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ABSTRACT Increase in ambient atmospheric temperature significantly
reduces the thermal output of gas turbines. Inlet fogging is one
of the power augmentation technique which is used to increase
the power output of gas turbines. In this study, experimental
work on the characteristics of a liquid film on to the surface of
cascade blade is reported. Shadowgraph images of different
regimes of the thin liquid film formed on the cascade blade were
taken at different air flow conditions. It was observed that air
flow velocity on the blade’s surface significantly affects the
instability and thickness of the liquid’s surface, while blade’s
angle of attack was found to enhance the instability pattern due
to the flow separation on the blade’s surface. From the
experimental results, it is concluded that the height to width
ratio of liquid film thickness remains constant at a particular
angle of attack and air flow velocity, and remained unchanged
with the change in the mass flow rate of the liquid.
NOMENCLATURE
Latin Symbols
𝐶 chord Length of the blade, m
ℎ height, m
𝑈 velocity, m/sec
�̇� volume flow rate, m3/sec
𝑡 thickness of the T.E. of the blade, m
𝑤 width, m
𝑔 acceleration due to gravity, m/sec2
𝑘 dimensional wave number, m
�̇� mass flow rate, kg/sec
�⃗� velocity vector, m/sec
𝑝 pressure, N/m2
𝑐𝑓 coeeficient of friction
𝑥, y x- and y- axis directions
Greek Symbols
𝜌 density, kg/m3
𝜇 dynamic viscosity, N.sec/m2
𝛾/ 𝜎 coefficient of surface tension, N/m
𝜆 wavelength, m
𝛼 dimensionless wave number
∑ complex tangential perturbation term
Π complex normal perturbation term
Subscripts
𝑎 air
𝑙/𝑓𝑖𝑙𝑚 liquid film
Dimensionless Numbers 𝑅𝑒 Reynolds Number of air (𝜌𝑎𝑈𝑎𝐶 𝜇𝑎⁄ )
𝑅 Reynolds Number of liquid (𝜌𝑙𝑈𝑙ℎ𝑙 𝜇𝑙⁄ )
𝑇 Inverse Weber Number (𝛾/𝜌𝑙ℎ𝑙𝑈𝑙2)
𝐺 Inverse Froude Number (𝑔ℎ𝑙/𝑈𝑙2)
𝑀𝐹𝑅 Dimensionless mass flow rate (�̇�𝑙/𝜇𝑙𝐶)
𝑀 Momentum ratio (𝜌𝑎 𝑈𝑎2 𝜌𝑙 𝑈𝑙
2⁄ )
INTRODUCTION
Gas turbines (GT) are the key energy production units to
stabilize the power generation of a grid system, because of being
simple in design and their ability to adapt to the load changes
rapidly. GT are often operated at high ambient temperature
environment, resulting in a decrease in their power output and
efficiency. According to Bhargava et al. [1], at an ambient
temperature of 35oC, the output of GT can drop to around 15-
20%, which is a significant loss. To overcome such losses
numerous augmentation techniques has been proposed, however,
the simplest in design and installation, and the cheapest one is
the fogging technique. In fact, fogging technique has been
applied from the early days of gas turbine technology. One of
Experimental Investigation on Characteristics of Liquid Film at
Different Angle of Attack
Baber Javed1, Toshinori Watanabe2, Takehiro Himeno2 and Seiji Uzawa2
1 School of Engineering, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JAPAN 2 Department of Aeronautics and Astronautics, The University of Tokyo
Fig. 1 Schematics of water droplets around cascade blades
International Journal of Gas Turbine, Propulsion and Power Systems October 2017, Volume 9, Number 3
Copyright © 2017 Gas Turbine Society of Japan
Manuscript Received on February 27, 2017 Review Completed on September 29, 2017
22
the main features of fogging is spraying more fog that will
evaporate under the given ambient temperature and humidity
conditions allowing the non-evaporated liquid water droplets to
enter into the compressor inlet. Fogging in modern gas turbines
is achieved by the direct ingestion of demineralized water
droplets into the inlet plenum of the gas turbines. Intercooling
is achieved due to the evaporation of droplets resulting in
lowering the temperature of the inlet air. This ultimately leads
to the reduction of the compressor load, providing a significant
power boost as well as an improved heat rate of the entire GT
system. Utamura et al. [2] concluded that an overspray of 1% of
water to that of air could results in the power output and thermal
efficiency to increase by 10% and 3% respectively for a 115
MW GT (Hitachi Frame 9E). Besides the thermodynamics
effects (see [3 and 4]), aerodynamic effects of the water droplets
presence in the GT systems must also be consider. So far, our
understanding of how water ingestion affects the aerodynamics
performance of the GT is very limited. In fact, according to
authors knowledge, their exist very few publication performing
the experimental studies in this field. Therefore, the objective of
this work study is to study the fundamental kinematics of liquid
presence around the cascade blade.
Figure 1 shows the schematics behaviour of inlet fogging
around a cascade blade. Fine water droplets impinge near the
leading edge (L.E.) of the cascade blade. Upon striking the blade,
the droplets undergo partial deposition and splashing
phenomenon, i.e., a large quantity of the droplets’ water is
deformed to form a thin liquid film on to the blade’s surface
whereas, few high-speed droplets further disintegrate into
smaller droplets and rebound. Due to aerodynamic forces, the
thin liquid film formed continues to move towards the trailing
edge (T.E.) of the cascade blade. Due to the liquid’s surface
tension property, the thin liquid starts to accumulate to form
globules at the T.E. of the blade. The aerodynamic forces
continue to overcome the liquid’s surface tension forces and
when it exceeds, a large number of droplets are stripped from
the T.E. of the blade. The stripped droplets are always bigger in
size than the ingested water droplets from the nozzles. The
stripped droplets further undergo deformation and breakup,
which are more likely to collide with the compressor blades
rather than passing through them.
EXPERIMENTAL SETUP
Experimental Facility and Measurement Setup: The experiments were carried out for a specifically designed
wind tunnel to cope with the humid conditions. The schematics
of the experimental layout is shown in Fig. 2. A centrifugal
blower is used to supply the air to the test facility. Air passes
through the settling chamber, which removes the turbulence as
well as straighten the incoming air before reaching to the test
section. At the end of the test section, a diffuser is attached to
allow the air to expand smoothly as well as to avoid the flow
separation at the end of the test section. A water droplet stopper
and collector setup is installed at the end of the test facility to
stop the droplets from being splashed out and to be drained off.
The cross section of the test section used is 80 x 100 mm2 and
is manufactured from the acrylic material to have an ease in
visualization.
Shadowgraph images were taken by placing a diffuser plate
between a high-speed camera (Photron FASTCAM APX-RS)
and the back lights (250W each), as shown in Fig. 2. Two sets
of shadowgraph images were taken. For the overall flow
visualization of the liquid film, the window size was chosen to
be 1024 x 1024 sq. pixels, having a frame rate and the shutter
speed of 1000 frames per seconds (fps) and 1/15,000 seconds
respectively. For the detailed visualization at the mid-chord of
the blade, the frame rate of the captured images was set at
10,000 fps having a shutter speed of 1/15,000 sec. The
resolution of shadowgraph images was 512 x 512 pixels, which
corresponds to the field of view of 30 x 30 mm2 approximately.
Water Supply setup: A water cylinder was used to supply the water to the test
blade, as shown in Fig. 3. This system consists of supplying
Fig. 2 Schematics of experimental layout
Fig. 3 Schematics of water supply mechanism
Fig. 4 Schematics of elliptical profile blade
JGPP Vol. 9, No. 3
23
water directly to the test blade via a 6mm diameter pipe. A flow
valve is equipped at the bottom of the water cylinder to control
the flow of water to the test blade. Similarly, the flow rate of
water is controlled by adjusting the height of water inside the
water tank. The test blade is mounted in a circular blade holder,
which was then placed inside the wind tunnel. Due to the
circular blade holder, the angle of attack (AOA) of the blade can
be adjusted with ease.
Test blade: The present study dealt with a geometrically simple aerofoil,
named elliptical profile blade, due to the elliptical curvature of
the upper and lower surface of the blade, as shown
schematically in Fig. 4. Such simple blade configuration allows
to understand the kinematics of the characteristics of liquid film
formation on the blade surface with ease and simplification. A
1mm diameter hole is made at the L.E., located at the mid-span
of the blade. The blade is connected directly to the water tank
via a connecting pipe, resulting in the ejection of water from a
ϕ1 mm hole. Additionally, by this method the droplets are
formed only from the T.E. of the blade, making it easy to
understand the role of T.E. thickness in the formation and the
break of droplets after the T.E. region, as compared to the water
ingestion from the nozzles. Table 1 gives a detail specifications
of the blade profile used in this study, having a chord length of
50 mm and a span length of 80 mm.
Flow conditions: Table 2 outlines the detail of the experimental flow
conditions. The air flow velocity is categorized as high- (Case
A), medium- (Case B and Case C) and low- (Case D) air
velocity case. Though, the flow velocity in the experimental
present study is very low compared to the real turbo-machines,
however, the order of Reynolds number based on chord length
of the blade corresponds to that of the real machines. All the
experiments were performed under the room temperature
conditions, and a room temperature water was used for water
ingestion. The mass flow rate of water is expressed in
dimensionless form by using the following relationship
𝑀𝐹𝑅 = �̇�𝑤
𝜇𝑤𝐶 (1)
Similarly, the momentum ratio was calculated by using the
Eq. (2)
𝑀 = 𝜌𝑎𝑈𝑎
2
𝜌𝑙𝑈𝑙2 (2)
Experiments were performed by varying the AOA from 0- to 10-
degree.
RESULTS AND DISCUSSIONS Figure 5 shows the schematics of the effect of AOA on the
air flow around the blade, based on the smoke visualization (not
shown). At low AOA, the flow remains attached to the blade.
However, as the AOA is increased gradually the separation point
moves towards the L.E., resulting in the airflow to detach from
the upper surface earlier. Such that when the AOA is increased
beyond a certain limit, stalls phenomenon occurred causing in a
largely separated flow region to expand from the upper surface.
Flow Visualization of Liquid film: When the water was ejected from the L.E. hole, it formed a
thin water film on the blade’s surface. It was observed that the
characteristics of film structure were mainly governed by the
stresses exerted by the aerodynamic forces upon the film
structure, which is dependent on the air velocity and AOA, and
the surface tension of the liquid. The liquid film characteristics
change gradually with a change in the air velocity as well as the
AOA of the blade. From the experimental flow visualization,
an increase in air velocity always destabilized the liquid film
pattern, however, an increase in AOA further helps in the
destabilization of the water film pattern, as shown in Fig. 6 and
7 for Case A and D respectively.
In the case of 0 – degree AOA, whatever, the air velocity is,
the ejected water from the L.E. flows on both the suction side
(S.S.) and the pressure side (P.S.) of the blade. However, when
the AOA was increased, the water film was formed only on the
Table. 1 Specifications of elliptical profile blade
Parameter Value
Material Aluminium
Chord length (C) 50 mm
Span length (S) 80 mm
Thickness ratio of the
blade at mid-chord 15 %
T.E. thickness ratio 4.5 %
Water ingestion hole ϕ1 mm
Table. 2 Experimental flow conditions
Parameter Value
Case
Air
Velocity
(m/sec)
Reynolds
Number
(Re)
High Air Velocity Case A 40 1.35 x 105
Medium Air Velocity Case B 30 1.01 x 105
Case C 25 0.82 x 105
Low Air Velocity Case D 20 0.67 x 105
Angle of attack (AOA) 0-, 3-, 5-, 7-, 10- degrees
Ambient temperature 298.5 K (approx.)
Water temperature Room water temperature
Dimensionless mass
flow rate (MFR) 2 – 32
Air density 1.23 (kg/m3)
Water density 1000 (kg/m3)
Fig. 5 Schematics of effect of AOA on flow distribution
JGPP Vol. 9, No. 3
24
S.S. of the blade. For all the cases, water film was seen to get
deposit at the T.E. of the blade, as shown in Fig. 6 and 7. From
the flow visualization, the amount of accumulated water at the
T.E. was found to increase as the AOA was increased, due to the
flow separation as shown in Fig. 6 and 7 for the Case A and D
respectively.
Classification of liquid film: To study the liquid film behaviour, more than thousand high-
speed images were captured for each mass flow rate condition
at different air flow velocity. Based on the extensive flow
visualization the water film pattern formed on the blade’s
surface is categorized into the following two categories; namely
wavy- and smooth- water film pattern.
i. Wavy film pattern – due to dominant effect of
aerodynamic forces: For high air momentum (Case A, Fig.
6), the wave-like structure appears on the blade surface, which
were primarily due to the dominant effect of the aerodynamic
forces. The shear energy transfer from the gaseous phase (i.e.,
aerodynamic force) to the liquid phase results in the appearance
of the wavy like structure (called wavy film pattern) on to the
blade surface and is discuss in detail by Fig. 16. Figure 6-(ii)
shows a more close-view of wavy film pattern. It can be seen
that an increase in AOA results in the film width to become
more widen and vice versa. From the high-speed images, for
low AOA cases, the wavelet pattern formed was nearly
symmetrical (i.e., waves of equal wavelength), however, as the
AOA is increased, the wavelet pattern became slightly
unsymmetrical due to an additional influence of flow separation.
At low AOA conditions, the wavelet’s thickness remained
nearly constant, as shown in Fig. 6-(ii-a). Whereas, for high
AOA (Fig. 6-(ii-c)), many smaller wavelets appeared near the
mid chord region of the liquid film, making the film to become
relatively thinner in thickness, whereas, the edges become
thicker due to the equivalent surface tension effects as explained
by [5]. Overall, the liquid film formed in this case moves with
high velocity and is thinner in thickness.
ii. Smooth film pattern – due to dominant effect of surface
tension: A completely different wave pattern is observed with
a decrease in air momentum (Case D), named Smooth film (or
Mirror like smooth) pattern, as shown in Fig. 7. Figure 7 shows
a dominance of liquid’s surface tension, making the film
relatively smoother with almost no wavelet appearing on the
blade’s surface at low AOA, as shown in Fig. 7-(i-c). From the
detailed visualization of high speed images, at high AOA some
wavelets have appeared at the film structure, which is thought
primarily due to the flow separation caused at such large AOA,
as shown in Fig. 7-(ii-c). Even at these high AOA the wave
structure is much smoother compared to that of high air
momentum case, Fig. 6. Overall in this case, due to superior
(a) 0 – degree AOA, MFR ≈ 10
Fig. 6 Water film visualization at high air velocity (Air velocity 40 m/sec, 𝑀 ≈ 192)
(b) 5 – degree AOA, MFR ≈ 16.85
(c) 10 – degree AOA, MFR ≈ 21.35 ii. Close View i. Far View
𝝀
JGPP Vol. 9, No. 3
25
surface tension effects over surrounding air, the molecular bond
is much stronger among the liquid particles resulting in thicker
liquid films, which is discuss later by Fig. 16. The liquid films
formed in this case moves with relatively low velocity and have
smaller width and greater film thickness compare to that of the
Case A.
The intermediate air velocity cases (Case B and Case C)
showed the intermediate phenomenon of the liquid film pattern.
Figure 8 shows the schematics image of the experimental study
conducted representing the water film formation on the blade’s
surface and the corresponding droplets size distribution after the
T.E. of the blade for high AOA. At the T.E. large amount of
water get accumulated which results in the formation of droplets
after the T.E..
The physical mechanism of change in film height due to
aerodynamic forces is schematically illustrated in Fig. 9. At high
air momentum, the aerodynamic shear force on the liquid film
is significantly larger compared to that of the low air momentum
cases which cause the film height to decrease and vice versa, as
shown in Fig. 9 (b). It is due to this reason that at a high air
velocity (Case A - Fig. 6 (b)) liquid film became wider and
thinner. On the other hand, low air speed (Case D) case is
dominated by the surface tension of the liquid resulting in a
thicker liquid film, as shown schematically in Fig. 9 (a). For the
fluids having large surface tension possesses stronger cohesive
force among the fluids molecules and results in a thicker film
than those with the weak surface tension force. In other words,
due to the weak adhesive forces it will have a minimum width
and vice versa, and therefore, resulted in thick and relatively
smooth water film pattern, as shown in Fig. 7.
(a) 0 – degree AOA, MFR ≈ 10
Fig. 7 Water film visualization at low air velocity (Air velocity 20 m/sec, 𝑀 ≈ 48)
(b) 5 – degree AOA, MFR ≈ 11.2
(c) 10 – degree AOA, MFR ≈ 13. 5
ii. Close View i. Far View
Fig. 8 Schematics of water film formation and droplets size
distribution at high angle of attack (AOA)
JGPP Vol. 9, No. 3
26
Liquid Film Thickness:
For the measurement of liquid film thickness, a theoretical
model is proposed based on the linear velocity profile and
Couette flow, as shown in Fig. 10. Figure 10 shows a schematic
image of the liquid film profile at the mid-chord of the elliptical
blade profile. Referring to Fig. 10, the steady flow of the liquid
film is assumed which is governed by the Navier-Stokes
equation, represented by Eq. (3) and (4)
∇. �⃗� = 0 (3)
(�⃗� . ∇)�⃗� = −∇𝑝
𝜌𝑙
+ 𝜐 (∇2�⃗� ) (4)
The liquid film moves only in the main air flow direction (x-
direction) whose height varies in the y-direction, as shown
schematically in Fig. 10. For such thin liquid films, the external
driving forces is expressed by the shear stresses due to the
aerodynamic forces by the main air flow and the volume flow
rate of the liquid film is expressed mathematically as
�̇� = 𝑤𝑓𝑖𝑙𝑚 ∫ 𝑢 (𝑦) 𝑑𝑦ℎ𝑓𝑖𝑙𝑚
0
(5)
Assuming, linear velocity profile and solving for 𝑢 (𝑦), by
using Eq. (4) the theoretical expression for the liquid film
thickness can be given by
ℎ𝑓𝑖𝑙𝑚 = 2√�̇�𝜇𝑙
𝑐𝑓𝜌𝑎𝑤𝑓𝑖𝑙𝑚𝑈𝑎2 (6)
From Eq. (6), the liquid film thickness is dependent on the
aerodynamic forces (i.e., air velocity), the liquid’s property of
surface tension and the liquid’s flow rate (MFR). Thus, greater
the aerodynamic forces are the thinner is the liquid film formed
and vice versa. Similarly, the liquid film thickness increase if
the liquid used is denser, i.e., greater the viscosity of the liquid
is thicker will be the liquid film formed.
In the present study, in order to measure the liquid film
velocity measurement, the tracer particles were mixed along
with the water in the water tank. High-speed images at the mid-
chord of the blade were taken using a high-speed camera, such
that the liquid film velocity was approximated by the
displacement of the tracer particles in two consecutive frames.
The liquid film width was measured manually from the
shadowgraph images by taking an average of about 100 frames.
Figure 11 shows the quantitative average water film thickness at
the mid-chord of the blade, based on Eq. (6), at different air
momentum cases when the AOA was set at 0 – degree. From
Fig. 11, the height of liquid film decreases with an increase in
air velocity and vice versa. The physical mechanism of change
in film height due to aerodynamic forces is already illustrated in
Fig. 9.
Figure 12 shows that the ratio of film height to its width ratio
for the 0 – degree case. The film height to width ration remains
nearly the same under the same aerodynamic load conditions for
the 0 – degree case. Such that for high air momentum cases the
Fig. 10 Schematics of liquid film at mid chord
Fig. 11 Liquid film thickness at mid chord – 0 degree
Fig. 12 Non-dimensional film thickness at mid chord – 0
degree
(a) Dominant surface tension effects (b) Dominant aerodynamic effects
ℎ1𝑓𝑖𝑙𝑚 > ℎ2𝑓𝑖𝑙𝑚
Fig. 9 Effect of external (aerodynamic) forces on the liquid having same surface tension and flow rate
JGPP Vol. 9, No. 3
27
liquid film became much wider compared to its height and
resulted in minimum height to width ratio (Case A), Fig. 12, and
vice versa. This phenomenon can be understood based on the
minimum energy principle. Under the same air flow conditions
the aerodynamic forces experiences the same restoring forces
from the liquid’s surface tension. Liquid films, especially those
driven by shear forces always have slightly greater width due to
the additional external forces (i.e., aerodynamic forces)
compared to the free air stream film. According to Lan et al. [5]
at high liquid flow rate the liquid film deformed near the contact
lines (i.e., edges of thin film) because of equivalent surface
tension force, whereas, the central part of the thin film results in
flatter film thickness as shown schematically in Fig. 13 (b). This
causes the water to eject towards the contact lines making the
film to increase in the width and height wise direction, Fig. 13.
As equilibrium was established, the expansion (i.e. in the width
wise direction) energy and the equivalent surface tension
balances each other and no further expansion of the film takes
place. On the other hand, at low flow rate the surface tension
forces avoids the expansion of the liquid film due to strong
(a) Case A (Air velocity 40 m/sec, 𝑀 ≈ 192)
(b) Case B (Air velocity 30 m/sec, 𝑀 ≈ 108)
(a) Case C (Air velocity 25 m/sec, 𝑀 ≈ 75)
(b) Case D (Air velocity 20 m/sec, 𝑀 ≈ 48)
Fig. 14 Water film thickness to width ratio
Fig. 13 Effect of flow rate of liquid under same aerodynamic and surface tension forces
(a) Low liquid flow rate (b) High liquid flow rate
𝒉𝟏𝒇𝒊𝒍𝒎
𝒘𝟏𝒇𝒊𝒍𝒎 ≈
𝒉𝟐𝒇𝒊𝒍𝒎
𝒘𝟐𝒇𝒊𝒍𝒎
JGPP Vol. 9, No. 3
28
intermolecular forces, resulting in a hat-column like structure,
as shown in Fig. 13 (a). In the present study, the surface tension
and aerodynamic forces remain the same due to which the
height per unit width ratio also remained the same, as shown in
Fig. 12. A similar argument can be extended to the cases when
the blade is inclined at higher AOA. From Fig. 14, the ratio of
film height to width ration remains unchanged at a particular
angle and air flow conditions due to the similar effects of
aerodynamic forces and surface tension forces, as explained
earlier for the 0 – degree case. In all the four cases, the water
film height to width ratio was recognized to maximize at 3 –
degree. This is thought to be chiefly due to the effect of aerofoil
shape generating optimal flow conditions on the blade surface
at this angle. However, as the AOA is increased the liquid film
thickness to width ratio decreases due to the reduced flow
effects on to the blade’s surface (caused by flow separation).
Similarly, the water film Reynolds number was calculated
mathematically as expressed by Eq. (7)
𝑅 = 𝜌𝑙𝑈𝑙ℎ𝑙
𝜇𝑙
(7)
Figure 15 shows the Reynolds number of the liquid film
based on the average velocity and height of the liquid film. From
Fig. 15, the order of the Reynolds number of the thin film is of
order 102, which seems to be a reasonable range under the
operating conditions of this study. From Fig. 15, an increase in
the flow rate of the liquid results in a linear increase in the
liquid’s Reynolds number at all AOA at which experiments
were performed in this study. The Reynolds number is always
maximum for low momentum case (Case D) whenever the AOA
is due to the corresponding thicker liquid film. Moreover, the
Reynolds number of thin liquid film at 3 – degree case showed
higher values when compared to the similar conditions of the
liquid’s flow rate at different AOA, which is also thought to be
due to the blade’s profile shape.
Liquid Film Instability: To understand the liquid film instability phenomenon Craik
[6] model is utilized. In his model, Craik assumed a
unidirectional liquid film and solved the Orr Sommerfield
equation to obtain the amplification factor equation as given by
the Eq. (8)
𝛼 𝑐𝑖𝑅𝑒𝑓𝑖𝑙𝑚 = (𝛼 𝑅𝑒𝑓𝑖𝑙𝑚)2
3 [Π𝑟 +
3 Σ𝑖
2 𝛼− 𝑇 𝛼2 − 𝐺] (8)
Readers are directed to ref. [6] for the detail derivation of the
Eq. (8). The corresponding instability criterion is given by the
term in the parenthesis, i.e.,
Π𝑟 + 3 Σ𝑖
2 𝛼> 𝑇 𝛼2 − 𝐺 (9)
Equation 9 defines the critical amplification factor of the thin
liquid film given by Eq. 8. The above equation can be
understood by referring to the Fig. 16. If liquid film possesses
enough restoring forces (due to the surface tension (T) and
inertia (G)) then it opposes the external shear forces
(aerodynamic forces) resulting in a smoother liquid surface, Fig.
16 (a). However, if the external forces exceed the restoring
forces, an instability pattern appears on the liquid surface, Fig.
16 (b). Due to the aerodynamic shear force, a normal force is
applied on to the surface of the liquid, which results in the
formation of an instability pattern at the liquid’s surface. This
normal stress (𝛱r) applies an upward force on the crest and a
downward force on the trough, causing the liquid to move away
from the troughs and towards the crests. The shear stresses (𝛴i)
due to the aerodynamic shear force accelerates the fluid in the
windward direction and deaccelerate the fluid in the leeward
direction. This process results in the acceleration of the liquid
crest’s and vice versa. The combined effect of both the normal
and shear stresses enhances the film pattern to become
destabilize, resulting in the formation of the waves having finite
wavelength, such as shown in Fig. 6. Figure 17 compares the
author’s measured wave length (filled round marks) with the
critical wave number calculated from Eq. (8). From Fig. 17,
(a) 0 – degree (b) 5 – degree (c) 7 – degree
Fig. 15 Reynolds number of the film (based on film thickness at the mid-chord)
(a) Liquid’s surface tension force dominant over aerodynamic
forces
(b) Aerodynamic forces dominant over liquid’s surface tension
forces
Fig. 16 Schematics of effect of dominant forces on liquid film
structure
JGPP Vol. 9, No. 3
29
whenever the wave number exceeds the critical value of
dimensionless amplification factor (i.e., in the positive region)
the liquid film surface get unstable and vice versa. In other
words, when the external forces are dominant (left term in Eq.
9), Eq. 8 exceeds the critical limit. Such instability pattern is
termed as the Kelvin-Helmholtz (K-H) instability of the thin
liquid films, which leads to the atomization due to the Rayleigh-
Taylor (R-T) instability [7]. Boukra et al. [7] showed a
simplified diagrammatic representation for the co-current gas
streams flowing over the liquid surface, as shown in Fig. 18. At
first, shear instability controlled by gas vorticity thickness
causes a K-H instability (Fig. 18 (b)), which results in the
generation of longitudinal waves having wavelength (𝜆𝐿 ) at the
free surface of the film. The crest of the liquid film further
undergoes transverse instability, also called R-T instability (𝜆𝑇).
According to Marmottant et al. [9] and Raynal et al. [10], the
transverse perturbation results in an elongation of the crest
waves leading to the formation of ligaments and which
ultimately breakup into droplets. The droplets formation after
the T.E. of the blade will be discuss in the Part II of this paper.
SUMMARY AND CONCLUSIONS: Experimental studies were conducted to understand the
liquid film pattern formed on the blade’s surface at various AOA
and air momentum conditions. Based on this study, following
conclusions can be withdrawn;
• Based on the mathematical model, the liquid film thickness
is governed by the liquid’s mass flow rate and surface
tension, and the air velocity,
• An increase in air momentum, a decrease in the liquid’s flow
rate and the surface tension causes the film thickness to
decrease and vice versa.
• For a particular angle of attack and air momentum, the liquid
film thickness to width ratio remain unchanged due to the
similar effects of the liquid surface tension and the
aerodynamic forces.
• For similar air momentum ratio, the liquid film thickness
increases with an increase in the angle of attack and vice
versa.
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Fig. 17 Instability pattern of liquid film (0 – degree)
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