refraction scattering of the light beam. In the case of the

FIG. 4: Location of the laminar–turbulent boundary-layer transition: is the transitionregion of the boundary layer determined by the new method; x is the boundary-layertransition determined by the method of kaolinic coating.

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laminar (laminated) flow character, such a mixing is almost absent. It follows from theexperiments that the absence of mixing leads to the density gradients that enable thelight scattering pattern to be observed clearly using the proposed method.

It was found in the process of the studies that the limitation of the light beam widthto a narrow band near the model surface enables the light scattering pattern to be clearlyobserved. However, the optical pattern observed in such a manner does not allow de-termination of the local direction of the scattered light beam that corresponds to thedirection of density gradient in this place. This direction can be determined by splittingthe light band near the model surface into separate light beams, in particular, by meansof using a perforated barn door.

Examples of photographs obtained by the proposed modified method without theincoming flow (a) and in the flow at M∞ = 0.6 and α = 0 (b) are shown in Fig. 5.

The light beam splitting into separate small rays makes it possible to reveal both thelight beam scattering degree and its direction at a given point.

4. INVESTIGATIONS OF THE EFFICIENCY OF BOUNDARY-LAYERTRANSITION TRIPS

The proposed optical method of investigation of the boundary-layer state based on thelight scattering registering showed its high sensitivity to the transverse gradient of flowdensity near the surface of the streamlined body. As was mentioned previously, in thecase of developed turbulent flow, the scattering of the parallel light beam was hardlyobserved. This effect can be used for estimation of the efficiency of the transition tripsin the wind-tunnel experiment applied for flow turbulization.

The choice of the type and location of transition trips depends on the Re number,boundary-layer thickness, pressure distribution on the model, initial turbulence of theflow, and other factors. For this reason, the choice of the transition trips in each particu-lar case is a separate problem [8]. From the practical point of view, it is desirable for the

FIG. 5: Optical patterns of light scattering over the airfoil upper surface: , without theflow; b, with the flow.

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New Method of Optical Investigations of Boundary Layer State 7

flow behind the transition trip to become turbulent as early as possible. In other words,the length of the intermittency region should be as minimal as possible. Therefore, whenchoosing a particular method of turbulization, the size of the transition region deter-mined by the new optical method can become a convenient criterion of the efficiency oftransition trips.

The studies of the efficiency of transition trips of the two known types (carborundumtrip and wire) by means of visualization of the light scattering pattern in the boundarylayer were performed on an example of the flow over an airfoil with an extended regionof laminar flow at M∞ = 0.6 and angle of attack α = 0.

The pattern of light scattering in the boundary layer on the airfoil model upper sur-face without transition trips shows that the complete natural turbulization of the bound-ary layer takes place at a distance of ∼0.8 of the airfoil chord, which corresponds toRet ≈ 1.9 × 106, calculated by the laminar region length and incoming flow parameters[Fig. 6(a)].

FIG. 6:Optical investigations of the laminar–turbulent transition on the airfoil: a, naturaltransition; b, forced transition (carborundum trip); c, forced transition (thin wire).

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Using the most widespread type of transition trip in the form of a carborundum tripwith an average roughness of approximately 0.1 mm located on the model surface within0.1–0.15 of the airfoil chord, the boundary-layer complete turbulization takes place at adistance of 0.55 chord [Fig. 6(b)].

Using the simplest type of transition trip in the form of a thin 0.1 mm diameter wireclued at a distance of 0.1 airfoil chord, a shorter transition region is observed behind thetransition trip, which ends at approximately 0.4 chord [Fig. 6(c)].

The given examples of the efficiency of two particular types of transition trips usedin applied aerodynamics showed that a sufficiently extended transition region (intermit-tency zone) is located behind them.

5. CONCLUSIONS

The developed new method of optical investigations based on the effect of light scatter-ing in the boundary layer allows determination of the sizes of zones of laminar, turbulent,and intermittent boundary layer in a non-contact manner.

By applying the proposed method, it is possible to compare the efficiencies of thedifferent-type artificial turbulence stimulators of the boundary layer, which are frequentlyused in wind-tunnel experiments. The experimental investigations of the efficiency of thetwo standard types of transition trips, performed on the airfoil models, showed that a suf-ficiently extended transition region (intermittency zone) is located behind them, whoselength is about 0.3–0.4 airfoil chord. The completely turbulent flow comes behind thetransition trip at a certain distance corresponding to Re ≈ (0.8–0.9) × 106.

REFERENCES

1. Holder, D. W. and North, R. J., Schlieren methods, Notes on Applied Science, no. 31, London,1963.

2. Skotnikov, M. M., Shadow Quantitative Methods in Gas Dynamics, Nauka, Moscow, 1976[in Russian].

3. Vasiliev, L. A., Shadow Methods, Nauka, Moscow, 1968 [in Russian].4. Pearcey, . ., Indication of boundary-layer transition on aerofoils in the N.P.L. 20 in. by 8 in.

highspeed tunnel, A.R.C.C.P., 10, 1950.5. Bokser, V. D., Dmitrieva, V. B., Nevskii, L. B., and Serebriiskii, Ya. M., Determination

of airfoil wave drag by interferometry method in near-sonic flow, Uchenye Zapiski TsAGI,6(1):103–107, 1975.

6. Potapchik, A. V., Experimental investigation of the flow field near an airfoil at near-sonicvelocities, Trudy TsAGI, 2010:22–35, 1979.

7. Brutyan, M. A. and Savitskii, V. I., Viscosity effect on a near-sonic flow without separationover an airfoil, Uchenye Zapiski TsAGI, 8(5):24–29, 1977.

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New Method of Optical Investigations of Boundary Layer State 9

8. Repik, E. U. and Sosedko, Yu. P., Turbulent Boundary Layer, Fizmatlit, Moscow, 2007 [inRussian].

Murad Abramovich Brutyan, Doctor in Physics and Math-ematics, Chief Researcher, TsAGI

Albert Vasilyevich Petrov, Doctor in Technical Sciences,Head of Division, TsAGI

Aleksandr Vladimirovich Potapchik, Leading Engineer,TsAGI

Volume 46, Number 6, 2015