Flow over macroscopic hexagonal structured surfaces. Experimental Investigation

Abbildungsverzeichnis

Fig 1: Various aspects and areas of investigations on a way to their application

Fig 2: Classification of methods of bluff-body drag reduction

Fig 3: Flow over a smooth and a golf ball

Fig 4: Distribution of drag on an aircraft wing, from Ref [14], used by permission

Fig 5: Classification of methods of reducing Skin-drag, from Ref [14], used by permission

Fig 6: Flow around a bluff body

Fig 7: Reversed flow in presence of adverse pressure gradient, from Ref [70], used by permission

Fig 8: separated flow over airfoil, by Ref [71] used by permission

Fig 9: Schematic diagram of the flow over flat plate

Fig 10: Drag coefficient for smooth, dimpled, and roughened cylinders: smooth [28]; dimpled (k/d=9x10^-3) [29];Sand roughened (k/d=9x10^-3, 4.5x10^-3) [25].  Here k is the height of roughness or depth of dimples, by Ref [8], used by permission

Fig 11: Variation of Strouhal number against Re for smooth and dimpled cylinder, by Ref [8], used by permission

Fig 12: Wind tunnel at Institute of Internal combustion and aero engines

Fig 13: Turbulence intensity along z-axis

Fig 14: Turbulence intensity along y-axis

Fig 15: Nut and bolt mechanism to vary the diameter of the cylindrical holder

Fig 16-a: Experimental setup for the determination of drag acting on the cylinder front view (top), side view (bottom)

Fig 16-b: Experimental setup for the determination of drag acting on the cylinder front view (top), side view (bottom)

Fig 17: Drag coefficient of cylinder vs Reynolds number, by Ref [72], used by permission

Fig 18: Experimental setup for the determination of drag of a structured plate

Fig 19: Pressure variation along the test plate

Fig 20: Experimental setup for determining the efficiency of the Turbine

Fig 21: Structures plates with four different orientations 0° and 90°(left), outwardly curved and inwardly curved (right)

Fig 22: Structured cylinders

Fig 23: Definitions of various angles in a velocity triangle, v_r = relative velocity, v = absolute velocity, ζ = blade angle with relative flow velocity, ω = angular velocity, r = radius, v_f = flow velocity, by Ref [72], used by permission

Fig 24: Turbine blades

Fig 25: Setup for smoke flow visualization

Fig 26: Setup for oil film interferometric visualization (left), typical fringe patterns evolution from oil film light reflections (right), by Ref [73], used by permission

Fig 27: Positioning of hot-wire probe near the surface by using mirror-image technique

Fig 28: Schematic of oil film interferometry, by Ref [74] used by permission

Fig 29: Fringe image on a flat test plate

Fig 30: Fringe image (top), intensity and spectral density curves (PSD) (bottom)

Fig 31: Temperature dependence of the viscosity of silicon oil

Fig 32: drag coefficients vs Reynolds Numbers: hexagonal patterns (k/d=1.98 x 10^-2), here k is the depth of hexagonal pattern

Fig 33: Variation of Mean velocity profiles behind the cylinders for Re=2.3x10⁵

Fig 34: Variation of rms velocity profiles behind the cylinders for Re=2.3x10⁵

Fig 35-a: location of separation points on structured cylinders

Fig 35-b: location of separation points on structured cylinders

Fig 35-c: location of separation points on structured cylinders

Fig 35-d: location of separation points on structured cylinders

Fig 35-d: location of separation points on structured cylinders

Fig 36: Surface oil film patterns on structured cylinders

Fig 37: Measurement locations on patterns

Fig 38-a: Profiles of the mean velocity and r.m.s velocity above configurations O90 (a) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 38-b: Profiles of the mean velocity and r.m.s velocity above configurations O90 (b) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 38-c: Profiles of the mean velocity and r.m.s velocity above configurations O0 (a) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 38-d: Profiles of the mean velocity and r.m.s velocity above configurations O0 (b) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 38-e: Profiles of the mean velocity and r.m.s velocity above configurations I0 (a) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 38-f: Profiles of the mean velocity and r.m.s velocity above configurations I0 (b) for Re = 2.3x10⁵, r/s=radialposition/pattern height

Fig 39: Flow separation indicated by a zig zag line on O90

Fig 40-a: Energy spectra of the flow over O90.a before (70°) and after partial separation (100°) atRe = 2.3x10⁵

Fig 40-b: Energy spectra of the flow over O90.b before (70°) and after partial separation (100°) atRe = 2.3x10⁵

Fig 40-c: Energy spectra of the flow over O0.a before (70°) and after partial separation (100°) atRe = 2.3x10⁵

Fig 40-d: Energy spectra of the flow over O0.b before (70°) and after partial separation (100°) atRe = 2.3x10⁵

Fig 41-a: Power spectrum of the flow over S at four different Reynolds numbers, (PSD = Power Spectral Density)

Fig 41-b: Power spectrum of the flow over O90 at four different Reynolds numbers, (PSD = Power Spectral Density)

Fig 41-c: Power spectrum of the flow over O0 at four different Reynolds numbers, (PSD = Power Spectral Density)

Fig 41-d: Power spectrum of the flow over I90 at four different Reynolds numbers, (PSD = Power Spectral Density)

Fig 41-e: Power spectrum of the flow over I0 at four different Reynolds numbers, (PSD = Power Spectral Density)

Fig 42:Strouhal number vs Reynolds number for investigated cylinders

Fig 43-a: Dimensionless mean velocity profiles at front of the test plate for the Reynolds number Re_x= 5.34 x 10⁵

Fig 43-b: Dimensionless mean velocity profiles at rear of the test plate for the Reynolds number Re_x= 7.99 x 10⁶

Fig 43-c: Dimensionless mean velocity profiles at front of the test plate for the Reynolds number Re_x= 6.7 x 10⁵

Fig 43-c: Dimensionless mean velocity profiles at Rear of the test plate for the Reynolds number Re_x= 10.04 x 10⁶

Fig 43-d: Dimensionless mean velocity profiles at Front of the test plate for the Reynolds number Re_x= 7.54 x 10⁵

Fig 43-e: dimensionless mean velocity profiles at rear of the test plate for the Reynolds number Re_x= 11.27 x 10⁶(Rear)

Fig 44-a: Dimensionless r.m.s velocity profiles at front of the test plate for the Reynolds number Re_x = 5.34 x 10⁵

Fig 44-b: Dimensionless r.m.s velocity profiles at rear of the test plate for the Reynolds number Re_x = 7.99 x 10⁶

Fig 44-c: Dimensionless r.m.s velocity profiles at front of the test plate for the Reynolds number Re_x = 6.7 x 10⁵

Fig 44-d: Dimensionless r.m.s velocity profiles at rear of the test plate for the Reynolds number Re_x = 10.04 x 10⁶

Fig 44-e: Dimensionless r.m.s velocity profiles at front of the test plate for the Reynolds number Re_x = 7.54 x 10⁵

Fig 44-f: Dimensionless r.m.s velocity profiles at rear of the test plate for the Reynolds number Re_x= 11.27 x 10⁶

Fig 45: Shear stress coefficient at the rear of the plates vs configurations obtained by Clauser chart method (left) and Oil film interferometry (right)

Fig 46: Momentum thickness at the rear of the test plates vs configurations behind the structured plates

Fig 47: Measurement locations, flow from right to left

Fig 48-a: measured velocity profiles fitted into the logarithmic law for the determination of uτover I0

Fig 48-b: measured velocity profiles fitted into the logarithmic law for the determination of uτover I90

Fig 49-a: Displacement thickness vs upstream distance (left), Momentum thickness vs upstream distance (right) over S

Fig 49-b: Displacement thickness vs upstream distance (left), Momentum thickness vs upstream distance (right) over O0

Fig 49-c: Displacement thickness vs upstream distance (left), Momentum thickness vs upstream distance (right) over O90

Fig 49-d: Displacement thickness vs upstream distance (left), Momentum thickness vs upstream distance (right) over I90

Fig 49-e: Displacement thickness vs upstream distance (left), Momentum thickness vs upstream distance (right) over I0

Fig 50-a: Velocity fluctuations over smooth surface at location ‘b’for velocities 19, 24 and 27m/s

Fig 50-b: Velocity fluctuations over smooth surface at location ‘c’for velocities 19, 24 and 27m/s

Fig 50-c: Velocity fluctuations over smooth surface at location ‘d’for velocities 19, 24 and 27m/s

Fig 51-a: Velocity fluctuations over O0 surface at location ‘b’for velocities 19, 24 and 27m/s

Fig 51-b: Velocity fluctuations over O0 surface at location ‘c’for velocities 19, 24 and 27m/s

Fig 51-c: Velocity fluctuations over O0 at location ‘d’ and velocities 19, 24, 27m/s

Fig 52-a: Velocity fluctuations over O90 at location ‘b’ and velocities 19, 24, 27m/s

Fig 52-b: Velocity fluctuations over O90 at location ‘c’ and velocities 19, 24, 27m/s

Fig 52-c: Velocity fluctuations over O90 at location ‘d’ and velocities 19, 24, 27m/s

Fig 53-a: Velocity fluctuations over I0 at location ‘b’ and velocities 19, 24, 27m/s

Fig 53-b: Velocity fluctuations over I0 at location ‘c’ and velocities 19, 24, 27m/s

Fig 53-c: Velocity fluctuations over I0 at location ‘d’ and velocities 19, 24, 27m/s

Fig 54-a: Velocity fluctuations over I0 at location ‘b’ and velocities 19, 24, 27m/s

Fig 54-b: Velocity fluctuations over I0 at location ‘c’ and velocities 19, 24, 27m/s

Fig 54-c: Velocity fluctuations over I0 at location ‘d’ and velocities 19, 24, 27m/s

Fig 55: Power Spectral Density (PSD) of the flow over O0 vs frequencies at 24 m/s

Fig 56: Power Spectral Density (PSD) of the flow over O90 vs frequencies at 24 m/s

Fig 57: Power Spectral Density (PSD) of the flow over I90 vs frequencies at 24 m/s

Fig 58: Power Spectral Density (PSD) of the flow over I0 vs frequencies at 24 m/s

Fig 59: Fringe images over O90

Fig 60: Fringe images over O0

Fig 61: Fringe images over I0

Fig 62: Fringe images over I90

Fig 63: Pressure holes for pressure measurement, flow direction from right to left

Fig 64: Pressure distribution over O0

Fig 65: Pressure distribution over O90

Fig 66: Pressure distribution over I0

Fig 67: Pressure distribution over I90

Fig 68: Efficiencies vs rpm for θ = 60° and vf = 6 m/s, ♦ smooth blades, ■ structured blades

Fig 69: Efficiencies vs rpm for θ = 60° and v_f = 9 m/s, ♦ smooth blades,■structured blades

Fig 70: Efficiencies vs rpm for θ = 60° and v_f = 12 m/s, ♦ smooth blades, ■ structured blades

Fig 71: Efficiencies vs rpm for θ = 60° and v_f = 15 m/s, ♦ smooth blades, ■ structured blades

Fig 72: Efficiencies vs rpm for θ = 60° and v_f = 18 m/s, ♦ smooth blades, ■ structured blades

The maximum efficiency is again delivered at an rpm of about 64% of the maximum (rpm at which the turbine is spinning without any load applied on it) possible revolution per minute. The operating point (point of maximum efficiency) remains independent of the blade incident angle as well as the surface finishing of the blades. The maximum efficiency achieved by a particular configuration seems also not be affected by the hexagonal structures or variation in the mean stream velocity. The only dependency of the efficiency in this case has been the blade incident angle θ.

Fig 73: Efficiencies vs rpm for θ = 40° and v_f = 6 m/s, ♦ smooth blades, ■ structured blades

Fig 74: Efficiencies vs rpm for θ = 40° and v_f = 9 m/s, ♦ smooth blades, ■ structured blades

Fig 75: Efficiencies vs rpm for θ = 40° and v_f = 12 m/s, ♦ smooth blades, ■ structured blades

Fig 76: Efficiencies vs rpm for θ = 40° and v_f = 15 m/s, ♦ smooth blades, ■ structured blades

Fig 77: Efficiencies vs rpm for θ = 40° and v_f = 18 m/s, ♦ smooth blades, ■ structured blades

Fig 78: Efficiencies vs rpm for θ = 20° and v_f = 6 m/s, ♦ smooth blades, ■ structured blades

Fig 79: Efficiencies vs rpm for θ = 20° and v_f = 9 m/s, ♦ smooth blades, ■ structured blades

Fig 80: Efficiencies vs rpm for θ = 20° and v_f = 12 m/s, ♦ smooth blades, ■ structured blades

Fig 81: Efficiencies vs rpm for θ = 20° and v_f = 15 m/s, ♦ smooth blades, ■ structured blades

Fig 82: Efficiencies vs rpm for θ = 20° and v_f = 18 m/s, ♦ smooth blades, ■ structured blades

Fig 83: Efficiencies vs rpm for θ = 10° and v_f = 6 m/s, ♦ smooth blades, ■ structured blades

Fig 84: Efficiencies vs rpm for θ = 10° and v_f = 9 m/s, ♦ smooth blades, ■ structured blades

Fig 85: Efficiencies vs rpm for θ = 10° and v_f = 12 m/s, ♦ smooth blades, ■ structured blades

Fig 86: Efficiencies vs rpm for θ = 10° and v_f = 15 m/s, ♦ smooth blades, ■ structured blades

Tabellenverzeichnis

Table1: Properties of the configurations of structured cylinders

Table2: Properties of the configurations of structured plates

Table3: Configurations of investigated blades

Tabel4: Boundary layer quantities at front and rear of the test plates with the help of Oil film Interferometry (OFI) and Clauser chart method (CL)

Table5: Global skin friction coefficient C_F for all the investigated configurations

Table6: Shear stress velocities on individual hexagonal structures using oil film interferometry

Abstract

The flow over macroscopicpatterned/structured surfaceswas investigated in a subsonic wind tunnel over Reynolds numbers ranging from 3.14x10⁴ to 2.77x10⁵for cylinders and from 5.34 x 10⁵ to 11.27 x 10⁶ for plates. The investigations were accomplished by measuring local and global drag,velocity profiles and by visualization of the flow above the surface. The investigations on structured cylinders revealed that a cylinder with outwardly curved structures has a drag coefficient of about 0.65 times of a smooth one. Flow visualization was carried out by using oil-film technique and velocity profile measurements to elucidate the observed effect, and hence present the mechanism responsible for theobserved drag reduction. The near-wall velocity profiles above the surface revealed that a hexagonal bump induces local separation generating large turbulence intensity along the separating shear layer. Due to this increased turbulence, the flow reattaches to the surface with a higher momentum and become able to withstand the pressure gradient delaying the main separation significantly. Besides that, the separation does not appear to occur in a straight line along the length of the cylinder, but follow the curved path forming a wave with its crest at 115° and trough at 110°, in contrast to the laminar separation line at 85° on a smooth cylinder. Investigations on structured plates were performed with the help of hot wire anemometry and oil film interferometry. The main concern of the experiments on structured plateswas to examine the effect of hexagonal structures on local and global drag of a structured plate. It was accomplished by determining and analyzing the boundary layer quantities like shear stress velocities, shear stress coefficients and momentum thicknesses over a selected Reynolds number range and various locations in streamwise direction. The results indicate that the values of shear stress coefficients measured by the conventional Clauser chart method are up to 13% higher than the ones deduced by the Oil film Interferometry. Additionally, a maximum of 19% reduction in shear stress coefficient behind the inwardly curved structured plate was observed. On the other hand, a dramatic increase of about 120% in global drag coefficient supersedes the observed reduction in shear stresses at rear of the test plates. Investigations on individual hexagonal structures by measuring the shear stresses and the pressure distribution above the surface revealed that an uneven pressure distribution contributing in total drag force is responsible for a huge increase in global skin drag coefficient. Finally, a number of configurations of a wind turbine made of smooth and structured blades were investigated to compare their efficiencies at various flow velocities. No significant deviation in the efficiencies was observed.

Key words: Aerodynamics, Oil film Interferometry, Drag reduction, Hot wire Anemometry

Kurzfassung

Im Rahmen dieser Arbeit, wurde die Strömung über makroskopisch strukturierten Oberflächen in einem Unterschall-Windkanal untersucht. Die Untersuchungen erfolgten bei Reynolds-Zahlen von 3.14x10⁴ bis 2.77x10⁵ für Zylinder und von 5.34 x 10⁵ bis 11.27 x 10⁶  für Platten.Weiterhin wurden Messungenlokaler undglobaler Widerstände, von Strömungsvisualisierungen undGeschwindigkeitsprofilen durchgeführt. Das Ziel der Untersuchungen an Zylindern war,denEinfluss dieser Strukturen auf die Strömungsgrössen wie Druckwiderstand und Wirbelablösefrequenzen  zu ermitteln. Die Untersuchungen zeigten, dass der strukturierte Zylinder mit nachaußen gewölbten Strukturen einen Widerstandkoeffizient mit einem Faktor von 0,65 dem eines glatten Zylinders aufweist. Messungen wurden durchgeführt mitder Öl-filmMethodeundderHitzdrahtAnemometrie.Die Geschwindigkeitsprofile in der Nähe der Wand zeigten, dass eine Hexagonal Struktureine lokale Ablösung verursacht und dadurch die Turbulenz in der Grenzschicht erhöht. Aufgrund des erhöhten Turbulenzgrades legt sich die Strömung mit einemhöheren Impuls an die Oberfläche an und ist somit fähig einennegativen Druckgradienten zu überstehen. Als Folge ist die Hauptablösung deutlich verzögert. Außerdem findet die Ablösung nicht linear und senkrecht zur Strömung statt, sondern in Form einer Welle mit ihremMaximum bei 115° und Minimum bei 110°.Dies steht im Gegensatz zu der laminaren Ablöselinie bei 85° für glatte Zylinder. Die strukturiertenPlatten wurden ebenfalls mit derHitzdrahtAnemometrie und der Öl-FilmInterferometry untersucht. Das Zielbei diesen Untersuchungen war esden Einfluss von hexagonalen Strukturen auf den lokalen und globalen Widerstand einer strukturierten Platte zu ermitteln. Über die Clauser-Chartmethodebestimmte Scherspannungen sind etwa 13% höher als die mit der Öl-FilmInterferometry ermittelten Werte. Zudem wurde eine Minderung von ca. 19% der Scherspannung hinter einer strukturierten Platte festgestellt. Der globale Widerstand der gesamten Platte steigtgleichzeitig dramatisch um 120%. Durch Messen der Scherspannung und der Druckverteilung über den individuellenStrukturenist festgestellt worden, dass die unregelmäßige Druckverteilungeinen zusätzlichen Druckwiderstand  erzeugt und für die enorme Vergrößerung des globalen Widerstandes verantwortlich ist. Letztendlich, wurde eine Vielzahl an Konfigurationen einer aus flachen als auch strukturierten Schaufeln gefertigten Windturbine bei unterschiedlichen Strömungsgeschwindigkeiten untersucht. Es konnte keine deutliche Änderung im Wirkungsgrad der Turbine aus strukturierten Schaufeln festgestellt werden.

Schlagwörter: Aerodynamik, Öl film Interferometrie, Widerstandsreduzierung, Hitz-draht Anemometrie

Symbols &Abbreviations

τ_w Shear stress

u_τ shear stress velocity

κ Von Ka’rma’n constant

ρ Density ofthe fluid

B logarithmic law constant

ν Kinematic viscosity

y Vertical distance

u Instantaneousvelocity

U_∞ Free stream Velocity

C_f Shear stress coefficient (local skin drag coefficient)

R Drag force

C_F Global drag coefficient of a plate

C_d Drag coefficient of a cylinder

p Local pressure

p₀ Pressure in undisturbed medium

b Width of the plate

l length of the plate

δ Boundary layer thickness

δ₁ Displacement thickness

δ₂ Momentum thickness

x Horizontal distance

Re Diameter based Reynolds number

D Diameter of the cylinder

y⁺ Dimensionless vertical distance

u⁺ Dimensionlessvelocity

Re_δ Reynolds number based on boundary layer thickness

v Instantaneous velocity

θ Angle of incidence of the turbine blade

v_r relative velocity

v_f flow velocity

r radius

O0 Configuration with outwardly curved structures at 0°

O90 Configuration with outwardly curved structures at 90°

I0 Configuration with inwardly curved structures at 0°

I90 Configuration with inwardly curved structures at 90°

U_max Maximum velocity

S Configuration with smooth surface

k Depth of the hexagonal structures

d Equivelent diameter of the hexagonal structures

u´, u_rms Fluctuating velocity

u_eff Effective velocity

φ Incident angle of the camera with vertical

r.m.s Root mean square

Investigation and Optimization of the flow over macroscopic hexagonal structured surfaces

Introduction

1.1            Motivation

The structured pre-products carry a huge potential to serve as raw material for the building blocks, especially in automotive industry, Railways and Aerospace due to their known advantages like high quality functional properties and light weight. For an efficient economic use of structured sheets, development of a comprehensive database of technological properties, processing techniques, design criteria’s and mastering of production and logistic processesis required. Currently, this data is not available due to lack of trained engineers in this field. To achieve the above mentioned goal, a state financed Graduate class named ‘Destrukt’ was established. The graduate class was divided into 9 different disciplines to investigate the various aspects of structured sheets as following.

Fig 1: Various aspects and areas of investigations on a way to their application

To examine the possible application of structured sheets in aerospace industry, aerodynamic properties of structured plates must be investigated. This dissertation deals with the various aspects of such investigations such as the pressure drag, skin drag,vortex shedding and boundary layer. One of the crucial and most important concerns of aerospace industry is the drag. A significant drag reduction results in a reduced fuel consumption and hence a lower operating cost and a higher efficiency. Numerous ways have been developed by the researchers and the designers in last decades to reduce the drag of flying bodies. The very first ways were to streamline the bodies as much as possible. The essence of this approach is to prolong the laminar flow regime on the surface. However, for very high Reynolds numbers such as in a flight of a conventional transport aircraft, in order of 10⁸, it seems doubtful that an economical method for maintaining the laminar flow regime can be developed under these conditions. Similarly, drag reduction for bluff bodies, which is of great importance especially in sports and automotive industry, requires other ways to achieve the desired goals as these are not to be streamlined. The major drag reduction methods for a bluff body can be segmented into four different categories (Fig. 2). It should be noted that all the methods considered here assume that the boundary layer be attached up to the rear separation point occurring at the contour of the body base. This obviously implies that the shape of the front part of the body be such that no global boundary layer separations occur (no sharp edges);

Fig 2: Classification of methods of bluff-body drag reduction

Applying Dimples on a golf ball, first investigated by Davis [1], is a practical example of manipulation of boundary layer conditions. The dimples on the surface of the ball turn thelaminar boundary layer into turbulent, increase its thicknessand delay the separation of the flow from the surface. Thisreduces the pressure difference in the upstream and the downstream direction and hence the drag actingon the ball (Fig. 3).

Fig 3: Flow over a smooth and a golf ball

Several other methods, which mostly fall in the same category,have also been developed to control the flow either in an active or in a passive way. Active ways involve periodic blowing and suction on the surface [2], placing smaller bodies in the upstream direction [3], application of electromagnetic field during the flow of electrically conducting fluids [4], placing a control plate upstream of the body [5] and a moving surface boundary layer [6]. Several passive ways have also been adopted which follow a similar mechanism of drag reduction as the dimples such as the roughened surfaces [7], dimples [8], grooves [9], seeps [10], circular rings placed at regular intervals along the length of a cylinder [11].

The total drag acting on a body moving in a medium is mainly composed of pressure drag and skin drag. Skin dragconstitutes very little in the drag of bluff bodies. Whereas, the major source of drag for a streamlined body such as the wing of a transport aircraft is skin drag, about 50 % (Fig. 4).Again, several active and passive flow control strategies have been improvised. Complaint walls [12], Riblets[13] and vertical sub-layer elements called as vertical large eddy break-up devices (LEBU) [14] are classified as passive techniques. Synthetic jets [15], loudspeakers [16], air micro blowing [17], MEMS [18] and periodic blowing/suction [19] affect the structure of near-wall turbulence in an active way. A more detailed classification of Skin drag reduction methods is presented in figure 5.

Fig 4: Distribution of drag on an aircraft wing, from Ref [14], used by permission        

Riblets have proven to be the most promising and practical tool of reducing the skin friction. Various hypotheses have been presented by Alving&Freeberg [20] to explain the mechanism of skin drag reduction by using riblets. One thing can confidently be said that the turbulent momentum exchange near the wall is reduced using riblets with an optimum geometry. The counter-rotating longitudinal vortices are the major flow structures in the puffer layer and can be identified by the propagation of near wall horse-shoe vortices. These are produced by the instabilities near the wall and self-replication of existing horse-shoe vortices.

Fig 5: Classification of methods of reducing Skin-drag, from Ref [14], used by permission

Due to the rotational motion of the vortices, the fluid is transported towards or away from the wall depending on the direction of rotation.Low energy regions are found among the vortices in longitudinal direction in the viscous sub layer. The side of these vortices, which is turning away from the surface, transports the energy away from the wall into the boundary layer. The counter rotating side enables the transfer of energy from the boundary layer to the wall. This contributes to the production of significant amount of energy besides blowing out the vortices. The longitudinal vortices, which create shear stress in the viscous sub-layer,have more or less similar strength. By obstructing the lateral movement of longitudinal vortices, the riblets weaken the three dimensional vortex structures reducing the vortex intensity near the wall. The wall shear stress is proportional to the gradient of the mean flow velocity above the wall.Due to reduction in surface friction caused by theriblets, the flow velocity near thewall is consequently reduced [21].

Some controversial results regarding the investigations of flow over dimpled plates exist in literature. According to some researchers such as the famous study by DLR Spiegel [22], a significant amount of skin drag reduction could be achieved for a dimpled surface, although no explanation is yet available for the observed effect. On the other hand Leinhart[23] proved with the help of experimental and numerical investigations that the drag of a dimpled plate rather increases slightly.

No such investigations on hexagonal structured surfaces are known yet. The main concern of this dissertation is to investigate the flow over hexagonal structured surfaces and assess their capability of affecting the drag of the body.Following fundamental questions are dealt in this dissertation, which were planned to be addressed by conducting a series of experiments in a Wind tunnel:

·         Investigation of the fundamental effects of hexagonal structures on the flow

·         Is Pressure or Skin drag reduction possible?

·         Mechanism responsible for any alteration in Pressure/Skin drag

·         Flow behavior/Visualization within/around the hexagonal structures

·         Examination of the validity of the scaling laws in a turbulent boundary layer

·         Optimization of classical measurement techniques to perform measurements on structured plates (considering measurement accuracies)

1.2            Aims and Approaches

In the present dissertation, the influence of hexagonal structured surfaces and their orientations to the flowon aerodynamic quantities such as Pressure and Skin drag, Vortex shedding and boundary layers,is investigated.Examination of each quantity requires a separate indigenous experimental setup. Hence, the experiments were divided into three categories i.e. experiments on bluff bodies (structured circular cylinders),streamlined bodies (structured plates) and finally a wind turbine. These were conducted in the laboratories of fluid mechanics at the institute of Fluid mechanics & Aerodynamics and the institute of Combustion and Aero engines at the Technical University of Cottbus. A constant mass flow rate was ensured during experiments by the use of a large nozzle and governing the angular speed of the impeller. Based on the diameter of the cylinder and the mean flow velocity, the investigations on cylinders were performed for Reynolds numbers Re = 3.14 x 10⁴ to2.77 x 10⁵. Whereas, the Reynolds numbers ranged fromRe_x= 3.4 x 10⁵ to 11 x 10⁶ for structured plates based on the length of the test plate and the mean flow velocity. The investigations on wind turbine took place for flow velocities from 3 m/s to 18 m/s. The objective of these experiments was to quantify the effects of hexagonal structures on the flow over the structured objects as well as examine their applications. Subsequently, the results of direct drag measurements, velocity profiles, flow visualizations and shear stress measurements were obtainedfor structured as well as for smooth surfaces to perform a comparisonbetween flow control methods in the literature and the present structures.

Various structured surfaces with identical hexagonal structures but different orientations along with a smooth surface were investigated during experiments. To perform a comparison of the results of present structures with other structures in literature,a depth to diameter ratio (k/D) for circular cylinders, where D is the diameter of cylinder and k/d for plates, where d is equivalent diameter of a hexagonal structure, was defined. The experimental setup and the measurement techniquesare explained in detail in fourthand fifth chapter.

The sixth chapter deals with the results of measurements on structured cylinders. Drag measurements predicted a direct effect of hexagonal structured surfaces on the pressure drag of a cylinder, i.e. a significant reduction in pressure drag. Velocity measurements in the wake of cylinders and smoke flow visualization vindicated the observed effect. Ultimately, a mechanism of the observed reduction in the drag of a cylinder is presentedwith the help of measured velocity profiles near the surface. A detailed comparison of the effect of various structured surfaces on Vortex-shedding behind a cylinder is also present in this chapter.

Second section of the sixth chapter presents the results ofthe experimentsperformed on structured plates and discusses the reproducibility of a fully turbulent flow. By using the velocity profiles measured above the surface of smooth and structured plates,several boundary layer quantities were determined and subsequently analyzed. These quantities predicted again some dramatic effects of hexagonal structures on the mean stream flow, i.e.fall in local skin drag and a rise in total drag. To comprehend these effects, shear stress and pressure measurements on individual hexagonal structures were performed. Besides that, r.m.s velocity profiles at various locations and power spectrum of the flowabove individual hexagonalstructureswas obtained to resolve any turbulent structures present in the flow. Quantitative flow visualization using oil film interferometry helped to articulate the near wall flow.

The third section of the sixth chapter describes the results of the experiments conducted on a wind turbine configurations made of structured as well as smooth blades. The results are compared, analyzed and discussed briefly.

Finally, the findings and conclusions are summarized in seventh chapter. Some still open questions and future prospects based on experimental results are identified. Some suggestions for further investigations are also presented in this chapter.

Theoretical background

Total drag is formally defined as the force corresponding to the rate of decrease in momentum in the direction of undisturbed external flow around the body, this decrease being calculated between stations at infinite distances upstream and downstream of the body. Thus it is the total force or drag in the direction of undisturbed flow. It is also the total force resisting the motion of the body through the surrounding fluid. There are number of separate contributions to total drag:

1.3            Pressure drag

This is the drag that is generated by the resolved components of the forces due to the pressure acting normal to the surface at all points. It may itself be considered as consisting of several distinct contributions:

       I.            Induced drag (sometimes Vortex drag)

    II.            Wave drag

 III.            Form drag

In case of bluff bodies such as circular cylinders only some 5% of the drag is skin-friction drag, the remaining 95% being from pressure drag, although these proportions depend on the Reynolds number. Bluff bodies are characterized by more or less premature separation of the boundary layer from the surface, and by wakes having significant lateral dimensions and usually unsteady velocity fields. Considering bluff bodies with fixed separation points, significantly different flow fields characterize the wakes of 2-D bodies perpendicular to the flow, and 3-D bodies that are elongated in the direction of the flow. Indeed, even if in both cases the wake velocity field is unsteady, the fluctuations are much higher in the first case, in which the wake flow is dominated by the alternate shedding of strongly and highly concentrated vortices, producing the well-known Ka´rma´n vortex street. The shedding of vortical structures is still present in the wake of axis-symmetric bodies with a rounded leading edge (and thus with attached boundary layer up to the rear separation line), but structures are weaker, less concentrated and less organized. The latter are directly connected with the magnitude of the fluctuating forces acting on the body.

Consider the case for example, the pier of a bridge in a river. The water speeds up around the leading edges and the boundary layer quickly breaks away from the surface. Water is sucked in from behind the pier in the opposite direction. The total effect is to produce eddy currents that are shed in the wake. There is a buildup of positive pressure on the front and negative pressure at the back. The pressure force results in form drag. When the breakaway or separation point is at the front corner, the drag is almost entirely due to this effect but if the separation point moves along the side towards the back, than a boundary layer forms and skin friction drag is also produced. A bluff body has high velocity, low pressure regions on the upper surface. The closer streamlines represent a faster velocity (Fig. 6). At the back of the body, this high speed, low-pressure flow has to return to the free stream conditions.

Fig 6: Flow around a bluff body

Thus, there is an adverse pressure gradient acting on the fluid particles. Particles closest to the body lose kinetic energy due to viscous losses. They come to a halt when they lose all their kinetic energy and lack sufficient kinetic energy to overcome the adverse pressure gradient (S₂ in Fig. 7)

Fig 7: Reversed flow in presence of adverse pressure gradient, from Ref [70], used by permission

This results in the flow separating from the surface creating a large wake of recirculating flow downstream of the surface. The turbulent boundary layer might reattach with the surface again forming a separation bubble. Form drag is due to pressure changes only. The pressure coefficient is denoted by C_d and is defined as following.

The force exerted by the pressure on a small surface area is pdA. If the surface is inclined at an angle ψ to the general direction of flow, the force is p cosψdA. The total force is found by integrating all over the surface.

The pressure coefficient is defined as:

Where p₀ is the static pressure of undisturbed fluid, u_∞ the velocity of undisturbed fluid and ρ the density of the fluid.

Flow separation caused by the adverse pressure gradient can have severe implications. Consider an aircraft wing flying at moderate speed, increasing the angle of attack of the wing would result in stall and the aircraft goes out of control. It is well known that the boundary layers on low-Reynolds-number airfoils would remain laminar at the onset of the pressure recovery unless artificially tripped. The behavior of the laminar boundary layer on low-Reynolds number airfoils would affect the aerodynamic performance of the airfoils significantly. Since laminar boundarylayers are unable to withstand any significant adverse pressure gradient, laminar flow separation is usually found on the airfoils, and post-separation behavior of the laminar boundary layers accounts for the deterioration in the aerodynamic performances of low-Reynolds-number airfoils. The deterioration is exhibited in a dramatic increase in drag and decrease in lift (Fig. 8).

It has been suggested in the literature that the separated laminar boundary layers around a low-Reynolds-number airfoils would behave more like free shear layers, which are highly unstable, therefore, rolling-up of Kelvin-Helmholtz vortex structures and transition to turbulent flows would be readily realized. When the adverse pressure gradient over the airfoil surface is adequate, the transition of the separated laminar boundary layer to turbulent flow could be conducted rapidly, and the increased entrainment of the turbulent flow could make the turbulent flows to reattach the airfoil surface as turbulent boundary layers. This would form what is called a laminar separation bubble. The reattached turbulent boundary could stay in attaching to the airfoil surface firmly up to the airfoil trailing edge. As the adverse pressure gradient become more severe with the increasing angle of attack, the separation bubble would burst suddenly, which result in airfoil stall subsequently.

Fig 8: separated flow over airfoil, by Ref [71] used by permission

1.4            Skin Drag

Skin friction drag is due to the viscous shearing that takes place between the surface and the layer of fluid immediately above it. This occurs on surfaces of objects that are longer in the direction of flow compared to their height. Such bodies are called streamlined. When a fluid flows over a solid surface, the layer next to the surface may become attached to it (it wets the surface). This is called the no ‘slip condition’ The layers of fluid above the surface are moving so there must be shearing taking place between layers of the fluid. The shear stress acting between the wall and the first moving layer next to it is called the wall shear stress and denoted byτ_w.

Fig 9: Schematic diagram of the flow over flat plate

It is essential to investigate the flow near the wall (the boundary layer) to comprehend the effects of structured surface on the skin drag and total drag of the plate. The shape of the velocity profiles near the wall depends upon various factors including Reynolds number, shear stress and density. Hence, they need to be determined. The boundary layer is mainly of two types, the laminar and the turbulent boundary layer. Only viscous and inertial forces play a vital role in case of a laminar boundary layer. The laminar layer becomes unstable and transforms into a turbulent boundary layer at a critical Reynolds number (Fig. 9). Various mathematical formulations are present in the literature to describe a turbulent boundary layer over a flat plate. The logarithmic law is the most commonly used description.

Where is the shear stress velocity, u(y) the velocity, y the vertical distance from the surface and κ and B are constants. Common values of κ and B are 0.41 and 5.2. The logarithmic law is used to determine the wall shear stress acting on the surface by assimilating it with the measured velocity profiles. This method of determining the wall shear stress was devised by Clauser [24]. It is explained in detail in Section 5.4.1. The wall shear stress and the dimensionless shear stress coefficient C_f can be computed by knowing the shear stress velocity and density of the fluid.

For a plate of length l and width b the skin drag can be determined by integrating the shear stresses over the area in streamwise direction.

Putting it in the definition of drag coefficient:

Globalskin drag (the total drag) can also be determined by using boundary layer quantities such as displacement and momentum thicknesses

1.5            Fundamentals of Boundary layer

The boundary layer thickness δ is taken as the distance required for the velocity to reach 99% of u_∞. It is possible, however, to define the boundary layer thickness in terms of an effect on the flow indirectly. The displacement thickness is defined as the distance the surface would have to move in the y direction in an inviscid fluid stream of velocity u_∞ to give the same flow rate as occurs between the surface and the reference plane in a real fluid.

Analogous, the momentum thickness is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an inviscid fluid stream of velocity u_∞ to give the same total momentum as exists between the surface and the reference plane in a real fluid.

By having known the momentum thickness of the boundary layer, the global skin drag of a plate of width b and length l can be determined.

By putting this relation in the definition of drag coefficient, following can be achieved;