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

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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

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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

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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)

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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

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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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