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UNIVERSITY OF SYDNEY

DEPARTMENT OF AERONAUTICAL ENGINEERING

ROTOR WAKE INVESTIGATIONUSING THE SMOKE FLOW

VISUALISATION TECHNIQUE

Osvaldo Maximo Querin

March 1993

This thesis is submitted in fulfilment of the requirements for the degree of Master of

Engineering (Research)

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Abstract

Experiments were carried out on a small four bladed rotor at different climb rates.

The smoke-filament technique was used to visualise the rotor tip vortices; video

equipment was then used to record the images produced. The recorded images were

digitised and enhanced to assist in the identification of the vortex location. The

vortex trajectories were compared with established data and with the paths generated

by the general tip vortex path equations. It was found that these equations over-

simplified the vortex trajectories, modelling neither the interaction between vortices

nor their meandering.

The wakes studied showed evidence of vortex interaction. It was found that vortices

close to one another combined in pairs and spun about a common centre as they

moved downstream. A new mean path equation was thus defined which could model

this type of behaviour. An exponential equation was selected to model the mean path.

To assist in the determination of the order which best suited the curve, the least

squares method was used. The meandering of the vortex trajectory about its mean

path was studied and the types of instability present were determined. Three types

of instability were found in tip vortices; short-wave, mutual-inductance and long-

wave. It was discovered that the helical path followed by a hovering rotors tip

vortex was unstable under most flight conditions and that fluid damping suppressed

the magnitude of these instabilities.

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Acknowledgements

I would like to take this opportunity to thank all the members of staff in the

Department of Aeronautical Engineering for their support and guidance over the past

few years, with special mention to Mr John Blackler and Mr John Curtis for those

words of wisdom when I most needed them. I would also like to give special thanks

to K.C. Wong and Alex Tan for putting up with me.

I also want to thank my parents for their support and guidance, and Abbie for her

support, understanding and patience.

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CONTENTS

Page

Abstract ii

Acknowledgements iii

List of Figures vii

List of Tables x

Nomenclature xi

1. INTRODUCTION

1.1 Background 1

1.2 Wake Path Equations 4

1.3 Flow Visualisation Techniques 5

1.4 Aim of this Research 5

1.5 Outline of Research Presentation 6

2. ROTOR WAKE VISUALISATION

2.0 Introduction 7

2.1 Smoke Filament Technique 7

2.2 Water Towing Tank Technique 10

2.3 Small Particles Technique 12

2.4 Schlieren Technique 13

2.5 Shadowgraph Technique 15

2.6 Shadowgraph and Schlieren Applications for Rotors Operating

at Low Mach Numbers 17

2.6.1 Hot-Wire Technique 17

2.6.2 Spark Technique 19

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2.7 Alternative Visualisation Techniques 20

2.7.1 Atmospheric Water Vapour Condensation 20

2.7.2 Hot-Wire Anemometer Tracking 20

2.7.3 Laser Velocimeter Tracking 22

2.8 Discussion 23

3. FLOW VISUALISATION EXPERIMENT

3.1 Experimental Equipment 24

3.1.1 Model Test Rotor 24

3.1.2 Rotor Test Stand 25

3.1.3 Wind Tunnel Facilities 26

3.1.4 Synchronisation Equipment 27

3.2 Experimental Procedure 28

3.3 Discussion 29

4. IMAGE PROCESSING

4.1 Image Digitising 30

4.2 Image Enhancement 31

5. ROTOR WAKE GEOMETRY RESULTS

5.0 Introduction 34

5.1 Wake Results 345.2 Wake Features 35

5.3 Wake Instabilities 49

5.4 Generalised Wake Geometries 53

5.4.1 Tip Vortex Mean Axial Path Equation 53

5.4.2 Axial Path Instability Criterion 56

5.4.3 Tip Vortex Mean Radial Path Equation 63

5.4.4 Radial Path Instability Criterion 64

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6. CONCLUSION 71

REFERENCES 74

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List of Figures

Figure 1 Typical oil smoke generator. 8

Figure 2 Smoke-flow visualisation of tip vortices with two vortex

cores shown. 9

Figure 3 Dye-layer visualisation technique illuminated with flood lights. 10

Figure 4 Dye-layer visualisation technique illuminated with laser sheet. 11

Figure 5 Localised-dye visualisation technique, with dye discharged

from blade tips and illuminated with laser sheet. 12

Figure 6 The Schlieren system. 13

Figure 7 Schematic diagram of the Z configuration Schlieren system. 14

Figure 8 Double-pass Schlieren system. 14

Figure 9 Shadowgraph systems; (a) divergent light rays,

(b) parallel light rays. 15

Figure 10 Typical Shadowgraph set-up for rotor wake visualisation. 16

Figure 11 Improved wide-field shadowgraph set-up using

a single beam splitter. 17

Figure 12 Hot-wire shadowgraph photograph of flow behind a propeller. 18

Figure 13 Spark shadowgraph photograph of flow behind a propeller. 19

Figure 14 Typical arrangement for a radially traversing hot-wire

probe spinning with the rotor. 21

Figure 15 Typical data indicating the position when the vortex core strikes the

hot-wire probe. 21

Figure 16 Typical tip vortex path determination data. 22Figure 17 Dimensioned diagram of the test rotor stand. 26

Figure 18 Arrangement of smoke rake and test stand in wind tunnel. 26

Figure 19 Schematic diagram of the synchronisation equipment. 28

Figure 20 Position of video camera in relation to rotor. 28

Figure 21 Digitised black and white video picture showing

tip vortices, vortex sheets and rotor blade. 31

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Figure 22 Digitised video picture with enhanced false colour

imaging. Vortex sheets, tip vortices and rotor blade

are easily identified. 32

Figure 23 Comparison between experimental and predicted wake

geometries; (a) radial, (b) axial. (Ct = 0.0018) 38









Figure 28 Comparison between the experimental wake of

Bagai et al (1992-b) and predicted wake geometries;

(a) radial, (b) axial. (Ct = 0.0074) 43


Swanson et al (1992) and predicted wake geometries;



Swanson et al (1992) and predicted wake geometries;


Figure 31 Individual vortex trajectories of the four vortices

from the wake of figure 27. 46

Figure 32 Individual vortex trajectories of the two vortices


Figure 33 Individual vortex trajectories of the three vortices


Figure 34 Instability mode shapes; the short-wave instability,

the mutual -inductance modes with /k = 5/2 and3/2,

and the long-wave instability with /k = 1/2. The dark

portions are outside the cylinder on the near side; the

light portions are inside. Reproduced from Widnall (1972). 50

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Figure 35 Stability boundaries for helical vortex filaments of finite

core. The value of the ratio of core-to-cylinder radius are

shown on each curve. Above the boundary, the helical

filament of that core size is unstable. Reproduced from

Widnall (1972). 51

Figure 36(a) Axial wake geometry and mean axial path. (Ct = 0.0018) 57

Figure 36(b) Meander of vortex about mean axial path. 57











Figure 42(a) Radial wake geometry and mean radial path. (Ct = 0.0018) 65

Figure 42(b) Meander of vortex about mean radial path. 65











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List of Tables

Table 1 Model Rotor Characteristics 25

Table 2 Rotor Test Parameters 35

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Nomenclature

b = Number of blades

c = Blade chord, m

CV = Velocity coefficient, Vz/(R)

CT = Rotor thrust coefficient, T/(2R4)

kR = (Pitch of the helix)-1

k = k/(1+k 2R2)

r = Radial dimension, m

r/R = Non-dimensional radial tip vortex displacement relative to tip-path-

plane

R = Rotor radius, m

T = Rotor thrust, N

Vz = Axial velocity, m/s

z = Axial dimension, m

z/R = Non-dimensional axial tip vortex displacement relative to tip-path-

plane

= Perturbation wave number

/k = Number of waves per cycle of the helix

twist = Blade twist angle, deg

1 = Measured parameter

= Atmospheric density, kg/m3

= Density gradient

x

= Change in density gradient2

x2

= Rotor solidity, bc/R

= Blade azimuth angle, deg

w = Tip vortex age, deg

= Rotor rotational frequency, rad/s

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Chapter

ONE

INTRODUCTION

1.1 BACKGROUND

Helicopters and related types of rotorcraft are versatile machines. Their capabilities

may include level flight, vertical flight and hover. Of these flight regimes, the most

important and critical to the rotorcraft is hover. The reason for this is that hover

performance can in most of these machines dictate their maximum usable payload.

Performance predictions, therefore, become a crucial element in the development and

analysis of rotorcraft.

The methods used to predict performance have expanded dramatically over the past

four decades. Momentum theory has been the simplest and most basic approach,

(Gessow et al 1985), in which the rotor was treated as an infinitesimally thin actuator

disk with uniformly accelerated air throughout. As more accurate performance

predictions became necessary, performance charts, such as those of Tanner (1964),

were produced for a large range of standard rotor blades and configurations. When

limitations in these charts became evident due to increases in the number of blades

and their loadings, the need for more general methods became necessary.

To achieve this task, the individual blade elements had to be considered. The analysis

which followed consisted of balancing momentum and two-dimensional aerofoil

theories to derive inflow and resulting lift and in-plane forces at each blade element.

This produced what is commonly known as blade element theory (Gessow et al 1985,

Stepniewski et al 1984). However, the performance predicted by this method was

still extremely optimistic. The reason for this was that although blade characteristics

had been accounted for, the influence of the real rotor wake with tip and sheet

vortices on the blades had not. To partially account for such an effect, researchers

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at the time introduced a Tip Loss Factor which assumed complete loss of lift over

a small percentage of the blade at the tip. Three dimensional tip effects and wake

non-uniformity caused by finite number of blades, however, limited the usefulness

of this method for detailed rotor analysis.

To solve the three dimensional problem with a finite number of blades, the rotor

wake had to be incorporated. This was originally done by using vortex theory. This

theory described the wake as a series of cylindrical vortex sheets representing the

radial variation of circulation. This was essentially the approach taken by Goldstein

(1929) and Lock (1931) with propellers and later the work of Willmer (1959), Piziali

et al (1962) and Miller (1962) with helicopter rotors improved this representation of

the wake. Their combined work redefined the representation of the wake into a mesh

of discrete line vortices. However, the spatial positioning of the wake elements was

still uniform with wake contraction and the interaction between wake elements still

not considered.

The work of Miller (1962) and Willmer (1959), which used an undisturbed prescribed

wake model, was followed by the work of Landgrebe (1969). In his work, although

for forward flight, the rotor was represented by numerous discrete vortex elements.

The wake was divided into a series of near and far wake regions. The analysis was

then achieved by the implementation of the classical Biot-Savart law with numerical

integration techniques. This method has been the most widely used means of

predicting performance for the past three decades. The work of Gray (1956, 1972)

and Landgrebe (1972), on the identification of the true path of tip vortices and vortex

sheets led to the incorporation of Landgrebes (1969) forward flight wake analysis

to the hover flight condition (Landgrebe, 1972).

Blade tip vortex trajectories were represented by Landgrebe (1972) as simple

analytical equations. The axial tip vortex path was modelled by two linear equations

which produced what is normally termed the classical two sloped linear path1. The

1Equation 1 of this presentation

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radial path was modelled with a first order exponential equation2. The work of

Kocurek et al (1977) improved these equations by considering parameters not

included in Landgrebes (1972) work.

Incorporation of the precise mean path of the wake as vortex filaments and of the

rotor blades as either segmented vortex filaments or vortex panels, led to the

development of Prescribed-Wake models for performance predictions (Kocureket al

1977, Reddy 1979). Limited availability of tip vortex trajectories produced by newly

designed rotors meant that a more generalised approach was required, in which the

vortex path did not have to be known. Free-Wake analysis methods were developed

(Clark et al 1970, Miller 1981, 1982), in which the tip vortex path was determined

by the time history of the induced velocities everywhere in the wake generated by

these vortex filaments.

Both Prescribed and Free-Wake methods have in the past two decades been

extensively used and improved to achieve better performance prediction accuracy.

But the studies of Reddy et al (1987) and Mba et al (1991), have shown that

performance predictions fall to within 5% by these two methods. Such apparent low

levels of uncertainty could lead to as much as 20% error in the estimation of

maximum payload (Clark et al, 1969). In trying to determine the parameters which

might cause such errors, the work of Reddy (1986) has shown that rotor thrust and

induced power are highly sensitive to small variations in tip vortex geometry. As

both methods depend greatly on the position of the wake, and as Free-Wake methods

place restrictions on the wake settling rates (Mba et al, 1991), one of the main causes

of such errors has been attributed to the inability of current wake vortex path models

to faithfully simulate the radial and axial tip vortex paths 3.

2Equation 6 of this presentation.

3In the work of Mba (1991), the vortex path was allowed to convect freely for the first revolution

of the rotor. Further downstream trajectories of the tip vortex were assumed to maintain the sameradial position with the axial rate equal to that at the end of the first revolution.

3

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1.2 WAKE PATH EQUATIONS

The current empirical equations used to describe tip vortex paths had their origins in

the work of Gray (1956, 1992) on single bladed rotors. He found that both the axial

and radial tip vortex paths could be easily represented by simple algebraic

expressions with very few measured parameters. The axial and radial paths of Grays

equation (1992) had the same format as equations 1 and 6 of this presentation.

However his radial equation had the extra term added to it. TheBe

1

sin()

multi-bladed nature of rotorcraft was considered by Landgrebe (1972) when he

derived the general forms of the parameters in Grays (1992) equations to account

for a wide range of rotor design and operating conditions4

. The extra term in Graysradial path equation may have been omitted due to blade aspect ratio on tip-shape

effects. The equations and parameters proposed by Landgrebe (1972) were only

simple generalised representations of the tip vortex trajectory during the first

revolution of the blade which produced it, neglecting the instabilities which arise

further downstream.

The work of Kocurek et al (1977) was able to incorporate the effects of number ofblades and twist to the parameters of the generalised equations of Landgrebe (1972).

The equations thus defined have remained unchanged and are still used as the

governing equations for the prediction of tip vortex paths of hovering rotors5. As

these equations are linear for the axial vortex path, and first order exponential for the

radial path, they produce a tip vortex structure which is everywhere symmetrical. The

research of Norman et al (1987) had demonstrated that hovering rotor wakes could

not be assumed to be symmetrical. The photographs reproduced in their publication

(Norman et al, 1987) revealed the instabilities in the tip vortices, the relationship

between tip vortex instability growth and increase in rotor thrust and the

asymmetrical structure of the vortex wake.

4Equation 2 of this presentation.

5Equations 3 and 8 of this presentation.

4

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Further investigation of hovering rotor wakes using the shadowgraph technique of

Swanson et al (1992) have corroborated the claim that tip vortex instabilities were

dependent on rotor thrust levels. The work of Swanson et al (1992) had also

formulated a relationship between tip vortex core growth rate and thrust coefficient

and another between vortex core growth rate and vortex age.

1.3 FLOW VISUALISATION TECHNIQUES

From the early years of rotorcraft research, flow visualisation investigations had been

carried out on rotor wakes in most flight regimes to observe and understand the

structure and behaviour of their tip vortex trajectories. The methods used for this type

of research have been various, some achieving great success. These were: Smoke-

filament technique (Gray 1992, Williams et al 1988, Landgrebe 1972), water-tank

technique (Jenks et al, 1987), small particle technique (Timm, 1965), schlieren

technique (Landgrebe 1972, Tangler et al 1973), shadowgraph technique (Norman et

al 1987, Swanson et al 1992, Bagai et al 1991, 1992(a), 1992(b)). Of these methods,

the smoke-filament and shadowgraph techniques have been the most successful.

However, in recent years, the shadowgraph technique has become the most widely

used. This has been due to its ability to accommodate large scale rotors operating at

Mach numbers greater than 0.45. Its success can be observed in the work of Norman

et al (1987) and Swanson et al (1992).

The smoke-filament technique has been shown by the results of this research to work

exceptionally well for rotors operating at low Mach numbers (M

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The aim of this thesis has been to study the radial and axial tip vortex paths of rotors

experiencing hover and axial flow using the smoke visualisation technique.

Compare the experimental tip vortex paths with trajectories generated by the

general equations formulated by Gray (1992), Landgrebe (1972) and Kocurek (1977).

Select an equation type which could better represent the mean vortex axial and

radial trajectories and determine its coefficients for the tested rotor configurations6.

Determine the meander of the vortex trajectories about their mean path, ascertain

the forms of instabilities present and determine their characteristics.

1.5 OUTLINE OF RESEARCH PRESENTATION

The proposed aims stated in the previous section have been substantially

accomplished. The different sections of this presentation describe more fully how this

was achieved.

The smoke flow visualisation technique was selected after careful consideration of

the experimental requirements and available resources. Chapter two examines in

detail the most common visualisation techniques and their suitability for the

requirements of this research.

Descriptions of available facilities, equipment used and the model test rotor have

been described in chapter three, together with detailed explanations of modifications

to the smoke filament technique and a full description of the experimental procedure.

The images produced by the smoke filament technique were recorded on video tape.

The processes involved in retreating each video frame and their enhancement

procedures to reveal the position of the tip vortex core were described in chapter

four.

The results of this research were described in chapter five, where the data obtained

was analysed to realise the aim of this work.

6 This study does not attempt to obtain a generalised tip vortex path equation, it only attempts to

determine a type of equation which could better represent the tip vortex mean path.

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Chapter

TWO

ROTOR WAKE VISUALISATION

2.0 INTRODUCTION

To understand the behaviour of rotor wakes, observations must be made of the basic

elements which constitute its structure, such as the tip vortex and vortex sheet. Such

observations have been made by researchers for many years (Lightfoot 1958, Landgrebe1972, Gray 1992). Visualisation techniques have been developed or reconfigured to

reveal the three dimensional characteristics of rotor wakes. This chapter describes the

suitability of the different visualisation techniques to rotor research.

2.1 SMOKE FILAMENT TECHNIQUE

This technique, used for low subsonic flow speeds, consisted of introducing into the

flow field one or more fine, turbulent free smoke filaments which follow the flow's path.

When illuminated, the smoke filaments reveal to the observer some characteristics of

the flow path.

The most common and safest method of smoke production requires kerosene or an

eucalyptus oil-based solution to be heated to boiling point and the vapours produced

mixed with air. On mixing, this produces a white cloud of smoke. A typical oil smoke

generator can be seen in figure 1.

The method of introducing smoke into the rotor's wake is very dependent on what part

of the flow the observer is interested in examining. The most common way of doing this

required the use of either a single tube (Williams et al, 1988) or a multi-tubed smoke

rake (Lightfoot 1958, Landgrebe 1972). Such a device allowed the smoke to be emitted

into the wake in a single plane. When illuminated with a stroboscopic light source, the

tip vortices and the trailing vortex sheets could be observed (figure 2). This method,

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Figure 1 : Typical oil smoke generator.

however, only allowed a two dimensional slice of the wake to be viewed at any one

time. To obtain a complete three dimensional image of the flow, pictures would need

to be taken at different azimuth positions and the results processed to construct a three

dimensional model of the wake.

A more direct way of viewing the full three dimensional wake can be achieved by

introducing smoke through the tip of the rotor blade. This can be done by forcing smoke

through ducts inside the blade, incorporated during the manufacturing process, and

exiting onto the tip. As the smoke leaves the blade tip, it becomes entrapped by the

strong tip vortex and travels downstream with it (Gray, 1992), revealing the wake

structure. The images produced resemble those obtained by either the schlieren or

shadowgraph techniques (Tangleret al1973,Norman et al1987). The rate at which

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smoke is introduced into the flow must be carefully regulated to diminish the effects of

flow injection into the tip vortex core. The work of Rinehart (1971) has shown that such

injections reduce the vortex swirl velocity component and their circulation strength as

they travel downstream. These effects alter the trajectory of the vortex, thus making the

results not representative of the rotor under investigation. Alternatively, the blade tips

could be manufactured to have a cavity filled with a porous material impregnated with

Titanium or Stannic Tetrachloride. Holes drilled at the tip would allow air to come into

contact with the solution, producing a dense white smoke which would escape from the

tip with negligible alteration to the vortex path.

Figure 2 : Smoke-flow visualisation of tip vortices,

with two vortex cores shown.

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Figure 3 : Dye-layer visualisation technique illuminated with

flood lights.

2.2 WATER TOWING TANK TECHNIQUE

The use of water in preference to air as the working medium has the advantage of no

recirculation problems, very low levels of turbulence and the capability of stratification

by means of a salinity gradient. The work of Jenks (1987) and Gad-el-Hak (1987) had

been aimed at investigating rotors in the forward flight regime and although the hover

flying regime would present obvious problems, rotors could still be studied at different

rates of climb. Figure 3 illustrates a possible arrangement for such a study. Towing tanks

of the types used by Jenks et al(1987), in which the water is stagnant and the model

moves, the recirculating type used by Sarpkaya (1971), where the water circulates and

the model is stationary, or the gravity fed type used by Werle (1986), where the water

flows by gravity draining, could all be used for this analysis. In these tanks, visualisation

of the flow would be better achieved by using food colour or fluorescent dyes. To

illuminate it, conventional flood lights or sheet laser light (Kogan et al1987) could be

used, the former providing overall views of the flow, the latter allowing for more detail

investigation of the flow region.

Introduction of the dyes into the flow field could be achieved in one of two ways, as

dye-layers or locally. If the dyes were introduced as layers, they would need to be placed

into the water as horizontal sheets prior to towing of the model. To achieve this a stable

density stratification would be necessary. Such a process would involve depositing

individual layers of water of slightly different density (controlled by the addition of salt),

one at a time in the tank. The water, once, settled would allow the layers to partially

diffuse into each other, establishing a continuous vertical gradient. To form the

horizontal sheet, a small diameter string saturated with dye crystals would be placed into

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Figure 4 : Dye-layer visualisation technique illuminated with a

laser sheet.

the tank and towed at a very low speed, allowing for the dye to be washed away from

the string as the water flows around it.

To introduce the dyes locally, they could either be pasted on to the rotor blades or be

discharged at the blade tips. If pasted, part of the blade would be covered with a dye

paste, and during the run this would dissolve directly off the blade and into the wake.

If discharged, the dyes would need to be introduced into the flow through small orifices

at the blade tips. These techniques require fresh water tanks (no density gradient),

having the advantage of allowing for large number of tests per day.

For rotor flow investigation with the dye-layer technique, figure 3 shows an arrangement

which could be implemented relatively easily. The rotor would need to be set

perpendicular to the towing direction, with its plane of symmetry coinciding with the

dye layer. When towed forward, the flow would be illuminated by either flood lights or

a laser sheet. If using flood lights, these would have to illuminate the dye-layer from

above (figure 3), but if the laser sheet were used, it would have to coincide with the dye

layer (figure 4). The camera would need to be positioned perpendicularly above the dye

layer (figures 3 & 4). If the localised dye technique were used, the dye would become

entrapped by the tip vortex, forming a helix like structure (figure 5) as the rotor is towed

through the tank. Although both illumination techniques could be used, the sheet of laser

light is preferred as it permits the helix to be viewed or filmed in different planes

parallel to the rotor's spinning axis (figure 5). As before, the camera would be located

perpendicularly above the sheet of laser light, focused on this plane. Due to the complex

nature of the flow, both means of dye introduction require the camera's shutter speed to

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be greater than the rotational speed of the rotor. This would be to enable the film to

capture the flow at various azimuthal blade positions.

Figure 5 : Localised-dye visualisation technique, with dye

discharged from blade tips and illuminated with a

laser sheet.

2.3 SMALL PARTICLES TECHNIQUE

In this technique, small solid particles would be introduced into the airstream and

observed by reflected or scattered light. The particles, however, would need to have low

inertia to follow the local direction of the fluid motion and not be affected by gravity.

In early work done on rotor wakes (Timm 1965), moderate success was achieved in

visualising the effects of obstacle-induced flow recirculation by using very small sugar

pine or spruce sawdust. Although in the work of Timm (1965), this technique worked

well, it had major disadvantages. The small size of the seeding particles created a lot of

debris which may remain floating in the air for some time. Such a situation could cause

health problems if the people operating the experiment were not suitably protected.

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Figure 6 : The Schlieren system.

2.4 SCHLIEREN TECHNIQUE

The basic Schlieren system, developed in 1864 by Tepler, is presented in figure 6.

Diverging light from a point source at A is converted into a parallel beam and passed

through the region of fluid to be viewed. The parallel beam then passes through another

lens and is focused at B, generating an image of the flow on the screen. Variations in the

working fluid's density cause the light rays to deviate from their original paths,

deflecting away from the focal point. When a knife edge is inserted at the focal point B,

rays that were deflected in one direction from the parallel would be prevented from

reaching the viewing screen. This elimination of rays from the image resulted in a

variation of illumination at the screen, which is proportional to the first derivative of the

density variation in the working fluid (Merzkirch 1987, Clancy 1978, Pope et al1965,

Pankhurst et al1965). Although the knife edge could be used in any orientation, if

placed perpendicular to the flow axis the density gradients will lighten or darken the

screen depending on their sign and on which side of the focal point B, the knife edge is

located. However, if orientated parallel to the flow, half the image would depict one

illumination pattern based on the density gradient whereas the other half would show

the reverse pattern for the same density gradient.

For rotor work investigation, more complex arrangements would be required. In the

work of Tangleret al(1973) a modified version of the ' Z ' configuration was used with

great success (figure 7). In such an arrangement, the lenses of figure 6 would be replaced

by two spherical or parabolic mirrors, enlarging somewhat the field of view. If greater

sensitivity were required, so that the vortex sheet could be viewed, the ' Double - Pass

Schlieren System ' could be used (figure 8). This system consists of a conical light

source passing twice through the working fluid.

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Figure 7 : Schematic diagram of the 'Z ' configuration Schlieren system.

Figure 8 : Double-pass Schlieren system

This system is very good for the visualisation of rotor wakes operating in the transonic

region (0.65 < M < 1.2), however its major drawback would be restrictions on the field

of view imposed by the size of the mirrors. Although this may be sufficient for rotors

of small diameter (Tangleret al1973), it would be inadequate for viewing wakes

generated by full scale rotors. If the wide-field schlieren system were used (Burton

1949) problems would be encountered in the manufacture of the large precision ruledgrids required.

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Figure 9 : Shadowgraph systems. (a) divergent light rays, (b) parallel light rays.

2.5 SHADOWGRAPH TECHNIQUE

The shadowgraph system, developed by Dovk in 1880, is the simplest optical

visualising process dependent on changes of the fluid refractive index, and has two

configurations. The optical elements required for configuration 1 (figure 9(a)) are a

high-intensity point light source (spark-electrode discharge (Bagai et al1992)) and a

retroreflective screen. For configuration 2, (figure 9(b)) the same equipment as for

configuration 1 would be used plus a lens or mirror. Both configurations could be used

for rotor wake visualisation, however, due to the large diameter of rotors, configuration

1 is better suited and more widespread (Bagai et al1992, Norman et al1987, Swanson

et al1992, Light et al1992).

The principle of the shadowgraph technique may be described as follows: As light rays

pass through a fluid medium of varying density, they will be deflected in proportion to

the density gradients (M/Mx). In regions where these gradients are constant, all light rays

will be deflected by the same amount and the light intensity at the screen will be

constant. In regions of the fluid where the gradients change, the deflection of light rayswill not be constant, altering the light intensity on the screen. Where the density

gradients increase (M /Mx > 0), the light rays will diverge, decreasing the illumination2 2

of the screen. Where the density gradients decrease, the light rays converge, increasing

the illumination on the screen.

For rotor wake investigation, it is customary to use configuration 1, with photographic

and video cameras to record the wake for quantitative analysis. Different optical

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Figure 10 : Typical shadowgraph set-up for rotor wake visualisation.

arrangements of the equipment can be observed in figures 10 and 11. The shadowgraph

arrangement of figure 10 has been successfully used in the past (Norman et al1987,

Swanson et al1992, Light et al1992), however in such systems the optical path of the

camera is "off-axis" to the incident light beam, resulting in the reflected light rays

travelling at slightly different angles to the incident rays. This causes two serious

problems. Firstly it produces a 'ghost' image which in some instances can obscure the

area of flow under scrutiny. Secondly, as the off-axis distance is increased, the intensity

of the reflected light back to the camera decreases almost exponentially with increasing

observation angle. It has been determined by Bagai et al(1992-a) that a change in the

observation angle by one degree would reduce the intensity of the light received by the

camera by a factor of 16.

To solve the problems associated with the off-axis alignment of the camera and light

source, Bagai et al(1992-a) performed experiments with the shadowgraph arrangement

of figure 11, with great success. By introducing a beam splitter they were able to achieve

a light intensity 4 times greater than for the previous arrangement, with the added effect

of permitting the use of higher camera shutter speeds and/or smaller lens apertures.

This technique has been very successful in visualising rotors operating at Mach numbers

greater than 0.65, and as research shows it has been the most frequently used technique

for full or near full scale rotor visualisation in recent years. However, as a distinctive

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Figure 11 : Improved wide-field shadowgraph set-up using a single beam splitter

(Bagai et al1992-a).

density gradient variation is required, the method doesn't suit rotors operating at low

Mach numbers (M < 0.3).

2.6 SHADOWGRAPH AND SCHLIEREN APPLICATIONS FOR ROTORSOPERATING AT LOW MACH NUMBERS

For studies on rotors operating at low Mach numbers, the density variation through the

wake becomes too low to be detected by methods dependent on changes in the fluid

refractive index. In the work of Townend (1931), two techniques were developed which

artificially altered the density of the fluid, permitting the shadowgraph and schlieren

systems to be used. The drawback of the system, however, is that forced changes in the

density of the fluid may cause its flow pattern to be altered.

2.6.1 Hot-Wire Technique

The technique consists of placing into the air stream a grid of fine electrically heated

wires. Their high temperature causes the density of the air passing over them to be

decreased, producing very fine streamlines of refractive index different to that of the

surrounding air. When such a pattern is illuminated by a stroboscopic light source in

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Although figures 12 and 13 were of flow generated by a propeller, they were7

displayed vertically to assist the reader in determining how the flow generated by ahovering rotor would appear when visualised using these techniques.

18

synchronisation with the spinning rotor, it would reveal a two dimensional view of the

wake, in a similar manner as the smoke filament technique. Figure 12 has been

reproduced from the work of Townend (1931), showing such a view .7

The grid recommended by Townend (1931) and Pankhurst et al (1965) should be

manufactured from platinum wire approximately 0.05 mm in diameter and between 13

to 26 mm long, with the individual wires set about 13 mm apart. The wire should be

heated to a dull red colour, requiring a 14 V battery and approximately 1 Amp for a flow

speed of approximately 10 m/s.

Figure 12 : Hot-wire shadowgraph photograph of flow

behind a propeller, (Townend 1931).

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2.6.2 Spark Technique

In this technique, a series of electric sparks are discharged into the flow causing small

volumes of air to be heated, and as was done for the Hot-Wire Technique, the paths of

these volumes could be tracked using the Shadowgraph or Schlieren Methods. These

volumes may be considered to be small enough to be thought of as particles. By using

synchronised stroboscopic light, the path of these particles could be determined, hence

supplying a time scale along the streamline from which the velocity at any point could

be determined. Again, as for the Hot-wire technique, the pictures produced represent a

two dimensional slice of the rotor's wake. Figure 13 has been reproduced from the work

of Townend (1931), showing such a view.

Figure 13 : Spark shadowgraph photograph of flow

behind a propeller, (Townend 1931).

Generation of the sparks could be achieved by the use of an ignition coil or an alternator.

In the work of Townend (1931), the latter method was found to be more favourable,

using a 0.5 h.p. alternator delivering 150 V at 2000 RPM. The output from the alternator

was then passed through a series resistance of about 100 ohms to a transformer which

stepped the voltage 100 times. The electrode was manufactured from oxidised piano

wire with a spark gap of approximately 9.5 mm.

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2.7 ALTERNATIVE VISUALISATION TECHNIQUES

The following direct and indirect methods of flow visualisation have not been widely

used, nor provide results of the calibre of the above mentioned techniques. However,

their unique means of producing quantitative wake trajectory data warrants a mention

in a review of different wake visualisation techniques.

2.7.1 Atmospheric Water Vapour Condensation

Under certain ideal conditions, the flow generated by a full scale rotor may be viewed

with the naked eye. The work of Jenney et al(1968) and Felkeret al(1986), has shown

that tip vortices could be seen on days of high humidity, with rotors operating in the

Ttransonic speed region (0.65 < M < 1.2) and at high thrust coefficients ( C > 0.16 ).

Under these conditions the water vapour in the air is condensed by the low-pressure

inside the vortex core, remaining visible for up to one and a half revolutions of the rotor.

2.7.2 Hot-Wire Anemometer Tracking

The methods described thus far comprise the direct flow visualisation techniques, where

one or more characteristics of the flow can be viewed by the observer as it happens. The

Hot-Wire Anemometer Tracking Technique, however is an indirect flow visualisation

method. In this technique, a hot wire probe is traversed radially through the wake at

different planes downstream of the rotor's tip path (figure 14). During each traverse it

records the radial position, axial distance behind the tip path, azimuthal position of the

blade with respect to the probe and the velocity profile signal. As the tip vortex can not

be seen, its location is determined when its core strikes the hot wire probe, producing

a very distinct dip (figure 15) in the velocity signal. On compilation of all the vortex

locations, the full tip vortex path can be reconstructed.

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Figure 14 : Typical arrangement for a radially traversing

hot-wire probe spinning with the rotor.

Figure 15 : Typical data indicating the position when the

vortex core strikes the hot-wire probe

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The only problem with this technique can be attributed to the unsteady nature of the tip

vortex. Due to the meandering of such vortices as they travel downstream, they become

almost impossible to locate, a problem experienced by Caradona et al(1981) when

using this technique.

2.7.3 Laser Velocimeter Tracking

This is also an indirect flow visualisation technique. In a similar way as for the Hot-

Wire technique, the velocity profile signal is measured at different radial and axial

positions. The vortex location is determined by the same dip in the velocity signal.

However, the velocity profile at each azimuth angle could be reconstructed from the

recorded signal to provide not only the tip vortex coordinates but also its size,

magnitude, and rate of growth or decay. This is illustrated in the results of figure 16,

obtained by Pouradieret al(1981). The technique, although more sophisticated than the

Hot-Wire, still has problems determining the vortex paths after one revolution due to

their meandering.

Figure 16 : Typical tip vortex path determination data.

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2.8 DISCUSSION

This chapter has given a brief overview of the many flow visualisation techniques which

could be applied to rotor wake investigation. In deciding the most suitable experimental

technique for this work, test parameters, equipment availability and rotor characteristics

were some of the factors considered.

The work of Caradona et al(1981), Light et al(1992) and Bagai et al(1991) have

shown that from the time a vortex is formed until the following blade passes over it, its

trajectory is approximately steady. But once the vortex from the following blade

develops the radial and axial paths of the previous vortex show a more erratic behaviour.

As this is the region of the flow of most interest in this study, both the Hot-Wire

Anemometer and Laser Velocimeter Tracking techniques could not be used.

Limitations on rotor size due to available wind tunnel facilities (see section 3.1.3), and

on the size of the drive unit (section 3.1.2) have restricted the operation of the rotor to

Tlow thrust coefficients (C < 0.01) and low Mach numbers (M < 0.25). These values

were too low for the Atmospheric Water Vapour Condensation, Schlieren and

Shadowgraph techniques. Although the Hot-Wire and Spark techniques could have beenused to assist the latter two techniques in revealing the wake, the density variation

within the working fluid caused by the nature of these techniques may have altered the

vortex trajectories.

The Small Particle Technique, although suitable for the test conditions, creates vast

amounts of debris, and as a Water Towing Tank was not readily available, the Smoke

Filament technique was selected as the technique for the visualisation of the model

rotor.

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Chapter

THREE

FLOW VISUALISATION

EXPERIMENT

3.1 EXPERIMENTAL EQUIPMENT

The facilities available at the time this project was initiated were not sufficient toaccommodate full scale investigation of rotor systems. For this reason, the decision was

made to use a small scale model rotor such as those used by Landgrebe (1972), Gray

(1992) and other researchers. Visualisation results obtained from such model rotors have

been successfully used by Landgrebe (1972), Gray (1992) and Kocureket al(1977) to

generate general vortex tip path equations for performance prediction of full scale rotors.

3.1.1 Model test rotor

The visualisation program involved subjecting the rotor to hover and positive climb

rates. Introduction of axial flow onto the rotor could only be achieved in the wind tunnel

of the Department of Aeronautical Engineering at the University of Sydney (section

3.1.3). Its size restricted the overall dimensions of the model rotor. Since the effect of

changing the parameters was not intended to be studied, a standard rectangular blade

with a NACA 0012 section was used. Table 1 lists the characteristics of the rotor system

tested.

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TABLE 1 : Model Rotor Characteristics

Number of Blades, b 4

Rotor Radius, R (m) 0.3145

Blade Chord, c (m) 0.0381Blade Root Cut Out (m) 0.08

Blade Twist (Deg) 0o

Blade Aspect Ratio, AR 6.15

Rotor Solidity, 0.1542

Blade Aerofoil NACA 0012

Blade Pitch Setting (Deg) 10o

Blade Taper Ratio 1.0Blade Tip Square

3.1.2 Rotor test stand

Testing of the rotor in the wind tunnel was achieved by the use of a test stand designed

and fabricated in the Department of Aeronautical Engineering. It was attached to the

wind tunnel balance, allowing the rotor thrust to be measured via the balance dragcomponent along the wind tunnel axis. For torque measurements, a strain gauge support

arm prevented the rotation of the drive relative to the test stand, however problems

associated with the size of the support arm prevented any such readings from being

taken.

The drive unit consisted of a 50 Watt electric motor with a speed adjustable up to 3000

RPM. The speed was controlled accurately by a variable voltage transformer. The

overall dimensions of the test stand are given in figure 17.

The rotor was mounted 0.8 m ahead of the wind tunnel supports to minimise any

interference effects between the rotor wake and the supports. This gave sufficient time

for the tip vortices in the wake to develop, become unstable and interact before

interference from the supports occurred.

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Figure 17 : Dimensioned diagram of the test rotor stand.

Figure 18 : Arrangement of smoke rake and test stand in wind tunnel.

3.1.3 Wind tunnel facilities

The experiments were carried out in the Department of Aeronautical Engineering's 7ft

x 5ft wind tunnel. It is a closed circuit tunnel operating at low speed, with atmospheric

pressure in the test section. For these experiments the normal closed test section wasremoved and the tunnel run in an open jet configuration, as shown in figure 18.

Introduction of the smoke into the flow was achieved by positioning the smoke rake

before the contraction region of the tunnel. This reduced any turbulence present as the

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smoke exited the rake. It was positioned vertically (figure 18), and facing downstream

towards the rotor. Its vertical position had to be altered every time the flow conditions

were changed. This allowed the smoke to highlight the tip and the trailing edge sheet

vortex.

3.1.4 Synchronisation equipment

Synchronisation of the blade cycle with the video recording camera was accomplished

using generally available electronic equipment. Figure 19 shows the layout of the test

stand and synchronisation equipment. To determine the rotational speed of the rotor, a

low intensity laser beam was aimed at a photoelectric cell. Its trajectory was close to the

rotor hub which had a small protruding arm parallel and offset from its rotational axis,

so that the beam could be interrupted once every revolution. Each interruption of the

beam caused the photoelectric cell to produce a step pulse which was transmitted to a

cathode-ray oscilloscope (CRO). The time between each pulse could be measured from

the CRO providing the rotational speed of the rotor. Also, the CRO was programmed

to produce a time delayed output signal which triggered the stroboscopic light source

at any intermediate azimuth angle for a complete revolution of the rotor. The flashes of

light produced by the stroboscopic unit were of high intensity and very short duration,less than 1/1000 of a second.th

The video camera used was a standard CCD model with reasonable low light level

recording capability and an effective shutter speed of about 1/25 of a second. Theth

combination of flash and shuttering speeds meant that the light sensitive elements of the

camera were illuminated for only a small fraction of the frame scan. The signal

amplitude was slightly low, but the frame was relatively free of the blurring that would

occur if a more intense strobe or continuous illumination was used.

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Figure 19 : Schematic diagram of the synchronisation equipment.

Figure 20 : Position of video camera in relation to

rotor.

3.2 EXPERIMENTAL PROCEDURE

Upon completion of the calibration process on the electronic flash equipment, the flow

visualisation and recording of the flow patterns was a reasonably simple procedure. The

most important step, however, was in the alignment of the video camera. It was locateda distance of 3 metres away from the rotor axis. It was set perpendicularly to the flow

direction and in the plane of the injected smoke (figure 20).

For each experiment, a calibration grid made of 30 mm squares was placed just behind

the rotor in the vertical plane passing through the rotor axis. The calibration grid was

recorded before and after each experiment was completed. Both records were used to

determine if the camera alignment had been altered during the experiment, and as a

position reference for the location of the vortex cores in the final processed images.

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Once the calibration grid was recorded, the rotor was set at the required rotational speed,

and when used, the wind tunnel was also set to the required speed. The smoke

streaklines were then introduced into the flow and illuminated by the synchronised

strobe light as they passed through or near the rotor. These illuminated flow patterns

were continuously recorded by the video camera.

Recordings were made at blade azimuth angle steps of between 10 and 15 for up to oneo o

full rotor revolution. At each azimuth setting the video recorded for an average of one

and a half minutes. This provided multiple frames of information for each required data

point and allowed the unsteady flow effects to be investigated and revealed in fine

detail.

3.3 DISCUSSION

The method of flow visualisation described in this chapter, although tedious and time

consuming, provided the most detailed information on the wake structure. When

reconstructing the axial and radial paths of the tip vortices, each vortex could be traced

back to the blade which generated it, thus enabling the path of each vortex to be

observed and studied individually, providing quantitative information on its oscillatorymotion, its instability, and its interactions with adjacent vortices.

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Chapter

FOUR

IMAGE PROCESSING

4.1 IMAGE DIGITISING

The recorded video images were played back through a standard video recorder and

appropriate frames were selected for processing. Individual frames were captured using

analog to digital conventional hardware connected to the serial port of a standard IBMcompatible personal computer.

The video digitising hardware was assembled locally within the Department of

Aeronautical Engineering and was based on a simple integrated circuit design (Circuit

Cellar Inc. 1987), using the CA3306 Flash A/D converter chip. The video signal was

scanned and its amplitude digitised to a stream of integer data. Each video frame

captured had a resolution of 256x244 picture elements (pels). Each element represented

a grey level with amplitudes in the range from 0 to 63. A sample digitised frame is

shown in figure 21. This equipment was chosen because of its simplicity and economy.

Once the digitised images had been transmitted to the computer they were stored as disk

files. A set of about 250 to 300 images were required to obtain an accurate vortex map

for a given rotor configuration. The first image processed was that of the reference grid.

A mapping was obtained between the grid points and the image picture elements. Using

this map, pel locations were translated into coordinate locations in the (YZ) vertical

plane passing through the axis of the rotor. The grid covering the whole video image

was mapped so that any picture distortions over the image area due to the camera or the

digitising process could be accounted for.

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Figure 21 : Digitised black and white video picture showing tip vortices,

vortex sheets and rotor blade.

4.2 IMAGE ENHANCEMENT

Several image processing techniques were applied to the captured video pictures in

order to enhance the images and thus more accurately locate the vortex cores. Several

initial methods used were based on edge detection filtering algorithms, such as that of

Seit et al(1988) and a much simpler outline algorithm described in the reference text

by Gonzales et al(1987). Using these processes, regions having a high intensity gradient

were brightened whereas regions of approximately constant amplitude were set to near

black. The result was typically an outline of the significant components contained within

the picture.

Because of the contrast between the dark vortex core and the bright smoke in the

rotating flow surrounding the core it was felt that the filtering technique would be most

appropriate. Pictures processed by this technique showed accurately the outline of the

rotor blade and the outlines of the smoke streaklines upstream of the rotor but were

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inconclusive in highlighting the vortex cores. In many cases only the initial blade tip

vortex could be seen with the successive helical spirals disappearing from the picture.

On closer examination of the video intensity levels near the vortices it was found that

the contrast between the core and the surrounding smoke rapidly diminished due to what

is assumed to be diffusion of smoke in the core.

A second processing technique was attempted by using false colour imaging of the

pictures. A computer program was written to convert the grey level image files into false

colour pictures (figure 22). The display hardware used on the computer was a Video

Graphics Array (VGA) so the limit of only 16 basic colours could be displayed.

However, by using the extra resolution of the VGA display (640x480), both VGA

display pages and a sequence of ditter patterns, it was possible to cover the range of 64

intensity levels within the original digitised frame.

Figure 22 : Digitised video picture with enhanced false colour imaging. Vortex

sheets, tip vortices and rotor blade easily identified.

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The screen images were further modified using the built-in hardware palette features of

the VGA display. The user could choose to have any one of the 16 screen colours

selected from a range of 64 RGB levels. In this way the smoke regions surrounding the

vortex cores were highlighted using false colour representation and thus the location of

the vortex was more easily distinguished.

Once the pattern of the circular vortex core had been recognised, its centroid position

was recorded as a row/column pel location and approximate diameter measured. Using

the digitised grid map the pel location was converted to a coordinate location (YZ) in

the plane perpendicular to the axis of the rotor. A single data point for the shed vortex

helix was obtained by combining the digitised coordinate location with the azimuth

angle for that particular frame. By superimposing all the vortex data points from one

frame with those of other frames recorded around a blade circuit, the path of each shed

vortex can be constructed in three dimensions.

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The axial flow speed relative to the lowest velocity coefficient value of 0.042 was8

2 m/s. Such a small axial velocity component would classify the rotor asexperiencing near pure hover conditions.

34

Chapter

FIVE

ROTOR WAKE GEOMETRIES

5.0 INTRODUCTION

The results obtained in this research were compared with the tip vortex path data

found in the work of Swanson et al(1992) and Bagai et al(1991, 1992-b). Blade tip

vortex axial and radial path data were plotted and compared with the paths generatedby the generalised vortex path equations of Landgrebe (1972) and Kocureket al

(1977). The paths which had evidence of vortex interaction were re-plotted with each

tip vortex marked; these were analysed and fitted with a mean path curve. The

meandering about this mean path was also plotted to determine the forms of

instability present.

5.1 WAKE RESULTS

Tip vortex path data for rotors in the hover regime was readily available from other

sources (Swanson et al1992, Bagai et al1992-b). For this reason experiments were

carried out with the rotor subjected to different rates of axial flow.

The hover tip vortex path data used came from the work of Bagai et al(1991, 1992-

b) and Swanson et al(1992). Most of their results had significant degrees of scatter

present to which the authors gave little significance. In wakes experiencing axial

flow, the tip vortex paths did not exhibit the scatter present in the hover wakes.

Hence experiments performed for this study were carried out at five different

vvelocity coefficients (C ), ranging from 0.042 to 0.18

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Table 2 : Rotor Test Parameters

v T TCase Figure C C C / Source

1 23 0.1 0.0018 0.012 Present Work

2 24 0.081 0.0042 0.027 Present Work 3 25 0.075 0.0048 0.031 Present Work

4 26 0.060 0.0063 0.041 Present Work

5 27 0.042 0.0078 0.051 Present Work

6 28 - 0.0074 0.08 Bagai et al(1992-b)

7 29 - 0.0113 0.099 Swanson et al(1992)

8 30 - 0.0167 0.146 Swanson et al(1992)

5.2 WAKE FEATURES

The tip vortex path data presented here show the important characteristics which the

equations formulated by Landgrebe (1972) and Kocureket al(1977) do not describe.

The most predominant feature can be observed in the wakes of rotors in pure hover.

The data of figures 27(b) through 30(b), representing the axial vortex paths, does not

in most cases follow the classical two sloped linear path. Instead, the axial vortex

path exhibited a smooth transition, from its trajectory immediately after being

generated to that after the following blade passed over it.

Once the vortex had passed its transition region, it maintained an almost constant

axial displacement rate for approximately 0.5 revolutions. Then the vortex could

follow one of two different axial paths, denoted by the forked shape of figures 27(b)

through 30(b). The significance of this was better understood when the paths of each

individual vortex filament was plotted (figures 31,32 and 33). These figures show

that as vortices are shed, they pair up with adjacent vortices and spin about a

common centre some distance between the two. As they move downstream, the

vortex cores move closer to each other, until they appear to both merge and diffuse.

In figures 31, 32 and 33, where this phenomenon can be observed, the axial paths

cross over each other approximately 1.13 and 1.33 revolutions after the vortex

formation.

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The tip vortex data reproduced from other sources (figures 28,29 & 30) did not

include the individual trajectories of each tip vortex produced by each rotor blade.

These vortex paths, however, behaved similarly to the vortex trajectory of the wake

with the lowest velocity coefficient (figure 27). The vortex path of figure 27 was

generated by combining the trajectories of all four vortices in the wake. To better

understand the behaviour of the wakes of the other researchers, a 'reverse' procedure

was performed on some of their data. The paths were very carefully studied and the

individual path of the three tip vortices of the wake of figure 30 were extracted and

re-plotted in figure 33. This figure shows the interaction between adjacent vortices.

In figure 33(b) the axial path of the vortex from blade 2 interacts with that of blade 3.

However at different times the vortex from blade 3 may interact with that of blade 1,

and that the vortex from blade 1 may interact with that of blade 2. Although it was

impossible to identify which blade generated each vortex, the selected arrangement

indicated that the axial crossing of the vortices generated by blades 2 and 3 occurred

after approximately 1.2 revolution in very good agreement with the experimental

results of this study.

In the work of Gray (1992), Landgrebe (1972) and Kocureket al(977), the radial

paths appeared to possess only smoothly defined trajectories. The hover tip vortexpaths presented here, however, enclosed a region formed approximately 0.75

revolutions after the vortex formation. When each individual radial vortex path was

plotted (figures 32(a), 33(a)), adjacent vortices crossed over each other between 0.67

and 0.75 revolutions after being formed, approximately half the time taken for the

axial paths to cross over. This is indicative of the spin rate of the two entrapped

vortices. On more careful examination of figure 31(a), the rate of spin diminished as

the vortices moved closer together and further downstream. This is verified by the

next vortex radial cross-over which occurred between 0.88 and 1.08 revolutions after

the first crossing, alternatively, the spin rate has slowed down by between 35% and

44%. The reason for such a reduction in rotational speed is not known, but a

proposed cause might be that as vortices become entrapped in each other's field, their

strength and similar rotational sense produce a detrimental interaction , causing them

to loose strength and diffuse.

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When the tip vortices were subjected to axial flow (figures 23 through 26), both the

radial and axial paths were significantly changed. The two-gradient axial trajectories

vanished and were replaced by a single path of almost constant gradient, but far

greater than those predicted by the equations of Landgrebe (1972) and Kocureket al

(1977). Such a change in the axial path was expected as the vortices experience axial

flow which carries them downstream at a constant speed, with a stabilising effect on

the wake structure.

The radial vortex paths are also significantly affected by the axial flow. Figures 23(a)

through 26(a), show that the vortices follow the general trajectory predicted by the

generalised equations for 0.125 revolutions after being formed, then the vortex

becomes affected by the axial flow and the radial paths are diverted away from its

predicted path. They become more linear, with a very small contraction gradient

which appeared to be dependent in the velocity and thrust coefficients. These paths

no longer cross over one another and are very stable, with a considerable less scatter

of points than in the pure hover case.

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Figure 23(b) : Comparison between experimental and predicted wake

geometries; (a) radial, (b) axial.

Figure 23(a)

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Figure 24(a)

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Figure 25(a)

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Figure 26(a)

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Figure 27(a)

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Figure 28(b) : Comparison between the experimental wake of Bagai et al

(1992-b) and predicted wake geometries; (a) radial, (b) axial.

Figure 28(a)

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Figure 29(b) : Comparison between the experimental wake of Swanson et al

(1992) and predicted wake geometry; (a) radial, (b) axial.

Figure 29(a)

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Figure 30(b) : Comparison between the experimental wake of Swanson et al

(1992) and predicted wake geometry; (a) radial, (b) axial

Figure 30(a)

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Figure 31(b) : Individual vortex trajectories of the four vortices from the wake

of figure 27.

Figure 31(a)

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Figure 32(b) : Individual vortex trajectories of the two vortices from the wake

of figure 28.

Figure 32(a)

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Figure 33(b) : Individual vortex trajectories of the three vortices from the wake

of figure 30.

Figure 33(a)

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5.3 WAKE INSTABILITIES

The presence of instabilities in rotor wakes have always been known to exist. In the

work of Landgrebe (1972), Gray (1956), Kocureket al(1977), Swanson et al(1992)

and Bagai et al(1992-b), these instabilities had been revealed by the visualisation

methods employed, and appeared to be related to the rotor's thrust. However, no

detailed experimental analysis appeared to have been done which attempted to

explain the causes and modes of these instabilities.

Theoretical studies have, however, been carried out on the stability of curved,

(Betchov 1965), and helical, (Widnall 1972), vortex filaments. The analysis of

Betchov (1965) showed that helical vortex filaments were unstable for perturbation

wavelengths longer than 2 times the local radius of curvature of the unperturbed

filament and stable for shorter waves. The work of Widnall (1972) verified this mode

of instability, but in performing a more thorough study of helical vortex wakes,

discovered two additional modes influenced by the entire vortex filament.

The investigation performed by Widnall (1972) on the stability of a helical vortexfilament following small sinusoidal displacements of its centre-line, consisted of

evaluating the self-induced velocities at the filament due to these perturbations.

These were then used kinematically to determine the resulting motion of the filament

and thus the growth rate of the perturbations. The results obtained showed three

distinct types of instabilities present in helical vortex filaments:

(1) Short-Wave Instability, where the number of oscillatory waves percycle (/k') is very high.

(2) Mutual-Inductance or Low-Wave Number Instability, where the

number of oscillatory waves per cycle are less than the pitch of the

helix (kR).

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(3) Long-Wave Instability, where successive turns of the vortex pass

within the distance of one radius from each other, ie: where the pitch

3of the helix is greater than or equal to 3 / .1

A sketch of the typical mode shapes for the various instabilities is given in figure 34,

2showing the short-wave instability, the mutual-inductance modes with /k' = / and5

2 2/ , and the long-wave instability with /k' = / . With the mutual-inductance3 1

instability the neighbouring filaments attempt to roll-up around one another in much

the same way as hovering rotor vortices do.

Figure 34 : Instability mode shapes; the short-wave instability, the

2 2mutual-inductance modes with /k' = / and / , and the5 3

2long-wave instability with /k' = / . The dark portions are1

outside the cylinder on the near side; the light portions are

inside. Reproduced from Widnall (1972).

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From his analysis, Widnall (1972) was able to obtain stability boundaries as function

vof helix pitch (kR), number of waves per cycle (/k') and vortex core radius (r /R).

These results for various core size ratios can be seen in figure 35. The general trends

for the stability boundary for a given core size were determined by Widnall (1972) to

be as follows:

For kR below some critical value two instability modes are present, the

Short-Wave mode and the Local-Induction instability; with increasing kR

(decreasing pitch), the Mutual-Inductance modes become unstable; with

further increases in kR the Mutual-Inductance modes merge and the helix is

unstable for almost all wavelengths. It is always stable for /k'/ 1 and there

is an upper boundary for the short-wave instability for any vortex core size.

In the limit of very, very small core sizes, wave numbers smaller than the

local circumference are unstable.

Figure 35 : Stability boundaries for helical vortex filaments of finite core. The

value of the ratio of core-to-cylinder radius are shown on each curve.

Above the boundary, the helical filament of that core size is unstable.

Reproduced from Widnall (1972).

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These statements imply that irrespective of vortex core size or helix pitch, helical

vortices are inherently unstable, the mode of instability dependent on the form of the

disturbance applied and on the helix's own structure. In relating these instability

criterion to rotor wakes, the following criterion for vortex stability were suggested:

(1) All rotor wakes in the hover or climb regime experience some sort of

tip vortex instability.

(2) Although in the work of Betchov (1965) and Widnall (1972),

damping effects were not accounted for, wakes experiencing Short-

Wake, Mutual-Inductance and Long-Wave instabilities, may beaffected by fluid damping to the extent of having the instabilities

suppressed completely or maintained but in a quasi-stable state.

(3) Increases in rotor thrust have been proven by Swanson et al(1992), to

cause the tip vortex core size to increase significantly, whilst having

comparatively small effects on the pitch of the helix. This means that

a wake with vortices in a quasi-stable state could become unstable

when the thrust is increased.

(4) Rotors producing high thrust have large vortex core sizes which result

in Mutual-Inductance instabilities becoming predominant, causing

adjacent vortices to pair up and spin together.

(5) Very heavily loaded rotors have completely unstable wakes with all

modes of instabilities present.

(6) The growth in size of the vortex core as it travels downstream has

been shown by the work of Thomson (1988) and Swanson et al1992.

This means that vortices formed under quasi-steady conditions could

become unstable and diffuse as they move further downstream.

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(1)

(7) Helical vortices excited with a perturbation occurring once per cycle

(/k' / 1) are inherently stable. It is therefore apparent that single

bladed rotors, which have a Mutual-Inductance induced disturbance

of once per revolution, should have very stable wakes. The

experimental results of Gray (1972) on single bladed rotors, show that

the axial and radial paths were very smooth and suffer from no major

2oscillatory motions, existing for over 3 / revolutions, far more than1

in any multi-bladed rotor.

5.4 GENERALISED WAKE THEORY

When observing figures 23 through 30, it become obvious that the semi-empirical

equations of Landgrebe (1972) and Kocureket al(1977) are in most instances unable

to accurately predict the vortex path. For these reasons one of the major tasks of this

research has been to identify equations which could better represent the mean vortex

path.

This research did not at any stage attempt to define generalised equations for

different rotor characteristics or working conditions. Such a task would require

extensive research, and facilities not available to the author. Instead, the forms of

these equations has been identified.

5.4.1 Tip vortex mean axial path equation

The vortex axial path equations in current use are:

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(2)

(3)

for Landgrebe's model:

for Kocurek's model:

where:

These equations have provided very good linear approximations for the axial vortex tip

path. However, they over simplify the complex nature of the vortex trajectory, because:

(1) They assume the vortex axial path to be linear.

(2) They imply that the rate of change of the gradient along the vortex path

to be zero everywhere, except where the following blade passes over it.

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(4)

(5)

At such a time and for an infinitesimal amount of time it has a positive

value.

(3) They assume the vortices to have no instabilities or fluctuations about

their mean path.

(4) They do not account for vortices pairing up and spinning.

For this reason, it became necessary to find new semi-empirical equations which could

better represent the vortex axial path. The characteristics of such a path were discovered

to be better modelled by exponential equations. The two forms selected were:

where:

= Wake Azimuth angle relative to blade (Radians)

= Function Ln(+1),1 was added to the angle to accommodate for = 0r

A,B,C,.. = Constants determined using the least squares method.

To determine the coefficients A,B,C,..., etc., the least squares method was used . It is

envisaged that when sufficient wake vortex data becomes available, general equations

accommodating all rotor characteristics and flight conditions may be derived.

When these equations were compared with the experimental axial vortex path, equation (5)

provided the better approximation to the mean path. The reason for this was that it

required two to three terms less than equation (4), providing a smoother mean axial vortex

path rather than an equation which tried to follow every data point.

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In pure hover conditions, the axial paths of the tip vortices cross over each other. Hence

two equations representing the wake may be required for each set of rotor parameters.

These coalesce into one curve, as axial flow is introduced into the flow.

The maximum number of terms necessary to provide a reasonable mean path using

equation (5) has been determined to be between three and five. Typical values of these can

be seen in the figures of the following section.

5.4.2 Axial path instability criterion

Each of the wakes listed in table 2 have been individually analysed to determine theinstabilities in the axial path of the vortices and how these became affected by the

introduction of axial flow. The individual vortex filaments of each wake were fitted with

their mean path curve, followed by a plot of the meandering about their mean path. This

was defined as the ratio between the difference of the actual axial vortex position and the

mean axial path to the rotor radius, plotted as a function of the azimuth angle. Due to the

large number of filaments produced, only one from each wake has been reproduced in the

following figures. These include the axial vortex path data, the mean path curve, the

coefficients of the equation, and the meandering about the mean path.

The important trends to observe in these figures is the meandering. From the analogies

described in section 5.3 of this presentation, the axial paths show evidence of Short-Wave,

Mutual-Inductance and Long-Wave instabilities. Figure 41(b) shows the once-per-blade

passage excitation induced by the forming vortex, clearly indicating the Mutual-Inductance

effect. Figures 36(b) through 40(b) show more clearly the Short-Wave instability which in

most instances appears to grow as the vortex moves downstream. Mutual-Inductance and

Long-Wave instability can also be seen. Both forms of instability appear to become much

more erratic after the vortex has been in existence for more than 1.25 revolutions. As the

axial flow is increased, the Short-Wave instabilities become affected by the fluid's

damping, leaving the Mutual-Inductance instability prominent, although also affected by

the damping.

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Figure 36(a) : Axial wake geometry and mean axial path.

Figure 36(b) : Meander of vortex about mean axial path.

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(6)

(7)

(8)

(9)

(10)

5.4.3 Tip vortex mean radial path equation

The tip vortex mean radial path equations in current use are:

for Landgrebe's model:

for Kocurek's model:

These equations, although providing a good first order exponential approximation to the

radial paths of the vortex filaments, did not model some of the important characteristics of

the vortex radial path, such as:

(1) The unstable path of the radial vortex path.

(2) The interactions and pairing between adjacent vortices.

(3) The trajectories of each individual blade tip vortex.

(4) The effect of induced axial flow in the wake to the radial vortex path.

In selecting the equation which could better represent the radial vortex path, exponential

equations were the better suited. The two forms selected were:

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where:

= Wake Azimuth angle relative to blade (Radians)

= Function Ln(+1), 1 was added to the angle to accommodate = 0r

A,B,C,.. = Constants determined using the least squares method.

As for the axial equations it is hoped that the coefficients may in future be determined as

functions of rotor parameters and flying conditions. However for the present work the least

squares method was used to find the mean path for each individual vortex filament. The

form of the exponential equation chosen was equation (10), requiring only two or three

terms to give the smoothest mean path, compared with equation (9) which required five tosix terms.

5.4.4 Radial path instability criterion

As for the axial component of the path, all vortex filaments for each of the wakes listed in

table 2 were analysed and only one from each wake was included in the figures which

follow. These figures contained the radial vortex path, the mean radial path curve and

equation, and their meander about the mean path. As before the meander was defined as the

ratio between the difference of the actual radial vortex position and the mean radial path to

the rotor radius, plotted as a function of azimuth angle.

The behaviour of the vortices radially shows evidence of all three types of instabilities.

Long-Wave instabilities could observed in figures 31(a) through 33(a), where adjacent

vortex filaments interact and spin about one another.

When the meandering about the mean path was studied, both Short -Wake and Mutual-

Inductance were observed to be present. However, the Mutual-Inductance appeared to be

heavily damped. The Short-Wave instability was also damped but maintained in an almost

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