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

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TsAGI Science Journal, 46 (6): 1–9 (2015)
NEW METHOD OF OPTICAL
INVESTIGATIONS OF BOUNDARY LAYER
STATE 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 of
boundary layer state influence on light scattering effect of a parallel beam passing through it. Some
examples of the new method practical application are given.
KEY WORDS: non-contact measurements, boundary layer, transition trips, aero-
dynamic experiment
1. INTRODUCTION
The phenomenon of optical refraction (deflection) of light rays in media with a variable
refraction index is well known. In particular, air is such a medium, which flows over
different bodies with boundary layer generation. A rigorous theory of refraction phe-
nomenon in media with a variable-in-space refraction index was developed by Newton
at the end of the 17th century. It is well known that only the refraction index gradient
component that is perpendicular to the direction of propagation of light rays affects the
refraction of light rays. The component along the direction of propagation of light rays
does 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 wind
tunnel 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 index
gradient is proportional to the density ρ gradient; therefore, the light beam propagation
is determined by the following equation:
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d2
Y/dX2
= K∂ρ/∂Y. (2)
The phenomenon of light refraction opens a possibility in principle for performing both
quantitative 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-speed
wind tunnel [4]. At TsAGI, the optical shadow methods were applied starting from the
forties of the 20th century to study the critical region of near-sonic flow over airfoils
and 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 aircraft
elements (for example, see [5, 6] and their references). The possibility of obtaining the
data about the state of the boundary layer on the bodies in flow is an important element
of experimental investigations, because viscosity (Reynolds number and boundary-layer
laminar–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, barn
door.
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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 the
pattern observed is not sufficiently contrast, because the effect of refraction of rays is
difficult to distinguish against a background of the main light flux that passes above the
boundary 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 refraction
zone 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 characteristic
thickness was taken to be equal to the boundary-layer thickness upon a corresponding
Reynolds number at a distance of approximately 0.5 chord from the leading edge of the
airfoil 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 near
the airfoil model surface. This method allows elimination of the effect of the main
light flux that propagates over the boundary-layer region on the pattern of refraction
of beams.
3. EXPERIMENTAL INVESTIGATIONS
Experimental investigations of the light scattering in the boundary layer were carried out
in the ejector-type wind tunnel T-112 based at TsAGI with test section lateral dimensions
of 0.6 × 0.6 m and a range of possible variation of Mach number M∞ from 0.6 to
1.25. The upper and lower walls of the wind-tunnel test section are perforated; the side
walls, which are not perforated, have transparent 265 mm diameter optical windows. The
investigations were performed with the models of different-type airfoils with thickness
ratios 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 within
a range of Re = (2.4–3.0) × 106. The tested airfoils were fixed between the optical
windows of the wind-tunnel test section on a special suspension connected with the
wind-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 door
made by the shape of the upper surface of the airfoil under study. The model sample was
used 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 layer
at M∞ = 0.6 and angle of attack α = 0 on the airfoil model upper surface, which were
obtained by conventional direct shadow method (a) and new method (b), is given in
Fig. 3.
It is well seen in the given photographs that the application of the conventional direct
shadow method does not allow obtaining a clear picture of light scattering owing to the
aforementioned reason [Fig. 3(a)].
The new method allows obtaining a contrast pattern of light scattering, which makes
it possible to consider the boundary-layer state. In Fig. 3(b), the refraction scattering of a
light beam is observed on a considerable part of the airfoil upper surface, where the flow
is laminar (1). In the rear part of the airfoil model upper surface, where the turbulent
flow without separation takes place (2), the light beam scattering is hardly observed. A
zone of a gradual attenuation of light scattering (3) is located between the regions of
laminar and turbulent flow. This zone corresponds to the laminar–turbulent transition
region (intermittency region).
The laminar state of the boundary layer in the regions where the refraction light
scattering was observed was confirmed by investigations using kaolinic coating. For this
purpose, a layer of kaoline with a thickness of approximately 0.1 mm was applied on the
airfoil 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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New Method of Optical Investigations of Boundary Layer State 5
method of kaolinic coating and by the proposed new optical method at different angles
of attack and free-stream velocities.
As a result of the experiments it was found that the results obtained by the two
studied methods are in a satisfactory correlation. The location of the laminar–turbulent
boundary-layer transition ¯xt, determined by the method of kaoline coating, depending
on M∞ and angle of attack, is within a region from the beginning to the middle of the
transition 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 the
boundary layer is clearly observed in the case of the boundary-layer laminar state and
is hardly observed in the case of the turbulent state. Because the refraction of light rays
is proportional to the density transverse gradient (2), the conclusion can be drawn based
on the optical pattern of light scattering in the boundary layer that the values of density
transverse gradients in the laminar boundary layer are considerably higher than those in
the 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 temperature
across the boundary layer is equalized; the density gradients become insignificant and
do 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 transition
region of the boundary layer determined by the new method; x is the boundary-layer
transition determined by the method of kaolinic coating.
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laminar (laminated) flow character, such a mixing is almost absent. It follows from the
experiments that the absence of mixing leads to the density gradients that enable the
light 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 width
to a narrow band near the model surface enables the light scattering pattern to be clearly
observed. 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 the
direction of density gradient in this place. This direction can be determined by splitting
the light band near the model surface into separate light beams, in particular, by means
of using a perforated barn door.
Examples of photographs obtained by the proposed modified method without the
incoming 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 the
light beam scattering degree and its direction at a given point.
4. INVESTIGATIONS OF THE EFFICIENCY OF BOUNDARY-LAYER
TRANSITION TRIPS
The proposed optical method of investigation of the boundary-layer state based on the
light scattering registering showed its high sensitivity to the transverse gradient of flow
density near the surface of the streamlined body. As was mentioned previously, in the
case of developed turbulent flow, the scattering of the parallel light beam was hardly
observed. This effect can be used for estimation of the efficiency of the transition trips
in 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 the
flow, 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 the
flow; 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, when
choosing 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 of
transition trips.
The studies of the efficiency of transition trips of the two known types (carborundum
trip and wire) by means of visualization of the light scattering pattern in the boundary
layer were performed on an example of the flow over an airfoil with an extended region
of 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 to
Ret ≈ 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, natural
transition; 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 trip
with an average roughness of approximately 0.1 mm located on the model surface within
0.1–0.15 of the airfoil chord, the boundary-layer complete turbulization takes place at a
distance of 0.55 chord [Fig. 6(b)].
Using the simplest type of transition trip in the form of a thin 0.1 mm diameter wire
clued at a distance of 0.1 airfoil chord, a shorter transition region is observed behind the
transition trip, which ends at approximately 0.4 chord [Fig. 6(c)].
The given examples of the efficiency of two particular types of transition trips used
in 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 the
different-type artificial turbulence stimulators of the boundary layer, which are frequently
used in wind-tunnel experiments. The experimental investigations of the efficiency of the
two standard types of transition trips, performed on the airfoil models, showed that a suf-
ficiently extended transition region (intermittency zone) is located behind them, whose
length is about 0.3–0.4 airfoil chord. The completely turbulent flow comes behind the
transition 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-sonic
velocities, Trudy TsAGI, 2010:22–35, 1979.
7. Brutyan, M. A. and Savitskii, V. I., Viscosity effect on a near-sonic flow without separation
over 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 [in
Russian].
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